University of Southern California Dissertations and Theses

Predictive real-time assessment for power grid monitoring and situational awareness using synchrophasors with partial PMU observability

(USC Thesis Other)

Predictive real-time assessment for power grid monitoring and situational awareness using synchrophasors with partial PMU observability

PDF

Download a page range

Download transcript

Copy asset link

Request this asset

Transcript (if available)

Content

PREDICTIVE REAL-TIME ASSESSMENT FOR POWER GRID MONITORING AND
SITUATIONAL AWARENESS USING SYNCHROPHASORS WITH PARTIAL PMU
OBSERVABILITY

by

Backer Abu-Jaradeh

A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
ELECTRICAL ENGINEERING

May 2022

Copyright 2022 Backer Abu-Jaradeh

ii

ACKNOWLEDGEMENTS
I wish to express my sincere gratitude to my advisor, Dr. Mohammed Beshir, who made this
work possible. His guidance and advice helped me tremendously during my research, and I could not
have imagined having a better mentor for my Ph.D. study. I would also like to thank the rest of the
members of my committee, Dr. Edmond Jonckheere and Dr. Kelly Sanders, for their encouragement
and support, and for making my defense an enjoyable experience.
I am extremely thankful to Dr. Frank Habibi-Ashrafi, the person who contributed to every
success in my career, studies, and my personal life. Dr. Ashrafi taught me what it means to be a mentor.
His guidance, patience, and support throughout the years helped me become the person I am today.
I am eternally grateful.
I would also like to thank my colleagues at Electric Power Group for their encouragement and
support throughout this journey. Their support helped me get to where I am today, and I couldn’t
have asked for a better team to surround myself with.

iii

DEDICATION

I dedicate this dissertation to my family, for their love, support, and encouragement. My father,
Nafiz, who dedicated all his life, health, and wealth to make our life easier. My mother, Asma, for her
endless love that enabled me to do the impossible. My wife, my love, and my soulmate, Nuha, for
always being there for me. My kids, Elaine and Mohammed, for being the spark in my life that keeps
me going. To my sisters, Lina, Farah, and Shereen, and my brothers, Omar and Hamzeh, who always
supported me.
I further dedicate this to my friends, Hassan, Imad, and Mohammed, who always helped and
encouraged me throughout my doctorate program.

iv

TABLE OF CONTENTS
Acknowledgements.......................................................................................................................................................... ii
Dedication ......................................................................................................................................................................... iii
List of Figures .................................................................................................................................................................. vi
List of Tables .................................................................................................................................................................. viii
List of Symbols ................................................................................................................................................................ ix
List of Abbreviations ..................................................................................................................................................... xi
Chapter 1: Introduction ................................................................................................................................................. 1
1.1 Motivation and Objective ........................................................................................................ 3
1.2 Background.................................................................................................................................13
1.2.1 Line Ratings and System Operating Limits (SOLs) ........................................16
1.2.2 Monitoring and Situational Awareness ...............................................................17
1.3 Enabling Technologies ...........................................................................................................17
1.3.1 Supervisory Control And Data Acquisition (SCADA) System ...................18
1.3.2 State Estimator (SE) .................................................................................................19
1.3.3 Synchrophasor systems............................................................................................20
1.3.4 Real-Time Contingency Analysis ..........................................................................24
Chapter 2: Power System Security ............................................................................................................................25
2.1. System Security and Real-Time Monitoring ......................................................................29
2.2 Real-Time Contingency Analysis .........................................................................................31
2.3 Linearization of the security analysis problem ................................................................32
2.4 Linear Shift Factors (LSFs)....................................................................................................33
2.5 Security Analysis Using Shift Factors.................................................................................35
2.6 Limited PMU deployment and effect on observability ................................................40
2.7 LSE to enhance and expand synchrophasor observability ..........................................41
2.8 Challenges with limited observability .................................................................................42
Chapter 3: Real-Time Assessment with Partial Observability..........................................................................43
3.1 Linear Contingency Analysis for Partial System Observability ..................................43
3.1.1 Formulation of equations........................................................................................43
3.1.2 Proof-of-Concept example.....................................................................................47
3.1.3 Case study and simulations.....................................................................................49
Chapter 4: Optimizing The Linear Security Analysis..........................................................................................55
4.1 Formulation of equations.......................................................................................................56
4.2 Case study and simulations....................................................................................................59
Chapter 5: Summary And Future Work..................................................................................................................64
v

Appendix A ......................................................................................................................................................................66
A.1 Fully observable 5-Bus System source code .................................................................66
A.2 Partially observable 5-Bus System source code ...........................................................66
A.3 14-Bus IEEE test system....................................................................................................67
Bibliography .....................................................................................................................................................................71
vi

LIST OF FIGURES
Figure 1.1 Basic Structure of the Electric System .................................................................................................. 3
Figure 1.2 Map of Power Grid Interconnections in the United States ........................................................... 5
Figure 1.3 Arizona-Southern California transmission system ............................................................................ 6
Figure 1.4 State Estimation Process in Energy Management Systems............................................................ 8
Figure 1.5 Real-Time Assessment and Analysis Process ..................................................................................... 9
Figure 1.6 PMU Deployments in the US in 2009 and 2014 .............................................................................11
Figure 1.7 Limited PMU deployments and effect on observability................................................................12
Figure 1.8 Example of a Transmission Line model and elements..................................................................16
Figure 1.9 Illustration of Phasor Measurement Unit wiring at substation ...................................................21
Figure 1.10: PMU Map at the transmission level in North America .............................................................22
Figure 2.1 Two-bus two-line system example .......................................................................................................26
Figure 2.2 Two-bus two-line system with one of the lines out-of-service ...................................................27
Figure 2.3 An Example of a possible Cascading Chain .....................................................................................28
Figure 2.4 Secure dispatch for two-bus two-line system ...................................................................................29
Figure 2.5 Post-contingency operation under Secure dispatch for two-bus two-line system ................29
Figure 2.6. Real-Time Contingency Analysis main process ..............................................................................32
Figure 2.7 Illustration of PTDF calculation process...........................................................................................34
Figure 2.8 Illustration of LODF calculation process ..........................................................................................35
Figure 2.9 Linear Contingency Analysis Process Using LSFs ..........................................................................37
Figure 2.10 Generic 5-Bus Power System ..............................................................................................................38
Figure 2.11 5-Bus Power System Base Case ..........................................................................................................38
Figure 2.12. Simulation of the loss of Line 2-3 on the 5-bus generic case...................................................39
Figure 2.13 Example power system model with PMU "direct" observability.............................................40
vii

Figure 2.14 Expanded observability with Linear State Estimation ................................................................41
Figure 3.1 Modified power flow of 5-Bus Power System from Figure 2.9..................................................48
Figure 3.2 Simulation of the loss of Line 2-3 on the updated 5-bus generic case .....................................49
Figure 3.3 IEEE 39-Bus System with Limited PMU Observability...............................................................50
Figure 3.4 Post-Contingency flow of line 3-18 for the loss of line 2-25.......................................................51
Figure 3.5 Post-Contingency flow overall system for the loss of line 2-25 .................................................53
Figure 4.1 5-Bus example with limited observability ..........................................................................................56
Figure 4.2 IEEE 14-Bus System with Limited PMU Observability...............................................................60

viii

LIST OF TABLES
Table 2-1. MW, PTDFs for transaction between buses 2 and 4, and LODFs for the outage of 2-3..39
Table 3-2: MW, PTDFs for transaction on buses 25 and 6..............................................................................50
Table 3-3: Updated MW flow with Lines only connected to substations 1 and 4.....................................52
Table 3-4: Accuracy of estimations for the loss of 2-25 with limited observability ..................................54
Table 4-1: powerflow data, PTDFs and LFDFs for transaction between buses 2-13, and LODFs for
contingency of branch 5-6...........................................................................................................................................61
Table 4-2: post-contingency flow estimations and error residuals for all branches, following the loss
of bank 5-6 .......................................................................................................................................................................62
ix

LIST OF SYMBOLS
𝑃𝑃 𝑃𝑃𝑃𝑃 𝑃𝑃 𝑎𝑎 , 𝑏𝑏 , 𝑙𝑙 Power Transfer Distribution Factor for line 𝑙𝑙 , given an injection and withdrawal at
buses a and b respectively.
𝛥𝛥 𝑓𝑓 𝑙𝑙 , 𝑎𝑎 , 𝑏𝑏 Change in line 𝑙𝑙 power flow for the transaction at buses a and b.
𝛥𝛥 𝑃𝑃 𝑎𝑎 , 𝑏𝑏 Power transferred in transaction between bus a to bus b
𝐿𝐿𝐿𝐿 𝑃𝑃 𝑃𝑃 𝑙𝑙 , 𝑐𝑐 Line Outage Distribution Factor for line 𝑙𝑙 , for the contingency for Line 𝑐𝑐
𝛥𝛥 𝑓𝑓 𝑙𝑙 Change in Line 𝑙𝑙 power flow
𝑓𝑓 𝑐𝑐 0
Pre-contingency power flow for contingency element 𝑐𝑐
𝑓𝑓 ̂
𝑙𝑙 , 𝑐𝑐 Post-contingency power flow for line 𝑙𝑙 for the removal of line 𝑐𝑐
𝑓𝑓 𝑙𝑙 0
Pre-contingency power flow of limiting element 𝑙𝑙
𝑓𝑓 ̂
𝑙𝑙 , 𝑐𝑐 𝑛𝑛𝑛𝑛𝑛𝑛 Post-contingency power flow for line 𝑙𝑙 for the removal of Line 𝑐𝑐
𝑓𝑓 𝑙𝑙 𝑛𝑛𝑛𝑛𝑛𝑛 0
New (updated) pre-contingency flow for line 𝑙𝑙
𝑓𝑓 𝑐𝑐 𝑛𝑛𝑛𝑛𝑛𝑛 0
New (updated) pre-contingency flow for contingency element 𝑐𝑐
𝑓𝑓 𝑙𝑙 𝑜𝑜 𝑙𝑙 𝑜𝑜 0
Pre-contingency flow for line 𝑙𝑙 in the previous sample
𝛥𝛥 𝑓𝑓 𝑙𝑙 0
Change in pre-contingency flow for line 𝑙𝑙 between previous and updated samples
𝑓𝑓 𝑐𝑐 𝑜𝑜 𝑙𝑙 𝑜𝑜 0
Pre-contingeny flow for contingency element 𝑐𝑐 in the previous sample
𝛥𝛥 𝑓𝑓 𝑐𝑐 0
Change in pre-contingency flow for contingency element 𝑐𝑐 between previous and
updated samples
𝐿𝐿 𝑃𝑃𝑃𝑃 𝑃𝑃 𝑙𝑙 , 𝑘𝑘 Line Flow Distribution Factor for line 𝑙𝑙 relative to element 𝑘𝑘
[ 𝛥𝛥 𝑓𝑓 ] Measurement change vector
[ 𝑃𝑃 𝑃𝑃 ] Line Flow Distribution Factor reciprocal vector
[ 𝛥𝛥 𝑓𝑓 𝑙𝑙 ] Change in flow to be estimated for line 𝑙𝑙
x

[ 𝑒𝑒 ] Estimation error vector
[ 𝑊𝑊 ] Diagonal matrix of measurement weights

xi

LIST OF ABBREVIATIONS
BES Bulk Electric System
CT Current Transformer
DF Distribution Factor
EI Eastern Interconnection
EMS Energy Management System
EPRI Electric Power Energy Institute
ERCOT Electric Reliability Counsil Of Texas
GPS Global Positioning System
LODF Line Outage Distribution Factor
LSA Linear Security Analysis
LSE Linear State Estimation
LSF Linear Shift Factor
NERC North American Electric Reliability Corporation
PC Planning Coordinator
PDC Phasor Data Concentrator
PMU Phasor Measurement Unit
PT Potential Transformer
PTDF Power Transfer Distribution Factors
RT Real-Time
RTA Real-Time Assessment
RTCA Real-Time Contingency Analysis
RTU Remote Terminal Unit
SCADA Supervisory Control and Data Acquisition
xii

SE State Estimator
SOL System Operating Limit
TOP Transmission Operator
UTC Coordinated Universal Time
WECC Western Electric Coordinating Counsil
WI Western Interconnection

xiii

ABSTRACT
Modern-day operation of power systems has become heavily dependent on advanced
applications to reveal system conditions that were once unobservable to operators. Recent Energy
Management Systems (EMSs) are equipped with real-time applications to help operators monitor the
health of the grid, and even observe areas of the system that are not generally metered. A conventional
State Estimator (SE) is an application within EMS that uses SCADA measurements as data sources
for an iterative non-linear engine to provide downstream applications with a fully observable error-
free system representation, for system monitoring and real-time assessments. Real-time network
applications, such as Real-Time Contingency Analysis (RTCA), use State Estimator results to conduct
iterative analysis to foresee system conditions in case unscheduled sadden outages occur in the power
system. Devices known as Phasor Measurement Units (PMUs), were first introduced in the 1980, and
started to provide a direct measurement to system state, as compared to legacy systems. The challenge
in using synchrophasor measurements for real-time assessments resides in the lack of enough PMUs
to provide full observability of the grid. This research investigates methods to overcome this limited
PMU deployment and introduces a methodology to provide wider observability for real-time
assessments to predict potentially dangerous operating conditions at a high rate.
1

CHAPTER 1: INTRODUCTION
Power systems have been designed and built incrementally over the last 140 years to satisfy
the ever-increasing electric power demand over those years. Power systems exist to achieve one
purpose; deliver energy reliably to customers. Electrical systems have always been designed with
reliability in mind. In other words, systems have been designed with enough generation to meet the
demand, and enough equipment redundancy and availability to ensure reliable delivery of power from
where it is generated, to where power is needed. However, the continuous increase in the demand to
satisfy customer needs around load centers in power systems have become more challenging in the
recent decades. This requires increasing the power supply, while maintaining stability and operational
limits of the system [1].
With the increase in availability of renewable energy resources, many large-scale renewable
generation plants such as wind and solar plants are being integrated to the grid to meet the increased
demand. Furthermore, these environment-friendly and often times, cost-effective alternatives, are
being commissioned to replace expensive or non-sustainable resources such as coal-based generation
and simple-cycle natural gas based steam power generations.
Large-scale generation plants are usually constructed far from load centers. This depends on
the location and availability of means to generate power. For instance, in order to maximize the
utilization of solar generation, solar farms are usually constructed in areas that are mostly sunny all-
year round. Similarly, hydro generation requires building of dams around running water which is
necessary to generating power. Other factors can also influence the location of new power plants,
such as unavailability of cost-effective real estate, which can offset the economic benefits of such
generation. Therefore, plants generating significant amount of power are usually located
geographically far from where the power is needed, which requires a transmission system to transfer
power from where it is generated, to where demand is located [1][2].

2

On top of such geographical and technical issues, deregulation to provide customers with the
option to purchase electricity at cheapest price has resulted in large power transfer across the grid.
This new situation contrasts strongly with the earlier deployment of the grid where generation and
distribution were more collocated. In regulated power systems the entities supplying and delivering
energy are usually the same for their entire service area, operating as a regional monopoly that’s
regulated by the state. Deregulation of energy markets separated generation entities from the
transmission provides, allowing a competitive model of power supply to the customers. Under
deregulated systems, customers are given access to the cheapest energy available, regardless of the
availability of local resources, adding another dimension to grid stress management, and causing more
congestion to the transmission grid [33-35]. Many strategies to mitigate power system congestions are
proposed in the literature, including Generators Rescheduling (GR), load shedding, Distributed
Generation (DG), Optimal Power Flow (OPF), and other methods mentioned in [33-36].
Power system transmission grids are the backbone infrastructure required to transmit power
from where power is generated, which is usually hundreds of miles away, to load centers [1][2].
Transmission systems usually span hundreds of miles, and are operated at high voltages in order to
minimize losses and provide large capacity for power transfers. They are also usually meshed or
interconnected to form a network to support the transfer of power across the system. Following the
load growth and increase in number of interconnected resources, transmission grids have also
incrementally evolved to support the gradual increase in the amount of power to be transferred, while
maintaining system security and reliability. Figure 1.1 shows the basic structure of the power system,
identifying the three major components of the grid: Generation, Transmission and Distribution
(Load).

3

Figure 1.1 Basic Structure of the Electric System [3]
The advancement of renewable energy generation in the past decade provided many solutions
to meet the electrical load growth. In addition, the availability of clean-energy sources incentivized the
industry to replace conventional generation that are not environment-friendly with solar and wind
resources. All that in addition to low-cost energy available from renewable energy resources, helping
to bring many renewable energy resources to the interconnection in a short period of time. Bulk power
transmission systems, on the other hand, have not evolved at the same rate as generation or demand.
Factors like high cost, Right-of-Way issues and environmental concerns prohibited transmission
owners from investing in the transmission sector [4]. This presents a significant challenge to system
operators in transferring the energy from generation plants to load centers, without compromising the
integrity of the power grid, and always ensuring reliable power delivery with limited transmission
capacity. Some areas of the transmission network are becoming bottlenecks in terms of transmitting
power to meet the load demand during peak load conditions, and operators must navigate the power
flow through the network while maintaining the reliability and integrity of the power system.
1.1 Motivation and Objective
Electric power grid in the United States started as small and independent isolated systems that
operate at different operating frequencies and voltages. However, with the increase in power demand,

4

and the need to transfer power over larger distances, utilities started to interconnect, to meet load
growth and increase security and reliability [1][4]. The relatively small systems continued to grow and
interconnect gradually, forming currently only three major interconnections: the Western
Interconnection (WI), the Eastern Interconnection (EI), and the Texas interconnection (overseen by
the Electric Reliability Council of Texas, or ERCOT) [5].
The three interconnections forming the power grid of the United States are shown in Figure
1.2, and are divided as follows:
- The Eastern Interconnection, covering the area east of the Rocky Mountains and part of
northern Texas. The Eastern Interconnection consists of 36 balancing authorities, 31 in the
United States and 5 in Canada.
- The Western Interconnection, over seen by Western Electricity Coordinating Counsil
(WECC) encompasses the area from the Rockies west and consists of 37 balancing authorities:
34 in the United States, 2 in Canada, and 1 in Mexico.
- The Electric Reliability Council of Texas (ERCOT) covers most, but not all, of Texas and
consists of a single balancing authority.

5

Figure 1.2 Map of Power Grid Interconnections in the United States [6]
With the increase in complexity of power grids, and with the large-scale systems spanning
across the United States, it became necessary to continuously monitor the power grid and protect its
elements in order to avoid major outages and system disturbances affecting system reliability [7]. In
fact, as a result of different power system events in the recent history and the contingencies that have
occurred, transmission system operators are mandated to monitor the Real-Time (RT) state of the
power system to timely respond to events and operating conditions that may compromise the grid.
One example of such events is the Pacific Southwest blackout, generally referred as Pacific Southwest
blackout. On September 8, 2011, a system disturbance occurred in the Pacific Southwest, and initiated
cascading outages in the system which ended in a partial blackout of Southern California, leaving

6

approximately 2.7 million customers without power [8]. The initiating event was a loss of a single
500kV transmission line, causing a series of events over the span of 11-minutes before the system
went dark. Figure 1.3 shows the major transmission system connecting the state of Arizona to
Southern California, including the 500kV line, Hassayampa-North Gila, that triggered the outage.

Figure 1.3 Arizona-Southern California transmission system [9]
NERC identified the root causes of the event leading to the cascading event, and provided
recommendations to minimize the risk of such events happening in the future. Recommendation 12
in the NERC report says: “TOPs should take measures to ensure that their real-time tools are adequate, operational,
and run frequently enough to provide their operators with the situational awareness necessary to identify and plan for
contingencies and reliably operate their systems” [8]. This event shows the significance of performing “timely”
Real-Time Assessment (RTA) of the power grid to reflect real-time conditions, and alarm operators if
signs of risk to system reliability are detected. Relying on pre-determined studies is not sufficient
anymore, and cannot account for all possible real-time scenarios, since real-time conditions might

7

deviate from pre-determined study assumptions. From the NERC recommendation, we understand
that the real-time assessment tools should:
1. Provide adequate information – RTA applications should be comprehensive enough to
provide all the situational awareness needed to ensure a reliable operation of the system, and
prepare the system to operate reliably in case contingencies and system disturbances happen.
Such applications that provide situational awareness (e.g., State Estimator (SE) and Real-Time
Contingency Analysis (RTCA)) should be ready for operators to leverage and use.
2. Be operational – RTA applications should be ready and available in real-time, and on-demand
to provide the resources needed by operators to maintain system reliability in some
“intelligent” possibly semi-autonomous way. These applications are heavily dependent on real-
time information availability, software models, hardware…etc. They should be designed to be
highly available, and function as expected especially during heavily-stressed power system
conditions.
3. Run frequently – to provide operators with timely information to mitigate issues. The real-
time advanced applications are very resource intensive, and can take time and effort to provide
the required information, especially since post-contingency system conditions require
simulation of thousands of contingencies and scanning the system conditions iteratively. The
design should guarantee fast and frequent operation using real-time conditions.
To summarize, RTA applications must be available, quickly, and reliably during all operating
conditions. Otherwise, system conditions that may lead to cascading events may go unnoticed, risking
the reliability and the integrity of the system.
State Estimator (SE) is the core application of Energy Management Systems (EMSs). It uses real-
time measurements from SCADA, including voltage and current magnitudes, real and reactive power,
and system models to estimate the state of the system and provide situational awareness to operators

8

in near real-time. The State Estimator provides all downstream advanced applications such as Real-
Time Stability Analysis, Voltage Stability Analysis (VSA), and other real-time applications with the
base cases needed to perform the real-time assessment [10]. Figure 1.4 shows the state estimation
process in Energy Management Systems.

Figure 1.4 State Estimation Process in Energy Management Systems [10]
The State Estimation is a multi-step process that involves iterative and complex mathematical
equations before a solution is reached. Typical State Estimators provide a solution to state of the
system once every 1-3 minutes, and create base-cases to be used for downstream applications in real-
time [10]. These base-cases represent a snapshot of all bus voltages and angles required to solve
powerflow. A powerflow solver is then used to solve the case and provide a full powerflow solution
to that base case, which can be used to perform real-time assessments. The main process of real-time
applications is shown in Figure 1.5.

9

Figure 1.5 Real-Time Assessment and Analysis Process
Real-Time Contingency Analysis (RTCA) is one of the main RTA applications that simulates
“what-if” scenarios to reveal any possible issues should any credible contingency happen during the
current operating conditions. The main goal of RTCA is to uncover any real-time overloads that were
not seen in the pre-determined studies. RTCA takes the SE latest base-case, simulates contingencies
one by one, solves powerflow using the powerflow solver for each contingency, and scans all
equipment for possible overloads. The RTCA process is very thorough, and includes thousands of
simulations and powerflow solutions for every SE case. Requirement 13 of the NERC TOP-001-4
standard requires TOPs to perform an RTA every 30 minutes [11]. This requirement specifies the
minimum measures required for compliance regarding RTA studies to reduce reliability risks. That
said, utilities and system operators usually run RTCA once every 5 minutes, to reduce risks and ensure
system reliability. However, even when running the RTCA frequently, any alarm that operators receive
from RTCA is about 8 minutes late given the complexity of solution and solving large models (3
minutes for SE and 5 minutes for RTCA).

10

For the Pacific Southwest blackout event, operators had only 11 minutes to respond to the
disturbance event before the whole system blackout. That said, with tools like RTCA readily available,
the outage could have been avoided knowing that the loss of the line would overload other equipments
and start the “domino-like” sequence of events. But that information needs to be made available to
operators quickly to allow them to assess the system condition and determine the best course of action.
The advancement of substation computing and metering devices led to the development of Phasor
Measurement Units (PMUs) in the early 1980s [12][13]. PMUs provide high-speed synchronized
phasor measurements known as synchrophasors. PMUs measure the phasors voltages and currents
form a wide area of the power system and stream the information in real-time to specific control
centers. This means that with PMUs, the state of the system is observed (measured) more rapidly and
accurately as compared the state of the system using the traditional EMS/SCADA system (estimated)
[12]. In other words, synchrophasors provide a reliable, fast, and guaranteed solution to the State
Estimation problem.
In the past decade, many researchers have developed and designed a Linear State Estimator (LSE)
that leverages PMU measurements. LSEs provide a solution to the system state as fast as 30-60
samples per second, as compared to traditional state estimators that can take up to 5 minutes to solve
[13-15]. Since 2015, many utilities and ISOs have deployed the Linear State Estimator to provide a
direct and real-time solution to the system state and compliment the traditional state estimator in EMS
[16][17]. And with the maturity of LSE, many efforts moved to real-time assessment using
synchrophasors, and developed a synchrophasor-based RTCA [18]. Some of the advantages of using
a synchrophasor-based RTCA include having an independent platform without dependency on EMS,
and a platform that uses LSE that provides guaranteed base cases in real-time at the synchrophasor
rate without delay.

11

Two challenges yet remain with the current synchrophasor-based RTCAs proposed up until today.
First, no changes have been performed to the operation process of RTCA. The process still requires
simulating thousands of contingencies in a powerflow simulator and evaluate all the cases for
violations in real-time. This means that even with synchrophasors at sampling rates of at least 30
samples per second, operators will be made aware of potential overloads around 5-10 minutes after
they occur. Secondly, the PMU deployment currently available is relatively low, and does not provide
adequate coverage of the Bulk Electric System (BES). Even though PMU devices were invented in
the 1980s, the deployment of PMUs was limited to cover critical substations and transmission interties,
with a focus on research efforts and initiatives [19][20]. The deployment of PMUs started to rapidly
increase in the last decade, with the availability of funds from American Recovery and Reinvestment
Act (ARRA) of 2009. Figure 1.6 demonstrates the increase in PMU deployments in the United States
between the years 2009 and 2014, where most of the new deployments have occurred. DOE and the
utility industry invested more than $350 million to deploy these additional PMUs in 2009-2014.

Figure 1.6 PMU Deployments in the US in 2009 and 2014
The PMU deployment has been slowing down in the past few of years since research funds
aimed to support PMU deployment have depleted. In addition, most of the PMUs that were deployed

12

for research do not meet the NERC CIP requirements to be used in production for real-time
operations. Also, new deployments that take NERC CIP compliance into account require a significant
investment due to the cost of cyber security upgrades, which negatively impacted the growth rate of
PMUs. Therefore, with no expectations to reach full BES visibility in the near future, applications that
use only synchrophasor measurements should have the capability to overcome partial observability of
the grid. Otherwise, operators will not be able to guarantee a secure operation of the grid.

Figure 1.7 Limited PMU deployments and effect on observability
Figure 1.7 demonstrates an example of how PMU deployment, even with Linear State
Estimation, affects the observability of the power system in real-time. PMU locations and observable
areas in Figure 1.7 are highlighted for illustration. The objective of this PhD research is to address the
two aforementioned challenges, including:

13

1. Address the limited observability of synchrophasor technology caused by the scattered
PMU deployment. This will be done by introducing a linear prediction process to provide
a fully observable power flow of the system to be used in real-time assessments.
2. Develop a real-time assessment methodology leveraging the predicted fully observable
system conditions and PMU measurements at a high rate, to provide real-time intelligence
to operators without delay.
To address the aforementioned objectives, Chapter 2 of this dissertation will introduce the
need for security analysis, present the processes that are currently deployed to provide situational
awareness needed, and propose a methodology that will be used as a foundation for real-time
assessments. Chapter 3 will address the limitations and challenges faced with partial system
observability, and introduce a novel prediction methodology to provide full visibility using the current
deployment of PMUs. Finally, Chapter 4 will present a complete solution to meet the real-time
assessment requirement by using synchrophasors, leveraging the methodologies introduced in the
previous Chapters 2 and 3.
1.2 Background
Power Systems are designed in a way that ensures a secure and reliable operation during normal
operating conditions. They are also designed to withstand interruptions and failures in system
components and ensure power is delivered safely and continuously during abnormal conditions [2].
These factors need to be considered early in the design phases of the system to allow the grid to
withstand sudden interruption of equipment (outages) without compromising on power delivery.
Transmission and generation outages are part of the daily operation of the power system.
Transmission outages are outages affecting the transmission elements of the power system, such as
transmission lines, transformers, capacitors, breakers, buses, and other equipment. Generation outages

14

are the ones that affect generators directly, including partial or total limitation of generation capability
for a power plant due to maintenance or disturbances [2].
Outages happen more frequently that one would think. In fact, the bulk power system almost
never operates with all equipment in service. Outages on power system components can be either
planned of forced. Planned outages are scheduled ahead-of-time to allow preventative maintenance
on equipment without compromising the stability or security of the bulk power system. Ahead-of-
time planning of outages allows engineers to prepare operating plans during the study time horizon,
in order to operate the system without violating operating limits. Forced outages, however, are outages
that are unplanned, and forced on the system in near real-time, due to equipment failure, expected
failure, or other circumstances that require immediate attention. Therefore, because equipment failure
causing forced outages is unpredictable, it is impossible to know which equipment is going to fail at
what time. Therefore, the system needs to be designed and operated somehow to guarantee that it can
withstand unpredictable equipment failures.
Transmission Operators are required to operate the system considering both planned and
forced equipment outages. For planned outages, operating plans are developed ahead-of-time during
the outage study time horizon by operations engineering support groups. This means that when an
outage is scheduled, engineering studies are conducted, and an operating plan is established to ensure
that the outage does not cause exceedances of equipment limits or result in system instability or
equipment damage. The unpredictability of forced outages occurrence adds another layer of
complexity to the problem. The operating plan somehow needs to protect the system from forced
outages as well. Therefore, the plan for a given system state requires that the system can withstand
any forced outage without violating system operating limits, at any given point of time. In other words,
studies need to be conducted such that the system does not exceed its pre-determined limits, for a
loss of any element in conjunction with the outage scheduled. This is referred to as the NERC N-1

15

criteria, where N is the number of elements that are energized at a point of time for that system
condition.
Knowing the system state ahead of time helps operate the system without allowing it to be
driven into instability or undesired operating conditions. This is only possible if outages are carefully
planned and scheduled, so that responsible entities can study the impact of outages and develop a
mitigation plan should outages push the system closer to its limits. Hence, Planning Coordinators
(PCs) implement outage coordination methodology, where all processes for outage studies are
outlined.
Outages are studied nowadays using software applications, where power systems are
represented mathematically respecting the principles of power system operation, referred to as
network models. Network models contain information including system equipment models (Lines,
generators, transformers, breakers, capacitors…etc.), system configuration and connectivity, and
equipment states and limits. Network models overlaid with a specific equipment operating condition,
where a certain generation and load profiles are assumed, along with a possible system topology, is
called a powerflow case. A powerflow case is considered a possible operating point of the power
system represented in the software environment [4]. Powerflow cases allow users to modify and study
certain operating conditions of the system to predict operating plans. Planning engineers study system
conditions for a requested outage by adjusting the state of the system in the powerflow case, and
recommend operating plans based on the study results. These studies are referred to as offline studies.
The other type of power system studies is what is referred to as real-time analysis, where in a
real-time environment, the network models are overlaid with real-time measurements representing the
real-time system condition. This includes line flows, bus voltages, equipment status, and other
measurements to create powerflow cases periodically in real-time.

16

1.2.1 Line Ratings and System Operating Limits (SOLs)
Power transfer capability of transmission lines depends on many factors, such as conductor’s
or the cable’s characteristics, thermal rating, current caring capability, weather conditions, and
overhead line clearance to ground, as well as vegetation in the right-of-way (ROW). Mainly, the
structure and material of the cables dictate the maximum amount of power the transmission line can
transfer without compromising the integrity of the cables. This is referred to as Line Rating. However,
there may be equipment that are connected in series with the transmission line with ratings that are
more limiting than the line rating, which limit the overall transfer capability. Therefore, the total power
that can be transferred through a transmission line is constrained by most limiting elements along that
transmission path. This is illustrated in Figure 1.8 below.

The transmission line connecting substation 1 to substation 2 in Figure 1.8 consists of multiple
breakers, switches, disconnects, series elements, in addition to the transmission line cable. Therefore,
if any of these elements is rated less than the rating of the cable, it limits the maximum power than
can be transferred from substation 1 to substation 2. For that reason, the operating conditions of the
power system should guarantee that the transmission line flow does not exceed these limits. The lowest
rating of the most limiting element of the transmission line is referred to as the System Operating
Limit (SOL) of the line. Monitoring of System Operating Limits in real-time is required to ensure that
the system is operated to respect those limits and provide awareness to operators once limits are
violated in order to implement the appropriate mitigation plan for relieving the overloads.
Breaker
Substation 2 Substation 1
Switch
Series Capacitor
Figure 1.8 Example of a Transmission Line model and elements

17

1.2.2 Monitoring and Situational Awareness
The integration of renewable generation in response to the load growth and Carbon Dioxide
reduction has increased the challenges at the transmission system level. The need to transfer additional
generation to load centers with the same transmission network as before deregulation pushes the flow s
closer to the transmission operating limits. Therefore, proper procedures and methodologies need to
be put in place to manage the flow of power to ensure System Operating Limits are not exceeded in
real-time. In addition, adequate tools need to be implemented and made available to provide operators
with real-time monitoring of transmission equipment in order to identify and mitigate potential
exceedances of SOLs. Supervisory Control And Data Acquisition (SCADA) systems and advanced
applications of Energy Management Systems (EMS) (e.g. State Estimation (SE)) assisted operators for
years in providing real-time situational awareness of the power system. Moreover, Real-Time
Contingency Analysis (RTCA) is deployed currently in most of modern control centers to enhance
situational awareness by performing real-time assessment of the power grid frequently. RTCA
provides a look ahead view on the system operating conditions should the power system experience
loss of equipment due to faults or failures. However, these applications are resource intensive, and
can take several minutes (usually 5 to 10 minutes) to provide a single solution that operators can use
to operate the system. Therefore, alternatives that may provide results in a faster timeframe can be
very beneficial to mitigate potential issues that require timely action by system operators.
1.3 Enabling Technologies
Grid control centers and operating personnel require certain visibility and real-time
information to allow for informed decision-making, to maintain a reliable operation of the power grid.
Advanced systems, tools, and applications are put together to provide operators with the information
they need, and the tools necessary to validate and study the real-time conditions of the system, and

18

make informed control decisions to guarantee continued and reliable power delivery. Energy
Management Systems, comprising Supervisory Control And Data Acquisition, communications, and
advanced real-time assessment applications, are vital to provide operators and with up-to-date
information necessary to maintain situational awareness of the grid.
1.3.1 Supervisory Control And Data Acquisition (SCADA) System
Most control centers at utilities and ISOs today use Supervisory Control And Data Acquisitio n
systems to provide operators and engineers with real-time monitoring of power system equipment in
the field. SCADA is a computer-based system that gathers and collects real-time measurements from
devices in the field, to allow monitoring for critical devices in the power system [21]. Typical SCADA
systems provide data at the rate of 0.1 Hz to 0.25 Hz, which varies from one system to another. With
its relatively slow data-rate, SCADA measurements are mainly used for steady-state monitoring of the
power system, as they do not provide enough resolution to reveal system dynamics. SCADA systems
provide continuous monitoring of metrics available through metering devices in the field, such as
magnitude of voltages and currents, active and reactive power, equipment statuses and other
measurements. These measurements, however, lack time-synchronization in SCADA systems and are
visualized as they arrive in real-time. Therefore, depending on communication delays and geographical
distance from the measurement sources, data is usually presented out-of-synchronization. That said,
the impact of synchronization is minimal if data is used for steady-state monitoring. SCADA has been
used for a long time to provide operators with the situational awareness needed to monitor the system.
With the real-time data available, operators can monitor equipment status and availability, and take
preventative and corrective action to ensure equipment are operated within limits.

19

1.3.2 State Estimator (SE)
A state estimator is one of the most widely used functions in EMS advanced applications.
State estimators estimate the state of the system in real-time to provide trust-worthy information that
validates system models to system operators [21]. System state is defined as the phasor voltages at all
system buses, comprising magnitude and angles, using real-time measurements (e.g. voltages, currents,
power, and topology) and the power system network model. State estimators provide data quality
control, including bad data identification and detection, expand visibility by predicting the state of the
system at unmetered substations and equipment to provide additional situational awareness, and
provide powerflow cases that can be used for on-demand simulations to study mitigation actions prior
to implementing them. In addition, the system state serves as the base for downstream simulation-
based applications, such as contingency analysis and voltage/transient stability analysis, providing
actionable information that operators can react to, and ensure safe and stable system operations.
State Estimators uses measurements from the field including voltage magnitudes, current
flows and injections, power flows and topology information, and runs powerflow-like equations to
calculate the state of the system representing the current operating condition. With the availability of
many measurements in the field, there are usually more measurements than state variables, forming
an over-determined problem. The solution to the state estimation problem is the system state, which
is the set of voltage phasors at all buses that satisfy the equations from the set of measurements with
minimum error. The State Estimator is considered non-linear in nature, given that the relationship
between the input measurements and the phasor voltages is non-linear.
EMS advanced applications are mostly operating based on solving powerflow cases that
represent current power system conditions, by simulating changes in the system and studying the
stability and operability of the system during those conditions. Operators use these “study modes” to
foresee system operating conditions for line outages, re-dispatching generation, shedding load…etc.

20

Solving the powerflow problem requires telemetry at all equipments of the power system,
which is not the case in most systems. In addition, existing metering equipments are subject to outages
and failures, which compromises the convergence of powerflow solution. State Estimation provides
a system representation that is fully observable, by filling in the gaps of telemetry, and removing bad
measurements prior to solving powerflow. State Estimator ensures that the powerflow engine is fed
with all the measurements that are required in an accurate manner. Usually, part of the State Estimator
is a powerflow engine that is fed with a fully observable representation of the system, to produce a
powerflow case will all unknown system states solved.
1.3.3 Synchrophasor systems
Synchrophasor technology offers many advantages over SCADA systems. Synchrophasors
provides measurements at a significantly higher resolution than SCADA, at rates ranging from 30
samples per second, to 120 samples per second. High data rate of synchrophasors adds many use case s
to increase system reliability including system dynamics monitoring, wide-are situational awareness
and automatic wide-area control [22]. For such applications, it is of great importance to have the data
represent the system in greater accuracy compared to conventional systems. Therefore, the phasors
measured by this technology are timestamped with synchronized time-source across all devices (hence
the name synchro-phasor), to ensure the measurements are made available to downstream applications
in a synchronized fashion. Another unique advantage of synchrophasors is the measurement of
voltage and current angles, which is not available in conventional measurement devices due to the lack
of synchronization. legacy systems rely on State Estimation to provide powerflow solutions, using
SCADA measurements, and system models in order to estimate angles at substation buses. With
synchrophasor technology, the availability of angles in the measurement stream allows the State
Estimation problem to focus on data-quality and redundancy, rather than solving powerflow-like
equations to estimate angles periodically for real-time system conditions. In addition, phase angle

21

metering at a significantly higher resolution allows the metering devices to calculate the frequency at
the metered location at the synchrophasor rate.
a. Phasor Measurement Units (PMUs)
Phasor Measurement Units are smart metering devices installed mostly at the substation-level
of the power system, to continuously measure and stream voltage and current phasors along with
other calculated values [22]. Measurements and provided periodically in milliseconds, sometimes even
microseconds, in synchronization with all other PMUs across the transmission grid, and sent in the
network as a stream of data flow to the collection devices at the control centers.
Currents and voltages of substation apparatus are available through Current Transformers
(CTs) and Potential Transformers (PTs). PMU devices installed at the substation require installation
of CTs and PTs for which devices requires synchrophasor monitoring. In addition, the need to
timestamp the measurements to provide a synchronized overlook of the system required a connection
to the substation GPS clock, which is tied to the GPS antenna for synchronization. Figure 1.9 below
illustrates the PMU wiring and connectivity at the substation-level.

Figure 1.9 Illustration of Phasor Measurement Unit wiring at substation

22

The PMU device measures phasor quantities in the form of magnitude and angle for voltages
and currents, in addition to the calculated frequency using measured voltage angle, and timestamps
the values with reference to UTC before sending the data out. The data is sent as a stream through
routable protocols to the control centers for visualization.
PMUs are becoming more attractive to Transmission Operator and Reliability Coordinator
entities, given the added monitoring benefits that are unavailable using conventional systems. Figure
1.10 shows the deployment of PMUs on the transmission level in North America, as of May 2017.

Figure 1.10 PMU Map at the transmission level in North America [23]
b. Phasor Data Concentrators (PDCs)
Similar to Remote Terminal Units (RTUs) in SCADA systems, the goal for synchrophasors is
to have PMUs devices spread out in the field to provide real-time monitoring and situational awareness

23

of the grid to operators in order to maintain system reliability. With the variability of geographical
distance and communication delays for various PMU deployments, data received from PMUs to the
control centers may arrive out of synchronization. For that reason, a process must be put in place to
align the measurements received at the control center using the timestamp of measurements. This
provides a representation of the grid from measurements taken at the same time. This is achieved by
Phasor Data Concentration. Figure 1.10 above shows locations of Data Concentrators installed to
collect data from PMUs at transmission level substations.
Phasor Data Concentrators collect all synchrophasor data sent by PMUs in the field, time-
align all the synchrophasor data using the measurements timestamp on all PMU streams, and provide
one stream representing the system snapshot for that timestamp for downstream applications for
visualization and analysis [21]. Phasor Data Concentration may also include functionality on bad data
filtering and conditioning, to ensure good quality stream of data in passed to operators for visualization
and analysis.
c. Linear State Estimator (LSE)
Synchrophasor technology provide the ability to measure angles in addition to magnitude
quantities, which means that the system state is known at those locations where PMUs are deployed.
This allows for the State Estimation problem to be simplified to become linear instead [17]. In other
words, the set of equations that are required to estimate the states of the power system are linearized,
allowing for a non-iterative state estimation process.
A linear state estimator comes with a main advantage over legacy State Estimator; the ability
to estimate system states at the sampling rate due to the linearity of relationship between estimated
states and measured states. Estimating at sampling rate provides visibility of system dynamics and fast
system changes, as opposed to monitoring using conventional systems. Also, Linear State Estimators

24

guarantee convergence of solution, since the systems uses linear equations to calculate observable
system states.
1.3.4 Real-Time Contingency Analysis
Operating plans are developed to ensure operating the system without violating System
Operating Limits. SOLs are established to avoid exceeding facility ratings of transmission equipment,
or stability limits, during normal or emergency conditions [2]. Once those limits are established in the
operations planning horizon, limits need to be monitored in real-time in order to meet the operating
criteria by mitigating any SOL exceedances. This is achieved by running periodic studies to simulate
the effect of any equipment failure in real-time, which is referred to as Real-Time Contingency
Analysis.
RTCA requires steady-state powerflow cases (or base cases) to be made available periodically
to the application, with updated base cases representing system conditions in near real-time [18].
Powerflow cases are usually passed from state estimation periodically, usually every 3-5 minutes.
Contingency Analysis is performed on the cases as they come in, to simulate the system steady-state
response for the loss of equipment, to allow operators to monitor and mitigate potential exceedances
of System Operating Limits in a timely manner. In this dissertation, we will focus on developing
methodologies to enhance existing real-time contingency analysis applications to provide information
at a high rate, by utilizing PMUs and synchrophasor-based methodologies.

25

CHAPTER 2: POWER SYSTEM SECURITY
Electrical power is made available to the end user instantly, on demand, at the correct level of
voltage and frequency, to allow safe and uninterrupted consumption at the user side [24]. That level
of availability and reliability comes from very careful planning, design, and operation of the power
system, causing the system to appear in steady-state condition, even though the system is prone to
failures and disturbances. The “steady-state” delivery of power comes as a result of the very large and
interconnected power system, and the quick remedial actions to system disturbances and isolation of
faulty equipment that may affect the operation of the power system. Those remedial actions are
implemented automatically using protective relays that are designed to monitor the system, sense any
disturbances that may occur, and take corrective actions to isolate the disturbance from the rest of the
system by removing the faulty equipment from the network. Therefore, to guarantee system reliability,
every piece of equipment connected to the power system is designed in a way to allow for it to be
isolated and disconnected from the network using Circuit Breakers (CBs) [2]. This allows transmission
owners to perform preventative maintenance on the equipment after disconnecting them from the
grid, and for protective relays to isolate them in emergency situations. Figure 1.1 shows a model for a
transmission line connected to two substations. Circuit Breakers, shown in Figure 1.1 as red boxes,
are the devices that are mainly used to isolate faulty equipment. For instance, if there are some line-
maintenance work needing to be performed, once approved, the line can be deenergized by opening
the two breakers at either end of the line.
Like any other equipment, power system devices require continuous maintenance to ensure
system reliability and meet life expectancy of equipment. However, taking equipment out-of-service
should not compromise the power system, or affect the delivery of power. Therefore, entities
responsible for operating the power system conduct “outage studies” to guarantee the reliable delivery
of power and operation of the system during planned outages. Since power system equipment are

26

designed to be operated within certain limits, outage studies are conducted to ensure that exceedances
of power system equipment limit does not occur because of the outage, in conjunction with all the
ongoing outages and system operating conditions forecasted for that period. These studies are
conducted ahead of time, and referred to as planning studies.
Adequate studies are performed ahead of time in the operations planning time horizon to
ensure the power system is operated safely and reliably in real-time. However, operating plans
sometime deviate from the studied conditions. This may happen due to changes in weather conditions
affecting load forecast, changes in outage schedules and operating plan, or even unplanned outages
that are forced in the real-time horizon due to equipment failure or emergency conditions. Therefore,
similar analyses are performed in the real-time horizon, usually at the control center, to reveal any
exceedances in System Operating Limits under the current system conditions and power dispatch.
Figure 2.1 shows an example of a certain system dispatch for a two-bus two-line system. Generator 1
is producing 400MW, while generator 2 is producing 300MW to serve the 700MW load on bus 2.
Both transmission lines are carrying 200MW each and are operated under the transmission operating
limits.

Figure 2.1 Two-bus two-line system example

Now, let us consider the situation where one of the lines is removed due to a disturbance, and was
forced out-of-service. Figure 2.2 shows the expected power flow for the system with the line removed.
With both generation and load remaining the same, and assuming the generation dispatch is
200 MW
(350 MW Limit)
(350 MW Limit)
400 MW
G
300 MW
G
200MW
1
2

27

unchanged, all the power generated by G
1
will be rerouted to move through the other line, exceeding
the line thermal limit and causing operational challenges affecting the reliability of power delivery.

Figure 2.2 Two-bus two-line system with one of the lines out-of-service
The example in Figure 2.2 demonstrates the necessity of predicting system conditions should
similar contingencies happen. The North American Electric Reliability Corporation (NERC) defines
a power system contingency as “The unexpected failure or outage of a system component, such as a generator,
transmission line, circuit breaker, switch, or other electrical equipment” [25]. Because these contingencies can
happen unpredictably, protective relays are designed to sense and monitor the transmission
equipment, and disconnect them in case they exceed the operating limits considerably due to
disturbances. However, if power systems are operated without consideration of operating limits,
protective relays may operate for overloading conditions, and automatically disconnect the equipment.
This event might cause other equipment to get overloaded, and consequently more equipment being
removed, causing what is referred to a cascading event, and possibly leading to system blackout.
Figure 2.3 shows a state diagram for a power system, with possible cascading events leading to
voltage collapse and system blackout. The transition from one state to another is caused by a relay
action for an exceedance of equipment limit, or in general, any an expected loss of an electrical
component. It is possible to have bounded cascading events with less impact on the power system (as
shown in terminal states in blue or yellow states), but there’s the risk of possible outages triggering a
cascading event that is catastrophic to the system (terminal states in red). For that reason, it is vital to
700 MW
0 MW
(350 MW Limit)
(350 MW Limit)
400 MW
300 MW
400MW

28

operate the system in a state that does not cause such events, and the best way to do that is by ensuring
that contingencies or outages do not cause overloads if they happen.

Figure 2.3 An Example of a possible Cascading Chain
To break every possible cascading chain in the power system, the system needs to be operated in
a way such that any single equipment failure or contingency will not cause an overload on any other
equipment in the system. Referring to Figure 2.3, operating the power system without allowing
contingencies to cause any further overloads will prevent the system from transitioning from the state
“SS” to the “N1” state, and consequently breaking the cascading chain. This is referred to as the
“NERC N-1 criterion” [2].
In the previous example, knowing that the contingency of a transmission line will cause an
overload on the other, generation can be re-dispatched to avoid possible overloads should the
contingency occur. Consider the operating condition for the same system in Figure 2.4. The total
generation and load for the same system has not changed in this scenario, but the power generated
around the system was reconfigured to allow for less power transfer through the lines. Even though

29

the lines are loaded to about 40% capacity, this margin allows for secure operation should any
contingency happen.

Figure 2.4 Secure dispatch for two-bus two-line system
The post-contingency flow after one of the lines is removed is shown in Figure 2.5. In
comparison to the operating conditions shown in Figure 2.2, the load here is served without
compromising the system should a contingency occur. Therefore, it is very important not only to
monitor current operating conditions of the system, but also predict how the system will operate for
any contingency, and ensure that the current operating conditions will not compromise the system
should that contingency happen.

Figure 2.5 Post-contingency operation under Secure dispatch for two-bus two-line system
2.1. System Security and Real-Time Monitoring
The role of system operators has evolved over time with the advancement of metering
technologies, communication infrastructure, and computing platforms, allowing near real-time
monitoring of all field equipment of the power system. System operators work continuously to
150 MW
(350 MW Limit)
(350 MW Limit)
300 MW
400 MW
700 MW
150 MW
700 MW
0 MW
(300 MW Limit)
(350 MW Limit)
300 MW
400 MW
300MW

30

maintain the reliability of the power system, by gathering as much information as possible through
any means available, to gain the situational awareness needed to operate the grid securely. This includes
monitoring transmission line flows, bus voltages, and other metrics that can be used as to assess the
real-time condition of the system.
Energy Management Systems are computing platforms that operators use to monitor real-time
conditions of the power grid. Measurements and calculations including voltages, currents, power
flows, status of equipment, and other data are available for almost every component in the power
system nowadays, allowing real-time monitoring for these devices. However, with so much
information, operators cannot monitor all system components in a reasonable amount of time to
mitigate any issues that are observed. Therefore, EMS applications are installed to monitor the
telemetered and calculated data, process them in real-time, and alarm operators of any conditions that
require operators’ attention. This monitoring covers current system operating conditions without
consideration of contingencies that may occur. This is referred to as the “pre-contingency” or the
“base case” state of the system.
To guarantee a secure operation of the power system, operators need to know what outages will
cause problems, and mitigate any overloads or violations before the contingency occurs. Therefore,
operators or operation personnel need to simulate contingency operation for every single equipment
failure in the power system. This requires having models available to represent the current state of the
system (flows, topology, generation dispatch…etc.), and the ability to simulate those contingencies
using a powerflow application solution. And with this type of analysis required for thousands of
equipment, this task cannot be performed manually by operators. Therefore, the process of simulating
all contingencies for a specific system conditions using powerflow simulators to reveal any post-
contingency violations is referred to as “contingency analysis” or “security analysis”. Contingency
analysis is an iterative process that simulates thousands of “what-if” scenarios, and compares all post-

31

contingency flows to their respective limits to reveal possible overloads. The solution is designed to
alarm and report any violations to operators for appropriate action.
Contingency analysis applications nowadays are integrated within EMS systems to use real-time
data, create powerflow cases, and perform the security analysis frequently over time, to monitor
conditions over time and continuously provide operators with timely alarms without user intervention.
These solutions are referred to as Real-Time Contingency Analysis (RTCA).
2.2 Real-Time Contingency Analysis
Real-Time Contingency Analysis, or sometimes referred to as Real-Time Security Analysis, has
evidently become one of the most important State Estimator based applications that are used to
monitor and operate the power grid in real-time [2][18]. Contingency Analysis not only reveals
exceedances in equipment flows and voltage limits as they happen, but also provides awareness on
violations that might occur should the system experience unexpected loss of equipment. Contingency
Analysis application simulates “what-if” scenarios to study the impact of outages, and analyzes the
powerflow as compared to System Operating Limits. RTCA uses a pre-defined list of all possible
credible contingencies, and iteratively performs powerflow studies for each of the defined
contingencies to reveal possible exceedances of system limits, and alarms operators for any detected
violations. Real-Time Contingency Analysis requires continuously updated base cases representing the
power flow and state of the system to provide the situational awareness required to operate the power
system within it’s acceptable limits. These base cases are provided in real-time by the State Estimator
(SE). RTCA uses the base cases provided by State Estimator in near real-time, to simulate
contingencies and run powerflow iteratively, as shown in Figure 2.6.
However, studying a significantly large number of contingencies requires time and resources,
which mean that operators would not have the information readily available as soon as the system

32

state changes. With access to synchrophasors and Linear State Estimation, the process can be
simplified to provide more actionable information to control centers operators and dispatchers.

Figure 2.6. Real-Time Contingency Analysis main process
2.3 Linearization of the security analysis problem
Real-time contingency analysis requires solving iterative powerflow equations for thousands
of system topological scenarios to reveal potential exceedances to System Operating Limits following

33

unscheduled loss of equipment in real-time. Multiple approaches have been proposed to perform
security analysis using synchrophasor measurements [18]. However, these methods suggest a
contingency analysis solution that runs iteratively over a multi-minute window, like SCADA-based
applications. Although such applications may provide a backup solution to existing contingency
analysis applications should they fail in real-time, they disregard the benefit of high-resolution
measurement availability in synchrophasor data. Synchrophasors offer synchronized phasor
measurements at rates of at least 30 samples per second (for 60 Hz systems), which allow monitoring
of system dynamics and transients, and can be leveraged to provide a quick and high-rate solution to
the security analysis problem. The bottleneck that exists in the currently available applications is due
to the powerflow-based simulations that is required to be performed iteratively for thousands of
elements. This research focuses on use of alternative approaches that leverage the DC models of the
power system to provide a linear approximation of power flow on transmission equipment to be used
for contingency analysis.
2.4 Linear Shift Factors (LSFs)
Linear Shift Factors provide a linear estimation for the security analysis problem, which allow
much faster calculations as compared to solving powerflow iteratively [26]. Shift Factors are constants
that can be used to estimate the powerflow on a specific transmission equipment, knowing the power
on another. Two types of Linear shift factors will be used in this research and are well studied in
literature; Power Transfer Distribution Factors (PTDFs) and Line Outage Distribution Factors
(LODFs) [2][26-30]. Power Transfer Distribution Factor is the change in power flow on a
transmission line relative to a power transfer transaction between two buses (injection and withdrawal
of power at two buses) [2]. PTDFs have the following mathematical definition:
𝑃𝑃 𝑃𝑃𝑃𝑃 𝑃𝑃 𝑎𝑎 , 𝑏𝑏 , 𝑙𝑙 =
𝛥𝛥 𝑓𝑓 𝑙𝑙 , 𝑎𝑎 , 𝑏𝑏 𝛥𝛥 𝑃𝑃 𝑎𝑎 , 𝑏𝑏 , (2.1)

34

Where,
𝑃𝑃 𝑃𝑃𝑃𝑃 𝑃𝑃 𝑎𝑎 , 𝑏𝑏 , 𝑙𝑙 = Power Transfer Distribution Factor for line 𝑙𝑙 , given an injection and withdrawal at buses
a and b respectively
𝛥𝛥 𝑓𝑓 𝑙𝑙 , 𝑎𝑎 , 𝑏𝑏 = Change in line 𝑙𝑙 power flow for the transaction at buses a and b.
𝛥𝛥 𝑃𝑃 𝑎𝑎 , 𝑏𝑏 = Power transferred in the transaction from bus a to bus b
Figure 2.7 demonstrates the approach to calculate PTDFs for transmission lines in the two-
machine two-bus system. A power transaction consisting of an injection and a withdrawal of power
at two different buses is applied as shown in Figure 2.7. The sensitivity of each transmission line flow
to the power transaction applied is the PTDF for that line. For instance, since the transmission lines
in Figure 2.7 are identical, each transmission line will see a change of power that equals 50% of the
power transaction. This percentage is the PTDF for each line

Figure 2.7 Illustration of PTDF calculation process
Another type of shift factors of interest is the Line Outage Distribution Factor. Line Outage
Distribution Factors are constants that represent the estimated change of power on a transmission
line or a transformer relative to a loss of another [2]. LODFs are defined as follows:
𝐿𝐿𝐿𝐿 𝑃𝑃 𝑃𝑃 𝑙𝑙 , 𝑐𝑐 =
𝛥𝛥 𝑓𝑓 𝑙𝑙 𝑓𝑓 𝑐𝑐 0
, (2.2)
Where,
𝐿𝐿𝐿𝐿 𝑃𝑃 𝑃𝑃 𝑙𝑙 , 𝑐𝑐 = Line Outage Distribution Factor for Line 𝑙𝑙 , after the contingency of Line 𝑐𝑐
𝛥𝛥 𝑓𝑓 𝑙𝑙 = Change in Line 𝑙𝑙 power flow following the contingency of Line 𝑐𝑐

35

𝑓𝑓 𝑐𝑐 0
= Power flow of contingency element 𝑐𝑐 before it was removed (pre-contingency flow)
LODFs represent the percentage of power transfer from one line to the other, when the
original line is removed. For instance, in Figure 2.8, for this transmission system, removing one of the
lines will transfer 100% of its flow to the other line. This means that the LODF for Line 1 on Line 2
is 100%.

Figure 2.8 Illustration of LODF calculation process
Following the examples from Figure 2.7 and Figure 2.8, using LSFs allowed us to estimate the
flow on the transmission line without the need to run power flow simulations or solve complicated
power flow equations. In the following sections, we will attempt to use LSFs to perform contingency
analysis, with the goal of reducing the complexity of real-time assessments, and provide information
to operators quickly for timely response.
2.5 Security Analysis Using Shift Factors
The objective of the using shift factors in contingency analysis is to provide real-time operators
and engineers with fast real-time results that uses synchrophasor measurements and Linear State
Estimation data [26]. Synchrophasors provide accurate and fast measurements to voltage and current
phasors, which can be used to provide accurate contingency analysis results. Many approaches to
calculate or estimate LSFs have been proposed in the literature [27-29]. In this research, it is assumed
that the LSFs are either available or pre-calculated, and made ready for use in real-time.

36

Equation (2.2) provides a linear relationship between the flow of the contingency element, and
the relative change on the limiting element after the contingency is removed. This means that if we
know the flow on contingency element before its removed, and the change in flow on the limiting
element after the contingency is removed, we can calculate the LODF for the same pair using equation
(2.2). This estimation is performed using the linear equation to provide operators with timely results.
Using equation (2.2), and with all the powerflow information readily available, we can use
LODFs to estimate the post-contingency flow for line 𝑙𝑙 following the loss of transmission line 𝑘𝑘 using
the equation below [2]:
𝑓𝑓 ̂
𝑙𝑙 , 𝑐𝑐 = 𝑓𝑓 𝑙𝑙 0
+ 𝐿𝐿𝐿𝐿 𝑃𝑃 𝑃𝑃 𝑙𝑙 , 𝑐𝑐  𝑓𝑓 𝑐𝑐 0
(2.3)
Where,
𝑓𝑓 ̂
𝑙𝑙 , 𝑐𝑐 is the power flow for line 𝑙𝑙 after the removal of Line 𝒄𝒄 (post-contingency flow)
𝑓𝑓 𝑙𝑙 0
= Pre-contingency power flow of limiting element 𝑙𝑙
The process to perform security analysis using shift factors is shown in Figure 2.2, and is
outlined in the following steps:
1. RTCA retrieves transmission elements power flows and a list of observable buses from
latest Linear State Estimation solution.
2. Based on observability analysis provided by LSE, a list of contingency definitions for the
observable power system is prepared. This list includes all the credible contingencies as
per the system operation criteria (N-1s, credible N-2s, and credible N-1-1s).
3. LODF parameters are retrieved for the synchrophasor-observable portion of the power
system. Many approaches to calculate LSFs have been proposed in the literature [27-29].
It is assumed that LODF parameters are pre-calculated and made available for use in real-
time.

37

4. Linear equations representing the contingency definitions and the limiting elements
identified are formulated.
5. Post-contingency flows are calculated with shift factor using equation (2.3).
6. Flows are compared against SOLs, and alarms are generated based on violations of limits.
As seen in Figure 2.9, linearizing the security analysis using shift factors eliminated the iterative
process in the traditional RTCA, and allowed for much timely results to be produced without the need
to run powerflow for each contingency.

Figure 2.9 Linear Contingency Analysis Process Using LSFs
Figure 2.10 below represents a generic 5-bus power system, which will be used to explain the
methodology explained in this chapter.

38

Figure 2.10 Generic 5-Bus Power System
PowerWorld simulator, a power system analysis and simulation package, is used for all
simulations required to validate the methodologies in this research. A powerflow case representing
the 5-bus power system is taken from Example 6-20 in [4]. A one-line representation of the powerflow
case in PowerWorld simulator is shown in Figure 2.11.

Figure 2.11 5-Bus Power System Base Case
Table 2-1 shows the line loading information for all transmission lines in the case. For this
example, we will attempt to estimate the post-contingency line flows for all lines, following the loss of
line 2-3. PTDFs for all lines relative to the injection/withdrawal of power at buses 2 and 4 respectively

39

are also shown in Table 2-1. Buses 2 and 4 represent the main source and sink of the system, which
in result will derive the highest PTDFs set for all major lines. Also, LODFs for all lines are provided
for the contingency of line 2-3.
Table 2-1: MW, PTDFs for transaction between buses 2 and 4, and LODFs for the outage of 2-3
𝑙𝑙 𝑓𝑓 𝑙𝑙 𝑜𝑜 𝑙𝑙 𝑜𝑜 0
% 𝑃𝑃 𝑃𝑃𝑃𝑃 𝑃𝑃 2, 4, 𝑙𝑙 % 𝐿𝐿𝐿𝐿 𝑃𝑃 𝑃𝑃 𝑙𝑙 , 2 − 3

𝑓𝑓 ̂
𝑙𝑙 , 2 − 3

(Estimated)
𝑓𝑓 ̂
𝑙𝑙 , 2 − 3

(Powerflow)
% Error
1-2 79 -17.14% -33.3% 59.97 60.02 0.083
1-3 62.14 17.14% 33.3% 81.17 80.98 0.23%
2-3 57.16 28.57% -100% 0 0 0%
2-4 52.35 36.19% 44.4% 77.73 77.31 0.54%
2-5 111.27 18.10% 22.2% 123.96 123.65 0.25%
3-4 -27.7 45.71% -66.7% -65.83 -66.02 0.29%
4-5 16.13 18.10% -22.2% 3.44 3.35 2.69%

With all the powerflow information readily available, we can use LODFs to estimate the post-
contingency flow for line 𝑙𝑙 following the loss of transmission line 𝑘𝑘 using equation (2.3). Results for
post-contingency flow are listed in column 5 of the table above. The last column of Table 2-1 shows
accuracy of estimations using Distribution Factors. Figure 2.12 presents the actual MW flow of all
lines in the case following the contingency. The results agree with the estimated results as expected.

Figure 2.12. Simulation of the loss of Line 2-3 on the 5-bus generic case in Figure 2.3

40

For real-time applications implementation, equation (2.3) can be fed with real-time
measurements continuously and estimate the post-contingency flow at the synchrophasor rate, and
provide an updated outlook to system operators on the monitored SOL without the need to
continuously solve full powerflow. 𝑓𝑓 𝑙𝑙 0
and 𝑓𝑓 𝑐𝑐 0
represent the real-time measurement of the limiting
element (monitored element) and the contingency element prior to the loss of the line respectively.
Therefore, the linear equation above can be used to estimate the post-contingency line flow for any
transmission line, given the flow-measurement availability of the limiting and contingency elements.
With measurement availability for both the limiting element to be monitored and the contingency
element, equation (2.3) can be updated continuously to provide continuous estimation of the post-
contingency flow on the limiting element. To apply that, equation (2.3) becomes,
𝑓𝑓 ̂
𝑙𝑙 , 𝑐𝑐 𝑛𝑛𝑛𝑛𝑛𝑛 = 𝑓𝑓 𝑙𝑙 𝑛𝑛𝑛𝑛𝑛𝑛 0
+ 𝐿𝐿𝐿𝐿 𝑃𝑃 𝑃𝑃 𝑙𝑙 , 𝑐𝑐  𝑓𝑓 𝑐𝑐 𝑛𝑛𝑛𝑛𝑛𝑛 0
(2.4)
Where 𝑛𝑛 𝑒𝑒 𝑛𝑛 denotes to the updated measurement for the line flow, as compared to the original
flow from the solved powerflow.
2.6 Limited PMU deployment and effect on observability
The term observability of synchrophasor systems defines the maximum area of the power
system with only the observable states, both measured and estimated.

Figure 2.13 Example power system model with PMU "direct" observability

41

The state of the system is the set of voltage phasors (magnitude and angle) for all the buses in
the system [13-17]. PMUs provide observability through direct measurement of voltage phasors of
substation equipment. The observability gained using PMUs is limited to only the set of equipment
measured directly by the PMU devices, as illustrated in Figure 2.13.
For the power grid to reach full observability using PMUs only, PMUs need to be installed at
every substation of the bulk power system to measure all bus voltages, and all transmission line and
transformer currents of the transmission grid. This requires a large upfront investment due to the cost
of the PMUs, and the amount of work required to deploy them for full coverage [20]. In addition, for
real-time operations applications, redundancy in measurement availability is required to ensure the full
observability level is maintained during PMU outages or communication issues. Linear State
Estimation provides a solution to that problem.
2.7 LSE to enhance and expand synchrophasor observability
Linear State Estimator provides expanded observability to the synchrophasor system. Figure 2.12
shows the increase in system observability gained through deployment of LSE, without any additional
PMU installations in the field.

Figure 2.14 Expanded observability with Linear State Estimation

42

LSE uses the measured states and the system model, and evaluates the extended observability
based on system topology and available measurements [10][14][16]. For Figure 2.14, with the
availability of a single measured state (the phasor voltage where the PMU is deployed) and three
current measurements at that substation, the LSE expanded the observability to in include all nearby
buses. These estimated states can be used to assist downstream application requiring additional
observability, and provide backup estimated states for states that are already measured.
2.8 Challenges with limited observability
The challenge in making use of LODFs with synchrophasor measurements resides in the lack
of sufficient PMU deployments to provide full observability, which is necessary to solve the linear
equations. This means that 𝑓𝑓 𝑙𝑙 0
𝑛𝑛𝑛𝑛𝑛𝑛 and 𝑓𝑓 𝑐𝑐 0
𝑛𝑛𝑛𝑛𝑛𝑛 in equation (2.4) (the updated limiting and contingency
elements flow measurements) might not be always available through direct measurements or LSE
estimations. Therefore, a practical methodology needs to be implemented to provide awareness for all
contingencies and limiting elements, given the lack of measurement availability. A methodology to
address observability for limited synchrophasor coverage is presented in chapter 3.

43

Chapter 3: Real-Time Assessment with Partial Observability
The relatively low number of synchrophasors available from the grid makes it challenging to
perform real-time assessments using PMU data, even when studies are localized to a relatively small
electrical area. The deployment of PMUs has been focused on key substations of the transmission
grid, such as heavily interconnected substations, or stations with key interties, without much
deployment at locations to optimally target full system observability [19]. In addition, because use of
synchrophasor applications is currently focused on wide area monitoring and situational awareness,
the deployment of PMUs has been spread out in the transmission systems to cover the wide area
characteristic of the system, regardless of observability.
3.1 Linear Contingency Analysis for Partial System Observability
Synchrophasor measurements are synchronized using universal time clock over GPS, and
provide time-aligned updated measurements at the rate of either 30, 60, or even 120 samples per
second. With the high sampling rate of synchrophasors, the linear equations presented in Chapter 2
can be used to perform linear contingency analysis leveraging synchrophasors, and provide post-
contingency results for the observable system. However, unobservable areas pose a challenge as
operators will not have visibility to ensure a secure operating state if contingencies happen. In this
chapter, we will propose a new methodology to extend the observability beyond the synchrophasor
footprint, and use that results for real-time assessment to compliment the observability from
synchrophasors, without compromising the speed of calculations accuracy of estimations.
3.1.1 Formulation of equations
The power grid is very dynamic and system conditions continue to change throughout the day
due to the variability of system load, generation, and topology. Therefore, frequent and continuous
assessment of real-time conditions is required to continuously monitor the system, and ensure that

44

the system is operated to a secure state all the time. Synchrophasors provide measurements at a very
high rate, and with the linear formulation for contingency analysis, post contingency flows can be
calculated iteratively for the observable system at the sampling rate.
With the high sampling rate of PMU measurements, the variations in load, generation, and
topology between samples are usually very small. This means that if we consider each set of PMU
measurements representing the system for a given time a “state”, then the state of the system in the
next sample is a basically the current state, with a little change. Therefore, if we can predict the change
in the flow of the power system for a given line, we can use the previous state and adjust it to reflect
the change. In other words, we can use the latest measurements from the latest run, and adjust the
measurements by adding the change between the last measurements and new measurements. This
approach helps in streamlining the process of estimating post-contingency flow for both observable
and non-observable branches.
To formulate this, we can rewrite equation (2.4) as the following,
𝑓𝑓 ̂
𝑙𝑙 , 𝑐𝑐 𝑛𝑛𝑛𝑛𝑛𝑛 = 𝑓𝑓 𝑙𝑙 𝑜𝑜 𝑙𝑙 𝑜𝑜 0
+ 𝛥𝛥 𝑓𝑓 𝑙𝑙 0
+ 𝐿𝐿𝐿𝐿 𝑃𝑃 𝑃𝑃 𝑙𝑙 , 𝑐𝑐  � 𝑓𝑓 𝑐𝑐 𝑜𝑜 𝑙𝑙 𝑜𝑜 0
+ 𝛥𝛥 𝑓𝑓 𝑐𝑐 0
� (3.1)
Where,
𝑓𝑓 𝑙𝑙 𝑜𝑜 𝑙𝑙 𝑜𝑜 0
= Pre-contingency flow of line 𝑙𝑙 in the previous sample/state
𝛥𝛥 𝑓𝑓 𝑙𝑙 0
= Change in pre-contingency flow of line 𝑙𝑙 between previous and updated samples/states
𝑓𝑓 𝑐𝑐 𝑜𝑜 𝑙𝑙 𝑜𝑜 0
= Flow of contingency element 𝑐𝑐 in the previous sample/state before the contingency
was removed
𝛥𝛥 𝑓𝑓 𝑐𝑐 0
= Change in pre-contingency flow of contingency element 𝑐𝑐 between previous and
updated samples/states
In other words,
𝛥𝛥 𝑓𝑓 𝑙𝑙 0
= 𝑓𝑓 𝑙𝑙 𝑛𝑛𝑛𝑛𝑛𝑛 0
− 𝑓𝑓 𝑙𝑙 𝑜𝑜 𝑙𝑙 𝑜𝑜 0
(3.2)

45

And,
𝛥𝛥 𝑓𝑓 𝑐𝑐 0
= 𝑓𝑓 𝑐𝑐 𝑛𝑛𝑛𝑛𝑛𝑛 0
− 𝑓𝑓 𝑐𝑐 𝑜𝑜 𝑙𝑙 𝑜𝑜 0
(3.3)
Where,
𝑓𝑓 𝑙𝑙 𝑛𝑛𝑛𝑛𝑛𝑛 0
= New (updated) pre-contingency flow of line 𝑙𝑙
𝑓𝑓 𝑐𝑐 𝑛𝑛𝑛𝑛𝑛𝑛 0
= New (updated) pre-contingency flow of contingency element 𝑐𝑐
Using equations (3.1), (3.2) and (3.3), linear contingency analysis can be performed with the
available synchrophasor measurements for transmission equipment, and their associated LODFs.
However, the power system may not be fully observable using PMUs, which limits the practicality of
the sensitivity factors. Therefore, an approach needs to be put in place to expand the situational
awareness provided by RTCA beyond the synchrophasor observable footprint of the system.
The challenge in using synchrophasors with the previously discussed approach is in the lack
of the level of PMU deployments necessary to make the power grid fully observable. This means that
data needed to solve equations (3.2) and (3.3) might not be always readily available through direct
phasor measurements, although they may be available at much lower rates from SCADA or EMS
through conventional methods. This section explains the details of an approach that uses a reference
measurement or estimation, and allow performing security analysis at a much higher rate by updating
the branch element flows using synchrophasors.
It is assumed that reference measurements at much lower rates are available from EMS or
State Estimator cases through conventional methods. Since most State Estimators run once every 3-
5 minutes, a value for unobservable PMU locations is available as a reference, and can be used and
updated using synchrophasor measurements. And since this value is used as a reference and gets
updated with new measurements, it is referred to as 𝑓𝑓 𝑜𝑜 𝑙𝑙 𝑜𝑜 . In this context, 𝑓𝑓 𝑜𝑜 𝑙𝑙 𝑜𝑜 is also continuously
updated, at much lower rate, as available by EMS/SCADA.

46

Let us define a new sensitivity factor called Line Flow Distribution Factor (LFDF), which is
derived from two lines PTDFs as the following,
𝐿𝐿 𝑃𝑃 𝑃𝑃 𝑃𝑃 𝑙𝑙 , 𝑘𝑘 =
𝑃𝑃 𝑃𝑃𝑃𝑃 𝑃𝑃 𝑙𝑙 , 𝑎𝑎 , 𝑏𝑏 𝑃𝑃 𝑃𝑃𝑃𝑃 𝑃𝑃 𝑘𝑘 , 𝑎𝑎 , 𝑏𝑏 , (3.4)
Substituting (2.1) into (3.9) gives,
𝐿𝐿 𝑃𝑃 𝑃𝑃 𝑃𝑃 𝑙𝑙 , 𝑘𝑘 =
𝛥𝛥 𝑓𝑓 𝑙𝑙 , 𝑎𝑎 , 𝑏𝑏 𝛥𝛥 𝑓𝑓 𝑘𝑘 , 𝑎𝑎 , 𝑏𝑏 , (3.5)
From this equation, it can be observed that the relationship between the change of flow on
two lines is constant and does not depend on the power injected in the power transfer transaction.
Therefore, if line 𝑙𝑙 is not observed, we can use equation (3.5) to estimate the change in flow on Line
𝑙𝑙 using another observed Line 𝑘𝑘 . Rewriting equation (3.5), and dropping the transaction index, we get,
𝛥𝛥 𝑓𝑓 𝑙𝑙 = 𝛥𝛥 𝑓𝑓 𝑘𝑘  𝐿𝐿 𝑃𝑃 𝑃𝑃 𝑃𝑃 𝑙𝑙 , 𝑘𝑘 , (3.6)
Or,
� 𝑓𝑓 𝑙𝑙 𝑛𝑛𝑛𝑛 𝑛𝑛 − 𝑓𝑓 𝑙𝑙 𝑜𝑜 𝑙𝑙 𝑜𝑜 � = 𝛥𝛥 𝑓𝑓 𝑘𝑘  𝐿𝐿 𝑃𝑃 𝑃𝑃𝑃𝑃
𝑙𝑙 , 𝑘𝑘 , (3.7)
Rearranging,
𝑓𝑓 𝑙𝑙 𝑛𝑛𝑛𝑛𝑛𝑛 = 𝑓𝑓 𝑙𝑙 𝑜𝑜 𝑙𝑙 𝑜𝑜 + 𝛥𝛥 𝑓𝑓 𝑘𝑘  𝐿𝐿 𝑃𝑃𝑃𝑃 𝑃𝑃 𝑙𝑙 , 𝑘𝑘 , (3.8)
Similarly, assuming 𝑓𝑓 𝑐𝑐 0
𝑛𝑛𝑛𝑛𝑛𝑛 (the updated contingency element power flow before the
contingency) is not observable, it can be written in terms of another line nearby flow 𝑓𝑓 𝑗𝑗 which is
observable. Applying equation (3.8) to equation (3.1), we get,
𝑓𝑓 ̂
𝑙𝑙 , 𝑐𝑐 𝑛𝑛𝑛𝑛𝑛𝑛 = 𝑓𝑓 𝑙𝑙 𝑜𝑜 𝑙𝑙 𝑜𝑜 0
+ 𝛥𝛥 𝑓𝑓 𝑘𝑘 0
 𝐿𝐿 𝑃𝑃𝑃𝑃 𝑃𝑃 𝑙𝑙 , 𝑘𝑘 + 𝐿𝐿𝐿𝐿 𝑃𝑃 𝑃𝑃 𝑙𝑙 , 𝑐𝑐  � 𝑓𝑓 𝑐𝑐 𝑜𝑜 𝑙𝑙 𝑜𝑜 0
+ 𝛥𝛥 𝑓𝑓 𝑗𝑗 0
 𝐿𝐿 𝑃𝑃𝑃𝑃 𝑃𝑃 𝑐𝑐 , 𝑗𝑗 � (3.9)
Equation (3.9) allows the estimation of post-contingency loading on line 𝑙𝑙 for the contingency
of Line 𝒄𝒄 , without the necessity of having updated measurements from Lines 𝑙𝑙 and 𝑐𝑐 . This provides
system operators with awareness of the system conditions for parts of the system that in not otherwise
observable, given the availability of nearby observable branches that can be used for the estimation.

47

This method is also applicable to reactive-power calculations, although the focus here is on
real power since most line overloads in power systems are caused by high real power flow. Pre-
calculating LFDFs allows a very fast procedure to scan the system for possible violations for all
possible contingencies. In addition, the linear nature of the equations enables performing the
calculations at synchrophasor rate. Furthermore, the key system assumptions are:
1. The system model and enough telemetry are available to calculate the sensitivity factors, or factors
are otherwise available them from other sources. Once the factors are retrieved, they are assumed
to be valid and correct as long as the system did not go through a major change that affects these
factors, such as a significant topology change or a major generation profile change. This
assumption is valid given that those changes are monitored and flagged in real-time to trigger the
re-calculation of all sensitivity factors.
2. This method applies to single and multiple contingencies, given that specific multiple
contingencies are pre-defined, and the corresponding sensitivity factors for the multiple
contingencies are available. Therefore, a separate set of sensitivity factors are required for multiple
outages scenarios, such as lines sharing, towers, right of ways, or critical transmission paths.
3. The sensitivity factors are calculated with an injection of power relatively far from the reference
bus, to ensure the accuracy of the calculated factors, without the slack bus contributing to reverse
the flow. An example of apply this method is presented in the following part of this section.
3.1.2 Proof-of-Concept example
For further illustration, let us consider a modified 5-bus system case, where only measurements
at buses 1 and 4 are available. Also, loads were modified slightly to simulate a change over time in
lines loading. Updated case information is presented in Table 3-1 under column
𝑓𝑓 𝑙𝑙 𝑛𝑛𝑛𝑛𝑛𝑛 0
. Figure 3.1 shows the modified power flow case for the 5-bus power system case.

48

Figure 3.15 Modified power flow of 5-Bus Power System from Figure 2.9

Table 3.1: Updated MW flow with Lines only connected to substations 1 and 4
𝐿𝐿 𝐿𝐿 𝑛𝑛 𝑒𝑒 𝑙𝑙 𝑓𝑓 𝑙𝑙 𝑜𝑜 𝑙𝑙 𝑜𝑜 0
𝑓𝑓 𝑙𝑙 𝑛𝑛𝑛𝑛𝑛𝑛 0
𝛥𝛥 𝑓𝑓 𝑙𝑙
2-3 57.16 MW Unobservable Contingency
2-4 52.35 MW 53.67 MW 1.32 MW
2-5 111.27 MW Unobservable Limiting Element
4-5 16.13 MW 17.20 MW 1.07 MW

To estimate the post-contingency flow on Line 2-5 for the contingency of Line 2-3 for
example, the equation becomes,
𝑓𝑓 ̂
2 − 5, 2 − 3
𝑛𝑛𝑛𝑛𝑛𝑛
= 𝑓𝑓 2 − 5
𝑜𝑜 𝑙𝑙 𝑜𝑜 0
+ 𝛥𝛥 𝑓𝑓 4 − 5
 𝐿𝐿 𝑃𝑃𝑃𝑃 𝑃𝑃 2 − 5, 4 − 5
+ 𝐿𝐿𝐿𝐿 𝑃𝑃 𝑃𝑃 2 − 5, 2 − 3
 � 𝑓𝑓 2 − 3
𝑜𝑜 𝑙𝑙 𝑜𝑜 0
+
𝛥𝛥 𝑓𝑓 2 − 4
 𝐿𝐿 𝑃𝑃𝑃𝑃 𝑃𝑃 2 − 3, 2 − 4
� (3.10)
This provides a post contingency estimation of 128.61 MW for the limiting element 2-5, for
the loss of the line 2-3. The result can be compared with the powerflow simulation result shown in
Figure 3.1. The resulting error in estimation is 0.4%.

49

Figure 3.16 Simulation of the loss of Line 2-3 on the updated 5-bus generic case
3.1.3 Case study and simulations
This section demonstrates the effectiveness of the methodology using the IEEE 39 bus
system, which is a reduced system model of the New-England’s power system. This case study
illustrates the methodology to perform linear security analysis using synchrophasor measurements by
taking advantage of distribution factors to estimate the post contingency flow on transmission
equipment where observability is not present. To demonstrate the numerical viability of this approach,
the results are compared to the powerflow simulations using PowerWorld Simulator.
The IEEE 39 bus test system is a 10-machine test system model that is reduced from New-
England Power System that has 10 generators and 46 lines [30][31]. The powerflow case was retrieved
from [31], while the original paper with the IEEE 39-bus system is by T. Athay et al [30]. A one-line
presentation of the power system model is shown in Figure 3.3 below.

50

Figure 3.17 IEEE 39-Bus System with Limited PMU Observability
PMU observable transmission lines and buses are shown in red. Table 3-2 shows the line
loading information for some transmission lines in the case.
As an example, we will attempt to estimate the post-contingency line flows for all lines,
following the loss of line 2-3. PTDFs for all lines relative to the injection/withdrawal of power at
buses 25 and 9 respectively are also shown in Table 3-2. Similar to the previous exercise, buses 25 and
6 represent the main source and sink of the meshed transmission system, which in result will derive
the highest PTDFs set for all major lines.
Table 3-2: MW, PTDFs for transaction on buses 25 and 6
Line 𝑙𝑙 𝑓𝑓 𝑙𝑙 𝑝𝑝𝑝𝑝 𝑛𝑛 % 𝑃𝑃 𝑃𝑃𝑃𝑃 𝑃𝑃 2 5, 6, 𝑙𝑙
2-3 364.72 MW 55.73%
2-25 231.50 MW 75.78%
3-18 34.09 MW 2.97%

51

17-27 -11.51 MW 24.22%
26-27 270.44 MW 24.22%

In order to demonstrate the numerical viability of the proposed method, we will attempt to
calculate the post contingency flow of multiple transmission lines, following the loss of the line 2-25.
As an example, to calculate the post-contingency flow on line 3-18, from equation (2.4) we get,
𝑓𝑓 ̂
3 − 1 8, 2 − 2 5
= 𝑓𝑓 3 − 1 8
0
+ 𝐿𝐿𝐿𝐿 𝑃𝑃 𝑃𝑃 3 − 1 8, 2 − 2 5
 𝑓𝑓 2 − 2 5
0
(3.11)
With a LODF of 73.6%, the estimated post-contingency line flow of line 3-18 for the
contingency of line 2-25 is equal to 204.08 MW. This is verified by simulation as shown in Figure 3.3,
with an error in estimation of 0.6%.

Figure 3.18 Post-Contingency flow of line 3-18 for the loss of line 2-25
Since both lines are not observable by PMUs, the change in pre-contingency line flow with
time cannot be calculated as the updated flow is not known for both lines, due to lack of PMU
observability. We can rewrite equation (3.11) using other observable lines k and j, in which equation
(3.11) becomes as follows,

52

𝑓𝑓 ̂
3 − 1 8, 2 − 2 5
𝑛𝑛𝑛𝑛𝑛𝑛 = 𝑓𝑓 3 − 1 8
𝑜𝑜 𝑙𝑙 𝑜𝑜 0
+ 𝛥𝛥 𝑓𝑓 𝑘𝑘  𝐿𝐿 𝑃𝑃𝑃𝑃 𝑃𝑃 3 − 1 8, 𝑘𝑘 + 𝐿𝐿𝐿𝐿 𝑃𝑃 𝑃𝑃 3 − 1 8, 2 − 2 5
 � 𝑓𝑓 2 − 2 5, 𝑗𝑗 𝑜𝑜 𝑙𝑙 𝑜𝑜 0
+ 𝛥𝛥 𝑓𝑓 𝑗𝑗  𝐿𝐿 𝑃𝑃𝑃𝑃 𝑃𝑃 2 − 2 5, 𝑗𝑗 � (3.12)
Let us assume that the system state changed a little, and the updated flows for the observable
lines from Table 3-1 are shown in Table 3-3. Similar to the previous exercise, loads were modified
slightly to simulate a change over time in lines loading.

Table 3-3: Updated MW flow with Lines only connected to substations 1 and 4
Line l 𝑓𝑓 𝑙𝑙 𝑜𝑜 𝑙𝑙 𝑜𝑜 0
𝑓𝑓 𝑙𝑙 𝑛𝑛𝑛𝑛𝑛𝑛 0
𝛥𝛥 𝑓𝑓 𝑙𝑙
2-3 364.72 MW 378.4 MW 13.68 MW
2-25 231.50 MW Unobservable Contingency
3-18 34.09 MW Unobservable Limiting Element
17-27 -11.51 4.97 MW 16.48 MW

From Figure 3.3, selecting line 17-27 as line k, and line 2-3 as line j, and substituting in equation
(3.12) we get,
𝑓𝑓 ̂
3 − 1 8, 2 − 2 5
𝑛𝑛𝑛𝑛𝑛𝑛 = 𝑓𝑓 3 − 1 8
𝑜𝑜 𝑙𝑙 𝑜𝑜 0
+ 𝛥𝛥 𝑓𝑓 1 7 − 2 7
 𝐿𝐿 𝑃𝑃𝑃𝑃 𝑃𝑃 3 − 1 8, 1 7 − 2 7
+
+ 𝐿𝐿𝐿𝐿 𝑃𝑃 𝑃𝑃 3 − 1 8, 2 − 2 5
 � 𝑓𝑓 2 − 2 5
𝑜𝑜 𝑙𝑙 𝑜𝑜 0
+ 𝛥𝛥 𝑓𝑓 2 − 3
 𝐿𝐿 𝑃𝑃𝑃𝑃 𝑃𝑃 2 − 2 5, 2 − 3
� (3.13)
Equation (3.13) calculates the post contingency line flow of Line 3-18 for the loss of line 2-25
to be 218.29 MW. Verification using powerflow simulations has been performed and provides a post-
contingency flow of 216.83 MW, with a tolerance of 0.67%, as shown in Figure 3.4.
Table 3-4 presents the Estimation of post contingency line flow for the major lines relatively
close to the observable lines, and demonstrates the accuracy of the proposed approach. All the
estimations are accurate with acceptable tolerances. It is worth mentioning that using this approach, a
security analysis was performed only using a base-case and two PMUs, to monitor System Operating
Limits, even for unobservable footprint.

53

Figure 3.19 Post-Contingency flow overall system for the loss of line 2-25
Table 3-4 shows the transmission lines surrounding the PMU observable lines, and other
simulation information, where,
Line 𝑙𝑙 – Transmission Line
𝑓𝑓 𝑙𝑙 𝑂𝑂 𝑙𝑙𝑜𝑜
0
– Base-case pre-contingency flows
𝑓𝑓 𝑙𝑙 𝑛𝑛𝑛𝑛𝑛𝑛 0
– Updated base case pre-contingency flows
LODF – Line Outage Distribution Factor
𝑓𝑓 ̂
𝑙𝑙 𝑛𝑛𝑛𝑛𝑛𝑛
(Estimate) – Estimated post-contingency flows
𝑓𝑓 ̂
𝑙𝑙 𝑛𝑛𝑛𝑛𝑛𝑛 (Powerflow) – Actual post-contingency flows
% Error – Percentage errors in estimation

54

Table 3-4: Accuracy of post-contingency estimations for the loss of 2-25 with limited observability
Line l
𝑓𝑓 𝑙𝑙 𝑜𝑜 𝑙𝑙 𝑜𝑜 0
(MW) 𝑓𝑓 𝑙𝑙 𝑛𝑛𝑛𝑛 𝑛𝑛 0
(MW)
LODF %
𝑓𝑓 ̂
𝑙𝑙 𝑛𝑛𝑛𝑛 𝑛𝑛
(Estimate)
𝑓𝑓 ̂
𝑙𝑙 𝑛𝑛𝑛𝑛 𝑛𝑛
(Powerflow)
% 𝐸𝐸 𝐸𝐸𝐸𝐸𝐸𝐸 𝐸𝐸
2-3 364.72 378.4 88 158.31 158.04 0.17
2-25 231.50 - -100 0 0 0
3-18 34.09 - 73.6 218.29 216.83 0.67
17-18 192.32 - 73.6 376.52 376.30 0.58
17-27 -11.51 4.97 100 239.59 245.37 2.36
25-26 78.61 - 100 329.71 342.22 3.66
26-27 270.44 - 100 521.54 530.75 1.74

With such small system models, the tolerance typically is contributed to by the swing bus or
the boundary buses as the external system is modeled with equivalent generators at the boundaries
and the slack is picked up at the boundaries and at the swing bus. It is also noticeable that error
percentage increases the further away the limiting element or the contingency element are from the
observable branch that is used for the calculation. Therefore, more PMU deployments means
increased accuracy of the estimations for contingency analysis results.

55

Chapter 4: Optimizing the Linear Security Analysis
In Chapter 3, we established a methodology that enables estimation of flow for unobserved
transmission equipment using nearby observable branches. That said, there might be multiple
observable branches that can be used for estimating the transmission line flow. Therefore, an approach
must be implemented to allow the best possible estimation using the candidate sources for each
branch.
Equation (3.11) is the main linear equation used in the linear contingency analysis approach
proposed in this research. To summarize, the information required for performing security analysis
(as shown in equation (3.11)) for any contingency and limiting-element combination are:
1. Pre-contingency flow of the limiting-element in the previous sample (previous LSE/LSA run)
� 𝑓𝑓 𝑙𝑙 𝑜𝑜 𝑙𝑙 𝑜𝑜 0
�
2. Pre-contingency flow of the contingency element in the previous sample (previous LSE/LSA
run) � 𝑓𝑓 𝑐𝑐 𝑜𝑜 𝑙𝑙 𝑜𝑜 0
�
3. Pre-contingency change in limiting-element flow between new measurement and previous
measurement ( 𝛥𝛥 𝑓𝑓 𝑙𝑙 0
)
4. Pre-contingency change in contingency element flow between new measurement and previous
measurement ( 𝛥𝛥 𝑓𝑓 𝑐𝑐 0
)
Items 1 and 2 are always available from previous LSE/LSA run, assuming that the
synchrophasor observability did not change in between the two samples, for a topology change or a
measurement availability change. Items 3 and 4 are available through one of the following:
1. Direct measurements for observable branches – calculated using equations (3.2) and (3.3)
2. Estimated for unobservable branches – using equation (3.8)

56

With more PMU deployments, and more LSE observability, more direct
measurements/estimations are readily available for security analysis. However, for the second category
of elements (unobservable elements), measurements of nearby branches can be used to estimate the
updated flow of one the unobservable branches using equation (3.8). The question is, which
observable branch to select in order to estimate the updated flow on the unobservable one. To
illustrate the proposed optimization methodology, an example scenario is shown in Figure 4.1

Figure 4.1 5-Bus example with limited observability
4.1 Formulation of equations
Let us assume that we have three branches 𝐿𝐿 , j, and 𝑘𝑘 , that are directly observable, any
observable line can be used to estimate the updated flow for line 𝑙𝑙 (the unobservable branch). It is
assumed that there is an acceptable tolerance that is introduced with the linearization of the equations.
To account for that, we will introduce the estimation error in equation (3.8) and rearranging, we get:
𝛥𝛥 𝑓𝑓 𝑖𝑖 =
1
𝐿𝐿 𝑃𝑃𝑃𝑃 𝑃𝑃 𝑙𝑙 , 𝑖𝑖 �
 𝛥𝛥 𝑓𝑓 𝑙𝑙 + 𝑒𝑒 1
(4.1)
Similarly, for j and k, we get,
𝛥𝛥 𝑓𝑓 𝑗𝑗 =
1
𝐿𝐿 𝑃𝑃𝑃𝑃 𝑃𝑃 𝑙𝑙 , 𝑗𝑗 �
 𝛥𝛥 𝑓𝑓 𝑙𝑙 + 𝑒𝑒 2
(4.2)

57

𝛥𝛥 𝑓𝑓 𝑘𝑘 =
1
𝐿𝐿 𝑃𝑃𝑃𝑃 𝑃𝑃 𝑙𝑙 , 𝑘𝑘 �
 𝛥𝛥 𝑓𝑓 𝑙𝑙 + 𝑒𝑒 3
(4.3)
rewriting in vector form, we get,
�
𝛥𝛥 𝑓𝑓 𝑖𝑖
𝛥𝛥 𝑓𝑓 𝑗𝑗 𝛥𝛥 𝑓𝑓 𝑘𝑘 � =
⎣
⎢
⎢
⎢
⎡
1
𝐿𝐿 𝑃𝑃𝑃𝑃 𝑃𝑃 𝑙𝑙 , 𝑖𝑖
�
1
𝐿𝐿 𝑃𝑃𝑃𝑃 𝑃𝑃 𝑙𝑙 , 𝑗𝑗 �
1
𝐿𝐿 𝑃𝑃𝑃𝑃 𝑃𝑃 𝑙𝑙 , 𝑘𝑘 �
⎦
⎥
⎥
⎥
⎤
[ 𝛥𝛥 𝑓𝑓 𝑙𝑙 ] + �
𝑒𝑒 1
𝑒𝑒 2
𝑒𝑒 3
� (4.4)
Or,
[ 𝛥𝛥 𝑓𝑓 ] = [ 𝑃𝑃 𝑃𝑃 ][ 𝛥𝛥 𝑓𝑓 𝑙𝑙 ] + [ 𝑒𝑒 ] (4.5)

Equation (4.5) presents an over determined system, i.e., a system with a set of equations in
which there are more equations than unknowns. Solving the overdetermined system provides all the
information necessary to calculate the post-contingency flow for unobservable branches. This
equation can also be altered to provide more confidence to estimations of post-contingency flow for
directly observed branches as well, by adding the self-measured parameter for the monitored element
as follows,
⎣
⎢
⎢
⎡
𝛥𝛥 𝑓𝑓 𝑙𝑙 𝛥𝛥 𝑓𝑓 𝑖𝑖
𝛥𝛥 𝑓𝑓 𝑗𝑗 𝛥𝛥 𝑓𝑓 𝑘𝑘 ⎦
⎥
⎥
⎤
=
⎣
⎢
⎢
⎢
⎢
⎡
1

1
𝐿𝐿 𝑃𝑃𝑃𝑃 𝑃𝑃 𝑙𝑙 , 𝑖𝑖
�
1
𝐿𝐿 𝑃𝑃𝑃𝑃 𝑃𝑃 𝑙𝑙 , 𝑗𝑗 �
1
𝐿𝐿 𝑃𝑃𝑃𝑃 𝑃𝑃 𝑙𝑙 , 𝑘𝑘 �
⎦
⎥
⎥
⎥
⎥
⎤
[ 𝛥𝛥 𝑓𝑓 𝑙𝑙 ] + �
𝑒𝑒 0
𝑒𝑒 1
𝑒𝑒 2
𝑒𝑒 3
� (3.4)
Or,
[ 𝛥𝛥 𝑓𝑓 ] = �
1
𝑃𝑃 𝑃𝑃 �[ 𝛥𝛥 𝑓𝑓 𝑙𝑙 ] + [ 𝑒𝑒 ] (3.5)
Where,
[ 𝛥𝛥 𝑓𝑓 ] = Measurement change vector
[ 𝑃𝑃 𝑃𝑃 ] = Line Flow Distribution Factor reciprocal vector

58

[ 𝛥𝛥 𝑓𝑓 𝑙𝑙 ] = Change in flow to be estimated for Line 𝑙𝑙
[ 𝑒𝑒 ] = Estimation error vector
Equations (4.5) and (4.7) are very similar to the Linear State Estimation problem introduced
in [8]. An estimated solution for this over-determined system can be achieved using Weighted Least
Squares (WLS) method. Least Squares method aims to minimize the sum of the squares of errors to
reach the optimal solution [6][7]. The weights are introduced to Least Squares to allow more emphasis
on some measurements considered important than others. Weighted Least Squares applied to equation
(4.6) or (4.7) gives,
𝑀𝑀 𝐿𝐿𝑛𝑛 𝑒𝑒 𝑇𝑇 𝑊𝑊 𝑒𝑒
such that [ 𝛥𝛥 𝑓𝑓 ] = [ 𝐻𝐻 ][ 𝛥𝛥 𝑓𝑓 𝑙𝑙 ] + [ 𝑒𝑒 ] (4.8)
where,
𝑊𝑊 = the diagonal matrix of measurement weights
And H represents either �
1
𝑃𝑃 𝑃𝑃 � 𝐸𝐸𝐸𝐸 [ 𝑃𝑃 𝑃𝑃 ], depending on whether the branch is observable, or
unobservable.
Therefore, the solution to the Weighted Least Squares equation is given by,
[ 𝛥𝛥 𝑓𝑓 𝑙𝑙 ] = [( 𝐻𝐻 𝑇𝑇 𝑊𝑊 𝐻𝐻 )
− 1
𝐻𝐻 𝑇𝑇 𝑊𝑊 ][ 𝛥𝛥 𝑓𝑓 ] (4.9)
It is evident by solving equation (4.9) that we can:
1. Provide expanded situational awareness by estimating the post-contingency flow for
unobservable branches, and therefore allow operators access to practical system for SOL
monitoring.
2. Optimize the estimation of post-contingency flow calculation by allowing multiple sources of
measurements for estimations, and thus, enhance the estimation quality and availability.

59

3. Allow other means of calculating post-contingency estimation of observable branches but not
only being dependent on direct measurements, but also estimate the post-contingency flow of
such elements through WLS estimations.
4.2 Case study and simulations
The IEEE 14 bus test system is a 14-machine test system model that is a reduced system
model of one of the American Electric Power (AEP) systems [32]. The system has 5 generators and
20 transmission lines and transformers, referred to as branches in research. A one-line presentation of
the power system model is shown in Figure 4.1. Highlighted in green show the observable branches
(current phasors) and Buses (voltage phasors) to demonstrate the proposed methodology. To
demonstrate the numerical viability of this method, the methodology was programmed in MATLAB,
and the results are compared to the powerflow simulations using PowerWorld Simulator. For this
power system model, it is obvious that there are two main corridors to transfer power from generation
(concentrated in the bottom side of the diagram) to the load center (the top side of the system one-
line); Transformer between buses 5-6, and path between buses 4-9. To demonstrate the proposed
methodology, we will attempt to estimate the post-contingency branch flow for transformer 4-9,
following the loss of transformer bank 5-6.
In practical implementations, it is assumed that other means of measurements are available
through SCADA or EMS, that are of lower sampling frequency. These values are used as a reference,
and will be updated using the method proposed in here. In this test case, the reference value is used
from the PowerWorld case. The case is also updated in small increments by scaling load and generation
to simulate a change over time in the power system operating state.

60

As shown in Figure 4.1, bank 5-6 is not observable, while bank 4-9 is observable with a direct
PMU measurement. We will attempt to estimate the change in flow on Bank 5-6, and then estimate
the post contingency flow on bank 4-9.

Figure 4.2 IEEE 14-Bus System with Limited PMU Observability (arrows represent PTDF factors,
not power flow)
Table 4-1 shows the original MW flow on all transmission lines in the case without changes
( 𝑓𝑓 𝑙𝑙 0
). LFDFs were calculated for bank 5-6 relative to all branches in the model, which are presented
in Figure 4.1.

61

Table 4-1: powerflow data, PTDF and LFDFs for transaction between buses 2-13, and LODFs for
contingency of branch 5-6
Line l
𝑓𝑓 𝑙𝑙 0
(MW) 𝛥𝛥 𝑓𝑓 𝑙𝑙 (MW) 𝐿𝐿 𝐿𝐿 𝑃𝑃 𝑃𝑃 5 − 6, 𝑙𝑙 𝑃𝑃 𝑃𝑃𝑃𝑃 𝑃𝑃 5, 6, 𝑙𝑙 𝐿𝐿 𝑃𝑃 𝑃𝑃 𝑃𝑃 5 − 6, 𝑙𝑙
1-2 173.6 - 0.06 0.205 -0.3406
1-5 82 - -0.06 -0.205 0.3406
2-3 77.7 7.3 0.051 -0.1495 0.2484
2-4 59.8 4.9 0.106 -0.3128 0.5197
2-5 44.1 3.8 -0.097 -0.3327 0.5527
3-4 - 0.051 -0.1495 0.2484
4-5 -65.7 -4.2 -0.843 -0.0642 0.1067
4-7 28.8 - 0.635 -0.2529 0.4202
4-9 16.5 1.8 0.365 -0.1451 0.2411
5-6 47.9 - -1 -0.6019 1
6-11 6.6 - -0.602 0.155 -0.2575
6-12 7.7 - -0.088 -0.1683 0.2796
6-13 17.4 3.2 -0.309 -0.5886 0.9779
7-8 0 - 0 0 0.00
7-9 28.8 3.3 0.635 -0.2529 0.4202
9-10 6 -0.2 0.602 -0.155 0.2575
9-14 9.9 - 0.398 -0.2431 0.4039
10-11 -3.1 - 0.602 -0.155 0.2575
12-13 1.5 0.4 -0.088 -0.1683 0.2796
13-14 5.2 - -0.398 0.2431 -0.4039

Many approaches can be used to decide what observable transmission lines to be used to
estimate the flow of bank 5-6. In this context, the nearby observable branches with highest LFDFs
represent the highest branch sensitivities to the change in bank flow, and will be used to estimate the
change. Specifically, branches 2-4, 2-5, and 6-13 will be used.
Substituting in equation (4.7) from Table 4-1, we get,

62

�
4.9
3.8
3.2
�=
⎣
⎢
⎢
⎢
⎡
1
−0.5197
�
1
−0.5527
�
1
0.9779
�
⎦
⎥
⎥
⎥
⎤
[ 𝛥𝛥 𝑓𝑓 5 − 6
] + �
𝑒𝑒 1
𝑒𝑒 2
𝑒𝑒 3
� (4.10)

Solving equation (4.10) using (4.9) we get 𝛥𝛥 𝑓𝑓 5 − 6
= 2.44 MW. Subsequently, solving equation
(3.1) for post-contingency flow, using 𝛥𝛥 𝑓𝑓 5 − 6
and Table 4-1, we get 𝑓𝑓 ̂
4 − 9, 5 − 6
𝑛𝑛𝑛𝑛𝑛𝑛 =36.68 MW.
Following the same approach, all flows are estimated, and security analysis results for the loss of bank
5-6 are shown in Table 4-2.

Table 4-2: post-contingency flow estimations and error residuals for all branches, following the loss
of bank 5-6
Line l 𝛥𝛥 𝑓𝑓 𝑙𝑙 (MW)
𝑓𝑓 ̂
𝑙𝑙 𝑛𝑛 𝑛𝑛𝑛𝑛
(MW)
(Estimate)
𝑓𝑓 ̂
𝑙𝑙 𝑛𝑛 𝑛𝑛𝑛𝑛
(MW)
(Powerflow)
Error %
1-2 - 178.02 189.2 5.91
1-5 - 80.26 85.7 6.35
2-3 7.3 87.57 88.8 1.39
2-4 4.9 70.04 71.5 2.05
2-5 3.8 43.02 43.8 1.79
3-4 - -24.03 -23 -4.49
4-5 -4.2 -112.34 -114.2 -1.63
4-7 - 64.14 66.6 3.70
4-9 1.8 36.67 37.9 3.23
5-6 - 0.00 0 0.00
6-11 - -24.48 -22.3 -9.78
6-12 - 4.08 5 18.40
6-13 3.2 5.04 4.5 12.11
7-8 - 0.00 0 0.00
7-9 3.3 64.07 66.5 3.66
9-10 -0.2 36.10 38.4 5.98
9-14 - 31.94 32.1 0.51
10-11 - 27.00 27.6 2.16
12-13 0.4 -2.53 -2.1 -20.47
13-14 - -16.04 -13.2 -21.48

63

As can be seen from Table 4-2, this methodology can be used to estimate the post-contingency
flows on transmission equipment with acceptable tolerance. The error (tolerance) is usually treated as
an absolute value for results validation, to ensure that the estimations are trustworthy and reflect the
actual state of the system. Higher error percentages are contributed to relatively small branch flows.
As an example, branch 12-13 shows an error of 20. However, the high percentage error is due to the
low power flow on the line. For this case, the actual flow of the line is 2.53MWs while the estimation
is 2.1MWs. The error in this estimation is 0.43MWs, which shows that the result of the estimation for
this case is very accurate. As shown, accurate estimations for the Security Analysis problem can be
provided for both PMU-observable and unobservable portions of the system, given that some PMU
deployment is available. In addition, this method allows for redundancy in calculating the post-
contingency branch flows regardless of observability, which increases the confidence of the
estimations. Weights can be assigned to measurements that are used to estimate LSA results to allow
more impact on specific measurements as compared to others.
It can be also noticed that errors increase closer to the slack bus of the system or the boundary
buses. The reason is that the slack bus is used to make up the difference in generation and load that
is changing with the system state.

64

Chapter 5: Summary and Future Work
This dissertation presented an approach that is developed to serve as the frontend of an
advanced EMS system driven purely with synchrophasor measurements. This was accomplished with
a two-fold solution: first, an advanced application was defined that uses synchrophasor PMU data to
assist in predicting operating conditions that require attention following any credible system
disturbance that may occur. Secondly, a synchrophasor-only prediction technique was developed and
validated to track the dynamic changes of the flows in the power system and provide a proper
mechanism to increase observability of the grid using shift factors. The resulting combination yields a
highly observable power system monitoring that can be used to provide situational awareness to
system operations, and allow for fast estimation of the post-contingency state of the power system for
all credible contingencies. The post-contingency system state estimation is the first of its kind novel
approach as it simplifies the estimation process by representing the unobservable portion of the
system with linear equations, which allows for fast calculations to be carried over the PMU sampling
rate.
Finally, to increase usability of the technology, and to allow for an estimation methodology
that is prone to data quality issues and high residual estimations, and approach was developed and
demonstrated to allow estimation of branch flows using multiple nearby branches, regardless of
observability. This adds another layer of data availability by enabling estimations even for branches
that are observable. This ensures maximum availability of states during equipment outages and
communication interruptions, which may prevent the measurements from being used in real-time.
As mentioned in Chapter 1, the PMU deployment at the transmission level is increasing every
day to boost the visibility of the grid and reveal conditions that were once not observable in real-time.
The low resolution of legacy systems, such as EMS and SCADA, caused many events and system
conditions to go unnoticed in real-time, and only revealed in post-event analysis studies. That said,

65

incomplete system representation from synchrophasors prevented operators from using the
technology in control centers. This methodology is designed to address the limited observability
conditions that transmission operators are currently experiencing, and complement solutions such as
State Estimator and legacy Real-Time Contingency Analysis in control rooms. In this dissertation, the
methodology was tested in MATLAB using simulated data from reduced powerflow cases, and
validated using simulations in PowerWorld. Testing and validation using real power system data and
models is left for the future due to the lack of access to data, due to restrictions on sharing Critical
Energy/Electric Identifiable Information (CEII). Following validation with real synchrophasor data
sets and models, a pilot deployment where the technology is implemented at a control center, and
provided with access to real-time measurements will help prove the use cases of such methodology in
real-time operations.
The work presented in this research was focused on developing a practical methodology to
expand system observability for system operations without additional PMU deployment, for real-time
assessment purposes. That said, this work can be expanded to provide additional guidance for optimal
PMU placement to boost the results of real-time assessments, by providing redundancy to the
measurements, and higher accuracy estimates. Signatures from the system studies indicating accuracy
of results and sensitivity of observable branches can be derived from the error vector to provide
intelligence on candidate locations for PMUs.
Furthermore, it was observed that transmission lines and transformers connected to load
buses show less accuracy of results, due to variability in the derived shift factors closer to load
variations. This work can be extended to derive compensation factors from the load patterns over
time, and bias the sensitivity parameters accordingly to boost the accuracy of results closer to load
buses.

66

Appendix A
A.1 Fully observable 5-Bus System source code
%Base case flows pre-contingency
f_old(1,2)=79;
f_old(1,3)=62.14;
f_old(2,3)=57.16;
f_old(2,4)=52.35;
f_old(2,5)=111.27;
f_old(3,4)=-27.7;
f_old(4,5)=16.13;

%Line Outage Distribution Factors for contingency of Line 2-3
LODF_2_3(1,2)=-33.3;
LODF_2_3(1,3)=33.3;
LODF_2_3(2,3)=-100;
LODF_2_3(2,4)=44.4;
LODF_2_3(2,5)=22.2;
LODF_2_3(3,4)=-66.7;
LODF_2_3(4,5)=-22.2;

%Post Contingency estimation for all lines
f_post = f_old + LODF_2_3/100 .* f_old(2,3);

A.2 Partially observable 5-Bus System source code
%Base case flows pre-contingency
f_old(1,2)=79;
f_old(1,3)=62.14;
f_old(2,3)=57.16;
f_old(2,4)=52.35;
f_old(2,5)=111.27;
f_old(3,4)=-27.7;
f_old(4,5)=16.13;

%Updated flows pre-contingency
f_new(1,2)=82.6;
f_new(1,3)= 64.3;
f_new(2,3)= 58.9;
f_new(2,4)= 53.8;
f_new(2,5)=115;
f_new(3,4)= -29.7;
f_new(4,5)= 17;

67

%Change in flows
Delta_f=f_new-f_old;

%PTDFs for transaction 2-4
PTDF_2_4(1,2)=-17.14%
PTDF_2_4(1,3)=17.14%
PTDF_2_4(2,3)=28.57%
PTDF_2_4(2,4)=36.19%
PTDF_2_4(2,5)=18.10%
PTDF_2_4(3,4)=45.71%
PTDF_2_4(4,5)=18.10%

%Line Outage Distribution Factors for contingency of Line 2-3
LODF_2_3(1,2)=-33.3%;
LODF_2_3(1,3)=33.3%;
LODF_2_3(2,3)=-100%;
LODF_2_3(2,4)=44.4%;
LODF_2_3(2,5)=22.2%;
LODF_2_ (3,4)=-66.7%;
LODF_2_3(4,5)=-22.2%;

%Line Flow Distribution Factor LFDFs for all lines
LFDF_2_5_4_5= PTDF_2_4(2,5)/ PTDF_2_4(4,5);
LFDF_2_3_2_4= PTDF_2_4(2,3)/ PTDF_2_4(2,4);

%Post Contingency estimation for all lines
f_post_2_5 = f_old(2,5)+Delta_f(4,5)* LFDF_2_5_4_5 + LODF_2_3(2,5)/100 *
(f_old(2,3)+Delta_f(2,4)*LFDF_2_3_2_4);

A.3 14-Bus IEEE test system
%Input data
%PTDF for Transaction from 2 to 13
PTDF_2_13(1,2)=-20.5;
PTDF_2_13(2,1)=20.5;
PTDF_2_13(1,5)=20.95;
PTDF_2_13(5,1)=-20.95;
PTDF_2_13(2,3)=14.95;
PTDF_2_13(3,2)=-14.95;
PTDF_2_13(2,4)=31.28;
PTDF_2_13(4,2)=-31.28;
PTDF_2_13(2,5)=33.27;
PTDF_2_13(5,2)=-33.27;
PTDF_2_13(3,4)=14.95;
PTDF_2_13(4,3)=-14.95;
PTDF_2_13(4,5)=6.42;

68

PTDF_2_13(5,4)=-6.42;
PTDF_2_13(4,9)=-14.51;
PTDF_2_13(9,4)=14.51;
PTDF_2_13(5,6)=60.19;
PTDF_2_13(6,5)=-60.19;
PTDF_2_13(6,11)=-15.5;
PTDF_2_13(11,6)=15.5;
PTDF_2_13(6,12)=16.83;
PTDF_2_13(12,6)=-16.83;
PTDF_2_13(6,13)=58.86;
PTDF_2_13(13,6)=-58.86;
PTDF_2_13(7,9)=25.29;
PTDF_2_13(9,7)=-25.29;
PTDF_2_13(9,10)=15.5;
PTDF_2_13(10,9)=-15.5;
PTDF_2_13(9,14)=24.31;
PTDF_2_13(14,9)=-24.31;
PTDF_2_13(10,11)=15.5;
PTDF_2_13(11,10)=-15.5;
PTDF_2_13(12,13)=16.83;
PTDF_2_13(13,12)=-16.83;
PTDF_2_13(13,14)=-24.31;
PTDF_2_13(14,13)=24.31;

%Line Flows in the initial case before adjustments - simulating load changes
f_old(1,2)=173.6;
f_old(2,1)=-173.6;
f_old(1,5)=82;
f_old(5,1)=-82;
f_old(2,3)=77.7;
f_old(3,2)=-77.7;
f_old(2,4)=59.8;
f_old(4,2)=-59.8;
f_old(2,5)=44.1;
f_old(5,2)=-44.1;
f_old(3,4)=-24.1;
f_old(4,3)=24.1;
f_old(4,5)=-65.7;
f_old(5,4)=65.7;
f_old(4,9)=16.5;
f_old(9,4)=-16.5;
f_old(5,6)=47.9;
f_old(6,5)=-47.9;
f_old(6,11)=6.6;
f_old(11,6)=-6.6;
f_old(6,12)=7.7;
f_old(12,6)=-7.7;
f_old(6,13)=17.4;
f_old(13,6)=-17.4;
f_old(7,9)=28.8;

69

f_old(9,7)=-28.8;
f_old(9,10)=6;
f_old(10,9)=-6;
f_old(9,14)=9.9;
f_old(14,9)=-9.9;
f_old(10,11)=-3.1;
f_old(11,10)=3.1;
f_old(12,13)=1.5;
f_old(13,12)=-1.5;
f_old(13,14)=5.2;
f_old(14,13)=-5.5;

%LODF For Contingency of Line 5-6 on Line 4-9
LODF_5_6(1,2)=6;
LODF_5_6(1,5)=-6;
LODF_5_6(2,3)=5.1;
LODF_5_6(2,4)=10.6;
LODF_5_6(2,5)=-9.7;
LODF_5_6(3,4)=5.1;
LODF_5_6(4,5)=-84.3;
LODF_5_6(4,7)=63.5;
LODF_5_6(4,9)=36.5;
LODF_5_6(5,6)=-100;
LODF_5_6(6,11)=-60.2;
LODF_5_6(6,12)=-8.8;
LODF_5_6(6,13)=-30.9;
LODF_5_6(7,8)=0;
LODF_5_6(7,9)=63.5;
LODF_5_6(9,10)=60.2;
LODF_5_6(9,14)=39.8;
LODF_5_6(10,11)=60.2;
LODF_5_6(12,13)=-8.8;
LODF_5_6(13,14)=-39.8;

%Line Flows in the updated case after adjustments - simulating load changes
f_new(1,2)=182.4;
f_new(2,1)=-182.4;
f_new(1,5)=87.5;
f_new(5,1)=-87.5;
f_new(2,3)=85;
f_new(3,2)=-85;
f_new(2,4)=64.7;
f_new(4,2)=-64.7;
f_new(2,5)=47.9;
f_new(5,2)=-47.9;
f_new(3,4)=-26.4;
f_new(4,3)=26.4;
f_new(4,5)=-69.9;
f_new(5,4)=69.9;
f_new(4,9)=18.3;

70

f_new(9,4)=-18.3;
f_new(5,6)=51.2;
f_new(6,5)=-51.2;
f_new(6,11)=8.7;
f_new(11,6)=-8.7;
f_new(6,12)=9;
f_new(12,6)=-9;
f_new(6,13)=20.6;
f_new(13,6)=-20.6;
f_new(7,9)=32.1;
f_new(9,7)=-32.1;
f_new(9,10)=5.8;
f_new(10,9)=-5.8;
f_new(9,14)=10.7;
f_new(14,9)=-10.7;
f_new(10,11)=-4.5;
f_new(11,10)=4.5;
f_new(12,13)=1.9;
f_new(13,12)=-1.9;
f_new(13,14)=6.7;
f_new(14,13)=-6.7;

%Calculate LFDF Matrix for Line 5-6
LFDF_5_6 = PTDF_2_13/PTDF_2_13(5,6);

%Form H Matrix
LFDF_5_6_H = [LFDF_5_6(2,4) LFDF_5_6(2,5) LFDF_5_6(6,13)]';
LFDF_5_6_H = 1./LFDF_5_6_H;

%Form Measurement Matrix
f_old_M = [f_old(2,4) f_old(2,5) f_old(6,13)]';
f_new_M = [f_new(2,4) f_new(2,5) f_new(6,13)]';
Delta_f_M_5_6 = f_new_M - f_old_M;

%Estimate Change in Branch flow
Delta_fl_5_6=(inv(LFDF_2_13_H'*LFDF_2_13_H)*LFDF_2_13_H')*Delta_f_M_5_6;

%calculate "new" pre-contingency flow on line 5-6
f_new_5_6_Estimated = f_old(5,6)+Delta_fl_5_6;

%Calculate post-contingency flow of Line 4-9 for contingency of line 5-6
f_post_4_9 = f_new(4,9)+(LODF_5_6(4,9)/100)*f_new_5_6_Estimated;

71

Bibliography
[1] Kundur, P., Balu, N. J., & Lauby, M. G. (1994). Power System Stability and Control. New
York: McGraw-Hill.
[2] Wood, A. J., Wollenberg, B. F., & Shelbe, G. B. (2014). Power Generation, Operation, And
Control. Hobohen, New Jersey: John Wiley & Sons Inc.
[3] North American Electric Reliability Corporation (NERC). Technical Analysis of the August 14,
2003, Blackout: What Happened, Why, and What Did We Learn? Report to the North American
Electric Reliability Council Board of Trustees. (2004). Princeton, NJ: Retrieved from Alexander
Street database.
[4] Glover, J. D., Sarma, M. S., & Overbye, T. J. (2008). Power system analysis and design.
Australia: Thomson
[5] Depratment of Energy (DOE). Learn More About Interconnections. Retrieved from Energy.gov:
https://www.energy.gov/oe/services/electricity-policy-coordination-and-
implementation/transmission-planning/recovery-act-0
[6] North American Reliability Corporation (NERC). NERC Interconnections. Retrieved from
https://www.nerc.com/AboutNERC/keyplayers/PublishingImages/NERC%20Interconne
ctions.pdf
[7] Usman, Muhammad Usama & Faruque, Md Omar. (2018). Applications of Synchrophasor
Technologies in Power Systems. Modern Power Systems. 6. 1-18. 10.1007/s40565-018-0455-8.
[8] Fedenra Energy Regulatory Comminion (FERC) and the North American Reliability
Corporation (NERC). (2012). FERC/NERC Staff Report on the September 8, 2011 Southwest
Blackout Event. Causes and Recommendations. FERC/NERC.

72

[9] Turner, M. (2011). San Diego Blackout. Retrieved from
https://www.markturner.net/2011/09/09/san-diego-blackout/
[10] Farantatos, D.E. (2015). State Estimation Advancements Enabled by Synchrophasor Technology.
Electric Power Energy Institute (EPRI)
[11] North American Electric Reliability Corporation (NERC). (n.d.). NERC TOP-001-4 .
Retrieved from https://www.nerc.com/pa/Stand/Reliability%20Standards/TOP-001-4.pdf
[12] Mynam, M. V., Harikrishna, A., & Singh, V. (2013). Synchrophasors Redefining SCADA Systems.
Schweitzer Engineering Laboratories, Inc.
[13] M. Donolo. (2007), Advantages of Synchrophasor Measurements Over SCADA Measurements for
Power System State Estimation, SEL Application Note (LAN2006-10). Retrieved from
http://www.selinc.com.
[14] K. D. Jones, J. S. Thorp, and R. M. Gardner. (2013), Three-phase linear state estimation using
phasor measurements. IEEE Power Eng. Soc. General Meeting, pp. 1–5.
[15] K. D. Jones. (2013), Synchrophasor-only dynamic state estimation & data conditioning.
[16] L. Zhang, A. Bose, A. Jampala, V. Madani and J. Giri. (2017) Design, testing, and implementation
of a linear state estimator in a real power system. IEEE Trans. Smart Grid., doi:
10.1109/TSG.2015.2508283.
[17] H. Chen, L. Zhang, J. Mo, and K. Martin. (2016). Synchrophasor-based real-time state estimation
and situational awareness system for power system operation. J. Mod. Power Syst. Clean Energy.
doi:10.1007/s40565- 016-0212-9.
[18] Nayak, N., Dobson, I., Zhang, L., Martin, K., & Bose, A. (2018). Practical implementation of
synchrophasor based real-time contingency analysis. North American Power Symposium (NAPS), (pp.
1-6). Fargo, ND.

73

[19] A. Pal, G. A. Sanchez-Ayala, V. A. Centeno, and J. S. Thorp. (2014) A PMU placement scheme
ensuring real-time monitoring of critical buses of the network. IEEE Trans. Power Del., vol. 29, no. 2,
pp. 510_517.
[20] Depratment of Energy (DOE). (2014). Factors Affecting PMU Installation Costs. SmartGrid.gov
[21] M. Kezunovic, A.P. & V. Venkatasubramanian, V. Vittal, (2014). Application of Time-
Synchronized Measurements in Power System Transmission Networks. 10.1007/978-3-319-06218-1.
[22] Nuthalapati, S. (2018). Power System Grid Operation Using Synchrophasor Technology. 10.1007/978-
3-319-89378-5.
[23] North American SynchroPhasor Initiative (NASPI). (2017, July). PMU Locations Map.
Retrieved January 2020, from http://www.naspi.org
[24] Horowitz, & Phadke, A. G. (1992). Power system relaying / Stanley H. Horowitz, Arun G. Phadke.
Research Studies Press.
[25] North American Electric Reliability Corporation (NERC). Glossary of Terms. Retrieved from
https://www.nerc.com/files/glossary_of_terms.pdf
[26] Song, C.-S., Park, C.-H., Yoon, M.-H., & Jang, G. (2011). Implementation of PTDFs and
LODFs for Power System Security. Journal of International Council on Electrical Engineering , (pp.
49-53).
[27] Guler, T., Gross , G., & Liu, M. (2007). Generalized Line Outage Distribution Factors.
IEEE Transactions on Power Systems, 22(2).
[28] Chen, Y. C., Domínguez-García , A. D., & Sauer, P. W. (2014). Measurement-Based
Estimation of Linear Sensitivity Distribution Factors and Applications. IEEE Transactions on
Power Systems, 29(3).
[29] Coffrin, C., & Van Hentenryck, P. (2012). A Linear-Programming Approximation of AC Power
Flows. INFORMS Journal on Computing. 26. 10.1287/ijoc.2014.0594.

74

[30] T. Athay, R. Podmore, and S. Virmani, (1979). A Practical Method for the Direct Analysis of
Transient Stability. IEEE Transactions on Power Apparatus and Systems, vol. PAS-98, no. 2,
pp. 573-584.
[31] Illinois Center for a Smarter Electric Grid (ICSEG), http://icseg.iti.illinois.edu/ieee-39-bus-
system/
[32] Illinois Center for a Smarter Electric Grid (ICSEG), Illinois Information Trust institute.
Power system test case archive. [Online]. Available:
http://www.ee.washington.edu/research/pstca/pf14/pg_tca14bus.htm
[33] Nurul Idayu Yusoff, Abdullah Asuhaimi Mohd Zin, and Azhar Bin Khairuddin. (2017)
Congestion Management in Power System: A Review. In 2017 3rd International Conference on
Power Generation Systems and Renewable Energy Technologies (PGSRET), Johor Bahru,
Malaysia, April 4-6 2017.
[34] A. Pillay, S. Prabhakar Karthikeyan, and D. P. Kothari. (2015) Congestion Management in Power
System: A Review. In International Journal of Electrical Power and Energy Systems, vol. 70, pp.
83-90, 2015.
[35] K.Vijayakumar. (2011). Optimal Location of FACTS Devices for Congestion Management in
Deregulated Power Systems. In International Journal of Computer Applications, Volume 16
No.6, February 2011.
[36] E. Jonckheere, R. Banirazi and E. Grippo, "Congestion management for cost-effective
power grid load balancing using facts and energy storage devices allocated via grid curvature
means", 2019 American Control Conference (ACC), pp. 3909-3915, 2019.

75

Abstract (if available)

Abstract Modern-day operation of power systems has become heavily dependent on advanced applications to reveal system conditions that were once unobservable to operators. Recent Energy Management Systems (EMSs) are equipped with real-time applications to help operators monitor the health of the grid, and even observe areas of the system that are not generally metered. A conventional State Estimator (SE) is an application within EMS that uses SCADA measurements as data sources for an iterative non-linear engine to provide downstream applications with a fully observable error-free system representation, for system monitoring and real-time assessments. Real-time network applications, such as Real-Time Contingency Analysis (RTCA), use State Estimator results to conduct iterative analysis to foresee system conditions in case unscheduled sadden outages occur in the power system. Devices known as Phasor Measurement Units (PMUs), were first introduced in the 1980, and started to provide a direct measurement to system state, as compared to legacy systems. The challenge in using synchrophasor measurements for real-time assessments resides in the lack of enough PMUs to provide full observability of the grid. This research investigates methods to overcome this limited PMU deployment and introduces a methodology to provide wider observability for real-time assessments to predict potentially dangerous operating conditions at a high rate.

Linked assets

University of Southern California Dissertations and Theses

Conceptually similar

PDF

Distribution system reliability analysis for smart grid applications

PDF

Electric vehicle integration into the distribution grid: impact, control and forecast

PDF

Utility – customer interface strategy and user application for electric vehicles and distributed generation management

$Data-driven aggregated fractal dynamic load modeling for early warning of voltage collapse$

PDF

Data-driven aggregated fractal dynamic load modeling for early warning of voltage collapse

PDF

An adaptive distance protection scheme for power systems with SFCL

PDF

Latent space dynamics for interpretation, monitoring, and prediction in industrial systems

PDF

Data-driven methods for increasing real-time observability in smart distribution grids

PDF

USC microgrid assessment study

PDF

USC microgrid development conceptual plan

PDF

Water desalination: real-time membrane characterization for performance prediction and system analysis for energetic enhancement

PDF

System stability effect of large scale of EV and renewable energy deployment

PDF

Mixture characterization and real-time extrusion quality monitoring for construction-scale 3D printing (Contour Crafting)

PDF

A function-based methodology for evaluating resilience in smart grids

PDF

Experimental and analytical studies of infrastructure systems condition assessment using different sensing modality

PDF

Theoretical foundations for modeling, analysis and optimization of cyber-physical-human systems

PDF

Towards a cross-layer framework for wearout monitoring and mitigation

PDF

Novel and efficient schemes for security and privacy issues in smart grids

PDF

Data and computation redundancy in stream processing applications for improved fault resiliency and real-time performance

PDF

Quantum feedback control for measurement and error correction

PDF

Thermally driven water treatment with membrane distillation: membrane performance, waste heat integration, and cooling analysis

Asset Metadata

Creator Abu-Jaradeh, Backer Nafiz (author)

Core Title Predictive real-time assessment for power grid monitoring and situational awareness using synchrophasors with partial PMU observability

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Electrical Engineering

Degree Conferral Date 2022-05

Publication Date 04/15/2022

Defense Date 04/15/2022

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag limited-observability,linear state estimator,OAI-PMH Harvest,phasor measurement unit,PMU,real-time monitoring,security analysis,synchrophasors

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Beshir, Mohammed (committee chair), Jonckheere, Edmond (committee member), Sanders, Kelly (committee member)

Creator Email abujarad@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-oUC110964823

Unique identifier UC110964823

Document Type Dissertation

Format application/pdf (imt)

Rights Abu-Jaradeh, Backer Nafiz

Type texts

Source 20220416-usctheses-batch-926 (batch), University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the author, as the original true and official version of the work, but does not grant the reader permission to use the work if the desired use is covered by copyright. It is the author, as rights holder, who must provide use permission if such use is covered by copyright. The original signature page accompanying the original submission of the work to the USC Libraries is retained by the USC Libraries and a copy of it may be obtained by authorized requesters contacting the repository e-mail address given.

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA

Repository Email cisadmin@lib.usc.edu