Analysis and Planning of Power Transmission Systems ...for more rigorous analysis and planning of power transmission systems. Stability issues in power transmission system are more

Analysis and Planning of Power Transmission Systems Subject to

Uncertainties in the Grid

Durga Aryal

Thesis submitted to the Faculty of the

Virginia Polytechnic Institute and State University

in partial fulfillment of the requirements for the degree of

Masters of Science

in

Electrical Engineering

Robert P Broadwater, Chair

Jamie De La Reelopez

Virgilio A Centeno

December 7, 2018

Blacksburg, Virginia

Keywords: Power Transmission System, Uncertainties, Renewable Energy Sources, Voltage

Stability Analysis, Probabilistic Transmission Planning.

Copyright 2018, Durga Aryal



Durga Aryal

(ABSTRACT)

Power transmission systems frequently experience new power flow pattern due to several

factors that increase uncertainties in the system. For instance, load shape uncertainty,

uncertainty due to penetration of renewable sources, changing standards, and energy de-

regulation threaten the reliability and security of power transmission systems. This demands

for more rigorous analysis and planning of power transmission systems.

Stability issues in power transmission system are more pronounced with the penetration of

utility-scale Photo-Voltaic (PV) sources. Synchronous generators provide inertia that helps

in damping oscillations that arise due to fluctuations in the power system. Therefore, as

PV generators replace the conventional synchronous generators, power transmission systems

become vulnerable to these abnormalities. In this thesis, we study the effect of reduced inertia

due to the penetration of utility-scale PV on the transient stability of power transmissions

systems. In addition, the effect of increased PV penetration level in the system during normal

operating condition is also analyzed. The later study illustrates that the PV penetration

level and the placement of PV sources play crucial roles in determining the stability of power

transmission systems.

Given increasing uncertainties in power transmission systems, there is a need to seek an al-

ternative to deterministic planning approach because it inherently lacks capability to cover

all the uncertainties. One practical alternative is the probabilistic planning approach. In

probabilistic planning approach, an analysis is made with a wide variety of scenarios by

considering the probability of occurrence of each scenario and the probability of contingen-

cies. Then, the severity of the contingencies risk associated with each planning practice

is calculated. However, due to the lack of techniques and tools to select wide varieties of

scenarios along with their probability of occurrence, the probabilistic transmission planning

approach has not been implemented in real-world power transmission systems. This thesis

presents a technique that can select wide varieties of scenarios along with their probability

of occurrence to facilitate probabilistic planning in Electricity Reliability Council of Texas

(ERCOT) systems.

iii



Durga Aryal

GENERAL AUDIENCE ABSTRACT

Reliability of power transmission systems are threatened due to the increasing uncertainties

arising from penetration of renewable energy sources, load growth, energy de-regulation and

changing standards. Stability issues become more prevalent than in past due to increasing

load growth as the demand for reactive power increases. Several researchers have been

studying the impact of increased load growth and increased penetration of renewables on

the dynamic stability of the distribution system. However, far less emphasis has been given to

the power transmission system. This thesis presents the transient stability analysis of power

transmission systems during overloading conditions. Our study also facilitates identification

of weak areas of the transmission system during overloading condition. In addition, the

impact of replacing conventional synchronous generator by Photovoltaics (PV) on voltage

stability of the system is also analyzed.

With increasing uncertainties in transmission systems, it is necessary to carefully analyze a

wide variety of scenarios while planning the system. The current approach to transmission

planning i.e., the deterministic approach does not sufficiently cover all the uncertainties.

This has imposed the need for the probabilistic transmission planning approach where the

overall system is planned based on the analysis of wide varieties of scenarios. In addition, by

considering the probability of occurrence of a scenario, the probability of contingencies and

severity of contingencies risk associated with each planning practice is calculated. However,

there is no well-established approach that is capable of selecting wide varieties of scenarios

based on their probability of occurrence. Due to this limitation, probabilistic approach is

not widely implemented in real-world power transmission systems. To address this issue,

this thesis presents a new technique, based on K-means clustering, to select scenarios based

on their probability of occurrence.

Dedication

To my parents.

v

Acknowledgments

I would like to express my deepest gratitude towards my research advisor Dr. Robert Broad-

water for his valuable guidance and support throughout my research. Words are not enough

to express my appreciation for his encouragement. I would also like to express my sincere

appreciation towards Dr. Jaime De La Ree and Dr. Virgilio Centeno for their support.

On a personal side, I would like to express my deep respect and love towards my grandparents,

parents, husband, brothers, sisters-in-law and my relatives for constantly supporting and

encouraging in various ups and downs of my life. Without the support of my parents in

every aspect, I would have never been able to make it to this day. I really appreciate my

husband for helping and believing in me. His motivation and push always held me high and

kept me going, many thanks to him.

Lastly, I would like to thank my intern supervisor Sun Wook Kang for his continuous guidance

and support throughout my intern project which is also the part of this thesis.

vi

Contents

1 Introduction 1

1.1 An Overview of Composite Power Transmission Systems . . . . . . . . . . . 1

1.2 Background and Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3 Summary of Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.3.1 Stability Analysis of Power Transmission Systems Subject to Utility-

Scale PV Penetration . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.3.2 A New Technique for Selecting Scenarios Probabilistically to Facilitate

Probabilistic Transmission Planning . . . . . . . . . . . . . . . . . . . 8

1.4 Thesis Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2 Stability Analysis of Power Transmission Systems 10

2.1 Intoduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.2.1 Power System Stability . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.2.2 System Model and Assumptions . . . . . . . . . . . . . . . . . . . . . 13

2.3 Stability Analysis Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . 15

vii

2.3.1 Steady State Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.3.2 Dynamic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.4 Case Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.4.1 Case Studies Showing the Use of Steady State Stability Analysis in

Wide Areas of Power System . . . . . . . . . . . . . . . . . . . . . . 21

2.4.2 Trasient Stability Analysis on IEEE 14 Bus System by Replacing Con-

ventional Synchronous Generator with PV . . . . . . . . . . . . . . . 24

2.4.3 Voltage Stability Analysis on IEEE 14 Bus Transmission System Fol-

lowing a Combination of Small and Large Disturbance . . . . . . . . 32

2.5 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3 Probabilistic Transmission Planning 38

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.2 Background and Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.3 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.3.1 Transmission Planning Approaches . . . . . . . . . . . . . . . . . . . 42

3.3.2 Overview of Major Transmission Planning Activities . . . . . . . . . 43

3.3.3 Framework of Probabilistic Transmission Planning . . . . . . . . . . . 45

3.3.4 Challenges in Probabilistic Transmission Planning . . . . . . . . . . . 47

3.4 Framework of Probabilistic Transmission Planning at ERCOT . . . . . . . . 48

3.4.1 Scenario Development . . . . . . . . . . . . . . . . . . . . . . . . . . 49

3.4.2 Scenario Selection and Case Study Development . . . . . . . . . . . . 50

3.4.3 Probabilistic Risk Analysis . . . . . . . . . . . . . . . . . . . . . . . . 53

viii

3.5 Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

3.5.1 System Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

3.5.2 Results and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . 55

3.6 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

4 Conclusions and Future Work 61

4.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

4.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

Bibliography 63

ix

List of Figures

2.1 IEEE-14 transmission system modeled in DEW . . . . . . . . . . . . . . . . 15

2.2 Overall model for PV system . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.3 Steady-state voltage stability curve at bus 3 with and without PV in the system 22

2.4 Stability margin of line 2-3 with and without PV integration at bus 3 . . . . 22



2.7 Relative rotor angle plot of machine at bus 6 following a fault at bus 3 with

and without PV in the system . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.8 Relative rotor angle plot of machine at bus 6 following a fault at bus 3 with

and without PV in the system . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.9 Relative rotor angle plot for generator at bus 8 following fault at bus 3 and

bus 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

2.10 Relative rotor angle plot for generator at bus 6 during various PV penetration

level in the system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.11 Terminal voltage at bus 1 during various PV penetration levels . . . . . . . . 30

2.12 Terminal voltage at bus 1 during various PV penetration levels . . . . . . . . 31

x

2.13 stability margin plot for the lines connected to bus 2 and 3 at increasing

loading conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

2.14 terminal voltage at bus 1 following the fault in line 2-3 during normal and

heavily loaded system conditions . . . . . . . . . . . . . . . . . . . . . . . . 34

2.15 steady state line stability margin plot at increasing loading conditions by

tripping the line 2-3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

2.16 terminal voltage at bus 1 following the fault in line 2-3 during heavily loaded

system conditions by adjusting generator reactive limits at bus 3 . . . . . . . 36

3.1 Block diagram of probabilistic transmission planning . . . . . . . . . . . . . 49

3.2 Block diagram of k-means clustering . . . . . . . . . . . . . . . . . . . . . . 51

3.3 Clustering entire system conditions into four clusters . . . . . . . . . . . . . 55

3.4 Elbow implementation to find the optimal value of clusters . . . . . . . . . . 56

3.5 System conditions sampled from entire state space . . . . . . . . . . . . . . . 57

xi

List of Tables

2.1 Summary of the IEEE 14 bus transmission systems . . . . . . . . . . . . . . 14

2.2 Dynamic models of synchronous generators for IEEE 14 bus system . . . . . 19

3.1 Results of 16 sampled scenarios . . . . . . . . . . . . . . . . . . . . . . . . . 58

xii

xiii

Chapter 1

Introduction

1.1 An Overview of Composite Power Transmission

Systems

A composite power system is the combination of generation, transmission, and distribution

resources. Power is generated normally at 11 kV to 33 kV at power plants or generating

sites, then using a step-up transformer, voltage is stepped up to 69 kV and above depending

upon the line ratings and is transmitted to the distribution substation via transmission

lines. Transmission lines carry electricity at voltages of 69 kV or greater over relatively long

distances, usually from generating station to main substations. An electrical power system at

the transmission level consists of synchronous generators, transformers for stepping up and

down voltages, high voltage transmission lines for transferring power, compensating devices

and loads.

Electric power transmission is the bulk movement of energy from a generation site to an

electrical substation. The interconnected lines known as transmission network facilitate this

flow. Transmission network usually carries electric power at very high voltages to reduce the

loss in lines due to I2R loss, that is to reduce resistive losses over a long distance in the wiring.

1

Durga Aryal Chapter 1. Introduction 2

The transmission system is operated at a voltage of 69 kV or greater and mainly consists

of transmission towers, power lines (transmission lines), and substations and is the major

component of a bulk power system. The power transmission system consists of multiple

power generation sources in contrast to the distribution system having a single source of

power. In addition to this, power transmission system being farther to load has low (RX

)

resistance to reactance ratio. Due to these characteristics, the power transmission system

possess different behavior and dynamics than power distribution systems. The transmission

system is a very complex interconnected network that requires the sophisticated planning

scheme to build the reliable, secure and economic system capable of transmitting the bulk

power at high voltages continuously.

It is not as easy as it sounds to transport power to the consumers through the existing

interconnected network. Network planners have to face a lot of challenges and issues in the

process of supplying power to the end users. Maintaining reliability and delivering quality

electricity has been an issue in this huge interconnected network lately. Due to increasing

load demand and increasing penetration of inverter-based generation in power transmission

systems, stability issues are becoming more prevalent than in the past. Solar PV and Wind

has become the major portion of grid among utility-scale renewable energy power plants,

which has caused various stability issues in the grid, especially during contingent conditions

in the system due to lack of necessary inertia to damp system oscillations. Therefore, careful

design considerations and system upgrades are needed for power transmission systems to

enhance the capacity and maintain acceptable reliability levels. In the context of the United

States, North American Electric Reliability Corporation (NERC) handles all the reliabil-

ity and adequacy issues related to bulk power transmission systems. National Electricity

Reliability Corporation (NERC) defines reliability as follows [1]:

• If your light comes on, reliability was met.

• If a major line is lost and the system remains stable, reliability was met.

• If a generation source is lost and the system remains stable, reliability was met.


Pertaining to the reliability standards of transmission planning defined by NERC [2], a

detailed study on voltage stability issues caused by uncertainties in transmission systems is

performed in this thesis. The effect of utility-scale penetration of PV on voltage stability

is shown by doing dynamic simulations in PSSE during various system conditions. Voltage

stability issues caused by a combination of small and large disturbances in transmission

systems is also shown. In addition to this, an approach that can identify weak components

in the system is discussed. Various simulations are made to show how removing the weak

components can help in improving the stability of the system.

Also with growing uncertainties in the system, the current approach of transmission planning

does not sufficiently cover the system impacts and risk associated with those uncertainties.

Therefore, a different or enhanced approach to transmission planning is needed. With this

consideration, a different framework of probabilistic transmission planning was developed at

ERCOT which is also presented in this thesis.

1.2 Background and Motivation

The power transmission system is frequently experiencing new power flow patterns due to

increasing uncertainties in the system. The main causes of uncertainties are the increasing

load demand, energy de-regulation, penetration of renewables in the grid, and changing

standards. Due to these uncertainties stability issues are becoming more prevalent than in

past. Stability issues are caused by operating system elements much closer to their transfer

limits during load growth, due to the large disturbances like loss of generation, line and

bus faults, etc. Moreover, increasing penetration of renewables in the system has added

stability issues due to its unique dynamics [3]. Since wind turbines and PV modules are

integrated into the system with power-electronic converters, it is hard for them to catch up

with changing frequency and change its generation to reduce or damp the oscillations caused

due to heavy disturbances.


Renewable energy sources like photovoltaic (PV), wind, hydro, etc. are integrated into com-

posite power transmission systems in utility-scale to replace conventional fossil fuel plants

and to address the increasing demand of load with increasing population. Since PV systems

are easy and cheap to install than other renewable sources, they are being integrated into

large scale worldwide. By the end of 2017, global solar installation reached 401 GW and is

expected to increase by 43 % until 2022. The increased PV penetration in utility-scale in

power transmission systems can significantly affect the steady state as well as transient sta-

bility of the system due to their distinct characteristics than that of conventional synchronous

machines [4].

With the increasing trend of penetrating PV to make a sustainable grid, today’s network

exhibits various grid modernization, which is the future of the grid. The part of grid mod-

ernization is the penetration of renewables in the grid to replace the conventional fossil fuel

generation supporting the bi-directional power flow in the grid and making it smart. Due

to the lack of necessary attributes to meet the demand in today’s network, grid modern-

ization is inevitable. Department of energy is working with public and private partners to

develop the concepts, tools, and technologies needed to measure, analyze, predict, protect,

and control the grid of the future [5]. Penetration of renewables particularly inverter-based

generation influence the dynamic stability of the system largely. It can be either beneficial

or detrimental for the normal operation of the system depending upon the penetration level

and penetrated system, which is discussed in the later section.

Grid modernization with the installation of utility-scale PV on the system affects the relia-

bility, security, and robustness of the power transmission systems. However, installation of

PV on distribution system or in small scale can be treated as the negative load as they have

small outputs with no reactive capability and causes fewer stability issues than integrating

into transmission level. On transmission level, a response of the system accompanied by a

fault worsen due to the unique dynamics of PV and not being able to respond to frequency

changes in the system as synchronous generators due to lack of inertia.


Effects of photovoltaics on distribution systems have been analyzed and studied by many

researchers. Reference [6] discusses the impact of a grid-connected PV system on the har-

monic distortion of distribution systems. Reference [7] focuses on imbalance in loading and

the voltage regulation on the distribution feeders. Reference [8] discusses the good side of

injecting power by PV plant modules by focusing on voltage profile improvement and loss

reduction. However, the effects of PV penetration on transmission has not been fully iden-

tified. It has been shown [ref 11 of paper] that, based upon the amount of PV penetration

on transmission systems, transient voltages of the system get better or worse.

The effect of PV penetration on transmission systems requires comprehensive static and

dynamic analyses. Utility-scale PV also have reactive power capability, so they are modeled

like conventional generators for static analysis and for dynamic analysis overall system models

for a converter, and electrical control is required. Transient stability analysis and control is

a need with the integration of photovoltaics in large scale.

Similarly, load demand is increasing day-by-day due with increasing population. Due to the

increasing load demand, a system is operating closer to their transfer limits. These condi-

tions, caused by natural load growth with a significant increase in long-distance transmission

usage, results in heavy transmission circuits loading, depressed bus voltage magnitudes, and

closer proximity to voltage instability [9]. Voltage instability has been reported as the main

reason for the blackout as mentioned in [10, 11]. Thus, it is very necessary to do voltage

stability analysis during various operating conditions of the system to gain valuable insights

while planning power transmission systems.

In addition to the stability issues, increasing uncertainties have necessitated the incorporation

of probabilistic or risk-based planning into existing transmission planning approach to ensure

secure and reliable operating condition of power transmission systems. Traditional method

of transmission planning i.e. N-1 deterministic planning approach does not incorporate risk

management into planning practice as it only considers the severity of event and not the

likelihood. For example, consequences of single component failures are analyzed but their


probabilities are usually ignored, and also multiple component failures are not considered

while planning the system [12]. If all the contingencies in the system are treated equally,

system planning is not as practical as in reality; different contingencies have a different

chance of occurring. For example, a long line is subjected to disturbances frequently than a

short line.

Moreover, deterministic N-1 planning criteria are based on worst case study [12]. In the

deterministic approach by analyzing the few worst cases of summer-peak and off-peak and

the severity of the contingencies during those cases, the overall system is planned. Neither,

it is certain that some serious issues in the system occur during those conditions nor it is

certain that they are more probable. Thus, the system might be at risk in terms of reliability

and economy. Therefore, wide varieties of representative scenarios generated by considering

all the uncertainties in the system should be analyzed and the probability, as well as severity

of all the contingent conditions that might happen during those scenarios, must be evaluated

before planning the system. In addition, if the probability of occurrence of all those scenarios

is known, the risk associated with each planning practice can be calculated.

The Electric Power Research Institute (EPRI) has been involved in risk-based planning ap-

proach since 2014 [13]. It is the multi-year R&D project, Various utilities are also involved

in this project. EPRI in collaboration with the Electric Reliability Council of Texas (ER-

COT) held the case study to test the use of probabilistic planning methods in ERCOT

transmission planning [14]. Reference [12] discusses British Columbia Transmission Corpo-

ration’s (BCTC) practice towards probabilistic transmission planning along with a different

framework of probabilistic transmission planning.

The load and generation dispatch scenario of peak and off-peak conditions might be less prob-

able in the system. Therefore, making analysis with only those scenarios and planning the

system on the basis of those analyses can lead to either over-investment or under-investment

for any transmission project as described in [12]. Thus, it is important to carefully generate

and select wide varieties of load and generation dispatch scenarios along with their probabil-


ity of occurrence to incorporate risk in planning practice. This thesis presents a technique

based on machine learning algorithm that is capable of selecting wide varieties of scenarios

along with their probability of occurrence.

1.3 Summary of Contributions

This thesis presents:

• Stability analysis of power transmission systems subject to the replacement of syn-

chronous generators with PV followed by large disturbance.

• Stability analysis of power transmission systems subject to small and large disturbances

and correlating the results of steady state and dynamic studies.

• A new technique to select scenarios along with their probability of occurrence to im-

plement probabilistic transmission planning method in ERCOT systems.

1.3.1 Stability Analysis of Power Transmission Systems Subject

to Utility-Scale PV Penetration

Due to the increasing trend of penetrating renewables in the grid to replace conventional

fossil fuel generation, the power system is experiencing a change in dynamic and operational

characteristics. In this thesis, the stability of a power transmission system is analyzed

when the conventional synchronous generators are replaced with PV systems as shown in

Section 2. The stability of the system during various transients largely depends upon the

initial operating conditions and the severity of disturbances. Therefore, the effect of PV

penetration on the system during different operating conditions in the system for different

levels of severity is evaluated by performing dynamic simulations in PSSE. The results of


different cases are compared with the base case results when there is no PV penetration at

all.

It is investigated that, due to reduced inertia in the system with PV penetration, some of the

generators in critical areas should be kept in service. In case when synchronous generators

are needed to be tripped, suitable measures like synchronous condensers need to be installed

to maintain sufficient damping when there is a disturbance in the system.

In addition, it is shown that even if the PV is operated for local V/Q control functionality,

depending upon the severity and location of disturbances, the system might or might not be

able to restore stability.

Various small and large disturbances in the system affect the stability of the power transmis-

sion system. Analyzing the effect of those disturbances in the system is imperative for the

reliable and secure operation of the system. With the increasing uncertainties, it is neces-

sary to study stability issue caused by a combination of a small and large disturbance. This

thesis, therefore, presents a case study in Chapter 2 for transmission systems where small

and large disturbances are applied to transmission systems at the same time. The voltage

response of the system is recorded for a time frame of 20 seconds and necessary measures to

improve the stability of the system are discussed.

Also, steady state line stability margins are calculated for small disturbances or at increasing

loading conditions to identify the weak links in the system that needs system adjustments

when there is a large disturbance to improve overall system stability. Steady-state line

stability is calculated using the approach described in Section 2.3.1.

1.3.2 A New Technique for Selecting Scenarios Probabilistically

to Facilitate Probabilistic Transmission Planning

Due to the growing uncertainties in the system, the traditional deterministic approach needs

enhancement and modifications as discussed in Section 1.2 by probabilistic planning ap-


proach. The main idea behind probabilistic planning is to make analysis with wide varieties

of scenarios to cover various system uncertainties and to incorporate risk management into

planning practice by considering the likelihood of scenario and likelihood and severity of

the events happening for that scenario. The main concern is how to develop and choose

those scenarios along with the probability of occurrence. To address this problem, a new

technique based on a machine learning algorithm that is developed for ERCOT systems is

presented in this thesis that is capable of selecting the scenarios along with their probability

of occurrence.

1.4 Thesis Organization

The rest of the thesis is organized as follows. Chapter 2 discusses the stability analysis of

IEEE 14 bus transmission system. This chapter focuses on stability issues caused by penetra-

tion of utility-scale PV. In addition, the transient and steady-state stability of transmission

systems subject to small and large disturbances are analyzed. Chapter 3 discusses a new

technique for selecting scenarios in probabilistic transmission planning. Chapter 4 concludes

the overall thesis and provides new directions for the research presented in this thesis.

Chapter 2

Stability Analysis of Power

Transmission Systems

2.1 Intoduction

Stability analysis of power transmission systems includes identifying key factors leading to

instability during various operating conditions of the system accompanied by small and

large disturbances, and finding the possible solutions to improve the response. Power system

stability is the ability of power systems to remain in operating equilibrium following small or

large disturbances. Power system stability can be classified as voltage, frequency, and angle

stability.

Rotor angle stability is one of the critical factors affecting the reliable and secure operation

of power transmission systems. Stability issues are introduced in the system due to load

growth, due to the penetration of renewables in the system, and due to bus and line faults.

Stability issues, if not analyzed properly and addressed in time, can lead to voltage collapse

in the system.

The remainder of this chapter is organized as follows. In Section 2.2, a brief introduction

10

Durga Aryal Chapter 2. Stability Analysis of Power Transmission Systems 11

of the power system, stability is given along with the types angle stability depending upon

the disturbances level. In Section 2.3, detailed approaches for analyzing steady state and

dynamic stability are presented. In Section 2.4, the topology of the system taken for our

study is described along with the data of generation, load, and branches. This section also

presents the case study and numerical results. Important conclusions are presented in Section

2.5 along with the future work.

2.2 Preliminaries

2.2.1 Power System Stability

Power system stability is getting a lot of attention due to highly stressed interconnected net-

work as a result of heavier loading and frequent disturbances. Power system stability is the

ability of a power system to remain in operating equilibrium during normal operating con-

dition and to regain an acceptable state of equilibrium after being subjected to disturbances

[15]. Despite using Automatic Voltage Regulators (AVR) for voltage control, generator reac-

tive power limit during heavy loading conditions, system’s inability to respond to frequency

changes during bus and line faults with inverter-based generations penetration are key fac-

tors for instability in the system. Instability arises from the attempt of load dynamics to

restore power consumption that is beyond the capability of the combined transmission and

generation systems [16].

In an interconnected power system, the rotor angle stability of each synchronous machine

dictates the ability to restore equilibrium [17]. PV being asynchronous in nature change

the dynamics of an overall system. The process of maintaining synchronism by conventional

synchronous generators is associated with synchronizing and damping torque in the system.

Rotor angle stability of the system can be classified into two broad categories:

• Transient stability


• Small signal stability

Transient Stability

Transient stability is associated with a system’s capability to maintain synchronism following

large disturbances, like bus faults, or loss of generation. As described in [15], determination

of transient and small-signal stability requires the examination of the nonlinear dynamic

performance of a system over a time-period. Therefore, dynamic simulations are required to

study the behavior of the system following the large disturbances. Transient stability study

is performed in this thesis by applying three-phase faults at a bus having a synchronous

generator. As mentioned in Section 2.1 there are five generators in the system, at buses 1,

2, 3, 6 and 8. A fault is applied at each of the buses except buses 1 and 2 during normal

loading conditions with PV at various locations, the rotor angle and the voltage response

are recorded for each scenario. The clearing time used to conduct the study is 4 cycles.

Following large disturbances, the restoring forces that bring the position of the affected

generators back to the nominal values are related to the interaction between synchronizing

forces and total system inertia [17]. Transient stability depends on both the initial oper-

ating condition of the system and severity of the disturbance. In the case of synchronous

machines, when there is a large disturbance in the system, it causes a corresponding increase

in rotor angle which causes the electrical load to increase. This increase in load provides a

synchronizing torque to the rotor and helps to bring the rotor back to synchronism [17].

However, in the case of inverter-based interfaces, the electrical power generated is controlled

by a current control loop of a converter. When the large disturbance, like a bus fault, occurs

in the system, the converter quickly controls the unit to produce the same power as before.

As a result, the potential inertial response is curtailed and the synchronizing torque is not

available, which greatly affects the system dynamic response. In addition, the stability of

the system with PV penetration is affected by the location and level of PV penetration in

the system. 2.4.2.


Small Signal Stability

Small signal stability is associated with a system’s ability to maintain synchronism following

the small disturbances in the system, like load growth. Since the loading of power systems

continuously increases in the developed and de-regulated energy market, it is necessary to

continuously monitor rotor angles of all machines and voltages at each bus in the system

to ensure a secure system. Small-disturbance voltage stability evaluation is sufficient with

a static analysis tool. In fact, both the static and dynamic analysis tools give accurate

evaluations even during small disturbances. But, when a small disturbance is followed by

a large disturbance, dynamic analysis is a must. Steady state analysis during the large

disturbance can facilitate dynamic studies, which is shown in Section 2.4.3.

Stability analysis in a steady state following a small disturbance can be done using dif-

ferent power flow approaches. Power flow methods are considered as steady-state analysis

methods, that include continuation power flow method [18], graph trace analysis method

[19], standard power flow method [20], and singular decomposition methods [20]. Since the

stability of power systems cannot be fully guaranteed with steady-state studies, dynamic

analysis followed by steady analysis is necessary to see the system’s response during various

disturbances in the system. Different scenarios of stressed system conditions are developed

for IEEE 14 bus transmission systems to see voltage response during those conditions by

doing dynamic simulations in PSSE.

2.2.2 System Model and Assumptions

The IEEE 14 bus transmission network was taken for our study. This test case represents

a portion of North American Electric Power Systems in Midwestern US [6]. This is the

interconnected power transmission network having both high and low voltage buses. To

represent it as a typical transmission system, all high voltage buses are set to 345 kV, and

all the low voltage buses are set to 138 kV. Below is the overall summary of the network with


the diagram of the network modeled in Distributed Engineering Workstation (DEW). There

are five synchronous generators in the system at buses 1, 2, 3, 6 and 8. A constant current

load model is assumed for all the loads in the network. The single line diagram of the IEEE

14 bus transmission system, as modeled in DEW, is shown in Figure 2.1. Bus numbers are

marked by numbers as shown in Figure 2.1.

Total generation MW 272.4

MVar 78.5

Total load MW 259

MVar 73.5

Total number of generators 5

Total number of buses 14

Total number of lines 16

Total transformers 4

Table 2.1: Summary of the IEEE 14 bus transmission systems


Figure 2.1: IEEE-14 transmission system modeled in DEW

2.3 Stability Analysis Techniques

2.3.1 Steady State Analysis

Steady state stability analysis is done by solving the algebraic equations for power systems

and is more computationally efficient than dynamic studies. Although the dynamic analy-

sis gives more detailed results than steady-state analysis, the steady-state voltage stability

analysis provides useful information. In steady state voltage stability analysis, it is assumed


that all dynamics have died out [9]. Power flow analysis tools have been developed for

steady state stability analysis as discussed in [18, 19, 20]. In this thesis, steady state line

stability margin is calculated using an approach described in [21] to show that steady state

line stability margins help identify weak links in the system. This is confirmed by dynamic

analysis.

Steady state voltage stability analysis is performed by solving the power flow for a series of

time points by increasing the load at each time step. The loading condition at which power

flow does not converge is considered as a steady state stability limit of the system. Reference

[21] discusses the approach for finding the steady state voltage at particular sections in single

phase radial distribution networks, and which is extended to multiphase transmission systems

in our case.

The mathematical formulation used in [21] is discussed here to show the approach used in the

calculation of steady-state voltage stability. A typical section of the balanced transmission

system between two buses, α and β, is taken. Let us assume that Vα and Vβ are the input

and load end voltages, Ik is the line current in that section and YK is the admittance of that

line. Four types of actual or equivalent loads are represented at the end of the line section:

• Actual constant power load

• Actual impedance type load represented by its admittance as YLK

• Equivalent constant power load STK representing the sum of all loads connected to the

downstream side of the line section and

• Equivalent constant power load SSK representing the sum of all the system losses in

all the sections connected to the downstream of that line section

Load flow equations for this section are represented as,

Sk = SCk + STk + SSk = Pk + jQk


The power flow at the ending bus β is given by:

VβIk∗ = Sk + |Vβ|2YLK∗

And the line current is given by:

Ik = Yk(Vα − Vβ)

Substituting the conjugate of Ik in the equation 2 we get, Sk.

Separating Sk into real and imaginary part i.e. Pk and Qk, which is the sum of all loads,

losses connected to the downstream side of that section along with actual constant power

load connected.

Adding and squaring the resulting equations of Pk and Qk, we get the quadratic equation of

Vβ as:

A|Vβ|4 +B|Vβ|2 + C = 0

Solving the above quadratic equation we get |Vβ|2 in terms of A, B and C.

|Vβ|2 =−B ± (B2 − 4AC)

12

2A

Above equation gives the lower and higher values of Vβ for different loading conditions which

helps to plot the steady-state voltage stability curves. The plus sign results in reasonable

voltage magnitudes in normal operating conditions and negative sign results in voltage mag-

nitude that are very low. For |Vβ|2 to be real, the following must be satisfied,

B24AC ≥ 0

Since A > 0 and C > 0, B24AC.

Also, B0.

For D to be positive,

2(AC)12 ≤ B ≤ 0


If the line loading is too large, above equation will fail to satisfy which might happen during

system expansion study. Thus, we can directly check if the system condition will provide

real solutions to the voltages or not.

On the other hand, the above equation can be used to calculate the steady state stability

margin for each of the components in the system. Stability margin of components will be

0 if the above conditions fail to be satisfied. Stability margin is another factor, which also

helps to determine the robustness or load handling capability of the system. Stability margin

provides the measure of how far the operating point of the network is from voltage collapse.

It varies from 1 to 0, where at 0 stability is lost. Components having less stability margin

means less robust, meaning they have low load handling capability, and lines having high

stability margin means more robust, which allows for larger loads. Stability margin normally

decreases with system changes like load growth, line loss, which is also shown in this work.

Steady state voltage stability analysis is performed to evaluate the maximum amount of

load the system can handle without causing stability issues. For that, quasi-static time se-

ries power flow analysis is done at an increased loading condition. These kind of studies are

very important while doing interconnection studies to analyze system impacts and discover

mitigation alternatives. Steady-state line stability margins are plotted to analyze and un-

derstand the system’s response to increasing load for IEEE 14 bus transmission systems to

identify weak links in the system as explained in Section 2.2.2.

2.3.2 Dynamic Analysis

The time domain simulations (i.e., dynamic analysis) capture the events and chronology lead-

ing to voltage instability. Dynamic analysis provides us with useful information concerning

different factors leading to instability in the system and also examines how the steady-state

equilibrium point is reached. The general structure of the system model for transient stabil-

ity analysis is similar to that for voltage stability analysis [15]. Dynamic analysis requires

appropriate modeling for all the equipment, such as generators, exciters, governors, loads,


transmission lines. The characteristics of this equipment highly influence the instability of

the system. But, in this thesis, we are focusing on the effects of different small and large

disturbances on transient stability rather, than the effect of system models and characteris-

tics. Dynamic analysis is useful for the detailed study of specific voltage collapse situations,

coordination of protection and controls, and testing of remedial measures [15]. On the other

hand, proper use of static analysis tools can give an idea of a wide range of operating con-

ditions and can be useful in identifying key contributing factors affecting stability, which is

also shown in this thesis.

Dynamic simulations are done mainly to study the effect of large-scale PV penetration on

transmission systems during the various level of severe disturbances. Dynamic simulations

are also done to understand the effect of a combination of small and large disturbances in

the system.

Dynamic simulations are done using PSSE. The steps for stability analysis in PSSE can be

found in Reference [22]. For overall modeling of the synchronous generator, generic round

rotor synchronous generator model (GENROU) is used, IEEE type 1 excitation control

systems are used for the voltage regulation of the power network and steam turbine governor

TGOV1 governor model for balancing active power demand by adjusting the frequency.

Table 2.2 shows the generator group combination used for the synchronous generator in our

case.

Bus Generator group combination

1 GENROU + IEEET1 + TGOV1





Table 2.2: Dynamic models of synchronous generators for IEEE 14 bus system


In case of PV system modeling, dynamics related to DC side of inverter (i.e., PV array

dynamics, inverter DC link, and voltage regulator) are ignored, as mentioned in the WECC

guide [23], because time constants associated with these dynamics may in some cases be too

short to ensure reliable numerical stability for the simulation time steps used in many bulk

system dynamics cases.

The overall model consists of generator or converter model REGCA to provide current injec-

tions into the network, an electrical control mode REECB for local active and reactive power

control, and an optional plant controller model (REPCA) to allow for plant-level active and

reactive power control.

We have used REGCA and REECB for our modeling. Current injection (included in REGCA

model) injects real and reactive components of inverter current into the external network

during the network solution in response to real and reactive current commands. The REECB

model has been used as an electrical control mode for local active and reactive power control.

The local active power control subsystem provides the active current command to the current

injection model. The active current in this control is derived from reference active power

and the inverter terminal voltage determined in the network solution. The reference active

power is the initial active power from the solved power flow case. Similarly, local reactive

power control provides the reactive current command to the current injection model. The

reactive current command shall be subject to current limiting, with user-selectable priority

between active and reactive current.


Figure 2.2: Overall model for PV system

For PVs, we have used the control mode 2, where the Q limits are based on the power factor

available in PSSE. It sets the reactive power limits on the basis of power factor and active

power from solved power flow case. Operating the PV system in this mode, it participates in

voltage control. For this functionality, models needed are REGCA and REECB as mentioned

in [23].

2.4 Case Studies

2.4.1 Case Studies Showing the Use of Steady State Stability

Analysis in Wide Areas of Power System

The IEEE-14 bus system is taken for analyzing load handling capability using steady state

stability curves of the bus and line stability margins. In our analysis, additional PV of

10 MW is integrated to the most critical bus in the system i.e. the bus with the highest

amount of load connected and it is the bus 3. Three interconnected lines 2-3, 2-4, and 3-4

are taken for the analysis. The overall system is modeled in DEW for steady-state analysis

that uses the Graph Trace Analysis (GTA) based power flow algorithm to solve the system


Figure 2.3: Steady-state voltage stability curve at bus 3 with and without PV in the system

Figure 2.4: Stability margin of line 2-3 with and without PV integration at bus 3





[19]. GTA based power flow approach can solve a very large composite transmission and

distribution systems [24]. It is computationally very efficient and accurate. [19] shows the

comparison of GTA based power flow approach with other power slow software like Grid

LAB-D, Open DSS, ATP, etc. using ten robustness testing circuits where GTA was found

to be computationally efficient and accurate even for larger systems.

For the analysis, load in the system was uniformly increased by 1% at each second for six

minutes and the quasi-static power flow analysis is performed at each time point i.e. the

system is solved for 360 loading conditions i.e. system load is increased by 360%. This

case study highlights the importance of quasi-static power flow analysis in power system

simulation studies. The steady-state voltage stability curve was plotted for bus 3 with and

without PV penetration as shown in Figure 2.3. We can see that integrating PV in the system

increased the steady-state stability limit of the bus, which is equivalent to the amount of

PV penetration. In our case, about 4% of PV was integrated into bus 3 with respect to the

total load in the system. Although PV penetration enhanced the steady state stability limit

of that bus, stability margin of neighboring lines is negatively impacted. Stability margin

of line 2-4 decreased with PV penetration at bus 3, which infers that the load handling

capability of the line 2-4 decreases with PV penetration.

PV integration on the system can negatively impact the system in steady state too as shown

in Figures 2.5 and 2.6. Dynamic simulations are done in IEEE 14 bus test case by replacing

the conventional synchronous generator at bus 2 with PV to see the impact of PV penetration

on transient stability of the system as described in Section 2.4.2.

2.4.2 Trasient Stability Analysis on IEEE 14 Bus System by Re-

placing Conventional Synchronous Generator with PV

System stability is largely affected by the penetration of renewables, particularly with the

inverter-based generation like photovoltaics in the system. Solar PV being asynchronous in


nature change the system dynamics with respect to the interaction of synchronous machine

rotors among themselves. It is because of the mechanism associated with the generation and

interfaces with the bulk power systems. Although it has a lot of positive sides as explained

in [4], stability issues are in fact increasing. This is because of the absence of rotating

mass that responds to the frequency change in the system quickly to bring the voltage to

a specified region of voltage level. Depending upon the location and severity of the faults,

remaining synchronous generators are adversely or favorably affected with PV penetration

on the system.

Reduced inertia in the system affects the system stability largely when there is a huge

disturbance like bus faults in the system leading to generation loss, especially when such

fault occurs nearby the renewable generations. A similar case is simulated here. For that,

a synchronous generator at bus 2 in IEEE 14 bus transmission system 2.1 is replaced with

PV model as described in Section 2.2.2. The functionality for PV, in this case, is local

coordinated V/Q control with REGCA as current injection model that injects active and

reactive power to the grid. RECCB is used to give active and reactive power control command

to REGCA. Since control mode chosen is +-Q limits based on power factor, so reactive control

command will be given by RECCB to set the reactive limits based on inverter power factor

and active power on solved power flow case. At first, dynamic simulation is performed for 10

seconds during the initial operating conditions of the system. A bus fault is applied at bus

number 3 and a generator connected to that bus is tripped as an action of protective relaying

scheme. The fault is cleared at the bus after 4 cycles and dynamic simulation is performed

for a couple of seconds as shown by the green curve in Figure 2.7. A similar analysis is also

performed for normal system conditions with no PV in the system as shown by the red curve

in Figure 2.7.


Figure 2.7: Relative rotor angle plot of machine at bus 6 following a fault at bus 3 with and

without PV in the system


Figure 2.8: Relative rotor angle plot of machine at bus 6 following a fault at bus 3 with and

without PV in the system

These case studies show that with PV replacing conventional synchronous generators at bus

2 that is at 15 % PV penetration level, there is a large excursion in rotor angle as shown by

green curve compared to no PV in the system as shown by the red curve in above plots.

Similarly, another case study is done by applying a fault at bus 6 to see the difference in

response of the system with fault at different locations as shown in Figure 2.9.


Figure 2.9: Relative rotor angle plot for generator at bus 8 following fault at bus 3 and bus

6

This case study shows that the fault located nearby PV penetration area cause large ex-

cursions in rotor angle than that of a fault located at farther distance. From these case

studies, it has been noted that the location of the faults impacts the system stability largely.

If the disturbance is located near to generators whose synchronizing capability has reduced

due to injection of PV, the system will be adversely affected. Whereas, if the faults are

located far enough from PV bus then system stability is not affected even during the heavier

disturbances.

In addition to these case studies, another case study is done by increasing PV penetration

level in the system to 30 %. For this, synchronous generators at bus 2 and 3 were replaced

with PV having some real power and less reactive power capability. The additional reactive

capability is adjusted to other generators in the system to produce the same reactive power

as in the base case. When PV replaces two synchronous generators in the system, the system


goes to dynamically unstable state as depicted by green curve in rotor angle plot 2.10 and

terminal voltage plot 2.11.

Figure 2.10: Relative rotor angle plot for generator at bus 6 during various PV penetration

level in the system


Figure 2.11: Terminal voltage at bus 1 during various PV penetration levels

From this case study, it has been noted that in absence of sufficient damping as a result

of replacing the synchronous generator with PV, some synchronous machines at critical

buses should be kept in service and not fully displaced by PV generators. If it is a need to

displace synchronous generator, then additional Var compensating devices like synchronous

condensers should be installed to maintain sufficient damping of low-frequency oscillations

in critical buses in the system.

Another case study is done by replacing synchronous generators at bus 2 and 6 instead of bus

2 and 3 as in previous case study. With PV at bus 2 and 6 that is at 30 % PV penetration

in the system, the system is able to maintain a stable operating condition as shown by the

red curve in terminal voltage plot 2.12.


Figure 2.12: Terminal voltage at bus 1 during various PV penetration levels

These case studies show that the stability of the interconnected power transmission systems

depends upon the location and level of PV penetration in the system. We can see that,

at 15 % PV penetration in the system, the system is able to regain it’s transient stability

although there are some large excursions in rotor angle. However, with 30 % PV replacing

conventional generators at critical buses, the system goes dynamically unstable even during

normal operating conditions of the system and if proper locations are chosen for a PV system,

it is able to maintain stable operating condition even at the higher level of PV penetration.


2.4.3 Voltage Stability Analysis on IEEE 14 Bus Transmission

System Following a Combination of Small and Large Dis-

turbance

At first, a heavily loaded scenario for IEEE 14 bus system is developed by doing the steady

state voltage stability analysis. Steady state voltage stability analysis helps to find the

steady-state stability limit of the bus as loading the system beyond this capability leads

to voltage collapse. Thus, quasi-steady-state time series analysis helps to define the loading

conditions within the steady state stability limit. In our case, the load is uniformly increased

at each bus by 1% for 100 seconds in an interval of one second and steady-state stability

margin of lines in the system are plotted as shown in Figure 2.13 and 2.15. The point at

which the steady-state stability margin of a line goes to 0 is the point of voltage collapse

for the system. Beyond this point, the load becomes voltage dependent and further increase

in load reduces the voltage leading to voltage collapse in the system. From this point, an

increase in reactive power does not increase the voltage, which is the definition of steady

state voltage instability.


Figure 2.13: stability margin plot for the lines connected to bus 2 and 3 at increasing loading

conditions

After calculating the steady state line stability margins for 100% load growth at each bus,

it has been realized that system does not reach to voltage collapse point as shown by plots

in Figure 2.13 and 2.15. Thus, 50% load growth is applied to each bus in the system after

ensuring that it is within the steady state stability limit of the whole system. In this way,

a heavily loaded scenario is created for the system. To understand the effect of generator

reactive power limits on large disturbance voltage stability, dynamic simulation is performed

by applying line fault to this stressed system. Dynamic simulation is started by running

the simulation for 0.1 seconds for the heavily loaded scenario at initial operating conditions

of the system. After 0.1 seconds of running system at the initial condition, a line fault is

applied in line 2-3 which is 345 kV line for 4 cycles i.e. 0.1 seconds. When the fault is

cleared after 4 cycles by tripping line 2-3, voltage stability of the system degraded as shown

in Figure 2.14. Although, line 2-3 is the weak link in the system as shown by the result of


steady state line stability margins in Figure 2.13 system stability degraded.

Figure 2.14: terminal voltage at bus 1 following the fault in line 2-3 during normal and

heavily loaded system conditions

To find the weakest link in the system after tripping the line 2-3, steady-state line stability

margins for all lines connected to bus 2 and bus 3 are calculated as shown in Figure 2.15.

As shown by the figure, line stability margin of 3-4 is degraded which suggests that system

adjustment is necessary for either bus 3 or 4 to bring the system back to the stable state.

When the generator reactive limits of the generator at bus 3 is increased by 60% voltage

stability is improved as shown in Figure 2.16.


Figure 2.15: steady state line stability margin plot at increasing loading conditions by trip-

ping the line 2-3


Figure 2.16: terminal voltage at bus 1 following the fault in line 2-3 during heavily loaded

system conditions by adjusting generator reactive limits at bus 3

This result shows the impact of generator reactive power limits on loading and stability of

the system. Load growth in the system is limited by generator reactive power limits.

2.5 Chapter Summary

Thus, in this chapter, the effect of PV penetration in transient stability of the system is shown

by doing dynamic simulations as discussed in Section 2.4.2. With PV replacing synchronous

generators, there are large excursions in rotor angle compared to no PV in the system. It

has been shown that system stability during PV penetration depends largely on the location

of faults and PV in the system as well as the level of PV penetration.

In addition to this, we studied the effect of generator reactive power limits on the combination


of small and large disturbances voltage stability as discussed in Section 2.4.3 and also in

loading capability of the system. Also, it is shown that identifying weak links in the system

facilitate dynamic simulations as system adjustments in weak links improve the stability of

the system as shown by Figure 2.16.

Chapter 3

Probabilistic Transmission Planning

3.1 Introduction

Power system planning refers to the planning done to integrate new elements like generators,

circuits, etc. into the grid while ensuring that the system will continue to operate under

changed system conditions by maintaining the acceptable reliability level as economically

as possible. The primary objective of power system planning is to develop the system that

maintains acceptable reliability level as economically as possible [25] without violating system

capabilities. In today’s network, due to the increase in uncertainties surrounding generation

and load, it is a huge challenge for planners and operators to supply the un-interrupted and

quality power at low cost. One of the essential goals of planners is to verify that new system

elements will not adversely affect the power grid and to assess the outcome of proposed

projects by doing interconnection and feasibility studies. Power system planning can be

divided into two levels in order to cover composite power system planning:

• Transmission system planning

• Distribution system planning

38

Durga Aryal Chapter 3. A new framework for Probabilistic transmission planning 39

Talking about the planning at the distribution level, planners design and redesign existing

circuits so that the network is capable of supplying power during an outage creating backup

power flow routes. In fact, planners look on reliability and resiliency of distribution systems

during a fault and an outage. Another common study is to examine the effect of new

distributed generation on the network and see if any topology changes are required.

On the other hand, transmission planning is the process of assessing the electric system and

its ability to deliver electricity reliably, efficiently and economically and planning system

reinforcements to meet the forecasted load demand. While planning at the transmission level,

planners will study the areas in the grid where a load is changing and how the topology will

change over the next five-plus years with load growth and additional generation penetration.

By forecasting the load and resource adequacy, planners give the hints for new projects

needed to be built to fulfill the load demand. And it requires a feasibility study, reliability

analysis, economic analysis, interconnection studies, etc.

Two types of planning studies are done for transmission systems. They are operational plan-

ning studies and transmission planning studies. Both of them as of now employ deterministic

approach. Operational planning is the study performed to help facilitate the day-to-day op-

eration of the system. It is performed on yearly basis to look at optimal utilization of existing

transmission facilities to maintain reliable and secure system during normal and contingent

system conditions as it is practically impossible to build new major transmission facilities

within a year. On the other hand, transmission planning involves simulation studies for

analyzing the extreme system conditions on long-term typically on five-plus year’s horizon.

The main goal of transmission planning is to identify the reliable, technically and economi-

cally sound transmission upgrades to ensure adequacy and security of power on normal and

contingent system conditions.


3.2 Background and Motivation

The North American Bulk Power System (BPS) is experiencing a significant change in gen-

eration and transmission facilities. The increasing penetration of renewables to replace con-

ventional units, the participation of load in system operations through demand response and

distributed generation, etc. have altered the operational characteristics of the grid and is the

challenge for system planners and operators to maintain reliability. These changes in power

grid have amplified system issues, which have challenged planners to plan the reliable and

economically sound system [26].

As discussed in the earlier section, existing transmission planning approach is based on

deterministic N-1 planning method. In this planning method, few cases of systems operating

conditions like summer-peak case, off-peak case, high wind low load case etc. for the network

under study are developed using forecasted load and generation dispatch scenarios for a

particular future year. After the case is ready, planning engineers conduct the study like

steady-state analyses, short circuit analyses and cascading analysis as a reliability assessment

procedure followed by economic analysis for near-term (1 to 5 years in the future) and long-

term planning horizon (5 to 10 years in the future). Reliability assessment help transmission

planners to identify system upgrades and new transmission projects to ensure continued

system reliability. After identifying the necessary topology changes, interconnection studies

are done in order to check the feasibility of system upgrades. Nowadays, sensitivity analysis

is also conducted to evaluate the effectiveness and robustness of the base cases under the

stressed system conditions. Sensitivity analysis is conducted to find the economically driven

projects i.e. the project that allow NERC reliability criteria to be met at a lower cost.

The major weakness of deterministic planning approach is it ignores the probabilities of

occurrence of single and multiple component failures in the system [12] for any scenario. Al-

though the deterministic approach has considered uncertainties using engineering judgment

and doing sensitivity analysis, more detail study and analysis is indeed essential. More detail

study is possible by making analysis with varieties of system conditions, which is supported


by probabilistic planning approach.

Furthermore, according to NERC TPL 001-4, all the contingencies described in Table 1 [27]

should be simulated to identify the critical contingency causing most severe system impacts.

Now the question is, is this possible with deterministic planning approach? The answer is no

because analyzing few system conditions might not be enough in most cases to find critical

contingencies in the system that causes the most severe system impact. The power grids,

at present, are affected by a large number of uncertainties like uncertainties imposed by

renewable generations, increasing the complexity of the network, changing weather pattern,

uncertainties surrounding load and demand-side management. Uncertainties are growing

exponentially and impacts associated with these uncertainties are highly undesirable for the

reliable and economic operation of the system.

All the aforementioned problems are the causes behind the development of a new concept

as probabilistic power system planning. In particular, the purpose of probabilistic power

system planning is to add a dimension to enhance system planning i.e. to plan the system

by considering both the probability as well as consequences for any given scenario. One of

the challenges in the broad adoption of probabilistic approaches in transmission planning

is that there are no established probabilistic indices and acceptable threshold values to be

maintained for probabilistic transmission planning [13].

Expected Unserved Energy (EUE) can be used as a risk-based index for doing probabilistic

reliability assessment. The first step in analyzing risk-based indices is to have an approach

to compute the probability of the system being in a particular state and the probability

of the contingency occurring for that state. Also, consequence of that contingency in form

of MW load curtailed is needed. For calculating the probability of contingency, EPRI has

defined formula as given in [28] but no any approach has been defined till date for evaluating

the probability of system being in a particular state. Another concern in implementing

probabilistic planning is, how many conditions will be enough to cover a wide range of

operating conditions and how to choose those conditions. Selecting system conditions along


with the probability of occurrence is the key step of probabilistic transmission planning

because making analysis with similar system conditions might not be able to address various

contingencies in the system. This problem is addressed in this thesis by presenting an

approach based on machine learning algorithm that is capable of selecting wide varieties of

scenarios along with the tentative probability of the system being in a particular state.

3.3 Preliminaries

3.3.1 Transmission Planning Approaches

Deterministic Planning Approach

In the deterministic approach, there is some course of events that are followed without

assessing risk for each of those events. This approach, in fact, makes it hard to address all

of the possibilities that may arise during system operation because they work on yes’, no’

framework on the basis of the severity of events. Existing transmission planning standards

are deterministic in nature. The drawback of the deterministic approach is that they only

consider the worst cases scenarios of the system without finding how likely those conditions

will occur. For example by making analysis with few extreme conditions of electric power

systems like summer peak, off-peak, high-wind low-load, etc. planners visualize the system.

Taking from a reliability perspective, deterministic criteria are designed such that the system

would be able to withstand relatively frequent contingencies without affecting the service

reliability while a loss of load is allowed for less frequent but more severe contingencies

(P-2 and higher). If selected contingencies do not represent all the important reliability

concerns, the system might be unreliable whereas if the selected contingencies are very

rare, an unnecessarily expensive system alternative may be selected [13]. Thus, we can say

that planning decision made based on deterministic approach can lead to overinvestment or

underinvestment.


Probabilistic Planning Approach

The probabilistic approach considers both the probability and consequences of the events to

quantify the system risk. It can consider deeper contingencies beyond P-1, making analy-

sis with deeper contingencies can help to find critical contingency in the system that causes

severe system impact as required by NERCs’ Transmission Planning (TPL) standards. Prob-

abilistic planning considers economic analysis in addition to the reliability evaluation, which

would be a good metric to look on while making the investment decision for planning. The

probabilistic approach also helps us to find the subset of contingencies to be studied based

on the likelihood and severity of the contingency.

3.3.2 Overview of Major Transmission Planning Activities

Long-Term System Assessment (LTSA)

Bulk transmission network usually consists of lines above 69 kV up to 500 kV transmission

lines and associated equipment. Transmission planning process covers several time horizons

to identify critical issues in the system and make new transmission investments. The long-

term system assessment provides an evaluation of potential issues and requirements of high

and extra high voltage transmission lines in the 10 plus year planning horizon. LTSA guides

the near term planning by providing the future needs of the system in terms of reliability

and economics. LTSA might give better decision than near-term planning in long run. It

identifies upgrades that is advantageous across a range of possible future scenarios.

Regional Transmission Plan (RTP)

Regional transmission plan is generally performed for a five-plus year planning horizon. It

focuses on meeting the system needs in five-plus years. Regional transmission plan identifies

steady state transmission needs during different cases like summer peak and off-peak and does


reliability analysis. It also performs sensitivity analysis to address uncertainty involved in the

transmission planning process. The reliability analysis is done by covering the NERC TPL

standards and includes steady-state contingency analysis, short-circuit analysis, cascading

analysis, etc. RTP tries to find the critical contingency in the system to meet the requirement

of NERC TPL standard. In a regional transmission plan, from the results of reliability

assessment, they identify and plan the system upgrades, new transmission facilities, and

new constraint management plans. Regional transmission plan consists of four processes,

case conditioning, base case reliability analysis, additional reliability analysis, and economic

analysis.

Regional Planning Group Project Review

After the future project and system upgrades for transmission improvements are identified

by LTSA and RTP, they undergo review by the regional planning group (RPG). Regional

planning group critically reviews the project and identifies the pros and cons of the project.

Generation Interconnection Studies

Generation interconnection process can be completed in three steps [29]:

• Interconnection studies and project development

• Resource modeling and registration

• Commissioning, testing, and commercial operations

Deterministic planning approach has been used in transmission planning to date. In deter-

ministic planning approach, all the specified list of contingencies are tested by selecting a set

of network configurations. These assessments involve a large number of computer simula-

tions of a set of network configurations, a list of outage events, and performance evaluation.


With deterministic planning approach, the planners should try to make analysis with credi-

ble system conditions i.e. system conditions likely to occur in the system. Also, the outage

event, network configuration, and operating conditions on which the decision is based should

result in most severe system impact.

The deterministic approach consists of following steps [30]:

• Select the time for study and loading condition i.e. peak, off-peak, high wind low load

etc.

• Select the network topology and generation schedule.

• Select the set of contingencies to be tested, all N-1 and few credible N-2.

• Refine the operating conditions in terms of dispatch and voltage profile to represent

the credible as well as severe system conditions.

• Perform the simulation for all those credible scenarios and identify the system viola-

tions.

• Define solutions to those violations.

Nowadays, due to the increasing penetration of utility-scale wind and solar in the transmis-

sion system and uncertainties caused by it, planners are focusing on enhancing the existing

method of transmission planning. Existing approach needs modifications to address risk

and resiliency issues caused by uncertainties of these inverter-based generations that causes

problem on transient stability of the system as depicted in 2. Hence, it is a need to de-

velop effective and realistic strategies that can enhance the current approach of transmission

planning by considering the uncertainties from variable generation and demand response.

3.3.3 Framework of Probabilistic Transmission Planning

Probabilistic planning can be visualized by the three major steps described below.


Scenario Development

Scenario development is the very first step in probabilistic planning. Considering all the

uncertainties, like weather, renewables, economic growth, and load forecast errors, realistic

load and generation dispatch scenarios should be developed which represents the wide range

of realistic system conditions. Scenarios will be more realistic if we use the past data of load

and generation variations with weather, economic growth, forecast errors, outage statistics,

etc. Scenario generation can be done by using various machine-learning algorithms like

Multiple Linear Regression, Support Vector Machine, Artificial Neural Network, etc.

Scenario Selection and Case Study Development

Scenario generation is followed by scenario selection where a particular number of representa-

tive scenarios should be chosen to make the study cases which is the key step. The next step

in probabilistic planning is the case study development where using the selected scenarios

and reliability base cases, modified power flow cases are developed for all the selected system

conditions. After the development of a practical case study, probabilistic risk assessment is

performed.

Probabilistic Reliability Analysis

The final step in probabilistic planning is the probabilistic reliability analysis. The main

purpose of probabilistic risk analysis is to evaluate risk for particular system conditions. By

considering the probability of each scenario, the probability and consequences of contingent

events during each scenario, the risk is evaluated and alternatives are presented. Looking at

the risk associated transmission system for particular study year, appropriate measures to

ensure reliability can be taken. Incorporating risk management into planning practice helps

to make better investment decision too. Since probabilistic planning evaluates risk for every

planning project, investment decision for the particular project which is made on the basis


of probabilistic planning approach can be the wise investment decision. This is the added

dimension of probabilistic planning.

3.3.4 Challenges in Probabilistic Transmission Planning

Tools for Scenario Selection and Probabilistic Risk Assessments

We discussed that scenario selection is the critical step in probabilistic planning but no

such tools are developed that can reasonably select the representative samples out of total

datasets used for the study. Risk-Based Planning Scenario Builder (RBPSB) was developed

by EPRI to build the set of load and generation dispatch scenarios in past. By considering

various uncertainties, the tool produces different load and generation dispatch scenarios but

later it was found that it dispatches generator based on the merit order rather than fuel

prices and production cost. It also neglects the impact of transmission capabilities, so the

load and generation dispatch scenarios generated using this tool were not realistic.

Another major challenge is to perform probabilistic reliability assessment, as there are no

established indices and acceptable threshold values to be maintained for risk-based planning

approach. There are many loopholes needed to be filled e.g. industry standard approach for

data collection and processing, establishing an industry-wide accepted approach to compute

risk-based indices, establishing acceptable thresholds based on those indices etc. EPRI has

developed the risk assessment tool called Transmission Contingency Analysis and Reliability

Evaluation (TransCARE) but the research is still going on.

Data Requirements

Probabilistic approaches are highly dependent on the data. System data like network data,

outage data, load data, unreliability costs, etc. are required to do the probabilistic analysis.


Network data includes all the information for each of the network components like nominal

voltage rating, impedances, and normal emergency ratings, minimum and maximum real and

reactive power limits, etc. that are necessary to run power flow cases. Planners normally

know them but the accuracy of the data is the concern.

Outage data is very important to calculate reliability indices. The basic outage data consists

of outage duration, outage frequency, and unavailability. NERC’s Transmission Availability

Data Systems (TADS) and Generation Availability Data Systems (GADS) datasets are being

used as default outage data until now for performing reliability assessment.

Other datasets like load-generation dispatch cases, unreliability cost, etc. are essential in

doing reliability evaluation and economic analysis. Reliability indices are generally reported

on an annual basis, so it is necessary to capture variations in system load and generation

dispatches over a one-year period.

This thesis focuses on finding the analytical method to probabilistically select load and

generation dispatch scenarios. A widely used machine learning technique has been introduced

in probabilistic planning to select the representative samples analytically.

In this section, we are going to discuss in detail about the methodology for probabilistic

transmission planning developed at ERCOT.

3.4 Framework of Probabilistic Transmission Planning

at ERCOT

The overall block diagram of framework of probabilistic transmission planning developed at

ERCOT is shown in Figure 3.1.


Figure 3.1: Block diagram of probabilistic transmission planning

3.4.1 Scenario Development

Load and generation dispatch scenarios are generated by performing security constrained

economic analysis in UPLAN. Load and generation dispatch scenarios are generated for the

year 2020 based on four weather patterns in the past i.e. 2006, 2007, 2009 and 2010. To

generate these scenarios, UPLAN Network Power Model is used. UPLAN-NPM performs co-

ordinated marginal cost-based energy and Security Constrained Unit Commitment (SCUC)

Simulation, Security Constrained Economic Dispatch simulations ensuring that all transmis-

sion constraints, line contingencies, outages and physical constraints for power delivery are

satisfied (

For developing all the load and generation dispatch scenarios, we make four UPLAN runs

where the input are load, wind, and solar profile representing various uncertainties under

four different weather patterns. The cost of operating the generators e.g. fuel, start-up,

operation and maintenance costs, etc. are uploaded for performing 8760-hour production


cost simulation. Based on the number of weathers patterns used in simulations, scenarios are

generated. For example, if there are 4 weather patterns then 4 * 8760 system conditions are

generated that represent varieties of scenarios like summer peak case, high wind low load,

low wind high load, high wind high load, etc. In this way, the entire system conditions are

obtained for the year 2020 based on four weather patterns in the past. All the generations

are dispatched economically and the units are committed respecting all system limits.

3.4.2 Scenario Selection and Case Study Development

Since making analysis with the entire system conditions is practically impossible, we need

to choose a particular number of scenarios that represent the entire system conditions. It is

a very arduous task since no information is given to us regarding the number of scenarios

needed for the analysis. Since it is a critical step in probabilistic planning, after making

careful judgment on information provided for the datasets, random sampling is done after

clustering the data using widely used machine learning algorithm K-means clustering. As

there are no explicit labels provided for the data, K-means clustering can cluster the dataset

into a specified number of clusters by using the algorithm mentioned in 3.2. After doing K-

means clustering, a general monte-carlo sampling technique is applied to select scenarios from

each cluster. This method is named as General Monte-Carlo sampling technique enhanced

with K-means clustering.

General Monte-Carlo Sampling Technique Enhanced with K-Means Clustering

Since we have no any information about the patterns and features in the data, a method is

needed that can find the natural groupings and patterns not explicitly labeled in dataset.

Taking this in concern, we decided to use K-means clustering to divide our datasets into a

particular number of clusters at first and do Monte-Carlo sampling. K-means clustering is

the widely used machine learning technique which is very popular in data mining, artificial


intelligence, and clustering analysis. It is unsupervised machine learning technique which is

used for unlabeled dataset as in our case. The main idea behind K-means clustering is to

find groups in the data, where user have to specify the number of groups we want to divide

our dataset that is represented by variable K.

Figure 3.2: Block diagram of k-means clustering

K-means clustering iterates between two steps:

• Data assignment step: In this step, K number of centroids are randomly selected

where, K is specified by the user. After that, distance between centroid and each data

points are computed. Each point is assigned to its nearest centroid based on squared

Euclidean distance where,

Squared Euclidean distance = argmin dist(Ci, x)2,where Ci ∈ C (3.1)


• Centroid update step: Centroid is updated until no points move the group. Cen-

troids are computed by taking mean of all points assigned to that centroid’s cluster

where new centroid is,

New centroid, Ci =1

|Si|∑xi∈Si

xi (3.2)

These two steps are repeated until no points move the group or until the maximum number

of iterations is reached.

Since K is the user-defined quantity, a good analytical guess for K should be made. As

K becomes bigger, the confidence level of similarity of scenarios in a cluster also increases

and vice versa. So, it is very necessary to find the optimal value of K for given datasets.

Unfortunately, there is no definite answer as an optimal number of clusters is subjective and

depends on the method used. There are different approaches to find the optimal value of

K in K-means clustering. In our case, we used direct method particularly named as Elbow

method.

Elbow method manipulate the squared sum of error (SSE). In this method, SSE is computed

for different values of k i.e. for k = 1, 2, 3 and so on, where

SSE =k∑i=1

∑x∈ci

dist(x, ci)2 (3.3)

After that, K is plotted against SSE and the point where SSE decreases sharply is the optimal

value of K for the given datasets. At that point, elbow effect is seen in the graph, which

helps us to better visualize the value of K.

After dividing the datasets into particular number of clusters, the samples were randomly

drawn out from each clusters using Monte Carlo technique along with the probability of

occurrence of each sampled scenario. The probability of each scenario can be determined

using the formula given below:


Pj =Ni∑ki=1Ni

× 1

ni(3.4)

where, Pj is the probability of each scenario j.

Ni is the number scenarios in each cluster i.

ni is the number of samples drawn from each cluster i.

The drawback of the above approach is that the probability of a scenario depends upon the

number of samples drawn from each cluster. After the scenario is selected, a case study is

developed for performing probabilistic reliability assessment.

Each starting case is built as per the Steady State Working Group (SSWG) procedure manual

and it represents the most updated system topology and demand forecast as provided by

the Transmission Service Providers (TSPs). This case contains all existing and planned

facilities, including reactive power resources and control devices [31]. SSWG start case is

used to develop reliability base case.

Reliability base cases are developed to determine the transmission upgrades and additional

needs to meet ERCOT and NERC reliability requirements, for example, summer peak relia-

bility case and off-peak reliability case. All the existing generation plants in reliability cases

are retained from SSWG start cases. Future generation resources will be added to the SSWG

start cases using information from the Resource Asset Registration Form (RARF) if the re-

quirements from ERCOT planning guide section 6.9 [32] is met. We took the summer-peak

reliability case of the year 2020 to make our analysis.

3.4.3 Probabilistic Risk Analysis

Probabilistic risk analysis is done to find the probabilistic reliability indices associated with

each sampled scenario. In our case, expected unserved energy (EUE) is defined as risk

metrics to quantify the risk of each scenario. It needs the results of modified power flow cases

built using sampled value, list of contingencies, results of SCOPF and outage statistics. It


quantifies the value of each contingency in terms of MW load curtailed needed to maintain all

system elements within their limits. This can be applied to all the contingencies happening

in every scenario. The expected unserved energy can be calculated using the formula given

below:

EUE =∑j

Pj∑i

Pi MWcurtailedi (3.5)

where, Pj is the probability of scenario j that can be calculated using equation 3.4. Pi is the

probability of contingency i, and MWcurtailedi is the amount of MW curtailed to maintain

the system limits for removing violations caused by a contingency i in the system.

Thus, EUE can be calculated for each scenario using the above formula. The approach

described in [28] is used in calculating the probability of each contingent events for a par-

ticular scenario. Thus, a new machine learning algorithm is used to evaluate the tentative

probability of the system being in a particular state which is the key step to find EUE.

3.5 Case Study

3.5.1 System Setup

A case study is performed according to the methodology described above. We generated

4*8760 load and generation dispatch scenarios using the data of wind, solar and load profile

as input in UPLAN. Also, economic growth, load forecast errors, transmission network model,

cost of operating generators, etc. are considered to cover all the uncertainties that might

occur in the system. We make four UPLAN runs for four different weather pattern to get

total scenarios for four years. The scenarios consist the information of solar, wind and load

profile for each day of the year 2020.


3.5.2 Results and Discussions

The general Monte-Carlo sampling technique enhanced with K-means clustering is used to

get the representative samples out of the total dataset. Knowing that there is no point in

making analysis with similar scenarios, we tried to sample wide varieties of scenarios by

using our own analytical technique. K-means clustering is implemented in our datasets, at

first, to find some pattern or group in the data. Assuming K-means clustering will group the

similar scenarios in a particular cluster, we divided our dataset into four different clusters at

first as shown in Figure 3.3.

Figure 3.3: Clustering entire system conditions into four clusters

Since there is no any information about the dataset, it is very hard to define the value of

K. Thus, the elbow method is implemented in our dataset to find the optimal number of

clusters. The elbow effect is seen at K = 4 as shown in Figure 3.4, so 4 is taken as the


optimal value of clusters for our datasets.

Figure 3.4: Elbow implementation to find the optimal value of clusters

After dividing our dataset into an optimal number of clusters obtained from the elbow

method, random sampling is done to get the representative scenarios from the system. The

figure 3.5 shows the result of pulling out 2, 4, 6, 8 and 10 samples from each cluster.


Figure 3.5: System conditions sampled from entire state space


In figure 3.5 black dots show the entire system conditions obtained by doing production cost

simulation in UPLAN and the red dot shows the sampled system conditions obtained by

using the approach described in Section 3.4.2. Since pulling out 4 samples from each of the

cluster is representing the entire system conditions more widely, sixteen sample conditions

can be used for developing power flow case for performing probabilistic reliability analysis.

Result for sixteen sampled scenario is tabulated in Table 3.1.

Scenario Solar (MW) Wind (MW) Load (MW) Probability of Occurrence

1 2000 7100 74581 0.11737

2 1500 5363 60854 0.11737

3 1375 2171 47794 0.13789

4 1601 6530 41851 0.13789

5 312 11432 48334 0.01281

6 500 17118 52190 0.01281

7 0 11349 43513 0.27644

8 0 14262 45262 0.27644

9 1534 10582 39951 0.06034

10 1209 6786 38813 0.06034

11 1967 11990 57105 0.08885

12 1800 12230 57909 0.08885

13 0 5708 34311 0.16456

14 0 6000 33154 0.16456

15 260 2000 36510 0.14173

16 0 4799 43658 0.14173

Table 3.1: Results of 16 sampled scenarios

Thus, sampling on the basis of K-means clustering is able to select wide varieties of scenarios

from the system along with their probability of occurrence. Now, these samples can be used


to perform probabilistic reliability analysis to calculate the EUE for the year 2020 based

on the formula 3.5. All the remaining steps are pretty straightforward as they are already

defined steps.

Using the probability of that sampled scenario, the probability of all contingencies occurring

for a particular scenario, and the MW load curtailed for all contingencies, EUE can be

calculated using the equation 3.5.

3.6 Chapter Summary

This chapter highlights the importance and challenges associated with probabilistic trans-

mission planning approach. Moreover, it discusses a new technique developed for selecting

scenarios probabilistically to implement probabilistic planning approach in ERCOT systems.

Since the uncertainties in electric power systems will continue to rise with the increasing de-

mand and rapid integration of inverter-based generation especially wind and solar in the

grid, the existing deterministic approach needs improvement and enhancement by adopting

probabilistic transmission planning approach.

In addition, the importance and advantages of adopting the probabilistic planning framework

developed at ERCOT are highlighted and explained. Load and generation dispatch scenarios

are created for the year 2020 based on four weather patterns in the past using the production

cost simulation tool (UPLAN). To probabilistically select representative samples from those

scenarios, General Monte Carlo Technique Enhanced with K-means Clustering is used which

makes our technique more analytical and reasonable. Using those samples and the base

cases, case study can be developed for the entire ERCOT system for doing probabilistic

reliability analysis. As demonstrated in Section 3.4.3, probabilistic reliability analysis help

us to quantify all the system issues using single risk metric called Expected Unserved Energy

(EUE). EUE can be calculated for each transmission planning alternative that provides the

hint of weak areas in the system, identifies critical contingency in the system as required by


NERC, evaluate project alternatives, and so on.

Therefore with the technique discussed in this chapter, implementation of probabilistic plan-

ning approach seems possible in real-world transmission systems. Although, it is shown that

General Monte Carlo enhanced with K-means clustering gives the reasonable and analytical

vision for selecting the scenarios probabilistically, there are places for improvement. It does

not ensure that K-means clustering appropriately cluster all the similar scenarios in the par-

ticular cluster, we need to enhance this method. Also, some statistical analysis is needed in

dataset to determine the optimal and reasonable value of k.

Chapter 4

Conclusions and Future Work

4.1 Conclusion

In this thesis, we have analyzed the stability of power transmission systems during small

and large disturbances with PV penetration in the system. The effect of reduced inertia and

reduced synchronizing force as a result of PV replacing conventional synchronous generators

has been shown. In doing so, we present several case studies which show that system stability

with PV penetration depends largely on the location of fault and PV as well as level of PV

penetration. From the Figure 2.9, we can see that if a fault is located near to PV then there

is a large excursion in rotor angle than that of a fault located at a farther distance.

Similarly, as PV penetration level increases in the system, the stability of the system is

threatened even during normal operating conditions. Therefore, it is very important to

properly locate the PV in the system. Although the PV is operated for V/Q control func-

tionality, if some critical buses are fully replaced with PV, the system can go dynamically

unstable as shown by Figure 2.10 and 2.11. This suggests that some of the generators in

the critical buses should not be fully replaced with PV. If it has to be replaced, additional

synchronous condenser or Var compensation is needed to maintain sufficient damping.

61

Durga Aryal Bibliography 62

In addition to this, this thesis presents voltage stability analysis of power transmission sys-

tems by stressing the system such as by applying a combination of a small and large dis-

turbance in the system. Doing various case studies, we have shown that voltage stability

of transmission systems can be improved by making reactive power adjustments by identi-

fying the weak links in the system. It has been shown that weak links in the system can

be identified by calculating the steady-state line stability margins without doing extensive

simulations.

Similarly, this thesis also presents a new technique for selecting scenarios probabilistically

that provides the hope of implementing a probabilistic planning approach in real-world power

systems. A reasonable method that is capable of selecting representative scenarios out of

thousands of scenarios in the system has been developed. General Monte-Carlo Enhanced

with K-means Clustering is capable of selecting representative scenarios as shown in Figure

3.5. Moreover, this method is capable of calculating the tentative probability of the scenario

in the system using the equation 3.4. Planners can use this method in doing probabilistic

reliability assessment for implementing probabilistic transmission planning approach in real-

world power systems.

4.2 Future Work

In this work, stability analysis of power transmission systems has been performed for sev-

eral scenarios with utility-scale PV penetration. Using the results from this work, proper

mitigating measures to improve the system stability can be established.

Similarly, a more concrete and more analytical way of selecting scenarios in the system can

be developed for probabilistic transmission planning as the current approach depends largely

on a number of data used.

Bibliography

[1] Western GovernorsAssociation. An introduction to electric power transmission.

[Online]. Available: https://openei.org/w/images/d/d9/An Introduction to Electric

Power Transmission Presentation.pdf

[2] NERC, “Transmission system planning performance requirements,” Tech. Rep.

[3] H. Bin and L. Dichen, “Modeling of a large-scale photovoltaic generation and analysis

of its security and stability operation in west-qinghai grid,” in 2013 Third International

Conference on Intelligent System Design and Engineering Applications, Jan 2013, pp.

958–962.

[4] S. Eftekharnejad, V. Vittal, G. T. Heydt, B. Keel, and J. Loehr, “Impact of increased

penetration of photovoltaic generation on power systems,” IEEE Transactions on Power

Systems, vol. 28, no. 2, pp. 893–901, May 2013.

[5] Department of Energy. Grid modernization initiative. [Online]. Available: https:

//www.energy.gov/grid-modernization-initiative

[6] M. K. M. Zambri, M. S. M. Aras, A. Khamis et al., “Investigating the impact of pho-

tovoltaic connection to the malaysian distribution system,” Journal of Telecommunica-

tion, Electronic and Computer Engineering (JTEC), vol. 8, no. 7, pp. 23–28, 2016.

63

https://openei.org/w/images/d/d9/An_Introduction_to_Electric_Power_Transmission_Presentation.pdf

https://openei.org/w/images/d/d9/An_Introduction_to_Electric_Power_Transmission_Presentation.pdf

https://www.energy.gov/grid-modernization-initiative

https://www.energy.gov/grid-modernization-initiative


[7] Y. Liu, J. Bebic, B. Kroposki, J. de Bedout, and W. Ren, “Distribution system voltage

performance analysis for high-penetration pv,” in 2008 IEEE Energy 2030 Conference,

Nov 2008, pp. 1–8.

[8] P. P. Barker and R. W. D. Mello, “Determining the impact of distributed generation

on power systems. i. radial distribution systems,” in 2000 Power Engineering Society

Summer Meeting (Cat. No.00CH37134), vol. 3, July 2000, pp. 1645–1656 vol. 3.

[9] N. Amjady and M. R. Ansari, “Small disturbance voltage stability evaluation of power

systems,” in 2008 IEEE/PES Transmission and Distribution Conference and Exposi-

tion, April 2008, pp. 1–9.

[10] L. Korpinen, “On-line voltage stability assessment of power system an approach of

black-box modelling,” 2001.

[11] N. Amjady and M. Esmaili, “Voltage security assessment and vulnerable bus ranking

of power systems,” Electric Power Systems Research, vol. 64, pp. 227–237, 03 2003.

[12] W. Li and P. Choudhury, “Probabilistic planning of transmission systems: Why, how

and an actual example,” in 2008 IEEE Power and Energy Society General Meeting -

Conversion and Delivery of Electrical Energy in the 21st Century, July 2008, pp. 1–8.

[13] EPRI, “Risk based transmission planning,” Tech. Rep., Dec. 2014.

[14] J. Bernecker, S. W. Kang, J. Billo, A. Gaikwad, N. Wintermantel, and K. Carden,

“Probabilistic transmission planning at ercot,” in 2016 IEEE Power and Energy Society

General Meeting (PESGM), July 2016, pp. 1–5.

[15] P. Kundur, N. J. Balu, and M. G. Lauby, Power system stability and control. McGraw-

hill New York, 1994, vol. 7.

[16] T. Van Cutsem and C. Vournas, Voltage stability of electric power systems. Springer

Science & Business Media, 2007.


[17] I. Singh, Effect of Reduced System Inertia Due to Increased Renewable Resource Pene-

tration on Power System Stability. Arizona State University, 2012.

[18] M. Huneault, A. Fahmideh-Vojdani, M. Juman, R. Calderon, and F. Galiana, “The

continuation method in power system optimization: applications to economy-security

functions,” IEEE transactions on power apparatus and systems, no. 1, pp. 114–124,

1985.

[19] A. Tbaileh, H. Jain, R. Broadwater, J. Cordova, R. Arghandeh, and M. Dilek, “Graph

trace analysis: An object-oriented power flow, verifications and comparisons,” Electric

Power Systems Research, vol. 147, pp. 145–153, 2017.

[20] Y. Mansour, “Suggested techniques for voltage stability analysis,” IEEE Technical Re-

port 93TH0620-5-PWR, IEEE/PES, 1993.

[21] R. Broadwater, A. Chandrasekaran, C. Huddleston, and A. Khan, “Power flow anal-

ysis of unbalanced multiphase radial distribution systems,” Electric Power Systems

Research, vol. 14, no. 1, pp. 23–33, 1988.

[22] J. McCalley. Power system simulation for engineers (pss/e version 30): Stability

analysis. [Online]. Available: http://home.engineering.iastate.edu/∼jdm/ee457/PSSE

Intro Stabilty Instructions.pdf

[23] A. Ellis, M. Behnke, and R. Elliott, “Generic solar photovoltaic system dynamic simu-

lation model specification,” Sandia Report, Sandia National Laboratories, Albuquerque,

New Mexico, 2013.

[24] H. Jain, “Dynamic simulation of power systems using three phase integrated transmis-

sion and distribution system models: Case study comparisons with traditional analy-

sis methods,” Ph.D. dissertation, Virginia Polytechnic Institute and State University,

Blacksburg, VA 24060, 7 2017.

http://home.engineering.iastate.edu/~jdm/ee457/PSSE_Intro_Stabilty_Instructions.pdf

http://home.engineering.iastate.edu/~jdm/ee457/PSSE_Intro_Stabilty_Instructions.pdf


[25] W. Li, “Framework of probabilistic power system planning,” CSEE Journal of Power

and Energy Systems, vol. 1, no. 1, pp. 1–8, 2015.

[26] NERC. Essential reliability services task force measures framework report. [Online].

Available: https://www.nerc.com/comm/Other/essntlrlbltysrvcstskfrcDL/ERSTF%

20Framework%20Report%20-%20Final.pdf

[27] L. Erichsen, D. Kempf, C. Lawrence, M. Tiemeier, M. Dantzler, “Standard application

guide TPL-001-4,” Tech. Rep., Nov. 2015.

[28] EPRI, “Risk based transmission planning,” Tech. Rep., 2016.

[29] ERCOT, “Guide to the interconnection process,” Tech. Rep., Nov. 2012.

[30] P. Pourbeik, B. Chakrabarti, T. George, J. Haddow, H. Illian, R. Nighot et al., “Review

of the current status of tools and techniques for risk-based and probabilistic planning

in power systems,” CIGRE, 2010.

[31] ERCOT, “2016 regional transmission plan,” Tech. Rep., 2016.

[32] ——, “Ercot planning guide,” Tech. Rep., Aug. 2017.

https://www.nerc.com/comm/Other/essntlrlbltysrvcstskfrcDL/ERSTF%20Framework%20Report%20-%20Final.pdf

https://www.nerc.com/comm/Other/essntlrlbltysrvcstskfrcDL/ERSTF%20Framework%20Report%20-%20Final.pdf

Analysis and Planning of Power Transmission Systems ...for more rigorous analysis and planning of power transmission systems. Stability issues in power transmission system are more

Documents