modeling unknown circuit breakers

Papcr accepted for prcscntation at PPT 2001 200 1 IEEE Porto Power Tech Conference IOth -13Ih Septcrnber, Porto, Portugal

Modeling Unknown Circuit Breakers in Generalized State Estimators

Antonio de la Villa J a h , Antonio Gbmez Expbsito

Abstmct- Modeling unknown circuit breakers in state estimation by adding their power flows t o the state vector leads t o estimated values which do not necessarily reflect feasible statuses. In this paper, this problem is overcome by adding two equality constraints so that the state estimator can only converge t o either of the two mutually exclusive statuses.

Keywords- Circuit Breaker Models, Generalized State Es- timators.

I. INTRODUCTION

TATE estimators make use of measurement redun- S dancy to obtain the “best” state vector. Subsequent analysis of measurement residuals allows detection and identification of bad data in the measurement set.

In conventional estimators the Topology Processor (TP) program builds a bus-branch model using circuit breaker (CB) information and network connectivity data [ll]. Ho- wever, errors in CB statuses may lead the T P to generate an incorrect network model. Such topology errors, in turn, give rise to large residuals in adjacent measurements [3],

More recently, the so-called generalized estimators [13], [2] perform a detailed modeling (bus section/ switch level) of suspected substations in which all branches are included. The objective is to be able to detect and identify topology errors which, otherwise, would appear as several interac- ting bad data. An exclusion error [12] arises when a line actually in service is deemed as open. The opposite, i.e., line disconnected apparently closed, is termed an inclusion error. Similar splitting/merging errors are posible for CBs connecting bus sections. In order to achieve this enhanced performance the state vector is augmented with power flows through all CBs included in the model and additional constraints representing the status of CBs are enforced [7], [SI, [9]. The normalized residuals and Lagrange multipliers provided by the generalized state estimator can then be used to detect and, if redundancy permits, identify topo-

Any series branch (line/tranformer) whose edge CBs are assumed to be open is excluded from the model in conventional state estimators, but should be handled by generalized state estimators. Sometimes, the status of a branch is unknown because the information pertaining to its asso- ciated CBs is missing or ambiguous. When this happens, additional checks based on adjacent measurements and CB statuses are performed a priori by the TP in conventional

[161.

logy errors PI , [41, [io], PI.

A. Villa and A. G6mez are with the Department of Electrical Engi- neering, University of Sevilla, Sevilla, Spain. Email: avillaOesi.us.es, exposi toQcica.es.

estimators in order to reach a conclusion on the most plau- sible branch status. This extra logic is unnecessary if the power flows through the unknown branch are added to the state vector, but then the local redundancy deteriorates as no new information compensates for these additional variables.

The customary two-stage procedure, in which a standard state estimator is first run and then suspected substations are modeled in detail, is not always successful, particularly in the presence of exclusion errors. This has led some re- searches to develop alternative methods [14], [15], [SI intended somewhat to reinforce the performance of conventional TP. The goal under this approach is to determine, as ac- curately as possible, the actual network topology before running the state estimator, for which the past history and approximate linear models are useful.

11. CIRCUIT BREAKER MODELING

The status of a circuit breaker (CB) connected between bus sections i and j can be modeled by adding the power flows Pij, Q i j to the state vector [8], [2]. If the CB is assumed open, then the constraints

Pij = 0

Q i j = 0

should be added to the model, whereas

must be enforced when it is assumed closed. The advan- tage of doing so is that bad data detection and identification techniques can be applied to the augmented model by means of the normalized multipliers [5], [4]. This way, the risk for a hidden topology error to appear as several wrong measurements is prevented.

No constraints are imposed, however, when there is no information about the CB status. In such cases, owing to measurement errors, the estimated power flow through an open CB and the estimated voltage drop across a closed CB are not exactly zero. This extra degree of freedom (i.e., decreased redundancy) leads to less accurate estimated measurements.

0-7803-7 139-9/0 1/$10.00 0200 I IEEE ~~~ ~~

Magnitude

P Flow 18-5 Q Flow 18-5 P Flow 19-2 Q Flow 19-2 P Inject. 15 Q Inject. 15 P Inject. 16 Q Inject. 16

TABLE I CASE 1: MEASUREMENTS

Measurements Exact Noisy 1,13261 1,15339 0,05030 0,04530 0.78490 0.75881

-0,09739 -0,09602 1.13261 1.14257 0,05029 0,04864 0.78490 0.81700

-0,09739 -0,10673

c l 1 I Open

-6 Unknown

Fig. 1. Substation example

111. PROPOSED TECHNIQUE

The key idea is to enforce the following two constraints for every unknown CB.

This way, the state estimator is forced to converge to either of the two mutually exclusive CB statuses, avoiding the "almost" closedlopen status that would otherwise result. When building the Jacobian, the following new terms

must be accomodated:

These terms are either null or very small at flat start, which means that they are useful only after the first iteration.

Note that the status of a CB forming a loop with closed CB's is irrelevant. The same happens with a CB belonging to a cut-set where the remaining CB's are open. In such cases, there is no need to add extra variables and constraints.

Iv. TEST RESULTS

The proposed method has been tested by modeling in detail several substations of the IEEE l4bus network. R e sults corresponding to substation 1, modeled as shown in figure 1, will be presented.

Note that, in addition to the original bus 1, buses 15 to 19 must be modeled in order to be able to check for topology errors. The six resulting buses contrast with the two electrical nodes generated by conventional Topology Processors if the unknown CB is finally labeled as open.

The set of measurements comprises all bus voltages and injections plus the power flow at one edge of all lines.

Two cases are considered.

TABLE I1 CASE 1: ESTIMATED VALUES

Magnitude Estimated Values Conv. I ProDosed


0,04358 0.76808

1.12816 0,05036 0,80772

-0,09799

1,14798 0,04697 0.78790

1.14798 0,04697 0.78790

-0,10138

-0,10138

A. Case 1: Unknown CB actually open.

Gaussian noise is added to exact measurements obtained from a load flow. Tables I and I1 show the exact and noisy power measurements related with substation 1 as well as the estimated values when the conventional approach is adopted and when the proposed constraints are enforced.

Table I11 shows the estimated values corresponding to the state variables related with CB 15-16. Note that, when the two constraints are not employed, the power flow across CB 15-16 is not null.

Obviously the results depend on the accuracy of avai- lable measurements. In order to show this influence, the experiment is repeated 200 times for different accuracy le- vels and the results corresponding to P15-16 are shown, in the form of histograms, in figures 2 and 3.

In all cases, for the same measurement values, the estimated value of P15-16 is null when the proposed constraints are enforced after the second iteration.

These results confirm that using the proposed constraints allows accurate identification of the CB status, which may not be clearly defined otherwise.

Figure 4 represents the average error of the estimated measurements versus the input measurement error, for the set contained in table I and different accuracy classes. In turn, every point in the diagram is the average of the 200 experiments, and the relative errors refer to full scales of 1.2 P.u., 2 p.u. and 0.2 p.u. for voltage, active and readi- ve power measurements respectively. Clearly, the filtering

60

50

40

.g - g30- n

t

TABLE 111 CASE 1: STATE VARIABLES RELATED TO CIRCUIT BREAKER 15-16

-

-

-

z.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 Active power flow

Magnitude


Fig. 2. Flow p1&16 histogram with 0.8 % mean measurement error

Measurements Exact Noisy 0,75507 0,75467 0,03353 0,03212 1,56979 1,65770

-0,19478 -0,18813 0,46497 0,46906

-0,03225 -0,03331 1,85989 1,93596

-0,12900 -0,14137

Active I)owerfIow

Fig. 3. Flow P15-16 histogram with 3 % mean measurement error

capability of the state estimator is enhanced when the constraints are added.

B. Case 2: Unknown CB actually closed

A new set of measurements, compatible with the closed status, is obtained. Table IV and V are the counterpart of tables I and I1 for this case.

Table VI shows that the voltage drop across CB 15-16 is not null when the two constraints are not employed, leading to different power flow values.

The same set of 200 experiments discussed in case 1 is performed for this case. Figure 5 is the counterpart of figure 4. Again, the noise filtering capability is improved when the proposed constraints are added, and the other conclusions of case 1 remain valid.

Method I Conv. 1 Proposed

0 0.5 1 1,5 2 2.5 3 3,5

46 Measurement error

+ Conventional --c With constraints

Fig. 4. Case 1: Estimated measurement error

V. CONCLUSIONS When doubtful circuit breakers are included in the state

estimation, the measurement noise leads to estimated statuses which are not fully compatible with the true status. In other words, the power flow (voltage drop) through open (closed) devices is not null.

Two quadratic constrains are proposed in this paper to prevent this problem. Experiments show that more accurate results are obtained when the proposed technique is employed, particularly when the local redundancy is low. In the presence of severe bad data, a few cases have been detected in which the wrong status is reached or the active/reactive submodels converge to different statuses. This

TABLE V CASE 2: ESTIMATED VALUES

Magnitude


Estimated Values Conv. 0,73599 0,02725 1,55619

0,45086

1,84132

-0,19301

-0,02946

-0,13630

Proposed 0,74336 0,03214 1,54906

0,45090

1,84153

-0,19637

-0,02880

-0,13543

TABLE VI CASE 2: STATE VARIABLES RELATED TO CIRCUIT BREAKER 15-16

I Method I Conv. I Proposed I

has nothing to do, however, with the constraints enforced, as they are only intended to more precisely define the state to which the state estimator is anyway converging after two iterations.

REFERENCES [1] A. Abur, H. Kim, and M. Celik, “Identifying the Unknown Cir-

cuit Breaker Statuses in Power Networks”, IEEE Transactions on Power Systems, Vol. 10, No. 4, pp. 2029-2037, August 1998.

[2] 0. Alsac, N. Vempati, B. Stott, and A. Monticelli, “Generalized State Estimation”, IEEE Transactions on Power Systems, Vol. 13, No. 3, pp. 1069-1075, August 1998.

[3] K.A. Clements, and P. W. Davis, “Detection and Identification of Topology Errors in Electric Power Systems”, IEEE Transactions on Power Systems, Vol. 3, No. 4, pp. 1748-1753, November 1988.

[4] K.A. Clements, and A. Simoes Costa, “Topologv Error Identifica-

0 1 2 3 4 5

% Measurement error

tion Using Normalized Lagrange Multipliers”, IEEE Transactions on Power Systems, Vol. 13, No. 2, pp. 347-353, May 1998.

[5] A. Gjelsvik, “The Significance of the Lagrange Multipliers in WLS State Estimation with Equality Constraints”, Proceedings PSCC, Vol. 11, pp. 619-625, Avignon, August-September 1993.

[6] Mili L., Steeno G . , Dobraca F., French D. “A Robust Estima- tion Method for Topology Error Identification”. IEEE 7tnns. on Power Systems, Vol. 14, No. 4, pp. 1469-1476, Nov 1999.

[7] A. Monticelli, “Modeling Circuit Breakers in Weighted Least Squares State Estimation”, IEEE Transactions on Power Systems, Vol. 8, No. 3, pp. 1143-1149, August 1993.

[8] A. Monticelli, “The Impact of Modeling Short Circuit Branches in State Estimation”, IEEE Transactions on Power Systems, Vol. 8, No. 1, pp. 364-370, February 1993.

[9] A. Monticelli, and A. Garcia, “Modeling Zero Impedance Bran- ches in Power System State Estimation”, IEEE Transactions on Power Systems, Vol. 6, No. 4, pp. 1561-1570, November 1991.

[lo] A. Monticelli, “Testing Equality Constraint Hypothesis in Weig- hted Least Squares State Estimation”, Santa Clara, PICA 1999.

[11] M. Prais, and M. Bose, “A Topology Processor that Tracks Net- work Modifications Over Time”, IEEE Transactions on Power Systems, Vol. PWRS-3, No. 3, pp. 992-998, August 1988.

[12] A. Simoes Costa, and J:A. Leao “Identification of Topology Errors in Power System State Estimation”, IEEE Transactions on Power Systems, Vol. 13, No. 2, pp. 347-353, May 1998.

[13] I. W. Slutsker, and S. Mokhtari, “Comprehensive Estimation in Power Systems: State, Parameter and Topology Estimation”, Proc. of the American Power Conference, Vol. 57-1, pp. 149-155, April 1955.

[14] Singh N., Glavitsch H., “Detection and Identification of Topo- logical Errors in Online Power System Analysis”, IEEE f i n s a c - tions on Power Systems, Vol. 6(1), pp. 324-331, Febrero 1991.

[15] Souza J.C.S., Leite da Silva A.M., Alves da Silva A.P., “On line topology determination and bad data suppression in power system operation using artificial neural networks”. IEEE Zhnsactions on Power Systems, Vol. 13, No. 3, pp. 796-803, Aug. 1998.

[16] F.F. Wu, and W. H. E. Liu, “Detection of Topology Errors by State Estimation”, IEEE Transactions on Power Systems, Vol. 4, No. 1, pp. 176-183, February 1989.

Antonio de la Villa JaGn was born in Riotinto, Spain, in 1960. He received his Electrical Engineering degree from the University of Seville where he is pursuing his Ph.D. degree a t the Dep. of Electrical Engineering. He has been a High-School teacher and he is presently an Assistant Professor at University of Seville. His primary areas of interest are computer methods for power system state estimation problems.

Antonio GBmez ExpBsito was born in Andujar, Spain, in 1957. He received his electrical engineering degrees from the University of Seville. Since 1982 he has been with the Dep. of Electrical Enginee- ring, University of Seville, where he is currently a h l l Professor. His primary areas of interest are sparse matrices, parallel computation, reactive power optimization, state estimation and computer relaying.

+- Conventional --c With constraints

Fig. 5. Case 2: Estimated measurement error

modeling unknown circuit breakers

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