please scroll down for article

This article was downloaded by: [INFLIBNET India Order] On: 4 November 2008 Access details: Access Details: [subscription number 792843137] Publisher Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK

Electric Power Components and Systems Publication details, including instructions for authors and subscription information: http://www.informaworld.com/smpp/title~content=t713399721

Electrical Power System State Estimation Meter Placement—A Comparative Survey Report L. Ramesh a; S. P. Choudhury b; S. Chowdhury c; P. A. Crossley d a Department of Electrical and Electronics Engineering, Dr. M. G. R. University, Chennai, India b Department of Electrical Engineering, Jadavpur University, Kolkota, India c Department of Electrical Engineering, Women's Polytechnique, Kolkota, India d Department of Electrical and Electronic Engineering, The University of Manchester, United Kingdom Online Publication Date: 01 October 2008

To cite this Article Ramesh, L., Choudhury, S. P., Chowdhury, S. and Crossley, P. A.(2008)'Electrical Power System State Estimation

Meter Placement—A Comparative Survey Report',Electric Power Components and Systems,36:10,1115 — 1129 To link to this Article: DOI: 10.1080/15325000802046918 URL: http://dx.doi.org/10.1080/15325000802046918

PLEASE SCROLL DOWN FOR ARTICLE Full terms and conditions of use: http://www.informaworld.com/terms-and-conditions-of-access.pdf This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, re-distribution, re-selling, loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.

Electric Power Components and Systems, 36:1115–1129, 2008 Copyright © Taylor & Francis Group, LLC ISSN: 1532-5008 print/1532-5016 online DOI: 10.1080/15325000802046918

Electrical Power System State Estimation Meter Placement—A Comparative Survey Report L. RAMESH,1 S. P. CHOUDHURY,2 S. CHOWDHURY,3 and P. A. CROSSLEY4

Downloaded By: [INFLIBNET India Order] At: 08:08 4 November 2008

1

Department of Electrical and Electronics Engineering, Dr. M. G. R. University, Chennai, India 2 Department of Electrical Engineering, Jadavpur University, Kolkota, India 3 Department of Electrical Engineering, Women’s Polytechnique, Kolkota, India 4 Department of Electrical and Electronic Engineering, The University of Manchester, United Kingdom Abstract The aim of this article is to provide a comprehensive survey on meter placement for monitoring a power system. The different applications of meter placement, such as transmission, distribution, load, harmonics, and voltage sags, are discussed. Algorithms that are used for power system state estimation optimum meter placement are discussed in detail. Comparative graphs are plotted for quantifying the research done in these areas. The authors are of the opinion that the scope of pursuing research in the area of state estimation meter placement is quite state-of-the-art and timely. Keywords placement

state estimation, neural network, tabu search, genetic algorithm, meter

1. Introduction State estimation (SE) is one of the main tools in real-time operation and control of modern power systems. Prof. Schweppe, the leading researcher of the power systems engineering group at MIT, was the first to propose and develop the idea of SE for power systems monitoring and control. The quality of the SE solutions is also highly dependent on the measurement configuration for a given network topology. The location and types of measurements should allow the state variable of the entire network to be calculated uniquely as well as providing enough redundancy to detect and eliminate bad data in the observable part of the network. The problem of choosing meters and their locations for optimal monitoring of a power system is referred to as the meter placement problem. In choosing the types and locations of new measurements, there may be several different concerns, such as maintaining a desired accuracy level for the state estimates obtained, maintaining an observable network when one or more measurements are lost, maintaining an observable network when one or more network branches are Received 11 May 2007; accepted 4 February 2008. Address correspondence to L. Ramesh, Dept. of Electrical and Electronics Engineering, Dr. M. G. R. University, Maduravoyal, Chennai, Tamilnadu, 600 095, India. E-mail: lramesh@ theiet.org or [email protected]

1115

1116

L. Ramesh et al.

disconnected, being able to detect and identify bad data in one or more measurements, and minimizing the cost of meters and remote terminal units (RTUs). In this article, meter placement for power system state estimation (PSSE), distribution systems, load estimation, harmonic estimation, phasor measurement units (PMUs), and voltage sags are discussed. In Section 2, different algorithms (genetic algorithm [GA], simulated annealing [SA], artificial neural network [ANN], integer programming [IP], linear programming [LP], tabu search [TS], sparse triangular factorization [STF]) that are used for PSSE meter placement are discussed in detail. In Section 3, the meter placement problem, formation of distribution systems, load estimation, harmonic estimation, and PMU and voltage sag estimation are explained. Section 4 contains a comparative study of the literature published with respect to number of years, and Section 5 concludes with a future scope of the research.


2. PSSE Meter Placement Algorithms 2.1. Addition and Elimination Algorithm An algorithm of optimal meter placement for the SE, was presented in [1], which minimizes the total investment cost subject to a constraint of SE accuracy. The optimal meter placement problem can be formulated by an optimization approach to minimize an appropriate performance index (PI) to certain system constraints. The PI is established in probabilistic consideration of measurement failures. In the analysis of the PI of a state estimator, it is assumed that the system adopts the least square error estimator in common use. The PI of the state estimator can be evaluated as J D EŒ.y

y/ O t w.y

y/; O

where w is weight matrix for interesting quantities y. The optimal meter placement problem can be formulated with the use of the PI as Minimize

m X

Ci ;

where Ci is the installation cost for measurement

i D1

Subject to

J D EŒ.y

y/ O t w.y

y/: O

The algorithm for the proposed method is as follows. 1. Establish an observable measurement system by an intuitive method. 2. Calculate the expectation of the PI for the measurement system. If the PI is greater than the critical value, go to step 3; otherwise, go to step 4. 3. Add a meter or a group of meters to the measurement system by applying the addition algorithm. Then, go to step 5. 4. Eliminate a meter or group of meters to the measurement system by applying the elimination algorithm. 5. Check the cycling of the algorithm and the number of iterations. If cycling occurs, or the number of iteration is greater than a specified number, terminate the algorithm; otherwise, go to step 2.

Power System State Estimation Meter Placement

1117

The proposed method is adopted for the IEEE 14-bus system and produced an optimal measurement system design that guarantees the observability for any single outage. The critical redundancy rate and the investment cost may, however, be reduced slightly. The above algorithm has the limitation of not being suitable for too many measurement failures due to excessive computation time. 2.2.

Covariance Matrix Algorithm


A meter placement algorithm [2], which uses the variance of the SE errors as indices, was proposed to enhance the accuracy and robustness of the SE solutions. The algorithm provides a list of buses with local redundancy in any observable area of a power network and a list of candidates to reduce the SE covariance. The objective function to identify the location of additional measurements is the variance of the SE errors defined as a covariance matrix. The covariance matrix (C ) is inverse of gain matrix C D .H t R 1 H / 1 ; where H is a Jacobian matrix, and R is a measurement covariance. Leverage points are situated far from the majority of the data in the factor space of regression defined by the measurement Jacobian. The leverage point is checked by sensitivity matrix S as S D H.H t R 1 H / 1 H t R 1 : The step-by-step description of the proposed algorithm follows. 1. Read in the input data that include the network data and real-time measurements. 2. Perform the observability analysis and find all of the observable islands of the network. 3. Calculate the diagonal entries of the covariance matrix. 4. Determine a list of buses with low local redundancy. 5. For a bus on the list determined at step 4, find all the candidate measurements. 6. Calculate the new covariance matrix for each of the candidate measurements. 7. Check if the candidate measurement is a leverage point. 8. Check if all of the buses on the list have already been analyzed. If so, include the measurements chosen by the user to the original measurement set and go to step 2; if not, go to step 5. The algorithm explained above has been tested using the IEEE 14-, 30-, 57-, and 118-bus systems, and it shows that the addition of the measurements suggested improves the SE solutions. It determines the numerically observable islands, ensuring that each island has a solvable and unique solution and a list of candidate measurements for each state variable that has poor accuracy. The cost of the meter is not considered in this article, and poor quality for the state variable of the new boundary buses due to lack of sufficient measurements are the limitations. 2.3.

Neural Network Algorithm

An ANN-aided design approach for the determination of the measurement scheme, which was to be employed for an on-line PSSE, was presented in [3], where the learning ability of a neural network to determine the PSSE measurement scheme that meets a prespecified

1118

L. Ramesh et al.


SE PI was demonstrated. The PI of the SE can be evaluated via the covariance matrix of the error of the estimated state vector and computation time, which are important for on-line monitoring and control. Based on these PIs, the inputs to the proposed ANN will be the estimated state error variance and running time. The assumptions made for modeling output layer are bus P -Q power in pair. Line P -Q power in pair, all available meters, line current, and phase angle are not considered. The structure of the proposed ANN is as follows. 1. The first layer (the input layer) comprises a number of neurons equal to Ns C 1, where Ns is the number of system states, representing the design objectives and required accuracy level of the SE solution and running time. 2. The second layer (the hidden layer) contains a number of neurons and is normally determined through experimental comparisons, depending on the system size, number of I/O variables, and number of I/O training patterns. 3. In the third layer (the output layer), three pieces of information are presented, namely the required number of measurements, the type of meters employed, and the meter location. According to the assumptions made in Section 3, two distinct models for the output layer are implemented and tested in this paper. A simple 6-bus power system is considered for testing the method presented in this article. Using the summarized training algorithm, a set of 90 I/O patterns is generated. Out of these available 90 patterns, a sub-set of 30 I/O patterns is used for training the ANN. A smaller, but different, subset of 5 I/O patterns is used for testing the ANN after being trained. After several experimentations, a satisfactory performance is achieved with two hidden layers and ten neurons in each hidden layer. Finally, for a pre-specified accuracy level of 0.005 for all estimated system states and a 1 p.u. running time, the recommended metering system for the 6-bus system is formulated. The limitation in this method is, it will not detect for bad data and system topology. 2.4. LP Algorithm A method for designing measurement systems that will not only make the systems observable but also will maintain observability against loss of network branches was presented in [4]. This is accomplished in two steps. The first step involves an LPbased measurement placement method with the objective to find a minimum number of additional measurements to make the system barely observable but vulnerable to branch outages. In the second step, an optimal number and type of measurements are found and appended to the measurement set to ensure observability against single-branch outages. The objective function for choosing a minimal set of essential measurements is Minimize Subjected to

CTy Ay D z

and

y 0;

where C D Œw1 ; w2; : : : ; wm , where and w is the weight for the i th measurement; A D ŒH j H jI jI j I , where I is the identity matrix, and H is a Jacobian matrix; z is the measurement vector; and y is the phase-angle mismatch vector matrix.


1119

The steps of the procedure are outlined below. 1. Assign very high confidence weights to the present measurement and include all possible candidate measurements to make a complete measurement set. 2. Compute the projection statistics (PS) by chi-square distribution. 3. Assign a weight for the candidate measurements. 4. Solve the LP problem using these weight assignments. Those measurements that are accepted by the least absolute value estimator will be the essential measurements.


The optimal meter placement problem is formulated as a binary IP problem as Minimize

ST x

Subject to

Ax 1;

xi D 1 or 0;

where S is the normalized installation cost, A is the matrix that relates the branches to the candidate measurements, and xi is the binary solution vector. The proposed LP algorithm is tested for IEEE 30- and 57-bus systems. 2.5.

TS Algorithm

In [5], the focus was on meter placement to enhance topological observability, and the relationship between meter placement and network configurations was discussed. Mathematically, the problem results in complicated combinatorial optimization. To sufficiently overcome this problem, a TS-based method was presented. The idea of a TS is based on the hill-climbing method, which is one of local search. The problem is F D min F .x/;

x 2 X;

where F is the cost function, and X is the set of feasible solutions. The algorithm is summarized as follows. 1. Set initial condition (x0 and iteration count k D 0 to tabu length (TL)). 2. Create neighborhood around solution x0 , where some attributes are placed into TL. 3. Set k D k C 1 and evaluate the minimum (xk ) in the neighborhood. 4. Stop if xk is not updated; otherwise, go to step 2. The proposed method is applied to IEEE 57- and 118-node systems. The redundancy is set to 1.31 and 1.45 for the 57- and 118-node systems, respectively. As a result, there exist 1:426 106 and 4:238 1014 combinations for the 57- and 118-node systems, respectively. To examine the performance of TS, this article makes a comparison of TS, SA, and the GA in terms of solution accuracy and computational effort. The test results indicated that standard deviation for cost function is zero for TS and fairly larger in the GA and SA. The CPU time for TS is 1:037 102 , which is 4.34 times faster than SA and the GA. 2.6.

IP and STF Algorithm

A systematic procedure by which measurement systems can be optimally upgraded was presented in [6]. The proposed procedure yields a measurement configuration that can

1120

L. Ramesh et al.

withstand any single-branch outage or loss of single measurement without losing network observability. It is a numerical method based on the measurement Jacobian and STF, making its implementation easy in existing state estimators. The problem is proposed to be solved in two stages.


1. Selecting candidates by modified Jacobian and STF. 0 mod 1 He { n, essential B C mod H D @ A { m n, redundant; Hemod

where H mod is the modified Jacobian with outage of tree branch k-j , m is the total number of measurements that are installed or likely to be installed. Triangular factorization of H mod with a pivoting row that is restricted to the first n essential measurement rows will yield a zero pivot at the last, nth diagonal of Hemod . This pivot will then be selected from the redundant measurements. Any one of these redundant smeasurement will be sufficient to restore observability in case of the outage of the considered branch k-j . 2. Optimal selection. The objective of the optimal selection procedure is to minimize the overall cost of this measurement system upgrade while making sure that all contingencies are properly taken into account. The following integer optimization problem will be then solved to obtain the optimal selection: Minimize

CT : X

Subject to

A : X b;

where Aij D

(

X.i / D

(

1

if measurement j is a candidate for contingency i

0

otherwise,

1

if measurement I is selected

0

otherwise.

The 30-bus example with its measurement configuration is considered to illustrate this method. The optimal measurement set for this system is determined to include injection measurements at buses 6, 9, and 11 and flow measurement in branch 27–29. Hence, inclusion of these additional measurements will guarantee network observability during any single-line outage or loss of any single measurement in the 30-bus system. 2.7. SA Algorithm Power system state estimators usually require a set of redundant measurements, which are appropriately chosen according to the type, number, and location of the measurement point in the supervised electric network. This article presents a metaheuristics-based methodology to solve the problem of meter placement for PSSE. A simple objective function is proposed, which takes into account the distribution and installation costs of a measuring device and whose minimization is sought via SA. The meter placement


1121

problem is achieved by the establishment of a cost function to be minimized, considering requisites such as observability, reliability, quality, and contingency. In this article, the last two requisites are not taken into account. (a) Cost function. The objective of the optimal measurement system selection is to minimize the overall cost of this system installation while making sure that the measurements are topologically well distributed so as to satisfy the observability requisite. Minimize

C D

X


1 XX C S C Sk S Nk 2 k

where K and are the measurement (flow or injection) numbers, C is the installation cost of the th measurement, ( 1 if the th measurement is selected S is measurement state ; 1 otherwise and Nk

is the neighborhood matrix element ( 1 if measurement k and are neighbors 0 otherwise

:

(b) Observability requisite. The requisite is satisfied if the gain matrix G D ŒH t R H of a candidate measurement system is non-singular. (c) Reliability requisite. A measurement system should have sufficient redundancy and be uniformly spread to assure the capability of detecting and identifying bad data. Two redundancy levels can be established as follows Level 0 is r .i / D z.i /

z 1 .i / D 0,

Level 1 is rN .i /=rN .j / D 1. Implementation of SA starts from an initial configuration; then new configuration are proposed through local changes, called moves, and accepted with the probability ( 1 if C.x/ C ; P D exp.C C.x/=T / if C.x/ > C where C and C.x/ are the costs of the current and proposed configurations, respectively, and T is the temperature. The algorithm is run until a stopping condition is reached, typically a minimum temperature value, specified as part of the annealing schedule. The proposed method is tested for the IEEE 30-bus system, in terms of the mean values obtained in 15 implementations of the algorithm and greater reliability at lower cost. The average computation time is 1770 sec for D 0. It proved that a sizeable number of configurations with no critical measurements and sets can be obtained in a short computing time.

1122

L. Ramesh et al.

2.8. GA


A methodology for designing optimal metering systems for real-time power system monitoring, taking into account different topologies that the network may experiment, was presented in [7]. The GA is employed to achieve a trade-off between investment cost and reliability of the SE process under many different topology scenarios. This is done by formulating a fitness function (FF) where the cost of the metering system is minimized, while no critical measurements are allowed in the optimal solution. This objective function can be formulated as Minimize

.Cmet C CRTU /

Subject to

performance requirements;

where Cmet and CRTU represent, respectively, the cost of meters and RTUs to be installed. The performance requirements refer to the SE process. The optimization problem represented above is combinatorial and adequate for the application of global search techniques, such as the GA. The optimization problem can be formulated as Maximize Subjected to

f .x/ g.x/ D 0;

h.x/ 0;

xeS;

where f .x/ is the objective function to be optimized.x/ represents problem equality constraints.x/ represents problem inequality constraints represents the vector of problem variables, and S represents the search space. The proposed methodology discussed in two stages 1. Encoding. The solution of a given optimization problem through the GA technique requires the generation of a successive population of individuals, where each new generated population is better than the previous one. The chromosome elements assume binary values, being equal to 1 when the installation of the corresponding meter is proposed and 0 otherwise. 2. FF. The FF values are needed to guide the search process in a GA. The FF is formulated as FF D Cmet CCRTU C

NT X

Œ.ki Pobs .i //C.NC m .i /PC m .i //C.NmC s .i /PC s .i //;

i D1

where Pobs.i / is the penalty factor applied to the i th non-observable scenario, N T is the number of topologies being considered, ki is condition of the topological scenario, NC m .i / represents the number of critical measurements, PC m .i / is a penalty factor applied when critical measurements are detected, NmC s .i / represents the total number of measurements, and PC s .i / is a penalty factor applied when critical sets are detected. The FF flexibility makes possible to reduce investment costs by partially satisfying the problem constraints. The proposed method is tested with the ELETROPAULO network with 61 buses and 74 branches. The GA chromosome is represented by a vector of


1123

209 genes, where 148 genes are associated with possible power flow measurement locations and 61 genes are associated with possible power injection measurement locations. It has been observed that the best result is obtained with less convergence times.

3. Meter Placement


3.1.

Distribution System Meter Placement

SE is important for the automatic management and control of complex distribution networks with significant distributed generations. SE has been used extensively on transmission systems where, generally, measurements of bus bar voltages and line power flow exist. However, distribution systems normally have only a limited number of measurements. In such systems, additional measurements are expensive, and careful selection of location becomes important. Data requirements for real-time monitoring and control of distribution systems through meter placement were identified in [8]. The main goal of meter placement is determining the number, place, and type of meters that need to be placed on a given feeder, such that the SE with these measurements will have the desired performance. The cost considerations usually limit the number of meters that can be placed on distribution feeders, usually below the minimum needed for SE. To overcome this observability problem, forecasted load data needs to be added as pseudo-measurements. The rule-based meter placement scheme is adapted in this article for identifying meters in distribution feeders. GA-based optimal meter placement methodology for real-time power distribution systems monitoring was presented in [9]. The characteristics of the proposed methodology are codification of the metering system, performance requirements, use of pseudomeasurements, and methodology description. Test results with the IEEE 14-bus system show that the proposed methodology is capable of obtaining optimal metering systems that attend constraints such as network observability and absence of critical measurements. The work in [10] presented a heuristic approach to identify potential points for location of voltage measurements for SE as part of a proposed distribution management system controller. The algorithm formulation for proposed method is discussed below. 1. Select bus bars on which measurements are assumed; run load flow to get V0m . m 2. Change; load randomly to calculate VRand and obtained error function .V0m m 2 VRand / . 3. Check error function for acceptable value. If acceptable, go to step 4; else, go to step 2. 4. Store voltage magnitude at all buses and check for minimum number of voltage set obtained. 5. If minimum number is satisfies, calculate standard deviation and check whether acceptable; else, go to step 2. 6. If voltage deviations are acceptable, end the process; else, go to step 7. 7. Move measurements to higher standard deviation and check for additional measurements. 8. If yes, add additional measurements and go to step 2; else, go to step 2. For this study, a small section of 11-KV overhead lines consisting of 95 busbars with 2 wind farms was used. Simulation results have shown that, in the case studied,

1124

L. Ramesh et al.

the estimator took four to five iterations to converge and was completed in less than a second.


3.2. Harmonic SE Meter Placement Harmonic state estimation (HSE) is a reverse process of harmonic simulation that analyzes the response of a power system to the given injection current sources. The HSE uses the harmonic measurements at selected busbars to identify the location and magnitude of harmonic sources. HSE is capable of providing information on harmonics at locations not monitored. A method based on the GA was proposed to solve the problem of optimal placement of meters for static estimation of harmonic sources in a power system [11]. The performance of the proposed technique has been compared with those of the complete enumeration technique and the sequential technique in four different test systems. The test result concluded that the proposed GA always finds the optimal meter location, while the sequential technique can guarantee only near-optimal solutions. A new HSE algorithm, based on singular-value decomposition (SVD) method, was presented in [12] along with a new solution technique for optimal measurement placement. The normal state equation is X D .H T H / 1 H T Z: The modified SVD for harmonic estimation is X D VW

1

U T Z;

where V and U are orthogonal matrices, M is the possible location, and N is the number of states. The algorithm for optimal harmonic meter placement is 1. Form the measurement matrix with possible location. 2. Each row of H is temporary eliminated one at a time and calculates the condition number of H . 3. The row of H that has minimum condition number is permanently eliminated. 4. When M D N , go to step 5; else, go to step 2. 5. The rest of the M row should be optimal measurement placement. Two test systems are used to test the proposed algorithm, namely the IEEE 14-bus and New Zealand 220-KV interconnected grid. It is found that the algorithm can yield a solution for measurement placement that makes the power system completely observable. 3.3. Voltage-sag Meter Placement Voltage sags are short duration reductions in RMS voltage. As a single event, voltage sag is characteristic by its magnitude and its duration. Voltage-sag indexes can be obtained over all nodes by using stochastic prediction methods. In [13], a meter placement method for voltage-sag monitoring in large transmission systems was presents. An IP-based modeling is proposed for choosing the location of power quality meters. A branchand-bound type algorithm is used to solve the optimization problem.


1125

The optimization problem can be formulated as Minimize Subjected to

.x1C ; x2C ; : : : ; xFp / MRA11 : x1C ; MRA21 : x2C ; : : : ; MRAn1 : xFp b1 ; MRA12 : x1C ; MRA22 : x2C ; : : : ; MRAn2 : xFp b2 ; :: :


MRA1Fp : x1C ; MRA2Fp : x2C ; : : : ; MRAnFp : xFp bFp ; where x is the decision row vector, and MRA (monitor reach area index) gives the number of meters. The problem is a binary integer optimization program, the solution of which minimizes the number of meters subject to the convergence of the entire network. The GA is implemented to explore the solution space. The Colombia 500-KV interconnected system is taken as example for demonstrating the proposed method. 3.4.

Load Estimation Meter Placement

A heuristic method [14] of optimal meter placement for load estimation in distribution systems was presented in this work. The approach can be used to efficiently find the meter location candidates for load estimation, and it has a two-stage approach. In the first stage, meters are placed using a heuristic method. In the second stage, the confidence interval is calculated to determine if the meters give satisfactory results when loads vary between the maximum and minimum. The optimization problem can be formulated as Minimum Subjected to

J D Cost.z/ Error i .z/ ˇ;

PLi

PLi PLi C

QLi

QLi QLi C

;

i D 1; : : : ; k;

where z represents the sets of possible candidates, the measurement scheme represents the upper limit for the errors, PL and QL are the real and reactive loads, respectively, represents the standard deviation of the loads, and k is the number of buses whose loads are estimated by the meter. The proposed method is tested on some sample systems that are straightforward and can handle large distribution systems with only moderate computation requirements. 3.5.

PMU Meter Placement

In recent years, the application of PMUs has been attracting more and more attention in power system security monitoring and control. This is due to the advantages that PMUs can offer real-time synchronized phasor measurements (voltage, current, power, frequency, etc.), contrary to the conventional SCADA measurement devices. The prerequisite for a sufficient and accurate control is the development of an adequate meter placement scheme that can realize the network full observability.

1126

L. Ramesh et al.

A fast analysis method for power system topology observability by optimal PMU placement was presented in [15]. The PMU placement problem is formulated as to minimize the number of PMU installations that are subjected to full network observability and enough redundancy. TS is proposed to solve the combinatorial optimization problem, and a priority list based on heuristic rule is embedded to accelerate optimization. The problem an be formulated as J D Minfmax R.np ; S.np //g np

Subjected to

Obs .np ; S.np // D 1;


where np represents the number of PMUs, S.np / represents the placement set, and Obs represents the observability evaluation function. The algorithm is as follows. 1. 2. 3. 4. 5. 6.

Initialize the PMU placement set and initial number np . Initialize the upper limit and lower limit and set current number. Select current placement using heuristic rule and check for observabilty. If system is observable, set new upper limit and go to step 6; else, go to step 5. Execute TS to generate new solution, check observability and go to step 6. Check diff .max; min/ D 1; if yes, stop the process; else, go to step 2.

The proposed algorithm has been tested for the IEEE 14-bus and New England 39bus systems. It can be seen that the average objective function values decrease along with the PMU placement number, and yet the redundancy performance also deceases.

4. Discussion SE is essential for the monitoring, control, and optimization of a power system. Regardless of the different estimation algorithms, the location, types of measurements, cost of meters, and cost of RTUs are always decisive factors for successful SE. In this article, the authors discussed different types of algorithms used for PSSE meter placement, distribution system meter placement, PMU placement, meter placement for voltage sag, harmonic meter placement, and meter placement for load estimation. A comparison of a number of papers for various years for PSSE meter placement is represented in Figure 1. Meter placement for PSSE started in the year 1975. In total, nine different approaches are discussed for optimal meter placement of PSSE in the past 30 years [16]. System observability and some hybrid methods are also discussed. Huge numbers of works are done in the years between 1999 to 2001, and still the work is continuing with new approaches like distributed generation. A comparison of the number of papers over various years for distribution system meter placement is represented in Figure 2. Distribution system meter placement work started in the year 1994. Only a limited number of algorithms with fewer works have been done in this area, where there is a huge scope for pursuing research work by considering distributed generation. A comparison of the number of papers of various years for PMU meter placement is represented in Figure 3. PMU meter placement work started in year 1990. Currently, more work is going on in this area that gives much better SE performance. More research must be done in this area for optimal operation and control of power system networks.


1127


Figure 1. Comparison of number of papers (with years) for PSSE meter placement.

Figure 2. Comparison of number of papers (with years) for distribution meter placement.

Figure 3. Comparison of number of papers (with years) for PMU placement.

A comparison of the number of algorithms and their CPU processing times for meter placement is represented in Figure 4. Various algorithms (SA, GA, TS, ANN, and one numerical method) are tested with the IEEE 30-bus system. It is seen that TS is better than the others in terms of cost function and average CPU processing time.

1128

L. Ramesh et al.


Figure 4. Comparison of various algorithms with processor times.

The optimum placement of meters for load estimation, harmonic estimation, and voltage-sag estimation are discussed in the last section of the article. More concentration must be given to these areas for security monitoring.

5. Conclusion This article presented a classified list of algorithms for PSSE meter placement covering approximately 30 years of extensive research, and it is a comprehensive survey report on electric PSSE meter placement. The authors welcome discussions on the missing algorithms, if any. To establish an overall idea about the time evolution of the total number of papers per year, three graphs are presented. The authors conclude that the scope of research in the area of meter placement in distribution systems, PMU, load estimation, harmonic estimation, and voltage-sag estimation is quite encouraging and timely.

References 1. Park, Y. M., Moon, Y. H., and Choo, J. B., “Design of reliable measurement system for state estimation,” IEEE Trans. Power Syst., Vol. 3, No. 3, pp. 830–836, 1988. 2. Celik, M. K., and Liu, W. H. E., “A meter placement algorithm for the enhancement of state estimation function in an energy management system,” IEEE PowerTech Conference, pp. 873– 876, 1994. 3. Abbasy, N. H., “Neural network aided design for metering system of power system state estimation,” IEEE CCECE ’96 Conference, pp. 741–744, 1996. 4. Abur, A., and Magnago, F. H., “Optimal meter placement for maintaining observability during single branch outages,” IEEE Trans. Power Syst., Vol. 14, No. 4, pp. 1273–1278, 1999. 5. Mori, H., and Sone, Y., “Tabu search based meter placement for topological observability in power system state estimation,” IEEE Conf., pp. 172–177, 1999. 6. Abur, A., and Mangnago, F. H., “A unified approach to robust meter placement against loss of measurements and branch outages,” IEEE Trans. Power Syst., Vol. 15, No. 3, pp. 945–949, 2000. 7. Souza, J. C. S., Filho, M. B. C., Schilling, M. T., and Capdeville, C., “Optimal metering systems for monitoring power networks under multiple topological scenarios,” IEEE Trans. Power Syst., Vol. 20, No. 4, pp. 1700–1708, 2005.



1129

8. Baran, M. E., Zhu, J., and Kelley, A. W., “Meter placement for real time monitoring of distribution feeders,” IEEE Trans. Power Syst., Vol. 11, pp. 332–338, 1996. 9. Souza, J. C. S., Filho, M. B. C., and Schilling, E. M. M., “Planning metering system for power distribution systems monitoring,” IEEE PowerTech Conference, Italy, 23–26 June 2003. 10. Shafiu, A., Jenkins, N., and Strbac, G., “Measurement location for state estimation of distribution networks with generation,” IEE Proc. Generat. Transm. Distrib., Vol. 152, No. 2, 2005. 11. Kumar, A., and Das, B., “Genetic algorithm based meter placement for static estimation of harmonic sources,” IEEE Trans. Power Delivery, Vol. 20, No. 2, pp. 1088–1096, 2005. 12. Madtharad, C., Premrudeepreechacharn, S., Watson, N. R., and Udom, R. S., “An optimal measurement placement method for power system harmonic state estimation,” IEEE Trans. Power Delivery, Vol. 20, No. 2, pp. 1514–1521, 2005. 13. Olguin, G., Vuinovich, F., and Bollen, M. H. J., “An optimal monitoring program for obtaining voltage sag system indexes,” IEEE Trans. Power Syst., Vol. 1, pp. 1–8, 2005. 14. Liu, H., Yu, D., and Chiang, H. D., “A heuristic meter placement method for load estimation,” IEEE Trans. Power Syst., Vol. 17, No. 3, pp. 913–917, 2002. 15. Peng, J., Sun, Y., and Wang, H. F., “Optimal PMU placement for placement for full network observability using tabu search algorithm,” Elect. Power Energy Syst., pp. 223–231, 2006. 16. Filho, M. B. C., Silva, A. M. L., and Falcao, D. M., “Bibliography on power system state estimation,” IEEE Trans. Power Syst., Vol. 5, No. 3, pp. 950–958, 1990. 17. Baran, M. E., Zhu, J., Zhu, H., and Garren, K. E., “A meter place method for state estimation,” IEEE Trans. Power Syst., Vol. 10, No. 3, pp. 1704–1710, 1995. 18. Antonio, A.B., Torreao, J.R.A., and Filho, M.B.D.C., “Meter placement for power system state estimation using simulated annealing,” IEEE Conference, Portugal, 2001. 19. Yang, V.C.X., Miu, K., and Nwankpa, C.O., “Instrumentation and measurement of a power distribution system laboratory for meter placement and network reconfiguration studies,” IEEE Trans. Instrument. Measur., Vol. 56, No. 4, August 2007.