Chapter Transmission Line

Chapter 2

Reactive Power Compensation of Transmission LineIndex

2.1 General Introduction 2.2 Power control in Transmission line

2.2.1 Convectional Control Mechanism2.2.1.1 Automatic Generation Control (AGC)2.2.1.2 Excitation Control 2.2.1.3 Phase-Shifting Transformers2.2.14

2.3 Uncompensated Transmission lines2.3.1 Load Compensation.2.3.2 System compensation.2.3.3 Lossless Distributed Parameter of Lines.

2.4 Basic principal of power compensation in transmission system2.4.1 Shunt Compensation.2.4.2 Series Compensation.2.4.3 Stability. 2.4.4 Transmission line Parameters.

2.4.4.1 Efficiency and regulation of lines. 2.4. 4.2 Length of transmission lines.

2.4.4.3 Surge impedance.2.4.4.4 Ferranti-effect.

2.5 Experimental Transmission Line model2.5.1 Transmission Line model of 750km (λ/8) transmission line.2.5.2 Design of scale down Artificial Transmission line. 2.5.3 Design of reactor for artificial line.2.5.4 Design of capacitor for shunt compensator.

2.6 Flexible AC Transmission Systems (FACTS) Controllers2.6.1Introduction 2.6.2 Shunt-connected controllers

2.6.21 Static Var Compensator (SVC) 2.6.1.2 Converter-based STATCOM Compensator

2.6.3 Series-connected controllers 2.6.4Combined Series-Series Controller

2.6.5 Combined Series-Shunt Controllers2.6.6 Various other Types of FACTS Controllers

2.7 Conclusion

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Chapter 2 Reactive Power Compensation of Transmission Lines

2.1 General Introduction

Modern civilization depends heavily on the consumption of electrical energy for

industrial, agriculture, domestics, commercial and social purposes. The demand for low

cost electrical energy has lead to the development of generation sites remotely located

from the load centers. Remote generating stations include hydroelectric stations, fossil

fuel stations, geothermal stations and tidal-power plants, wind power plant which are site

bound; and nuclear Power plants built at distant from urban centers. Hence generation of

bulk power at remote locations necessitates the use of transmission lines to connect

generation sites to distant distribution network. Furthermore, to increase system

reliability, multiple lines that connect load centers to several sources, led to the

development of complex interconnected electrical transmission networks. An electrical

power transmission network comprises mostly 3-phase alternating-current (ac)

transmission lines operating at different transmission voltages (generally at 230 kV and

higher). The choice of transmission voltage basically depends on distance of transmission

(V= 1KV per km ) With increasing requirement of power-transmission capacity and/ or

longer transmission distances, the transmission voltages continue to increase( as P α V2);

indeed, increases in transmission voltages are linked closely to decreasing transmission

losses. For a system comprising multiple sources and numerous loads, line impedance

and the voltages at its terminals determine the flow of active and reactive powers. The

long-distance separation of a generating station from a load center requiring long

transmission lines of high capacity and, active- and reactive-power control in ac

transmission networks was exercised by carefully adjusting transmission line

impedances, as well as regulating terminal voltages by generator excitation control and

by transformer tap changers.

During the past two decades, the increase in electrical energy demand has

presented higher requirements from the power industry. More power plants, substations,

and transmission lines need to be constructed. However, the most commonly used

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devices in present power grid are the mechanically-controlled circuit breakers. The long

switching periods and discrete operation make them difficult to handle the frequently

changed loads smoothly and damp out the transient oscillations quickly. In order to

compensate these drawbacks, large operational margins and redundancies are maintained

to protect the system from dynamic variation and recover from faults. This not only

increases the cost and lowers the efficiency, but also increases the complexity of the

system and augments the difficulty of operation and control. Severe black-outs happened

recently in power grids worldwide and these have revealed that conventional transmission

systems are unable to manage the control requirements of the complicated interconnections

and variable power flow.

Therefore, investment is necessary for the studies into the security and stability of

the power grid, as well as the improved control schemes of the transmission system.

Different approaches such as reactive power compensation and phase shifting have been

applied to increase the stability and the security of the power systems. The demands of

lower power losses, faster response to system parameter change, and higher stability of

system have stimulated the development of the Flexible AC Transmission systems

(FACTS) [1]. Based on the success of research in power electronics switching devices

and advanced control technology, FACTS has become the technology of choice in

voltage control, reactive/active power flow control, transient and steady-state

stabilization that improves the operation and functionality of existing power transmission

and distribution system [2], [3]. The achievement of these studies enlarge the efficiency

of the existing generator units, reduce the overall generation capacity and fuel

consumption, and minimize the operation cost.

2.11 CONVENTIONAL CONTROL MECHANISMS

In the foregoing discussion, a lack of control on active- and reactive-power flow on a

given line, embedded in an interconnected ac transmission network, was stated. Also, to

maintain steady-state voltages and, in selected cases, to alter the power-transmission

capacity of lines, traditional use of shunt and series impedances was hinted. In a

conventional ac power system, however, most of the controllability exists at generating

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stations. For example, generators called spinning reserves maintain an instantaneous

balance between power demand and power supply. These generators, in fact, are

purposely operated at reduced power. Also, to regulate the system frequency and for

maintaining the system at the rated voltage, controls are exercised on selected generators.

2.1.2 Automatic Generation Control (AGC)

The megawatt (MW) output of a generator is regulated by controlling the driving

torque, Tm, provided by a prime-mover turbine. In a conventional electromechanical

system, it could be a steam or a hydraulic turbine. The needed change in the turbine-

output torque is achieved by controlling the steam/ water input into the turbine.

Therefore, in situations where the output exceeds or falls below the input, a speed-

governing system senses the deviation in the generator speed because of the load-

generation mismatch, adjusts the mechanical driving torque to restore the power balance,

and returns the operating speed to its rated value. The speed-governor output is invariably

taken through several stages of mechanical amplification for controlling the inlet (steam/

water) valve/ gate of the driving turbine. Figure 1.1 shows the basic speed-governing

system of a generator supplying an isolated load. The operation of this basic feedback-

control system is enhanced by adding further control inputs to help control the frequency

of a large interconnection. In that role, the control system becomes an automatic

generation control (AGC) with supplementary signals.

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Figure A speed-governor system.

2.1.3 Excitation ControlThe basic function of an exciter is to provide a dc source for field

excitation of a synchronous generator. A control on exciter voltage results in controlling the field current, which, in turn, controls the generated voltage. When a synchronous generator is connected to a large system where the operating frequency and the terminal voltages are largely unaffected by a generator, its excitation control causes its reactive power output to change. In older power plants, a dc generator, also called an exciter, was mounted on the main generator shaft. A control of the field excitation of the dc generator provided a controlled excitation source for the main generator. In contrast, modern stations employ either a brushless exciter (an inverted 3-phase alternator with a solid-state rectifier connecting the resulting dc source directly through the shaft to the field windings of the main generator) or a static exciter (the use of a station supply with static rectifiers). An excitation-control system employs a voltage controller to control the excitation voltage. This operation is typically recognized as an automatic voltage regulator (AVR). However, because an excitation control operates quickly, several stabilizing and protective signals are invariably added to the basic voltage regulator. A power-system stabilizer (PSS) is implemented by adding auxiliary damping signals derived from the shaft speed, or the terminal frequency, or the power—an effective and frequently used technique for enhancing small-signal stability of the connected system. Figure 1.3 shows the functionality of an excitation-control system.

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Figure A conceptual block diagram of a modern excitation controller.

2.1.4 Transformer Tap-Changer Control

In addition to increasing and decreasing nominal voltages, many transformers are

equipped with tap-changers to realize a limited range of voltage control. This tap control

can be carried out manually or automatically. Two types of tap changers are usually

available: offload tap changers, which perform adjustments when deenergized, and on-

load tap changers, which are equipped with current-commutation capacity and are

operated under load. Tap changers may be provided on one of the two transformer

windings as well as on autotransformers. Because tap-changing transformers vary

voltages and, therefore, the reactivepower flow, these transformers may be used as

reactive-power-control devices. On-load tap-changing transformers are usually employed

to correct voltage profiles on an hourly or daily basis to accommodate load variations.

Their speed of operation is generally slow, and frequent operations result in electrical and

mechanical wear and tear.

2.1.5 Phase-Shifting Transformers

A special form of a 3-phase–regulating transformer is realized by combining a

transformer that is connected in series with a line to a voltage transformer equipped with

a tap changer. The windings of the voltage transformer are so connected that on its

secondary side, phase-quadrature voltages are generated and fed into the secondary

windings of the series transformer. Thus the addition of small, phase-quadrature voltage

components to the phase voltages of the line creates phase-shifted output voltages

without any appreciable change in magnitude. A phase-shifting transformer is therefore

able to introduce a phase shift in a line. Figure 1.4 shows such an arrangement together

with a phasor diagram. The phasor diagram shows the phase shift realized without an

appreciable change in magnitude by the injection of phase-quadrature voltage

components in a 3-phase system.

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Figure A phase-shifting transformer: (a) a schematic diagram and (b) a phasor diagram.

When a phase-shifting transformer employs an on-load tap changer, controllable phase-shifting is achieved. The interesting aspect of such phase shifters is that despite their low MVA capacity, by controlling the phase shift they exercise a significant real-power control. Therefore, they are used to mitigate circulating power flows in interconnected utilities. A promising application of these devices is in creating active-power regulation on selected lines and securing active-power damping through the incorporation of auxiliary signals in their feedback controllers. From this description, it is easy to visualize that an incremental in-phase component can also be added in lines to alter only their voltage magnitudes, not their phase.

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It is found that reactive power Qr- is directly proportional to the magnitude of voltage

drop. So, voltage and reactive power control are analogous to each other and their control

is interrelated. For a good quality of power supply voltage at the consumer end must be

kept constant irrespective of the type or magnitude of load. The maintenance of voltage is

a complicated problem as system is supplied from various sources and is supplied to

various consumers at various voltage levels. In order to maintain the voltage under

prescribed limits, it is necessary to maintain the balance of reactive power in the system

that is reactive power generation should be equal to reactive power consumption. Any

discrepancy in these two quantities leads to voltage exceeding prescribed limits thereby

damaging various appliances connected to the system. Also the presence of reactive

power in the system leads to undesirable heating and lowering of the system stability. So,

compensation of transmission lines is necessary. For this, various compensating

techniques are adopted.es is necessary. For this, various compensating techniques are

adopted.

2.1.6 Fixed or mechanically switched capacitors

Shunt capacitors were first employed for power factor correction in the year 1914 [16]. The leading current drawn by the shunt capacitors compensates the lagging current drawn by the load. The selection of shunt capacitors depends on many factors, the most important of which is the amount of lagging reactive power taken by the load. In the case of widely fluctuating loads, the reactive power also varies over a wide range. Thus, a fixed capacitor bank may often lead to either over-compensation or under-compensation. Variable VAR compensation is achieved using switched capacitors [17]. Depending on the total VAR requirement, capacitor banks are switched into or switched out of the system. The smoothness of control is solely dependent on the number of capacitors switching units used. The switching is usually accomplished using relays and circuit breakers. However, these methods based on mechanical switches and relays have the disadvantage of being

sluggish and unreliable. Also they generate high inrush currents, and require frequent

maintenance [16].

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2.1.7 Synchronous Condensers

Synchronous condensers have played a major role in voltage and reactive power control

for more than 50 years. Functionally, a synchronous condenser is simply a synchronous

machine connected to the power system. After the unit is synchronized, the field current

is adjusted to either generate or absorb reactive power as required by the ac system. The

machine can provide continuous reactive

power control when used with the proper automatic exciter circuit. Synchronous

condensers have been used at both distribution and transmission voltage levels to

improve stability and to maintain voltages within desired limits under varying load

conditions and contingency situations.

However, synchronous condensers are rarely used today because they require substantial

foundations and a significant amount of starting and protective equipment. They also

contribute to the short circuit current and they cannot be controlled fast enough to

compensate for rapid load changes. Moreover, their losses are much higher than those

associated with static compensators, and the cost is much higher compared with static

compensators. Their advantage lies in their high temporary overload capability

2.3 Uncompensated transmission lines

To develop a good, qualitative understanding of the need for reactive-power

control, let us consider a simple case of a lossless short-transmission line connecting a

source Vs to a load (For simplicity, the line is represented only by its inductive

reactance XL) Figure 2.2 shows such a network with its parameters, as well as a phasor

diagram showing the relationship between voltages and currents. From Fig. 2.2(b), it is

clear that between the sending- and the receiving-end voltages, a magnitude variation, as

well as a phase difference, is created. The most significant part of the voltage drop in the

line reactance (DV1 c j IxXl) is due to the reactive component of the load current, Ix. To

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keep the voltages in the network at nearly the rated value, two control actions seem

possible:

1. load compensation, and

2. system compensation.

2.3.1 Load Compensation

It is possible to compensate for the reactive current Ix of the load by adding a parallel

capacitive load so that Ic c − Ix. Doing so causes the effective power factor of the

combination to become unity. The absence of Ix eliminates the voltage drop DV1,

bringing Vr closer in magnitude to Vs; this condition is called load compensation.

Actually, by charging extra for

Figure 2.2 A short, lossless transmission line feeding a load.

Figure 2.3 The reactive-power control for voltage regulations.

supplying the reactive power, a power utility company makes it advantageous for

customers to use load compensation on their premises. Loads compensated to the unity

power factor reduce the line drop but do not eliminate it; they still experience a drop of

∆V2 from jIrXL .

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2.3.1.2 System Compensation

To regulate the receiving-end voltage at the rated value, a power utility may install a

reactive-power compensator as shown in Fig. 2.3. This compensator draws a reactive

current to overcome both components of the voltage drop ∆V1 and ∆V2 as a consequence

of the load current Il through the line reactance XL. To compensate for ∆V2, an

additional capacitive current, ∆Ic, over and above Ic that compensates for Ix, is drawn by

the compensator. When ∆IcXlc ∆V2, the receiving-end voltage, VR, equals the sending-

end voltage, VS. Such compensators are employed by power utilities to ensure the quality

of supply to their customers [1].

2.3.1.3 Lossless Distributed Parameter of Lines

Most power-transmission lines are characterized by distributed parameters:

series resistance, R ; series inductance, L; shunt conductance, G; and shunt capacitance,

C- all per-unit (pu) length. These parameters all depend on the conductors’ size, spacing,

clearance above the ground, and frequency and temperature of operation. In addition,

these parameters depend on the bundling arrangement of the line conductors and the

nearness to other parallel lines. The characteristic behavior of a transmission line is

dominated by its L and C parameters. Parameters R and G account for the transmission

losses. The fundamental equations governing the propagation of energy along a line are

the following wave equations:

Where zy = (R + jQL) (G + jQC).

For a lossless line, the general solutions are given as

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These equations are used to calculate voltage and current anywhere on line, at a distance

x from the sending end, in terms of the sending-end voltage and current and the line

parameters. In Eqs. (2.4) and (2.5),

Ω = the surge impedance or characteristic impedance

rad/km = the wave number

rad = the electrical length of an a-km line

where L is the line inductance in henries per kilometer (H/ km), C is the line shunt

capacitance in farads per kilometer (F/ km), and is the propagation velocity of

electromagnetic effects on the transmission line. (It is less than the velocity of light.)

From Eq. (2.5), we get

If and then

Therefore, the power at the sending end is given as

(7)

Likewise, power at the receiving end is given as

(8)

Comparing Eqs. (2.7) and (2.8) and taking the directional notation of Fig. 2.4

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into account, it is concluded that for a lossless line, PS =PR , as expected.However,

because of the reactive-power absorption/ generation in theline. From Eqs. (2.7)

and (2.8), the power flow from the sending end to the receiving

end is expressed as

In electrically short power lines, where is very small, it is possible to make a

simplifying assumption that , or where

is the total series reactance of a line. This substitution results in the following well-

recognized power equation:

(2.9)

Accordingly, the maximum power transfer is seen to depend on the line length.Then the

power-transfer requirement for a given length of a line increases, higher transmission

voltages of Vs and Vr must be selected. This chapter is not intended to provide a

comprehensive analysis of transmission lines. Rather, its objective is to examine those

aspects that enhance the understanding of the interplay between voltages on the line and

the resulting reactive-power flows.

2.4 Basic principal of power compensation in transmission system.

Figure 2.2.1(a) shows the simplified model of a power transmission system. Two power

grids are connected by a transmission line which is assumed lossless and represented by

the reactance XL. V1 < δ1 and V2 < δ2 represent the voltage phasors of the two power grid

buses with angle δ =δ1-δ2 between the two. The corresponding phasor diagram is shown

in Figure 2.1(b).

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Figure 2.1 Power transmission system: (a) simplified model; (b) phase diagram

The magnitude of the current in the transmission line is given by:

(2-1)

The active and reactive components of the current flow at bus 1 are given by

, (2-2)

The active power and reactive power at bus 1 are given by:

, (2-3)

Similarly, the active and reactive components of the current flow at bus 2 can be given

by:

, (2-4)

The active power and reactive power at bus 2 are given by:

, (2-5)

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Equations (2-1) through (2-5) indicate that the active and reactive power/current flow can

be regulated by controlling the voltages, phase angles and line impedance of the

transmission system. From the power angle curve shown in Figure (c), the active power

flow will reach the maximum when the phase angle δ is 90º. In practice, a small angle is

used to keep the system stable from the transient and dynamic oscillations [4].

Generally, the compensation of transmission systems can be divided into two main

groups: shunt and series compensation.

2.4.1 Shunt compensation

Shunt compensation, especially shunt reactive compensation has been widely used in

transmission system to regulate the voltage magnitude, improve the voltage quality, and

enhance the system stability [5]. Shunt-connected reactors are used to reduce the line

over-voltages, by consuming the reactive power, while shunt-connected capacitors are

used to maintain the voltage levels by compensating the reactive power to transmission

line.

A simplified model of a transmission system with shunt compensation is shown in Figure

2.2(a). The voltage magnitudes of the two buses are assumed equal as V, and the phase

angle between them is δ. The transmission line is assumed lossless and represented by the

reactance XL. At the midpoint of the transmission line, a controlled capacitor C is shunt-

connected. The voltage magnitude at the connection point is maintained as V.

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Figure 2.2 Transmission system with shunt compensation: (a) simplified model; (b) phase

diagram; (c) power-angle curve [2]

As discussed previously, the active powers at bus 1 and bus 2 are equal.

(2-6)

The injected reactive power by the capacitor to regulate the voltage at the mid-point of the

transmission line is calculated as:

(2-7)

From the power angle curve shown in Figure 2.2(c), the transmitted power can be

significantly increased, and the peak point shifts from δ=90º to δ=180º. The operation

margin and the system stability are increased by the shunt compensation. The voltage

support function of the midpoint compensation can easily be extended to the voltage

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support at the end of the radial transmission, which will be proven by the system

simplification analysis in a later section. The reactive power compensation at the end of

the radial line is especially effective in enhancing voltage stability

2.4.2 Series compensation

Series compensation aims to directly control the overall series line impedance of the

transmission line. Tracking back to Equations (2-1) through (2-5), the AC power

transmission is primarily limited by the series reactive impedance of the transmission

line. A series-connected can add a voltage in opposition to the transmission line voltage

drop, therefore reducing the series line impedance. A simplified model of a transmission

system with series compensation is shown in Figure 2.3(a). The voltage magnitudes of

the two buses are assumed equal as V, and the phase angle between them is δ. The

transmission line is assumed lossless and represented by the reactance XL. A controlled

capacitor is series-connected in the transmission line with voltage addition Ving. The

phase diagram is shown in Figure 2.3(b)

Figu

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re 2. 3 Transmission system with series compensation: (a) simplified model; (b) phase

diagram; (c) power-angle curve [2]

Defining the capacitance of C as a portion of the line reactance,

(2-8)

The overall series inductance of the transmission line is,

(2-9)

The active power transmitted is,

(2-10)

The reactive power supplied by the capacitor is calculated as:

(2-11)

In Figure 2.3(c) shows the power angle curve from which it can be seen that the

transmitted active power increases with k.

2.6 Transmission line Parameters

An Electrical transmission line can be represented by a series combination of

resistance, inductance and shunt combination of conductance and capacitance. these

parameters are symbolized as R,L,G and C respectively, of these R and G are least

important in the sense that they do not effect much the total equivalent impedance of the

line and hence the transmission capacity. They are of course very much importance when

transmission efficiency and economy are to be evaluated as they completely determine

the real transmission line losses

The resistance of a conductor is given by

R= power loss in conductor / I2ohms

Where R is the effective resistance of the conductor and I the current flowing

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through the conductor. The effective resistance is equal to the D.C resistance of the

conductor only if the current is uniformly distributed throughout the section of the

conductor. Difference in the D.C resistance and effective resistance to frequencies less

than 50 Hz is less than 1 percent for copper conductors of section less than 350,000

circular mils. The loss on the overhead transmission line is due to

1. Ohmic loss in the power conductors

2. corona loss

3. leakage at the insulators which support the lines at the towers

2.6.1 Efficiency and regulation of lines

The performance of lines is meant the determination of efficiency and regulation of

lines

% Efficiency= power delivered at the receiving endpower sent ¿

the sending end ¿∗100

(2-19)

Regulation of a line is defined as the change in the receiving end

voltage, expressed in percent of full load voltage, from no load to full load, keeping the

sending end voltage and frequency constant. Expressed mathematically

% regulation=(V R−VR1)¿/V R1∗100 (2-20)

Where VR is the receiving end under no load condition and VR1 the receiving end

voltage under full load condition. It is to be noted here that VR and VR1 are the

magnitudes of voltage.

2.6.2 Length of transmission lines

A transmission line is a set of conductors being run from one place to another

supported on transmission towers. Such lines, therefore, have foure distributed

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parameters, series resistance and inductance and shunt capacitance and conductance. The

voltage and current vary harmonically along the line with respect to the distance of the

point under consideration. This observation is very important in representing the lines of

different lengths. It is to be noted that the electrical power is being transmitted over the

overhead lines at approximately the speed of light .in order to get one full wave variation

of voltage or current on the line, the length of the line for 50 Hz supply will be given by

(2-21)

where f is the frequency of supply , λ is wavelength i.e the length of the in this case and v

the velocity of the wave i.e the velocity of light

(2-22)

This means that if the length of the line is 6000 Km the voltage or current wave at the

two ends of the line. Transmission lines have been classified as lang and medium and

short lines depending on the length of the lines. These are

Upto 80km---short line

80 to 160km-----medium line

Above 160km----long transmission line

The transmission system selected for our study is a long transmission line with a 4

π network representation. The resistance of a line has been neglected and the line is

considered to be purely reactive. It means that I2R losses are neglected. This is because

the project is mainly concerned with the reactive power control, and the resistance has no

effect on the reactive power absorbed or generated by the system. The load is considered

purely resistive.

2.6.3 Surge impedance

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The surge impedance of a typical overhead line is 400Ω. The transmission

network is so selected as to satisfy these conditions.

Surge impedance: The surge impedance of a line is calculated from the formula

(2-23)

Where ZS=Surge Impedance, L=line Inductance/km and C=line capacitance./km

Practical Considerations In general, the values of line parameters L and C remain

reasonably independent of the transmission voltage. For example, typical values of L and

C may lie in the following ranges:

L= the line inductance/ km =0.78–0.98 mH/ km

C= the line capacitance/ km =12.1–15.3 nF/ km On the basis of these parameters, the

surge impedance, ZS, lies in the range of 225 to 285.

2.6.4 Ferranti-effect

When a long line is operating under no load or light load condition, the receiving

end voltage is greater than sending end voltage, this is known as Ferranti-effect. Ferranti-

effect can be given by approximating the distributed parameters of the line by lumped

impedance shown in figure below. Since usually the capacitive reactance of the line is

quite large as compared to the inductive reactance, under no load or light loaded

condition the line current is of leading p.f. The charging current produces drop in the

reactance of the line which is in phase opposition to the receiving end voltage and hence

the sending end voltage becomes smaller than the receiving end voltage.

Ferranti-effect is based on the net reactive power flow on the line .it is shown that

if the reactive power generated at a point is more than the reactive power absorbed, the

voltage at that point becomes higher than the normal value and vice versa. The inductive

reactance of the line is a sink for the reactive power where as the shunt capacitances

generate reactive power.

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In fact, if the line loading corresponds to the surge impedance loading, the voltage

is same everywhere as the reactive power absorbed than equals the reactive power

generated by the lines. the SIL,therefore ,gives definite meaning to the terms lightly

loaded or fully loaded lines. if the loading is less than SIL, the reactive power generated

is more than absorbed, therefore the receiving end voltage is greater than the sending end

voltage. This explains, therefore, the phenomenon due to Ferranti-effect

Fig 3.2(a) Line representation under no load Fig 3.2(b) phasor diagram

2.6.5 Transmission line model of 750km (λ/8) transmission line

The implementation of the Reactive power compensation schemes are usually carried out

on long lines (>250 km of length).A specific long line with its parameters as was chosen

for this work. The specifications of the line are as follows:

Power rating of the line: 100 MVA

Voltage rating of the line: 220 kV.

Resistance: 0.073 Ω per km.

Inductive reactance: 0.4794 Ω per km.

Shunt admittance: 3.35 µ mho per km.

Therefore at a frequency of 50 Hz, the values of series inductance and shunt capacitance

works out to be:

Series Inductance L: 1.525 x 10-5 H per km.

Shunt capacitance C: 11.3 nF per km.

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Propagation Constant γ: 4.15 x 10-6.

From equation

Base Impedance of 220kv line = = 484Ω

Therefore SIL is

= =100MW

Symetrical Lines : When the voltage magnitudes at the two ends of line are equal , that

is Vs=Vr, the line is said to be symmetrical .Because of power networks operate as

voltage sources, attempts are made to hold almost all node voltage at nearly rated values

From equation 7 and 8 following relationship are derived

and

Therefore for this line to operate as symmetrical line VS=Vr =220 kV We have from

equation

2.5.2 Scale down parameters of artificial transmission line

This long line with the parameters obtained as above is scaled down for the fabrication of

the Scale down model by choosing a base of 5 kVA and 400 V.

The scale down model of the transmission line is obtained by maintaining the per unit

values of the resistance and reactance the same as that of the actual long line.

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R p.u. = Actual Resistance*BaseMVA/(Base kV)2

= 1.508*10-4 p.u. er unit value of Reactance

XL p.u. = Actual Reactance*Base MVA/(Base kV) 2

= 9.904*10-4 p.u

Therefore the actual values of the resistance and reactance in the scaled down model

work out to be:Actual value of Resistance

RSD = Per unit value of resistance*Base impedance

= 0.0048 Ω per km.

Actual value of Reactance

XLSD = Per unit value of reactance*Base impedance

= 0.0316 Ω per km .

Inductance LSD = 0.10089 mH per km.

The value of the shunt capacitance is obtained by keeping the ratios of XL / R and γ

constant.

Actual value of shunt capacitance

C s.d = γ² / L s.d = 0.1625 x 10-6 F per km.

Using the above data the transmission line was fabricated to represent a 750 km line by

as that of 50 km assembling six pi models comprising of series resistance and inductance

and shunt capacitance with their values line model and the Six Pi models were connected

in series . Thus in the scaled down model

For long lines the reactance r mpensation can

be evaluated as

Phase constant, β = 2* π * f * √(L*C)

= 1.266*103 radians.

Surge impedance, Zc = √ (L/C) = 24.81 Ω

Under no load conditions there is no real power transferred

(Since IR=0). Therefore under ideal conditions VS =VR

But practically, in most of the transmission lines the Ferranti Effect is predominant and

the receiving end voltage is greater than that of the sending end voltage at light loads.

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Henceforth a shunt reactor is installed in the line for absorbing the excess VARs in the

line. The value of the reactance required for this purpose was evaluated as follows

2.5.3 Reactor design for artificial line

The reactor to be employed for shunt compensation is expected to have the following

ratings:

Voltage: 230V

Current: 6A.

The volt-ampere rating of the reactor is therefore 1370 VA. Henceforth an iron-core

reactor with air gap in the core is selected

Linearity test The reactor was fabricated and it was tested for its linearity. The average inductive

reactance of the reactor was found to be 39.5 ohms. It was found that the Reactor

responded linearly in the operating region with an average inductance of 0.127H .

Under lagging load conditions, sometimes shunt capacitor compensation may be required

.So, the amount of capacitive compensation required at different lengths of the

transmission line are calculated and implemented as below

Calculation of the value of shunt compensator under loaded condition

Specifications of the 3 φ load:

Voltage : 400 V

Power : 5 kVA,

Calculation of capacitive reactance for a 1φ 750km long line

x = Zc*sinβl = 22.668 Ω

100% compensation is obtained by making the sending end voltage and the receiving end

voltage equal .( VS = VR ).

The reactive power in the line

Q = VR² * ( cos δ - cos βl ) / x

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= 3.652* kVAR.

The reactive power demanded by the load

QL= Load kVA* sin (φ)

= 4.33 kVAR

Therefore ,Net Reactive power to be injected,

Qi = Q– QL

=0.677 kVAR

The capacitive Reactance Xc = VR² / Qi

= 236.178 Ω.

The value of Capacitor to be installed ,C= 1 / (2* π * f * Xc)

C = 13.47* 10-6 F.

Calculation of capacitive reactance for a 3φ 300 km long line

x = Zc*sinβ l = 8.4053 Ω

sin δ = PR * x / VR²

sin δ = 0.1313

δ = 0.1317 radians.

100% compensation is obtained by making the sending end voltage and the receiving end

voltage equal .( VS = VR ).

The reactive power in the line

Q = VR² * ( cosδ - cos βl ) / x

= 1.1943 kVAR.

The reactive power demanded by the load QL

= Load kVA* sin (φ) = 4.33 kVAR

= 3.1357 kVAR

The capacitive Reactance Xc = VR² / Qi=51.0253 Ω.

The value of Capacitor to be installed , C= 1 / (2* π * f * Xc)

= 62.36* 10-6 F.

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.

Design aspect for compensation of reactive power

In case of radial transmission line let sending end real power Flow is P S, sending

end reactive power flow QS , receiving end real power flow PR and receiving end reactive

power flow QR can be express as

(2-12)

(2-13)

(2-14)

(2-15)

From the above equations we can conclude that transfer of real power depends only on

angle δ, the power angle and not on the relative magnitudes of sending end and receiving

end voltage .More over the transmitted power varies approximately as the square of

voltage level .The maximum power transfer takes place when δ= 900

(2-16)

From equations (2.13) and (2.15) it is clear that reactive power Q will flow in the

direction of lower voltage. If the system operates with δ= 0, the average reactive power

flow over the line is given as

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(2-17)

This equation (2.17) shows that the reactive power flow strongly depends on the

difference in square of voltages.

Line power loss is given as:

(2-18)

Equation (2-18) shows that both real and reactive power contributes to line losses.

Therefore, it important to reduce reactive power flow to reduce line losses.

Referring equations (3) and (4) the voltage magnitudes VS and VR at sending end

and receiving end of long lines are held within permissible limits by means of

compensation of reactive power .Compensation of reactive power helps in improving

steady state stability. For long line, if compensation of reactive power not made, will

results in voltage instability.

Stability of power system

For achiving stable operating conditions ,both active power P and reactive power Q

should be controlled under stesdy state and also under dynamic state (during

disturbance ) the objective of reactive power flow control are twofold

1. Under study state condition:

Optimization of voltage profile in the network, minimize losses and reduction of

unnecessary VAr flow within the network.

2. Under dynamic condition:

Control of under voltage, over voltage during disturbances, to provide voltage

support , at intermediate points ,improves power transfer without losing stability

;improve dynamic stability.

Hence it can conclude that

1. Active Power flow P determined by power angle.

2. Reactive Power VAr flow determines voltage magnitudes.

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2.6 Flexible AC Transmission System (FACTS)

Introduction

The history of FACTS controllers can be traced back to 1970s when Hingorani

presented the idea of power electronic applications in power system compensation. From

then on, various researches were conducted on the application of high power

semiconductors in transmission systems. The shunt-connected Static VAR compensator

(SVC) using solid-state switches and the series-connected controllers were proposed in

AC transmission system application. In 1988, Hingorani defined the FACTS concept and

described the wide prospects of the application in [6]. Nowadays, FACTS technology has

shown strong potential. Many examples of FACTS devices and controllers are in

operation

As presented in [7], FACTS and FACTS controllers are defined in IEEE Terms and

Definitions as:

• Flexible AC Transmission System (FACTS): Alternating current transmission

systems incorporating power electronic-based and other static controllers to

enhance controllability and increase power transfer capability.

• FACTS Controller: A power electronic-based system and other static equipment

that provide control of one or more AC transmission system parameters.

As new technology for power transmission system, FACTS and FACTS controllers not

only provide the same benefits as conventional compensators with mechanically-

controlled switches in steady state but also improve the dynamic and transient

performance of the power system. The power electronics-based switches in the functional

7 blocks of FACTS can usually be operated repeatedly and the switching time is a portion

of a periodic cycle, which is much shorter than the conventional mechanical switches.

The advance of semiconductors increases the switching frequency and voltage-ampere

ratings of the solid switches and facilitates the applications. For example, the switching

frequencies of Insulated Gate Bipolar Transistors (IGBTs) are from 3 kHz to 10 kHz

which is several hundred times the utility frequency of power system (50~60Hz). Gate

turn-off thyristors (GTOs) have a switching frequency lower than 1 kHz, but the voltage

and current rating can reach 5-8 kV and 6 kA respectively [8].

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FACTS controllers have many configurations and broadly divided into four categories,

which are

1. Shunt controllers.

2. Series controllers.

3. Combined series-series controllers.

4. Combined series-shunt controllers

2.6.1 Shunt-connected controllers

FACTS controllers can be impedance type, based on thyristors without gate turn-off

capability, which are called Static Var Compensator (SVC) for shunt-connected

application. Another type of FACTS controllers is converter-based which is usually in the

form of a Static Synchronous Compensator (STATCOM).

2.6.1.1 Static Var Compensator (SVC)

Static Var Compensator is “a shunt-connected static Var generator or absorber whose

output is adjusted to exchange capacitive or inductive current so as to maintain or control

specific parameters of the electrical power system (typically bus voltage)” [5].

SVC is based on thyristors without gate turn-off capability. The operating principal and

characteristics of thyristors realize SVC variable reactive impedance. SVC includes two

main components and their combination: (1) Thyristor-controlled and Thyristor-switched

Reactor (TCR and TSR); and (2) Thyristor-switched capacitor (TSC). In Figure 1.4

shows the diagram of SVC.

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Figure 1. 4 Static VAR Compensators (SVC): TCR/TSR, TSC, FC and Mechanically

Switched Resistor [2] TCR

TCR and TSR are both composed of a shunt-connected reactor controlled by two parallel,

reverse-connected thyristors. TCR is controlled with proper firing angle input to operate

in a continuous manner, while TSR is controlled without firing angle control which

results in a step change in reactance.

TSC shares similar composition and same operational mode as TSR, but the reactor is

replaced by a capacitor. The reactance can only be either fully connected or fully

disconnected zero due to the characteristic of capacitor.

With different combinations of TCR/TSR, TSC and fixed capacitors, a SVC can meet

various requirements to absorb/supply reactive power from/to the transmission line.

1.3.1.2 Converter-based STATCOM Compensator

Static Synchronous Compensator (STATCOM) is one of the key Converter-based

Compensators which are usually based on the voltage source inverter (VSI) or current

source inverter (CSI), as shown in Figure 1.5(a). Unlike SVC, STATCOM controls the

output current independently of the AC system voltage, while the DC side voltage is

automatically maintained to serve as a voltage source. Mostly, STATCOM is designed

based on the VSI.

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Figure 1. 5 STATCOM topologies: (a) STATCOM based on VSI and CSI (b) STATCOM

with storage [5]

Compared with SVC, the topology of a STATCOM is more complicated. The switching

device of a VSI is usually a gate turn-off device paralleled by a reverse diode; this

function endows the VSI advanced controllability. Various combinations of the switching

devices and appropriate topology make it possible for a STATCOM to vary the AC

output voltage in both magnitude and phase. Also, the combination of STATCOM with a

different storage device or power source (as shown in Figure 1.5(b)) endows the

STATCOM the ability to control the real power output.

STATCOM has much better dynamic performance than conventional reactive power

compensators like SVC. The gate turn-off ability shortens the dynamic response time

from several utility period cycles to a portion of a period cycle. STATCOM is also much

faster in improving the transient response than a SVC. This advantage also brings higher

reliability larger operating range.

1.3.2 Series-connected controllers

As shunt-connected controllers, series-connected FACTS controllers can also be divided

into either impedance type or converter type. The former includes Thyristor-Switched

Series Capacitor (TSSC), Thyristor-Controlled Series Capacitor (TCSC), Thyristor-

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Switched Series Reactor, and Thyristor-Controlled Series Reactor. The latter, based on

VSI, is usually in the form of a Static Synchronous Series Compensator (SSSC). The

composition and operation of different types are similar to the operation of the shunt-

connected peers. Figure 1.7 shows the diagrams of various series-connected controllers.

Figure 1. 7 Series-connected FACTS controllers: (a) TCSR and TSSR; (b) TSSC; (c) SSSC [5]

2.2.3 Combined Series-Series Controllers A combined series-series controller Fig 2.17 may have two configurations. One

configuration consists of series controllers operating in a coordinated manner in a multi-

line transmission system. The other configuration provides independent reactive power

control for each line of a multi-line transmission system and, at the same time, facilitates

real power transfer through the power link.

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Fig 2.17 series-series controller

Example: Interline power flow controllers (IPFC)

Which helps in balancing both the real and reactive power flows on the lines?

2.2.4 Combined Series-Shunt Controllers

A combined series-shunt controller Fig 2.18 may have two configurations, one

being two separate series and shunt controllers that operate in a coordinated manner and

the other one being an interconnected series and shunt component. In each configuration,

the shunt component injects a current into the system while the series component injects a

series voltage. When these two elements are unified, a real power can be exchanged

between them via the power link.

Fig 2.18 series-shunt controller.

Example: Unified power flow controller (UPFC)

These make use of the advantages of both series and shunt controllers and, hence,

facilitate effective and independent power/current flow and line voltage control.

Unified Power Flow Controller (UPFC)

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A combination of static synchronous compensator (STATCOM) and a static

series compensator (SSSC) which are coupled via a common dc link Fig 2.19, allow bi-

directional flow of real power between the series out put terminals of the SSSC and the

shunt output terminals of the STATCOM, and are controlled to provide concurrent real

and reactive line compensation without an external electrical energy source. The UPFC,

by means of angularly unconstrained series voltage injection, is able to control,

concurrently, or selectively, the transmission line voltage, impedance, and angle or,

alternatively, the real and reactive power flow in the line. The UPFC may also provide

independently controllable shunt reactive compensation.

Fig 2.19 Unified power flow controller (UPFC)

In UPFC, which combines a STATCOM and an SSSC, the active power for the

series unit (SSSC) is obtained from the line itself via the shunt unit STATCOM the latter

one is also used for voltage control with control of its reactive power. This is a complete

control for controlling active and reactive power through the line, as well as for the line

voltage control.

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As discussed in the previous section, STATCOM is a very popular FACTS

controller application effective in transmission system voltage control. Since 1980 when

the first STATCOM (rated at 20 Mvar) using force-commutated thyristor inverters was

put into operation in Japan [10], many examples have been installed and the ratings have

been increased considerably. In 1991, KEPCO and Mitsubish Motors installed a

±80MVar STATCOM at Inuyama Switching Station [11]. In 1996, TVA, EPRI and

Westinghouse installed a ±100MVar STATCOM at Sullivan 500 kV Substation [12]. In

2001, EPRI and Siemens developed a ±200MVar STATCOM at Marcy 345kV substation

[13]. It is expected that more STATCOMs will be installed due to the advances in

technology and commercial success.

STATCOM could have many topologies, but in most practical applications it employs the

DC to AC converter, which can also be called a Voltage Source Inverter (VSI) in 3-phase

configuration as the primary block. The basic theory of VSI is to produce a set of

controllable 3-phase output voltages/ currents at the fundamental frequency of the AC

bus voltage from a DC input voltage source such as a charged capacitor or a DC energy

supply device. By varying the magnitude and phase angle of the output voltage and

current, the system can exchange active/reactive power between the DC and AC buses,

and regulate the AC bus voltage.

Various other Types of FACTS Controllers

Advanced SVC.

NGH-SSR Damper.

Thyrister Controlled Phase Angle Regulator (TCPAR).

Thyrister Controlled Phase Shifter (TCPS).

Dynamic Voltage Limiters.

Fault Current Limiters.

Load Tap Changer.

Ferro-Resonance Damper.

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Inter line power flow controllers (IPFC).

Conclusion

[1]N. G. Hingorani and L. Gyugyi, Understanding FACTS, IEEE Press, New York,

1999.

[2 ]IEEE Power Engineering Society, FACTS Applications, Publication 96TP116-0,

IEEE Press, New York, 1996.

[3] R. Mohan Mathur; Rajiv K. Varma : Thyristor –Based FACTS Controller for

Electrical Transmission Systems 2002 Jons Wiley & Sons.

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