Microsoft Word - Voltage Collapse in Power System & Simulation to Eliminate Voltage Collaspe Through MATLAB

VOLTAGE COLLASPE IN POWER SYSTEM AND DESIGN METHOD TO ELIMINATE VOLTAGE COLLAPSE BY SIMULATION PROCESS

By

Abu Hena MD Shatil 0402106

Aminul Haque

0402050

Supervisor

Prof. Dr. Poritosh Kumar Shadhu Khan Dean

Department of Elctrical and Computer Engineering

DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING

CHITTAGONG UNIVERSITY OF ENGINEERING AND TECHNOLOGY

Abstract

The problem of voltage stability may be simply explained as inability of the power

system to provide the reactive power or the egregious consumption of the reactive power

by the system itself. It is understood as a reactive power problem and is also a dynamic

phenomenon. The objective of this paper is to develop a fast and simple method, which

can be applied in the power system online, to estimate the voltage stability margin of the

power system. In general, the analysis of voltage stability problem of a given power

system should cover the examination of these aspects:

- How close is the system to voltage instability or collapse?

- When does the voltage instability occur?

- Where are the vulnerable spots of the system?

- What are the key contributing factors?

- What areas are involved?

Voltage stability analysis often requires examination of lots of system states and many

contingency scenarios. For this reason, the approach based on steady state analysis is

more feasible, and it can also provide insights of the voltage reactive power problems. A

number of special algorithms have been proposed in the literature for voltage stability

analysis using static approached, however these approaches are laborious and does not

provide sensitivity information useful in a dynamic process. Voltage stability is indeed a

dynamic phenomenon. Some utilities use Q-V curves at some load buses to determine

the proximity to voltage instability. One problem with Q-V curve method is that by

focusing on small number buses, the system-wide voltage stability problem will not be

readily unveiled. An approach, model analysis of the modified load flow Jacobian matrix,

has been used as static voltage stability index to determine vulnerable bus’s voltage

stability problem. This paper explores the online monitoring index of the voltage

stability, which is derived from the basic static power flow and Kirchoff law. A

derivation will be given. The index of the voltage stability predicts the voltage problem

of the system with sufficient accuracy. This voltage stability index can work well in the

static state as well as during dynamic process.

Certification

We certify that the ideas, designs and experimental work, results, analyses and conclusions set out in this dissertation are entirely my own effort, except where otherwise indicated and acknowledged. we further certify that the work is original and has not been previously submitted for assessment in any other course or institution, except where specifically stated. A.H.M. SHATIL AMINUL HAQUE ID NO- 0402106 ID NO- 0402050 Signature Signature Date Date

Acknowledgements

We would like to express our sincere thanks to Prof. Dr. Poritosh Kumar

Shadhu Khan for giving us the opportunity to study this phenomenon and for

his help and valuable advice.

we would like to thank Mr. Nurul Alam and Mr. Iftekhar Mahmood from

PDB for their relentless support and motivation in order for us to complete

our bachelor thesis. Especially we want to thank our beloved parents and all

of our friends. They were the pillars and our inspiration and our enthusiasm

infusion to complete our studies and extend our efforts even when the road

started to look dreadfully rocky.

Glossary

Contents Abstract Acknowledgement Certification Glossary Nomenclature Chapter 1 Introduction 1-8 1.1 Voltage stability and collapse [1-2] 1.2 Voltage collapse definition [2-5] 1.3 Some real phenomena of voltage collapse [5-8]

Chapter 2 Mechanism of voltage collapse 1-6 2.1 Overview [1] 2.2 Basic steps for collapse mechanisms [1-6]

Chapter 3 Electrical load ability & power quality disturbances 1-10 3.1 power quality issue and problem formulation [1-2] 3.2 Power quality disturbances [2-10]

Chapter 4 Static voltage stability system 1-6 4.1 overview [1-2] 4.2 definition of static load [2] 4.3 Static voltage algorithm[3-4] 4.4 Voltage collapse with static load [4-6]

Chapter 5 Dynamic load and voltage stability 1-8 5.1 Overview [1-2] 5.2 Dynamic load definitions [2-3] 5.3 System model [3-4] 5.4 General dynamic simulation [4-5] 5.5 transient Dynamic simulation [5] 5.6 Long term dynamic simulation [5-6] 5.7 Dynamic load model [7-8]

Chapter 6 Software specification 1-7 6.1 PSS/E [1-3] 6.2 MATLAB [3-5] 6.3 EUROSTAG [6] 6.4 EXTAB [6] 6.5 SIMPOW[6] 6.6 ETMSP [7]

6.7 LTSP [7]

Chapter 7 Algorithm for voltage collapse 1-9 7.1 Basic algorithms [1-3] 7.2 Proposed algorithm [4-5] 7.3 Interval load flow problem [5-6] 7.4 Fundamental voltage collapse equation [7-9]

Chapter 8 Process simulation and test results of Voltage collapse 1-24 8.1 IEEE 14 bus introduce [1] 8.2 IEEE 30 bus introduce [2] 8.3 Lod flow result for 14 bus [3-5] 8.4 Load flow result for 30 bus [6-11] 8.5 voltage decrease due to load increase data [11-15] 8.6 voltage decrease due to reactive power imbalance [16-20] 8.6 Loads versus voltage curve [21-22] 8.7 Reactive power versus load curve [23-24]

Chapter 9 Voltage collapse mitigation 1-27 9.1 Power capacitor [1-3] 9.2 Difference kind of power capacitor [3-7] 9.3 Introduction to SVC [8-10] 9.4 SVC control system structure and m0odes of operation [10-12]

9.5 Simulation and test results using Capacitor on collapse bus [12-14] 9.6 Some other mitigation scheme [15-27]

Chapter 10 Conclusion 1-4 Chapter 11 Future Work 1-3 11.1 load modeling [1] 11.2 Improvements of generator capabilities [2] 11.3 Adaptive relay techniques [2] 11.4 Phasor measurements [2-3] 11.5 User definable relays [3]

APPENDIX A Matlab coding for load flow APPENDIX B Matlab coding for P-V and Q-V curve

Chapter 1

Introduction

1.1 Voltage instability and collapse This research area concerns disturbances in a power system network where the voltage

magnitude becomes uncontrollable and collapses. The voltage decline is often

monotonous in the beginning of the collapse and difficult to detect. A sudden increase in

the voltage decline often marks the end of the collapse course. It is not easy to distinguish

this phenomenon from transient stability where voltages also can decrease in a manner

similar to voltage collapse. Only careful post-disturbance analysis may in those cases

reveal the actual cause.

Fig1.1: Example of a voltage decline and a fast voltage drop

During the last twenty years there have been one or several large voltage collapses almost

every year somewhere in the world. The reason is the increased number of

interconnections and a higher degree of utilization of the power system. Also load

characteristics have changed. Two examples are the increased use of air conditioners and

electrical heating appliances which may endanger system stability radically. The

incidents that lead to a real breakdown of the system are rare, but when they occur they

Have large repercussions on the stability of power systems. It is believed by many

professionals that the power system will be used with a smaller margin to voltage

collapse in the future. The reasons are twofold: the need to use the invested capital

efficiently, and the public resistance to building new transmission lines and new power

plants. Voltage stability is therefore believed to be of greater concern in the future.

Nearly all types of contingencies and even slow-developing load increases could cause a

voltage stability problem. The time scale for the course of events which develop into a

collapse varies from seconds to several tens of minutes. This makes voltage collapse

difficult to analyze since there are many phenomena that interact during this time.

Important factors that cause interaction during a voltage decline are among others:

generation limitation, behavior of on-load tap changers, and load behavior. An interesting

point is that many researchers discard voltage magnitude as a suitable indicator for the

proximity to voltage collapse, although this is in fact the quantity that collapses. One

question that has been discussed is whether voltage stability is a static or dynamic

process. Today it is widely accepted as a dynamic phenomenon but much analysis is

performed using static models.

1.2 Voltage collapse definition

In the literature several definitions of voltage stability can be found. The definitions

consider time frames, system states, large or small disturbances etc. The different

approaches therefore reflect the fact that there is a broad spectrum of phenomena that

could occur during a voltage stability course. Since different people have various

experiences of the phenomenon, differences appear between the definitions. It could also

reflect that there is not enough knowledge about the phenomenon itself to establish a

generally accepted definition at this stage.

Definitions by CIGRÉ:

CIGRÉ defines voltage stability in a general way similar to other dynamic stability

problems. They define:

• A power system at a given operating state is small-disturbance voltage stable if,

following any small disturbance; voltages near loads are identical or close to the pre-

disturbance values. (Small-disturbance voltage stability corresponds to a related

liberalized dynamic model with eigenvalues having negative real parts. For analysis,

discontinuous models for tap changers may have to be replaced with equivalent

continuous models).

• A power system at a given operating state and subject to a given disturbance is voltage

stable if voltages near loads approach post disturbance equilibrium values. The disturbed

state is within the region of attraction of the stable post-disturbance equilibrium.

• Following voltage instability, a power system undergoes voltage collapse if the post-

disturbance equilibrium voltages are below acceptable limits. Voltage collapse may be

total (blackout) or partial.

• Voltage instability is the absence of voltage stability, and results in progressive voltage

decrease (or increase). Destabilizing controls reaching limits, or other control actions

(e.g., load disconnection), however, may establish global stability.

Definitions according to Hill at al:

Another set of stability definitions is proposed by Hill et al. The phenomenon is divided

into a static and a dynamic part. For the static part the following must be true for the

system to be stable:

• The voltages must be viable i.e. they must lie within an acceptable band.

• The power system must be in a voltage regular operating point. Here Hill et al. use two

forms of regularity. One could say that if reactive power is injected into the system or a

voltage source increases its voltage, a voltage increase is expected in the network. For the

dynamic behavior of the phenomenon, Hill et al. propose the following concepts:

• Small disturbance voltage stability: A power system at a given operating state is small

disturbance stable if following any small disturbance, its voltages are identical to or close

to their predisturbance equilibrium values.

• Large disturbance voltage stability: A power system at a given operating state and

subject to a given large disturbance is large disturbance voltage stable if the voltages

approach post-disturbance equilibrium values.

• Voltage collapse: A power system at a given operating state and subject to a given large

disturbance undergoes voltage collapse if it is voltage unstable or the post-disturbance

equilibrium values are nonviable.

Definitions according to IEEE:

A third definition of this phenomenon is presented by IEEE. The following formal

definitions of terms related to voltage stability are given:

• Voltage Stability is the ability of a system to maintain voltage so that when load

admittance is increased, load power will increase, and so that both power and voltage are

controllable.

• Voltage Collapse is the process by which voltage instability leads to loss of voltage in a

significant part of the system.

• Voltage Security is the ability of a system, not only to operate stably, but also to remain

stable (as far as the maintenance of system voltage is concerned) following any

reasonably credible contingency or adverse system change.

• A system enters a state of voltage instability when a disturbance, increase in load, or

system changes causes voltage to drop quickly or drift downward, and operators and

automatic system controls fail to halt the decay. The voltage decay may take just a few

seconds or ten to twenty minutes. If the decay continues unabated, steady-state angular

instability or voltage collapse will occur.

Definitions according to Glavitch: Another approach is presented by Glavitch. In this approach different time frames of the

collapse phenomenon are illustrated:

• Transient voltage stability or collapse is characterized by a large disturbance and a rapid

response of the power system and its components, e.g. induction motors. The time frame

is one to several seconds which is also a period in which automatic control devices at

generators react.[1]

• Longer-term voltage stability or collapse is characterized by a large disturbance and

subsequent process of load restoration or load change of load duration. The time frame is

within 0.5-30 minutes. Glavitch also proposes a distinction between static and dynamic

analysis. If differential equations are involved, the analysis is dynamic. “Static does not

mean constant, i.e. a static analysis can very well consider a time variation of a

parameter.”[1]&[6]

Of these definitions, Hill seems to be the closest to mathematics and the IEEE-definition

is related to the actual process in the network. The framework in these definitions on

voltage stability includes mainly three issues: the voltage levels must be acceptable; the

system must be controllable in the operating point; and it must survive a contingency or

change in the system.

1.3 Some real phenomena of Voltage Collapse

The tripping of fairly small generators could, if they are placed in positions that need

voltage support (voltage weak positions), cause a large increase of reactive power losses

in the transmission network. This causes large voltage drops which can generate stability

problems. Two examples are the 1970 New York disturbance and the disturbance at

Zealand in Denmark 1979 . In the New York disturbance, an increased loading on the

transmission system and a tripping of a 35 MW generator resulted in a post-contingency

voltage decline. At Zealand, a tripping of the only unit in the southern part of the island

producing 270 MW caused a slow voltage decline in that part. After 15 minutes the

voltages had declined to 0.75 pu, making the synchronization of a 70 MW gas turbine

impossible. Both systems were saved by manual load shedding.[3]

The Belgian collapse in August 4, 1982 also had problems with the transmission

capacity. The collapse was initiated by a fortuitous tripping of one of the relatively few

operating production sources. The low load made it economically advantageous to use

[5]just a few plants for production. This resulted in that they were operating quite close to

their operating limits. When the generator tripped the surrounding area was exposed to a

lack of reactive power and several generators were field current limited. After a while the

generators tripped one after another due to the operation of the protection system. During

this period, the transmission system was unable to transmit the necessary amount of

reactive power to the voltage suppressed area and this caused a continuous voltage

decline. When the fifth generator was tripped, the transmission-protective relays

separated the system and a collapse resulted .

The collapse in Canada, in B. C Hydros north coast region in July 1979 is also interesting

in this respect. A loss of 100 MW load along a tie-line connection resulted in an

increased active power transfer between the two systems. The generators close to the

initial load loss area were on manual excitation control (constant field current), which

aggravated the situation. When voltages started to fall along the tie-line due to the

increased power transfer, the connected load decreased proportionally to the voltage

squared. This increased the tie-line transmission even more since there was no reduction

in the active power production. About one minute after the initial contingency, the

voltage in the middle of the tie-line fell to approximately 0.5 pu and the tie-line was

tripped due to over current at one end and due to a distance relay at the other.

Also Czechoslovakia experienced a similar collapse as B. C. Hydro in July 1985 but on a

much shorter time-scale. Before the disturbance, there were three interconnected systems,

two strong ones, I and II and one weak system, III, in the middle of I and II. A large

amount of power was delivered from I to III, while II was approximately balanced. When

the connection between I and III was lost, the II-III connection was expected to take over

the supply of power to III. However, one of the overhead lines between II and III tripped

due to over current and the remaining transmission capacity was too low and the voltage

collapsed within one second on the other line.

Fig1.2: The Czechoslovakian network during the collapse.

On 23 July 1987, Tokyo suffered from very hot weather. After the lunch hour, the load

pick-up was ~1%/min. Despite the fact that all the available shunt capacitors were put

into the system, the voltages started to decay on the 500 kV-system. In 20 minutes the

voltage had fallen to about 0.75 pu and the protective relays disconnected parts of the

transmission network and by that action shed about 8000 MW of load. Unfavourable load

characteristics of air conditioners were thought to be part of the problem .

In the collapse in Sweden, on 27 December 1983, the load behaviour at low voltage

levels was also a probable source leading to a collapse . Transmission capacity from the

northern part of Sweden was lost due to an earth fault. Virtually nothing happened the

first ~50 seconds after the initial disturbance when the remaining transmission lines from

the northern part of Sweden were tripped. Since these lines carried over 5500 MW, the

power deficit in southern Sweden was too large for the system to survive. The cause of

the cascaded line trippings was a voltage decline and a current-increase in the central part

of Sweden. The on-load tap changer transformers contributed to the collapse when they

restored the customer voltage level. Field measurements performed afterwards in the

Swedish network have also shown the inherent load recovery after a voltage decrease .

This recovery aggravated the situation when voltages started to decline. The cause of this

load recovery in the Swedish network is believed to be due to electrical heating

appliances.

On the fourth of November 2004, a prolonged voltage dip was experienced at Blackwater

132kV Substation located in Central Queensland. The voltage fluctuation corresponded

to a decrease of 6% of nominal voltage (132kV) for approximately 9 minutes as indicated

in Figure 3. Events of this type affecting Power Quality are of concern as failure to

comply with regulatory limits for voltage magnitude, balance and frequency results in

penalties by regulatory authorities such as the National Electricity Market Management

Company (NEMMCO) and possible litigation by industrial customers adversely affected

by such failures.

Fig1.3: Blackwater 132kV Bus Voltage (Jones, R 2005, pers. comm., 22 March) Blackwater substation voltage levels are regulated by a device called a Static Var

Compensator (SVC). Immediately prior to the voltage dip the SVC was providing

transmission system voltage support, operating in capacitive mode. As shown by the

voltage.

Chapter 2

Mechanism of Voltage Collapse

2.1 Overview

Voltage instability occurs when the reactive power available to a portion of the grid falls

below that required by customers, transmission lines, and transformers in that portion of the grid.

The period of "instability" is not so much an instability as it is the behavior and interaction of

various elements following the instant when the reactive shortage first develops and until

intervention occurs, voltage collapse occurs, or, hopefully, a stable voltage is reached. This

period of "slow dynamics" involves generator excitation limiting controls, on-load tap changers,

operator actions, and the response of customer loads to decaying voltage (e.g., thermostats and

manual activities that respond to the decaying voltage and attempt to restore the load to its

original demand in spite of decaying voltage). As voltage decays, the resulting drop in customer

load allows continued operation. However, the action of distribution transformer on-load-tap

changers and self-restoring load elements pull voltage ever lower. While voltage may stabilize in

systems with relatively strong ties to healthy neighbors, others will require heroic action by

operators or under voltage load shedding to prevent voltage collapse.

2.2 Basic Steps Of collapse Mechanism

Voltage collapse involves one of two mechanisms or a combination of the two where one

leads to the other. One is angular instability, either steady state angular instability as was

the case in the Western Interconnection (WI) on July 2, 1996, or growing oscillations as

was the case in the WI on August 10, 1996. When voltage instability leads to angular

instability, the event is usually labeled as angular instability though the fact that it was

initiated by a reactive deficiency and decaying voltage should not be forgotten in the

analysis and search for ways to reduce the risk of future similar events. The problem of

decaying voltage leading to steady state instability is relatively straight forward. The

reactive shortage and low voltage cause an increasing number of Generator excitation

systems to reach excitation limits. Under this condition voltage continues to be regulated

only beyond the bounds of the affected area. If power is flowing through the affected

Fig2.1: Different time response for voltage stability phenomena [1]

Area, the angle between points where voltage is being controlled can reach the critical

ninety degree point where the well-understood steady state instability results.[13]

The second possible voltage collapse mechanism is stalling motors. Motors typically stall

when voltage drops below about 80% of nominal at the terminals of the motor. At this

voltage motor torque falls below load torque and the motor slows to a standstill where it

draws a large reactive Current further depressing voltage. Since the first motor to stall

will pull voltage lower and cause nearby motors to also stall, it is the one of concern.

That motor may be overloaded or served at a lower than rated voltage and thus may stall

at 85% or higher. Clearly, grid voltage much below 90% puts any load area at risk of

voltage collapse from stalling motors. While some low voltage protection does exist on

industrial motors, it is typically set at about 90% voltage and operates slowly since its

intended function is to prevent thermal damage. The "protection" that is referenced in the

Interim Report that disconnects larger motors and industrial motors during voltage

collapse is in fact not protection, but the inherent behavior of electromagnetically held

contactors that are used in motor "starters" to switch the motors on and off. The contactor

simply opens when voltage drops into the 60 to 70% range.

Motors in most industrial light industrial plants are served by contactors and will drop

from the system as voltage falls due to motor stalling or angular instability. Refrigeration

loads (A/C, residential and grocery refrigeration) are “trip-free” and leave the system

only after overload devices “time-out.” This can take 10 to 20 seconds. While in some

situations the self-shedding of industrial motors occurs early enough in the voltage decay

to prevent cascading from angular instability and cascade motor stalling, but where A/C

and refrigeration motor content is high, the loss of industrial motors is unlikely to halt the

cascading.

It is not unusual for a voltage instability event to lead to both angular instability and

motor stalling. Because angular instability depresses voltage and inevitably causes motor

stalling, and motor stalling depresses voltage and can cause angular instability, it can be

difficult to assign the cause to one or the other when an event involves both. The

difficulty in identifying motor stalling and angular instability in the procession of a

voltage collapse can be complicated by the operation of distance protection on

transmission lines. While there is no doubt that angular instability will cause distance

protection on transmission lines to operate (in the absence of out-of-step blocking), it is

also possible for the large reactive flows and low voltages from motor stalling to cause

the same distance protection to operate

Though it is now widely recognized that voltage is not usually a good early indicator of

voltage instability, whenever that observation is made, it should also be pointed out that

the period of diminishing reactive reserves that precedes the decay in voltage is fairly

easy to detect in real time and to evaluate in operations planning studies. Some control

centers have real time reactive margin displayed for operator use. This is readily done for

areas that can be identified as being at risk of reactive problems and less readily done

where the area of reactive shortage can take any shape and is only identifiable once

Contingencies have occurred and created a reactive short area. Nonetheless, there are

voltage security analysis tools that have been developed to address this problem.

Where it is sometimes difficult to anticipate areas of reactive shortage and provide

operators with appropriate reactive margin displays and alarms, another approach is

available. When contingencies cause a reactive shortage, one of the first signs of an

impending problem will be generator reactive outputs hitting excitation limits. Even one

generator hitting its reactive limit should be a red flag for operators. When several

generators hit limits it may be time for heroic actions such as dropping load. Displays

addressing voltage instability risk should emphasize the status of reactive reserve and

limits of generator, synchronous condenser, and static var compensators. When a

reactive-short area develops without such reactive sources, voltage will fall early and will

be a useful indicator of an impending problem. Displays should advise operators when an

area of low voltage is developing. Displays that color or shade an area of low voltage are

available.

Generation excitation control on voltage collapse is one of the important causes. Till now

an infinite bus was assumed at the sending end. But no bus is an infinite section it is

assumed that a synchronous generator is driving the sending end bus. With increasing

load, the line current increases and machine excitation increase terminal voltage constant.

But soon the machine field current reaches the ceiling further increase in line current the

terminal voltage decreases. Decreasing terminal further decrease in receiving end voltage

and results in further voltage collapse. Upper limit on field current of generator is to

aggravate the voltage collapse at receiving In fact the problem is more complicated than

that. When the collapse process is fast increases fast. If the excitation system of generator

is slow, the terminal voltage keep up with the increasing line current and collapse process

will be further intensified sending voltage conditions - even though field current has not

reached ceiling excitation system simulates infinite bus better.

Voltage collapse with composite Loads, at a load bus varies in a complex fashion with

voltage and is neither dynamic. Modeling the load as a composite of equivalent static

load and at the bus has been attempted by various researchers. While induction motor

load tends to induce voltage instability and disturbances and load disturbances, static

loads tend to tone down the voltage during same conditions. Of course, sustained low

voltage conditions will exist if line is over-loaded. But dynamic loads can provoke

instability even system under contingencies. A good mix of static load and induction

motor long way towards curbing the tendency to voltage instability. As already pointed

out, it is the interplay between bus voltage elasticity and reactive power elasticity with

respect to bus voltage that decides voltage any measure that tends to reduce bus voltage

sensitivity with respect to voltage instability. These measures will include i) reducing the

electrical generator and load buds (use of parallel lines, series compensation etc) flow in

the line by shunt capacitor compensation at load bus. The first method (a tight bus

approaches infinite bus; its short circuit MVA is high) maximum power transfer

capability whereas the second measure shifts regions where bus voltage is less sensitive

to power variations. Similarly, make P & Q of load elastic with respect to voltage will aid

in maintaining automatic secondary voltage regulation either by utility or by detrimental

from voltage stability point of view. Similarly a slow response fast response in capacitor

switching systems or use of SVC, fast responding generator etc. are seen to be helpful in

curtailing voltage instability. mention is that capacitors can save a system from voltage

collapse due are switched on right at the inception of instability or preferably before .that

automatically controlled fast responding static var compensators become capacitors for

management of voltage collapse. A typical spontaneous voltage collapse (i.e. not due to

overload, but due to instability system or load disturbances) takes about 15 minutes to 30

minutes for competition. Drop is slow during the beginning but toward the end of the

voltage collapse interval decisive turns and flops down fast. The exact evolution of

collapse will be governed static and dynamic loads, loading level of equivalent induction

motor changer dynamics, action taken by operators, injection of shunt compensation,

equipment functioning etc.

Voltage collapse in a general power system behind a particular load bus may be

equivalence equivalent in the form of a voltage source (infinite bus) in series with a

reactance at that bus). Thus, the voltage stability at a load bus may be studied using

covered till now. However, this Thevenin’s equivalent method suffers from a

shortcoming. Load at a bus change the voltages everywhere (not only at that particular

bus) change voltage stability at a particular node is tied up with voltage stability at other

nodes large extent depending on electrical distances between the nodes. The principles

enumerated and the qualitative conclusions arrived at in the case link are valid for any

load bus in a general power system. But the exact quantitative of voltage stability

margins at the various load buses will require complex computations due to the coupling

which exists between various load nodes.

Chapter 3

Electrical Load ability and Power quality disturbances

3.1 Power Quality Issue and Problem Formulation The rapid change in the electric load profile from being mainly a linear type to greatly

nonlinear, has created continued power quality problems which are difficult to detect and

is in general complex. The most important contributor to power quality problems is the

customers’ (or end-user electric loads) use of sensitive type nonlinear load in all sectors

(Industrial, Commercial and Residential).

Power Quality issues can be roughly broken into a number of sub-categories:

� Harmonics (integral, sub, super and interharmonics)

� Voltage swells, sags, fluctuations, flicker and Transients

� Voltage magnitude and frequency, voltage imbalance

� Hot grounding loops and ground potential rise (GPR)

� Monitoring and measurement of quasi-dynamic, quasi-static and transient type

phenomena.

Nonlinear type loads contribute to the degradation in the electric supply’s Power Quality

through the generation of harmonics. The increased use of nonlinear loads makes the

harmonic issue (waveform distortion) a top priority for all equipment manufacturers,

users and electric utilities. Severe Power System harmonics are usually the steady state

problem not the transient or intermittent type, and these harmonics can be mitigated by

using the new family of modulated/switched power filters.

Lower order harmonics cause the greatest concern in the electrical distribution/utilization

system. Harmonics interfere with sensitive-type electronic communications and

networks. Low order triple harmonics cause hot-neutrals, grounding potential rise (GPR),

light flickering, malfunction of computerized data processing equipment and computer

networks and computer equipment.

There are several defined measures commonly used for indicating the harmonic severity

and content of a waveform. One of the most common measures is total harmonic

distortion in current iTHD)( .

( )

=

∑∞

=

1

2

2

I

I

THD nn

i;

Where 1I : Fundamental (60Hz) Current; n: Harmonic order and nI : Harmonic current.

3.2 Power Quality disturbances In an electrical power system, there are various kinds of power quality disturbances. They

are classified into categories and their descriptions are important in order to classify

measurement results and to describe electromagnetic phenomena, which can cause power

quality problems. Some disturbances come from the supply network, whereas others are

produced by the load itself. The categories can be classified below

Short-duration voltage variations

• Long-duration voltage variations

• Transients

• Voltage imbalance

• Waveform distortion

• Voltage fluctuation

• Power frequency variations

Short-Duration Voltage Variations There are three types of short-duration voltage variations, namely, instantaneous,

momentary and temporary, depending on its duration. Short-duration voltage variations

are caused by fault conditions, exercitation of large loads, which require high starting

currents or loose connections in power wiring. Depending on the fault location and the

system conditions, the fault can generate sags, swells or interruptions. The fault condition

can be close to or remote from the point of interest. During the actual fault condition, the

effect of the voltage is of short-duration variation until protective devices operate to clear

the fault.

Sag

A sag (also known as dip) is a reduction to between 0.1 and 0.9 pu in rms voltage or

current at the power frequency for a short period of time from 0.5 cycles to 1 min. A 10%

sag is considered an event during which the RMS voltage decreased by 10% to 0.9 pu.

Voltage sags are widely recognized as among the most common and important aspects of

power quality problems affecting industrial and commercial customers. They are

particularly troublesome Since they occur randomly and are difficult to predict. Voltage

sags are normally associated with system faults on the distribution system, sudden

increase in system loads, lightning strikes or starting of large load like induction motors.

It is not possible to eliminate faults on a system. One of the most common causes of

faults occurring on high-voltage transmission systems is a lightning strike. When there is

a fault caused by a lightning strike, the voltage can sag to 50% of the standard range and

can last from four to seven cycles. Most loads will be tripped off when encounter this

type of voltage level. Possible effect of voltage sags would be system shutdown or reduce

efficiency and life span of electrical equipment, particularly motors.

Equipment sensitivity to voltage sag occurs randomly and has become the most serious

power quality problem affecting many industries and commercial customers presently.

An industrial monitoring program determined an 87% of voltage disturbances could be

associated to voltage sags. Most of the faults on the utility transmission and distribution

system are single line-to-ground faults (SLGF).

Swell A swell (also known as momentary overvoltage) is an increase in rms voltage or current

at the power frequency to between 1.1 and 1.8 pu for durations from 0.5 cycle to 1 min.

Swells are commonly caused by system fault conditions, switching off a large load or

energizing a large capacitor bank. A swell can occur during a single line-to-ground fault

(SLGF) with a temporary voltage rise on the unfaulted phases. They are not as common

as voltage sags and are characterized also by both the magnitude and duration. During a

fault condition, the severity of a voltage swell is very much dependent on the system

impedance, location of the fault and grounding. The effect of this type of disturbance

would be hardware failure in the equipment due to overheating.

Interruption

An interruption occurs when there is a reduction of the supply voltage or load current to

less than 0.1 pu for duration not exceeding 1 min. Possible causes would be circuit

breakers responding to overload, lightning and faults. Interruptions are the result of

equipment failures, power system faults and control malfunctions. They are characterized

by their duration as the voltage magnitude is always less than 10% of the nominal. The

duration of an interruption can be irregular when due to equipment malfunctions or loose

connections. The duration of an interruption due to a fault on the utility system is

determined by the utility protective devices operating time.

Long-Duration Voltage Variations Long-duration variations can be either overvoltages or undervoltages. They contain root-

mean-square (rms) deviations at power frequencies for a period of time longer than 1

min. They are usually not caused by system faults but system switching operations and

load variations on the system.

Over voltage An overvoltage is defined as an increase in the rms ac voltage greater than 110% at the

power frequency for duration longer than 1 min. Overvoltages can be the result of

switching off a large load, energizing a capacitor bank or incorrect tap settings on

transformers. These occur mainly because either the voltage controls are inadequate or

the system is too weak for voltage regulation. Possible effect could be hardware failure in

the equipment due to overheating.

Under voltage An undervoltage (also known as brownout) is defined as a decrease in the rms ac voltage

to less than 90% at the power frequency for a period of time greater than 1 min.

Undervoltage is the result of switching on a load, a capacitor bank switching off or

overloaded circuits. Possible effect include system shutdown. Most electronic controls

are very sensitive as compared to electromechanical devices, which tend to be more

tolerant.

Transients Transients can be classified into two categories, namely, impulsive and oscillatory. These

terms reflect the wave shape of a current or voltage transient.

Impulsive Transient

An impulsive transient is defined as a sudden, non-power frequency change in the steady-

state condition of voltage, current, or both, which is unidirectional in polarity (either

positive or negative). Impulsive transients are usually measured by their rise and decay

times and also their main frequency. Lightning is the most common cause of impulsive

transients. The shape of impulsive transients can be changed quickly by circuit

components and may have different characteristics when viewed from different parts of

the power system when high frequencies are involved. Impulsive transients can even

stimulate the natural frequency of power system circuits and produce oscillatory

transients.

Oscillatory Transient An oscillatory transient describes as a sudden, non-power frequency change in the

steady-state condition of voltage, current, or both, which includes positive and negative

polarity values. It consists of a voltage or current whose instantaneous value changes

polarity rapidly. They are characterized by its duration, magnitude and main frequency. A

back-to-back capacitor energization result in oscillatory transient currents is termed a

medium frequency transient. Medium frequency transients can also be the result of a

system response to an impulsive transient. Depending on the type of loads, worst case

could cause voltage spikes that break insulation somewhere in the system.

Capacitor switching, which associated with transient, is a daily utility operation to correct

the power factor. Many heavy industrial loads such as induction motors and furnaces

operate at low power factor. Heavy inductive loads cause excess current to flow in the

lines, which increase losses. The effects include equipment damage or failure, process

equipment shutdown and computer network problems.

Installation of capacitor banks can save energy and improve on the system security. A

reduction in power loss and an improved voltage profile can be achieved when capacitors

are dynamically controlled to changes in the feeder’s load. These benefits depend on how

capacitors are sized, placed and in controlled so that savings are maximized.

In general, the total capacity of capacitor banks is approximately 50% of the total

generating capacity in a typical power distribution system. The factors that affect the

transient magnitude and characteristics are source strength, transmission lines, other

transmission system capacitor banks and switching devices. Pre-insertion resistors and

synchronous closing are some of the techniques that involved in the reduction of

capacitor switching transients.

The capacitor voltage is not possible to change instantaneously when exercitation of a

capacitor bank occurs. This results in a sudden drop of system voltage towards zero,

followed by a fast voltage overshoot and finally an oscillating transient voltage imposed

on the 50Hz waveform. Depending on the instantaneous system voltage at the moment of

switching, the peak voltage magnitude can reach two times the normal system peak

voltage under severe conditions. Typical distribution system over voltages due to

capacitor switching range from 1.1 - 1.6 pu with transient frequency ranging from 300 –

1 kHz.

Oscillatory transients with frequencies less than 300 Hz can also be found on the

distribution system. They are associated with ferroresonance and transformer

energization. Some common methods to limit transient overvoltages on the DC bus of

sensitive equipments are:

• Arrange a reactor in series with AC input terminal.

• Use of static var compensators (SVCs) in the distribution systems.

Voltage Imbalance

Voltage imbalance (or unbalance) is a condition in which the maximum deviation from

the average of the three-phase voltages or currents, divided by the average of the three-

phase voltages or currents, expressed in percentage. Voltage imbalance can be the result

of blown fuses in one phase of a three-phase capacitor bank. Severe voltage imbalance

greater than 5% can cause damage to sensitive equipments.

Waveform Distortion

Waveform distortion is a condition whereby a steady-state deviates from an ideal sine

wave of power frequency characterized by the main frequency of the deviation. There are

generally five types of waveform distortion, namely, dc offset, harmonics,

interharmonics, notching and noise.

DC Offset

DC offset is the presence of a dc current or voltage in an ac power system. This can occur

due to the effect of half-wave rectification. Direct current found in alternating current

networks can have a harmful effect. This can cause additional heating and destroy the

transformer.

Harmonic

Harmonics are a growing problem for both electricity suppliers and users. A harmonic is

defined as a sinusoidal component of a periodic wave or quantity having a frequency that

is an integral multiple of the fundamental frequency usually 50Hz or 60Hz. Harmonic

refers to both current and voltage harmonics. Harmonic voltages occur as a result of

current harmonics, which are created by electronic loads. These nonlinear loads will draw

a distorted current waveform from the supply system. The amount of current distortion is

dependent upon the kVA rating of the load, the types of load and the fault level of the

power system at the point where the load is connected.

Industrial loads like electric arc furnaces, and discharge lighting can cause harmonic

distortion. The effect of harmonics in the power system includes the corruption and loss

of data, overheating or damage to sensitive equipment and overloading of capacitor

banks. The high frequency harmonics may also cause interference to nearby

telecommunication system.

Fourier analysis can be used to describe distortion in terms of fundamental frequency and

harmonic components from a given distorted periodic waveform. By using this technique,

we can consider each component of the distorted wave separately and apply

superposition. Using the Fourier series expansion, we can represent a distorted periodic

waveshape by its fundamental and harmonic: It is also common to use a single quantity,

the Total Harmonic Distortion (THD) as a measure of the effective value of harmonic

distortion. The development of Current Distortion Limits is to:

• Reduce the harmonic injection from each single consumer so that they will not

cause unacceptable voltage distortion levels for normal system characteristics.

• Restrict the overall harmonic distortion of the system voltage supplied by the

utility.

The harmonic distortion caused by each single consumer should be limited to an

acceptable level and the whole system should be operated without existing harmonic

distortion. The harmonic distortion limits recommended here provide the maximum

allowable current distortion for a consumer.

Interharmonics

Interharmonics are defined as voltages or currents having frequency components that are

not integer multiples of the frequency at which the supply system is designed to operate.

The causes include induction motors, static frequency converters and arcing devices. The

effects of interharmonics are not well known.

Notching A periodic voltage disturbance caused by normal operation of power electronics devices

when current is commutated from one phase to another is termed notching. Notching

tends to occur continuously and can be characterized through the harmonic spectrum of

the affected voltage. The frequency components can be quite high and may not be able to

describe with measurement equipment used for harmonic analysis.

Noise

Noise is unwanted distortion of the electrical power signals with high frequency

waveform superimposed on the fundamental. Noise is a common source by

electromagnetic interference (EMI) or radio frequency interference (RFI), power

electronic devices, switching power supplies and control circuits. Noise disturbs

electronic devices such as microcomputer and programmable controllers. Use of filters

and isolation transformers can usually solve the problem.

Voltage Fluctuation

Voltage fluctuation is defined as the random variations of the voltage envelope where the

magnitude does not exceed the voltage ranges of 0.9 to 1.1 pu. Flicker usually associates

with loads that display continuous variations in the load current magnitude causing

voltage variations. The flicker signal is measured by its rms magnitude expressed as a

percent of the fundamental whereas voltage flicker is measured with respect to the

sensitivity of human eye. It is possible for lamp to flicker if the magnitudes are as low as

0.5% and the frequencies are in the range of 6 to 8 Hz. One common cause of voltage

fluctuations on utility transmission and distribution system is the arc furnace.

Power Frequency Variations Any deviation of the power system fundamental frequency from its nominal value

(usually 50 or 60 Hz) is defined as power frequency variations. The power system

frequency is associated with the rotational speed of the generators supplying the system.

The size and duration of the frequency shift depends on the load characteristics and the

response of the generation control system to load changes. As the load and generation

changes, small variations in frequency occur.

Frequency variations can be the cause of faults on power transmission system, large load

being disconnected or a large source of generation going off-line. Frequency variations

usually occur for loads that are supplied by a generator isolated from the utility system.

The response to sudden load changes may not be sufficient to adjust within the narrow

bandwidth required by frequency sensitive equipment. Possible effect could result in data

loss, system crashes and equipment damage.

Chapter 4

Static Voltage stability System 4.1 Overview

Static voltage instability is mainly associated with reactive power imbalance. Reactive

power support that the bus receives from the systems can limit load ability of that bus. If

the reactive power support reaches the limit, the system will approach the maximum

loading point or voltage collapse point. In static voltage stability, slowly developing

changes in the power system occur that eventually lead to a shortage of reactive power

and declining voltage. This phenomenon can be seen from the plot of the voltage at

receiving end versus the power transferred. The plots are popularly referred to as P-V

curve or “Nose” curve. As the power transfer increases, the voltage at the receiving end

decreases. Eventually, the critical (nose) point, the point at which the system reactive

power is out of use, is reached where any further increase in active power transfer will

lead to very rapid decrease in voltage magnitude. Before reaching the critical point, the

large voltage drop due to heavy reactive power losses can be observed. The maximum

load that can be increased prior to the point at which the system reactive power is out of

use is called static voltage stability margin or loading margin of the system. The only way

to save the system from voltage collapse is to reduce the reactive power losses in the

transmission system or to add additional reactive power prior to reaching the point of

voltage collapse. This has to be carried out in the planning stage with several system-

wide studies.

In static voltage stability study, Continuation Power Flow (CPF) and optimization

methods are the main analysis techniques and they are used to find voltage stability

margin or loading margin (LM) of the system. Utilities and researchers are developing

software based on these techniques, for the study. The CPF technique involves in solving

a series of load flow calculation with predictor and corrector steps. Optimization

technique involves in solving equations of necessary conditions based on an objective

function and constraints. However, utilities or researchers require devoting a Great deal

of effort to create a program. Adding to this, they may face a difficulty to ensure the

correct answers.

4.2 Definition of Static Load

Uncontrollable decay of system voltage at one or more load buses or even over of the

network as a response to load variations, generation or structure disturbances observed in

Power systems world wide. This has been termed as voltage Instability of voltage

decrease has been termed as a voltage collapse process. With the rest of the system

conditions remaining in charged, if the load varied, the voltage at the bus will also vary.

[Voltage at other nodes wills also this load change]. In other words voltage at a load bus

is elastic with respect and reactive power delivered at that node.

This elasticity may be quantitatively & where P, Q, V are active power, reactive

power and voltage of conditions these factors are generally negative. Power system loads

are generally dependent on voltage and frequency. The reactive power loading (i.e.

constant, independent of bus voltage) quite often and other similar studies, is , at best a

mathematical idealization of the power In general, the loads take active power and

reactive power as functions example, a constant admittance load draws active & reactive

power, which square of voltage.

A load is called static if the power taken by the load is dependent only frequently changes

in voltage collapse analysis) and not on time. Impedance load, lighting load, a constant

current load etc are static loads. By these loads vary in time it is because the voltage

varies with time and with the voltage in such loads.

4.3 Static Voltage Algorithm

The transmission system can be represented using a hybrid representation, by the

following set of equations

The H matrix can be evaluated from the Y bus matrix by a partial inversion, where the

voltages at the load buses are exchanged against their currents. This representation can

then be used to define a voltage stability indicator at the load bus, namely Lj which is

given by,

Where,

The term V0j is representative of an equivalent generator comprising the contribution

from all generators. The index Lj can also be derived and expressed in terms of the power

terms as the following.

Where,

The complex power term component S jcorr represents the contributions of the other

loads in the system to the index evaluated at the node j.

It was demonstrated in earlier works that when a load bus approaches a steady state

voltage collapse situation, the index L approaches the numerical value 1.0. Hence for a

system wide voltage stability assessment, the index evaluated at any of the buses must be

less than unity. Thus the index value L gives an indication of how far the system is from

voltage collapse.

From the derivation it is seen that for computing L index, at any load bus, one requires

only the knowledge of the state variables, power information and the network topology.

These measurements can be obtained very quickly in real-time. Since most of the earlier

indices developed on the basis of steady state power flow model has been able to estimate

the system for a dynamic phenomenon like voltage stability, the authors felt worthwhile

to explore the applicability of the index L for predicting a dynamic voltage collapse

situation.

4.4 Voltage collapse with a Static load A static load of constant admittance is assumed in this section. In Section with a constant

power load there can be two operating points. Which one does the answer is that we can

not know. Similarly we can not know what will happen if the load is above the maximum

power that can be supplied by the line. But questions are found in the fact that there can

not be a constant power loads exhibit a nonzero elasticity with voltage. In this section we

Which his static and of constant admittance nature.

In fact the conclusions applicable for any static load where and where

n 0 ,n=m=2 represent constant admittance, n=m=1 represent constant current The load

power characteristics of a constant admittance load is shown in fig4 curve A. In this case

there will be in general, only one operating point. Also it is clear no question of the load

demanding more power that the maximum power. As the load operating point shifts

along the line characteristics and gets in to positive slope region load B in fig 4. Also the

effect of power factor on the operating point can

Fig 4.1 Voltage collapse due to load variation

With a static load, all operating points are generally stable i.e. line operates maybe with a

very low load voltage, high current and low efficiency) everywhere. Is in step with load

change. The voltage variation with time is decided by load variation for every load there

is a fixed voltage and voltage does not run away with load remaining at a constant level.

Thus, in this case collapse can take place only if the fig4. The load is assumed to be at

upf and is assumed to vary from a low value to minutes linearly. The corresponding

voltage variation is shown.

If the line is operating near the critical point but in the upper portion of the change in load

conductance can cause a disproportionate drop in the voltage. the conductance will result

in an increase in power delivered, as it should.

But if load conductance is taken to such a level where operating point is in the of the

curve, not only that there is abnormal voltage drop and excessive heating of high current)

but also the power delivered comes down. In this region, when power increased by

increasing the load, what we get is a decreased power delivery. In this lose the

controllability of power in this operating region. The same kind of voltage collapse and

inefficient operation can result in the cases a line in a parallel line link (ii) loss of

capacitor in a series compensated link even load power change. The effect of increase in

the link impedance is to shift maximum curve to the left.

To sum up, with a static load, abnormal reduction of voltage and stable operation

voltages can result as a consequence of over-loading or increase in line impedance. Under

such conditions will be quite loss due to high line currents. However there is away

phenomenon associated with static load in general. Of course, where line operation the

critical point, small changes in load will result in large changes in voltage and large line

efficiency. The collapse is more severe and faster if the load is at a low.

Chapter 5

Dynamic Load and Voltage Stability 5.1 Overview

Power transmission capability has traditionally been limited by either angle stability or by

the thermal loading capabilities of the lines. But with the developments in faster short

circuit clearing times, quicker and effective excitation systems and developments in

several stability control devices, the system problems associated with transient instability

have been largely reduced. However, voltage instability limits are becoming more

prominently significant in the context of a secure power system operation. In the

deregulated power market regime, economic competition has lead to an interest in

maintaining an optimum, secure and reliable power system operation. One such security

issue is the voltage stability of the system. Several voltage instability incidents have been

Reported, in the recent past, all over the globe. These are results of operating the system

with very less voltage stability margin under normal conditions. Thus, lot of work is

being carried out to understand voltage stability better, to detect it faster.

Traditional methods of voltage stability investigation have relied on static analysis using

the conventional power flow model. This analysis has been practically viable because of

the view that the voltage collapse is a relatively slow process thus being primarily

considered as a small signal phenomenon. The various analytical tools classified under

steady state analysis mode have been able to address the otherwise dynamic phenomenon

of voltage collapse. A variety of tools like the P-V curve, Q-V curve, eigenvalue, singular

value, sensitivity and energy based methods have been proposed. They are

computationally intensive which makes it less viable for fast computation during a

sequence of discontinuities like generators hitting field current or reactive limits, tap

changer limits, switchable shunt capacitor’s susceptance limits etc. In a dynamic voltage

stability computation regime, considering all these discontinuities into the analysis are

necessary. Moreover, a quick computation is necessary to take necessary corrective

action in time to save the system from an impending voltage collapse.

Fig5.1: A fast and dynamic voltage collapse

5.2 Dynamic Load Definitions

A load is called dynamic if the power drawn by the load is a function of time, example;

consider an induction motor driving a constant toque load. Suddenly, the motor

decelerates and the power (both the P & Q) drawn of speed (slip) and hence of time. P &

Q will stabilize at new values corresponding voltage after sufficient time decided by

mechanical time constant of the stabilized values may correspond to a stalled condition].

Another dynamic stabilized by using a continuous tap changer [i.e. automatic tap

changing automatic electronic voltage stabilizer etc]. These tap changers change delay.

Thus the load presented to the power system after a voltage varying due to time varying

turns ratio in the tap changer. The interplay of the two factors viz. bus voltage elasticity

with power elasticity with bus voltage results in abnormal sustained increases slightly or

one of the two parallel lines trips, or local the case of static loads. In the case of dynamic

loads, this interplay of voltage even in the absence of further disturbances.

5.3 System Model

The dynamic power system is modeled as a set of algebraic differential equations.

Where x are the state variables, and y are the algebraic variables, usually bus voltages.

Load model

Voltage sensitive load can be modeled as

Where are P0 is the real power at V=1.0 pu, Q0 is the reactive power at V=1.0 pu, V is

the bus voltage magnitude, β is the voltage sensitivity exponent of the real power, and η

is the voltage sensitivity exponent of the reactive power. Thus, with β=2, and η=2 , the

load becomes a constant impedance type. Dynamic loads are modeled as induction

motors. The load at one node can be represented as a combination of different kinds of

loads, e.g. one portion of the load is consumed by an impedance load and the rest could

be modeled as dynamic induction motor loads.

Generator modeling

Several different types of exciters may be installed within a system, such as the DC1A,

ST1A, and ST3A etc. Some generators may be equipped with PSS, and a

turbine/governor sub-system.

ULTC(under load tap changers modeling)

A ULTC can automatically adjust and keep the load-side bus voltage constant given that

enough buck or boost taps exist. A model of the ULTC is shown as follows:[19]

Here d is the step size of the transformer and n is the turn ratio. and

Time delays of ULTC action at the first instance is usually much longer than the time

delays associated with successive actions of the ULTC. Each ULTC has finite (usually

32) taps and step size is usually 0.000625.

5.4 General Dynamic Simulations

In dynamic simulation the network solution at each time step (figure) is of the form

I=Y•E where I is a vector of complex source currents and E is a vector of complex bus

voltages. In the case of a network of pure impedance elements, including loads, the

solution is a straightforward algebraic operation without iterations. More realistically,

load characteristics are nonlinear and the network load flow solution involves iterations

with nonlinear load effects introduced as current injections.[16]

Stated in slightly more formal terms, the behaviour of a system is described by a set of

differential equations. At every time step of the simulation, the time derivative of each

state variable in the system is calculated, using the constant and variable parameters

which describe the system condition at that time instant as initial conditions. The state

variable values at the next time step (statenew) are determined from the present value of

each state variable (stateold) and its rate of change (i.e., its time derivative). Simulation

time is advanced and the process is repeated. In the form of a formal equation the

procedure mentioned above will be:[12]

Fig5.2: Basic logic flow for Dynamic Simulation

5.5 Transient Dynamic Simulation

The explicit numerical integration algorithm used to solve the differential equations for

these phenomena is the modified Euler algorithm. This is the ordinary algorithm used in

Programm. The advantage of the simplicity of the explicit algorithm is partly offsetby

numerical stability considerations which require integration time steps smaller than the

smallest time constant describing the process. Figure shows how the time step affects

numerical stability.

5.6 Long Term Dynamic simulation

In many cases where the system survives the initial disturbance, the higher frequency

effects (i.e., rotor angle swings) subside after a few seconds and then the transition to a

new post contingency state occurs over minutes. While this process can be solved by

extending the stability run through minutes with 1/2 cycle time step using the explicit

integration method, the computation time can be very excessive. The extended term

option of Programm (figure 3.1), was created to analyse system behaviour over the period

of many seconds to minutes following disturbances where the load restoration, excitation

limiters, tap changing transformers, switching of capacitors and reactors etc., come into

account. This is the situation when studying long-term voltage stability. A more efficient

algorithm in these cases is the implicit trapezoidal integration method [4]. As mentioned

before, this algorithm is numerically stable. But with larger time steps, high frequency

modes and transients are filtered out and only the solutions for the slower modes are

accurate. Figure 3.4 shows the effect when the time steps are increased.

Fig5.3: Explicit solution method for transient dynamic simulation

Fig5.4: Trapezoidal algorithm for long term dynamic simulation

5.7 Dynamic Load model

The dynamic model proposed by Karlsson is a special case of a dynamic load model

given by Hill. The model implemented is described by the following equations:

When there is a voltage drop of 5-10% on load nodes, field measurements show that αt is

around 2. This means that the transient behavior of the load can be regarded as constant

impedance. In most of the measurements, αs is well below 1, which indicates a changed

voltage dependence for the active power, and the load characteristic tends to be more like

constant power. The time constant Tpr for this changing phase is around some hundred

seconds. This phenomenon has been explained by the power characteristic in electrical

domestic heating.

Fig5.5: Solution algorithm for dynamic load

Chapter 6

Software Specification

6.1 PSS/E (Power System Simulator for Engineering) Introduction

In order to simulate voltage collapse it is important to have suitable software since

dynamic effects can be both of a fast and a slow nature. Voltage collapse can occur not

only as the immediate consequence of a contingency, but can also be the result of

changes in system conditions due to restoration of loads, limitation of generator currents

or capacitor/reactor switching etc. These varying conditions will increase the demands on

the solution algorithms used in the program. It is also important to be able to implement

user-written models of the equipment used in the system since there is no model library

that covers all details or models of the equipment used in power systems. According to

the requirements mentioned above, the PSS/E1 program was suitable for voltage collapse

simulations. The outcome of that PSS/E met the requirements regarding long-term

dynamic simulation and model implementation, though it has to be mentioned that

comparison with other software was not made.

Structure

PSS/E is an integrated, interactive program for simulating, analyzing and optimizing

power system performance. The program contains a set of modules which handle a

number of different power system analysis calculations. All the modules operate from the

same set of data whose structure is divided into four different “working files”, shown in

figure . These working files are set up in a way that optimizes the computational aspects

of the key power system simulation functions: network solution and equipment dynamic

modeling. The user has a variety of ways of operating PSS/E, depending upon the type of

study being performed. However, he never needs to address these working files by name,

though he must be aware that he is processing these files every time he uses PSS/E. The

modules used for voltage collapse simulations are Power flow, Dynamic simulation and

Extended term dynamic simulation.

Fig6.1: structure of PSS/E software

The four working files have the following names and general functions:

LFWORK Contains a complete set of power flow data (Load Flow WORKing file)

FMWORKWorking file for all operations involving the factorized system admittance

matrix (Factorized Matrix WORKing file).

SCWORK Working files for fault analysis (Short Circuit WORKing file).

DSWORK Scratch files for dynamic simulation activities (Dynamic Simulation

WORKing file).

6.2 MATLAB (Matrix Laboratory)

Introduction

MATLAB® is a high-performance language for technical computing. It integrates

computation, visualization, and programming in an easy-to-use environment where

problems and solutions are expressed in familiar mathematical notation. Typical uses

include Math and computation Algorithm development Data acquisition Modeling,

simulation, and prototyping Data analysis, exploration, and visualization Scientific and

engineering graphics Application development, including graphical user interface

building MATLAB is an interactive system whose basic data element is an array that

does not require dimensioning. This allows you to solve many technical computing

problems, especially those with matrix and vector formulations, in a fraction of the time it

would take to write a program in a scalar no interactive language such as C or Fortran.

The name MATLAB stands for matrix laboratory. MATLAB was originally written to

provide easy access to matrix software developed by the LINPACK and EISPACK

projects. Today, MATLAB engines incorporate the LAPACK and BLAS libraries,

embedding the state of the art in software for matrix computation. MATLAB has evolved

over a period of years with input from many users. In university environments, it is the

standard instructional tool for introductory and advanced courses in mathematics,

engineering, and science. In industry, MATLAB is the tool of choice for high-

productivity research, development, and analysis. MATLAB features a family of add-on

application-specific solutions called toolboxes. Very important to most users of

MATLAB, toolboxes allow you to learn and apply specialized technology. Toolboxes are

comprehensive collections of MATLAB functions (M-files) that extend the MATLAB

environment to solve particular classes of problems. Areas in which toolboxes are

available include signal processing, control systems, neural networks, fuzzy logic,

wavelets, simulation, and many others.[11]

Proposed simulation approach Power flow or load flow consists of solving real and reactive power balance equations at

all buses in power systems to obtain all state variables when control variables are

specified. According to this, Symbolic toolbox in MATLAB can be used to create power

flow equations when the system data and control variables are known. Then, a simple

command called “lsqnonlin” in Optimization toolbox is used to find the solution for all

state variables. The steps behind the proposed method can be summarized as shown in

the Fig.

Fig6.2: Load flow calculation using MATLAB

From Fig., system parameters are read from input data to create power balance equations

using Symbolic toolbox. The solution is then found by using a single “lsqnonlin”

command. It can be noticed that Jacobian is not required to compute in the formulation

process since it is already embedded in Optimization toolbox. The solution is found in a

simple way, as only one command is used.

Continuation Power Flow is basically a series of load flow calculation with predictor and

corrector steps. The formation of CPF is complicated and it is required good

programming skill. However, with the help of Symbolic and Optimization toolboxes, the

formulation is much easier. Figure 3 illustrates steps behind the CPF process with

Symbolic and Optimization toolboxes. From Fig. 3, the system data is read first, and then

Symbolic toolbox is introduced to create power flow equations. The power flow

calculation is performed to find the load flow Jacobean for the following predictor step.

In the predictor step, state variables are predicted from the current status of load flow

Jacobian to predict the bus angles and voltages at higher LF. In the corrector step, the

actual value of state variables are computed from load flow equations and initial

condition obtained from the predictor step. Prior to the collapse point, parameterization

step is performed to avoid convergence difficulty of CPF process by switching state

variable from LF to the voltage at the weakest bus, which is found from a bus having

highest voltage decrease. The process is repeated until the PV curve is completed.

Fig6.3: Continuation power flow logic diagram

6.3 EUROSTAG

The EUROSTAG program, jointly developed by Tractabel and EdF covers the domains

of transient, mid-term, and long-term stability by means of an automatically and

continuously variable step size integration algorithm. It allows a complete simulation of

voltage stability phenomena and includes models for transformer on-load tap changing,

dynamic loads, field current limiters, etc. The implicit method used for the numerical

solution is based on the backward differentiations’ algorithm treated according to the

GEAR implementation.

6.4 EXTAB

The EXSTAB program, developed by Tokyo Electric Power Company and General

Electric, allows for dynamic simulation over an extended range of the time domain.

Explicit as well as implicit integration technique is used. The program includes detailed

models of AGC with frequency and interchange control, power plants, dynamic and

thermostatically controlled loads, OLTC's, and many protective functions. Simulation

modes allow for automatic continuously variable time step integration, as well as a fast

algebraic quasi-steady state mode for slowly varying system conditions.

6.5 SIMPOW

SIMPOW (simulation of power systems), developed by ABB Power Systems AB, covers

dynamic simulations in a wide range of time. The program is used for all types of static

and dynamic simulations of electrical power systems: long term, short term and fast

transients caused by switching and lightning, etc. SIMPOW has models of most power

system elements but the user-oriented Dynamic Simulation Language (DSL), allows

implementation of power system elements which are not available in the standard library

of models.

6.6 ETMSP

ETMSP (Extended Transient/Midterm Stability Program), developed by Ontario Hydro,

has been enhanced to meet the modeling requirements for dynamic analysis of voltage

stability. These include representation of transformer LTC action, generator field current

Limits, dynamic loads, constant energy loads, special relaying, and under voltage load

shedding.

6.7 LTSP

LTSP (Long Term Stability Program) is capable of simulating fast as well as slow

dynamics of power systems and is based on the ETMSP program. In addition to all the

features of ETMSP, LTSP includes detailed models for fossil-fuelled, nuclear, and

combustion turbine plants. The basis for and the details of modeling and solution

techniques used in these programs can be found in.

Chapter 7

Algorithm of voltage Collapse

7.1 Basic Algorithms Algorithm for Jacobin iteration We assume that the system Ax = b has been rearranged so that for each row of A the

diagonal elements[8]

have magnitudes that are greater than the sum of the remaining elements in the

corresponding row. That is,

|ai,i| > (sum (j=1 to n) |ai,j|) - ai,i i =1,2,3...n

This is a sufficient noation for both this method and the one that follows to converge.

We begin with an initial approximation to the solution vector, which we store in the

vector: old_x

For i = 1 to n

b[i] - b[i]/a[i,i]

new_x[i] = old_x[i]

a[i,j] = a[i,j]/a[i,i]: j = 1,...n and i <> j

End For i

Repeat

For i = 1 to n

old_x[i] = new_x[i]

new_x[i] = b[i]

End for i

For i = 1 to n

For i = 1 to n

If (j !=i) then

new_x[i] = new_x[i] - a[i,j]*old_x[j]

End If

End For

End For

Until new_x and old_x converge to each other

Algorithm for Gauss seidal iteration

We assume, as we did in the previous algorithm, that the system Ax = b has been

rearranged so that for

each row of A the diagonal elements have magnitudes that are greater than the sum of the

remaining

elements in the corresponding row. That is,

|ai,i| > sum(j = 1 to n, i!=j)|ai,j| i = 1,2,3,....n

This is a sufficient condition for both this method and the previous one. As before we

begin with an

initial approximation to the solution vector, which we store in the vector, x.

For i = 1 to n

b[i] = b[i]/a[i,i];

a[i,j] = a[i,l]/a[i,i]; j = 1, ,..n and i !=j

End For

While (not yet convergent) do

For i = 1 to n

x[i] = b[ii]

For j = 1 to n

if (j != i) then

x[i] = x[i] - a[i,j]* x[j]

End if

End For

End For

End While

Interval Newtons Method

The problem is to find bounds on the solution of a nonlinear continuous function f : Rn !

Rn in a given box x(0) 2 IRn. Using the mean value theorem we have for any x_ that

f(x_) 2 f(˜x) + J(x)(x_ − ˜x), where J(x) is the interval Jacobian matrix with [5]

The interval linear system given by the equation can be solved for x_ to obtain an outer bound on

the solution set, say N(˜x, x). The notation includes both ˜x and x to show the dependence on

both terms. It follows that 0 2 f(˜x)+J(x)(N(˜x, x)− ˜x), which suggests the following iteration, for k =

0, 1, . . . and ˜x(k) 2 x(k):

A reasonable choice for ˜x(k) is the center, denoted by ˇx, of x. In this work, we decided to use it,

however other choices are available . The linear system given by equation can be solved using

an appropriate interval method to give the Newton operator

7.2 Proposed Algorithm

In this section we briefly present the main aspects of our approach to computationally

solve the power flow problem.

(i) Data Input

The data provided by the user are classified into two types: transmission-line data

(resistance, reactance, susceptance of the circuits etc.) and bus data (magnitude and phase

of the voltage at slack bus, generated real power at PV buses etc.). In the second group

we find the load data, which are given as interval data, since they are specified

considering the probable measurement errors5.

(ii) Initial Guesses

The initial guesses are provided by a punctual algorithm for the power flow problem [2],

transformed into intervals that considers the maximal measurement relative error.

(iii) Applying Newton’s Iteration

According to the iteration given by equations (3.4)-(3.6), we implemented the algorithm

shown in Figure 1. The implementation was done in Matlabr using the Intlab toolbox.

Notice that a real interval x = [x1, x2] in Intlab can be stored by using either the

command infsup(x1, x2), where x1 and x2 are, respectively, the infimum and supremum

of the interval x, or the command midrad(mp, rd), which represents x by its midpoint mp

= x1+x2 /2 and radius rd = x2−x1/ 2 . In this algorithm, e and f denote, respectively, the

real and imaginary parts of the interval complex voltage at all buses, whereas e intv and f

intv are conceived as the initial guesses, as stated in (ii). The real and reactive powers are

evaluated according Section 2. The power mismatches are evaluated using equations in

order to obtain the box fx. In the given algorithm, bsf means a vector with all bus indices

except the slack bus and bpq is a vector containing the bus indices for PQ buses. After the

evaluation of the Jacobian matrix6, the linear system given by the equation is solved

using the Matlabr command “\”. Then, the nonlinear system variables are updated

according equations.

(iv) Stop Criteria

In order to assess the process convergence, we use two stop criteria. Firstly, it is verified

if the box fx includes the zero, which means that an approximation for the solution was

found. After, it is verified the possibility of improving the solution (that is, the possibility

of reducing its diameter according to an admissible tolerance).

(v) Final Result in Polar Coordinates

The algorithm shown in Figure 1 provides a solution for the power flow problem in

cartesian coordinates. In general, it is more usual to express the complex voltages in polar

coordinates. Then, we have added a routine in order to calculate the interval polar

coordinates.

7.3 Interval Load flow Problem

The equation describing the performance of the network of a power system using the bus

frame of reference in admittance form is

I = YbusE

Where I is a vector related to the current injection at the system buses, Ybus is the

admittance matrix and E is a vector with the complex nodal voltages.

it is possible to write,

-----------------1

Real and reactive power at any bus P is,

---------------------2

This load flow problem can be solved by the Newton’s method using a set of nonlinear

equations to express real and reactive powers in terms of bus voltages Substituting Ip

from equation(1) into equation(2) results in

--------------------------3

Using cartesian coordinates, we have Ep = ep + jfp and Ypq = Gpq + jBpq, and then

equation (3) becomes Pp − jQp = (ep − jfp)Pn ,q=1(Gpq + jBpq)(eq + jfq). Separating the

real and imaginary parts, we have

This formulation results in a set of nonlinear equations, two for each bus of the system.

Note that the real and reactive powers are given by Pp = Pgp − Pdp and Qp = Qgp−Qdp ,

respectively, where Pgp and Qgp are the generated real and reactive powers at bus p, and

Pdp and Qdp are the real and reactive power loads at bus p, respectively. At this point, it

is important to point out that the known real and reactive power loads Pdp and Qdp

present an uncertainty due the measurement errors. Pdp and Qdp belong to an interval

that is estimated at beginning of the process, since the accuracy of the instrument is

known a priori. This implies it is necessary to admit that the real and reactive powers Pgp

and Qgp , which are specified in the beginning of the process, may range in an interval

with an admissible radium determined by an heuristic method based on the experience of

a system operator. The real and imaginary components of voltage ep and fp are unknown

intervals for all buses except the slack bus, where the voltage interval is specified and

remains fixed. Thus there are 2(n − 1) equations to be solved for a load flow problem. In

Order to reach the solution; we use the interval version of the Newton’s algorithm.

7.4 Fundamental voltage collapse equation

A simple power system is considered, through which the useful index of the voltage

stability is derived. As showed in Fig.1, whereby bus 1 is assumed as a generator bus and

bus 2 is a load bus whose voltage behavior will be our interest.

Fig: Single generator and load system

This simple system can be described by the following equations (where the dot above a letter represents a vector):

Thereby an indicator has been derived which can be used for monitoring the voltage

stability problem of the system and for assessing the degree of risk for a potential voltage

collapse. When S2 =0 , the indicator will be zero and indicates that there will be no

voltage problem. When S2 =1 , the voltage at load bus will collapse.

Chapter 8

Process Simulation and Test Results of voltage collapse 8.1 IEEE-14 bus introduce It consists of five synchronous machines with IEEE type-1 exciters, three of which are

synchronous compensators used only for reactive power support. There are 11 loads in

the system totaling 259 MW and 73 Mvar. The dynamic data for the generators exciters

was selected from [19].

Fig 8.1: IEEE 14 bus test system

8.2 IEEE 30 bus introduce

Fig: IEEE 30 bus test system

8.3 Load flow result for 14 bus -----------------------------------------------------------------------------------------

Newton Raphson Loadflow Analysis

-----------------------------------------------------------------------------------------

| Bus | V | Angle | Injection | Generation | Load |

| No | pu | Degree | MW | MVar | MW | Mvar | MW | MVar |

-----------------------------------------------------------------------------------------

1 1.0600 0.0000 225.531 -13.754 225.531 -13.754 0.000 0.000

-----------------------------------------------------------------------------------------

2 1.0450 -4.7936 25.000 32.591 46.700 45.291 21.700 12.700

-----------------------------------------------------------------------------------------

3 1.0100 -12.5745 -94.200 8.746 -0.000 27.746 94.200 19.000

-----------------------------------------------------------------------------------------

4 1.0132 -10.0871 -47.800 3.900 -0.000 -0.000 47.800 -3.900

-----------------------------------------------------------------------------------------

5 1.0166 -8.6191 -7.600 -1.600 -0.000 0.000 7.600 1.600

-----------------------------------------------------------------------------------------

6 1.0700 -14.3015 -11.200 15.521 0.000 23.021 11.200 7.500

-----------------------------------------------------------------------------------------

7 1.0457 -13.0843 -0.000 -0.000 -0.000 -0.000 0.000 0.000

-----------------------------------------------------------------------------------------

8 1.0800 -13.0843 0.000 21.026 0.000 21.026 0.000 0.000

-----------------------------------------------------------------------------------------

9 1.0305 -14.6688 -29.500 -16.600 0.000 0.000 29.500 16.600

-----------------------------------------------------------------------------------------

10 1.0299 -14.8858 -9.000 -5.800 0.000 0.000 9.000 5.800

-----------------------------------------------------------------------------------------

11 1.0461 -14.7102 -3.500 -1.800 0.000 0.000 3.500 1.800

-----------------------------------------------------------------------------------------

12 1.0533 -15.1514 -6.100 -1.600 0.000 0.000 6.100 1.600

-----------------------------------------------------------------------------------------

13 1.0466 -15.1850 -13.500 -5.800 -0.000 -0.000 13.500 5.800

-----------------------------------------------------------------------------------------

14 1.0193 -15.9226 -14.900 -5.000 0.000 0.000 14.900 5.000

-----------------------------------------------------------------------------------------

Total 13.231 29.828 272.231 103.328 259.000 73.500

Line Flow and Losses

-------------------------------------------------------------------------------------

|From|To | P | Q | From| To | P | Q | Line Loss |

|Bus |Bus| M | MVar | Bus | Bus| MW | MVar | MW | MVar |

-------------------------------------------------------------------------------------

1 2 151.170 -16.093 2 1 -147.184 28.264 3.986 12.171

-------------------------------------------------------------------------------------

1 5 74.360 8.069 5 1 -71.670 3.036 2.690 11.105

-------------------------------------------------------------------------------------

2 3 73.583 5.918 3 2 -71.238 3.961 2.345 9.879

-------------------------------------------------------------------------------------

2 4 56.337 2.842 4 2 -54.643 2.296 1.693 5.138

-------------------------------------------------------------------------------------

2 5 42.264 4.587 5 2 -41.322 -1.709 0.943 2.878

-------------------------------------------------------------------------------------

3 4 -22.962 7.671 4 3 23.347 -6.689 0.385 0.983

-------------------------------------------------------------------------------------

4 5 -59.067 11.347 5 4 59.537 -9.863 0.470 1.484

-------------------------------------------------------------------------------------

4 7 27.087 -15.396 7 4 -27.087 17.330 0.000 1.934

-------------------------------------------------------------------------------------

4 9 15.476 -2.641 9 4 -15.476 3.935 0.000 1.294

-------------------------------------------------------------------------------------

5 6 45.854 -20.837 6 5 -45.854 26.602 0.000 5.765

-------------------------------------------------------------------------------------

6 11 8.266 8.903 11 6 -8.144 -8.647 0.122 0.256

-------------------------------------------------------------------------------------

6 12 8.062 3.177 12 6 -7.981 -3.009 0.081 0.168

-------------------------------------------------------------------------------------

6 13 18.326 9.984 13 6 -18.075 -9.488 0.252 0.496

-------------------------------------------------------------------------------------

7 8 0.000 -20.358 8 7 -0.000 21.026 0.000 0.668

-------------------------------------------------------------------------------------

7 9 27.087 14.791 9 7 -27.087 -13.833 0.000 0.958

-------------------------------------------------------------------------------------

9 10 4.414 -0.910 10 9 -4.408 0.927 0.006 0.016

-------------------------------------------------------------------------------------

9 14 8.650 0.317 14 9 -8.560 -0.127 0.090 0.191

-------------------------------------------------------------------------------------

10 11 -4.592 -6.727 11 10 4.644 6.847 0.051 0.120

-------------------------------------------------------------------------------------

12 13 1.881 1.409 13 12 -1.870 -1.399 0.011 0.010

------------------------------------------------------------------------------------

13 14 6.445 5.088 14 13 -6.340 -4.873 0.105 0.214

-------------------------------------------------------------------------------------

Total Loss 13.231 55.728

8.4 Load Flow result for 30 bus -----------------------------------------------------------------------------------------

Newton Raphson Loadflow Analysis

-----------------------------------------------------------------------------------------

| Bus | V | Angle | Injection | Generation | Load |

| No | pu | Degree | MW | MVar | MW | Mvar | MW | MVar |

-----------------------------------------------------------------------------------------

1 1.0600 0.0000 260.928 -17.118 260.928 -17.118 0.000 0.000

-----------------------------------------------------------------------------------------

2 1.0430 -5.3474 18.300 35.066 40.000 47.766 21.700 12.700

-----------------------------------------------------------------------------------------

3 1.0217 -7.5448 -2.400 -1.200 -0.000 0.000 2.400 1.200

-----------------------------------------------------------------------------------------

4 1.0129 -9.2989 -7.600 -1.600 0.000 0.000 7.600 1.600

-----------------------------------------------------------------------------------------

5 1.0100 -14.1542 -94.200 16.965 -0.000 35.965 94.200 19.000

-----------------------------------------------------------------------------------------

6 1.0121 -11.0880 0.000 0.000 0.000 0.000 0.000 0.000

-----------------------------------------------------------------------------------------

7 1.0035 -12.8734 -22.800 -10.900 -0.000 0.000 22.800 10.900

-----------------------------------------------------------------------------------------

8 1.0100 -11.8039 -30.000 0.691 0.000 30.691 30.000 30.000

-----------------------------------------------------------------------------------------

9 1.0507 -14.1363 0.000 0.000 0.000 0.000 0.000 0.000

-----------------------------------------------------------------------------------------

10 1.0438 -15.7341 -5.800 17.000 0.000 19.000 5.800 2.000

-----------------------------------------------------------------------------------------

11 1.0820 -14.1363 0.000 16.270 0.000 16.270 0.000 0.000

-----------------------------------------------------------------------------------------

12 1.0576 -14.9416 -11.200 -7.500 0.000 -0.000 11.200 7.500

-----------------------------------------------------------------------------------------

13 1.0710 -14.9416 -0.000 10.247 -0.000 10.247 0.000 0.000

-----------------------------------------------------------------------------------------

14 1.0429 -15.8244 -6.200 -1.600 -0.000 0.000 6.200 1.600

-----------------------------------------------------------------------------------------

15 1.0384 -15.9101 -8.200 -2.500 -0.000 0.000 8.200 2.500

-----------------------------------------------------------------------------------------

16 1.0445 -15.5487 -3.500 -1.800 -0.000 -0.000 3.500 1.800

-----------------------------------------------------------------------------------------

17 1.0387 -15.8856 -9.000 -5.800 -0.000 -0.000 9.000 5.800

-----------------------------------------------------------------------------------------

18 1.0282 -16.5425 -3.200 -0.900 -0.000 -0.000 3.200 0.900

-----------------------------------------------------------------------------------------

19 1.0252 -16.7273 -9.500 -3.400 0.000 0.000 9.500 3.400

-----------------------------------------------------------------------------------------

20 1.0291 -16.5363 -2.200 -0.700 0.000 -0.000 2.200 0.700

-----------------------------------------------------------------------------------------

21 1.0293 -16.2462 -17.500 -11.200 -0.000 0.000 17.500 11.200

-----------------------------------------------------------------------------------------

22 1.0353 -16.0738 -0.000 -0.000 -0.000 -0.000 0.000 0.000

-----------------------------------------------------------------------------------------

23 1.0291 -16.2528 -3.200 -1.600 -0.000 -0.000 3.200 1.600

-----------------------------------------------------------------------------------------

24 1.0237 -16.4409 -8.700 -2.400 -0.000 4.300 8.700 6.700

-----------------------------------------------------------------------------------------

25 1.0202 -16.0539 -0.000 -0.000 -0.000 -0.000 0.000 0.000

-----------------------------------------------------------------------------------------

26 1.0025 -16.4712 -3.500 -2.300 0.000 0.000 3.500 2.300

-----------------------------------------------------------------------------------------

27 1.0265 -15.5558 0.000 -0.000 0.000 -0.000 0.000 0.000

-----------------------------------------------------------------------------------------

28 1.0109 -11.7436 0.000 -0.000 0.000 -0.000 0.000 0.000

-----------------------------------------------------------------------------------------

29 1.0067 -16.7777 -2.400 -0.900 -0.000 0.000 2.400 0.900

-----------------------------------------------------------------------------------------

30 0.9953 -17.6546 -10.600 -1.900 0.000 0.000 10.600 1.900

-----------------------------------------------------------------------------------------

Total 17.528 20.921 300.928 147.121 283.400 126.200

-----------------------------------------------------------------------------------------

-------------------------------------------------------------------------------------

Line Flow and Losses

-------------------------------------------------------------------------------------

|From|To | P | Q | From| To | P | Q | Line Loss |

|Bus |Bus| MW | MVar | Bus | Bus| MW | MVar | MW | MVar |

-------------------------------------------------------------------------------------

1 2 173.143 -18.108 2 1 -167.964 33.617 5.179 15.509

-------------------------------------------------------------------------------------

1 3 87.785 6.248 3 1 -84.669 5.140 3.116 11.388

-------------------------------------------------------------------------------------

2 4 43.619 5.194 4 2 -42.607 -2.113 1.011 3.081

-------------------------------------------------------------------------------------

3 4 82.269 -3.772 4 3 -81.412 6.235 0.858 2.463

-------------------------------------------------------------------------------------

2 5 82.293 4.033 5 2 -79.347 8.342 2.945 12.374

-------------------------------------------------------------------------------------

2 6 60.353 1.403 6 2 -58.406 4.503 1.946 5.906

-------------------------------------------------------------------------------------

4 6 72.272 -17.521 6 4 -71.631 19.753 0.641 2.231

-------------------------------------------------------------------------------------

5 7 -14.853 11.796 7 5 15.015 -11.387 0.162 0.409

-------------------------------------------------------------------------------------

6 7 38.195 -1.201 7 6 -37.815 2.370 0.381 1.169

-------------------------------------------------------------------------------------

6 8 29.490 -3.214 8 6 -29.387 3.574 0.103 0.361

-------------------------------------------------------------------------------------

6 9 27.799 -18.485 9 6 -27.799 20.698 0.000 2.213

-------------------------------------------------------------------------------------

6 10 15.882 -5.306 10 6 -15.882 6.781 0.000 1.475

-------------------------------------------------------------------------------------

9 11 -0.000 -15.799 11 9 0.000 16.270 0.000 0.470

-------------------------------------------------------------------------------------

9 10 27.799 7.041 10 9 -27.799 -6.222 0.000 0.819

-------------------------------------------------------------------------------------

4 12 44.147 -16.795 12 4 -44.147 21.983 0.000 5.188

-------------------------------------------------------------------------------------

12 13 0.000 -10.119 13 12 -0.000 10.247 -0.000 0.128

-------------------------------------------------------------------------------------

12 14 7.790 2.390 14 12 -7.717 -2.238 0.073 0.152

-------------------------------------------------------------------------------------

12 15 17.639 6.705 15 12 -17.429 -6.290 0.211 0.415

-------------------------------------------------------------------------------------

12 16 7.518 3.420 16 12 -7.460 -3.299 0.058 0.121

-------------------------------------------------------------------------------------

14 15 1.517 0.638 15 14 -1.511 -0.633 0.006 0.005

-------------------------------------------------------------------------------------

16 17 3.960 1.499 17 16 -3.946 -1.468 0.014 0.032

-------------------------------------------------------------------------------------

15 18 6.291 1.829 18 15 -6.249 -1.742 0.043 0.087

-------------------------------------------------------------------------------------

18 19 3.049 0.842 19 18 -3.043 -0.830 0.006 0.012

-------------------------------------------------------------------------------------

19 20 -6.457 -2.570 20 19 6.473 2.601 0.016 0.031

-------------------------------------------------------------------------------------

10 20 8.749 3.471 20 10 -8.673 -3.301 0.076 0.170

-------------------------------------------------------------------------------------

10 17 5.067 4.367 17 10 -5.054 -4.332 0.013 0.035

-------------------------------------------------------------------------------------

10 21 18.286 11.764 21 10 -18.135 -11.439 0.151 0.325

-------------------------------------------------------------------------------------

10 22 5.780 3.107 22 10 -5.751 -3.048 0.029 0.059

-------------------------------------------------------------------------------------

21 23 0.635 0.239 23 21 -0.635 -0.239 0.000 0.000

-------------------------------------------------------------------------------------

15 23 4.449 2.593 23 15 -4.424 -2.544 0.025 0.050

-------------------------------------------------------------------------------------

22 24 5.751 3.048 24 22 -5.706 -2.977 0.045 0.071

-------------------------------------------------------------------------------------

23 24 1.859 1.183 24 23 -1.853 -1.171 0.006 0.012

-------------------------------------------------------------------------------------

24 25 -1.142 1.748 25 24 1.149 -1.734 0.008 0.014

-------------------------------------------------------------------------------------

25 26 3.544 2.366 26 25 -3.500 -2.300 0.044 0.066

-------------------------------------------------------------------------------------

25 27 -4.694 -0.632 27 25 4.717 0.677 0.024 0.045

-------------------------------------------------------------------------------------

28 27 17.998 -3.529 27 28 -17.998 4.791 -0.000 1.262

-------------------------------------------------------------------------------------

27 29 6.189 1.667 29 27 -6.103 -1.505 0.086 0.162

-------------------------------------------------------------------------------------

27 30 7.091 1.661 30 27 -6.930 -1.358 0.161 0.303

-------------------------------------------------------------------------------------

29 30 3.703 0.605 30 29 -3.670 -0.542 0.033 0.063

-------------------------------------------------------------------------------------

8 28 -0.613 -0.241 28 8 0.614 0.242 0.000 0.001

-------------------------------------------------------------------------------------

6 28 18.670 -3.094 28 6 -18.611 3.304 0.059 0.209

-------------------------------------------------------------------------------------

Total Loss 17.528 68.888

-------------------------------------------------------------------------------------

8.4 Voltage decrease due to load increase data From the above data analysis we observe that every bus has its own load capability.

When we increase the individual load of every bus by 0.1 MW then some bus shows real

collapse phenomena. Only 3 buses showed some voltage decrease picture which we can

observe by below data’s:

Load increase 0.1 MW

Bus no Initial voltage Present voltage

1 1.060 3.1780

2 1.045 3.0887

3 1.010 0.9860

4 1.0132 2.9036

5 1.016 0.9987

6 1.07 3.2383

7 1.0457 3.0929

8 1.08 1.011

9 1.035 3.0299

10 1.0299 3.001

11 1.0461 3.0982

12 1.0533 3.1380

13 1.0466 3.0982

14 1.0193 2.9837

Load increase 0.2 MW

Bus no Initial voltage Present voltage

1 1.060 3.2656

2 1.045 3.1650

3 1.010 0.9689

4 1.0132 2.9753

5 1.016 0.9949

6 1.07 3.3182

7 1.0457 3.1692

8 1.08 1.0197

9 1.035 3.1047

10 1.0299 3.0742

11 1.0461 3.1717

12 1.0533 3.2155

13 1.0466 3.1747

14 1.0193 3.0112

Load increase 0.3 MW

Bus no Initial voltage Present voltage

1 1.060 3.331

2 1.045 3.2395

3 1.010 0.9478

4 1.0132 3.0456

5 1.016 0.9884

6 1.07 3.3963

7 1.0457 3.2438

8 1.08 1.0258

9 1.035 3.1778

10 1.0299 3.1456

11 1.0461 3.2463

12 1.0533 3.2911

13 1.0466 3.2494

14 1.0193 3.0821

Load increase 0.4 MW

Bus no Initial voltage Present voltage

1 1.060 3.4080

2 1.045 3.3123

3 1.010 0.9220

4 1.0132 3.1138

5 1.016 0.9789

6 1.07 3.4727

7 1.0457 3.3167

8 1.08 1.0295

9 1.035 3.2492

10 1.0299 3.2172

11 1.0461 3.3193

12 1.0533 3.3651

13 1.0466 3.3224

14 1.0193 3.1542

Load increase 0.5 MW

Bus no Initial voltage Present voltage

1 1.060 3.4813

2 1.045 3.3835

3 1.010 0.8894

4 1.0132 3.1807

5 1.016 0.9629

6 1.07 3.5473

7 1.0457 3.881

8 1.08 1.0308

9 1.035 3.3191

10 1.0299 3.2864

11 1.0461 3.3906

12 1.0533 3.4375

13 1.0466 3.3939

14 1.0193 3.2191

Load increase 0.6 MW

Bus no Initial voltage Present voltage

1 1.060 3.5531

2 1.045 3.4533

3 1.010 0.8465

4 1.0132 3.2463

5 1.016 0.9487

6 1.07 3.6205

7 1.0457 3.4579

8 1.08 1.0295

9 1.035 3.3875

10 1.0299 3.3542

11 1.0461 3.4606

12 1.0533 3.5084

13 1.0466 3.4639

14 1.0193 3.2855

Load increase 0.7 MW

Bus no Initial voltage Present voltage

1 1.060 3.6255

2 1.045 3.5217

3 1.010 0.7826

4 1.0132 3.3106

5 1.016 0.9258

6 1.07 3.6922

7 1.0457 3.5264

8 1.08 1.0253

9 1.035 3.4546

10 1.0299 3.4206

11 1.0461 3.5291

12 1.0533 3.5778

13 1.0466 3.5325

14 1.0193 3.3506

8.5 Voltage decrease due to reactive power imbalance data

From the load flow data’s we got the values for reactive power Q in MVar ratings. In

these criteria we just imbalanced the reactive power by some value and observe that 1 bus

is showing collapse due to change the Q. The data schemes are given below:

Bus no Reactive power Q Initial voltage Present voltage

1 -0.0573 1.060 1.7993

2 -0.0573 1.045 1.7738

3 -0.0573 1.010 1.7144

4 -0.0573 1.0132 1.7504

5 -0.0573 1.016 1.7256

6 -0.0573 1.07 1.8162

7 -0.0573 1.0457 1.0500

8 -0.0573 1.08 1.7653

9 -0.0573 1.035 1.7568

10 -0.0573 1.0299 1.7432

11 -0.0573 1.0461 1.7757

12 -0.0573 1.0533 1.7879

13 -0.0573 1.0466 1.7765

14 -0.0573 1.0193 1.7302

Bus no Reactive power Q Initial voltage Present voltage

1 0.0422 1.060 1.8583

2 0.0422 1.045 1.8320

3 0.0422 1.010 1.7706

4 0.0422 1.0132 1.8078

5 0.0422 1.016 1.7822

6 0.0422 1.07 1.8758

7 0.0422 1.0457 0.9500

8 0.0422 1.08 1.8323

9 0.0422 1.035 1.8144

10 0.0422 1.0299 1.8055

11 0.0422 1.0461 1.8393

12 0.0422 1.0533 1.8465

13 0.0422 1.0466 1.8348

14 0.0422 1.0193 1.7869

Bus no Reactive power Q Initial voltage Present voltage

1 0.126 1.060 1.9155

2 0.126 1.045 1.8883

3 0.126 1.010 1.8251

4 0.126 1.0132 1.8634

5 0.126 1.016 1.8370

6 0.126 1.07 1.9353

7 0.126 1.0457 0.8500

8 0.126 1.08 1.8793

9 0.126 1.035 1.8703

10 0.126 1.0299 1.8611

11 0.126 1.0461 1.8903

12 0.126 1.0533 1.9033

13 0.126 1.0466 1.8912

14 0.126 1.0193 1.8419

Bus no Reactive power Q Initial voltage Present voltage

1 0.1808 1.060 1.9517

2 0.1808 1.045 1.9241

3 0.1808 1.010 1.8597

4 0.1808 1.0132 1.8987

5 0.1808 1.016 1.8712

6 0.1808 1.07 1.9701

7 0.1808 1.0457 0.7500

8 0.1808 1.08 1.9701

9 0.1808 1.035 1.0957

10 0.1808 1.0299 1.8963

11 0.1808 1.0461 1.961

12 0.1808 1.0533 1.9394

13 0.1808 1.0466 1.9271

14 0.1808 1.0193 1.8768

Bus no Reactive power Q Initial voltage Present voltage

1 0.2273 1.060 1.9765

2 0.2273 1.045 1.9485

3 0.2273 1.010 1.8832

4 0.2273 1.0132 1.9228

5 0.2273 1.016 1.8955

6 0.2273 1.07 1.9951

7 0.2273 1.0457 0.4

8 0.2273 1.08 1.9192

9 0.2273 1.035 1.9248

10 0.2273 1.0299 1.92981.9203

11 0.2273 1.0461 1.9505

12 0.2273 1.0533 1.9540

13 0.2273 1.0466 1.9515

14 0.2273 1.0193 1.90006

Bus no Reactive power Q Initial voltage Present voltage

1 0.1332 1.060 1.9901

2 0.1332 1.045 1.9619

3 0.1332 1.010 1.8962

4 0.1332 1.0132 1.9360

5 0.1332 1.016 1.9360

6 0.1332 1.07 1.9086

7 0.1332 1.0457 0.200

8 0.1332 1.08 1.8525

9 0.1332 1.035 1.9525

10 0.1332 1.0299 1.9531

11 0.1332 1.0461 1.9535

12 0.1332 1.0533 1.9640

13 0.1332 1.0466 1.9775

14 0.1332 1.0193 1.9649

Bus no Reactive power Q Initial voltage Present voltage

1 0.0893 1.060 1.9982

2 0.0893 1.045 1.9699

3 0.0893 1.010 1.9039

4 0.0893 1.0132 1.9439

5 0.0893 1.016 1.9164

6 0.0893 1.07 2.0170

7 0.0893 1.0457 0.15

8 0.0893 1.08 1.9600

9 0.0893 1.035 1.9510

10 0.0893 1.0299 1.9414

11 0.0893 1.0461 1.9720

12 0.0893 1.0533 1.9855

13 0.0893 1.0466 1.9729

14 0.0893 1.0193 1.9214

8.6 Loads versus Voltage Curve As seen from the load variation and the voltage value we have some ratio aspects. Bus

no3, Bus no 5 , Bus no 8 shows decrease value voltage. If we plot the load versus voltage

curve then we can find that the voltage decrease with the superlative increase of the load.

Assign all those load value and voltage we got,

Bus no 8--------------------------

Bus no 5--------------------------; Bus no 3--------------------------

LOAD---------------------

Fig8.3: Load versus voltage curve

|V2|

Some comments regarding the PV curves:

• Each curve has a maximum load. This value is typically called the maximum

system load or the system load ability.

• If the load is increased beyond the load ability, the voltages will decline

uncontrollably.

• For a value of load below the load ability, there are two voltage solutions. The

upper one corresponds to one that can be reached in practice. The lower one is

correct mathematically, but I do not know of a way to reach these points in

practice.

• In the lagging or unity power factor condition, it is clear that the voltage

decreases as the load power increases until the load ability. In this case, the

voltage instability phenomena are detectable, i.e., operator will be aware that

voltages are declining before the load ability is exceeded.

• In the leading case, one observes that the voltage is flat, or perhaps even

increasing a little, until just before the load ability. Thus, in the leading

condition, voltage instability is not very detectable. The leading condition occurs

during high transfer conditions when the load is light or when the load is highly

compensated

8.7 Reactive power versus Load curve From the data which we analysis within the reactive power imbalance chart, we find that

one single bus is going to collapse very fast. It may call dynamic voltage collapse. Other

buses act well with this unbalancing reactive power value. If we plot that curve then we

can clearly depict how voltage can decrease with moderate reactive power shortage

Fig 8.4: reactive power versus load curve

Some comments regarding the QV Curves

• In practice, these curves may be drawn with a power flow program by

1. modeling at the target bus a synchronous condenser (a

generator with P=0) having very wide reactive limits

2. Setting |V| to a desired value

3. Solving the power flow.

4. Reading the Q of the generator.

5. Repeat 2-4 for a range of voltages.

• QV curves have one advantage over PV curves:

�They are easier to obtain if you only have a power flow (power flows will not solve

near or below the “nose” of PV curve but they will solve completely around the “nose”

of QV curves.)

Chapter 9

Voltage Collapse Mitigation 9.1 Power Capacitor Power capacitor is basically an electrical device used for improving power factor of the

electrical power system when the load is inductive. Most of the industries use induction

motors, which results Low power factor in the neighboring distribution line. This causes

big KVAR loss and wastage of energy. Therefore, Improvement of power factor is

considered to be one of the important measures of energy conservation. Use of power

capacitors improves the power factor of the line to which they are connected and thereby

improving power factor for neighboring industry also. In certain applications, capacitors

are used to store energy also, but with limited use [21]

Almost all the Electricity authorities have now made compulsory to install L.T. Power

Capacitors in the case of all industrial loads. This implies for every induction motor, LT

power capacitor is a must. Due to massive rural electrification and use of electric pumps

in irrigation and industrial purposes the motor load is increasing day by day. Hence,

demand for power capacitors is increasing.

At present, there are a number of units manufacturing LT power capacitors. However, as

the demand for this item is ever increasing, there is scope for more units to come up.

The watt loss or alternatively the power dissipated by a power capacitor is an important

parameter among many other parameters of a power capacitor. Right in the purchasing

stage, power capacitors of different makes are evaluated based upon the guaranteed

power loss claimed by the manufacturers. The reasons for attaching importance to the

power dissipated by the power capacitors can be classified as follows.[23]

1) Higher power loss means higher running costs hence longer payback period.

2) Higher power loss means increased temperature of power capacitor, which

reduces the operating life of capacitors.

3) Higher power loss means poor quality raw materials used and/or improper

manufacturing process employed.

Ideally a power capacitor is desired to have zero power loss. This ideal condition can be

achieved only if one uses zero resistance interconnecting leads and dielectric materials

like paper, oil etc with ideal characteristics. Practically, the materials used in manufacture

of power capacitors have non-ideal characteristics, like finite resistance of inter

connecting leads and non-ideal electrical characteristics of insulating materials. This

places a limit to which the power loss of power capacitors can be minimized. The most

important factor determining the power loss is the quality of manufacturing process, such

as prevention of ingress of moisture and other contaminations and proper formation of

electrodes by metal spraying.

The power loss experienced by power capacitors can be broadly classified, as arising due

to the following:

1) Power loss due to the introduction of discharge resistors.

2) Power loss due to resistance of inter- connecting wires.

3) Power loss due to internal fuses if employed.

4) Power loss due to dielectric properties of insulating material polypropylenes

Fig9.1: Industrial Power Capacitor

9.2 Different kind of Power capacitor

Shunt capacitors

Shunt capacitors installed in transmission and distribution networks will increase

transmission capability, reduce losses and improve the power factor. High voltage banks

for any voltage and power rating can be designed by series and parallel connection of

single-phase capa-citor units. Shunt capacitors are primarily used to improve the power

factor (cos ϕ) in the network. Inductive loads consume reactive power, e.g.

magnetization power for transformers, motors and reactors. The reactive power needed is

generated by capacitors. By applying capacitors adjacent to equipment consuming

reactive power, several advantages are obtained:

- Improved power factor

- Reduced transmission losses

- Increased transmission capability, since the load on the generators, transformers and

supply lines is reduced

- Improved voltage control

- Improved Power Quality.

Filter Capacitors

Many of the loads in a power network such as converters, rectifiers, welding equipment

and arc furnaces generate harmonics. Increased losses and damage to electronic

equipment are among the problems that may occur. Harmonic filters eliminate the

problem by reducing the harmonic content in the network and also improve the power

factor by generating reactive power

Modern electrical equipment generates harmonic currents which are transmitted to the

supply network. Most of the harmonics arise from electronically controlled equipment

such as converters, variable speed drives, static con-verters, welding equipment etc. but

also from arc furnaces. Among the problems that may occur due to excessive harmonic

currents are:

- Increased losses in motors, transformers and cables which may lead to overheating

- Overloading of capacitors

- Damage to or malfunction in electronic equipment

- Malfunction of receiver relays in ripple control system

- Interference with telephone circuits.

The most common method of solving this problem is to install harmonic filters. The filter

components are capacitors, reactors and sometimes resistors, of which the most important

part is the capacitor since it generates the reactive power.

Series Capacitors

Series capacitors in transmission systems increase power transfer capability and reduce

losses. Series capacitors are also installed in distribution systems, mainly to improve the

voltage stability.

Series capacitors are installed in transmission systems mainly in order to increase the

power transfer capability and to reduce losses by optimizing load distribution between

parallel transmission lines. Series capacitors are also installed in distribution systems.

Here, the main reason is to improve the voltage stability of the network.

Series compensation of a network positively affects the voltage and the reactive power

balance. When the load current passes through the capacitor, the voltage drop over the

capacitor varies in proportion to the current. The voltage drop is capacitive, i.e. it

compensates the inductive voltage drop, which also varies with the load current. The

result is an automatic stabilizing effect on the voltage in a network. Simultaneously,

series capacitors generate reactive power, the power factor in the network is improved,

whereby the line current and the line losses are reduced and the load capacity is

increased. The generated reactive power varies proportionally to the square of the load

current thus the reactive power is automatically regulated.

SVC Capacitors In static var compensation (SVC) thyristors are used for switching and control of

capacitors and reactors. Ever since the first installation in 1972, ABB Capacitors has been

the supplier of capacitor banks for ABB´s static var compen-sation.

In static var compensation, (SVC) thyristors are used for switching and control of

capacitors and reactors. Instant transient-free switching is obtained, as well as

continuously variable control of the reactive power.

Static var compensators in transmission systems increase the transmission capacity,

improve voltage control and stability, and damp power swings due to network faults or

tripping of heavy loads in interconnected systems. They are also used in distribution

systems and for difficult loads, e.g. arc furnaces, where asymmetrical fluctuations in the

current occur due to the instability of the consumption of the arc. Fluctuations in current

resulting in variations in the consumption of reactive power can be controlled and the

furnace is provided with more active power, thus increasing productivity.

Fig 9.2: SVC capacitors

HVDC Capacitors Power capacitors form an important part of an HVDC transmission system for harmonic

filtering as well as supply of reactive power. Capacitors with high quality and reliability

are essential to the overall performance of the system.

Power capacitors form an important part of an HVDC transmission system for filtering of

harmonic and supply of reactive power. Their high quality and reliability are essential to

the overall performance of the system. ABB therefore, uses self-protected capacitors in

HVDC applications. The self-protected capacitors can be either of a patented fuseless

design or equipped with internal fuses. The self-protected design offers advantages of

vital importance for all applications where high reliability is an absolute necessity, such

as in HVDC systems.

Single element failures do not affect the performance and protection coordination is

easier, enabling increased selectivity compared to other protection solutions. High quality

and reliability not only improve the electrical performance of the capacitors, also the

ability to resist severe climatic and seismic conditions is enhanced.

Fig9.3: HVDC Capacitors TSC

A thyristor switched capacitor (TSC) is a capacitor connected in series with two opposite

poled thyristors so that one thyristors conducts in each positive half cycle of the supply

frequency, while the other conducts in the corresponding negative half cycle. The current

flowing through the capacitor may be controlled by blocking the thyristors. To achieve

controlled reactive power a TSC is always configured in groups (ABB 1999a).

One disadvantage in utilising a TSC is the switching transients produced. Since a TSC

blocks current when the thyristors are blocked and allows current to flow when the

thyristors are gated, severe transients will occur if a TSC is switched off while the current

through it is not zero (Tyll 2004, p. 9). Similarly, to avoid generation of transients during

switch on, the thyristor must receive its firing pulse at a particular instant of the voltage

cycle. That is, transient free switching may be obtained when the voltage across a

capacitor is either at its positive peak or negative peak such that the current through the

capacitor is zero.

9.3 Introduction to SVC

A Static Var Compensator (SVC) consists of thyristor controlled reactive plant, either

capacitor banks, reactors or both, in combination with fixed reactive plant. This variable

static equipment provides continuously variable reactive power injection or absorption to

the network, facilitating dynamic Var balancing and so improves the efficiency,

controllability and quality of power systems. SVCs are commonly connected at

transmission substations via star-delta vector group step down transformers, and consist

of shunt connected inductors or capacitors, or more commonly a combination of the two,

where at least one is variable (ABB 1999a). Variable inductors take the form of thyristor

controlled reactors. Within an SVC, capacitors usually take the form of fixed or

mechanically switched banks which may also be subdivided into harmonic filtering

circuits tuned to the dominant frequencies. Thyristor switched capacitors are used when

fast or varied frequency capacitor switching is required (Janke 2002, p. 4). The main

purpose of an SVC is to regulate and control substation bus voltage to the desired level,

providing fast control of steady state and dynamic voltages and improving system

stability by reactive power control of dynamic loads (Janke 2002, p. 7). This will result in

increased power transfer capacity as SVCs present a variable impedance of controllable

power angle (ABB 1999b) and maintain a stable voltage profile along the transmission

line.

SVCs also provide dynamic compensation of variable, unbalanced loads. Damping of

system electro-mechanical oscillations between generators is enhanced by controlling the

power oscillations in transmission lines (ABB 1999b). Therefore SVCs enhance ‘First

Swing’ stability by maintaining system voltages during large disturbances, providing

active damping of power swings between weak interconnecting power systems

(Hingorani & Gyugyi 2000, p. 139). Dynamic, fast response reactive power

compensation following system contingencies such as network short circuits, line and

generator disconnections and load shedding is also established by SVCs.

The use of SVCs for power system compensation provide the added benefit of reducing

required insulation levels by providing fast overvoltage control and suppression of

voltage fluctuations caused by disturbing loads such as large thyristor drives and electric

arc furnaces. This provides improvement of the efficiency of industrial processes by

voltage stabilization and fast power factor correction (ABB 1999b).

There are two main SVC types in common use, and are defined by the manner in which

the reactive power is utilised for compensation. SVCs are primarily used for

compensation of transmission lines and for balancing of single-phase railway loads, that

is, voltage imbalance. Static Var Compensators for transmission applications are required

to:

• Regulate and control voltage at the point of connection;

• Enhance damping of system electro-mechanical oscillations, and;

• Provide fast reactive Var support following system contingencies.

Static Var Compensators for load balancing applications are required to:

• Convert single phase load into balanced three phase load;

• Reduce negative sequence components in system voltage, and;

• Regulate positive sequence components in system voltage.

SVCs utilized for transmission applications generally have symmetrical phase control and

the same swing range in all three phases. Compensators for load balancing are single

phase controlled and may have different swing ranges in different phase groups (ABB

1999b).

Fig 9.4: Single line diagram of a typical SVC

9.4 SVC control system structure and modes of operation The primary purpose of an SVC control system is to produce firing signals to thyristor

valves to phase angle control the reactor in such a manner that a continuous controllable

output of reactive power is obtained on a cycle by cycle basis produces the desired effect

on the transmission system (Janke 2002, p.5). When the thyristors in the thyristor valve

are fully conducting, the reactor consumes more than the reactive power generated in the

fixed capacitor bank and the net output from the compensator is inductive. When the

thyristors are blocked, there is no current in the reactor and the output from the

compensator will be all the reactive power generated in the capacitor bank. To fulfill its

primary purpose, a SVC control system may utilise input signals such as voltage,

summated current and synchronizing signals. Output signals would include the firing

signals to the thyristor valves. A simplified view of SVC control system function is

illustrated in Figure 9.5

Fig 9.5: SVC control system structure An SVC control system consists of:

• A measurement and comparison system;

• Automatic voltage regulator (AVR), and

• A calculated susceptance output, BREF .

Fig 9.6: Basic SVC control system composition

SVC control systems may have both a manual and an automatic operating mode. Manual

operating modes are often referred to as BREF control and the automatic mode as VREF

control. In BREF control mode, the SVC operates as if it were static reactive plant

providing fixed susceptance to the power system.

When selected to VREF control mode, the SVC attempts to maintain target voltage and

the SVC susceptance output will vary according to the system voltage. If the measured

power system voltage was greater than the target, the control system response is such as

to create an inductive reactance to decrease system voltage. For measured power system

voltages less than the target value, control system response is intended to present a

capacitive reactance to the power system and thus raise voltage levels

9.5 Simulation and test result using Capacitor on Collapse buses

0 0.2 0.4 0.6 0.8 1 1.2 1.40

0.2

0.4

0.6

0.8

1

1.2

1.4

load-P,kw

vola

tge-v

,V

collapse mitigation using capacitor bank in bus 8

Fig 9.7: bus no 8 characteristics From the figure 9.7 we can observe that at normal condition when bus is going to

collapse , if we use SVC on the bus at that time it can prevent collapse with very fast

recovery of reactive power. In that analysis we use a 10 MVar value SVC for IEEE 14

bus test system. We also use the SVC for all 3 collapse bus. Rest of the bus simulation

figure is given below:

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.2

0.4

0.6

0.8

1

1.2

1.4

load-P,kw

vo

latg

e-v

,V

collapse mitigation using capacitor bank in bus 5

Fig 9.8: bus no 5 characteristics using SVC From fig 9.8 it is clearly shown that bus 5 collapse problem can be eliminated with the

use of the SVC.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

0.2

0.4

0.6

0.8

1

1.2

1.4

load-P,kw

vola

tge-v

,V

collapse mitigation using capacitor bank in bus 3

Fig 9.9: bus no 3 characteristics using SVC

-0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.250.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

voltage,V

reactive power-Q,VAR

collapse mitigation using capacitor bank in bus 7

Fig9.10: bus no7 characteristics with the use of SVC

9.6 Some other Mitigation Scheme Reactive drop Control & Load compensation These are addressed together here because they are closely related, but have opposite

effects. A control voltage that is proportional to the reactive power generated by the

machine is applied to the sensed terminal voltage being supplied to the voltage regulator.

With reactive droop control, this control voltage is added to the sensed terminal voltage

causing the regulator to sense too high a feedback voltage, resulting in a decrease in

excitation. With load compensation, this control voltage is subtracted from the sensed

terminal voltage causing the regulator to sense too low a feedback voltage, resulting in an

increase in excitation. With reactive droop control, the end result is a sharing of the

voltage regulation of a bus to which multiple generators are connected in parallel.

Without droop, the voltage regulators would be unstable as more than one regulator

would attempt to control the same voltage. The machines would just circulate large

quantities of Vars, and voltage regulation would be poor. Droop is critical for generators

bussed together, but it needs to be set carefully so that adequate voltage levels are

maintained. That is, too much droop will result in voltage levels unacceptably below

nominal. With load compensation, the end result is better regulation of a point in the

system somewhat remote from the terminals of the machine. Without load compensation,

the controlled point is the point where the terminal voltage is sensed - the point where the

generator vts tap into the isolated phase bus. Load compensation moves the controlled

point out closer to the main power transformer's high voltage terminals by compensating

for a portion of the voltage drop that occurs across the transformer due to the loading of

the generator. This must be set carefully to avoid wide reactive power swings on the

machine that occur if it attempts to control voltage at a point too far away in the system,

electrically speaking. A plant with more than one generator can be made to control the

voltage on the transmission system some distance from the plant by the use of joint Var

control (JVC) equipment. JVC allows several generators to control the voltage at a single

point without reactive power swings which would result from independent voltage

control action on each of the generators. This equipment ensures that all generators take

an equal share of reactive power as they attempt to control the voltage at a common

point. Compensation for at least part of the reactive drop in a generator step up

transformer is one way of allowing generators to more directly control system voltage. In

addition to the stability concerns, the voltage at the generator terminals must also be

controlled to within acceptable limits. Given the wide variation in generator reactive

power capability, it may be necessary to depend on other controllers such as the volts/Hz

limiter or MEL for additional control.

VAR regulator

The Var limiter acts to limit the Var loading of a generator if the output reaches its

threshold. Otherwise, the regulator is free to adjust excitation as necessary to control

voltage without regard to Var swings. The Var regulator is different from the limiter. This

control feature, rather than controlling the voltage to a set point, controls the Var output

of the machine to a set point. Var regulation is wellsuited to a system that has a steady,

baseload need for Var support. Both of these devices have application with smaller

machines ("small" relative to the connected system) because of their inability to

significantly alter the transmission bus voltage, regardless of their Var loading. However,

it should be recognized that when these limiters are in operation, the generator will not

act to help support system voltage during emergencies.

Power factor limiter

The power factor limiter acts to keep the power factor of a given machine within

specified limits while on voltage control. This device is especially useful in situations

where economic penalties are imposed for operating with a power factor outside of a

published acceptable range. The power factor regulator, like the Var regulator, controls to

a specific power factor without regard for the voltage. This can be troublesome for the

bus voltage as the excitation will vary, and hence the voltage will vary, with changes in

generator watt loading. Again, this is more typically used with smaller generators or with

large synchronous motors seeking to operate at or near unity power factor (for economic

or other reasons). The increasing penetration of non utility generators in power systems

results in increasing effect of their excitation control systems on power system voltage

stability. Care is required to ensure their reactive power capability is not incorrectly

assumed to be dynamic, when in fact they may be operating under a power factor

controller or Var limiter that restricts their reactive output to much less than the units are

capable of producing.

Power system stabilizer

“Modern generating units equipped with high gain voltage regulators enhance transient

stability (the ability to recover from large disturbances), but tend to detract from steady-

state stability (the ability to recover from small disturbances about the steady-state

operating condition). Power System Stabilizers (PSS) improve steady-state stability by

providing damping of power system modes of oscillation via modulation of generator

excitation." So described, the PSS is a device that reduces low frequency oscillations of a

generator rotor (typically in the range of 0.1 to 2.5 Hz). Regardless of how it measures

the speed changes (electrical frequency or mechanical speed), the PSS is tuned to output

a control voltage that is in phase with the speed changes that acts to increase excitation if

the speed change is in the positive (speed-increasing) direction and decrease excitation if

the speed change is in the negative (speed-decreasing) direction. The increased excitation

tightens the rotor's coupling with the power system, providing a retarding torque that

tends to slow the rotor, bringing it back to nominal speed. Decreased excitation loosens

the rotor's coupling with the power system, providing an accelerating torque that tends to

let the rotor accelerate back up to nominal speed. The purpose of the PSS is to minimize

generator "hunting" and the attendant low frequency power surges, thereby stabilizing

system voltage and enhancing system stability. As larger machines have far greater

impact on the system and on each other in this regard, PSS's are most effective on such

large machines. PSS’s are presently being fitted on many existing larger machines, and

most new machines which can significantly impact low frequency oscillations. PSS's

must be correctly set with regard to their gain and phase lead parameters to avoid

exacerbating the oscillation problem. There are no protective elements that the PSS must

Coordinate with.

Generator protection relays

It is important that generator and auxiliary protection relays coordinate with excitation

control functions. Lack of such coordination has often been a factor in voltage collapse or

near collapse situations. Some critical protective relays are loss-of-field, volts/Hz, rotor

overload, excitation system overload, and auxiliary under voltage protection. The loss-of-

field relay must coordinate with the MEL on a dynamic basis as well as on a steady state

basis. The time delay in which an MEL can act to limit under excitation may not be stated

in exciter application guides. Under transient conditions it is possible for the operating

point of a generator to suddenly enter a region beyond the MEL or loss of field protection

characteristics. If the time delay of the loss of field relay is too short, or the MEL takes

too long to operate, miscoordination and unnecessary loss of the generator can occur. The

lack of coordination can easily be missed if the exciter gain or feedback settings are

adjusted after commissioning without subsequent check of the speed of operation of the

control function. Regular exercising of the generator to its MEL control point will help

minimize the risk of miscoordination. Rotor and exciter overload protections must

coordinate with maximum excitation limiters, again on a dynamic basis as well as on a

steady state basis. Since overload protection time delays are often somewhat longer than

loss-offield protection delays, the speed of response of the maximum excitation control is

not of as great a cause of concern as that of the MEL. However, the possibility for

miscoordination is still present. Exciter overcurrent protection settings may be applied

with more concern about short circuit sensitivity than with rotor overload capability.

Further, if such protection is provided by electromechanical relays, their accuracy around

the pickup current level may not be as good as the accuracy of the overexcitation limiter.

Exercising of the generator at its maximum excitation limit is the best way to ensure

coordination is maintained. Dynamic coordination of the volts/Hz protection with the

volts/Hz controller is relatively easily achieved, because their time/flux characteristics are

both well defined. A point of concern can arise when the volts/Hz protection is provided

by one or two definite time relays set at specific levels of volts/Hz. It may be difficult to

coordinate the definite time characteristics with inverse time characteristics of the control

device. It is of course also important to coordinate the volts/Hz protection with the

maximum voltage regulator control voltage. The maximum voltage regulator setting may

be very close to the maximum rated continuous operating voltage, leaving little room for

the volts/Hz protection pick up point to fit between the two limits. Auxiliary equipment

may be protected by undervoltage relays to ensure the generator is shut down safely

before any essential auxiliary equipment stalls or becomes disconnected due to low

voltage. It is possible that low terminal voltage could impose a limit in the underexcited

region that the MEL must coordinate with. Since the undervoltage protection would

normally have a significant time delay, dynamic coordination with the MEL may not be

as much of a concern as static coordination. In spite of the difficulties in operating

generators at reactive power limits, regular testing of the coordination of protection and

control devices at those limits remains the best way of ensuring important reactive power

reserves are available when required during system emergencies.

System Backup relays

System backup relays are generally of three types: phase distance, phase overcurrent, and

ground overcurrent. Of these, the ground overcurrent is not affected by excitation levels,

so it will not be addressed here. The phase distance and phase overcurrent relays,

however, can be affected by excitation. In the case of the phase distance relay, depending

upon its reach, the combination of low system voltage (due to a collapse) and high load

(due to high Var output in response to the collapsing voltage) could be interpreted as a

low magnitude three phase fault resulting in an undesirable trip. This is a problem

especially if the generator is connected to a stiff system because of the generator's relative

inability to control the system voltage regardless of its excitation level. In the case of the

phase overcurrent relays, they are typically set with a pickup below rated load, relying on

healthy voltage as a restraint. With the same scenario as in the case above, if the voltage

falls below the set-point, the relay could operate on load, again causing an undesirable

trip. As with the distance relay, this is more likely to occur when the generator is

connected to a stiff system. It should be noted that undesirable trips could occur under

low excitation conditions, as well, because low excitation translates to low terminal

voltage, especially when the generator is connected to a weak system. However, the

combination of low voltage due to under excitation, and heavy load is unlikely, so this is

seldom a problem. The probability of undesirable trips of backup protection systems is

reduced by detailed application studies when applying such protection and when

calculating settings. System simulations for multiple or low probability contingencies

may be required to ensure the backup devices are secure under such conditions. If time

delays of backup relays are short, dynamic system simulations may be required as well as

static simulations. If reliable backup transmission protection exists at the switching

substation, backup phase distance relays may not be needed. Consideration could be

given to either removingsuch relays, or reducing their reach such that undesirable

trippings under low voltage conditions are highly unlikely.

Switched capacitance

Manual switching, or conventional voltage control devices are often adequate for

switching capacitors in the longer time frame. Capacitors are considered to be static

reactive power sources when applied for long term voltage control. Static capacitors may

be switched seasonally, weekly, or daily for this type of application, where the switching

devices may be circuit breakers or circuit switchers. The design of the capacitor

installation must consider the possible speed and frequency of switching, as well as the

voltage support requirements. Very frequent switching would put a significant amount of

wear on the switching device. When the time frame of the voltage stability phenomena

approaches the transient region, automatic switching is almost always required.

Capacitors are often switched by voltage relays with time delays. To achieve the higher

switching speed, additional controls may be required to prevent excessive switching and

wear on the switching device. The voltage relays used for switching may not be the

conventional voltage control relays. They may need higher accuracy, or different

techniques, similar to those used for undervoltage load shedding. For instance, the

requirement for switching may need the three phase voltages to be inside a certain

window, or the requirement may be controlled by the status of other dynamic reactive

power sources such as nearby synchronous condensers, or static Var compensators. BC

Hydro uses a PLC to coordinate the measurement of the output of synchronous

condensers (rated 2x100 Mvar and 2x50 Mvar) and the switching of 2x50 Mvar capacitor

banks. Figure IV-1 shows the simplified logic diagram of the PLC used to control the

capacitors. The capacitor banks are switched if the total output exceeds 60% of the rating

of units in service with automatic voltage regulators. The PLC is used to calculate the

output from all units. If the output is high, and system voltage is not too high, one

capacitor bank will be switched on. If the output is very high, and the voltage is not too

high, both capacitors will be switched on. The same device automatically switches the

capacitors off if the output of the synchronous condensers goes low, and if the system

voltage is not also low. By this means, the utility can control the system such that the

synchronous condenser is available for dynamic supply of reactive power by keeping the

condenser output low under normal steady state conditions. This is an example of using

relatively slow speed switching of a capacitor to increase reactive reserve earlier than

required for an emergency situation. Early switching of static sources means more

dynamic power is available for quick support during emergencies. To minimize wear and

tear on the switching equipment, the automatic control is sometimes unidirectional. The

reactive equipment is automatically switched on or off, to quickly regulate the voltage

excursion, and operator control is used to restore normal conditions when the disturbance

is over. This is a major difference between special schemes and normal voltage control

devices which switch reactive equipment after very long time delays.

Automatic reclosing

Fast reclosure of high voltage transmission is used as the first attempt to restore lost

transmission as quickly as possible to minimize exposure to excessive and unacceptable

voltage declines and to enhance the stability of the system. Ontario Hydro has

implemented a scheme using faster than normal automatic reclosure to prevent voltage

collapse in the event of a transmission line outage coincident with outages on other parts

of the transmission system. The reclosure attempt must occur within 1.5 seconds after the

initial loss of the transmission line. This time frame is dictated by the effectiveness of

subsequent load shedding should the reclosure not be successful. A reclosure time of

1.175 seconds can be achieved with the slowest breakers in the region (closing time 0.225

s). The total reclosure time includes 0.5 s dead time before reclosing the energizing

breaker (lead terminal) and 0.1 s delay for closing the follow terminal on restoration of

potential from the lead terminal. If reclosure is unsuccessful, and the load is high, load

shedding is required to ensure an acceptable voltage profile. Load shedding must be

initiated as soon as possible after unsuccessful reclose attempt if the voltage is lower than

85% of normal levels. A total of 504 MW distributed at nine different stations is available

for shedding. Each block of load can be armed by operator action and will be tripped

when the local station voltage drops below a preset value for a preset time period. The

scheme is based on monitoring the transmission voltage with undervoltage relays on

either side of the main or backup potential sources (automatic transfer for loss of the

main source). The undervoltage relays are duplicated, and both relays, set to 85% of the

normal operating voltage, must operate to shed load. The load is shed if the undervoltage

condition persists for more than 1.5 seconds. Load shedding is blocked if both the main

and alternate sources are lost (as detected by another undervoltage relay). A total of 36

capacitor banks (both transmission and distribution banks) in 17 transformer stations in

the region are equipped with automatic switching features that are voltage and time

dependent. The capacitors maintain the voltage levels at or above the minimum

acceptable level of about 90% of nominal. A predetermined sequence of capacitor

switching can occur up to 8 seconds after the initial loss of transmission. The effect of

capacitor switching following load shedding is that of fine tuning the voltage levels to

within the normal band.

Distribution voltage control

Electric utilities utilize load tapchangers (LTC) to maintain customer voltage levels as the

system conditions change. Typically, as load increases, the LTC will act to raise the tap

position in order to maintain the voltage level. The LTC control relay will be set to

operate in one of two modes - bus voltage regulation or load center voltage regulation

using the line drop compensator. Load Center voltage regulation requires a line drop

compensator to regulate the voltage at the load center. Transformers at distribution

substations are more likely to use load center voltage regulation than those at

transmission substations. Therefore, it is important to know the mode of LTC control

operation when modeling the effect of the tapchanging transformer operation during

voltage collapse. During a period of voltage collapse, the LTC control relays will detect a

low voltage and begin timing to raise the tap position of the transformer. When the

voltage collapse occurs slowly, the controls will time out and begin to raise the

transformer tap position. Assuming no change in the load on the transformer during this

period, the LTC can often be considered a constant power load (i.e., a and b are near

zero) as long as the tapchanger can maintain a constant load voltage. Since the primary

voltage level drops, the current flow in the transmission system is increased to maintain

the load power. This increasing current flow will further reduce the transmission system

voltage, making the voltage collapse more severe. In some cases, tap changers can also

have a beneficial effect. Consider for instance, a case where a transformer is supplying

predominantly motor load with power factor correction capacitors. The LTC keeps the

supply voltage high and hence does not affect the real power consumption (which is

relatively independent of voltage), and also maximizes the reactive support from the

power factor correction capacitors. Due to this regulating Effect the LTC is an important

part of voltage collapse scenario.

Power buffering Active dynamic buffers are a method for mitigating the effects of constant-power loads in

Weak power systems. These devices act as an interface that decouples the dynamics of

the load from the system. Even though power buffers and uninterruptible power supplies

(UPS) are seemingly similar, and both deal with power quality, the two classifications of

devices have very different objectives. While a UPS supplies power to an end load during

an outage, little to no consideration is given to the state of the power system. In contrast,

a power buffer’s objective is to offer beneficial dynamic characteristics that help stabilize

a marginal system, while still supplying the end load with power. Because of its concern

only for the load and not the system, a UPS typically contains a much larger energy

storage device than a buffer, and consequently can supply the load for a longer period.

An interpretation of buffer operation during a dynamic event is seen in Figure. During a

transient, the buffer exhibits desirable dynamic characteristics, such as constant current or

constant impedance while supplying the load with constant power. The selection of the

dynamic characteristics of the buffer is dependent on the nature of the power system and

the likely faults that are to be buffered.

Fig 9.11: Power buffer function illustration

A power buffer presents dynamically controlled impedance at its input, and supplies an

independent load at its output. This broad definition can manifest as a wide range of

physical topologies, depending on the nature of the system and the desired response. The

circuit in Figure 22 is an example of a three-phase, six-pulse active rectifier that can be

used as a dynamic buffer. With this buffer topology, the six-pulse silicon controlled

rectifier (SCR) bridge operates at a nominal phase angle during normal operation. When

a fault occurs, the buffer senses the voltage sag and then controls the phase angle of the

rectifier to decrease Vrec and draw less power from the system, while energy from dc-link

capacitor C is used to supply the load. When the fault clears, the control slowly raises Vrec

back to its nominal value, recharging C. Another example of a dynamic power buffer

topology is depicted in Figure 9.13. This circuit operates in a fashion similar to Figure

9.12, with the exception that the power from each phase can be controlled independently.

In the case of a severe single-phase fault, this circuit can limit power draw from the

faulted phase while extracting additional power from the other two phases until the fault

clears. Depending on the line impedance of the no faulted phases, the buffer may not

need to enter an impedance control scheme at all. However, an obvious disadvantage of

this topology is the added complexity.

Fig 9.12: Rectifier buffer circuit

Fig 9.13: Three boost buffer circuit

On Load Tap Changer s(OLTC)

OLTC tap blocking can limit the restoration of load during voltage decay and thus

provide some relief to the bulk system. However, it is only effective where load does in

fact drop measurably with voltage. It is not useful on most industrial loads where it can

reduce the output of shunt capacitors in industrial plants while having little impact on the

plant active power demand. Even where OLTC can curtail load by reducing voltage on

customers, the benefit is largely only a delay in the restoration of load since some

customer load adjusts to the the low voltage and returns to its original demand over a 15

to 20 minute period regardless of the applied voltage.

Dynamic Vars (D-VAR)

� Fully integrated STATCOM with proprietary 3 times continous rating overload

capabilities.

� Instantenously injects precise amounts of reactive power into network.

� Optional real power with SMES energy storage.

Fig 9.14 : D-VAR by American superconductor

Fig 9.16: D-VAR installation Super var

Super VAR is a synchronous condenser that employs HTS superconductor field winding

This allows it to be much more efficient, compact and reliable. As compared to

conventional rotating machine.

Fig 9.17: Super Var system

Chapter 10

Conclusion The power system can be divided into three sub-systems: The generating part, the

transmission part and, the distribution part with the load demand. Voltage stability

problems can arise in any of these sub-systems and can be studied separately or in

combination. In this dissertation, the following aspects have been studied:

The generation part

Field and armarture current limiters have a major impact on the generator capability. The

transition between different control modes of the generator seems to be non-reversible

from a system point of view if no radical control actions are taken.

The distribution part including the load demand

Load characteristics of asynchronous motors and dynamic load recovery due to electrical

heating appliances may set the voltage stability limit for the system. The load

characteristics are very important for the system behaviour. One significant boundary of

this characteristic is a load behaving as a constant current load. For loads responding as

an impedance, a voltage drop will unload the system whereas the opposite is valid for a

constant power load. Note the strong coupling between dynamic loads and OLTCs. If the

time constants are in the same order, an overshoot in power demand can arise.

Interaction between the generation and the transmission system

In case of field current limitation, the generator “synchronous reactance” is included into

the transmission system. This alone can cause a collapse, force load voltages to a low

value due to the increased reactance of the system. The field current limiter may force the

working. point to the lower side of the U-P-curve which is an unstable operating point for

certain loads.

Interaction between the generation and the distribution system

The armarture current limiter causes the generator to be very sensitive to the voltage

characteristics of the load. If the load increases its current demand for a decreasing

voltage, a severe voltage stability problem occurs. The on-load tap changer may also play

an important role causing high currents in the generator.

Interaction between the transmission system and the distribution system

Transformers with on-load tap changers are usually located between the transmission

system and the distribution system. The system response of a tap changing step is not

obvious and depends on the load behaviors and the strength of the transmission system. A

whole range of different responses is possible when OLTCs and loads interact.

From the mitigation analaysis and statistical results and better acting properties of

collapse technique with the load flow analysis I do believe that , we have to do below

steps for collapse mitigation:

Anticipate the problem by using load flow and stability studies to identify system

conditions that may lead to voltage instability. Conditions that lead to voltage collapse

may be caused or aggravated by heavy power transfer between regions; so coordination

among the affected regions is essential to develop the appropriate mitigative action.

Results of these studies can be used to develop special operating procedures to minimize

the probability of collapse. Where studies show that operating procedures alone are not

sufficient to ensure voltage stability, special control and protection schemes can be

applied to mitigate the conditions leading to collapse.

Use appropriate diagnostic techniques to provide early warning of the onset of voltage

Stability problems. Since voltage collapse is a wide area problem, these techniques often

need communications assistance. The communications are not necessarily high speed, but

must be reliable. The techniques involve measurement of relevant factors such as voltage

magnitude, status and output of sources of reactive power, rate of change of reactive

power generation with respect to load, and magnitudes of real and reactive power flows.

Provide temporary reactive support until operator action can stabilize system. This may

require taking advantage of temporary overload capabilities of generators and

synchronous condensers in the affected area. To ensure full capability of all sources are

available, they should be operated from time to time at maximum and minimum reactive

outputs to ensure all protective devices coordinate properly with control devices.

Provide permanent reactive support. Since it is deficiency of reactive power sources that

causes voltage to drop, provision of these sources are an effective means of maintaining

voltages. Switched capacitors are a popular means of providing such support, but care

must be taken to avoid depending entirely on fixed support such as is provided by

capacitors. Fixed sources do not provide the control of system voltage which is critical in

near collapse situations.

Provide an appropriate mix of static and dynamic sources of reactive support.

Although dynamic sources of reactive power are much more expensive than fixed

sources, they do have the advantage of being able to control voltages. Some relatively

economical means of providing dynamic support include use of LDC so that generators

regulate voltages some distance from their terminals. Conversion of uneconomic

Generators to synchronous condensers and fast switching of capacitors are sometimes

options for increasing the availability of sources of dynamic reactive support. Where

possible, dynamic sources of reactive power may be operated as near to mid output as

possible to maximize dynamic reactive reserve. Manual or automatic switching of static

sources (or sinks) of reactive power is a better means of keeping dynamic sources near

the middle of their operating range than adjusting their reference voltage.

Provide temporary load relief by blocking tap changers or reducing distribution supply

voltage. The amount of load relief provided by these means is determined entirely by the

static and dynamic characteristics of the real and reactive components of the load with

respect to voltage level. These characteristics vary widely, and may need to be

determined by test. The reduction in reactive power demand with voltage is often larger

than the reduction in real power demand. It must be ensured that voltage quality is not

degraded so much that the alternative of load shedding would not have been preferable to

the customer.

Chapter 11

Future Work

There is an international tendency to increase the power transfer limits in the networks

and to improve the efficiency of existing power plants. The reasons are on the one hand

the huge economical costs for new investments and the growing environmental concern

and on the other hand the considerable economic benefits to be gained. This will raise the

requirements for more sophisticated computer programs and model and there will be

ongoing efforts to maintain and to improve the reliability in the power systems. Therefore

the need to improve planning and operation in power systems, underlines the importance

of future work in the voltage stability field.

11.1 Load modeling

Today power system operators have access to a large number of dynamic models which

quite well can illustrate a voltage collapse in a computer environment. But there is one

important exception regarding certainty in dynamic load models. The reliability in these

models is still too low, particularly as the dynamic load behaviour seems to be one of the

major reasons for voltage collapse in power systems. It is therefore necessary to improve

our knowledge of the load dynamics considered from the transmission level. The existing

load models are more based on measurements and theoretical analyses of individual load

devices than on field measurements, and the few measurements that have been made are

mainly done on the distribution level. This is the reason why the dynamic voltage

dependency of the aggregated load representation is hard to define. The dynamic load

models that exist are certainly general enough, but all of them contain key parameters

which have not been verified. The lack of field measurements on higher voltage levels

and the economical benefits of using more accurate load models implies that dynamic

load models is an important issue for further research and development.

11.2 Improvements of generating capability

When studying current limitation in large generators it is evident that current limiting

causes a strong reduction of the voltage stability mar gin in the area near the generator.

This reduction in voltage stability or reactive power generation is a contributive factor to

voltage collapse in power systems. Since both the armature and the field current limiters

are intended to protect the generator from exceeding its thermal limit, it is necessary to

analyse the possibility to use the thermal capacity in a more efficient way. A strategy

could be to use the remaining thermal capacity in the generator windings in order to

provide a stressed network with extra reactive power. It might be feasible to exceed the

thermal limits over a period of minutes in order to start gas turbines, but this approach

needs an analysis of the pay-off between an acceptable ageing and the consequences of a

collapse. A better utilization of the thermal capability of existing generators might be an

economical way to improve voltage stability in a power system.

11.3 Adaptive relay techniques

Adaptive relays can change settings as system conditions change. To cope with voltage

problems, the shedding of load is based on voltage measurements, and is initiated when

the local voltage falls below a certain setting. The setting, location, and amount of the

load to be shed should be changed to adapt the load shedding scheme to the varying

system conditions. The protection against voltage instability can be designed as a part of

the hierarchical structure. Decentralized actions are performed at substations with local

measurements which may be modified by measurements or decisions from a wider area,

using a communications system. Better decisions can be made at a higher hierarchical

level, but larger numbers of relevant system measurements are required.

11.4 Pharos Measurements

Phasor measurements are useful to speed up state estimation to determine collapse in real

time fast enough for automatic action. Instead of using a relatively slow communication

with conventional SCADA, one can envision using faster communication links with

phasor measurement units which do not require much post-processing of measurement

data, and could possibly be used for real-time control of some transients in power

networks. Phasor measurement units, and similar high-speed measurement devices are a

predecessor of a new, faster, and more sophisticated generation of data acquisition

devices for system-wide monitoring in near real-time conditions for a variety of

disturbances, including voltage instabilities.

11.5 User Definable Relays

User definable relays may be useful for special applications where unique measurements

are required. For instance, they may be set for specific rate of change of voltage, if rate or

shape of voltage collapse can be defined. User configured relays may discriminate

between collapse due to instability and depression due to fault or motor starting. They

may also be used in measurement of reactive power being used for voltage support, as a

percentage of maximum available reactive power.

References

1. voltage collapse in power system_theinfluence of generator current limiter, on

load tap changers and load dynamics.--------stefan johanson & Fredrik siogren,

SWEDEN.

2. Cause and effets of voltage collapse case studies with dynamic solutions—IEEE

3. Testing a differential algebric equation solver in long term voltage stability

simulation.-----jose.o.pessanha, 7th july 2005

4. Detection of dynamic voltage collapse----Garng & Nirmal kumar (IEEE)

5. Sensitivity of loading margin to voltage collapse with respect to arbitary

parameters-----scott greene, Ian Doboson .USA, IEEE,vol12,feb-1997

6. Static and dynamic assessment of voltage stability---N biglari , Iran

7. Measurement based voltage monitoring power system----liang zaho, USA

8. Static voltage stability study with matlab symbolic and optimization---IEEE

9. The intricacies of voltage instability and collapse----Harrison K Clark

10. voltage collapse in power system.-----suresh kumar

11. Matlab Fundamentals

12. A power flow in matlab------L. alvardo

13. time domain simulation investigates voltage collapse---James W Feltez

14. Modeling and simulation of IEEE14 bus system with controller.—IEEE

15. Simulation of tanjanian network under mathlab environment.-----ISSSN v25

16. Power flow with load uncertainty.

17. Power quality----pierre kreidi

18. Intelligent load shedding----CRISP journal

19. Maintain electricity contracts in streesed powere system---Victor, germany

20. Voltage collapse mitigation -----IEEE

21. Power capacitors-----ABB, LUDVIKA, SWEDEN

22. Mitigation of voltage collapse through active dynamic buffer---W.W Weaver

23. Voltage collapse avoidance in power system----M. Alamir

24. Applications of DVAR------Amercan super conductors

Appendix A

% Returns Initial Bus datas of the system...

function busdt = busdatas(num)

% Type....

% 1 - Slack Bus..

% 2 - PV Bus..

% 3 - PQ Bus..

% |Bus | Type | Vsp | theta | PGi | QGi | PLi | QLi | Qmin | Qmax |

busdat14 = [1 1 1.060 0 0 0 0 0 0 0;

2 2 1.045 0 40 42.4 21.7 12.7 -40 50;

3 2 1.010 0 0 23.4 94.2 19.0 0 40;

4 3 1.0 0 0 0 47.8 -3.9 0 0;

5 3 1.0 0 0 0 7.6 1.6 0 0;

6 2 1.070 0 0 12.2 11.2 7.5 -6 24;

7 3 1.0 0 0 0 0.0 0.0 0 0;

8 2 1.090 0 0 17.4 0.0 0.0 -6 24;

9 3 1.0 0 0 0 29.5 16.6 0 0;

10 3 1.0 0 0 0 9.0 5.8 0 0;

11 3 1.0 0 0 0 3.5 1.8 0 0;

12 3 1.0 0 0 0 6.1 1.6 0 0;

13 3 1.0 0 0 0 13.5 5.8 0 0;

14 3 1.0 0 0 0 14.9 5.0 0 0;];

% |Bus | Type | Vsp | theta | PGi | QGi | PLi | QLi | Qmin | Qmax |

busdat30 = [1 1 1.06 0 0 0 0 0 0 0;

2 2 1.043 0 40 50.0 21.7 12.7 -40 50;

3 3 1.0 0 0 0 2.4 1.2 0 0;

4 3 1.06 0 0 0 7.6 1.6 0 0;

5 2 1.01 0 0 37.0 94.2 19.0 -40 40;

6 3 1.0 0 0 0 0.0 0.0 0 0;

7 3 1.0 0 0 0 22.8 10.9 0 0;

8 2 1.01 0 0 37.3 30.0 30.0 -10 40;

9 3 1.0 0 0 0 0.0 0.0 0 0;

10 3 1.0 0 0 19.0 5.8 2.0 0 0;

11 2 1.082 0 0 16.2 0.0 0.0 -6 24;

12 3 1.0 0 0 0 11.2 7.5 0 0;

13 2 1.071 0 0 10.6 0.0 0.0 -6 24;

14 3 1.0 0 0 0 6.2 1.6 0 0;

15 3 1.0 0 0 0 8.2 2.5 0 0;

16 3 1.0 0 0 0 3.5 1.8 0 0;

17 3 1.0 0 0 0 9.0 5.8 0 0;

18 3 1.0 0 0 0 3.2 0.9 0 0;

19 3 1.0 0 0 0 9.5 3.4 0 0;

20 3 1.0 0 0 0 2.2 0.7 0 0;

21 3 1.0 0 0 0 17.5 11.2 0 0;

22 3 1.0 0 0 0 0.0 0.0 0 0;

23 3 1.0 0 0 0 3.2 1.6 0 0;

24 3 1.0 0 0 4.3 8.7 6.7 0 0;

25 3 1.0 0 0 0 0.0 0.0 0 0;

26 3 1.0 0 0 0 3.5 2.3 0 0;

27 3 1.0 0 0 0 0.0 0.0 0 0;

28 3 1.0 0 0 0 0.0 0.0 0 0;

29 3 1.0 0 0 0 2.4 0.9 0 0;

30 3 1.0 0 0 0 10.6 1.9 0 0 ];

% |Bus | Type | Vsp | theta | PGi | QGi | PLi | QLi | Qmin | Qmax |

busdat57 = [1 1 1.040 0 0.0 0.0 0.0 0.0 0.0 0.0;

2 2 1.010 0 3.0 88.0 0.0 -0.8 50.0 -17.0;

3 2 0.985 0 41.0 21.0 40.0 -1.0 60.0 -10.0;

4 3 1.000 0 0.0 0.0 0.0 0.0 0.0 0.0;

5 3 1.000 0 13.0 4.0 0.0 0.0 0.0 0.0;

6 2 0.980 0 75.0 2.0 0.0 0.8 25.0 -8.0;

7 3 1.000 0 0.0 0.0 0.0 0.0 0.0 0.0;

8 2 1.005 0 150.0 22.0 450.0 62.1 200.0 -140.0;

9 2 0.980 0 121.0 26.0 0.0 2.2 9.0 -3.0;

10 3 1.000 0 5.0 2.0 0.0 0.0 0.0 0.0;

11 3 1.000 0 0.0 0.0 0.0 0.0 0.0 0.0;

12 2 1.015 0 377.0 24.0 310.0 128.5 155.0 -150.0;

13 3 1.000 0 18.0 2.3 0.0 0.0 0.0 0.0;

14 3 1.000 0 10.5 5.3 0.0 0.0 0.0 0.0;

15 3 1.000 0 22.0 5.0 0.0 0.0 0.0 0.0;

16 3 1.000 0 43.0 3.0 0.0 0.0 0.0 0.0;

17 3 1.000 0 42.0 8.0 0.0 0.0 0.0 0.0;

18 3 1.000 0 27.2 9.8 0.0 0.0 0.0 0.0;

19 3 1.000 0 3.3 0.6 0.0 0.0 0.0 0.0;

20 3 1.000 0 2.3 1.0 0.0 0.0 0.0 0.0;

21 3 1.000 0 0.0 0.0 0.0 0.0 0.0 0.0;

22 3 1.000 0 0.0 0.0 0.0 0.0 0.0 0.0;

23 3 1.000 0 6.3 2.1 0.0 0.0 0.0 0.0;

24 3 1.000 0 0.0 0.0 0.0 0.0 0.0 0.0;

25 3 1.000 0 6.3 3.2 0.0 0.0 0.0 0.0;

26 3 1.000 0 0.0 0.0 0.0 0.0 0.0 0.0;

27 3 1.000 0 9.3 0.5 0.0 0.0 0.0 0.0;

28 3 1.000 0 4.6 2.3 0.0 0.0 0.0 0.0;

29 3 1.000 0 17.0 2.6 0.0 0.0 0.0 0.0;

30 3 1.000 0 3.6 1.8 0.0 0.0 0.0 0.0;

31 3 1.000 0 5.8 2.9 0.0 0.0 0.0 0.0;

32 3 1.000 0 1.6 0.8 0.0 0.0 0.0 0.0;

33 3 1.000 0 3.8 1.9 0.0 0.0 0.0 0.0;

34 3 1.000 0 0.0 0.0 0.0 0.0 0.0 0.0;

35 3 1.000 0 6.0 3.0 0.0 0.0 0.0 0.0;

36 3 1.000 0 0.0 0.0 0.0 0.0 0.0 0.0;

37 3 1.000 0 0.0 0.0 0.0 0.0 0.0 0.0;

38 3 1.000 0 14.0 7.0 0.0 0.0 0.0 0.0;

39 3 1.000 0 0.0 0.0 0.0 0.0 0.0 0.0;

40 3 1.000 0 0.0 0.0 0.0 0.0 0.0 0.0;

41 3 1.000 0 6.3 3.0 0.0 0.0 0.0 0.0;

42 3 1.000 0 7.1 4.4 0.0 0.0 0.0 0.0;

43 3 1.000 0 2.0 1.0 0.0 0.0 0.0 0.0;

44 3 1.000 0 12.0 1.8 0.0 0.0 0.0 0.0;

45 3 1.000 0 0.0 0.0 0.0 0.0 0.0 0.0;

46 3 1.000 0 0.0 0.0 0.0 0.0 0.0 0.0;

47 3 1.000 0 29.7 11.6 0.0 0.0 0.0 0.0;

48 3 1.000 0 0.0 0.0 0.0 0.0 0.0 0.0;

49 3 1.000 0 18.0 8.5 0.0 0.0 0.0 0.0;

50 3 1.000 0 21.0 10.5 0.0 0.0 0.0 0.0;

51 3 1.000 0 18.0 5.3 0.0 0.0 0.0 0.0;

52 3 1.000 0 4.9 2.2 0.0 0.0 0.0 0.0;

53 3 1.000 0 20.0 10.0 0.0 0.0 0.0 0.0;

54 3 1.000 0 4.1 1.4 0.0 0.0 0.0 0.0;

55 3 1.000 0 6.8 3.4 0.0 0.0 0.0 0.0;

56 3 1.000 0 7.6 2.2 0.0 0.0 0.0 0.0;

57 3 1.000 0 6.7 2.0 0.0 0.0 0.0 0.0];

switch num

case 14

busdt = busdat14;

case 30

busdt = busdat30;

case 57

busdt = busdat57;

end

% Returns Line datas of the system...

function linedt = linedatas(num)

% | From | To | R | X | B/2 | X'mer |

% | Bus | Bus | pu | pu | pu | TAP (a) |

linedat14 = [1 2 0.01938 0.05917 0.0264 1

1 5 0.05403 0.22304 0.0246 1

2 3 0.04699 0.19797 0.0219 1

2 4 0.05811 0.17632 0.0170 1

2 5 0.05695 0.17388 0.0173 1

3 4 0.06701 0.17103 0.0064 1

4 5 0.01335 0.04211 0.0 1

4 7 0.0 0.20912 0.0 0.978

4 9 0.0 0.55618 0.0 0.969

5 6 0.0 0.25202 0.0 0.932

6 11 0.09498 0.19890 0.0 1

6 12 0.12291 0.25581 0.0 1

6 13 0.06615 0.13027 0.0 1

7 8 0.0 0.17615 0.0 1

7 9 0.0 0.11001 0.0 1

9 10 0.03181 0.08450 0.0 1

9 14 0.12711 0.27038 0.0 1

10 11 0.08205 0.19207 0.0 1

12 13 0.22092 0.19988 0.0 1

13 14 0.17093 0.34802 0.0 1 ];

% | From | To | R | X | B/2 | X'mer |

% | Bus | Bus | pu | pu | pu | TAP (a) |

linedat30 = [1 2 0.0192 0.0575 0.0264 1

1 3 0.0452 0.1652 0.0204 1

2 4 0.0570 0.1737 0.0184 1

3 4 0.0132 0.0379 0.0042 1

2 5 0.0472 0.1983 0.0209 1

2 6 0.0581 0.1763 0.0187 1

4 6 0.0119 0.0414 0.0045 1

5 7 0.0460 0.1160 0.0102 1

6 7 0.0267 0.0820 0.0085 1

6 8 0.0120 0.0420 0.0045 1

6 9 0.0 0.2080 0.0 0.978

6 10 0.0 0.5560 0.0 0.969

9 11 0.0 0.2080 0.0 1

9 10 0.0 0.1100 0.0 1

4 12 0.0 0.2560 0.0 0.932

12 13 0.0 0.1400 0.0 1

12 14 0.1231 0.2559 0.0 1

12 15 0.0662 0.1304 0.0 1

12 16 0.0945 0.1987 0.0 1

14 15 0.2210 0.1997 0.0 1

16 17 0.0824 0.1923 0.0 1

15 18 0.1073 0.2185 0.0 1

18 19 0.0639 0.1292 0.0 1

19 20 0.0340 0.0680 0.0 1

10 20 0.0936 0.2090 0.0 1

10 17 0.0324 0.0845 0.0 1

10 21 0.0348 0.0749 0.0 1

10 22 0.0727 0.1499 0.0 1

21 23 0.0116 0.0236 0.0 1

15 23 0.1000 0.2020 0.0 1

22 24 0.1150 0.1790 0.0 1

23 24 0.1320 0.2700 0.0 1

24 25 0.1885 0.3292 0.0 1

25 26 0.2544 0.3800 0.0 1

25 27 0.1093 0.2087 0.0 1

28 27 0.0 0.3960 0.0 0.968

27 29 0.2198 0.4153 0.0 1

27 30 0.3202 0.6027 0.0 1

29 30 0.2399 0.4533 0.0 1

8 28 0.0636 0.2000 0.0214 1

6 28 0.0169 0.0599 0.065 1 ];

% | From | To | R | X | B/2 | X'mer |

% | Bus | Bus | pu | pu | pu | TAP (a) |

linedat57 = [ 1 2 0.0083 0.0280 0.0645 1

2 3 0.0298 0.0850 0.0409 1

3 4 0.0112 0.0366 0.0190 1

4 5 0.0625 0.1320 0.0129 1

4 6 0.0430 0.1480 0.0174 1

6 7 0.0200 0.1020 0.0138 1

6 8 0.0339 0.1730 0.0235 1

8 9 0.0099 0.0505 0.0274 1

9 10 0.0369 0.1679 0.0220 1

9 11 0.0258 0.0848 0.0109 1

9 12 0.0648 0.2950 0.0386 1

9 13 0.0481 0.1580 0.0203 1

13 14 0.0132 0.0434 0.0055 1

13 15 0.0269 0.0869 0.0115 1

1 15 0.0178 0.0910 0.0494 1

1 16 0.0454 0.2060 0.0273 1

1 17 0.0238 0.1080 0.0143 1

3 15 0.0162 0.0530 0.0272 1

4 18 0.0 0.5550 0.0 0.970

4 18 0.0 0.4300 0.0 0.978

5 6 0.0302 0.0641 0.0062 1

7 8 0.0139 0.0712 0.0097 1

10 12 0.0277 0.1262 0.0164 1

11 13 0.0223 0.0732 0.0094 1

12 13 0.0178 0.0580 0.0302 1

12 16 0.0180 0.0813 0.0108 1

12 17 0.0397 0.1790 0.0238 1

14 15 0.0171 0.0547 0.0074 1

18 19 0.4610 0.6850 0.0 1

19 20 0.2830 0.4340 0.0 1

21 20 0.0 0.7767 0.0 1.043

21 22 0.0736 0.1170 0.0 1

22 23 0.0099 0.0152 0.0 1

23 24 0.1660 0.2560 0.0042 1

24 25 0.0 1.1820 0.0 1

24 25 0.0 1.2300 0.0 1

24 26 0.0 0.0473 0.0 1.043

26 27 0.1650 0.2540 0.0 1

27 28 0.0618 0.0954 0.0 1

28 29 0.0418 0.0587 0.0 1

7 29 0.0 0.0648 0.0 0.967

25 30 0.1350 0.2020 0.0 1

30 31 0.3260 0.4970 0.0 1

31 32 0.5070 0.7550 0.0 1

32 33 0.0392 0.0360 0.0 1

34 32 0.0 0.9530 0.0 0.975

34 35 0.0520 0.0780 0.0016 1

35 36 0.0430 0.0537 0.0008 1

36 37 0.0290 0.0366 0.0 1

37 38 0.0651 0.1009 0.0010 1

37 39 0.0239 0.0379 0.0 1

36 40 0.0300 0.0466 0.0 1

22 38 0.0192 0.0295 0.0 1

11 41 0.0 0.7490 0.0 0.955

41 42 0.2070 0.3520 0.0 1

41 43 0.0 0.4120 0.0 1

38 44 0.0289 0.0585 0.0010 1

15 45 0.0 0.1042 0.0 0.955

14 46 0.0 0.0735 0.0 0.900

46 47 0.0230 0.0680 0.0016 1

47 48 0.0182 0.0233 0.0 1

48 49 0.0834 0.1290 0.0024 1

49 50 0.0801 0.1280 0.0 1

50 51 0.1386 0.2200 0.0 1

10 51 0.0 0.0712 0.0 0.930

13 49 0.0 0.1910 0.0 0.895

29 52 0.1442 0.1870 0.0 1

52 53 0.0762 0.0984 0.0 1

53 54 0.1878 0.2320 0.0 1

54 55 0.1732 0.2265 0.0 1

11 43 0.0 0.1530 0.0 0.958

44 45 0.0624 0.1242 0.0020 1

40 56 0.0 1.1950 0.0 0.958

56 41 0.5530 0.5490 0.0 1

56 42 0.2125 0.3540 0.0 1

39 57 0.0 1.3550 0.0 0.980

57 56 0.1740 0.2600 0.0 1

38 49 0.1150 0.1770 0.0015 1

38 48 0.0312 0.0482 0.0 1

9 55 0.0 0.1205 0.0 0.940];

switch num

case 14

linedt = linedat14;

case 30

linedt = linedat30;

case 57

linedt = linedat57;

end

% Program for Bus Power Injections, Line & Power flows (p.u)...

function [Pi Qi Pg Qg Pl Ql] = loadflow(nb,V,del,BMva)

Y = ybusppg(nb); % Calling Ybus program..

lined = linedatas(nb); % Get linedats..

busd = busdatas(nb); % Get busdatas..

Vm = pol2rect(V,del); % Converting polar to rectangular..

Del = 180/pi*del; % Bus Voltage Angles in Degree...

fb = lined(:,1); % From bus number...

tb = lined(:,2); % To bus number...

nl = length(fb); % No. of Branches..

Pl = busd(:,7); % PLi..

Ql = busd(:,8); % QLi..

Iij = zeros(nb,nb);

Sij = zeros(nb,nb);

Si = zeros(nb,1);

% Bus Current Injections..

I = Y*Vm;

Im = abs(I);

Ia = angle(I);

%Line Current Flows..

for m = 1:nl

p = fb(m); q = tb(m);

Iij(p,q) = -(Vm(p) - Vm(q))*Y(p,q); % Y(m,n) = -y(m,n)..

Iij(q,p) = -Iij(p,q);

end

Iij = sparse(Iij);

Iijm = abs(Iij);

Iija = angle(Iij);

% Line Power Flows..

for m = 1:nb

for n = 1:nb

if m ~= n

Sij(m,n) = Vm(m)*conj(Iij(m,n))*BMva;

end

end

end

Sij = sparse(Sij);

Pij = real(Sij);

Qij = imag(Sij);

% Line Losses..

Lij = zeros(nl,1);

for m = 1:nl

p = fb(m); q = tb(m);

Lij(m) = Sij(p,q) + Sij(q,p);

end

Lpij = real(Lij);

Lqij = imag(Lij);

% Bus Power Injections..

for i = 1:nb

for k = 1:nb

Si(i) = Si(i) + conj(Vm(i))* Vm(k)*Y(i,k)*BMva;

end

end

Pi = real(Si);

Qi = -imag(Si);

Pg = Pi+Pl;

Qg = Qi+Ql;

disp('################################################################

#########################');

disp('-----------------------------------------------------------------------------------------');

disp(' Newton Raphson Loadflow Analysis ');

disp('-----------------------------------------------------------------------------------------');

disp('| Bus | V | Angle | Injection | Generation | Load |');

disp('| No | pu | Degree | MW | MVar | MW | Mvar | MW | MVar |

');

for m = 1:nb

disp('-----------------------------------------------------------------------------------------');

fprintf('%3g', m); fprintf(' %8.4f', V(m)); fprintf(' %8.4f', Del(m));

fprintf(' %8.3f', Pi(m)); fprintf(' %8.3f', Qi(m));

fprintf(' %8.3f', Pg(m)); fprintf(' %8.3f', Qg(m));

fprintf(' %8.3f', Pl(m)); fprintf(' %8.3f', Ql(m)); fprintf('\n');

end

disp('-----------------------------------------------------------------------------------------');

fprintf(' Total ');fprintf(' %8.3f', sum(Pi)); fprintf(' %8.3f', sum(Qi));

fprintf(' %8.3f', sum(Pi+Pl)); fprintf(' %8.3f', sum(Qi+Ql));

fprintf(' %8.3f', sum(Pl)); fprintf(' %8.3f', sum(Ql)); fprintf('\n');

disp('-----------------------------------------------------------------------------------------');

disp('################################################################

#########################');

disp('-------------------------------------------------------------------------------------');

disp(' Line FLow and Losses ');

disp('-------------------------------------------------------------------------------------');

disp('|From|To | P | Q | From| To | P | Q | Line Loss |');

disp('|Bus |Bus| MW | MVar | Bus | Bus| MW | MVar | MW | MVar

|');

for m = 1:nl

p = fb(m); q = tb(m);

disp('-------------------------------------------------------------------------------------');

fprintf('%4g', p); fprintf('%4g', q); fprintf(' %8.3f', Pij(p,q)); fprintf(' %8.3f',

Qij(p,q));

fprintf(' %4g', q); fprintf('%4g', p); fprintf(' %8.3f', Pij(q,p)); fprintf(' %8.3f',

Qij(q,p));

fprintf(' %8.3f', Lpij(m)); fprintf(' %8.3f', Lqij(m));

fprintf('\n');

end

disp('-------------------------------------------------------------------------------------');

fprintf(' Total Loss ');

fprintf(' %8.3f', sum(Lpij)); fprintf(' %8.3f', sum(Lqij)); fprintf('\n');

disp('-------------------------------------------------------------------------------------');

disp('################################################################

#####################');

% Program for Newton-Raphson Load Flow Analysis..

nbus = 14; % IEEE-14, IEEE-30, IEEE-57..

Y = ybusppg(nbus); % Calling ybusppg.m to get Y-Bus Matrix..

busd = busdatas(nbus); % Calling busdatas..

BMva = 100; % Base MVA..

bus = busd(:,1); % Bus Number..

type = busd(:,2); % Type of Bus 1-Slack, 2-PV, 3-PQ..

V = busd(:,3); % Specified Voltage..

del = busd(:,4); % Voltage Angle..

Pg = busd(:,5)/BMva; % PGi..

Qg = busd(:,6)/BMva; % QGi..

Pl = busd(:,7)/BMva; % PLi..

Ql = busd(:,8)/BMva; % QLi..

Qmin = busd(:,9)/BMva; % Minimum Reactive Power Limit..

Qmax = busd(:,10)/BMva; % Maximum Reactive Power Limit..

P = Pg - Pl; % Pi = PGi - PLi..

Q = Qg - Ql; % Qi = QGi - QLi..

Psp = P; % P Specified..

Qsp = Q; % Q Specified..

G = real(Y); % Conductance matrix..

B = imag(Y); % Susceptance matrix..

pv = find(type == 2 | type == 1); % PV Buses..

pq = find(type == 3); % PQ Buses..

npv = length(pv); % No. of PV buses..

npq = length(pq); % No. of PQ buses..

Tol = 1;

Iter = 1;

while (Tol > 1e-5) % Iteration starting..

P = zeros(nbus,1);

Q = zeros(nbus,1);

% Calculate P and Q

for i = 1:nbus

for k = 1:nbus

P(i) = P(i) + V(i)* V(k)*(G(i,k)*cos(del(i)-del(k)) + B(i,k)*sin(del(i)-del(k)));

Q(i) = Q(i) + V(i)* V(k)*(G(i,k)*sin(del(i)-del(k)) - B(i,k)*cos(del(i)-del(k)));

end

end

% Checking Q-limit violations..

if Iter <= 7 && Iter > 2 % Only checked up to 7th iterations..

for n = 2:nbus

if type(n) == 2

QG = Q(n)+Ql(n);

if QG < Qmin(n)

V(n) = V(n) + 0.01;

elseif QG > Qmax(n)

V(n) = V(n) - 0.01;

end

end

end

end

% Calculate change from specified value

dPa = Psp-P;

dQa = Qsp-Q;

k = 1;

dQ = zeros(npq,1);

for i = 1:nbus

if type(i) == 3

dQ(k,1) = dQa(i);

k = k+1;

end

end

dP = dPa(2:nbus);

M = [dP; dQ]; % Mismatch Vector

% Jacobian

% J1 - Derivative of Real Power Injections with Angles..

J1 = zeros(nbus-1,nbus-1);

for i = 1:(nbus-1)

m = i+1;

for k = 1:(nbus-1)

n = k+1;

if n == m

for n = 1:nbus

J1(i,k) = J1(i,k) + V(m)* V(n)*(-G(m,n)*sin(del(m)-del(n)) +

B(m,n)*cos(del(m)-del(n)));

end

J1(i,k) = J1(i,k) - V(m)^2*B(m,m);

else

J1(i,k) = V(m)* V(n)*(G(m,n)*sin(del(m)-del(n)) - B(m,n)*cos(del(m)-

del(n)));

end

end

end

% J2 - Derivative of Real Power Injections with V..

J2 = zeros(nbus-1,npq);

for i = 1:(nbus-1)

m = i+1;

for k = 1:npq

n = pq(k);

if n == m

for n = 1:nbus

J2(i,k) = J2(i,k) + V(n)*(G(m,n)*cos(del(m)-del(n)) + B(m,n)*sin(del(m)-

del(n)));

end

J2(i,k) = J2(i,k) + V(m)*G(m,m);

else

J2(i,k) = V(m)*(G(m,n)*cos(del(m)-del(n)) + B(m,n)*sin(del(m)-del(n)));

end

end

end

% J3 - Derivative of Reactive Power Injections with Angles..

J3 = zeros(npq,nbus-1);

for i = 1:npq

m = pq(i);

for k = 1:(nbus-1)

n = k+1;

if n == m

for n = 1:nbus

J3(i,k) = J3(i,k) + V(m)* V(n)*(G(m,n)*cos(del(m)-del(n)) +

B(m,n)*sin(del(m)-del(n)));

end

J3(i,k) = J3(i,k) - V(m)^2*G(m,m);

else

J3(i,k) = V(m)* V(n)*(-G(m,n)*cos(del(m)-del(n)) - B(m,n)*sin(del(m)-

del(n)));

end

end

end

% J4 - Derivative of Reactive Power Injections with V..

J4 = zeros(npq,npq);

for i = 1:npq

m = pq(i);

for k = 1:npq

n = pq(k);

if n == m

for n = 1:nbus

J4(i,k) = J4(i,k) + V(n)*(G(m,n)*sin(del(m)-del(n)) - B(m,n)*cos(del(m)-

del(n)));

end

J4(i,k) = J4(i,k) - V(m)*B(m,m);

else

J4(i,k) = V(m)*(G(m,n)*sin(del(m)-del(n)) - B(m,n)*cos(del(m)-del(n)));

end

end

end

J = [J1 J2; J3 J4]; % Jacobian Matrix..

X = inv(J)*M; % Correction Vector

dTh = X(1:nbus-1); % Change in Voltage Angle..

dV = X(nbus:end); % Change in Voltage Magnitude..

% Updating State Vectors..

del(2:nbus) = dTh + del(2:nbus); % Voltage Angle..

k = 1;

for i = 2:nbus

if type(i) == 3

V(i) = dV(k) + V(i); % Voltage Magnitude..

k = k+1;

end

end

Iter = Iter + 1;

Tol = max(abs(M)); % Tolerance..

end

loadflow(nbus,V,del,BMva); % Calling Loadflow.m..

% Polar to Rectangular Conversion

% [RECT] = RECT2POL(RHO, THETA)

% RECT - Complex matrix or number, RECT = A + jB, A = Real, B = Imaginary

% RHO - Magnitude

% THETA - Angle in radians

function rect = pol2rect(rho,theta)

rect = rho.*cos(theta) + j*rho.*sin(theta);

% Program to for Admittance And Impedance Bus Formation....

function Y = ybusppg(num) % Returns Y

linedata = linedatas(num); % Calling Linedatas...

fb = linedata(:,1); % From bus number...

tb = linedata(:,2); % To bus number...

r = linedata(:,3); % Resistance, R...

x = linedata(:,4); % Reactance, X...

b = linedata(:,5); % Ground Admittance, B/2...

a = linedata(:,6); % Tap setting value..

z = r + i*x; % z matrix...

y = 1./z; % To get inverse of each element...

b = i*b; % Make B imaginary...

nb = max(max(fb),max(tb)); % No. of buses...

nl = length(fb); % No. of branches...

Y = zeros(nb,nb); % Initialise YBus...

% Formation of the Off Diagonal Elements...

for k = 1:nl

Y(fb(k),tb(k)) = Y(fb(k),tb(k)) - y(k)/a(k);

Y(tb(k),fb(k)) = Y(fb(k),tb(k));

end

% Formation of Diagonal Elements....

for m = 1:nb

for n = 1:nl

if fb(n) == m

Y(m,m) = Y(m,m) + y(n)/(a(n)^2) + b(n);

elseif tb(n) == m

Y(m,m) = Y(m,m) + y(n) + b(n);

end

end

end

%Y; % Bus Admittance Matrix

%Z = inv(Y); % Bus Impedance Matrix

Appendix B

% pf = 0.97 lagging

beta=0.25

pdn=[0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.78];

v2n=sqrt((1-beta.*pdn - sqrt(1-pdn.*(pdn+2*beta)))/2);

pdp=[0.78 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0];

v2p=sqrt((1-beta.*pdp + sqrt(1-pdp.*(pdp+2*beta)))/2);

pd1=[pdn pdp];

v21=[v2n v2p];

% pf = 1.0

beta=0

pdn=[0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.99];

v2n=sqrt((1-beta.*pdn - sqrt(1-pdn.*(pdn+2*beta)))/2);

pdp=[0.99 0.9 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0];

v2p=sqrt((1-beta.*pdp + sqrt(1-pdp.*(pdp+2*beta)))/2);

pd2=[pdn pdp];

v22=[v2n v2p];

% pf = .97 leading

beta=-0.25

pdn=[0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3];

v2n=sqrt((1-beta.*pdn - sqrt(1-pdn.*(pdn+2*beta)))/2);

pdp=[1.3 1.2 1.1 1.0 0.9 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0];

v2p=sqrt((1-beta.*pdp + sqrt(1-pdp.*(pdp+2*beta)))/2);

pd3=[pdn pdp];

v23=[v2n v2p];

plot(pd1,v21,pd2,v22,pd3,v23)

v1=1.0;

b=1.0;

pd1=0.1

v2=[1.1,1.05,1.0,.95,.90,.85,.80,.75,.70,.65,.60,.55,.50,.45,.40,.35,.30,.25,.20,.15];

sintheta=pd1./(b*v1.*v2);

theta=asin(sintheta);

qd1=-v2.^2/b+v1*b*v2.*cos(theta);

plot(qd1,v2);