fp455.pdf

A Two-Stage Orthogonal Estimator to Incorporate Phasor Measurements intoPower System Real-Time Modeling

Antonio Simoes Costa Andre AlbuquerqueFederal University of Santa Catarina Federal University of Santa Catarina

Florianopolis, Brasil Florianopolis, [email protected] [email protected]

Abstract - This paper proposes the use of an orthogonalstate estimator with capability to process a priori informationas a means to incorporate the benefits of synchronized pha-sor measurements into power system state estimation. Theproposed strategy promotes the enhancement of results pro-vided by a conventional, SCADA-based estimator by means ofa post-processing stage, where those estimates are treated as apriori information to be improved by the processing of PMUdata through the orthogonal algorithm. The procedure doesnot interfere with the structure of conventional estimators,which can be based on any available method. Computationalefficiency is ensured by the properties of the particular ver-sion of the orthogonal Givens rotations employed in the post-processing stage, which easily accommodates the processing ofa priori information without extra computational cost. The ap-plication of the proposed methodology is illustrated throughseveral case studies conducted on the IEEE 14-bus, 57-bus and118-bus test systems.

Keywords - Power System State Estimation, synchronizedphasor measurements, phasor measurement units (PMUs), or-thogonal Givens rotations.

1 Introduction

During the last several decades, Power System State Es-timation (PSSE) has established itself as the basic tool forreal-time modeling of large electric power networks. As theemerging Smart Grid concepts expand previous paradigmsfor power system operation and control, PSSE must evolveto keep pace with the current trends [1]. This requires theincorporation of new technologies to fulfill more stringentaccuracy and observability requirements posed to state esti-mators.

Conventional state estimators process data gathered bySCADA systems by scanning remote terminal units (RTUs)located at the power system substations. The advent ofthe phasor measurement technology has made it possibleto accurately measure bus voltage and branch current pha-sors through Phasor Measurement Units (PMUs), some-thing previously infeasible with SCADA. Therefore, the useof phasor measurements in power system state estimationhas deserved much attention in recent years.

Despite the clear advantages of the phasor measurementtechnology, it is unlikely that SCADA systems for powersystem real-time modeling are to be simply replaced byPMU installations in the near future. A number of argu-ments can be raised to support that claim, such as the still in-sufficient number of PMU measurements usually available

to provide full system observability; the fact that other ap-plications which can take better advantage of the high PMUsampling rate tend to hold preference in the deployment ofthat equipment, and the existence of a complex and expen-sive SCADA infrastructure that should not be simply dis-carded.

A sensible solution is to combine the widespread avail-ability of conventional measurements with the enhancedquality of observations provided by the PMU technology,available at certain points of the power network. For thatpurpose, however, one faces the problem of how to con-ceive state estimation strategies able to benefit most fromboth technologies. It is of course possible to devise stateestimators able to simultaneously process both SCADA andPMU measurements [2, 3, 4]. However, as pointed out in[5], this would require significant changes to existing StateEstimation software, since most estimators presently oper-ating worldwide are based solely on SCADA measurementsand thus not prepared to process phasor data.

This paper proposes a new approach to take full advan-tage of the superior quality of PMU measurements withoutthe need of introducing changes to the structure of existingestimators. As in [5, 6], this is accomplished through a post-processing stage to the conventional estimator. Therefore,the whole estimation procedure is composed of two mod-ules: (a) a conventional, SCADA-based state estimator, and(b) a PMU-based estimator, intended to enhance the qualityof state estimation and the degree of network observabilityby processing only the available PMU measurements.

The proposed approach relies on the concept of a prioristate information, and for that reason it will be referred toas APSI state estimation. It conceptually differs from othermethods previously proposed in the literature in two as-pects:

i) SCADA-based state estimates obtained from the firststage are treated by the PMU-based module as apriori information, that is, initial knowledge about thestate variables, whose quality is expected to be im-proved by processing the available phasor measure-ments, and

ii) The estimation algorithm in the post-processing mod-ule is based on a particular version of orthogonalGivens rotations which, in addition to enhanced nu-merical robustness, easily accommodates a priori in-formation at virtually no extra computational cost[7, 8].

17th Power Systems Computation Conference Stockholm Sweden - August 22-26, 2011

This paper is organized as follows. Section 2 reviews thebackground of power system state estimation and extendsthe conventional normal equation approach in order to takeinto account the availability of a priori state information.Section 3 describes the three-multiplier version of Givensrotations and shows how this variant of the orthogonal ro-tations makes provision to take a priori information intoaccount. The proposed method to enhance SCADA-basedestimates through the processing of phasor measurementsis discussed in Section 4, followed by some additional re-marks related to the methods performance and possible im-provements, in Section 5. Section 6 presents the results ofseveral case studies performed with three IEEE test systems.Finally, concluding remarks are listed and discussed in Sec-tion 7.

2 State Estimation Background2.1 Measurement Model and Weighted Least Squares Es-

timator

Consider a N bus power network for which m measure-ments are taken. Assuming a nonlinear model for the elec-trical network, the relationships between measured quanti-ties and the n = 2N 1 state variables can be expressedas:

z = h(x) + (1)where z is the m1 measurement vector, x is the n1 vec-tor of state variables to be estimated, h(x) is the m1 vec-tor of nonlinear functions relating measurements to states,and is the m 1 measurement error vector, whose mmcovariance matrix is assumed diagonal and denoted by R.Therefore,

R =diag{21 , 22 , . . . , 2m} (2)where 2i is the variance of measurement errors i.

Power system state estimation is formulated as the fol-lowing weighted least squares problem:

min J(x) =1

2[z h(x)]tR1 [z h(x)] (3)

where x represents the vector of state estimates, and thefunction to be minimized is the weighted sum of the squaredresiduals.

2.2 Solution through Gauss-Newton Method

The solution of the minimization problem (3) throughthe Gauss-Newton method leads to an iterative process inwhich the following normal equation is solved in each iter-ation [9], [10], [11]

(HtR1H

)x = Ht R1z (4)

whereH is the Jacobian matrix of h(x) computed at a givenpoint xk and

z = z h(xk).Solving Eq. (4) provides the vectorx of increments to thestates, so that the updated state vector is obtained as

xk+1 = xk +x

The iterative procedure goes on until x becomes smallerthan a pre-specified tolerance.

The coefficient matrix on the left-hand side of Eq. (4) isoften referred to as gain matrix. As shown in [9], the inverseof the gain matrix, that is,

P =(HtR1H

)1 (5)

can be interpreted as the covariance matrix of the estima-tion errors. Thus, it provides a measurement of confidenceon the accuracy of the state estimates [9].2.3 Embedding A Priori State Information

There are practical situations in which, in addition tomeasured data, some reliable knowledge on values of thestate variables is available prior to state estimation. This apriori information, which we will denote by x, may arisein different forms, such as state estimates determined on thebasis of a previous set of measurements, or mean valuesbased on the expected range of values for the state vari-ables. In addition, it is often possible to know additionalstatistics concerning the a priori state vector, such as its co-variance matrix. As remarked in [12], a priori informationcontributes to the estimation process in a similar fashion asthe measured data. Also, the statistics required for model-ing a priori information is the same statistics of the error(x x) [12]. If we denote by P the n n covariance ma-trix of x, the weighted least-squares problem of equation (3)can be extended to account for the a priori state informationby augmenting the objective function of problem (3) as [12]

min J(x) = 12 [z h(x)]tR1 [z h(x)] +12 (x x)tP1(x x)

(6)

It can be shown that the optimality conditions for the aug-mented problem lead to the following extended normalequation:[HtR1H+P1

]x = HtR1z+P1x (7)

where x =(x xk). Therefore, whenever a priori in-

formation is considered, Eq. (7) replaces Eq. (4) in the pro-cess of solving the weighted least squares problem. We willrefer to this problem as state estimation in the presence of APriori State Information or, for short, APSI state estimation.

In practice, the values in x are often assumed uncorre-lated, in which case matrixP is diagonal. The i-th diagonalentry of P will be denoted by 2i , and corresponds to thevariance of the a priori information xi. Ascribing infinitevalues to 2i , i = 1, . . . , n, means that nothing is knownin advance about the state variables. As a consequence,P1 0 so that the second term on the right-hand sideof expression (6) would be null, and the problem reducesitself to the conventional state estimation in which a prioriinformation is neglected.

Although employed to solve many practical problems,the Gauss-Newton method is somewhat prone to numericalill-conditioning [13]. For this reason, algorithms that avoidthe explicit calculation of the gain matrix, such as the or-thogonal methods discussed in next section, are often pre-


ferred when dealing with large real problems whose numer-ical conditioning cannot be easily assessed beforehand.

3 APSI State Estimation via Givens Rotations

3.1 Outline of three-multiplier Givens RotationsWeighted least-squares problems can be solved by a

faster, three-multiplier (3-M) version of Givens rotations,proposed in [14] to improve the computational performanceof the original four-multiplier rotations. To outline themethod, consider that one wishes to solve the linearizedweighted least-squares problem whose measurement modelis given by

z = Hx+

and the objective function is the linearized version of (3).According to the orthogonal approach, a sequence of ele-mentary rotations are applied to matrix H and vector z(both previously scaled by matrixR1/2) in order to obtainan upper triangular linear system of equations. If Q repre-sents the matrix that stores the individual rotations, we have[13]:

Q(R

1

2

[H z

])=

[U c

0 e

](8)

where U is an upper n n triangular matrix, and c and eare n 1 and (m n) 1 vectors, respectively.

The 3-M version of Givens rotations is based on the de-composition of matrix U as [14],[13]:

U = D1

2 U (9)

where U is a unit upper triangular matrix, that is, its diago-nal entries are all equal to 1, andD =diag{d1, d2, . . . , dn}.Vector z is considered as an extra column of H, so thatc is also scaled in the transformation. The resulting scaledvector is denoted by c.

The artifice of scaling U as above provides significantcomputational benefits, such as the reduction on the num-ber of operations and the elimination of square-root compu-tations during the factorization given by Eq. (8). In prac-tice, D 12 is not actually required, so that only D needs tobe computed. Also, matrix Q does not have to be explicitlyformed.

Givens rotations are a row-processing scheme throughwhich every augmented row composed of a particular mea-surement zi and the corresponding row of H is processedone at a time, until all information contained in the aug-mented row is transferred to matrix U. The cumulative ef-fect of all elementary rotations required for that purpose isrepresented by matrixQ in Eq. (8). After all measurementshave been processed, estimates x are obtained by simplysolving the upper triangular system

U x = c (10)

by back-substitution. The weighted sum of squared residu-als is determined from e, as a by-product of the estimationprocess.

3.2 Elementary Rotations and Interpretation of ScalingFactors

We now focus the attention on the elementary 3-MGivens rotations. The purpose is to show how this variantof the rotations facilitates the implementation of APSI es-timators through the proper interpretation of the triangularmatrix scaling factors introduced in Eq. (9). For concise-ness, we omit the mathematical details and developments.The interested reader is referred to [14] and [13].

We first consider the case in which no a priori informa-tion is taken into account. In this case, prior to the process-ing of any measurement matrix U and vector c in Eq. (8)are both initialized as zero. From Eq. (9), this obviouslyrequires that all scaling factors for the rows of U be madeequal to zero, since matrix U must always be unit upper tri-angular. Therefore, the entries di of diagonal matrix D arealso initialized as zero. As the measurements and the cor-responding rows of H are individually processed, the val-ues of di are repeatedly updated and, as a result, becomenonzero. In addition, the updating rule is such that di willalways be nonnegative [14].

The 3-M version of the rotations assumes that every aug-mented row formed by a measurement and the correspond-ing row of matrix H is also scaled. Let us denote that scal-ing factor by

w. In weighted least squares problems, the

value initially assigned to w is the weight attributed to thecorresponding measurement. From Eqs. (2) and (3) , weconclude that, in the specific case of PSSE, the initial valuefor the scaling factor for measurement zj should be the in-verse of its variance, that is, wj = 1/2j [13]. Measurementscaling factors are also updated at each elementary rotation,and their nonnegative values steadily decrease towards zeroas the information contained in the augmented row is grad-ually absorbed by the triangular matrix U.

Having established the statistical role of the measure-ment scaling factor w, an interpretation of the scaling fac-tors di of the U rows is now in order. As shown in thesequel, this interpretation is intrinsically connected with theway a priori state information can be taken into account inthe 3-M Givens framework. Analogy with w suggests thatthe initial value d(0)i can also be seen as a weight, but inthis case assigned to the state variables (notice that thereare as many ds as states), and before any measurement isprocessed. In other words, d(0) can be interpreted as theweighting factor for the a priori information possibly avail-able on state variable xi. In addition, the value for d(0)i mustbe in agreement with the second term on the right-hand sideof Eq. (6), which establishes how a priori information istaken into account in the estimation process. This leads tothe conclusion that

d(0)i = 1/

2i (11)

where 2i is the variance of the a priori information on statevariable i.

As mentioned in the beginning of this subsection, thepractice in previous applications of the 3-M rotations toPSSE (which neglect a priori state information) has been


to initialize c = 0 and D = 0, which amounts to assumingthat U is initially a null triangular matrix [13]. This is con-sistent with the discussion in Subsection 2.3, since D = 0actually means that nothing is known in advance about thestates, so that their a priori variances are infinite.

To sum up, from Eqs. (8), (9) and (10) we concludethat previous information on the state variables can be eas-ily considered in the 3-M version of Givens rotations frame-work by adopting the following simple steps:

i) To initialize vector c as the available a priori stateinformation, that is,

c(0)= x (12)

ii) To initialize di as given by Eq. (11).Since the original formulation of 3-M Givens rotations

already makes provision for those variables, no extra com-putational cost is actually incurred when a priori state in-formation is taken into account.

4 Proposed Strategy to Enhance PSSE by ProcessingPMU Data

As previously mentioned in this paper, the proposed ap-proach to take advantage of PMU data for real-time model-ing recognizes the difficulties to fully merge information ob-tained from PMUs and data gathered by traditional SCADAsystems. In addition to technological aspects, such as dif-ferences in instrumentation and distinct data gathering rates,relevant arguments from the software standpoint can also beput forward in favor of separating the processing of PMUand SCADA measurements, as already mentioned. This ofcourse raises the challenge as how to combine the informa-tion provided by both sources in the most beneficial way, interms of both reliability and accuracy.

In this paper, the proposed solution to meet such chal-lenge consists of a two-stage scheme, in which each stageprocesses a single type of data (either SCADA or PMU).Figure 1 illustrates the suggested methodology. The firststage consists of a conventional state estimator which pro-cesses SCADA measurements only. There is no restrictionsconcerning the algorithm employed at this stage, so that anyexisting state estimator can be used. This estimator shouldprovide the SCADA-based state estimates, xS , as well asthe corresponding covariance matrix of estimation errors,PS , as given by Eq. (5). However, as it will become appar-ent in the sequel, only the diagonal elements of PS are ac-tually needed. Ideally, those values would be directly avail-able as a byproduct of state estimation, since they are alsorequired to compute the normalized residuals for bad dataprocessing [10]. However, if that is not the case for a givenstate estimator, the diagonal entries of PS can be easily re-built from the Jacobian matrix H and the measurement er-ror covariance matrix R. The sparse inverse matrix methodprovides an efficient means to calculate only the requiredelements of PS [15].

In the second stage depicted in Fig. 1, the APSI or-thogonal state estimator described in Section 3 is employed.

Measurements processed by that estimator are restricted tothose gathered from available PMUs, but the SCADA-basedestimates determined in the first stage also take part in theestimation process. This is ensured by treating the latter asa priori state information to the APSI estimator. To accom-modate all that, the procedure discussed in Subsection 3.2are employed. We thus make use of Eqs. (11) and (12)to define the a priori information and respective variancesapplicable to this particular problem. From previous argu-ments, we can easily conclude that:

c(0) = xS

d(0)i = 1/PS,ii

(13)

As the PMU measurements are sequentially processedby the APSI estimator, the a priori state information deter-mined in the first stage, that is, the former SCADA-basedestimates, undergo successive changes so that they are re-peatedly updated by the Givens rotations row-processingmechanism. Since PMU measurements are usually consid-ered more accurate than SCADA data, it is expected thatthe quality of the state estimates will be enhanced by theprocessing in the second estimation level.

Figure 1: Proposed 2-stage APSI state estimator.

5 Additional Remarks

The following remarks are intended to complement andexploit some features of the two-stage estimator describedin the previous section:

Although observability is assumed at the first-levelSCADA-based estimation process, the network does nothave to be observable with respect to the measurementsubset composed by PMU measurements only. In fact, ifthe network is observable at the SCADA level, than thecondition to obtain an state estimation solution is ensuredby the a priori information scheme described in Section4. In other words, observability at the SCADA-basedlevel ensures the observability for the overall estimationprocess. This is a convenient result, since in most exist-ing power systems the number of PMU installations arenot enough as yet to cover the whole electric network;


On the other hand, the existence of PMU measurementsin a given part of the electric network tends to enhance thequality of state estimation results, due to the superior ac-curacy of those measurements with respect to SCADAs.A convenient form to understand that is to think of thePMU data as providing an improved estimation finish-ing coat on top of the primer already provided by thea priori SCADA-based state information;

Another benefit of processing PMU measurement in thesecond stage is to improve the degree of redundancy inthose parts of the network where phasor measurementsare available. As illustrated through simulations in thenext section, this could be very helpful in filtering outthe effects of bad data contaminating conventional mea-surements, particularly when the SCADA measurementredundancy in the same region is poor;

In case of loss of all PMU information, the proposed es-timator would still provide the state estimates based onthe SCADA measurements, that is, the conventional stateestimates;

The state estimation model employed in this paper for thesecond stage of Fig. 1 is based on polar coordinates andis nonlinear. However, there is no apparent theoreticalreason to impede the adoption of another formulation ofstate estimation equations leading to a linear estimationmodel. This objective will be pursued in the next stagesof the research on this topic;

Likewise, further investigation on the potential benefitsof the proposed method concerning other issues relatedto state estimation is also needed. This is the case of baddata processing at the second estimation level in Fig. 1.

6 Simulation ResultsThis section illustrates the application of the proposed

APSI orthogonal estimator through several case studies con-ducted with the IEEE 14-bus, 57-bus and 118-bus test sys-tems. A conventional SCADA-based state estimator is em-ployed as a reference to evaluate the performance of the pro-posed approach for all cases. Both estimators have beenprogrammed in Fortran and run on a 2.9 GHz, 4.0 GB ofRAM Intel Core2 Duo computer. The measurement ac-curacy levels employed to perform the tests are 1% forSCADA and 0, 1% for PMU measurements.

To assess the performance of the estimators we makeuse of the voltage metric defined in [16]:

Maccv =V error

2=

j

V truej V estj2

1

2

(14)

where V truej and V estj are the true and estimated complexphasor voltage at the j-th bus, respectively. In addition, themean and standard deviation of the bus voltage magnitudeand phase estimation errors are also employed as perfor-mance indices in some of the test cases.

6.1 IEEE 14-bus system

The metering scheme for the IEEE 14-bus system is in-dicated on the one-line diagram shown in Figure 2. Table 1

presents the number of measurements of each type to beprocessed by both conventional and APSI estimators. Bysimple inspection, we can easily conclude that the networkis not PMU-observable, since only 9 phasor measurementsare available. On the other hand, the system is SCADA-observable, despite the presence of some critical measure-ments in the corresponding metering scheme.

Two test cases are performed with the IEEE 14-bus sys-tem, as follows:

Case A-1: The base case, in which all SCADA measure-ments processed at the first stage are all free of grosserrors, thus providing error-free a priori informationfor the APSI Estimator;

Case A-2: The voltage magnitude SCADA measurement atbus 10 is considered contaminated with a gross errorof size equal to 10 times the measurements standarddeviations. As a consequence, the a priori state infor-mation transferred to the APSI estimator is biased bythe simulated error.

Figure 2: IEEE 14-bus system with SCADA and PMU measurements

P Q |V | t u V ISCADA measurements 7 6 8 10 9 0 0PMS measurements 0 0 0 0 0 8 1

Table 1: Number of SCADA and PMU measurements for IEEE 14-bussystem.

2 4 6 8 10 12 140

1

2

3

4

5

6x 103

APSI EstimatorSCADAbasedestimatorUnobservable stateswith PMU meas. only

Figure 3: Voltage magnitude error for IEEE 14-bus system. Case A-1.


2 4 6 8 10 12 140

0.5

1

1.5

2

2.5

3

3.5

x 103

APSI EstimatorSCADAbased estimatorUnobservable stateswith PMU meas. only

Figure 4: Voltage angle error for IEEE 14-bus system. Case A-1.

The results for Case A-1 are presented in Figures 3 and4, which show the estimation errors for voltage magnitudesand angles at each bus of the network. The solid and dashedlines drawn in both figures have the sole purpose of facili-tating the identification of the APSI and SCADA-based esti-mates. Some interesting conclusions can be extracted fromboth plots, namely:

The results of the APSI estimator show that the esti-mates of state variables which are not PMU-observableare equal to the corresponding a priori estimates providedby the SCADA-based estimator. This is indicated in bothfigures by the coincidence of APSI and SCADA-basedestimation errors for those buses at which no PMU is in-stalled (the exception is the voltage phase at bus 1, wherethe identical error values are due to the definition of thatvariable as the angular reference for both estimators);

On the other hand, the APSI estimation errors for thebuses at which there is at least one adjacent phasor mea-surement are considerably reduced, as a consequence ofthe enhanced quality of the PMU data. These results alsoconfirm the effectiveness of the data weighting strategyadopted in the proposed APSI formulation, since the apriori information in this case are assigned much lessweight than the PMU measurements.

Case A-2 differs from the previous one in that a baddata is simulated on the voltage magnitude SCADA mea-surement at bus 10. As it turns out, that measurement iscritical, what magnifies the influence of the gross error onthe SCADA-based estimate for that state variable, as de-picted in Fig. 5 (for case A-2, only the voltage magnitudeerrors are shown). In fact, the estimate for voltage magni-tude at bus 10 is exactly equal to the value of the erroneousmeasurement. Since bad data on critical measurements areundetectable [10], this is a particularly delicate situation.However, Fig. 5 also shows that, even starting from ana priori information contaminated by the gross error, theAPSI estimator is able to filter the error out, since thereis a reliable phasor measurement (current measurement onbranch 9-10) adjacent to the affected state variables. Re-sults for the voltage metric of Eq. (14) for the same case aregiven in Table 2 and corroborate the previous analysis.

A situation similar to case A-2 but with no PMU mea-surement adjacent to the faulty measurement has also been

evaluated. In this case, the measurements processed at thesecond stage add no information to enhance the estimatefor state variable |V10| . Consequently, the final estimate forthat variable equals the erroneous value originated from theSCADA-based estimator.

Additional results considering the presence of bad datacontaminating members of critical sets of the SCADA me-tering scheme have also been simulated, but the details areomitted of this paper due to space limitations. As in case A-2, it has been observed that the APSI estimator is also ableto filter out the gross errors for those cases, provided thatthe region where the errors occur is properly monitored byPMU measurements.

2 4 6 8 10 12 140

0.02

0.04

0.06

0.08

0.1

0.12

0.14

APSI EstimatorSCADAbased estimator

Figure 5: Voltage magnitude error for IEEE 14-bus system. Case A-2.

Voltage MetricEstimator Case A-1 Case A-2SCADA-based 1.7658e-002 1.5292e-001APSI 1.0141e-002 1.0141e-002

Table 2: IEEE 14-bus performance index

6.2 IEEE 57-bus and 118-bus systems

The proposed APSI estimator has been also appliedto the IEEE 57-bus and 118-bus test networks. The me-tering schemes employed for both systems are presentedin Tables 3 and 5, and exhibit some common characteris-tics: all bus injection and branch flow power measurementsare taken in active/reactive pairs and branch current mea-surements are considered at both estimation stages, eitheras magnitude measurements (SCADA) or phasor measure-ments (PMUs). Both systems are SCADA-observable, butPMUs are not widely deployed throughout neither network,so that they are not PMU-observable. Finally, the cases re-ported in this paper do not include any bad data simulation.

The results for the 57-bus and 118-bus systems are pre-sented in Tables 4 and 6, respectively. They include valuesof the voltage metric defined in Eq. (14), as well as bus volt-age magnitude and angle mean and standard deviation val-ues, computed for both the SCADA and APSI state estima-tors. As expected, voltage metric and error mean values forthe APSI scheme are much lower than those obtained fromthe conventional SCADA estimator. For phase angles, theobserved reduction is larger than 55% in both systems. Er-ror standard deviation values are of the same order of mag-nitude for both estimators, but it is possible that the APSIvalues become larger than SCADAs. This is certainly due


to the non-uniform distribution of the PMU measurementsthroughout both networks, that is, the coexistence of zoneswith large concentration of PMUs and zones with no instal-lled PMUs, leading to a larger estimation error spreadingaround the error mean value in the APSI case.

P,Q |V | |I| t,u V ISCADA measurements 39 36 39 52 0 0PMS measurements 0 0 0 0 30 20


Voltage Error Mean Error Std DevEstimator Metric |V | |V | SCADA-based 4.42e-3 2.70e-4 4.82e-4 2.30e-4 1.70e-4APSI 2.60e-3 1.88e-4 1.77e-4 1.45e-4 2.14e-4


P,Q |V | |I| t,u V ISCADA measurements 72 67 45 116 0 0PMS measurements 0 0 0 0 63 65


Voltage Error Mean Error Std DevEstimator Metric |V | |V | SCADA-based 6.69e-3 2.78e-4 4.27e-4 1.24e-4 3.40e-4APSI 4.47e-3 1.99e-4 1.91e-4 1.81e-4 2.59e-4


7 ConclusionsA two-stage state estimator to allow the incorporation

of PMU measurements into power system real-time mod-eling without the risk of disrupting existing SCADA-basedestimators is proposed. Any existing conventional state esti-mator can be employed in the first stage. The resulting esti-mates are treated as a priori state information by the estima-tor at the second level, which processes only PMU measure-ments. The latter, referred to as APSI estimator, is based onan specialized orthogonal row-processing algorithm whichexhibits as one of its properties the capability of process-ing a priori information at virtually no extra computationalcost. An attractive feature of the proposed scheme is thatPMU-observability is not required, as long as the system isSCADA-observable.

The results presented in the paper show that the APSIestimator is able to take full advantage of the superior qual-ity of PMU data in order to enhance the a priori informa-tion generated by the SCADA estimator. This applies evento cases in which the SCADA estimates are obtained in thepresence of bad data, provided that reliable PMU measure-ments are available in the vicinity of the SCADA gross mea-surements.

The proposed estimator architecture is such that an EMSequipped with a conventional state estimator and accessto PMU measurements taken on the SCADA-monitorednetwork could easily update its real-modeling capabilitythrough the APSI scheme. The amount of informationneeded to be transferred between both modules is not large,since it consists of the SCADA state estimates and corre-sponding estimation error variances.

Finally, a number of issues still deserve further researchefforts, such as bad data processing at the second level and

the measurement model employed by the APSI estimator,which is presently based on polar coordinates and nonlin-ear. Since there is no theoretical reason to prevent the adop-tion of other modeling frameworks, the use of a linear mea-surement model seems to be feasible. Those topics will bepursued in the next stages of this research.

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