strategic and robust deployment of. synchronized phasor measurement units with. restricted channel...

Strategic and Robust Deployment of

Synchronized Phasor Measurement Units with

Restricted Channel Capacity

A Thesis Presented

by

Mert Korkalı

to

The Department of Electrical and Computer Engineering

in partial fulfillment of the requirements

for the degree of

Master of Science

in

Electrical and Computer Engineering

Northeastern University

Boston, Massachusetts

December 2010

http://www.korkali.com

http://www.ece.neu.edu/

http://www.northeastern.edu/

c© copyright by Mert Korkalı 2010

All Rights Reserved

NORTHEASTERN UNIVERSITY

Graduate School of Engineering

Thesis Title: Strategic and Robust Deployment of Synchronized Phasor

Measurement Units with Restricted Channel Capacity

Author: Mert Korkalı

Department: Electrical and Computer Engineering

Approved for Thesis Requirements of the Master of Science Degree

Thesis Adviser: Professor Ali Abur Date

Thesis Reader: Professor Hanoch Lev-Ari Date

Thesis Reader: Professor Aleksandar M. Stankovic Date

Department Chair: Professor Ali Abur Date

Graduate School Notified of Acceptance:

Director of the Graduate School: Sara Wadia-Fascetti Date

Northeastern University

Abstract

Department of Electrical and Computer Engineering

Master of Science in Electrical and Computer Engineering

by Mert Korkalı

http://www.northeastern.edu/

http://www.korkali.com

iv

Synchronized phasor measurements are changing the way power systems are moni-

tored and operated. Their efficient incorporation into various applications which are

executed in energy management control centers requires strategic placement of these

devices. Earlier studies which consider placement of synchronized phasor measure-

ment units (PMUs) to be used for state estimation assume that these devices will

have unlimited channel capacities to record as many phase voltages and currents as

needed. What differentiates this study from those already reported in the literature

is the fact that it accounts for the number of available channels for the chosen type

of PMU since all existing PMUs come with a limited number of channels and their

costs vary accordingly. This is shown to be a critical factor in strategic placement

of these devices. In this study, a revised formulation of the placement problem and

its associated solution algorithm will be presented. Examples will be used to illus-

trate the impact of having limited number of channels on the location and number of

required PMUs to make the system observable. Developed methods will take into ac-

count existing injection measurements, in particular the virtual measurements such

as zero-injections that are available at no cost at electrically passive buses.

Moreover, despite the advances in related technologies, it is almost impossible

to guarantee occasional device or communication failure that will lead to loss of

data to be received from a given PMU. This work is also aimed to illustrate how the

measurement design can be made reliable against such events while maintaining the

cost of PMU installations at a minimum by using strategically placed PMUs with

the proper number of channels.

Furthermore, it is also demonstrated that depending upon the topology of the

network, there will be an upper limit on the number of channels for the PMUs beyond

which installation costs will not be reduced any further. Accordingly, numerical

results of applying the developed optimization method to power systems with varying

sizes and topologies will be presented to illustrate the typical numbers of PMUs and

their channel capacities that are required for optimal performance. The results of

this work will be more useful as the number of PMU installations increases to levels

that will make the system fully observable based solely on PMUs with different

number of channel capacities.

Acknowledgments

I am deeply indebted to my mentor and research advisor, Professor Ali Abur, for an

incomparably rewarding educational and personal experience. I have been indescrib-

ably enlightened and inspired by his patient teaching and vast technical expertise.

His constant support, gentle guidance, and warm encouragement gave a positive

impetus to the successful completion of my thesis. His inspiring ability to treat

problems from a new perspective integrated with many hours of constructive discus-

sions were the raison d’etres of the progressive improvements in this thesis. Indeed,

being a research assistant to him will definitely fortify my competence to stay in the

forefront of my current research area.

In the meantime, this is an opportunity to thank some of the people who have

shaped my academic personality prior to my arrival to Northeastern. Special thanks

go to my undergraduate advisor, Professor Bulent Bilir, for his invaluable patience

and incessant encouragement throughout my studies at Bahcesehir University and

Professor H. Fatih Ugurdag for his irreplaceable endeavor that undoubtedly paved

the way for my being a graduate student in the United States. I am more than grate-

ful for experiencing a mentor–younger friend relationship as well as an instructor–

student relationship with them.

I would like to express my heartfelt gratitude to Professor Hanoch Lev-Ari and

Professor Aleksandar M. Stankovic not only for serving as my thesis committee

members, but also giving me an inspiration and immense knowledge of their areas

of expertise during my graduate studies.

My deepest gratitude and love are reserved for my parents, who made me who I

am and whose love embraces me everywhere regardless of the wide distance between

us.

v

Contents

Abstract iii

Acknowledgments v

List of Figures viii

List of Tables ix

1 Introduction 1

1.1 Motivations for the Study . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Contributions of the Thesis . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Optimal PMU Placement for State Estimation 5

2.1 Historical Overview of Phasor Measurement Units . . . . . . . . . . . 5

2.2 Applications of Synchronized Phasor Measurements in Power Systems 7

2.3 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3 Strategic Placement of Phasor Measurement Units with OptimalNumber of Channels 14

3.1 Statement of the PMU Placement Problem . . . . . . . . . . . . . . . 14

3.2 Proposed Formulation for the PMU Placement Problem . . . . . . . . 16

3.3 Modeling of Zero-Injection Buses . . . . . . . . . . . . . . . . . . . . 21

3.3.1 Case 1—Arbitrary Selection of Neighbor Buses . . . . . . . . . 21

3.3.2 Case 2—Selection of Neighbor Buses which Have MinimumNumber of Neighbors . . . . . . . . . . . . . . . . . . . . . . . 21

3.3.3 Case 3—Selection of Neighbor Buses which Have MaximumNumber of Neighbors . . . . . . . . . . . . . . . . . . . . . . . 22

3.3.4 Case 4—Modeling of Zero-Injection Buses as Linear Constraints 23

3.4 Effect of Network Sparsity on PMU Placement . . . . . . . . . . . . . 25

3.5 Optimal Placement Accounting for Single PMU Loss . . . . . . . . . 28

4 Simulation Results 31

4.1 Conventional PMU Placement with Fixed Channel Capacity . . . . . 31

vi

Contents vii

4.2 Impact of Network Sparsity on Strategic Placement of PMUs . . . . . 32

4.3 Reliable Measurement Design Against Loss of PMUs . . . . . . . . . 34

4.4 Illustration of Unified PMU Placement Schemes . . . . . . . . . . . . 35

5 Concluding Remarks and Further Study 49

5.1 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

5.2 Further Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

A Functions and Scripts Used in the PMU Placement Algorithm 51

A.1 Read Network Parameters and Build the Single-Hop Connectivity Ma-trix A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

A.2 Find the Required Number of PMUs for Complete Network Observ-ability (Ignoring Zero-Injection Measurements) . . . . . . . . . . . . . 54

A.3 Find the Required Number of PMUs for Complete Network Observ-ability (Considering Zero-Injection Measurements) . . . . . . . . . . . 57

B IEEE Test Systems Data Used in the PMU Placement Algorithm 64

B.1 IEEE 14-Bus Test System Data . . . . . . . . . . . . . . . . . . . . . 65



B.4 IEEE 118-Bus Test System Data . . . . . . . . . . . . . . . . . . . . 79

Bibliography 94

List of Figures

3.1 Phasor measurements provided by PMU. . . . . . . . . . . . . . . . . 17

3.2 7-bus system for illustration. . . . . . . . . . . . . . . . . . . . . . . . 19

3.3 PMU placement for IEEE 14-bus system when the channel limit is 3. 20

3.4 Network diagram and measurement configuration for the IEEE 14-bussystem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.5 Configuration of 3 one-channel PMUs in 7-bus system. . . . . . . . . 25

3.6 Network diagram for the 7-bus system with two-hop neighborhoodtopology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.7 Reliable placement against single PMU loss for the IEEE 14-bus sys-tem when the channel limit is 3. . . . . . . . . . . . . . . . . . . . . . 30

3.8 Zero-injections and optimally placed 22 PMUs for the IEEE 57-bussystem assuming no channel limits. . . . . . . . . . . . . . . . . . . . 30

4.1 Optimally placed 7 PMUs for the IEEE 14-bus system when the chan-nel limit is 1 (ignoring the zero-injections). . . . . . . . . . . . . . . . 37

4.2 Optimally placed 15 PMUs for the IEEE 30-bus system when thechannel limit is 1 (ignoring the zero-injections). . . . . . . . . . . . . 38



4.5 Zero-injection and optimally placed 3 PMUs for the IEEE 14-bussystem when the channel limit is 4. . . . . . . . . . . . . . . . . . . . 41

4.6 Zero-injections and optimally placed 7 PMUs for the IEEE 30-bussystem when the channel limit is 4. . . . . . . . . . . . . . . . . . . . 42



4.9 Reliable placement against single PMU loss for the IEEE 14-bus sys-tem when the channel limit is 3 (considering the zero-injection). . . . 45

4.10 Reliable placement against single PMU loss for the IEEE 30-bus sys-tem when the channel limit is 3 (considering the zero-injections). . . . 46

4.11 Reliable placement against single PMU loss for the IEEE 57-bus sys-tem when the channel limit is 3 (considering the zero-injections). . . . 47

4.12 Reliable placement against single PMU loss for the IEEE 118-bussystem when the channel limit is 3 (considering the zero-injections). . 48

viii

List of Tables

4.1 Conventional PMU Placement without Zero-Injections for Miscella-neous Power Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.2 PMU Placement with Zero-Injections for IEEE Test Systems . . . . . 33

4.3 Conventional PMU Placement with 2-Hop Connectivity for Five IEEETest Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.4 Reliable Placement Against Loss of PMUs without Zero-Injections forMiscellaneous Power Systems . . . . . . . . . . . . . . . . . . . . . . 35

4.5 Reliable Placement Against Loss of PMUs with Zero-Injections forIEEE Test Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

B.1 System Information of Studied IEEE Test Systems . . . . . . . . . . 64

ix

To my beloved parents,

Selma and Hasan Korkalı,

with love and gratitude

x

“A good companion shortens the longest road.”

—Turkish Proverb

xi

Chapter 1

Introduction

Power systems have long been monitored based on measurements provided by remote

terminal units (RTU). These measurements typically include branch power flows, bus

power injections, and magnitude of bus voltages. A critical quantity of interest is the

phase difference between a given pair of bus voltage phasors in the system. Until

recently, this quantity was not easily measurable. Direct measurement of phase

angles of voltage and/or current phasors is now possible by phasor measurement

units (PMUs) thanks to the availability of the Global Positioning System (GPS)

that facilitates time synchronization of measured signals at geographically remote

locations. However, even when there are no phase angle measurements, phase angle

associated with each bus voltage phasor can be estimated along with its magnitude

provided that there are sufficient number of power flow and bus injections measured

with negligible time skew. This is accomplished by the help of a power system state

estimator.

Having synchronized phasor measurements for bus voltages and branch currents

in a given power system has a significant effect on the application functions in control

centers. In particular, the state estimation application will be affected in a rather

fundamental manner in that the problem formulation can transform from nonlinear

to linear if sufficiently large number of such phasors can be measured. Hence, there

is interest on the part of state estimator users with respect to the requirements of

such a transformation, namely the cost associated with installing the right number

1

Chapter 1. Introduction 2

and type of PMUs at strategic locations in order to drastically improve their state

estimators.

1.1 Motivations for the Study

Synchronized phasor measurement units are rapidly populating power systems as

their benefits become more and more evident for various power system applications.

One such function is the state estimation [1]. In fact, state estimation provides the

much needed real-time database for several application functions which facilitate

power system control and efficient operation. Given the limited resources, it is

practical to place these devices strategically in order to minimize the cost/benefit

ratio.

Optimal placement methods to account for contingencies, loss of measurements

as well as existing conventional measurements and zero-injections have already been

presented in previous publications. A common assumption in all of these studies

is that each PMU can measure unlimited number of voltages and currents. This

assumption allows the PMU placement problem to be formulated in a straightforward

manner since placement of a PMU at a given bus automatically ensures availability

of phasors at all of its neighboring buses. This is true as long as the network

connectivity and associated branch parameters are perfectly known, which is also

commonly assumed by all state estimators. Available PMUs have limited number of

channels which are used to sample voltage or current signals. These sampled signals

are processed to generate a positive-sequence phasor voltage and current from the

three-phase voltages and currents. Hence, channel capacities of PMUs may play an

important role in their strategic placement for maximum coverage.

1.2 Contributions of the Thesis

The main contribution of this thesis is to recognize the effect of channel capacity

of a given type of PMU on their optimal placement for network observability and


to develop an optimal solution to the PMU placement problem given a specified

number of available channels for the candidate PMUs. As in earlier studies, problem

formulation accounts for bus injections which may be known due to measurements

or due to their zero values at passive buses.

In formulating the problem it is realized that for a given number of channel ca-

pacity there will be a finite combination of possible assignments of incident branches

to a given PMU placed at a bus. Hence, the choices will increase with the number of

incident branches for a given bus, but will remain bounded irrespective of the overall

system size, thanks to the sparse interconnection of power system buses.

1.3 Thesis Outline

This thesis comprises five chapters. It is organized as follows. In the current chapter,

the motivations for the research problem and our contributions to PMU placement

problem are discussed.

In the succeeding chapter (Chapter 2), we first present the general background

information about synchronized phasor measurement units and review the relevant

literature to the existing PMU placement strategies flourished in the field of power

systems state estimation.

Chapter 3 delineates the method of determining optimal number and locations

of PMUs, so that the system state of an entire power system will be observable. In

doing so, the technique to be introduced is a numerical procedure where the problem

is formulated as an integer linear programming (ILP) problem. In addition, different

cases are suggested for the modeling of zero-injection buses.

Chapter 4 is devoted to the simulation results of our optimization model includ-

ing various conditions where zero-injections are considered and ignored, the sparsity

of the studied networks is reduced fictitiously; and the reliability is maintained under

a single PMU failure. Several case studies are conducted to evaluate the algorithm’s

performance and effectiveness.


Finally, Chapter 5 concludes this thesis with the discussion on the benefits of

the proposed formulation for optimal PMU placement along with its usability in

the existing power systems. Also, we express our ideas about what can be done for

further study.

Chapter 2

Optimal PMU Placement for State

Estimation

This chapter is mainly devoted to the history of the evolution of synchronized phasor

measurement units used for the purpose of state estimation and provides an overview

of the applications and miscellaneous techniques that have been introduced so far in

the power systems literature regarding PMU placement.

2.1 Historical Overview of Phasor Measurement

Units

Synchronized phasor measurements are considered as a promising measurement tool

for electric power systems. They supply positive-sequence voltage and current mea-

surements synchronized to within a microsecond thanks to the availability of Global

Positioning System (GPS) and the sampled data processing algorithms designed

for computer relaying applications. Apart from the positive-sequence voltage and

current measurements, these systems are able to quantify both local frequency and

frequency rate-of-change. Moreover, they can be altered according to the several

needs of users in order to extract the data relating to zero- and negative-sequence

quantities, harmonics, as well as individual phase voltages and currents. Currently,

5

Chapter 2. Optimal PMU Placement for State Estimation 6

there are 24 commercial PMU manufacturers. In this respect, standards established

by the IEEE Power System Relaying Committee have enabled the data sharing capa-

bility among distant units from different manufacturers. Considering that blackouts

are occurring overwhelmingly on the existing power networks, widespread allocation

of PMUs has gained tremendous interest. In particular, positive-sequence measure-

ments provide the accessibility to the power system state at any instant. Various

applications of synchronized phasor measurements have been presented in the liter-

ature, and more applications will certainly be developed in coming years [2].

The modern era of phasor measurement technology has its origin in research

conducted on computer relaying of transmission lines. Early study on transmis-

sion line relaying with relays based on microprocessors unveiled that the available

computer power in 1970s was not substantial enough to manage the computations

required to execute all the line relaying operations.

Positive-sequence voltages of a network constitute the state vector of a power

system, and it is of fundamental importance in all of power system analyses. The

first paper to identify the importance of positive-sequence voltage and current pha-

sor measurements, and some of the uses of these measurements, was published in

1983 [3], and this work can be viewed as the starting point of modern synchronized

phasor measurement technology. The GPS was being entirely installed around these

years. Later on, it became evident that this system provided the most effective way of

synchronizing power system measurements over long distances. The first prototypes

of the existing PMUs using GPS were developed at Virginia Tech in 1980s. These

prototype PMUs built at Virginia Tech were placed at certain substations of the

Bonneville Power Administration (BPA), the New York Power Authority (NYPA),

and the American Electric Power Service Corporation (AEPSC) [2]. For the mo-

ment, a number of commercial manufacturers offer PMUs and placement of PMUs

on the modern power systems is being carried out profoundly in many countries.

Along with the development of PMUs, there is substantial amount of continuing

research on the applications of the measurements provided by the PMUs. In this

respect, the recent advancement in synchronized phasor measurements is reaching


towards improvements in its maturity, and a majority of modern power systems

across the globe are continually placing wide-area measurement systems made up of

the phasor measurement units.

2.2 Applications of Synchronized Phasor Measure-

ments in Power Systems

Advances and applications in research studies of synchronized phasor measurement

units have been presented by several recent papers. Reference [4] introduces a pos-

sible approach towards formulating a standard that would facilitate interoperability

of PMUs under transient conditions. In [5], the authors propose a wide-area network

of phasor measurement units as a means for monitoring and control of voltage sta-

bility. A new technique for wide-area protection utilizing PMU is suggested in [6].

In particular, the proposed protection scheme is dependent upon the comparison

of the positive-sequence voltage magnitudes for certain areas along with the differ-

ences of positive-sequence current phase angles for each line between two areas in

the power system. The authors of [7] show that the realization of optimal measure-

ment designs can be achieved in order to determine the types and locations of few

extra measurements that will considerably improve the capability of topology error

processing. To accomplish this task, emerging PMUs are suggested for use in addi-

tion to the conventional power flow and injection measurements. In order to help

prevent a large-scale blackout, the authors of reference [8] present an online voltage

security assessment scheme making use of synchronized phasor measurements as well

as decision trees which are periodically updated.

With the latest progress in smart grid technology, the use of phasor measure-

ment units has definitely drawn substantial interest in order to render power system

reliability within transmission and distribution infrastructure. Hence, the utilization

of wide-area monitoring systems (WAMS) using synchrophasor measurements has

gained momentum achieving improved system monitoring, control, and protection.


In one of recent studies [9], the authors discuss the detailed architecture and the re-

cent implementations and applications of a wide-area frequency monitoring network

(FNET). In [10], it is shown that single line outages can be detected by using pha-

sor angle measurements data provided by PMUs even if there is extremely limited

coverage. In a two-paper set [11, 12], the authors present a PMU-based technique

for fault detection/location as well as multifunction transmission line protection for

both arcing and permanent faults by processing the synchronized voltage and current

phasors. In order to avoid reclosure on a permanent fault, arcing fault discrimination

technique is proposed via processing the synchronized harmonic voltage and current

phasors.

In [13], energy function analysis has been adapted using phasor data in order

to monitor the dynamic security of power transfer paths. Utilizing the phasor data

provided by a system of well-located PMUs, the transfer paths and their associated

parameters are identified and the transfer path reactances and equivalent inertias

are estimated by using the power-angle curves and the oscillation frequencies. A

wide-area identification of long-term voltage instability from the bus voltage pha-

sors provided by synchronized phasor measurements is devised in [14, 15]. A gener-

alized fault section selector, as well as fault locator, is proposed by Liu et al. [16] for

multiterminal transmission lines based on synchronized phasor measurement units.

In [17], the authors investigate the feasibility of estimating the rotor angle of syn-

chronous generators from the measurements of field voltage of the generator and

terminal voltage measurements acquired from PMUs.

2.3 Related Work

In order to estimate the system state, power system state estimator makes use of the

set of available measurements. Given a set of measurements and their corresponding

locations, the network observability analysis will determine if a unique estimate

can be found for the system state. This analysis are carried out offline during

the initial phase of a state estimator installation in order to check the sufficiency

of the existing measurement configuration. If the system is not found observable,


then additional meters may have to be installed at certain locations. Observability

analysis is executed online prior to performing the state estimator. It ensures that a

state estimate can be obtained using the set of measurements at the last measurement

scan. Telecommunication errors, telemetry failures, or changes in topology may at

times result in the cases where the state of the whole system cannot be estimated.

Network observability test allows detection of such cases right before the execution

of the state estimator. Observability of a given network is determined by the type

and location of the available measurements as well as by the topology of the network.

Therefore, the analysis of network observability exploits the graph theory since it has

connection with networks, their respective equations and solutions. Also, the system

is said to be topologically observable if the meters are placed such that there exists at

least one spanning measurement tree of full rank [18]. On the other hand, installing

a PMU at every bus in a wide-area interconnected network is neither reasonable

nor prudent. For that reason, the optimal PMU placement problem deals with

determining the minimum number of PMUs to achieve full network observability.

Intrinsically, the optimal PMU placement problem is shown to be NP-complete

with a solution space having 2N possible combinations for an N -bus electric net-

work [19]. In this respect, it is regarded as a combinatorial optimization problem

and a considerable amount of work has been done by several researchers, accordingly.

These approaches are broadly classified into two main categories: the metaheuristic

techniques and conventional deterministic optimization methods. As formulations

based on metaheuristics (e.g., simulated annealing (SA), genetic algorithm (GA),

Tabu search (TS), etc.) do not involve derivative of cost functions and the variables

of the meter placement problem are discrete; they have been extensively used in

dealing with discrete variables when solving the optimal PMU placement problem.

The utilization and development of PMUs are first introduced in [20] and [21].

An algorithm for finding the minimum number of PMUs required for power system

state estimation is developed in [22] and [23] in which the simulated annealing (SA)

method and the graph theory are utilized in formulating and solving the problem.

Nuqui and Phadke [24], [25] utilize a simulated annealing (SA) technique in their

graph-theoretic approach to determine the optimal PMU locations. In their work, a


novel concept of “depth-of-unobservability” is presented and how this has an effect

on the PMU placement is also shown. An optimal placement method founded on

nondominated sorting genetic algorithm (NSGA) is proposed by Milosevic and Be-

govic [26]. The algorithm unites the graph theory and a simple GA to estimate each

optimal solution of the objective function. The best tradeoff between the competing

objectives is then searched by customized NSGA. This method is limited by the size

of the problem as it requires more complex computations. Another GA-based proce-

dure for the placement problem is presented by Marın et al. [19]. In this letter, the

relationship between the number of current phasors that must be measured on each

PMU and the required number of PMUs is also sought by the authors. Cho, Shin,

and Hyun [27] propose three approaches aiming at alleviating computational burden

of the optimal placement problem. First, SA method is modified in setting the ini-

tial temperature and cooling procedure. Second, direct combination (DC) method

is suggested using a simple yet effective heuristic rule to identify the most effective

sets in the observability sense. At the end, TS method is utilized to diminish the

searching spaces effectively. A novel technique established upon TS and augmented

incidence matrix is introduced by Peng, Sun, and Wang [28]. Aminifar et al. [29]

investigate the applicability of immunity genetic algorithm (IGA) for minimal PMU

placement problem. Chakrabarti et al. [30] propose a methodology based on binary

particle swarm optimization (BPSO). In this study, the objectives of the optimization

problem lie at the intersection of minimization of the required number of PMUs and

maximization of the measurement redundancy. Analogously, Hajian et al. [31] use a

modified BPSO algorithm as an optimization tool for obtaining the minimal num-

ber of PMUs for complete system observability. Sadu, Kumar, and Kavasseri [32]

solve the placement problem by particle swarm optimization (PSO) algorithm, and

the idea of introducing randomness in selecting the buses for the PMU placement

is suggested by the authors. Chakrabarti and Kyriakides [33] propose binary search

algorithm as a technique for solving the problem.

In addition to the metaheuristic methods, several conventional deterministic

techniques are applied to the optimal PMU placement problem [34–46]. In [34]

and [35], the algorithm for optimal placement of PMUs is developed using integer


programming (IP) established upon the network observability and installation costs

of PMUs. Gou [36] makes a simplification in the placement algorithm by using

ILP and considering both the presence and absence of the conventional flow and

injection measurements. In his another simultaneously published work [37], the

author extends the formerly developed model and generalizes the ILP formulation

to satisfy various needs by integrating redundant PMU placement, full observability

and incomplete observability cases. Dua et al. [42] propose another formulation using

ILP. Integer quadratic programming (IQP) model is proposed as a solution method

in [40] and [41].

Among the published techniques, a certain number of those take into account

the power system contingencies broadly associated with the line outages and/or

measurement losses [33, 38–44, 47–51]. The integration of such contingencies in the

placement problem would certainly contribute to the reliable measurement designs.

A sequential meter addition/elimination process based on the measurement sensi-

tivities has been presented by Park et al. [47]. Abur and Magnago [38] propose an

LP-based method in which a number of additional measurements are then systemat-

ically added to ensure full observability under the loss of any single network branch.

The same authors propose a numerical algorithm based on the measurement Jaco-

bian and sparse triangular factorization to optimally upgrade the measurements and

yield a configuration which can remain robust against loss of single measurement

and single branch outage without sacrificing network observability [48]. Xu, Yoon,

and Abur [39] address a binary integer programming method taking into account

the loss of a single PMU in order to lessen the vulnerability of state estimation to

PMU breakdowns. The identical efforts to obtain a reliable measurement system

based on numerical observability are made by Rakpenthai et al. [49]. The authors

utilize the minimum condition number of the normalized measurement matrix as a

criterion. Then, the sequential addition and elimination methods are employed to

determine the essential measurements and to identify the redundancy measurements

under the contingency, respectively. Later work by Chakrabarti and Kyriakides [33]

propose a strategy utilizing a binary search algorithm to find the minimum number

of PMUs for full topological observability under normal operating conditions, as well


as single branch outages. In the paper, the search process is said to be exhaustive;

as a result, they aspire to overcome the restrictions of the conventional optimization

methods such as the integer programming and the uncertainties of the evolutionary

programming techniques such as the genetic algorithm. In their another collabora-

tive works [40], [41], they propose an IQP approach to minimize the total number

of PMUs required to maintain the complete observability of the system for normal

operating conditions and under the outage of a single PMU or a transmission line.

Also, they aim to provide the maximization of the measurement redundancy at all

system buses. Dua et al. [42] devise a procedure for optimal multistage scheduling

of PMU placement phased over multiple time horizons. Furthermore, they suggest

zero-injection constraints be modeled as linear constraints in an ILP framework. The

two indices, Bus Observability Index (BOI) and System Observability Redundancy

Index (SORI), are utilized to rank the multiple solutions obtained via minimum

PMU placement problem. In their generic PMU placement formulation, the authors

offer some modifications to deal with the issues of PMU loss and communication

line outage. Likewise, Abbasy and Ismail [43] study the impact of single PMU loss

or multiple PMU losses on the decision strategy of the PMU placement problem.

In [50] and [51], the authors come up with the so-called branch PMUs which are

designed to monitor a single branch by measuring the associated current and termi-

nal voltage phasors. Further, they also address the robustness of the measurement

design by considering not only the cases of PMU loss or failure, but contingencies

stemming from line or transformer outages. More recently, Aminifar et al. [44] of-

fer a practical ILP-based model taking account of several contingency conditions

involving communication constraints, loss of measurements, and line outages.

Chen and Abur [45], [46] propose an IP-based solution that leads to the smallest

number of strategically located PMUs eliminating the measurement criticality in the

system. In these papers, it is shown that the bad data detection and identification

capability of a system can be enhanced greatly with few additional PMUs.

A fault location scheme for transmission networks using PMUs is developed and

the idea of fault location observability is presented by Lien et al. [52]. A method

for placing minimum number of PMUs to locate any fault in a power system is


proposed by Pokharel and Brahma [53]. The method is formulated on the basis

of ILP structure which is introduced in [34]. Mahmoodianfard et al. [54] utilize

a scheme based on decision trees to find an optimum PMU placement for voltage

security assessment. In the work by Zhou et al. [55], a virtual data preprocessing

technique and a matrix reduction algorithm are introduced to show the effectiveness

in reducing the computational effort for determining the optimal placement set.

The performance validation for the proposed algorithm is proven by applying the

method of Lagrangian relaxation to calculate the lower bound of the minimal number

of PMUs.

Chapter 3

Strategic Placement of Phasor

Measurement Units with Optimal

Number of Channels

3.1 Statement of the PMU Placement Problem

Power systems are assumed to operate in pseudo-steady-state due to the slow dy-

namics of system loads and generation. Hence, measurements of various quantities

such as power flows, voltages, and currents at various substations are used to ap-

proximately determine the operating conditions of this pseudo-steady-state of the

system. These measurements typically have time skew which may be in the order

of minutes and therefore an estimate of the system state obtained based on these

measurements will only be an approximation. Time skew among collected mea-

surements is eliminated when the measurements are replaced by those provided by

synchronized phasor measurement units (PMU). These devices are quickly becoming

the preferred metering choice at bulk power transmission substations. They provide

magnitude and phase angle measurements of bus voltages and branch currents for

the positive-sequence components of three-phase signals. These measurements are

time-stamped and phase angles are defined with respect to a common reference

14

Chapter 3. Strategic Placement of Phasor Measurement Units with OptimalNumber of Channels 15

determined by the global positioning satellite system. PMU measurements can im-

prove the performance and capabilities of various network applications due to their

unique features. One of the applications which will benefit most from availability

of PMU measurements is the state estimator. In fact, if the entire network can be

made fully observable by just using PMU measurements, then the state estimation

problem will become linear and will be solved directly without requiring the use of

iterative methods. If these devices can be strategically placed at proper substations

in sufficient numbers, then such a transformation will be possible, making a very

significant improvement in the performance of existing state estimators, essentially

eliminating the issues of divergence due to numerical problems.

All of the aforementioned studies in Section 2.3 consider the PMU placement

problem in such a way that these devices are assumed to have unlimited number of

channels. Hence, placing them at a given bus ensures that in addition to the phasor

voltage at that bus, phasor voltages of all its immediate neighbors will be available

due to the monitored phasor currents along all the branches incident to that bus.

In practice, every PMU comes with a channel limit and therefore a more realistic

placement of the PMUs should take into account their varying channel capacities.

The authors of [56] attempt to introduce the limit on the number of measurements

each PMU can make and a modified PageRank placement algorithm is utilized in the

importance modeling of the network nodes. However, the optimal numbers required

to make the studied test systems observable are not provided explicitly. Rather, the

effect of the number of measurements on the nodes to fully observe the network is

given as a criterion for the usefulness of the method.

In this study, the PMU placement problem is revisited with the aim of relaxing

the abovementioned assumption based on the fact that the bus voltage phasor and

all current phasors along branches connected to that bus are available. The problem

is reformulated where the number of channels for each PMU can be changed and

the problem can be solved repeatedly to find the optimal locations. Furthermore,

the formulation takes into account any existing injection measurements, in partic-

ular those virtual measurements provided by the zero-injections of passive buses.

Afterwards, the formulation is extended to account for loss of PMUs so that the


final PMU measurement design remains robust against loss of a PMU due to device

or communication link failures. Another contribution of this study is to recognize

the effect of channel capacity of a given type of PMU on their optimal placement

for network observability and to develop an optimal solution to the PMU placement

problem given a specified number of available channels for the candidate PMUs.

The approach taken in this study is one of exhaustive search among all possible

combinations at a given bus for a given limit on the number of available channels.

In formulating the problem it is realized that for a given number of channel capacity

there will be a finite combination of possible assignments of incident branches to

a given PMU placed at a bus. Hence, the choices will increase with the number

of incident branches for a given bus, but will remain bounded irrespective of the

overall system size, thanks to the sparse interconnection of power system buses.

The developed measurement placement procedure will be outlined and illustrated

by examples in the succeeding sections. Precisely, the main goal is to allow optimal

placement of PMUs which may have limited number of channels.

3.2 Proposed Formulation for the PMU Place-

ment Problem

Formulation of optimal PMU placement problem for the case of varying channels will

be briefly reviewed first. Subsequently, the revision of this formulation to account

for a PMU loss will be described in Section 3.5.

Consider a PMU which has L channels and installed at bus k as shown in

Figure 3.1. Also assume that bus k is connected to Nk number of buses. Note that the

actual number of channels may be three times more since the phasor measurements

are usually the positive-sequence components derived from sampled waveforms of

three-phase signals. So, it is understood that the number of channels refers to

the number of positive-sequence phasor measurements that can be produced by the

considered PMU.


PMU ......

Bus 1

Bus 2

Bus Nk

V phasor

I phasors

Bus k

Figure 3.1: Phasor measurements provided by PMU.

If the number of channels, L, is larger than the number of neighbors Nk, then a

single PMU placed at the bus will provide phasor voltages at all its neighbor buses.

Otherwise, there will be rk combinations of possible channel assignments to branches

incident at bus k:

rk =

NkCL if L < Nk,

1 if Nk ≤ L.

where the number of possible combinations of L out of Nk branches is defined as:

NkCL =Nk!

(Nk − L)!L!(3.1)

Since a PMU is able to measure both the voltage phasor of the bus at which it is

installed and the current phasors of all the lines in the neighborhood of this bus,

the placement of PMUs becomes a problem with an objective of finding a minimal

set of PMUs such that a bus must be observed at least once by the solution set of

the PMUs. This leads us to define the binary connectivity matrix H consisting of

all possible combinations at a given bus for a given limit on the number of available


channels such that each bus k will have rk rows, each row containing (L+1) nonzeros

for the bus itself and its neighbor buses. However, when Nk < L, i.e., the number of

branches incident to bus k is less than the channel limit of the PMUs, the associated

row needs to be kept unchanged. The channel limit constraints can thus be imposed

so that a PMU placed at a bus will observe its neighboring buses by selecting the

appropriate combination(s) of L.

Description of the procedure can be illustrated using a 7-bus system example

shown in Figure 3.2. Assuming a channel limit of 2 for the PMUs, the number of

rows for each bus is found to be r1 = r5 = r6 = r7 = 1, r2 = 6, and r3 = r4 = 3. In

fact, consider the buses connected to bus 2, which are buses 1, 3, 6, and 7; therefore,

the 2-combinations of this set will result in the pairs 1− 3, 1− 6, 1− 7, 3− 6, 3− 7,

and 6−7. In this sense, each row associated with bus 2 in the matrix H will include

a 1 corresponding to bus 2 and its neighbor pairs. Accordingly, let H be defined as

H =

1 1 0 0 0 0 0

1 1 1 0 0 0 0

1 1 0 0 0 1 0

1 1 0 0 0 0 1

0 1 1 0 0 1 0

0 1 1 0 0 0 1

0 1 0 0 0 1 1

0 1 1 1 0 0 0

0 1 1 0 0 1 0

0 0 1 1 0 1 0

0 0 1 1 1 0 0

0 0 1 1 0 0 1

0 0 0 1 1 0 1

0 0 0 1 1 0 0

0 1 1 0 0 1 0

0 1 0 1 0 0 1

Bus 1

Bus 2

Bus 3

Bus 4

Bus 5

Bus 6

Bus 7


Using this approach, the relevant PMU placement problem can be formulated as

follows:

7

6

1 2 3 4 5

Figure 3.2: 7-bus system for illustration.

Minimizen∑i=1

wixi

Subject to HTX ≥ U

X = [x1 x2 · · · xn]T

xi ∈ {0, 1}

(3.2)

where

n =N∑j=1

rj, U =

1

1...

1

N×1

, and w = [1 1 · · · 1]1×n.

Here, w represents the vector of installation cost of the PMUs, elements of which

are assumed to be uniform for simplicity, and xi are binary variables for the PMU

placement, and N denotes the number of buses in the system. In the above matrix

inequality, X represents a binary vector of all possible PMU channel assignments.


Correspondingly, the nonzero entries in X will point to the rows of associated buses,

voltage angles of which can be observed by these PMU measurements.

The solution of the aforecited PMU placement problem where the specified

channel limit for PMUs is 2, that is,

X =[

0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0]T

yields a total of 3 PMUs, two of which are to be located at bus 2, and one at bus

4, enabling the entire network observability. Indeed, one PMU installed at bus 2

measures the voltage phasor at bus 2 as well as the current phasors for branches

2− 1 and 2− 6; whereas, the other PMU at bus 2 measures branch current phasors

2 − 1 and 2 − 7. Furthermore, a PMU located at bus 4 will measure the voltage

phasor at bus 4 and current phasor on two of the incident branches 4− 3 and 4− 5.

Similarly, the location of PMUs for the IEEE 14-bus system with the channel

limit of 3 is illustrated in Figure 3.3. The optimal solution for this case points out

that 4 PMUs are required to achieve full network observability. A PMU located at

bus 2 will observe buses 1, 2, 3, and 5; the one at bus 6 will observe buses 6, 11, 12,

and 13; and so on.

Figure 3.3: PMU placement for IEEE 14-bus system when the channel limit is3.


3.3 Modeling of Zero-Injection Buses

The procedure of forming the constraint equations is straightforward for a system

without conventional measurements and/or zero-injections. However, when the zero-

injection pseudomeasurements are considered, the method of topology transforma-

tion introduced in [35] should be utilized in reforming the constraint equations.

Consider the IEEE 14-bus system shown in Figure 3.4, where the dot next to

bus 7 indicates that bus 7 is a zero-injection bus. It is obvious that if the phasor

voltages at any three out of the four buses 4, 7, 8, and 9 are known, then the fourth

one can be calculated using the power balance equations at bus 7 where the net

injection is known to be zero. Topology transformation method is then used to

merge the bus having the zero-injection measurement, with the buses connected to

that bus. In the selection of the candidate buses, three different strategies are first

considered and comparatively evaluated:

3.3.1 Case 1—Arbitrary Selection of Neighbor Buses

In this case, the bus which has the injection measurement is merged with one of its

arbitrarily chosen neighbors.

3.3.2 Case 2—Selection of Neighbor Buses which Have Min-

imum Number of Neighbors

In this case, the bus which has the injection measurement is merged with its neighbor

having the least number of neighbors.


3.3.3 Case 3—Selection of Neighbor Buses which Have Max-

imum Number of Neighbors

In this case, the bus which has the injection measurement is merged with its neighbor

having the most number of neighbors.

Figure 3.4: Network diagram and measurement configuration for the IEEE 14-bus system.

For Case 1, the appropriate algorithm is developed so that any of the neighbor buses

connected to bus 7, say bus 9, is chosen randomly. Since bus 8 has only one neighbor,

it is selected in the second case; whereas, bus 4 is to be selected in Case 3 since it has

five neighbors connected to it. The network will be updated after the merger of zero-

injection bus and the selected neighbor bus into a new single bus. In this context,

it is realized that the number of required PMUs can be reduced with the growing

system size, or almost equivalently, the increased availability of zero-injection buses.

Apart from these suggested cases involving intuition, we have developed a more

systematic methodology to incorporate the zero-injection buses into the problem

formulation by using linear constraints as shown in the following case.


3.3.4 Case 4—Modeling of Zero-Injection Buses as Linear

Constraints

In this case, zero-injection buses, which provide “free” measurements to the system,

are incorporated into the optimization formulation as done in [42]. Particularly, zero-

injections can be used to reduce the number of required PMUs by selectively allowing

some buses to be unreachable by the PMU measurements, as long as these buses

belong to a certain set of buses. This set is defined as the union of all zero-injection

buses and their immediate neighbors.

Let us define a set Ni as a set of buses including zero-injection bus i and all

its neighbors. Assuming “`” zero-injection buses to be present in the system, the

following set can be defined:

Φ =⋃i∈I

Ni = Ni1 ∪Ni2 ∪ · · · ∪ Ni`,

where I = {i1, i2, · · · , i`} designates the set of zero-injection buses.

Thus, the inequality constraints in (3.2) can be reestablished based on the above

considerations as follows: HT C

0 D

X

b

≥ R

c

(3.3)

where

Cjk =

−1 if j ∈ Ni and k ∈ {Φj},

0 otherwise.

Djk =

1 if j ∈ {Ii}i∈I and k ∈ {Φm}m∈Ni,

0 otherwise.


and X , R, b, and c are vectors of dimension n, N , |Φ|, and |I|, respectively, with

|{•}| denoting the cardinality of a set; and the matrices H, C, 0, and D in (3.3) are

of sizes n × N , N × |Φ|, |I| × n, and |I| × |Φ|, respectively. Also, ci are equal to

(|Ni| − 1) such that i ∈ I.

In building the matrices C and D, the set {Φε}ε∈E is defined such that the

elements of set Φ are indexed or labeled by means of set E . For the sake of con-

venience, the first row associated with the first partitioned matrix on the left-hand

side of (3.3) splits up into two parts in such a way that the zero-injection buses and

their neighbors are heaped together on the top of the new matrix. In this way, the

elements of the matrix D are clustered in the order of union set Φ. Moreover, the

elements of vector R on the right-hand side of (3.3) take on a “0” for the variables

related to zero-injection buses, and a “1” for those of the remaining buses.

For the sake of illustration, consider 7-bus system shown in Figure 3.5 where

single-channel PMUs are used and the dots designate the zero-injection buses present

in the system. Then, we can build the sets NBus 4 = {3, 4, 5, 7}, NBus 6 = {2, 3, 6},

and Φ = NBus 4 ∪ NBus 6 = {2, 3, 4, 5, 6, 7} based on the definitions above. In this

context, Ineq. (3.3) will take form of Ineq. (3.4) as shown in the following:

[HT

1

]6×16

−1

−1

−1

−1

−1

−1

[HT

2

]1×16 01×6

02×161 1 1 1

1 1 1

9×22

X

u2

u3

u4

u5

u6

u7

22×1

≥

0

0

0

0

0

0

1

3

2

9×1

(3.4)


The inequalities b3 + b4 + b5 + b7 ≥ 3 and b2 + b3 + b6 ≥ 2 with bi ∈ {0, 1} ensure that

there is at most one unobservable bus in these sets provided that their observability

is realized via the use of zero-injection buses in the corresponding sets. Indeed,

b6 = b7 = 0, meaning that bus 6 is not reached by a PMU by taking advantage of its

being zero-injection bus and bus 7 is observed via zero-injection bus 4. Figure 3.5

also illustrates the installed 3 PMUs along with the associated branches through

which the corresponding buses are observed.

7

6

1 2 3 4 5

PMU PMU PMU

Figure 3.5: Configuration of 3 one-channel PMUs in 7-bus system.

3.4 Effect of Network Sparsity on PMU Place-

ment

Buses in typical power networks are known to be sparsely connected. However, spar-

sity of systems may vary significantly depending on the geographic and operational

requirements. In order to study the effect of sparsity on the PMU placement, sys-

tems with increasingly dense bus interconnections are defined. This is accomplished

by systematically adding connections between second, third, etc. neighbors.

First, the binary adjacency matrix A is defined to describe the topology of the

network in which the ij-th entry is 1 if there is a connection between bus i and bus

j, and zero otherwise. All diagonal entries will also be 1 by default. The matrix A


for the simple network of Figure 3.2 will be given by:

A =

1 1 0 0 0 0 0

1 1 1 0 0 1 1

0 1 1 1 0 1 0

0 0 1 1 1 0 1

0 0 0 1 1 0 0

0 1 1 0 0 1 0

0 1 0 1 0 0 1

.

This matrix will be referred to as single-hop connectivity matrix since it represents

the connectivity of the buses with their immediate neighbors. Those buses that can

be reached from a given bus by a single hop over an existing branch will contain

nonzero entries. Similarly, matrices representing systems where buses have direct

connections to those buses that can be reached in two, three or more hops in the

original network can be easily generated by multiplying the single-hop connectivity

matrix by itself as many times as the number of hops [57]:

A(m+1) = A(m) ×A. (3.5)

Let A(1) = A. Then, A(m+1) is defined as follows:

A(m+1)(i, j) =

m + 1 if A(m)(i, j) = 0 and

A(m+1)(i, j) > 0;

A(m)(i, j) if A(m)(i, j) > 0.


Hence, the 2-hop connectivity matrix A(2) will be given by:

A(2) =

1 1 2 0 0 2 2

1 1 1 2 0 1 1

2 1 1 1 2 1 2

0 2 1 1 1 2 1

0 0 2 1 1 0 2

2 1 1 2 0 1 2

2 1 2 1 2 2 1

Bus 1

Bus 2

Bus 3

Bus 4

Bus 5

Bus 6

Bus 7

Bus 1 2 3 4 5 6 7.

which shows all the bus pairs that can reach each other within two hops. From the

1-hop connectivity matrix, we can obtain all (m+1)-hop connectivity matrices, thus

all possible (m + 1)-hop routes.

The binary version of the multi-hop connectivity matrix B(m+1) can be defined

by simply replacing nonzeros in the matrix A(m+1) by 1’s, as given below:

B(2) =

1 1 1 0 0 1 1

1 1 1 1 0 1 1

1 1 1 1 1 1 1

0 1 1 1 1 1 1

0 0 1 1 1 0 1

1 1 1 1 0 1 1

1 1 1 1 1 1 1

Bus 1

Bus 2

Bus 3

Bus 4

Bus 5

Bus 6

Bus 7

Bus 1 2 3 4 5 6 7.

The effect of reduced sparsity on the number and location of required PMUs

can then be studied by using this matrix instead of the original connectivity matrix.

The corresponding network connectivity is shown in Figure 3.6.

Again, from the newly formed network topology, we can easily build the matrix

H consisting of all potential set of combinations incident to each and every bus.


7

6

1 2 3 4 5

Figure 3.6: Network diagram for the 7-bus system with two-hop neighborhoodtopology.

When the PMU channel limit is assumed to be 2, the number of rows related to

each bus in the new matrix H becomes r1 = 6, r2 = r4 = r6 = 10, r3 = r7 = 15,

and r5 = 3. In this case, the solution of the PMU placement problem still yields 3

PMUs as the optimal number; however, the locations for these PMUs will now be

at buses 1, 4, and 7.

3.5 Optimal Placement Accounting for Single PMU

Loss

The initial studies consider a simplified model to represent the “reach” of individual

PMUs. Each PMU is assumed to provide the voltage phasor at the bus it is connected

and the current phasors at all of its neighbors as well. This assumption is relaxed in

[58] where the effects of channel capacity of a given type of PMU on their optimal

placement for network observability are taken into account.

In this section, the formulation is extended to account for loss of PMUs so that

the final PMU measurement design remains robust against loss of a PMU due to

device or communication link failures.


It is worth mentioning that PMUs are prone to failures like any other measuring

device even though they are highly reliable. Therefore, it is necessary to guard

against such unexpected failures of PMUs. In [34] and [39], the primary set of

PMUs is backed up by a secondary set which is determined based on the same

optimization formulation. In this study, the formulation of (3.2) is modified as done

in [41–43] to ensure that each bus will be observed by at least two PMUs. This

ascertains that a PMU loss will not lead to loss of observability. In the integer linear

programming framework, this can be easily achieved by multiplying U by 2, viz.,

U = [2 2 · · · 2]T1×N .

In this regard, the solution of the aforecited PMU placement problem where the

specified channel limit for PMUs is 2, will be given as:

X =[

0 0 1 1 0 0 0 0 0 1 1 0 1 0 0 0]T

which yields a total of 5 PMUs, two at buses 2 and 4 each and the remaining one

at bus 3, enabling the entire network to be observable even when the measurements

from any one of the PMUs are lost.

Similarly, the location of PMUs for the IEEE 14-bus system with the channel

limit of 3 is illustrated in Figure 3.7. The optimal solution for this case requires

placement of 9 PMUs to achieve full network observability under loss of a single

PMU.

Figure 3.8 illustrates the results of solving the above problem of PMU placement

for the IEEE 57-bus system assuming no channel limits for PMUs, accounting for

loss of a single PMU and making use of zero-injection measurements based on the

fourth case. The solution validates that each and every bus in the network is reached

at least twice either by PMUs or zero-injection measurements located at the bus or

its neighbors. Zero-injection buses are designated by dots next to the bus names in

Figure 3.8.


Figure 3.7: Reliable placement against single PMU loss for the IEEE 14-bussystem when the channel limit is 3.

Figure 3.8: Zero-injections and optimally placed 22 PMUs for the IEEE 57-bussystem assuming no channel limits.

Chapter 4

Simulation Results

4.1 Conventional PMU Placement with Fixed Chan-

nel Capacity

Simulations of the proposed method are carried out on various power systems. The

binary integer programming problem is solved using the TOMLAB /CPLEX Solver

Package [59]. The simulation results for the optimum number of PMUs with respect

to channel limits for the cases where zero-injections are ignored and considered, are

presented in Tables 4.1 and 4.2, respectively. As shown in Table 4.1, simulations are

carried out using five IEEE test systems as well as one larger-size system with 4520

buses. Also, Table 4.2 illustrates the results of simulations performed on the IEEE

14-, 30-, 57-, and 118-bus systems. For the case without zero-injection measurements,

the upper channel limit of the PMUs is determined by the maximum number of

branches incident to a certain bus in the corresponding test system. For those cases

where zero-injection measurements are considered, these limits are the number of the

branches incident to the fictitious bus, which is created by merging one or several

actual buses. Four ways to account for zero-injections are considered and compared

via simulations. The third case appears to have an advantage over the others in

particular when using multichannel PMUs. Second case may, however, be a better

choice when single-channel PMUs are to be used.

31

Chapter 4. Simulation Results 32

As evident from Table 4.2, zero-injections help reduce the number of required

PMUs. In Table 4.1, νmin/N is the ratio of the minimum number of required PMUs

to the number of buses in the system.

Table 4.1: Conventional PMU Placement without Zero-Injections for Miscella-neous Power Systems

Channel System under studyLimit

for theIEEE IEEE IEEE IEEE IEEE

4520-BusPMUs14-Bus 30-Bus 57-Bus 118-Bus 300-Bus

1 7 15 29 61 167 25432 5 11 19 41 105 16393 4 10 17 33 91 14904 4 10 17 32 89 14545 4 10 17 32 88 14366 10 17 32 88 14307 10 32 88 14298 32 87 14279 32 87 142210 87 142211 87 142212 142213 142214 142215 142216 1422

νmin/N 0.2857 0.3333 0.2982 0.2712 0.2900 0.3146

4.2 Impact of Network Sparsity on Strategic Place-

ment of PMUs

Considering the densely connected topologies, revised topologies with 2-hop connec-

tivity are obtained for five IEEE test systems. PMU placement problem is then

solved using these revised systems and the results are shown in Table 4.3. Among

the five power systems studied, it is observed that this ratio ranges from 27% to 33%


in Table 4.1, and from 10% to 21% in Table 4.3. In a similar vein, one can clearly

observe how the loss of sparsity leads to strategic placement of smaller number of

PMUs having larger number of channels.

Table 4.2: PMU Placement with Zero-Injections for IEEE Test Systems

ChannelIEEE Test Number of Limit Number of PMUsSystem Zero-Inj.’s for

the PMUs CASE 1 CASE 2 CASE 3 CASE 4

14-Bus 1

1 7 7 7 72 5 5 5 53 4 4 5 44 3 3 4 35 3 3 4 3

30-Bus 6

1 13 14 14 142 9 8 9 93 7 7 8 84 7 7 7 75 7 7 7 76 7 7 7 77 6 78 69 610 611 612 6

57-Bus 15

1 22 21 23 232 14 14 14 163 12 12 12 144 12 11 11 145 12 11 11 146 12 11 11 147 118 11

118-Bus 10

1 57 56 57 572 39 39 39 383 30 31 31 324 28 30 28 315 28 30 28 296 28 30 28 297 28 30 28 298 28 30 28 299 28 30 28 29


Table 4.3: Conventional PMU Placement with 2-Hop Connectivity for Five IEEETest Systems

IEEE Test SystemChannel Limitfor the PMUs

14-Bus 30-Bus 57-Bus 118-Bus 300-Bus

1 7 15 29 59 1502 5 10 19 40 1013 4 8 15 30 774 3 6 12 24 685 3 5 10 21 596 3 5 97 4 8

...

...17 3 ·20 823 4127 13

νmin/N 0.2143 0.1000 0.1404 0.1102 0.1367

4.3 Reliable Measurement Design Against Loss of

PMUs

PMU placement problem as formulated in Section 3.5 is solved for power systems of

different sizes. The solutions for the optimum number of PMUs for different channel

limits for the cases where zero-injections are ignored and considered, are presented

in Tables 4.4 and 4.5. Table 4.4 presents solutions that are obtained for five IEEE

test systems as well as for a 4520-bus utility system when zero-injections are ignored.

When the zero-injections are taken into account, results change significantly as shown

in Table 4.5 for four IEEE test systems. Once again, for the cases with and without

zero-injection measurements, the upper channel limit of the PMUs is determined

by the maximum number of incident branches to a bus in the corresponding test

system. Among the six power systems studied, it is observed that this ratio ranges

from 58% to 69%. As evident from Table 4.5, zero-injections help reduce the number

of PMUs required for complete network observability while maintaining robustness

against single PMU failure.


Table 4.4: Reliable Placement Against Loss of PMUs without Zero-Injectionsfor Miscellaneous Power Systems

Channel System under studyLimit

for theIEEE IEEE IEEE IEEE IEEE

4520-BusPMUs14-Bus 30-Bus 57-Bus 118-Bus 300-Bus

1 14 30 57 121 332 50802 10 22 38 82 219 34393 9 20 34 68 189 31604 9 20 33 68 190 31255 9 21 33 68 190 31356 21 33 68 193 31517 21 68 193 31628 68 195 32059 68 195 322410 195 323211 202 323512 326113 326514 326515 326516 3283

νmin/N 0.6429 0.6667 0.5789 0.5763 0.6300 0.6914

4.4 Illustration of Unified PMU Placement Schemes

In order to provide a more comprehensive picture of our overall methodology and

draw attention to the effect of channel limits on PMU placement accounting for

various combinations of abovementioned criteria, we have illustrated a number of

PMU placement strategies as shown in Figures 4.1–4.12. In cases where the zero-

injection measurements are considered, we have bounded our simulations merely by

the fourth case since it allows for a more systematic treatment of zero-injections.


Table 4.5: Reliable Placement Against Loss of PMUs with Zero-Injections forIEEE Test Systems

ChannelIEEE Test Number of Limit Number of PMUsSystem Zero-Inj.’s for

the PMUs CASE 1 CASE 2 CASE 3 CASE 4

14-Bus 1

1 13 13 13 122 9 9 9 83 7 7 8 74 8 7 8 75 8 7 7 7

30-Bus 6

1 26 28 28 212 18 16 19 143 15 14 15 134 14 14 14 135 15 15 14 136 16 15 14 137 13 138 139 1310 1311 1312 17

57-Bus 15

1 44 42 46 342 28 28 29 233 24 24 24 224 24 23 24 225 24 23 24 226 24 23 23 227 238 23

118-Bus 10

1 111 110 112 1032 75 76 77 693 62 63 62 584 61 63 61 585 61 63 60 586 62 63 63 587 62 63 63 598 62 63 63 599 62 63 63 59


Figure 4.1: Optimally placed 7 PMUs for the IEEE 14-bus system when thechannel limit is 1 (ignoring the zero-injections).


Figure4.4:

Op

tim

ally

pla

ced

41P

MU

sfo

rth

eIE

EE

118-

bu

ssy

stem

wh

enth

ech

an

nel

lim

itis

2(i

gn

ori

ng

the

zero

-in

ject

ion

s).


Figure 4.5: Zero-injection and optimally placed 3 PMUs for the IEEE 14-bussystem when the channel limit is 4.


Figure 4.6: Zero-injections and optimally placed 7 PMUs for the IEEE 30-bussystem when the channel limit is 4.


Figure 4.7: Zero-injections and optimally placed 14 PMUs for the IEEE 57-bussystem when the channel limit is 3.


Figure4.8:

Zer

o-i

nje

ctio

ns

and

opti

mal

lyp

lace

d29

PM

Us

for

the

IEE

E118

-bu

ssy

stem

wh

enth

ech

an

nel

lim

itis

5.


Figure 4.9: Reliable placement against single PMU loss for the IEEE 14-bussystem when the channel limit is 3 (considering the zero-injection).


Figure 4.10: Reliable placement against single PMU loss for the IEEE 30-bussystem when the channel limit is 3 (considering the zero-injections).


Figure 4.11: Reliable placement against single PMU loss for the IEEE 57-bussystem when the channel limit is 3 (considering the zero-injections).


Figure

4.12:

Rel

iab

lep

lace

men

taga

inst

sin

gle

PM

Ulo

ssfo

rth

eIE

EE

118-

bu

ssy

stem

wh

enth

ech

an

nel

lim

itis

3(c

on

sid

erin

gth

eze

ro-i

nje

ctio

ns)

.

Chapter 5

Concluding Remarks and Further

Study

5.1 Concluding Remarks

This thesis presents a new problem formulation and its associated solution based on

mixed integer linear programming method for obtaining the best locations of syn-

chronized phasor measurement units. The main contribution of the new formulation

is the way it accounts for the available number of PMU channels. Furthermore, zero-

injection measurements are incorporated into the problem formulation in order to

further minimize the required number of PMUs. Applying the developed technique

to different size systems, it is observed that PMUs having more than 4 channels

(positive-sequence) may not reduce the overall installation cost for medium-size sys-

tems. Moreover, it is observed that the channel limits which reduce the overall

installation cost will be larger for larger-size and/or more densely connected sys-

tems. In order to demonstrate the effect of sparsity on the required channel limits,

certain test systems are artificially modified by increasing connectivity in a system-

atic manner. The results indicate that densely connected systems will allow efficient

utilization of PMUs with large number of channels.

49

Chapter 5. Concluding Remarks and Further Study 50

This study also extends the results of conventional PMU placement to the case

where the solution is expected to be robust against failure of any single PMU. Any

existing injection measurements in the system, in particular those virtual ones at

passive buses with no generation or load, are also accounted for in the modified

optimization formulation. In this case, results of simulations on different type and

size test systems imply that using PMUs with large number of channels does not

minimize the investment in the measurement system. In most cases, having more

than 4 channels (positive sequence) does not reduce the required PMU count. Fur-

thermore, by strategic placement of PMUs, a very reliable metering design can be

achieved by placing PMUs at less than 70% of the buses in the system. This number

may be reduced significantly by taking advantage of zero-injection buses.

Ultimately, these results may be useful for the system planners as well as PMU

manufacturers when they make decisions on the next set of PMUs to be purchased

and installed or to be designed and marketed, respectively.

5.2 Further Study

We have studied and solved the problem of using PMUs with limited input capabil-

ities to achieve complete observability of the network. In other words, it is intended

to monitor at most a fixed number of currents from a bus. As a further study, the

PMU placement problem can be reinvestigated by taking into account the fact that

each PMU may have variations in channel capacity for a particular placement strat-

egy. Additionally, the costs for the proposed placement strategy and the prospective

placement procedures may be comparatively evaluated in order to determine the

best option. Undoubtedly, novel methodologies can also be implemented for model-

ing of zero-injection buses and reliable PMU placement to investigate the feasibility

of further reducing the number of PMUs required for entire network observability.

Appendix A

Functions and Scripts Used in the

PMU Placement Algorithm

A.1 Read Network Parameters and Build the Single-

Hop Connectivity Matrix A

function [y NoBran branch external_bus internal_bus] =

readAndBuildA(PowerFlowInputData,NoBus)

% read parameters of the network

fnet = fopen(PowerFlowInputData,’r’);

line = fgetl(fnet);

line = fgetl(fnet);

iter1 = 0;

iter2 = 0;

iter3 = 0;

while 1

51

Chapter A. Appendix A 52

line = fgetl(fnet);

iter1 = iter1 + 1;

if line(1:4) == ’BRAN’

break;

end

bus(iter1,1) = str2num(line(1:4));

end

bus(end,:) = []; % this entry corresponds to -9999

for ii = 1 : NoBus

% specify external bus numbers

external_bus(ii,1) = bus(ii,1);

% internal bus numbers

internal_bus(external_bus(ii),1) = it;

end

while 1

line = fgetl(fnet);

if line(1:4) == ’-999’

break;

end

iter2 = iter2 + 1;

cir(iter2,1) = str2num(line(17));

if cir(iter2,1) == 0

iter3 = iter3 + 1;

From_Bus(iter3,1) = str2num(line(1:4));

To_Bus(iter3,1) = str2num(line(6:9));

end

end

NoBran = iter3;


From_Bus = internal_bus(From_Bus);

To_Bus = internal_bus(To_Bus);

branch = [From_Bus To_Bus];

% create the bus admittance matrix, Y, with jX = j1.0.

ys = 1; [rowBran colBran] = size(From_Bus);

for iter = 1 : rowBran

Yi(ys) = From_Bus(iter,1);

Yj(ys) = To_Bus(iter,1);

Yv(ys) = 1; ys = ys + 1;

Yi(ys) = To_Bus(iter,1);

Yj(ys) = From_Bus(iter,1);

Yv(ys) = 1; ys = ys + 1;

Yi(ys) = From_Bus(iter,1);

Yj(ys) = From_Bus(iter,1);

Yv(ys) = 1; ys = ys + 1;

Yi(ys) = To_Bus(iter,1);

Yj(ys) = To_Bus(iter,1);

Yv(ys) = 1; ys = ys + 1;

end

y = sparse(Yi,Yj,Yv,NoBus,NoBus);

A = spones(y) + zeros(NoBus,NoBus);

disp(’Matrix A is found to be as follows: ’);

ST = fclose(fnet);


A.2 Find the Required Number of PMUs for Com-

plete Network Observability (Ignoring Zero-

Injection Measurements)

clear;

clc;

A = readAndBuildA(’pfinput14.dat’,14);

% A = readAndBuildA(’pfinput30.dat’,30);



%% reduce the network sparsity by adding 2nd, 3rd, etc. neighbors

% B2 = spones(A ^ 2) + zeros(size(A,1))

% B3 = spones(A ^ 3) + zeros(size(A,1))

[m,n] = size(A);

L = [];

for j = 1 : n

for i = 1 : j

if A(i,j) == 1

if j ~= i

L(i,j) = 1;

L(j,i) = 1;

end

end

end

end L;


ChannelLimit = input(’Choose a channel limit for the PMUs: ’);

H = [];

for k = 1 : n

if sum(L(:,k)) < ChannelLimit

V = find(L(:,k));

T = sparse(1,n);

T(1,k) = 1;

T(1,V) = 1;

H = sparse([H;T]);

else

V = nchoosek(find(L(:,k)),ChannelLimit);

[a,b] = size(V);

T = sparse(a,n);

for i = 1 : a

for j = 1 : b

T(:,k) = 1;

T(i,V(i,j)) = 1;

end

end

H = sparse([H;T]);

end

fprintf(’%d\n’,k)

end

H;

tic

f = ones(size(H,1),1);

Hnew = -H’;

b = -ones(n,1);


N = length(f);

x_L = zeros(N,1);

x_U = ones(N,1);

IntVars = ones(N,1);

PriLev = 1;

cpxControl.EPGAP = 0.1/100;

cpxControl.TILIM = 60*5;

[x, slack, v, rc, f_k, ninf, sinf, Inform, basis, lpiter, ...

glnodes, confstat, iconfstat, sa, cpxControl, presolve] = ...

cplex(f, Hnew, x_L, x_U, -inf*ones(n,1), b, ...

cpxControl, [], PriLev, [], IntVars);

disp(’The optimum number of PMUs is: ’)

fprintf(’%d\n’,sum(x))

toc


A.3 Find the Required Number of PMUs for Com-

plete Network Observability (Considering Zero-

Injection Measurements)

clear;

clc;

A = readAndBuildA(’pfinput14.dat’,14);




[m,n] = size(A);

L = [];

for j = 1 : n

for i = 1 : j

if A(i,j) == 1

if j ~= i

L(i,j) = 1;

L(j,i) = 1;

end

end

end

end

L;

ChannelLimit = input(’Choose a channel limit for the PMUs: ’);


H = [];

for k = 1 : n

if sum(L(:,k)) < ChannelLimit

V = find(L(:,k));

T = zeros(1,n);

T(1,k) = 1;

T(1,V) = 1;

H = [H;T];

else

V = nchoosek(find(L(:,k)),ChannelLimit);

[a,b] = size(V);

T = zeros(a,n);

for i = 1 : a

for j = 1 : b

T(:,k) = 1;

T(i,V(i,j)) = 1;

end

end

H = [H; T];

end

fprintf(’%d\n’,k)

end

H;

tic

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%% for the IEEE 14-bus test system

C = zeros(size(H,2),4);

C(4,1) = 1; C(7,2) = 1;


C(8,3) = 1; C(9,4) = 1;

D = zeros(1,4);

D(1,1:4) = -1;

R = -ones(n,1);

% use R = -2 * ones(n,1) for reliable PMU placement, instead

R(4) = 0; R(7) = 0; R(8) = 0; R(9) = 0;

c = -3;

f = [ones(size(H,1),1);zeros(size(D,2),1)];

Hnew = [-H’,C;[zeros(size(D,1),size(H,1)),D]];

RHS = [R; c];

X = bintprog(f,Hnew,RHS);

X = X(1:size(H,1));

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


% C = zeros(size(H,2),17);

%

% C(2,1) = 1; C(4,2) = 1; C(6,3) = 1; C(7,4) = 1;

% C(8,5) = 1; C(9,6) = 1; C(10,7) = 1; C(11,8) = 1;

% C(21,9) = 1; C(22,10) = 1; C(24,11) = 1; C(25,12) = 1;

% C(26,13) = 1; C(27,14) = 1; C(28,15) = 1; C(29,16) = 1;


% C(30,17) = 1;

%

% D = zeros(6,17);

% D(1,1:7) = -1; D(1,15) = -1; D(2,3) = -1;

% D(2,6:8) = -1; D(3,7) = -1; D(3,9:11) = -1;

% D(4,11:14) = -1; D(5,12) = -1; D(5,14:17) = -1;

% D(6,9) = -1; D(6,11) = -1; D(6,14:15) = -1;

%

% R = -ones(n,1);

% R(2) = 0; R(4) = 0; R(6) = 0; R(7) = 0;

% R(8) = 0; R(9) = 0; R(10) = 0; R(11) = 0;

% R(21) = 0; R(22) = 0; R(24) = 0; R(25) = 0;

% R(26) = 0; R(27) = 0; R(28) = 0; R(29) = 0;

% R(30) = 0;

%

% c = [-7 -3 -3 -3 -4 -3]’;

%

% f = [ones(size(H,1),1);zeros(size(D,2),1)];

% Hnew = [-H’,C;[zeros(size(D,1),size(H,1)),D]];

% RHS = [R; c];

% X = bintprog(f,Hnew,RHS);

% X = X(1:size(H,1));

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



% C(3,1) = 1; C(4,2) = 1; C(5,3) = 1;


% C(6,4) = 1; C(7,5) = 1; C(8,6) = 1;

% C(9,7) = 1; C(11,8) = 1; C(13,9) = 1;

% C(14,10) = 1; C(15,11) = 1; C(18,12) = 1;

% C(20,13) = 1; C(21,14) = 1; C(22,15) = 1;

% C(23,16) = 1; C(24,17) = 1; C(25,18) = 1;

% C(26,19) = 1; C(27,20) = 1; C(29,21) = 1;

% C(32,22) = 1; C(34,23) = 1; C(35,24) = 1;

% C(36,25) = 1; C(37,26) = 1; C(38,27) = 1;

% C(39,28) = 1; C(40,29) = 1; C(41,30) = 1;

% C(43,31) = 1; C(44,32) = 1; C(45,33) = 1;

% C(46,34) = 1; C(47,35) = 1; C(48,36) = 1;

% C(49,37) = 1; C(56,38) = 1; C(57,39) = 1;

%

% D = zeros(15,39);

% D(1,1:4) = -1; D(1,12) = -1; D(2,4:6) = -1;

% D(2,21) = -1; D(3,7:9) = -1; D(3,30:31) = -1;

% D(4,13:15) = -1; D(5,14:16) = -1; D(5,27) = -1;

% D(6,16:19) = -1; D(7,17) = -1; D(7,19:20) = -1;

% D(8,22:24) = -1; D(9,24:26) = -1; D(9,29) = -1;

% D(10,25:28) = -1; D(11,26) = -1; D(11,28) = -1;

% D(11,39) = -1; D(12,25) = -1; D(12,29) = -1;

% D(12,38) = -1; D(13,11) = -1; D(13,32:33) = -1;

% D(14,10) = -1; D(14,34:35) = -1; D(15,27) = -1;

% D(15,35:37) = -1;

%

% R = -ones(n,1);

% R(3:9) = 0; R(11) = 0; R(13:15) = 0;

% R(18) = 0; R(20:27) = 0; R(29) = 0;

% R(32) = 0; R(34:41) = 0; R(43:49) = 0;

% R(56:57) = 0;

%

%


% c = [-4 -3 -4 -2 -3 -3 -2 -2 -3 -3 -2 -2 -2 -2 -3]’;

%



% RHS = [R; c];


% X = X(1:size(H,1));

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



% C(3,1) = 1; C(4,2) = 1; C(5,3) = 1;

% C(6,4) = 1; C(8,5) = 1; C(9,6) = 1;

% C(10,7) = 1; C(11,8) = 1; C(17,9) = 1;

% C(26,10) = 1; C(30,11) = 1; C(33,12) = 1;

% C(34,13) = 1; C(35,14) = 1; C(37,15) = 1;

% C(38,16) = 1; C(39,17) = 1; C(40,18) = 1;

% C(59,19) = 1; C(61,20) = 1; C(63,21) = 1;

% C(64,22) = 1; C(65,23) = 1; C(68,24) = 1;

% C(69,25) = 1; C(70,26) = 1; C(71,27) = 1;

% C(72,28) = 1; C(73,29) = 1; C(80,30) = 1;

% C(81,31) = 1; C(116,32) = 1;

%

% D = zeros(10,32);

% D(1,1:5) = -1; D(1,8) = -1 ; D(2,5:7) = -1;

% D(3,5) = -1; D(3,9:11) = -1; D(3,16) = -1;

% D(4,12:18) = -1; D(5,11) = -1; D(5,15:16) = -1;


% D(5,23) = -1; D(6,19) = -1; D(6,21:22) = -1;

% D(7,20:23) = -1; D(8,23:25) = -1; D(8,31:32) = -1;

% D(9,26:29) = -1; D(10,24) = -1; D(10,30:31) = -1;

%

%

% R = -ones(n,1);

% R(3:6) = 0; R(8:11) = 0; R(17) = 0;

% R(26) = 0; R(30) = 0; R(33:35) = 0;

% R(37:40) = 0; R(59) = 0; R(61) = 0;

% R(63:65) = 0; R(68:73) = 0; R(80:81) = 0;

% R(116) = 0;

%

% c = [-5 -2 -4 -6 -3 -2 -3 -4 -3 -2]’;



% RHS = [R; c];


% X = X(1:size(H,1));

disp(’The optimum number of PMUs is: ’)

fprintf(’%d\n’,sum(X))

toc

Appendix B

IEEE Test Systems Data Used in

the PMU Placement Algorithm

This appendix section contains the data regarding the IEEE 14-, 30-, 57-, and 118-

bus test systems [60], which are utilized in our simulations. The system information

of these IEEE test systems is shown in Table B.1 given below:

Table B.1: System Information of Studied IEEE Test Systems

Test Number of Number of Zero-InjectionSystem Branches Zero-Injections Bus(es)

IEEE20 1 7

14-BusIEEE

41 6 6, 9, 22, 25, 27, 2830-BusIEEE

78 154, 7, 11, 21, 22, 24, 26, 34,

57-Bus 36, 37, 39, 40, 45, 46, 48IEEE

179 105, 9, 30, 37, 38, 63, 64, 68,

118-Bus 71, 81

64

B.1

IEE

E14-B

us

Test

Syst

em

Data

08/19/93UWARCHIVE

100.0

1962WIEEE14BusTestCase

BUSDATAFOLLOWS

14ITEMS

1Bus1

HV

11

31.060

0.0

0.0

0.0

232.4

-16.9

0.0

1.060

0.0

0.0

0.0

0.0

0

2Bus2

HV

11

21.045

-4.98

21.7

12.7

40.0

42.4

0.0

1.045

50.0

-40.0

0.0

0.0

0

3Bus3

HV

11

21.010-12.72

94.2

19.0

0.0

23.4

0.0

1.010

40.0

0.0

0.0

0.0

0

4Bus4

HV

11

01.019-10.33

47.8

-3.9

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

5Bus5

HV

11

01.020

-8.78

7.6

1.6

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

6Bus6

LV

11

21.070-14.22

11.2

7.5

0.0

12.2

0.0

1.070

24.0

-6.0

0.0

0.0

0

7Bus7

ZV

11

01.062-13.37

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

8Bus8

TV

11

21.090-13.36

0.0

0.0

0.0

17.4

0.0

1.090

24.0

-6.0

0.0

0.0

0

9Bus9

LV

11

01.056-14.94

29.5

16.6

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.19

0

10Bus10

LV

11

01.051-15.10

9.0

5.8

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

11Bus11

LV

11

01.057-14.79

3.5

1.8

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

12Bus12

LV

11

01.055-15.07

6.1

1.6

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

13Bus13

LV

11

01.050-15.16

13.5

5.8

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

14Bus14

LV

11

01.036-16.04

14.9

5.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

-999BRANCHDATAFOLLOWS

20ITEMS

12

1110

0.01938

0.05917

0.0528

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

15

1110

0.05403

0.22304

0.0492

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

23

1110

0.04699

0.19797

0.0438

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

24

1110

0.05811

0.17632

0.0340

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

25

1110

0.05695

0.17388

0.0346

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

34

1110

0.06701

0.17103

0.0128

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

45

1110

0.01335

0.04211

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

47

1110

0.0

0.20912

0.0

00

000

0.978

0.00.0

0.0

0.0

0.0

0.0

49

1110

0.0

0.55618

0.0

00

000

0.969

0.00.0

0.0

0.0

0.0

0.0

56

1110

0.0

0.25202

0.0

00

000

0.932

0.00.0

0.0

0.0

0.0

0.0

611

1110

0.09498

0.19890

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

612

1110

0.12291

0.25581

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

613

1110

0.06615

0.13027

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

78

1110

0.0

0.17615

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

79

1110

0.0

0.11001

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

910

1110

0.03181

0.08450

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

914

1110

0.12711

0.27038

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

10

11

1110

0.08205

0.19207

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

12

13

1110

0.22092

0.19988

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

13

14

1110

0.17093

0.34802

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

-999LOSSZONESFOLLOWS

1ITEMS

1IEEE14BUS

-99INTERCHANGEDATAFOLLOWS

1ITEMS

12Bus2

HV

0.0

999.99

IEEE14

IEEE14BusTestCase

-9TIELINESFOLLOWS

0ITEMS-999

ENDOFDATA

B.2

IEE

E30-B

us

Test

Syst

em

Data

08/20/93UWARCHIVE

100.0


BUSDATAFOLLOWS

30ITEMS

1GlenLyn132

11

31.060

0.0

0.0

0.0

260.2

-16.1

132.0

1.060

0.0

0.0

0.0

0.0

0

2Claytor

132

11

21.043

-5.48

21.7

12.7

40.0

50.0

132.0

1.045

50.0

-40.0

0.0

0.0

0

3Kumis

132

11

01.021

-7.96

2.4

1.2

0.0

0.0

132.0

0.0

0.0

0.0

0.0

0.0

0

4Hancock

132

11

01.012

-9.62

7.6

1.6

0.0

0.0

132.0

0.0

0.0

0.0

0.0

0.0

0

5Fieldale132

11

21.010-14.37

94.2

19.0

0.0

37.0

132.0

1.010

40.0

-40.0

0.0

0.0

0

6Roanoke

132

11

01.010-11.34

0.0

0.0

0.0

0.0

132.0

0.0

0.0

0.0

0.0

0.0

0

7Blaine

132

11

01.002-13.12

22.8

10.9

0.0

0.0

132.0

0.0

0.0

0.0

0.0

0.0

0

8Reusens

132

11

21.010-12.10

30.0

30.0

0.0

37.3

132.0

1.010

40.0

-10.0

0.0

0.0

0

9Roanoke

1.0

11

01.051-14.38

0.0

0.0

0.0

0.0

1.0

0.0

0.0

0.0

0.0

0.0

0

10Roanoke

33

11

01.045-15.97

5.8

2.0

0.0

0.0

33.0

0.0

0.0

0.0

0.0

0.19

0

11Roanoke

11

11

21.082-14.39

0.0

0.0

0.0

16.2

11.0

1.082

24.0

-6.0

0.0

0.0

0

12Hancock

33

11

01.057-15.24

11.2

7.5

0.0

0.0

33.0

0.0

0.0

0.0

0.0

0.0

0

13Hancock

11

11

21.071-15.24

0.0

0.0

0.0

10.6

11.0

1.071

24.0

-6.0

0.0

0.0

0

14Bus14

33

11

01.042-16.13

6.2

1.6

0.0

0.0

33.0

0.0

0.0

0.0

0.0

0.0

0

15Bus15

33

11

01.038-16.22

8.2

2.5

0.0

0.0

33.0

0.0

0.0

0.0

0.0

0.0

0

16Bus16

33

11

01.045-15.83

3.5

1.8

0.0

0.0

33.0

0.0

0.0

0.0

0.0

0.0

0

17Bus17

33

11

01.040-16.14

9.0

5.8

0.0

0.0

33.0

0.0

0.0

0.0

0.0

0.0

0

18Bus18

33

11

01.028-16.82

3.2

0.9

0.0

0.0

33.0

0.0

0.0

0.0

0.0

0.0

0

19Bus19

33

11

01.026-17.00

9.5

3.4

0.0

0.0

33.0

0.0

0.0

0.0

0.0

0.0

0

20Bus20

33

11

01.030-16.80

2.2

0.7

0.0

0.0

33.0

0.0

0.0

0.0

0.0

0.0

0

21Bus21

33

11

01.033-16.42

17.5

11.2

0.0

0.0

33.0

0.0

0.0

0.0

0.0

0.0

0

22Bus22

33

11

01.033-16.41

0.0

0.0

0.0

0.0

33.0

0.0

0.0

0.0

0.0

0.0

0

23Bus23

33

11

01.027-16.61

3.2

1.6

0.0

0.0

33.0

0.0

0.0

0.0

0.0

0.0

0

24Bus24

33

11

01.021-16.78

8.7

6.7

0.0

0.0

33.0

0.0

0.0

0.0

0.0

0.043

0

25Bus25

33

11

01.017-16.35

0.0

0.0

0.0

0.0

33.0

0.0

0.0

0.0

0.0

0.0

0

26Bus26

33

11

01.000-16.77

3.5

2.3

0.0

0.0

33.0

0.0

0.0

0.0

0.0

0.0

0

27Cloverdle33

11

01.023-15.82

0.0

0.0

0.0

0.0

33.0

0.0

0.0

0.0

0.0

0.0

0

28Cloverdle132

11

01.007-11.97

0.0

0.0

0.0

0.0

132.0

0.0

0.0

0.0

0.0

0.0

0

29Bus29

33

11

01.003-17.06

2.4

0.9

0.0

0.0

33.0

0.0

0.0

0.0

0.0

0.0

0

30Bus30

33

11

00.992-17.94

10.6

1.9

0.0

0.0

33.0

0.0

0.0

0.0

0.0

0.0

0


41ITEMS

12

1110

0.0192

0.0575

0.0528

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

13

1110

0.0452

0.1652

0.0408

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

24

1110

0.0570

0.1737

0.0368

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

34

1110

0.0132

0.0379

0.0084

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

25

1110

0.0472

0.1983

0.0418

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

26

1110

0.0581

0.1763

0.0374

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

46

1110

0.0119

0.0414

0.0090

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

57

1110

0.0460

0.1160

0.0204

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

67

1110

0.0267

0.0820

0.0170

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

68

1110

0.0120

0.0420

0.0090

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

69

1110

0.0

0.2080

0.0

00

000

0.978

0.00.0

0.0

0.0

0.0

0.0

610

1110

0.0

0.5560

0.0

00

000

0.969

0.00.0

0.0

0.0

0.0

0.0

911

1110

0.0

0.2080

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

910

1110

0.0

0.1100

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

412

1110

0.0

0.2560

0.0

00

000

0.932

0.00.0

0.0

0.0

0.0

0.0

12

13

1110

0.0

0.1400

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

12

14

1110

0.1231

0.2559

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

12

15

1110

0.0662

0.1304

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

12

16

1110

0.0945

0.1987

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

14

15

1110

0.2210

0.1997

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

16

17

1110

0.0524

0.1923

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

15

18

1110

0.1073

0.2185

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

18

19

1110

0.0639

0.1292

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

19

20

1110

0.0340

0.0680

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

10

20

1110

0.0936

0.2090

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

10

17

1110

0.0324

0.0845

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

10

21

1110

0.0348

0.0749

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

10

22

1110

0.0727

0.1499

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

21

22

1110

0.0116

0.0236

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

15

23

1110

0.1000

0.2020

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

22

24

1110

0.1150

0.1790

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

23

24

1110

0.1320

0.2700

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

24

25

1110

0.1885

0.3292

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

25

26

1110

0.2544

0.3800

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

25

27

1110

0.1093

0.2087

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

28

27

1110

0.0

0.3960

0.0

00

000

0.968

0.00.0

0.0

0.0

0.0

0.0

27

29

1110

0.2198

0.4153

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

27

30

1110

0.3202

0.6027

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

29

30

1110

0.2399

0.4533

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

828

1110

0.0636

0.2000

0.0428

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

628

1110

0.0169

0.0599

0.0130

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0


1ITEMS

1IEEE30BUS


1ITEMS-9

12Claytor

132

0.0

999.99

IEEE30

IEEE30BusTestCase

TIELINESFOLLOWS

0ITEMS-999

ENDOFDATA

B.3

IEE

E57-B

us

Test

Syst

em

Data

08/25/93UWARCHIVE

100.0


BUSDATAFOLLOWS

57ITEMS

1Kanawha

V1

11

31.040

0.0

55.0

17.0

128.9

-16.1

0.0

1.040

0.0

0.0

0.0

0.0

0

2Turner

V1

11

21.010

-1.18

3.0

88.0

0.0

-0.8

0.0

1.010

50.0

-17.0

0.0

0.0

0

3Logan

V1

11

20.985

-5.97

41.0

21.0

40.0

-1.0

0.0

0.985

60.0

-10.0

0.0

0.0

0

4Sprigg

V1

11

00.981

-7.32

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

5Bus5

V1

11

00.976

-8.52

13.0

4.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

6BeaverCkV1

11

20.980

-8.65

75.0

2.0

0.0

0.8

0.0

0.980

25.0

-8.0

0.0

0.0

0

7Bus7

V1

11

00.984

-7.58

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

8ClinchRvV1

11

21.005

-4.45

150.0

22.0

450.0

62.1

0.0

1.005

200.0

-140.0

0.0

0.0

0

9SaltvilleV1

11

20.980

-9.56

121.0

26.0

0.0

2.2

0.0

0.980

9.0

-3.0

0.0

0.0

0

10Bus10

V1

11

00.986-11.43

5.0

2.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

11Tazewell

V1

11

00.974-10.17

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

12GlenLyn

V1

11

21.015-10.46

377.0

24.0

310.0

128.5

0.0

1.015

155.0

-150.0

0.0

0.0

0

13Bus13

V1

11

00.979

-9.79

18.0

2.3

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

14Bus14

V1

11

00.970

-9.33

10.5

5.3

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

15Bus15

V1

11

00.988

-7.18

22.0

5.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

16Bus16

V1

11

01.013

-8.85

43.0

3.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

17Bus17

V1

11

01.017

-5.39

42.0

8.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

18Sprigg

V2

11

01.001-11.71

27.2

9.8

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.10

0

19Bus19

V2

11

00.970-13.20

3.3

0.6

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

20Bus20

V2

11

00.964-13.41

2.3

1.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

21Bus21

V3

11

01.008-12.89

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

22Bus22

V3

11

01.010-12.84

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

23Bus23

V3

11

01.008-12.91

6.3

2.1

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

24Bus24

V3

11

00.999-13.25

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

25Bus25

V4

11

00.982-18.13

6.3

3.2

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.059

0

26Bus26

V5

11

00.959-12.95

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

27Bus27

V5

11

00.982-11.48

9.3

0.5

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

28Bus28

V5

11

00.997-10.45

4.6

2.3

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

29Bus29

V5

11

01.010

-9.75

17.0

2.6

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

30Bus30

V4

11

00.962-18.68

3.6

1.8

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

31Bus31

V4

11

00.936-19.34

5.8

2.9

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

32Bus32

V4

11

00.949-18.46

1.6

0.8

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

33Bus33

V4

11

00.947-18.50

3.8

1.9

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

34Bus34

V3

11

00.959-14.10

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

35Bus35

V3

11

00.966-13.86

6.0

3.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

36Bus36

V3

11

00.976-13.59

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

37Bus37

V3

11

00.985-13.41

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

38Bus38

V3

11

01.013-12.71

14.0

7.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

39Bus39

V3

11

00.983-13.46

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

40Bus40

V3

11

00.973-13.62

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

41Tazewell

V6

11

00.996-14.05

6.3

3.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

42Bus42

V6

11

00.966-15.50

7.1

4.4

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

43Tazewell

V7

11

01.010-11.33

2.0

1.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

44Bus44

V3

11

01.017-11.86

12.0

1.8

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

45Bus45

V3

11

01.036

-9.25

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

46Bus46

V3

11

01.050-11.89

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

47Bus47

V3

11

01.033-12.49

29.7

11.6

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

48Bus48

V3

11

01.027-12.59

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

49Bus49

V3

11

01.036-12.92

18.0

8.5

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

50Bus50

V3

11

01.023-13.39

21.0

10.5

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

51Bus51

V3

11

01.052-12.52

18.0

5.3

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

52Bus52

V5

11

00.980-11.47

4.9

2.2

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

53Bus53

V5

11

00.971-12.23

20.0

10.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.063

0

54Bus54

V5

11

00.996-11.69

4.1

1.4

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

55SaltvilleV5

11

01.031-10.78

6.8

3.4

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

56Bus56

V6

11

00.968-16.04

7.6

2.2

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

57Bus57

V6

11

00.965-16.56

6.7

2.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0


80ITEMS

12

1110

0.0083

0.0280

0.1290

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

23

1110

0.0298

0.0850

0.0818

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

34

1110

0.0112

0.0366

0.0380

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

45

1110

0.0625

0.1320

0.0258

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

46

1110

0.0430

0.1480

0.0348

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

67

1110

0.0200

0.1020

0.0276

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

68

1110

0.0339

0.1730

0.0470

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

89

1110

0.0099

0.0505

0.0548

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

910

1110

0.0369

0.1679

0.0440

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

911

1110

0.0258

0.0848

0.0218

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

912

1110

0.0648

0.2950

0.0772

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

913

1110

0.0481

0.1580

0.0406

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

13

14

1110

0.0132

0.0434

0.0110

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

13

15

1110

0.0269

0.0869

0.0230

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

115

1110

0.0178

0.0910

0.0988

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

116

1110

0.0454

0.2060

0.0546

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

117

1110

0.0238

0.1080

0.0286

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

315

1110

0.0162

0.0530

0.0544

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

418

1110

0.0

0.5550

0.0

00

000

0.970

0.00.0

0.0

0.0

0.0

0.0

418

1110

0.0

0.4300

0.0

00

000

0.978

0.00.0

0.0

0.0

0.0

0.0

56

1110

0.0302

0.0641

0.0124

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

78

1110

0.0139

0.0712

0.0194

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

10

12

1110

0.0277

0.1262

0.0328

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

11

13

1110

0.0223

0.0732

0.0188

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

12

13

1110

0.0178

0.0580

0.0604

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

12

16

1110

0.0180

0.0813

0.0216

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

12

17

1110

0.0397

0.1790

0.0476

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

14

15

1110

0.0171

0.0547

0.0148

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

18

19

1110

0.4610

0.6850

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

19

20

1110

0.2830

0.4340

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

21

20

1110

0.0

0.7767

0.0

00

000

1.043

0.00.0

0.0

0.0

0.0

0.0

21

22

1110

0.0736

0.1170

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

22

23

1110

0.0099

0.0152

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

23

24

1110

0.1660

0.2560

0.0084

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

24

25

1110

0.0

1.1820

0.0

00

000

1.000

0.00.0

0.0

0.0

0.0

0.0

24

25

1110

0.0

1.2300

0.0

00

000

1.000

0.00.0

0.0

0.0

0.0

0.0

24

26

1110

0.0

0.0473

0.0

00

000

1.043

0.00.0

0.0

0.0

0.0

0.0

26

27

1110

0.1650

0.2540

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

27

28

1110

0.0618

0.0954

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

28

29

1110

0.0418

0.0587

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

729

1110

0.0

0.0648

0.0

00

000

0.967

0.00.0

0.0

0.0

0.0

0.0

25

30

1110

0.1350

0.2020

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

30

31

1110

0.3260

0.4970

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

31

32

1110

0.5070

0.7550

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

32

33

1110

0.0392

0.0360

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

34

32

1110

0.0

0.9530

0.0

00

000

0.975

0.00.0

0.0

0.0

0.0

0.0

34

35

1110

0.0520

0.0780

0.0032

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

35

36

1110

0.0430

0.0537

0.0016

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

36

37

1110

0.0290

0.0366

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

37

38

1110

0.0651

0.1009

0.0020

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

37

39

1110

0.0239

0.0379

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

36

40

1110

0.0300

0.0466

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

22

38

1110

0.0192

0.0295

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

11

41

1110

0.0

0.7490

0.0

00

000

0.955

0.00.0

0.0

0.0

0.0

0.0

41

42

1110

0.2070

0.3520

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

41

43

1110

0.0

0.4120

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

38

44

1110

0.0289

0.0585

0.0020

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

15

45

1110

0.0

0.1042

0.0

00

000

0.955

0.00.0

0.0

0.0

0.0

0.0

14

46

1110

0.0

0.0735

0.0

00

000

0.900

0.00.0

0.0

0.0

0.0

0.0

46

47

1110

0.0230

0.0680

0.0032

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

47

48

1110

0.0182

0.0233

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

48

49

1110

0.0834

0.1290

0.0048

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

49

50

1110

0.0801

0.1280

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

50

51

1110

0.1386

0.2200

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

10

51

1110

0.0

0.0712

0.0

00

000

0.930

0.00.0

0.0

0.0

0.0

0.0

13

49

1110

0.0

0.1910

0.0

00

000

0.895

0.00.0

0.0

0.0

0.0

0.0

29

52

1110

0.1442

0.1870

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

52

53

1110

0.0762

0.0984

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

53

54

1110

0.1878

0.2320

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

54

55

1110

0.1732

0.2265

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

11

43

1110

0.0

0.1530

0.0

00

000

0.958

0.00.0

0.0

0.0

0.0

0.0

44

45

1110

0.0624

0.1242

0.0040

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

40

56

1110

0.0

1.1950

0.0

00

000

0.958

0.00.0

0.0

0.0

0.0

0.0

56

41

1110

0.5530

0.5490

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

56

42

1110

0.2125

0.3540

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

39

57

1110

0.0

1.3550

0.0

00

000

0.980

0.00.0

0.0

0.0

0.0

0.0

57

56

1110

0.1740

0.2600

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

38

49

1110

0.1150

0.1770

0.0030

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

38

48

1110

0.0312

0.0482

0.0

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

955

1110

0.0

0.1205

0.0

00

000

0.940

0.00.0

0.0

0.0

0.0

0.0


1ITEMS

1IEEE57BUS


1ITEMS-9

18ClinchRvV1

0.0

999.99

IEEE57

IEEE57BusTestCase

TIELINESFOLLOWS

0ITEMS-999

ENDOFDATA

B.4

IEE

E118-B

us

Test

Syst

em

Data

08/25/93UWARCHIVE

100.0


BUSDATAFOLLOWS

57ITEMS

1Riversde

V2

11

20.955

10.67

51.0

27.0

0.0

0.0

0.0

0.955

15.0

-5.0

0.0

0.0

0

2Pokagon

V2

11

00.971

11.22

20.0

9.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

3HickryCk

V2

11

00.968

11.56

39.0

10.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

4NwCarlsl

V2

11

20.998

15.28

30.0

12.0

-9.0

0.0

0.0

0.998

300.0

-300.0

0.0

0.0

0

5Olive

V2

11

01.002

15.73

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

-0.40

0

6Kankakee

V2

11

20.990

13.00

52.0

22.0

0.0

0.0

0.0

0.990

50.0

-13.0

0.0

0.0

0

7JacksnRd

V2

11

00.989

12.56

19.0

2.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

8Olive

V1

11

21.015

20.77

0.0

0.0

-28.0

0.0

0.0

1.015

300.0

-300.0

0.0

0.0

0

9Bequine

V1

11

01.043

28.02

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

10Breed

V1

11

21.050

35.61

0.0

0.0

450.0

0.0

0.0

1.050

200.0

-147.0

0.0

0.0

0

11SouthBnd

V2

11

00.985

12.72

70.0

23.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

12TwinBrch

V2

11

20.990

12.20

47.0

10.0

85.0

0.0

0.0

0.990

120.0

-35.0

0.0

0.0

0

13Concord

V2

11

00.968

11.35

34.0

16.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

14GoshenJt

V2

11

00.984

11.50

14.0

1.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

15FtWayne

V2

11

20.970

11.23

90.0

30.0

0.0

0.0

0.0

0.970

30.0

-10.0

0.0

0.0

0

16N.E.

V2

11

00.984

11.91

25.0

10.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

17Sorenson

V2

11

00.995

13.74

11.0

3.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

18McKinley

V2

11

20.973

11.53

60.0

34.0

0.0

0.0

0.0

0.973

50.0

-16.0

0.0

0.0

0

19Lincoln

V2

11

20.963

11.05

45.0

25.0

0.0

0.0

0.0

0.962

24.0

-8.0

0.0

0.0

0

20Adams

V2

11

00.958

11.93

18.0

3.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

21Jay

V2

11

00.959

13.52

14.0

8.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

22Randolph

V2

11

00.970

16.08

10.0

5.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

23CollCrnr

V2

11

01.000

21.00

7.0

3.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

24Trenton

V2

11

20.992

20.89

0.0

0.0

-13.0

0.0

0.0

0.992

300.0

-300.0

0.0

0.0

0

25TannrsCk

V2

11

21.050

27.93

0.0

0.0

220.0

0.0

0.0

1.050

140.0

-47.0

0.0

0.0

0

26TannrsCk

V1

11

21.015

29.71

0.0

0.0

314.0

0.0

0.0

1.015

1000.0-1000.0

0.0

0.0

0

27Madison

V2

11

20.968

15.35

62.0

13.0

-9.0

0.0

0.0

0.968

300.0

-300.0

0.0

0.0

0

28Mullin

V2

11

00.962

13.62

17.0

7.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

29Grant

V2

11

00.963

12.63

24.0

4.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

30Sorenson

V1

11

00.968

18.79

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

31DeerCrk

V2

11

20.967

12.75

43.0

27.0

7.0

0.0

0.0

0.967

300.0

-300.0

0.0

0.0

0

32Delaware

V2

11

20.964

14.80

59.0

23.0

0.0

0.0

0.0

0.963

42.0

-14.0

0.0

0.0

0

33Haviland

V2

11

00.972

10.63

23.0

9.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

34Rockhill

V2

11

20.986

11.30

59.0

26.0

0.0

0.0

0.0

0.984

24.0

-8.0

0.0

0.14

0

35WestLima

V2

11

00.981

10.87

33.0

9.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

36Sterling

V2

11

20.980

10.87

31.0

17.0

0.0

0.0

0.0

0.980

24.0

-8.0

0.0

0.0

0

37EastLima

V2

11

00.992

11.77

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

-0.25

0

38EastLima

V1

11

00.962

16.91

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

39NwLibrty

V2

11

00.970

8.41

27.0

11.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

40WestEnd

V2

11

20.970

7.35

20.0

23.0

-46.0

0.0

0.0

0.970

300.0

-300.0

0.0

0.0

0

41S.Tiffin

V2

11

00.967

6.92

37.0

10.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

42Howard

V2

11

20.985

8.53

37.0

23.0

-59.0

0.0

0.0

0.985

300.0

-300.0

0.0

0.0

0

43S.Kenton

V2

11

00.978

11.28

18.0

7.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

44WMVernon

V2

11

00.985

13.82

16.0

8.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.10

0

45N.Newark

V2

11

00.987

15.67

53.0

22.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.10

0

46W.Lancst

V2

11

21.005

18.49

28.0

10.0

19.0

0.0

0.0

1.005

100.0

-100.0

0.0

0.10

0

47Crooksvl

V2

11

01.017

20.73

34.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

48Zanesvll

V2

11

01.021

19.93

20.0

11.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.15

0

49Philo

V2

11

21.025

20.94

87.0

30.0

204.0

0.0

0.0

1.025

210.0

-85.0

0.0

0.0

0

50WCambrdg

V2

11

01.001

18.90

17.0

4.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

51Newcmrst

V2

11

00.967

16.28

17.0

8.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

52SCoshoct

V2

11

00.957

15.32

18.0

5.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

53Wooster

V2

11

00.946

14.35

23.0

11.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

54Torrey

V2

11

20.955

15.26

113.0

32.0

48.0

0.0

0.0

0.955

300.0

-300.0

0.0

0.0

0

55Wagenhls

V2

11

20.952

14.97

63.0

22.0

0.0

0.0

0.0

0.952

23.0

-8.0

0.0

0.0

0

56Sunnysde

V2

11

20.954

15.16

84.0

18.0

0.0

0.0

0.0

0.954

15.0

-8.0

0.0

0.0

0

57WNwPhil1

V2

11

00.971

16.36

12.0

3.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

58WNwPhil2

V2

11

00.959

15.51

12.0

3.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

59Tidd

V2

11

20.985

19.37

277.0

113.0

155.0

0.0

0.0

0.985

180.0

-60.0

0.0

0.0

0

60SWKammer

V2

11

00.993

23.15

78.0

3.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

61W.Kammer

V2

11

20.995

24.04

0.0

0.0

160.0

0.0

0.0

0.995

300.0

-100.0

0.0

0.0

0

62Natrium

V2

11

20.998

23.43

77.0

14.0

0.0

0.0

0.0

0.998

20.0

-20.0

0.0

0.0

0

63Tidd

V1

11

00.969

22.75

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

64Kammer

V1

11

00.984

24.52

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

65Muskngum

V1

11

21.005

27.65

0.0

0.0

391.0

0.0

0.0

1.005

200.0

-67.0

0.0

0.0

0

66Muskngum

V2

11

21.050

27.48

39.0

18.0

392.0

0.0

0.0

1.050

200.0

-67.0

0.0

0.0

0

67Summerfl

V2

11

01.020

24.84

28.0

7.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

68Sporn

V1

11

01.003

27.55

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

69Sporn

V2

11

31.035

30.00

0.0

0.0

516.4

0.0

0.0

1.035

300.0

-300.0

0.0

0.0

0

70Portsmth

V2

11

20.984

22.58

66.0

20.0

0.0

0.0

0.0

0.984

32.0

-10.0

0.0

0.0

0

71NPortsmt

V2

11

00.987

22.15

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

72Hillsbro

V2

11

20.980

20.98

0.0

0.0

-12.0

0.0

0.0

0.980

100.0

-100.0

0.0

0.0

0

73Sargents

V2

11

20.991

21.94

0.0

0.0

-6.0

0.0

0.0

0.991

100.0

-100.0

0.0

0.0

0

74Bellefnt

V2

11

20.958

21.64

68.0

27.0

0.0

0.0

0.0

0.958

9.0

-6.0

0.0

0.12

0

75SthPoint

V2

11

00.967

22.91

47.0

11.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

76Darrah

V2

11

20.943

21.77

68.0

36.0

0.0

0.0

0.0

0.943

23.0

-8.0

0.0

0.0

0

77Turner

V2

11

21.006

26.72

61.0

28.0

0.0

0.0

0.0

1.006

70.0

-20.0

0.0

0.0

0

78Chemical

V2

11

01.003

26.42

71.0

26.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

79CapitlHl

V2

11

01.009

26.72

39.0

32.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.20

0

80CabinCrk

V2

11

21.040

28.96

130.0

26.0

477.0

0.0

0.0

1.040

280.0

-165.0

0.0

0.0

0

81Kanawha

V1

11

00.997

28.10

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

82Logan

V2

11

00.989

27.24

54.0

27.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.20

0

83Sprigg

V2

11

00.985

28.42

20.0

10.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.10

0

84BetsyLne

V2

11

00.980

30.95

11.0

7.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

85BeaverCk

V2

11

20.985

32.51

24.0

15.0

0.0

0.0

0.0

0.985

23.0

-8.0

0.0

0.0

0

86Hazard

V2

11

00.987

31.14

21.0

10.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

87Pinevlle

V3

11

21.015

31.40

0.0

0.0

4.0

0.0

0.0

1.015

1000.0

-100.0

0.0

0.0

0

88Fremont

V2

11

00.987

35.64

48.0

10.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

89ClinchRv

V2

11

21.005

39.69

0.0

0.0

607.0

0.0

0.0

1.005

300.0

-210.0

0.0

0.0

0

90Holston

V2

11

20.985

33.29

78.0

42.0

-85.0

0.0

0.0

0.985

300.0

-300.0

0.0

0.0

0

91HolstonT

V2

11

20.980

33.31

0.0

0.0

-10.0

0.0

0.0

0.980

100.0

-100.0

0.0

0.0

0

92Saltvlle

V2

11

20.993

33.80

65.0

10.0

0.0

0.0

0.0

0.990

9.0

-3.0

0.0

0.0

0

93Tazewell

V2

11

00.987

30.79

12.0

7.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

94Switchbk

V2

11

00.991

28.64

30.0

16.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

95Caldwell

V2

11

00.981

27.67

42.0

31.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

96Baileysv

V2

11

00.993

27.51

38.0

15.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

97Sundial

V2

11

01.011

27.88

15.0

9.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

98Bradley

V2

11

01.024

27.40

34.0

8.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

99Hinton

V2

11

21.010

27.04

0.0

0.0

-42.0

0.0

0.0

1.010

100.0

-100.0

0.0

0.0

0

100GlenLyn

V2

11

21.017

28.03

37.0

18.0

252.0

0.0

0.0

1.017

155.0

-50.0

0.0

0.0

0

101Wythe

V2

11

00.993

29.61

22.0

15.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

102Smythe

V2

11

00.991

32.30

5.0

3.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

103Claytor

V2

11

21.001

24.44

23.0

16.0

40.0

0.0

0.0

1.01

40.0

-15.0

0.0

0.0

0

104Hancock

V2

11

20.971

21.69

38.0

25.0

0.0

0.0

0.0

0.971

23.0

-8.0

0.0

0.0

0

105Roanoke

V2

11

20.965

20.57

31.0

26.0

0.0

0.0

0.0

0.965

23.0

-8.0

0.0

0.20

0

106Cloverdl

V2

11

00.962

20.32

43.0

16.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

107Reusens

V2

11

20.952

17.53

28.0

12.0

-22.0

0.0

0.0

0.952

200.0

-200.0

0.0

0.06

0

108Blaine

V2

11

00.967

19.38

2.0

1.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

109Franklin

V2

11

00.967

18.93

8.0

3.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

110Fieldale

V2

11

20.973

18.09

39.0

30.0

0.0

0.0

0.0

0.973

23.0

-8.0

0.0

0.06

0

111DanRiver

V2

11

20.980

19.74

0.0

0.0

36.0

0.0

0.0

0.980

1000.0

-100.0

0.0

0.0

0

112Danville

V2

11

20.975

14.99

25.0

13.0

-43.0

0.0

0.0

0.975

1000.0

-100.0

0.0

0.0

0

113DeerCrk

V2

11

20.993

13.74

0.0

0.0

-6.0

0.0

0.0

0.993

200.0

-100.0

0.0

0.0

0

114WMedford

V2

11

00.960

14.46

8.0

3.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

115Medford

V2

11

00.960

14.46

22.0

7.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

116KygerCrk

V2

11

21.005

27.12

0.0

0.0

-184.0

0.0

0.0

1.005

1000.0-1000.0

0.0

0.0

0

117Corey

V2

11

00.974

10.67

20.0

8.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0

118WHuntngd

V2

11

00.949

21.92

33.0

15.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0


80ITEMS

12

1110

0.03030

0.09990

0.02540

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

13

1110

0.01290

0.04240

0.01082

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

45

1110

0.00176

0.00798

0.00210

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

35

1110

0.02410

0.10800

0.02840

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

56

1110

0.01190

0.05400

0.01426

00

000

0.0

0.00.0

0.0

0.0

0.0

0.0

67

1110

0.00459

0.02080

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