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Improving Transformer Tap Changer Processing In Distribution State Estimators

O.M. Ruiz-García, Student Member IEEE, A. Gómez-Expósito, Fellow IEEE, A. de la Villa, E. Romero, Member IEEE, D. Trebolle

Abstract— Unión Fenosa Distribución, a Spanish distribution

utility, is developing a state estimator tool intended for off-line ap-plications. Its main goal is to produce realistic base cases at the sub-transmission and distribution levels, allowing systematic network studies to be undertaken. From this experience, a detailed research work has been carried out regarding the best way of dealing with automatic tap changer settings, no matter if tap measurements are available or not. This paper reports preliminarily on the heuristic procedures developed for this purpose, showing by means of a case study the improved results provided by the state estimator.

Keywords — state estimation, tap changers, inequality con-straints, distribution systems.

I. INTRODUCTION HE context in which electrical distribution companies are doing business nowadays, taking into account the size of

their networks, the market liberalization process and the con-tinuous incorporation of distributed generation systems; is leading to the generalized use of different back-office studies, formerly restricted to transmission networks. Among other tasks, electrical distribution companies are required to con-tinuously use and improve software tools to simulate the be-haviour of their networks, usually from snapshots.

The state estimation (SE) technique is been applied in the last four decades to monitor in real-time the operation of elec-trical networks at the transmission level [1]. The available software can be employed also in off-line mode to generate feasible states from the information provided by historical re-cords, data bases, forecasting tools and Transmission System Operator (TSO) communication links. Such network states are useful in operation and short-term planning to analyze the ef-fect of equipment outages, to schedule maintenance routines, etc.

The quality and accuracy of the results provided by the es-timation process depend to a great extent on the type and re-dundancy of available measurements (voltage magnitudes, power flows, tap settings, etc.). In general, the redundancy of

O.M. Ruiz works as a consultant engineer in Madrid, Spain (e-mail:

oct_ruiz@hotmail.com) A. Gómez-Expóxito, A. de la Villa and E. Romero are with Department of

Electrical Engineering of University of Sevilla D. Trebolle works for Unión Fenosa Distribución, Madrid, Spain (e-mail:

dtrebolle@unionfenosa.es) The authors from the University of Seville acknowledge the financial support of the Spanish DGI under grant ENE-2007-62997.

the measurement system at the distribution level is much lower than that of the high voltage levels, being advisable to resort to as much information as possible. A way of increasing the redundancy is by means of ampere measurements, very common at the distribution level [2].

On the other hand, the tap settings of primary distribution transformers, remotely modified by local controllers, are not always available or the existing information may not be reli-able enough. For this reason, it is customary to include the tap settings as additional state variables that must be estimated.

Unión Fenosa Distribución is working in the last years on the development of a proprietary SE, designed to provide fea-sible network states to be used as starting points for back-office studies, such as load flows, contingency analysis, resto-ration process, etc. [3]. The last SE version is based on the it-eratively reweighted Huber algorithm and allows the inclusion of ampere measurements and tap settings.

It is important to realize that, for the resulting state to be credible and acceptable by the user, it must take into account physical and operational constraints imposed by the network elements, such as voltage limits, discrete tap positions, power flow directions, etc. Experience shows, however, that the SE sometimes leads to solutions which are not realistic from the operational point of view. This is most likely to happen when the network under study encompasses heterogeneous subsys-tems, different sources of information (e.g., combination of real-time snapshots with data retrieved from past archives) and/or low measurement redundancy. A way to enforce these limits consists of incorporating inequality constraints to the state estimation. The resulting inequality optimization problem can be solved, for example, by an interior point method [4]. Reactive power limits at generators as well as limits on trans-former tap settings are considered in [4]. In practice, the main drawback of this solution methodology, in addition to its com-putational cost, lies in the difficulty of adjusting some key pa-rameters associated to the interior point technique.

One of the most conflictive cases refers to the estimation of tap changer positions, which can be out of physical limits or, alternatively, lead to unrealistic voltage magnitudes at the con-trolled bus. A solution consists of augmenting the state vector, as proposed in [5]. Initially, transformer taps are modelled as continuous variables and a best fit is calculated. Then, the best fit is set to its nearest feasible discrete tap position and is re-moved from the state vector. The normal equations are solved again allowing changes in the state vector resulting form the tap discretization.

T

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Based on the experience acquired during the commission-ing phase [3], this paper describes a series of simple modifica-tions to the standard SE procedure, oriented to keep both the tap setting and the controlled voltage magnitude within feasi-ble bounds during the iterative process. The basic idea con-sists of using appropriately selected pseudomeasurements, as an alternative to the systematic, but much more expensive and complex, use of inequality constraints.

II. IMPLEMENTED STATE ESTIMATOR The SE iterative process can choose, upon user selection,

between the conventional weighted least squares (WLS) solu-tion scheme and the iteratively reweighted Huber estimator (IRLS) [6].

A. State estimator and bad data processor Consider the measurement equation given by:

( ) exhz += where: z is a vector of power injections, power flows, voltage magni-tudes, line current magnitudes, bus current injection magni-tudes and monitored taps of some transformers. x is a vector of voltage magnitudes and phase angles, plus a set of transformers taps to be estimated. h is the nonlinear function relating error free measurements to the state variables given in vector x. e is the vector measurement errors.

Measurement errors are assumed to be independent, having

a Normal distribution with zero mean and known variance. A diagonal covariance matrix, R is assumed as follows:

[ ] ( )22

221 ,..., m

T diageeECov σσσ==

where σi is the standard deviation of the error associated with the measurement i, and m represents the total number of meas-urements.

The weighting matrix adopted, W, is the inverse of R mul-tiplied by the diagonal matrix of Huber weights, Q. Matrix Q is initially set to the identity matrix and remains constant if the user selects the WLS algorithm.

Multiple measurements of the same magnitude, being fully compatible with the above formulation, are allowed by the SE. For instance, bus voltage magnitudes may be available from two or more measuring instruments at a given substation bus. Instead of resorting to a simple averaging process, those meas-urements are included as separate entries in the measurement vector z, each one being characterized by its respective stan-dard deviation of the error.

Both implemented estimation algorithms (IRLS and WLS) will minimize the weighted squares of residuals of the meas-urements given below:

∑=

=m

iiirwJ

1

2

where:

( )xhzr iii ˆ−= is the measurement residual,

x̂ is the estimated state vector.

The estimated state can be obtained by iteratively solving the following equation:

( ) ( ) ( )[ ]kkkTkk xhzWxHxxG −=Δ

where: ( ) ( )xHWxHG kT= is the gain matrix,

xhH

∂∂

= is the measurement Jacobian,

kkk xxx −=Δ +1

In IRLS algorithm, , where: 111 −++ = RQW kk

⎪⎩

⎪⎨⎧

>

≤= thresholdHuberr

rthresholdHuber

thresholdHuberrq w

iwi

wi

kii

1

i

iwi

rr

σ=

k is the iteration counter.

Iterations are terminated when an appropriate tolerance is reached on Δx. Once the process is converged, the bad data processing function is activated. This function’s role is to de-tect, identify and eliminate bad analogue measurements. Bad data detection is usually accomplished based on the largest normalized residual test. (The user can alternatively select the Huber estimator, which automatically downweights measure-ments whose residual exceeds a given threshold. This signifi-cantly reduces the computation time, at the risk of not properly identifying all bad data). If the detection test fails, then the measurement corresponding to the largest normalized residual will be declared bad and its corresponding row will be ignored in vector z.

State estimation is repeated as many times as needed after each bad data identification-correction cycle. Note that, repeti-tive solutions will start from the most recent estimate instead of flat start, and hence will take less iteration to converge. In spite of that, particularly during the SE tuning phase, this process may lead to a significant increase in the number of iterations, and hence solution time unless it is efficiently im-plemented (the sparse inverse method described in [7] has been adopted to reduce the computational burden).

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B. Practical issues The estimator developed for this project incorporates line cur-

rent magnitude and bus current injection magnitude measure-ments, which are typically not considered by conventional esti-mators. Furthermore, selected transformer taps are included in the unknown variable list so that their values can be estimated as part of the solution. These features call for derivation of new terms in the measurement Jacobian. Detailed derivation of all Jacobian entries can be found in Chapters 2 and 7 of [1] for the current magnitude measurements and tap variables, respectively. It is worth noting that clever application of the shortcuts pro-posed in [8] leads to very efficient code for computing and updat-ing Jacobian entries for those columns corresponding to taps.

A great deal of effort has been devoted to certain practical as-pects of the state estimator that, in spite of not involving new knowledge, play an important role in achieving a reliable and really accurate application. This is the case of the subroutine de-voted to ensure unique observability. After numerous tests it has been checked that certain pseudomeasurements result more effec-tive than others in order to get the right estimate. In this respect, complex power pseudomeasurements, computed from actual cur-rent measurements and assumed power factor, in places of the system where the power flow direction is well known, have al-lowed the state to be estimated in zones where only current measurements exist. It is well documented in the literature (see references [9], [10], [11]) that ampere measurements alone are not enough to guarantee unique observability.

A systematic study has been undertaken also to select ade-quate standard deviations for each measurement type. In this sense, not only the precision class of the measurement device, but also its nominal power have been used to better tune this impor-tant parameter. In general, all tests have confirmed the improve-ment of the state estimation results and the bad data detection and elimination capability in those cases where current measurements are incorporated.

Regarding the detection and identification of bad data, the im-plemented application allows typical bad performance of meters, wrong scale factor or bias, reversed connections, etc., to be iden-tified. Additionally, topology errors, and in some cases out-standing parameter errors, have been detected after carefully and individually analyzing the results of the estimate. Almost always, those errors were identified after noticing that large measurement residuals accumulated at certain specific points. As the imple-mented tool does not incorporate in a systematic manner the to-pology error and network parameter estimation functions, this task has been carried out manually.

Examples of such errors include wrong status information transmitted by a switching device or a drastic change in the pa-rameters of a line that has been redesigned without the new val-ues being adequately updated in the data base.

III. TAP CHANGERS PROCESSING As stated in the Introduction, depending on the type, quality

and redundancy of available measurements, it frequently happens that the estimated tap setting and/or the regulated voltage magni-

tude lie outside permissible values. In this section, a straightforward methodology is presented,

intended to handle the resulting inequality constraints without having to resort to complex mathematical programming tech-niques, such as the interior point method.

A. Treatment of tap settings The way tap settings are handled by the SCADA system

affects the quality and reliability of the estimate. From this point of view, three situations are possible: • The tap position is transmitted via the respective RTU and

handled within the SCADA as an integer (digital) variable, without any possible error. In those cases, there is no need for the tap setting to be estimated, the transformer π model remaining fixed throughout the iterative process.

• The tap position is unknown or there is no full certainty about the accuracy of the available value. This may happen for instance when the RTU sends only incremental up/down steps and the SCADA is responsible for tracking the absolute tap setting value. In those cases, a temporary failure of the communication channel may lead to discrep-ancies between the data base and actual tap setting values.

• The tap position is not telemetered at all. In those cases, only guesses can be made about the actual tap setting, based on historical records.

Clearly, in the last two cases, the tap position should be

considered a variable to be estimated, rather than a known pa-rameter.

In order to improve the estimate accuracy and to prevent potential observability problems, any available information on the tap setting value should be converted to a regular meas-urement or a pseudomeasurement, to be used in the estimation process. When doing so, the weight associated to such meas-urements is crucial to prevent abnormal or trivial solutions from being reached. Although this issue deserves a more care-ful theoretical analysis, it was found experimentally that using a standard deviation (s.d.) equal to one half of the step be-tween consecutive taps provides acceptable results. A possible justification for this choice lies in the fact that continuous tap estimates must be finally rounded to their nearest discrete set-ting. When doing so, any tap value +/- one half step leads to the same tap position. Therefore, the resulting uncertainty is proportional to the step size.

Regarding the way state variables corresponding to tap set-tings are initialized, a value compatible with the flat voltage profile ( t 0 = 1 pu ) usually reduces the number of iterations required to achieve convergence, compared to the use of exist-ing data base values. This is consistent with earlier findings in load flow solutions, where previous converged cases do not necessarily reduce the number of iterations compared to the use of flat start.

During the SE iterative process, estimates of the tap set-tings ( t k ) should be kept within minimum and maximum

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physically feasible limits. This is easily achieved by limiting the tap setting increment ( Δt ) so that the updated value ( t k+1 = t k + Δt ) does not exceed any of the limits.

Once the process converges, tap setting estimates should be adjusted to their closest discrete value, according to the physical tap changer arrangement. This can be implemented in two different manners • All tap settings are rounded to their nearest discrete value.

Then, those variables are removed from the state vector and the SE is run again. This has the drawback that the structure of all involved matrices and vectors is modified, which means extra cost in building new sparse structures, LU refactorization, etc.

• For each tap changer a virtual (exact) measurement is in-troduced, which is set to the discrete value closest to the initial estimate. Then, the SE is run again. This approach may further introduce ill-conditioning on the equation sys-tem, depending on the way equality constraints are imple-mented (the use of QR factorization is helpful to alleviate this potential problem).

B. Treatment of voltage setpoints

U

t

refU

UUref Δ+

UUref Δ−

Tap changer steps

Fig. 1. Typical evolution of regulated voltage magnitude

As the objective is to produce a network model that resem-

bles the reality as much as possible, the resulting voltage mag-nitudes at the controlled buses should lie within the specified bounds, keeping in mind that the tap changer regulator has a dead band and reacts only when one of the limits is violated, as suggested in Figure 1.

Therefore, in addition to the tap setting being within feasi-ble limits, the regulated voltage magnitude must lie in the in-terval . UUref Δ±

Much like in the case of the tap setting, the adopted meth-odology consists of adding, for each regulated voltage, a pseu-domeasurement equal to with s.d. . refU UΔ

After convergence of the SE, a weighted residual

σzz

r medw ˆ−= , corresponding to any of those pseudomeasure-

ments, being larger than 1 in absolute value means that the estimated voltage is out of the regulator limits. This is an indi-cation of something wrong with the measurement set or the network model.

Start

Initial point:Voltage: 1.0 puPhase: 0.0 radRatio: 1.0Wii = 1 / (σii)2

Compute H(x)

Compute U by QR factorizationof H(x)W1/2

Compute Δx solving (UT U) Δx = (HT W) Δz

Δzi = zi - hi(x)

Δxi < ThresholdV i?

no

Analysis of error measurements

yes

Regulated voltagein limits? (*)

Error measurements?

sí

yes

no

End

Discard measurement with the highestprobability to be bad.Start weights.

Updateweights

IRLS?

yesno

no

Increase virtual measurement weights (*)

Tap position out of limits?

yesFix tap position to the reached limit

no

(*) If the ratio is at a limit, only takes into account the unique sense of regulation

Add an exact measurement set to the discrete value closest to the initial estimate

First step?

yes

no

Fig. 2. Flowchart of the procedures implemented

In such cases, the respective pseudomeasurement weight is

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increased in proportion to the weighted residual r , after which the iterative process is repeated. This way all regulated voltages are smoothly shifted towards one of the limits. A nice feature of this heuristic methodology is that the larger the de-viation from the permissible bound the stronger the “force” shifting the voltage to the limit. Obviously, when convergence is achieved, all weigthed residuals corresponding to controlled voltages are less than 1 in absolute value.

w

Next, the normalized residual test is performed. In case a bad data is detected in the surroundings of a regulated voltage, the respective pseudomeasurement weight is restored to its initial value and the bad data is removed or made “dormant” before the iterative process is repeated. The fact that the pseu-domeasurement weight is not artificially increased during this extra SE run, would be a clear indication that the removed bad data was responsible for the initial voltage violation.

The flowchart of Figure 2 summarizes the procedures de-scribed above.

C. Case Study This case study, intended to illustrate the benefits provided

by the application of the proposed schemes, is taken from one of the many base cases generated so far during the SE com-missioning process.

Figure 3 shows a 45kV / 15.348kV transformer equipped with a 21-step tap changer (t = 1 , ... , 21), each tap being nominally equal to 0.6kV. Assuming ideal conditions, the low voltage side, feeding a radial distribution system, can be regu-lated between 13.2kV ( t = 1 ) and 17.496kV ( t = 21 ).

The set of measurements available in this case study is also shown in Figure 3. This comprises active and reactive power flows at both sides, voltage magnitudes at both buses, current magnitude at the high voltage side and the tap setting. Hence, the redundancy level is quite satisfactory in this case.

According to previous evidence, it is known a priori that the low voltage magnitude measurement, V2, is wrong. The tap regulator attempts to control V2 within the interval 15.5kV ± 1.3% (15.2985 ÷ 15.7015kV). When a conventional SE is run, ignoring inequality con-straints, the estimate for V2 is 14.3kV (just the measured value) and the tap setting measurement is labelled as bad data

Fig. 3. Example. Snapshot from the application

(t = 6 is estimated, far from the true value t = 12), which is in-correct. On the other hand, following the proposed method to handle bounds on state variables, if a pseudomeasurement is included (V2 = 15.5kV), with s.d. equal to 1.3%, the estimate is V2 = 15.55kV which corresponds to t = 12. This time, it is the original voltage magnitude measurement which is cor-rectly declared as bad data.

Other experiments confirm that the proposed procedures are indeed helpful to prevent limit violations and/or conver-gence to the wrong solution, at the cost of extra iterations.

IV. CONCLUSIONS This paper focuses on the need to adjust the solutions of

conventional SE’s in order to incorporate certain practical constraints the estimate must satisfy. At the subtransmission level, this is frequently the case of tap changers and the re-spective regulated voltages, which should be constrained to lie within the limits imposed by the device for the results to be acceptable to the user.

A heuristic and simple technique is proposed to handle the resulting inequality constraints. The method is based on the addition of key pseudomeasurements, along with appropri-ately selected weights.

Test results obtained on realistic networks show that the proposed methodology provides satisfactory results. This is achieved at the cost of a significant increase in the number of iterations, which is not very relevant in off-line applications. In any case, the use of more complex but systematic tech-niques, such as interior point schemes, would exacerbate this problem, as the computational effort at each iteration would be much higher.

Future research efforts are currently directed to investigate the statistical correlation between eliminated bad data and added pseudomeasurements.

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REFERENCES [1] A. Abur, A. Gómez-Expósito, “Power System State Estimation: Theory

and Implementation”, Marcel Dekker, 2004. [2] de la Villa Jaén A., Gómez Expósito A., “Including ampere measure-

ments in generalized state estimators” IEEE Transactions on Power Sys-tems, pp 603-610 Vol. 20, No. 2, May. 2005.

[3] Ruiz García O., Romero Ramos E., Gómez Expósito A., Abur A., Ordi-ales Botija M., Trebolle Trebolle D., “Building Distribution Level Base Cases Through a State Estimator", Proceedings of the IEEE Power Tech 2007, Lausanne July 2007.

[4] Clements, K.A.; Davis, P.W.; Frey, K.D.,“Treatment of inequality con-straints in power system state estimation” IEEE Transactions on Power Systems, Vol. 10 (2), May 1995 Pp. 567.

[5] Teixeira P., Brammer S., Rutz W., Merritt W., Salmonsen J., “State Estimation of Voltaje and Phase-Shift Transformer Tap Settings”. IEEE Transactions on Power Systems, V l. 7 (3), pp. 1386-1393, August 1992.

[6] Baldick R., Clements K.A., Pinjo-Dzigal Z., Davis P.W., “Implement-ing Nonquadratic Objective Functions for State Estimation and Bad Data Rejection” IEEE Transactions on Power Systems, pp 376-382, Vol. 12, No. 1, Feb. 1997.

[7] K. Takahashi, J. Fagan, M.S. Chen, “Formation of a Sparse Bus Im-pedance Matrix and its Application to Short Circuit Study”, PICA Pro-ceedings, May 1973, pp.63-69.

[8] F. González Castrejón and A. Gómez Expósito. “Modeling transformer taps in block-based state estimation”, Proceedings of the IEEE Porto Power Tech Conference, Porto, 2001.

[9] A. Abur and A. Gómez Expósito. “Algorith for determinig phase-angle observability in the presence of line-current-magnitude measurements”, IEE Proc.-Gener. Transm. Distrib., Vol. 142, No 5, pp 453-458, Sep-tember 1995.

[10] A. Abur and A. Gómez Expósito. “Detecting multiple solutions in State Estimation in the presence of current magnitude measurements”, IEEE Transactions on Power Systems, Vol. 12, No 1, pp 370-375, February 1997.

[11] A. Abur and A. Gómez Expósito. “Bad data identification when using ampere measurements”, IEEE Transactions on Power Systems, Vol. 12, No. 2, pp 831-836, May 1997.

Octavio M. Ruiz García was born in Spain in 1972. He completed his studies in Electrical Engineering at the University of Seville, where he is doing his doctoral thesis under the programme 'Technical and financial management systems for generation, transmission and distribution of electricity'. Since 2000, he was working at an engineering services company (Applus - Norcon-trol), in the area of electrical engineering, in Madrid. He currently works as a consultant engineer, helping companies to incorporate research results on elec-trical networks studies to their systems. His main areas of interest are network analysis and state estimation. Antonio Gómez Expósito was born in Spain, in 1957. He received his elec-trical and doctor engineering degrees from the University of Seville, where he is currently a Professor and Head of the Department of Electrical Engineering. His primary areas of interest are optimal power system operation, state estima-tion, FACTS devices and digital signal processing. Antonio de la Villa Jaén was born in Riotinto, Spain, in 1960. He received his electrical and doctor engineering degrees from the University of Seville. He is presently an Associated Professor at University of Seville. His primary areas of interest are computer methods for power system state estimation problems. Esther Romero Ramos was born in Spain, in 1967. She received her electri-cal and doctor engineering degrees from the University of Sevilla in 1992 and 1999 respectively. From 1992 to 1993 she worked for Sainco. Since 1993 she has been with the Department of Electrical Engineering, University of Sevilla, where she is currently an Associated Professor. She is interested in State Esti-mation, Load Flow problems and Analysis and Control of Distribution Sys-tems. David Trebolle Trebolle was born in Spain, 1977. He obtained his Master in economics and regulatory framework of the electrical business and his degree in Electrical Engineering at the University Pontificia Comillas in 2001. From

2001 to 2002 he worked as a planning engineer at the control room centre of National Grid Company in Wokingham, United Kingdom. Since 2002 he has been working at Union Fenosa Distribución and he has also been studying for his PHd in Industrial Engineering at the University Pontificia Comillas. His interests include distribution planning, the operation of electrical power sys-tems, power quality assessment, distributed generation and the regulatory framework in transmission and distribution businesses.