15

CHAPTER 2

POWER SYSTEM STATE ESTIMATION

STRATEGIES AND PERSPECTIVES

2.1 INTRODUCTION

Energy Management is the process of monitoring, coordinating and

controlling the generation, transmission and distribution of electrical energy.

An energy control centre utilizes the computer aided tools to monitor, control

and optimize the generation, transmission and distribution of electrical

energy. The functions of a typical control centre can be categorized into three

subsystems as shown in Figure 2.1 namely the data acquisition and processing

subsystem, the energy management / automatic generation control subsystem

and the security monitoring and control subsystem.

SCADA (Supervisory Control and Data Acquisition System) forms

the front end for Energy Management Systems (EMS). A simple SCADA

provides the raw data of the operating condition of the system to the control

centre operators. State Estimation forms the backbone for Energy

Management System. Although reliability remains a central issue, the need

for the real time network models becomes more important than before due to

new energy market related functions are to be added to the existing EMS.

These models are based on the results yielded by state estimation and are used

in network applications such as security monitoring, contingency analysis,

optimal power flow, economic dispatch, unit commitment, automatic

generation control and economic interchange evaluation.

16

Figure 2.1 Functional Diagram of Modern Energy Management System

Important aspect of a system’s operation is obtaining a clear picture

of the state of the system. The possible states of the power system are

Normal, Alert, Emergency, InExtremis and Restorative (Kundur 2010).

During a particular time stamp, the power system would be in any one of the

states. In the ‘Normal’ state, all load and operating constraints are satisfied.

The system is stable for any foreseeable and probable contingency. In the

‘Alert’ state, all the load and operating constraints are satisfied for the system,

but not for one or more of the possible contingencies from the list of pre-

defined contingencies. Preventive control actions are taken to bring the

system from vulnerable operating state to a normal secure operating state. If

these preventive actions fail, then the system moves to the ‘Emergency’ state.

In case of the Emergency state, all the load constraints are satisfied, but one or

more operating constraints are violated. By taking proper corrective control

actions, the system state moves from emergency operating state to the normal

Optimal

Power Flow

Security

Dispatch

EnvironmentalDispatch

Security Monitoring

And Control Subsystem

Security

Monitoring

RestorativeControls

VAR

Dispatch

PreventiveControls

Normal State

Alert State

Emergency

State InExtremis

StateEmergency

Controls

Data Acquisition and

Processing Subsystem

Parameter

Estimation

SCADA

measurements

State

Estimation

Network

Topology

Displays

ExternalEquivalents

Energy / Economy

Functions Subsystem

Load Forecast

Unit Commitment

Economic

InterchangeEvaluation

EconomicDispatch

Automatic

Generation

Control

ContingencyAnalysis

17

or alert operating state. If the corrective control actions fail, the system

moves to the ‘InExtremis’ state wherein one or more load constraints and one

or more operating constraints are violated. Emergency control actions are

taken which will bring the emergency operating state to a ‘Restorative’ state.

In order to bring back the system from the ‘Restorative’ state to the normal or

alert state, restorative control actions are taken such that all operating

constraints are satisfied, but one or more loads are disconnected. All these

controls are generally referred to as the ‘security controls’.

A state estimator is capable of filtering the information to provide a

more accurate picture of the status of the system. The state estimation can be

defined as a process which determines the operating state of the power system

to allow the system operator to make decisions aimed at maintaining the

security of the power system. Weighted Least Square (WLS) algorithm is

normally used for estimating the state of the system. The traditional objective

of the state estimation is to reduce measurement errors by utilizing the

redundancy available in the most measurement systems. In particular, the

objectives are to reduce the variance of the estimate and to improve the

overall efficiency. The other major objectives of traditional state estimation

are (Alvarado 2001):

Detection of erroneous measurements and bad data

Detection of erroneous assumptions about the system,

particularly the status of switches and breakers.

Ability to provide information for unmetered or unmonitored

parts of the system.

Use of redundancy in order to improve the parameters for the

electrical models of the system.

18

The various roles and functions of state estimation in Energy

Management System are shown in Figure 2.2 (Zhu et al 2009).

Figure 2.2 Roles of State Estimation in EMS

From its limited use during 1980s to its expanded but not central

role in the operation of the system in 1990s, state estimation has now become

nothing less than the cornerstone upon which a modern control centre for a

power system is built. State estimation stands in between the real time

information and power system control and monitor applications, playing a

very crucial role in the real time power system control and operation (Zhu

2008). The SCADA data, phasor measurement data, network model and the

pseudo measurements form the input for the power system state estimation

algorithm. The applications such as contingency analysis, security analysis,

optimal power flow etc., are carried out based on the estimates provided by

the state estimator.

Old Estimates,

Scheduled Values

NetworkModel

Conventional

Measurements

SCADA

MEASUREMENTS

PHASOR

MEASUREMENTS

PSEUDO

MEASUREMENTS

TOPOLOGY

PROCESSOR

CONTINGENCY

ANALYSIS

OPTIMAL

POWER FLOW

OTHER

APPLICATIONS

SECURITY

ANALYSIS

STATE

ESTIMATION

19

2.2 STATE ESTIMATION CONCEPTS

State estimation is a digital processing scheme, which provides a

real time data for many of the central control and dispatch functions in a

power system. Its purpose is to improve the dispatch of energy, system

reliability and planning capabilities by understanding the operating state of

the power system. In general the state variables in power system are the

voltage magnitudes and phase angles at all the buses except the slack bus. In

order to ensure secure and economical operation of the power systems, the

operator must be aware of the exact state of the power system at regular

intervals.

Today’s complex large scale power systems require highly

sophisticated techniques for monitoring and control to maintain the system in

a secure and reliable state. There is constant need to update information about

the system to be used for security assessment, load frequency control and a

host of other purposes. In this context, two aspects of the problem stand out

prominently. Firstly, it is uneconomical and in many cases not feasible to

monitor all possible information about the power system. Secondly, the

measuring and equipments that are used are subjected to random errors, which

make the data highly suspicious from the point of view of reliability.

The main objective of state estimation in power systems is

therefore to build a complete and reliable database. Such a database is

obtained by feeding the measured data to a central real time computer, which

on the basis of a prewritten mathematical program, filters the data and extends

it to cover all information regarding the system. In short, state estimation

guarantees reliable information even if some of the measurements are

inaccurate. Thus, the central task of the state estimator is to validate the

information supplied to the system operator. The major ingredients of

20

state estimation are: measurement devices located at strategic points on the

system, high speed data transfer system to convey the measured information

to the control centre, a real time computer with interfacing equipment to

accept and display information and efficient estimation algorithm.

The state of a system may be defined as the minimal amount of

information that one has to know about the system in order to predict its

future evaluation. From this view point, the complex voltages in all buses in a

power system are qualified to be assigned as state variables. Specifically, for

an N bus system, taking a particular bus (preferably the swing bus) as

reference, we may assign N voltage magnitudes and (N – 1) phase angles of

voltages, which are to be called as state variables. Thus, for an N bus system,

the dimension of the state vector is (2N – 1).

The rationale behind this choice is that, knowing these variables

along with the active and reactive power injections at the N buses (real Pi and

reactive Qi at all buses except Pi at the swing bus) and system parameters it is

possible to compute all measurements pertaining to the system. When

observation errors are present the success of state estimation depends on the

redundancy of observed data. Thus, if the state variables are ‘n’ (equal 2N – 1) in

number and if ‘n’ load injections at the buses are given then the problem

reduces to a load flow calculation.

State estimation is different from load flow studies in that the

number of input variables ‘m’ should be greater than (2N – 1), the dimension

of the state vector. It is this redundant information (number of unknown

variables being less than the number of defining equations) which is to be

effectively used in some form of averaging process to filter the data. The

relationships between the different variables involved in the state estimation

are explicitly given in Figure 2.3.

21

X - True System State Vector

Z - Measurement Vector

u - Input Vector

v - Observation Vector

X̂ - Estimated State Vector

Figure 2.3 General Block diagram - State Estimation

The basic relation between Z, X and v is given as below:

Z = h(X) + v (2.1)

where h(X) is the non-linear function of the state X.

Depending on the number of measurements made available to the

control centres, the dimension ‘m’ of the measurement vector ‘Z’ may vary.

Different measurement schemes are identified with respect to state estimation

for an N bus system with M lines.

Case i: Z1 = h1(X) + v1 (2.2)

Z1 consists of (2N - 1) load injection measurements (active and

reactive). The dimension of Z1 is (2N - 1).

Case ii: Z2 = h2(X) + v2 (2.3)

Z2 consists of load injection measurements plus voltage magnitude

measurements at N buses. The dimension of is Z2 is (3N - 1).

verror

u

Physical SystemMeasurement

SystemState Estimator

X ZX̂

22

Case iii: Z3 = h3(X) + v3 (2.4)

Z 3 consists of measurement of active and reactive line flows at both

ends of each line. Here the dimension of Z3 is 4M, where M is the

number of lines.

Case iv: Z4 = h4(X) + v4 (2.5)

Z4 consists of measurements as in Z3 plus voltage magnitude

measurements at N buses. Dimension of Z4 is (4M+N).

Case v: Z5 = h5(X) + v5 (2.6)

Z5 consists of maximum possible measurements. It comprises of

(2N-1) load injections, N voltage magnitudes, (N-1) voltage phase

angles at N buses and 4M line flows. The dimension of Z5 is

(4N+4M-1).

A reliable state estimation is essential to guarantee a reliable

operation of the power system. The reliability of the estimation depends on

the number, type and location of the measurements. The first requirement to

obtain a state estimation is the observability of the system, i.e., the available

measurement set must contain enough information to obtain an estimate of all

states of the system. Also, in order to be reliable, the state estimator must be

robust to the presence of gross errors in the measurements and must be able to

cope with the loss of some of them.

London et al (2000) have proposed a method to identify the

redundancy level of each measurement associated to an observable power

system. The proposed method identifies the critical measurements and sets of

measurements that removed from the measurement set make the power

system unobservable. The redundancy level is very important to operators in

23

order to guide the search for adequate reinforcement of the available

measurement set. The robustness of state estimation can be guaranteed only if

the level of redundancy of the available measurements is high enough and

properly distributed throughout the system.

In other words, the information of each state can be extracted from

different measurements in such a way that the loss of some measurement does

not affect the observability of the system or the reliability of the estimation.

A measure of the redundancy may be denoted by the redundancy factor ,

which is defined as:

n

m

XofDimension

ZofDimension (2.7)

In practice the range of the redundancy factor , has been found

useful if its value is in between 1.5 and 2.8. i.e., 1.5 2.8. If too low

value of is chosen then the measurement errors are inadequately filtered. If

too high is chosen it leads to high investment cost in data acquisition.

2.3 RECENT TRENDS IN POWER SYSTEM STATE

ESTIMATION

Many researchers have analyzed the importance of state estimation

in real time monitoring of large scale power systems. Power system state

estimation provides an estimate for all metered and unmetered quantities. The

main aim of state estimation is to filter out small errors due to model

approximations and measurement inaccuracies and to detect and identify

discordant measurements called bad data. A state estimator is designed to

process the real time meter readings and handle all the uncertainties,

producing a real time reliable database, which is a true representation of the

actual system. The different perspectives with regard to the state estimation

24

problem can be widely classified as various solution methodologies, state

estimation in presence of FACTS (Flexible AC Transmission System)

devices, state estimation using different optimization techniques and presently

state estimation with PMU data.

Kurzyn (1983) has proposed an efficient two level hierarchical state

estimation (HSE) algorithm, suitable for real time monitoring of large scale

power systems. As a first step, state estimation is carried out simultaneously

and independently for all subsystems. In the second step, the subsystem

estimators are coordinated to find the state estimation solution. The mean

error of the proposed hierarchical state estimation algorithm is close to the

error of the weighted least square algorithm and the error of the HSE

algorithm does not necessarily increase with the increasing number of

subsystems. The method is very flexible, allowing fast state estimation.

Suitability of the method and the algorithm are examined using two 220 kV

networks. Several comparisons are made with the classical and centralized

state estimation methods to illustrate the practicality of the hierarchical

method.

Power system state estimation is usually formulated as a weighted

least-squares problem and solved iteratively by the normal equations method.

Gu et al (1983) refers to the power system state estimator as the heart of the

data processing activities in the modern electric utility energy control centre.

The normal equation solution methods for finding the state variables are well

known to exhibit a tendency to be numerically unstable on some networks.

As a result, long precision arithmetic is usually employed in solving the

normal equations. In extremely ill-conditioned cases, the state estimator may

fail to converge. A suitable numerical measure of matrix conditioning has

been defined and a linear analysis of the condition of some simple measured

networks is performed. It provides an insight into the cause of ill-conditioning

25

in realistic networks. The technique for arriving at a compromise between the

conflicting requirements of numerical stability (good conditioning) and

sparsity has been described. Thus an analysis on the sources of

ill-conditioning in the power system state estimation problem and an

alternative solution by Peters and Wilkinson state estimator algorithm that

overcomes the ill-conditioning without losing matrix sparsity has been

presented.

Allemong (2005) has commented on the various requirements for

the successful implementation of state estimation in a utility Energy

Management System. The following requirements of three basic categories of

information had been enforced.

A redundant, reliable and accurate measurement set

Accurate network topology, constructed from the real time

states of the switching elements

Accurate parameters of the network elements.

Pajic (2007) has proposed improvements in Power System State

Estimation and Contingency Constrained Optimal Power Flow (CCOPF) in

stochastic multiple contingencies framework. The existing Newton

Orthogonal factorization algorithms for state estimation are too slow and too

fragile numerically. A new and more robust method that is based on Trust

Region Method (TRM) has been proposed. TRM is based on a globalization

of Newton’s method which is very often the key to the success (finding a

global minimum) of the algorithm. For the first time, TRM has been tested on

the power system state estimation problem.

Li et al (2011) have reviewed the algorithms for power system state

estimation namely the least square algorithm, fast decoupled method,

26

orthogonal transformation algorithm, state estimation algorithm based on

measurement transformation, district coordinated algorithm, etc. The

advantages and disadvantages of each method are also reviewed.

Researchers have also focused on the usage of various linear and

evolutionary programming algorithms for solving the power system state

estimation problem. Hybrid algorithms have also been proposed for

estimating the state of the system. The meta-heuristic methods are iterative

techniques that can search not only local optimal solutions but also a global

optimal solution depending on the problem domain and time limit. In the

meta-heuristic methods, the techniques frequently applied to the state

estimation problem are Genetic Algorithms (GA), Tabu Search (TS),

Evolutionary Programming (EP), Simulated Annealing (SA), Particle Swarm

Optimization (PSO), etc. They are general purpose search techniques based

on the principles inspired from the chromosomes and particles observed in

natural systems and populations of living beings. These methods have the

advantage of searching the solution space more thoroughly.

Gremling and Passino (2000) describes Genetic Algorithm (GA)

that can perform on-line adaptive state estimation for linear and non-linear

systems. The construction of a genetic adaptive state estimator and the way in

which GA evolves the model in a state estimator in real time are discussed.

The operation and performance of the genetic adaptive state estimator has

been illustrated. The genetic adaptive state estimator has the potential to offer

higher performance for non-linear systems compared with the other methods.

Hybrid Particle Swarm Optimization based distribution state estimation have

been proposed by Naka and Fukuyama (2001). This method considers both

non-linear characteristics of the practical equipment and actual limited

measurements in distribution systems and estimates load and distributed

generation output values at each node by minimizing difference between

27

measured and calculated voltages and currents. The number of calculations

involved in the PSO and the HPSO, is found to vary minimally whereas the

results indicates that HPSO generates high quality solutions compared with

the PSO.

In sequential state estimation, each measurement is processed

sequentially, by avoiding matrix procedures. They work for very small

networks but not for medium to large networks. In transformation methods,

the measurements are transformed into new ‘measurements’ that are functions

of the state and of the original measurements. The functional relationships are

via the network structure of the system. The WLS formulation may be

decoupled by separating the measurement set into real and reactive power

groups and by using the same simplifying assumptions as used in the fast

decoupled load flow. The use of state estimation techniques for real world

process applications of significant size is believed to be ground breaking and

the developments described allow a new generation of applications to be

considered.

2.4 STATE ESTIMATION WITH PHASOR MEASUREMENT

UNITS

Phasor measurement units are devices which by employing widely

used satellite technology offer new opportunities in power system monitoring,

protection, analysis and control. Post-disturbance analyses are much improved

due to precise snapshots of the system states, which are obtained through

Global Positioning Satellite (GPS) synchronization. Advanced protection

could be implemented based upon synchronized phasor measurements with

options for improving overall system response to catastrophic events. The

estimate obtained from the phasor measurement unit provides the current

operating state of the power system which primarily helps in maintaining the

28

security of the power system and for several other applications. Synchronized

Phasor Measurement Unit is a monitoring device, which was first introduced

in early 1980s. It gives the real time status of the power system operating

conditions, which is required for power system analysis and control. Real

time monitoring of power systems has become possible with the advent of

phasor measurement units.

Recent developments in time synchronizing techniques coupled

with the computer based measurement technique have been explained by

Phadke (1993). This provides a novel opportunity to measure the phasor and

phase angle differences in real time. Measuring systems using digital

computers are introduced in the power industry. The author gives an insight

into the measurement process, its limitations and its potentialities after the

advent of computer relaying. The importance of the phase angle in electric

power engineering has been emphasized.

PMU measures voltage and current phasors in a power system,

which has higher accuracy than conventional measurements. Synchronism

among phasor measurements is achieved by sampling of voltage and current

waveforms using a common synchronizing signal from the GPS. A PMU

provides time-stamped measurements of active power, reactive power,

frequency, current, voltage magnitude, and phase angle. The time-stamped

characteristic of a PMU is one of its most innovative features which makes it

useful for many other applications such as system protection, control and

stability assessment, aid topology error identification, parameter error

detection and correction and improves the accuracy of state estimation.

With regard to the unpredictable changes in the size and

interconnections of the power system network, optimal location of the phasor

measurement units has also to be changed in order to maintain the complete

29

network observability. State estimation results become more accurate with

the PMU data received from the optimally located PMUs in a power system

network. By strategically locating PMUs, the effects of measurement errors

can be reduced. The principal developments in state estimation and related

areas are observability analysis, erroneous data processing, network topology

processing, topology estimation, and parameter estimation.

The first prototype of the PMU was developed and tested in

Virginia Tech in the early 1980s. The first commercial phasor measurement

unit, the Macrodyne 1690 was developed in 1991. In the late 1990s,

Bonneville Power Administration (BPA) developed a Wide Area

Measurement System (WAMS), which initiated the usage of PMUs for large

scale power systems. A PMU, when placed at a bus, can provide a highly

accurate measurement of the voltage phasor at that bus, as well as the current

phasors through the incident transmission lines (depending on the available

measurement channels). The major advantages of using Synchronized

Measurement Technology (SMT) are that the measurements from widely

dispersed locations can be synchronized with respect to a Global Positioning

System clock. The voltage phase angles can be measured directly which was

so far technically infeasible and the accuracy and speed of energy

management system applications (e.g., state estimation) increase manifold.

Bai et al (2006) have proposed the process-oriented state estimation

using innovation network graph based PMUs. Process-oriented state

estimation is being carried out using all the measurements within a period of

time, which can provide characteristic states. In order to develop the new

method, the operating process is divided into several processes and sub-

processes according to the topology change. In each process or sub-process, a

characteristic state is derived which can represent the average status of this

30

process or sub-process. In order to compute the expected states, an expected

innovation network graph is derived. The innovation network graph has good

robustness on the topology changes in the network. Instead of dealing with

the huge measurements within the process, an innovation network graph is

computed from where the expected states of the network can be derived.

IEEE 5-Bus system is used to illustrate the effectiveness of this method.

The key factor for widespread deployment of the PMUs is to

provide appropriate penetration and redundancy of synchronized

measurements. Such widespread deployment can be achieved when

integrating the PMU function with modern microprocessor based relays for

metering, fault recording and sequence of event recording capabilities

(Kasztenny 2007). Zhu and Abur (2007) revisited the state estimation

problem formulation by assuming availability of at least one phasor

measurement unit in the system. The author investigates on the requirements

to ensure robust state estimation in the presence of single PMU errors. The

requirements are verified by implementing a GPS referenced state estimator

using test systems containing one or more PMU measurements. One of the

issues faced by the state estimators is the choice of reference bus phase angle

when phase angle measurements are present. This issue is easily resolved by

eliminating the reference phase angle from the conventional formulation. This

revised formulation will yield consistent state estimation results even when

any one of the phasor measurements is in error, provided that certain

redundancy conditions are satisfied.

Kamireddy (2008) has proposed a technique in which various

sensors distributed across different parts of the electric power grid will be able

to provide measurements to the control centre operator for situational

awareness of the system. The voltage transformer, current transformer, relay

31

and phasor measurement units are the types of sensors for power system

monitoring. The utilities monitor the operating condition of the system by

processing the measurements received from these sensors using a state

estimator. The measurements are refined and compensated for any lost data

thus providing a snapshot of the power system. Further analysis can be done

based on the most recent data and required state of the system. The electric

power grid is vulnerable to blackouts caused by physical disturbances, human

errors and external disasters. These disturbances can also cause loss of data,

sensor failure or communication link failure. Focus is towards comparing

state estimation algorithms with loss of measurement data. Weighted Least

Square (WLS), Least Absolute Value (LAV) and Iteratively Reweighted

Least Squares (IRLS) implementation of Weighted Least Absolute Value

(WLAV) algorithms are compared for state estimation with clustered and

scattered loss of data.

Chakrabarti et al (2010) have proposed a comprehensive

formulation of the hybrid state estimator incorporating conventional, as well

as PMU measurements. The performance of the state estimators is compared

in terms of the convergence properties and the variance in the estimated

states. Modern PMUs have features like frequency measurement,

measurement of derived quantities (i.e., power components, power quality

related indicators, etc.,) and monitoring of the status of substation apparatus.

The properties of state estimation problem solution can be

essentially improved owing to the new phasor measurements provided by

PMU. The PMUs are the main measurement equipments of WAMS, that

allows the electric power system state to be controlled synchronously and

with high accuracy. As compared to a standard set of measurements received

from SCADA, a PMU installed at a bus can measure voltage phases at that

bus and current phases in some or all branches adjacent to this bus depending

32

on capacity of communication channels. The measurements obtained from

PMU can solve a number of problems concerning low redundancy of

measurements and considerably enhance the efficiency of state estimation

problem solution. The proposed methodology (Glazunova et al 2008) of joint

use of PMU and SCADA measurements for state estimation is checked on the

test network. The results show that PMU measurements allow one to

essentially enhance the efficiency of bad data detection in measurements and

increase the accuracy of the estimates obtained.

Valverde et al (2009) have proposed a multi area state estimator

based on wide area measurements where only boundary buses are considered

in the coordination level. The power injection measurements are not used

during the coordination level thus reducing the number of states and therefore

size of the problem. Instead a set of pseudo measurements are included

whenever a power injection measurement is available in boundary buses. The

proposed methodology can be used when information regarding the

surrounding boundary buses is unavailable at the coordination level and

delivers similar quality of results compared to those obtained when including

internal buses adjacent to boundary buses, but with reduced size, computation

time and complexity at the coordination level.

Ghassemian et al (2009) have proposed new implementation and

testing strategies for phasor assisted state estimation of New York State

Transmission System. Phasor measurement units with GPS synchronization

was incorporated into the data acquisition subsystem of the energy

management system. The modified state estimator was subjected to pre-field

and post-field installation testing. The pre-field installation testing was done

to verify the correctness of the solution algorithm, to identify the impact of

phasor metering accuracy on the quality of estimator solution, to show the

relative effectiveness of phasor measurements with respect to other

33

measurements, to identify the effect of the reference bus selection, to detect

the impact of PMUs on the state estimator convergence and to establish the

minimum clock synchronization sampling accuracy required for the PMUs.

The post-field installation tests were conducted to identify the effectiveness of

the PMUs in the state estimator solution using the real time data as well as to

detect the effect of time skewing and measurement weights on the state

estimator solution.

Hoffman et al (2010) have proposed practical state estimation

techniques for primarily radial distribution networks. From their view, the

smart meter information at the customer side may not be readily usable in

state estimation, but they can be used to verify its power quality and its

voltage levels. Measurements those are inaccurate due to meter, telemetry or

other types of errors will deteriorate the state estimation if they are not

detected, identified and eliminated. Thus, bad data detection and identification

in state estimation will play a crucial role to ensure the quality of state

estimation results.

Chakrabarti et al (2010) have proposed a comprehensive

formulation of the hybrid state estimator in the presence of conventional and

PMU measurements and investigated three different methods of inclusion of

current measurements by PMUs in a power system state estimator. The three

possible ways of including PMU current measurements into the conventional

state estimator are given as follows:

Current phasor magnitude and phase angle measurement.

Real and imaginary part of the complex current measurement.

Pseudo-voltage measurement with the help of current phasor

measurement and known line parameters.

34

The performance of the state estimator in the presence of

conventional measurements and optimally placed PMUs is evaluated in terms

of convergence characteristics and estimator accuracy. Test results on the

IEEE 14-Bus and IEEE 300-Bus systems are analyzed to determine the best

possible method of inclusion of PMU current phasor measurements.

Valverde et al (2010) have proposed a constrained formulation for

hybrid state estimation of power systems. The conventional and

synchrophasor measurements are simultaneously incorporated in the

estimation problem without using any transformation of measurements. This

constrained formulation makes it possible to take advantage of information

from phasor measurement unit branch current and voltage measurements,

improving the accuracy of the estimator.

Hurtgen (2008) explains that observability is a crucial factor when

trying to solve the state estimation problem. A PMU placement method based

on meta-heuristics is proposed and compared to an integer programming

method. A given PMU placement can provide full observability or

redundancy. The PMU configuration can also take into account the zero

injection nodes which further reduce the number of PMUs needed to observe

the network. Finally, a method is proposed to determine the order of the

PMU placement to gradually extend the observable area.

Jaime De La Ree et al (2010) have explained about the uses of

phasor measurements for improved monitoring, protection and control of

power networks. In the early stages these measurements were used only for

the post-event monitoring. This was due to the difficulties faced with regard

to the communication channels required for real time monitoring, control and

protection application. With the occurrence of major blackouts in many

power systems around the world, the value of data provided by PMUs has

35

been recognized and installation of PMUs on power transmission networks of

most major power systems have become an important current activity.

After 1996 U.S West Coast blackouts and 2003 North Eastern U.S

blackouts, the PMU monitoring has become very essential for the post-fault

analysis of the events. One of the recommendations from the United States-

Canada Task force on the 14 August 2003 blackout is to “require use of time

synchronized data recorders” at all utilities. Hence the Eastern Interconnection

Phasor Project [EIPP], now known as North American Synchrophasor Project

Initiative (NASPI) was created. The EIPP performed the first real time wide

area monitoring in U.S to solve some interesting problems such as the

determination of a common phase for the whole eastern grid. With the PMU

installation cost ranging from 10 K to 70 K, (depending on the utility, location

and availability of communication channels) placing PMUs in the optimum

locations is one of first steps of a wide area monitoring system. At present,

phasor measurement units are the most widely used Synchronized

Measurement Technology based devices for power system applications.

2.4.1 Optimal Placement of Phasor Measurement Units

PMUs are increasingly being used in different parts of the world as

the major technology enabler of the Wide Area Monitoring, Protection and

Control system. The general objective of these PMU installation activities is

to eventually make a transition from the conventional supervisory control and

data acquisition based measurement system to a more advanced measurement

system that will utilize synchronized measurements from geographically

distant locations and increase the situational awareness by monitoring a wide

area of the power system in real time. The optimal placement of phasor

measurement units is an off-line problem to be solved during the planning

stage and the results obtained such as number of PMUs to be installed and

their locations are considered as planning data. Several researchers have

proposed algorithms for solving power system state estimation problem using

36

both SCADA and PMU data. From their analyses using different test cases, it

is clear that use of the data obtained from the optimally located PMUs in a

network shortens the computer time and increases the precision of the

estimate obtained.

The main purpose of optimal PMU placement problem is to

minimize the number of installed PMUs and for an n-bus system the

optimization problem is given as follows:

Minimizen

iiixw (2.8)

Subject to f(X) î

where X is a binary decision variable vector, whose entries are defined as:

xi = { 1, if a PMU is installed at bus i , 0 otherwise

wi is the installation cost of the PMU at bus i.

f(X) is a vector function representing the constraints, whose entries

are non-zero if the corresponding bus voltage is solvable using the

given measurement set and zero otherwise.

î is a vector whose entries are all equal to 1.

Several test cases are considered (6-Bus, Anderson and Fouad

9-Bus, IEEE 14, IEEE 30 and IEEE 118-Bus systems) to solve for the optimal

PMU placement using Binary Integer Linear Programming (BILP) technique.

Also real time State Electricity Board systems such as 110kV (North and

South), 230kV and 400kV sub networks are considered to find the Optimal

PMU placement solution.

The Spanning Tree for different test systems considered has been

obtained (Sodhi and Srivastava 2008). Multi partitioning algorithm is applied

37

to form various blocks from the respective spanning tree. For each block the

objective function and the constraint equations are formulated and solved

using Integer Linear Programming. The number and location of PMUs for

the IEEE test systems and the different subsystems of State Electricity

network are given in Table 2.1. It shows one of the optimum feasible

solutions for the PMU placement problem.

Table 2.1 Optimal Number and Location of PMUs

NetworkNumber

of PMUsLocation of PMUs

6-Bus system 2 3, 4

Anderson and Fouad 9-Bus system 3 4, 7, 9

IEEE 14-Bus system 4 2, 6, 7, 9

IEEE 30-Bus system 10 1, 2, 6, 9, 10, 12, 15, 19, 25, 27

IEEE 118-Bus system 32 2, 5, 9, 11, 12, 17, 21, 24, 25, 28,

34, 37, 40, 45, 49, 52, 56, 62, 63,

68, 73, 75, 77, 80, 85, 86, 90, 94,

101, 105, 110, 114

110 KV (North) 16 6, 8, 9, 11, 13, 15, 20, 24, 27, 29,

32, 40, 42, 45, 47, 48

110 KV (South) 14 2, 7, 14, 15, 16, 21, 27, 28, 32, 36,

43, 44, 48, 50

230 KV 3 3, 6, 8

400 KV 10 2, 6, 9, 17, 18, 20, 26, 29, 34, 36

Fang Chen et al (2008) have proposed a reduced state estimation

model including phasor measurement units. In the proposed model, each

PMU can supply two state variables, and hence the number of unknown state

variables is decreased. If a system of N buses is configured with NA number

of PMUs, the redundancy factor is raised as follows:

= m / (2N-1-2NA) (2.9)

Correspondingly, the capability of state estimation to detect bad

data is improved. If the state variables supplied by PMU are accurate, then

the redundancy level of the system will be higher. The ability to measure the

38

voltage phasors at buses directly by PMU has implications on the traditional

state estimation. It is of no doubt that direct measurement of state can

improve the observability and the accuracy of state estimation.

State estimator provides the optimal estimate of the system state

based on the received measurements and the knowledge of the network

model. Measurements may include power injections (real / reactive), power

flows (real / reactive), bus voltage magnitude, line current magnitude and

current injection magnitude. PMUs provide two other types of measurements

namely, the bus voltage phasor and branch current phasor. Depending on the

type of the PMUs, the number of channels used for measuring voltage and

current phasors will vary. Generally, it is assumed that each PMU has enough

channels to record the bus voltage phasor at its associated bus and current

phasors along all branches that are incident to that bus.

Considering the IEEE 14-Bus system and IEEE 30-Bus system, the

redundancy factors with SCADA measurements and with measured data from

PMUs are given in Table 2.2.

Table 2.2 Estimation of Redundancy Factor with SCADA and PMU

Measured Data

Parameters

SCADA Measured Data PMU Measured Data

IEEE 14

Bus system

IEEE 30

Bus system

IEEE 14

Bus system

(4 PMUs)

IEEE 30

Bus system

(10 PMUs)

Number of Buses (N) 14 30 14 30

Number of state variables

(n)27 59 27 59

Number of measurements

(Nm)42 81 38 100

Redundancy Factor ( ) 1.56 1.37 1.407 1.69

39

If the redundancy factor is within the range, 1.5 2.8, the

measurement obtained from the state estimator is more accurate with less

investment cost in data acquisition. Redundancy seeks more than

observability. Additional measurement locations are needed to increase the

redundancy and strengthen the network observability. Regardless which state

estimation formulation is used, the accuracy of state estimation solutions is

dependent on the quality of data as well as measurement configuration and

redundancy. The quality of data can be improved by using high quality

metering devices and communication systems. On the other hand, the

measurement configuration needs to be well designed to ensure robust and

accurate performance of the state estimator. The locations and types of

measurements should allow the state variables of the entire network to be

calculated uniquely, i.e. the network should be observable. There should be

enough redundancy to filter the inevitable random noise associated with the

data, and to detect and eliminate bad data in the observable areas. Low

redundancy causes the state estimators to be very sensitive to the noise and

also limits the bad data detection and identification capability.

2.4.2 Observability

Observability analysis is a fundamental component of real time

state estimation, which checks for enough available measurement in order to

estimate all the states of the electric power system. Two methods used to

determine the system observability are the numerical observability and

topological observability based methods. The topological observability based

approaches utilize the graph theoretical concept to find the optimal locations

and thus to make the system topologically observable. The topological

methods are based on whether a spanning tree of full rank can be constructed.

The numerical methods rely on whether the measurement information gain or

Jacobian matrix is of full rank. If the voltage of a node can be measured

40

directly or can be calculated by other voltage phasor and current phasor, the

node is observable. For making the system topologically observable using

PMUs, following rules are followed:

If voltage phasor and current phasor at one end of a branch are

known, voltage phasor at the other end of the branch can be

calculated using Ohm’s law

If voltage phasor at both the ends of a branch are known,

branch current can be calculated

If there is zero injection bus without a PMU, whose outgoing

currents are known except for one, then the unknown outgoing

current can be calculated using Kirchhoff’s Current Law

Complete observability refers to the PMU placement scenario when

the number and location of the PMUs are sufficient to determine the complete

set of state variables of the network being considered.

In the practical power system, the time required to send the

measurement from SCADA to the control centre is about 2 seconds whereas

the measurement from PMU needs only 40 milliseconds to reach the control

centre (Xue et al 2007). There will be 50 times measurements from PMU sent

to the control centre in the interval that two measurements from SCADA were

sent to the control centre. Thus the remedial actions in case of a contingency

can be carried out more faster and effectively.

Synchronized measurement devices are being deployed in certain

parts of the world and used in applications such as system monitoring, post

disturbance analysis, monitoring of inter-area oscillations and system

modelling. In North America more than two hundred PMUs have been

installed and more are in the pipeline under the North American

41

Synchrophasor Initiative (NASPI). A number of utilities in the United States,

Canada and Mexico are involved in this project. Central and Western

European Countries have started using PMUs extensively. Their major focus

is on developing systematic ways for monitoring and damping of inter-area

oscillations, such as the feedback control of High-Voltage DC (HVDC) links

or Static Var Compensators (SVCs) by using the PMU measurements.

In China, the State Grid Company and manufacturers have issued

the standard on PMUs and WAMS in 2005. More than 700 PMUs are already

in operation and according to the 11th five-year plan of the power grid, all

500kV substations and 300MW and above power plants in the Chinese power

grid will install PMUs within the next five years. Major applications that are

currently in use are the real time visualization of the system dynamics and

transmission capacity, wide area data recording and playback and monitoring

of inter-area low frequency oscillations. The other major objectives for which

the work is in progress include applications such as enhanced state estimation,

on-line security assessment, adaptive protection and emergency control.

The PowerGrid, an Indian central transmission utility is planning to

install 20 to 25 PMUs at critical buses in different regional grids. The

synchronized measurements from these PMUs will be used for model

validations and for the development of a common state estimator combining

the regional state estimators. Based on the success of this stage, more PMUs

are planned to be installed to explore different advantages of SMT and

develop remedial action schemes and System Integrity Protection Schemes

(SIPSs). Similarly Brazil, Russia and other countries are also in the

development of PMU related protection and control for their power networks

(Chakrabarti et al 2009).

The beneficial impacts of PMU data on state estimation depend on

PMU measurement accuracy and calibration, the number of PMUs, PMU

42

locations and related SCADA data accuracy (Wu and Giri 2006). The PMU

data can improve the estimation of inaccurate active power measurements

close to a PMU substation. The wrong measurement may come from the same

substation or neighbouring substations. PMU data with high accuracy is

especially effective when the measurement has a large error. PMU data has

no obvious effect on reactive power and voltage magnitude estimations if

only the phase angle measurement is used. Phasor measurement units should

be installed in substations evenly distributed in the whole system to achieve

the best performance. The location of the reference PMU has no impact on

state estimation. A single PMU can not necessarily improve state estimation

performance. PMU data from the external areas may help operators locate the

outside problem quickly and prevent cascading events. PMU data trend

analysis can detect circuit breaker or switch status changes in the network,

which may improve the topology estimation and error detection.

2.5 STATE ESTIMATION IN PRESENCE OF FACTS DEVICES

Flexible AC Transmission Systems (FACTS), based on either

voltage or current source converters (VSC / CSC), can be used to control

steady state as well as transient performance of the power systems. Interline

Power-Flow Controller (IPFC) is a voltage source converter based FACTS

controller used for series compensation with the unique capability of power

flow management among multi-lines of a substation. IPFC was first proposed

by Gyugyi in 1998 and has the capability to equalize both real and reactive

power flow between transmission lines, transfer power from overloaded to

under loaded line, compensate against reactive voltage drop and the

corresponding reactive line power. Due to these features there is an

increasing interest in the analysis of IPFC in power system state estimation.

Traditional state estimation methods without integrating FACTS devices will

not be suitable for power systems with FACTS devices embedded in the

network.

43

Xu and Abur (2003) presented an algorithm for State estimation of

networks embedded with FACTS devices. State estimation formulation is

modified in order to incorporate the detailed model of the Unified Power-

Flow Controller (UPFC). This necessitates the use of equality and inequality

constraints that account for the limits associated with the device operation and

ratings. The proposed algorithm by them is not only used for state estimation

but also can be used for determining the controller settings of FACTS devices

for a desired operating condition. Initially they introduced a steady state

model of the Unified Power-Flow Controller with operating and parameter

limits. The issues of network observability and bad data analysis have been

discussed using the proposed state estimation algorithm for networks

embedded with FACTS devices. Simulation results on IEEE 14-Bus and 30-

Bus systems are provided to illustrate the performance of the algorithm as a

state estimator in the presence of bad data and also as a solver for determining

UPFC settings for controlling power flows in a power system.

Qifeng et al (2000) have proposed an efficient method suitable for

state estimation embedded with FACTS devices and Multi-Terminal DC

(MTDC) systems, called as the improved sequential method. The proposed

approach is sequential in nature and exhibits good convergence characteristics

compared to conventional techniques. The variables and measurement

equations of the FACTS and MTDC systems related to the problem

formulation are discussed. FACTS devices and MTDC systems can be

included in the existing state estimation algorithms and hence the model

reduces the software development efforts and maintenance costs. Since the

method is developed from the WLS gain matrix, it maintains good

convergence property as the conventional WLS method. The effectiveness of

the algorithm has been demonstrated using test systems and the results are

compared with the other state estimators.

44

The dynamic behaviour of two different FACTS devices namely

the Interline Power-Flow Controller and the Unified Power-Flow Controller

have been discussed by Zhang and Yokoyama (2006). The small signal

model of the Interline Power-Flow Controller is developed and validated

using detailed electromagnetic transients simulation. Using this validated model,

the damping capabilities of the IPFC and the UPFC are compared and

rationalized. The IPFC’s two series branches in contrast to the UPFC's single

series branch permit more opportunities for network segmentation. Hence, the

IPFC is found to have greater potential for improving the system's dynamic

performance.

With the FACTS devices incorporated, the power flow in the

interconnected power systems can be controlled flexibly. A model for state

estimation with IPFC is introduced with power injections and the effect of

IPFC on the power flow is transferred to the lines which are connected to it.

The Interline Power-Flow Controller employs a number of dc to ac inverters

in order to offer series compensation for each line. As a new concept for the

compensation and effective power flow management, it addresses the target

of compensating a number of transmission lines at a given substation.

Generally, the Interline Power-Flow Controller is a combination of

two or more independently controllable static synchronous series

compensators (SSSC) which are solid-state voltage source converters which

inject an almost sinusoidal voltage at variable magnitude and couples via a

common DC link as shown in Figure 2.4. Conventionally, series capacitive

compensation fixed, thyristor controlled or SSSC based IPFC is employed to

increase the transmittable real power over a given line and to balance the

loading of a normally encountered multi-line transmission system. They are

controlled to provide a capability to directly transfer independent real power

45

between the compensated lines while maintaining the desired distribution of

reactive flow in the line (Zhang and Yokoyama 2006).

Figure 2.4 Simplified Schematic of the IPFC Model

In the simplified schematic of IPFC model, each compensating

inverters are linked together at their dc terminals. With this scheme, in

addition to providing series reactive compensation, any inverter can be

controlled to supply real power to the common dc link from its own

transmission line.

Thus, an overall surplus power can be transferred from the

underutilized lines which can be used by other lines for real power

compensation. Evidently, this arrangement maintains the overall power balance

at the common dc terminal by appropriate control action. The injection power

flow IPFC model is based on the representation of IPFC in steady-state

conditions by two voltage sources, each in series with a reactance. A

conventional Newton Raphson power flow program has been modified in

order to incorporate the power injection IPFC model. The simplest IPFC

consists of two back-to-back dc to ac converters, which in a substation are

connected in series with two transmission lines via transformers and the dc

terminals of the converters are connected together via a common dc link.

46

An IPFC can be represented in steady-state conditions by two

voltage sources representing fundamental components of output voltage

waveforms of the two converters and impedances being the leakage reactance

of the two coupling transformers. In the two voltage source model both the

voltage sources, Vser are controllable in both magnitudes and phase angles.

Vser is defined as:

Vser = r Vi e (2.10)

The values of r and are defined within specified limits given by

equation (2.11). The variable r represents certain percent of the voltage

magnitude Vi at bus i.

0 r rmax and 0 2 (2.11)

According to the operating principle of the IPFC, the operating

constraint representing the active power exchange (Pser) among the converters

via the common dc link is given by:

Pser2 = - Pser1 (2.12)

The above equality is valid when the losses are neglected. If the

IPFC is located between nodes i, j and k in a power system, the admittance

matrix is modified by adding a reactance equivalent to Xser between nodes i

and j and nodes i and k. The Jacobian matrix is modified by addition of

appropriate injection powers. The detailed solution steps of the proposed

algorithm can be summarized as:

Step 1: Input system data and telemeter measurements

Step 2: Set iteration count k = 0

47

Step 3: Calculate system measurements

Step 4: Initialize the state vector v(0)

, e(0)

Step 5: Compute Jacobin matrix H(x(k)

) with IPFC

Step 6: Obtain V(k+1)

and(k+1) .

V(k+1)

V(k)

V(k+1)

,(k+1) (k) (k+1)

Step7: Check for convergence.

If max {| V(k+1)| , | (k+1)|} > €, set k = k + 1, go to Step 4

else go to Step 8

Step 8: Print results.

Anderson and Fouad 9-Bus system shown in Figure 2.5 has been

considered to find the estimate of the state of the system with the IPFC

incorporated in the buses 4, 5, and 6.

Figure 2.5 Anderson Fouad 9-Bus System with IPFC

The estimates of the state of the system with and without IPFC are

given in Table 2.3. The solution is found to be more accurate, the computational

effort is reduced and there is an improvement in the voltage profile of the

system considered. The tolerance assumed for convergence is 104.

48

Table 2.3 State Estimation Results for 9-Bus System

Bus

No.

Without IPFC With IPFC

V/pu (°) V/pu (°)

1 1.0400 0 1.0400 0

2 1.0250 9.280 1.0256 8.817

3 1.0250 4.665 1.0250 4.043

4 1.0258 -2.217 1.0259 -2.217

5 0.9956 -3.989 0.9972 -4.306

6 1.0127 -3.687 1.0129 -4.464

7 1.0258 3.720 1.0254 3.254

8 1.0159 0.728 1.0155 0.195

9 1.0324 1.967 1.0321 1.345

The algorithm retains good convergence property as the traditional

WLS method and it possesses the main merit of extending the state estimation

algorithm including the effects of Interline Power-Flow Controller.

2.6 CONCLUSION

The significance of state estimation for proper monitoring and

control of power system operations is reviewed. This chapter is dealt with the

study and application of phasor measurements in power system state

estimation. The importance of phasor measurements in state estimation has

been envisaged. The measurements from PMU are proven to increase the

observability of power systems by strategic placement of minimal number of

phasor measurement units.

Due to the increase in the complex data to be handled in a power

system there is a need for flexible and expandable information integration

environment such that the interaction with different power utilities can be

49

done effectively and efficiently. The deregulation policies, ever increasing

load demand and changing conditions in the topological structure of a power

system have resulted in a requirement for integration of heterogeneous legacy

power system applications as well as new applications inside and outside an

electric utility organization. Thus the architectural model to be proposed

needs to allow pluging-in of new services or upgrading existing services in a

granular fashion to address the new requirements.

The utilities tend to adopt on-line based approach for power system

analysis. With this approach a real time estimation of the system state

variables are continuously updated by distributed data measurements and

adopted as reference for the solution of system state equations. This analysis

if integrated with advanced tool for dynamic loadability assessment of power

equipments, leads to an improvement of the infrastructures allowing system

operators to provide more realistic operational guidance in planning, preventive

and corrective actions aimed to mitigate the effect of critical contingencies.

Information integration and interoperability are two serious

problems in distributed systems, which mainly include communication

networks and communication protocols. For this purpose the International

Electro-technical Committee (IEC) standards are proposed. Some of these

standard protocols can be used over IP-based WANs. However, future power

systems, which contain many renewable energy sources in all voltage levels,

can employ the Internet / Intranet WAN for both control and telemeter. There

are several standards available which can be applied for the control and telemeter

over Internet / Intranet WAN. The standard protocols are to be compared and

the factors for choosing the right protocol for particular purpose are to be

analyzed. In the next chapter, a generalized service oriented model, which

will be customized exclusive for power system applications, is presented.