State estimation in control centres

State estimation in control centres T E Dy Liacco The Dy L~acco CorporatTon, 651 Radford Drwe, Cleveland, OH 44143, USA

The provision o f facihttes for system security or the implementation o f security control ts the dlstmgutshmg feature of modern power system control centres. After a rather slow begmnmg, the provision o f security functions has now become virtually a standard o f control centre design. The practical reahzation o f known real-time analytical techtuques for security functzons has been made possible by the successful development o f static state esttmauon methods for onhne application. The need for state estimation is exambwd and the experience of the electric power industry in the development and use of this function is discussed. Keywords" electric power systems + security, state esumatzon, control centres

In the operation of a power system, decision-making generally becomes very difficult during emergency and restorative state conditions or during certain normal state condlt~ons when the security of the system is imperilled Many of these difficulties could be overcome with the aid of a set of monitoring and control functions designed to preserve system security. These functions will be refer~ed to as 'security functions" Over the years there has been a steady increase in the number of power system control centres that have or wall have onhne security functions 1 The analytical approaches to these functions known at present cannot be practically implemented in real tune without a static state estimator as a prerequisite funcuon. While this requirement is well understood by those directly involved in the specification and design of control centres, the value of state estimation to system secumy and therefore to power system operation has not been widely appreciated by others - In many cases not even by those who have the responsxbdlty for the security of the system The purpose of this paper IS to delineate the role of state estimation m the power system operation, particularly as the basis for system security functions In addition, a survey of state estimation methods is presented, not of what has been published in abundance in the technical hterature, but of what Is actually being done (although on a more limited scale) at existing control centres Recmved 3 August 1983

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I. Three views of state estimation The principal strategy used in the operaUon of electric power systems is that of security control in wtuch actions are taken to prevent an impending emergency, to correct an existing emergency, or to recover from an emergency Basic to security control is the knowledge of the 'system state' under steady-state conditions. The most practical way of obtaining this knowledge o f the system state is through state estimation (SE). As defined by Schweppe 2, who was the first to investigate the apphcation of estimation theory to power system operation, the system state is the vector of steady-state bus voltage magnitudes and angles Once the bus voltage magmtudes and angles are known, all of the steady-state electrical variables, including those that are not telemetered or that are, for some reason, missing, can be readily calculated The system state could conceivably be obtained by other means such as by telemetering voltage phase angles in addition to the voltage magnitudes Alternatwely, the measured bus injections could be used as inputs to a power network model and the load-flow solution would yield the system state. Both of these theoretical alternatives are impractical In spite of previous investigations of the problem, no practical method of measuring voltage phase angles throughout the system has been developed With the avallabihty of SE, the development of a system-wide phase-angle telemetry system is no longel required. State estimation will produce the phase angles. As to the load-flow approach, a solution cannot be accomphshed in a straightforward manner since the algorithm has no systematic way of deahng with data inconsistency, random errors, bad data, and missing or nontelemetered injections The load-flow approach always requires that the data be correct, consistent, and up-to-date, which of course is seldom true with current data-acquisition systems As a result, load-flow convergence IS not always assured or, If a solution is obtained, the calculated flows may not necessarily match the measured values. The problem of obtaining a load-flow solution in real time and m the presence of data uncertainty was, in fact, a major motivation for Schweppe in proposing state estimation 2. SE may thus be characterized as a phase-angle telemetry system via software or as a real-time load flow A third view of SE arises from its ability to detect the presence of bad data and to identify which data is in gross

0142-0615/83/040218-04 $03 00 © 1983 Butterworth & Co (Pubhshers) Ltd

Electrical Power & Energy Systems

error. SE may thus be considered as a filter for raw data. This property by itself is important and could be sufficient justification for including SE in a control centre. Some specifications for control centres call for raw data validation routines involving adding flows around a bus and checking flows at both ends of a line. When one starts checking data using network laws, one might just as well do it correctly and efficiently through SE.

II. Security functions The most basic security function is that of security monitoring (SM), which is the identification of the actual operatIng conditions of the power system. This is carried out basically by detecting alarm conditions in the power system by monitoring equipment status and by checking electrical variables against operating hmlts. In a general sense, no system whether for electric power service or for some other Industrial process, whether physical or nonphysical - can be operated or controlled without some kind of security monitoring. That IS, SM is a mandatory operating function. SM has always been an inherent part of power system operation. Only the forms and effectiveness by which the function is carried out have changed. In the past, the SM function depended upon a combination of manual surveillance by station operators, remote alarming, manual recording, and telephone reporting. Today, the Implementation of SM IS accomphshed using real-time computer systems, remote terminal units (RTUs), communications channels hnklng the RTUs with the control centre, and colour graphic CRT displays to Interface with the system operator Reference 1 lists approximately 200 control centres throughout the world, In service or under development, which are provided with the SM function in modern form. The hardware and software resources reqmred to support SM account for the major cost Items of a control centre project. These items consist of the computer system, the RTUs, the communications network and the man-machine Interface. In addition, because of SM, a nearly complete real-time database is made available in the control centre computer. Thus, with computing and man-machine interface resources and a nearly complete real-time database already in place owing to SM, it would be feasible to implement SE with little or no additional hardware The addition of SE would enhance the SM function, because the database would be made complete, in the sense that all of the electrical network data would be available - even that which is not directly telemetered Voltage phase angle information would also be available if required for certain SM procedures SE would further enhance SM by making the system data dependable, thereby increasing the operator's confidence In the Information presented to him. It has been recognized that for most power systems, SM is Insufficient for analysing and enhancing the security of the system. Other security functions, such as contingency evaluation and optimal power flows, are needed for this purpose. The execution of these functions requires a realtime AC load-flow solution as a base. Such a base AC load flow would be obtainable, as already mentioned, only through SE. Also relevant to system security is the facility

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for making study load flows or load-flow-related simulations. These studies would require realistic operating data obtained from the statistics of the SE results.

III. State-estimation methods in practice The fundamental approach to SE is the basic weighted least squares (WLS) method. A brief review of the algorithm and definitions of the terminology are given in the Appendix. As can be gathered from equations (2) and (3), implementing the basic WLS in a straightforward manner is timeconsuming since the gain matrix would have to be calculated and factorized at every Iteration. However, this is not necessary. At approximately 20 control centres that have the WLS SE, solutions are obtained successfully with only Infrequent calculations or with just one calculation of the gain matrix at the start of a solution cycle. Provided there is no change in network topology, repeat solutions are obtained over a certain number of cycles without recalculation of the gain matrix. Although with the constant-gain matrix approach, the computation time is reduced significantly, the WLS processing could still be relatively long for medium-to-large networks and becomes even longer in the presence of gross data errors and the procedures for bad data rejection. Since the pubhcatlon of Schweppe's paper 2 several different alternatives to the WLS approach have been Investigated and tried at control centres Among these alternatives are sequential estimators, transformation methods, and fastdecoupled estimators In sequential state estimation, each measurement is processed sequentially thereby avoiding matrix procedures. Sequential estimators have so far been found to be workable for very small networks but not for medium-to-large networks. The only control centre with a sequential state estimator working is for a network of less than ten buses. The method was tried several years ago for one large system and as recently as one year ago for a medium-size system, both with no success. The first of these two centres has recently developed a state estimator using WLS: the second is still developing the WLS. 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. Two methods are at present in use at control centres. The AEP 'hne-flow only' algorithm 3 transforms only P and Q line flows. Injection and voltage measurements (except for a reference voltage) are ignored. The ASEA current transformation algorithm 4 is more general as it transforms all types of measurements In total, there are three control centres using the original AEP method. The very first centre to implement this method has recently replaced it with the WLS. There is a fourth control centre that uses the AEP method modified to include injection measurements There IS only one centre using the ASEA method. These five control centres with the AEP and ASEA methods will probably be the last of the breed. The WLS formulation may be decoupled by separating the measurement set into real and reactive power groups and

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by using the same slmphfylng assumptmns as used in the fast-decoupled load flow 6. As a result of this decouphng, the gain matrix becomes a constant matrix, in block diagonal form, the terms of winch a~ e functions of the network admittances only. Fm ther slmphflcatlons may be made by decouphng the Jacoblan matrix m the light-hand side of equation (2) and by making It constant, neglecting resistances in the calculation of the gain matrix, and dividing the real and reactive power measurements by thmr associated voltages 7 The last-mentioned technique is actually a transfmnIatlon lather than a slmphficatlon This device mlproves the convergence properties of the algorithm j u s t as it does for the fast-decoupled load flow The various simplifications that may be made with the decoupled fmmulatlon and with combinations of these simplifications have recently been explored thoroughly 6 The conclusions of Reference 6 support the results of Reference 7 At present, thele are only three control centres with the fast-decoupted estimator m service. Two more centres are scheduled to have this type of SE before the end of 1983 To detect and identify bad data, i e data with gross errors, the commonly apphed method is first to detect the presence of bad data by using the so-called J(x)-test or chl-square test The value of J(x) is compared to a threshold value based on the chi-square distribution The presence of bad data, with a certain probability of being correct, is assumed if the threshold Is exceeded If bad data Is detected, the identification of which data points are bad Is next performed using either the weighted residuals or the normahzed residuals The majority of cont m l centres with SE use weighted residuals for bad-data ldenUflcatlon, generally with satisfactory results Reference 8 has pointed out the superiority of normalized residuals. However, the weighted residual test is simpler and less time-consuming New versions of SE programs from some control centre suppliers make available both types of resv duals The user then has the option o f using rather one at any time during onhne operation. After the weighted or normahzed residuals ale obtained, the measurement with the largest residual value is removed from the measurement set A new estimate using the reduced measurement set is made and the J(x)-test repeated If bad data is still indicated, the measurement with the next largest residual is ~emoved and the process repeated In most cases, the data with the largest residual is indeed the bad one Owing to the additional computational burden revolved in the re-estnnations, which require recalculatlons of the gain matrix of the reduced measurement set, the zesponse times with bad data can take up to several minutes m the control centres. However, the successful rejection of bad data and its replacement with a good estimate is worth the delay An approach used at some control centres to reduce the overall response times is to remove some suspected bad data at the same time If the normahzed residual test and a single bad data suppresslon scheme are lmplelnented, the bad data can be corrected without removing it from the measurement s e t 7 This method has been m service in one control centre.

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In most power systems, there are external networks, l e networks or subnetworks that are not being telemetered by the control centre and that are permanently unobservable. These external networks are parts of the outside interconnected system and some parts of underlying lower voltage networks or of large lndusmal customers. Moreover, parts of the internal network may become temporarily unobservable owing to measurement or communications failures. The states o f both permanently and temporarily unobservable buses or subnetworks are needed for the security database. One philosophy for deahng with unobservablhty is not to deal with it at all. In this approach, only the observable part Is solved. For the unobservable part a message is given to the operator stating that regrettably the subnetwork is unobservable A better philosophy Is to provide as much assistance as possible to the operator by making an estimate using pseudo-measurements. There are two methods currently being used for estimating unobservable states. The first method uses pseudo-measurements at the active nodes of the unobservable network, assigns to them relatively low weights, and includes the pseudo-measurements as part of the measurement set In this approach, extensive tests and tuning of the weighting factors have to be made to ensure that any corrupting effects on the observable subnetwork are minimal and that the bad-data identification properties are not impaired. The second method is to perform the state estimate only for the observable system The state of the unobservable subnetwork is then obtained by finding a load-flow solution using the pseudo-measurements as inputs with the boundary nodes held at the voltages and phase angles found from the state estimate of the observable subnetwork The concept of using pseudo-measurements for unobservable buses requires the periodic update of the vector of bus injections for the entire network based on the statistics of the state estimation runs Several injection vectors for several typical operating levels and days should be stored and dynamically updated. These Injection vectors provide the data for the pseudo-measurements and would also be used to study load flows In fact, a study load flow can be considered as a completely unobservable case.

IV. Trends Out o f the approximately 200 modern control centres throughout the world that are m service or under development, about 90 or 45% are provided with state estimation. The great majority (about 70%) o f control centre specifications now call for SE. The majority of control centres with SE also have the security functions of contingency evaluation and online load-flow. The next step m the evolution o f the application of state estimation to power system operation is the implementation of multilevel state estimation for a hierarchical system of control centres. Such an advance is desirable and should not be long in coming just as surely as improved computer communlcaUon methods and practical techniques m

Electrical Power & Energy Systems

Handschin, E et al. 'Bad data analysis for power system static state estimation' IEEE Trans. Power Appar. & Syst. Vol PAS-94 (March/April 1975)

decomposition become available. This development would offer an improved approach to the problem o f unobservability o f external systems.

V. Conclusions

VIII.

State estlmatmn is a necessary part of the underlying hardware and software structure that supports power system operation. Since state estimation processes the raw database such that an enhanced and dependable real-time database Is obtained, state estimation is an integral part o f the basic system, independent of the application functions.

The determination o f the estimated state vector, x, by state estimation is based on the weighted least squares (WLS) method The redundant set of measurements, z, consisting o f P and Q line flows, P and Q rejections and bus voltages, is modelled as z = h(x) + v, where v is the vector of measurement errors and h ( x ) is the vector of nonlinear functions relating the measurements to the state. [ z - - h ( x ) ] is the vector of measurement residuals

In modern control centres, the concept of security control cannot be fully realized without the complete information that is based on the voltage magnitudes and phase angles of all buses in a power system. State estimation is a simple and efficient way o f prowdlng that Information.

Appendix: Basic weighted least squares

The estimated state is obtained by mmlmlzmg the sum of the weighted squared residuals, I.e. J(x) = [z - h ( x ) ] T w [z -- h(x)]

V l . Acknowledgements

by using the lteratlve procedure

The author wishes to thank Dr R Lugtu for his help in the preparation of this paper

VII.

References

1 Dy Llacco, T E and Rosa, D L Survey of system control centers for generation-transmission systems Dy Llacco Corp., USA

Schweppe, F C, Wildes, J and Rom, D Pl~ower system statm state est=matmn, Parts I, II, II1' IEEE Power Appar. & Syst. Vol PAS-89 (January 1970) pp 120-135 Dopazo, J F, Klitin, O A, Stagg, G W and Van Slyck, L S 'State calculation of power systems from line flow measurements' IEEE Power Appar. & Syst. Vol PAS-89 (September/October 1970) pp 1698-1708 4 Johnsson, S L 'An algorithm for state estlmatmn m power systems' IEEE PICA Conf. (June 1973) Allemong, J J, Radu, L and Sasson, A M 'A fast and reltable state estmmatmn algor=thm for AEP's new control center' IEEE Security Monitoring Conf. 343-3

(1)

G ' [x '+1 - x'] = H r W [z - h(x)]

(2)

G is the gain matrix, the superscript l is the Iteration count, H is the Jacoblan matrix H = dh/dx of the network equations h, and W is the inverse of the diagonal covarlance matrix of the measurement error v The gain matrix G may be any positive-definite matrix of rank 2 N - - 1, where N is the number of buses in the network model. However, from the llnearlzation of the optlmahty condition for equaUon (1), the most logical choice for G is given by G' = H r ( x i) W H ( x ' )

(3)

Substituting equation (3) in equatxon (2) and solving the latter by sparse-matrix methods for (x ~+1 _ x z) constitutes the basic WLS algorithm. The Iteration is continued until the value of x has converged to within a desired tolerance, e g. 0 001 p.u The estimate is usually denoted by x. Other useful basic concepts are the following. •

(July 1981 )

Stott, B and Alsac, O 'Fast decoupled load flow' IEEE PowerAppar. & Syst. Vol PAS-93 (May/June 1974) pp 859-867

The weighted residual o f a measurement l is the measurement residual divided by the standard deviation of i The normahzed residual of a measurement l is the measurement residual divided by the square root of the ith diagonal element of the lesldual covariance matrix

Garcia, A, Monticelli, A and Abreu, P 'Fast decoupled state estlmatmn and bad data processing' IEEE Power Appar & Syst. Vol PAS-98 (September/October 1979) pp 1645-1652

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•

The residual covarlance matrix is given by S = W -1 -- H(x)

G-l(x) HT(x)

(4)

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