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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
Analysis and Planning of Power Transmission Systems Subject to
Uncertainties in the Grid
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
Analysis and Planning of Power Transmission Systems Subject to
Uncertainties in the Grid
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
2.5 Stability margin of line 2-4 with and without PV integration at bus 3 . . . . 23
2.6 Stability margin of line 3-4 with and without PV integration at bus 3 . . . . 23
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.
Durga Aryal Chapter 1. Introduction 3
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.
Durga Aryal Chapter 1. Introduction 4
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.
Durga Aryal Chapter 1. Introduction 5
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
Durga Aryal Chapter 1. Introduction 6
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-
Durga Aryal Chapter 1. Introduction 7
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
Durga Aryal Chapter 1. Introduction 8
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-
Durga Aryal Chapter 1. Introduction 9
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
Durga Aryal Chapter 2. Stability Analysis of Power Transmission Systems 12
• 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.
Durga Aryal Chapter 2. Stability Analysis of Power Transmission Systems 13
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
Durga Aryal Chapter 2. Stability Analysis of Power Transmission Systems 14
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
Durga Aryal Chapter 2. Stability Analysis of Power Transmission Systems 15
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
Durga Aryal Chapter 2. Stability Analysis of Power Transmission Systems 16
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
Durga Aryal Chapter 2. Stability Analysis of Power Transmission Systems 17
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
Durga Aryal Chapter 2. Stability Analysis of Power Transmission Systems 18
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,
Durga Aryal Chapter 2. Stability Analysis of Power Transmission Systems 19
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
2 GENROU + IEEET1 + TGOV1
3 GENROU + IEEET1 + TGOV1
6 GENROU + IEEET1 + TGOV1
8 GENROU + IEEET1 + TGOV1
Table 2.2: Dynamic models of synchronous generators for IEEE 14 bus system
Durga Aryal Chapter 2. Stability Analysis of Power Transmission Systems 20
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.
Durga Aryal Chapter 2. Stability Analysis of Power Transmission Systems 21
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
Durga Aryal Chapter 2. Stability Analysis of Power Transmission Systems 22
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
Durga Aryal Chapter 2. Stability Analysis of Power Transmission Systems 23
Figure 2.5: Stability margin of line 2-4 with and without PV integration at bus 3
Figure 2.6: Stability margin of line 3-4 with and without PV integration at bus 3
Durga Aryal Chapter 2. Stability Analysis of Power Transmission Systems 24
[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
Durga Aryal Chapter 2. Stability Analysis of Power Transmission Systems 25
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.
Durga Aryal Chapter 2. Stability Analysis of Power Transmission Systems 26
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
Durga Aryal Chapter 2. Stability Analysis of Power Transmission Systems 27
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.
Durga Aryal Chapter 2. Stability Analysis of Power Transmission Systems 28
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
Durga Aryal Chapter 2. Stability Analysis of Power Transmission Systems 29
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
Durga Aryal Chapter 2. Stability Analysis of Power Transmission Systems 30
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.
Durga Aryal Chapter 2. Stability Analysis of Power Transmission Systems 31
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.
Durga Aryal Chapter 2. Stability Analysis of Power Transmission Systems 32
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.
Durga Aryal Chapter 2. Stability Analysis of Power Transmission Systems 33
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
Durga Aryal Chapter 2. Stability Analysis of Power Transmission Systems 34
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.
Durga Aryal Chapter 2. Stability Analysis of Power Transmission Systems 35
Figure 2.15: steady state line stability margin plot at increasing loading conditions by trip-
ping the line 2-3
Durga Aryal Chapter 2. Stability Analysis of Power Transmission Systems 36
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
Durga Aryal Chapter 2. Stability Analysis of Power Transmission Systems 37
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.
Durga Aryal Chapter 3. A new framework for Probabilistic transmission planning 40
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
Durga Aryal Chapter 3. A new framework for Probabilistic transmission planning 41
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
Durga Aryal Chapter 3. A new framework for Probabilistic transmission planning 42
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.
Durga Aryal Chapter 3. A new framework for Probabilistic transmission planning 43
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
Durga Aryal Chapter 3. A new framework for Probabilistic transmission planning 44
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.
Durga Aryal Chapter 3. A new framework for Probabilistic transmission planning 45
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.
Durga Aryal Chapter 3. A new framework for Probabilistic transmission planning 46
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
Durga Aryal Chapter 3. A new framework for Probabilistic transmission planning 47
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.
Durga Aryal Chapter 3. A new framework for Probabilistic transmission planning 48
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.
Durga Aryal Chapter 3. A new framework for Probabilistic transmission planning 49
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
Durga Aryal Chapter 3. A new framework for Probabilistic transmission planning 50
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
Durga Aryal Chapter 3. A new framework for Probabilistic transmission planning 51
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)
Durga Aryal Chapter 3. A new framework for Probabilistic transmission planning 52
• 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:
Durga Aryal Chapter 3. A new framework for Probabilistic transmission planning 53
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
Durga Aryal Chapter 3. A new framework for Probabilistic transmission planning 54
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.
Durga Aryal Chapter 3. A new framework for Probabilistic transmission planning 55
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
Durga Aryal Chapter 3. A new framework for Probabilistic transmission planning 56
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.
Durga Aryal Chapter 3. A new framework for Probabilistic transmission planning 57
Figure 3.5: System conditions sampled from entire state space
Durga Aryal Chapter 3. A new framework for Probabilistic transmission planning 58
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
Durga Aryal Chapter 3. A new framework for Probabilistic transmission planning 59
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
Durga Aryal Chapter 3. A new framework for Probabilistic transmission planning 60
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.
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