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IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 25, NO. 1, FEBRUARY 2010

Robust Measurement Design by Placing Synchronized Phasor Measurements on Network Branches Roozbeh Emami, Student Member, IEEE, and Ali Abur, Fellow, IEEE

Abstract—This paper is concerned about optimal placement of synchronized phasor measurements that can monitor voltage and current phasors along network branches. Earlier investigations on placement of phasor measurement units (PMUs) have assumed that a PMU could be placed at a bus and would provide bus voltage phasor as well as current phasors along all branches incident to the bus. This study considers those PMUs which are designed to monitor a single branch by measuring the voltage and current phasors at one end of the monitored branch. It then determines the optimal location of such PMUs in order to make the entire network observable. The paper also addresses the reliability of the resulting measurement design by considering loss or failure of PMUs as well as contingencies involving line or transformer outages. Developed placement strategies are illustrated using IEEE test systems. Index Terms—Contingencies, critical measurements, meter placement, network observability, phasor measurements, state estimation.

I. INTRODUCTION

S

YNCHRONIZED phasor measurement units (PMUs) are rapidly populating substations in transmission systems. These devices provide unprecedented advantages for system operation and control due to the availability of phasor voltages and currents with respect to a common global time reference, even though they are measured at physically remote parts of a given system. Practical budget constraints do not allow installation of these devices at each and every network branch, at least not in the near future. Hence, transmission operators are faced with the decision of how best to utilize their limited number of PMUs so that their benefits can be maximized. These issues are recognized early on by the researchers and articulated in related publications [1], [2]. Initial work on PMU placement is based on the assumption that PMUs will have infinite number of channels to monitor phasor currents of all branches that are incident to the bus where a PMU will be installed [3], [4]. While there are manufacturers which produce PMUs with several channels to measure currents and voltages, the number of channels is typically limited. Also, note that PMUs capture samples of phase voltages and currents that are received from the instrument transformers connected to Manuscript received June 24, 2009; revised July 25, 2009. First published December 15, 2009; current version published January 20, 2010. This work was supported in part by the Entergy Corporation and in part by the Power System Engineering Research Center (PSERC). Paper no. TPWRS-00056-2009. The authors are with the Department of Electrical and Computer Engineering, Northeastern University, Boston, MA 02115 USA (e-mail: [email protected]. edu; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPWRS.2009.2036474

a bus or a breaker in the substation. The sampled three phase signals are converted into positive sequence phasors at regular intervals and then telemetered to the phasor data concentrators. Phasor measurements are used by various application functions at energy control centers. One such application is state estimation which not only provides the best estimate of the system state but also acts as filter for gross errors in analog and digital measurements. Moreover, results of state estimation are used by many applications as inputs and therefore have a significant impact on the overall performance of the energy management systems. Some of the applications that rely on state estimation results include real-time contingency analysis, voltage stability assessment, transient stability assessment, real-time power flow, security constrained optimal power flow, load forecasting as well as the market applications. In addition to the types of PMUs discussed so far having several channels, there are also PMUs that are designed to monitor a single line or transformer, i.e., they provide positive sequence voltage and current phasors measured at one terminal of the monitored branch. These types of PMUs will be referred as the “branch PMUs” in the sequel. Such PMUs are currently installed and in use at substations of large utility companies in the world [5] and preliminary studies are conducted to determine best locations for their placement [6]. Certain utility companies are known to use branch PMUs and daisy-chain them as needed to increase capacity at a given bus. This paper presents an optimal placement strategy for such companies to achieve a reliable monitoring system design at minimum installation cost. Previous studies on placement of PMUs implicitly assumed static topologies and ignored the possibility of PMU loss or failure. Hence, proposed designs provide observable systems as long as the system operating conditions do not necessitate switching of major lines or transformers and all of the PMUs provide continuous uninterrupted measurements. However, event logs for any utility company carry enough evidence to invalidate these assumptions. This constitutes the main motivation of the work presented in this paper where PMU placement problem is formulated by using branch PMUs and by taking into account major contingencies that are analyzed for system security and loss of any single PMU. Guarding against the loss of a single PMU implicitly ensures that gross errors in any single PMU measurement can be detected. The paper first describes an optimal placement strategy for “branch” PMUs in order to have a fully observable network using only such PMUs. Realizing that this may be a too ambitious project to complete in one shot, the study then considers any existing system and looks at improving bad data detection capability by optimal placement of “branch” PMUs in order to transform all existing critical measurements into redundant ones,

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EMAMI AND ABUR: ROBUST MEASUREMENT DESIGN

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making all bad data detectable. The paper then presents placement strategies to maintain network observability during a set of predefined line outage contingencies as well as loss of PMUs. II. OBSERVABILITY PROBLEM The problem of multichannel PMU placement in power systems is well documented [3], [4], [7] where one PMU is assumed to have the capability to measure voltage phasor at a given bus and current phasors along all incident branches to that bus. The method of earlier studies is based on the assumption that a PMU can measure as many signals as available. In other words, a PMU can measure a voltage phasor corresponding to the bus where PMU is installed, along with phasor current of all branches incident to that bus. Although this can simplify calculations, this assumption is not realistic. It is shown in [4] that using multichannel PMUs for an bus system, placement of roughly PMUs will lead to a fully observable system. However this number may decrease if zero injections are considered. This section investigates the problem of optimal placement of “branch” PMUs in the system to make it fully observable. A branch PMU is capable of measuring the voltage phasor of the corresponding bus, and the phasor current of only one of the branches incident to the bus where PMU is installed. Thus, each PMU provides two phasor measurements in the system. Therefore, for an N bus system, the minimum number of branch PMUs needed to make the system fully observable will be the next larger . This can be proven easily by assuming integer after a strictly radial system where every other branch will have to be assigned a PMU in order to make the entire network observable. Also, it is noted that incorporating any existing zero injections will modify the optimal locations and reduce the required number of PMUs. One way to accomplish this is described in [4]. Since it does not change the formulation of the PMU placement problem considered in this paper, zero injections will be ignored in the sequel. If needed, they can be accounted for by using the same approach as illustrated in [4]. The problem of PMU placement for a system with buses and branches can be formulated as follows:

(1) where number of branches in the system; vector of size whose th element, , is the binary variable which is 1 or 0 depending on whether a PMU is placed on branch or not; cost of installation of PMU on branch ; bus to branch connectivity matrix, which is defined as if branch is incident to bus otherwise; .

Fig. 1. Five-bus system network diagram.

Fig. 2. The 14-bus system network diagram.

Note that branch PMUs can be placed at either end of the branch since in either case both terminal bus voltages will be known due to the availability of the branch current. So, the problem formulated in (1) assigns PMUs to branches and not to buses. If a PMU is assigned to a branch, it can be placed arbitrarily at either end of that branch without changing the outcome of network observability analysis. Solution of the integer programming (IP) problem given in (1) will yield the optimal locations where branch PMUs should be installed. The bus-branch incidence matrix T for a

simple five-bus system of Fig. 1 can be formed as follows. Assuming that the cost of installation for all PMUs is the same, one optimal solution for PMU placement for this system will be given by

This implies that branch no. 1, 3, and 4 are the optimal locations for branch PMUs. When the same procedure is applied to the 14-bus system shown in Fig. 2, optimal branch PMU placement results will be as given in Table I. III. BAD DATA PROBLEM In the above section, the problem of branch PMU placement is considered for a system initially having no measurements.

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IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 25, NO. 1, FEBRUARY 2010

TABLE I OPTIMAL LOCATIONS OF PMUS FOR THE 14-BUS SYSTEM

Fig. 3. Six-bus system used for bad data problem.

This is based on the assumption that the entire system will be observed by PMUs only. A more realistic scenario in the short term would consider a system which contains a significant amount of conventional measurements and few branch PMUs are to be placed for maximum benefit. This section considers this case. Detection of bad data in analog measurements is one of the essential benefits of any state estimator. Bad data detection capability depends primarily on the measurement configuration or more specifically on the absence of the so-called “critical” measurements. Loss of these measurements will cause the system to become unobservable and furthermore any bad data in these measurements cannot be detected. An approach to optimally place PMUs with multiple channels in order to transform all critical measurements into redundant ones is recently presented in [8]. In this paper, this approach is revised so that it can optimally place branch PMUs for the same purpose. The steps of the revised algorithm are as follows: 1) Form the measurement Jacobian . 2) Augment the rows of by adding rows corresponding to all candidate branch PMUs. Let the added submatrix be . denoted as 3) Apply rectangular LU factorization to the augmented using the Peters-Wilkinson method described in [9]. Row pivoting during this factorization is limited to the rows corresponding to the existing measurements only. Using this limited pivoting, if a zero pivot is encountered, then it will imply that the system is unobservable. In this case, row pivoting limit will be relaxed to first use the candidate PMU measurements in order to make the system observable. 4) After step 3, the first n rows of will correspond to a minimally observable measurement set for the system. Hence, the measurement Jacobian can be partitioned as follows:

6) Calculate the test matrix

:

Any null column in matrix will signal existence of a critical measurement which will correspond to the pivot row above. Let column m be the null column, then this in critical measurement can be transformed into a redundant one by adding any one of the PMUs whose row entry is nonzero in column m of the submatrix . The main difference between the formulation given in [8] and this one is in the definition of the candidate PMUs and therefore is formed. in the way model is used, nonzero eleDue to the fact that the ment in a column represents a phasor measurement at the bus corresponding to that column. Also, a branch PMU provides the phasor information at both terminal buses of the line where PMU is installed. As a result, a branch PMU can be modeled by nonzero elements at the columns corresponding to the terminal buses. As an example consider a simple six-bus system shown in Fig. 3. for this system is given as follows: The corresponding

where the rows of the submatrices will correspond to minimally observable measurements; existing redundant measurements; branch PMU measurements. 5) Factorize

and obtain its partitioned factors:

Injections at buses 1 and 5 and power flow in branch 3–2 are identified as critical measurements. Solving the integer programming problem yields branch 3–5 as the optimal location to install a PMU to transform all the critical measurements into redundant ones. Note that, in this particular case, the same task could have been accomplished by placing at least two power flow measurements.

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Applying the Peters-Wilkinson factorization, the lower triangular factor “ ” will be obtained as

Fig. 4. Contingency case: Line 3–4 is out of service.

IV. ROBUSTNESS AGAINST CONTINGENCIES System observability relies on location and type of the measurements as well as the network topology. Network topology may change due to daily switching operations. It is prohibitively expensive to design the measurement system to maintain observability during all possible topology changes. Therefore, a list of most important contingencies is drawn for a given system and the measurement system is designed to be robust against these contingencies. One possible placement strategy using multichannel PMUs is presented in [5]. In this paper this problem is reformulated for the case of branch PMUs. The first stage involves determining whether the considered contingency causes any change in system observability. If the system remains observable after topology change, then no action is required. Else a set of candidate PMUs will be identified such that placing any of those will restore the observability of the system. Identification of candidate PMUs can be done as follows: which contains all ex1) Form the augmented Jacobian isting measurements followed by the candidate PMU measurements. For each contingency, remove the line which is opened during the contingency and modify the relevant entries in . 2) Factorize by limiting the row pivoting to the rows associated with the existing measurements only. If the contingency causes unobservability, a zero pivot will be encountered. 3) Trace the column below the zero pivot in the lower triangular factor and the candidate PMU measurements will be given by those with nonzero entries in this column. In order to illustrate this approach, consider the four-bus system measurement configuration given in Fig. 4. In addition to the given measurements, every branch will be assumed to have a candidate PMU. Line 3–4 outage will be used as the only contingency. Note that the system will become unobservable if line 3–4 is removed. Note that when a branch PMU is placed on branch 1–3, the voltage phasor at bus 1 and the current phasor in branch 1–3 will both be measured. Modified after the removal of line 3–4 is shown below. Please note that after the outage of line 3–4, the modified Jacobian matrix which includes candidate PMUs will be given as

Note that a null column is introduced as the fourth column in order to highlight the rank deficiency of H using only the existing measurements. Furthermore, the rows of H (columns of ) corresponding to the candidate PMUs include phase angles at the sending-end bus as well as the phase angle differences between the terminal buses of the branches where candidate PMUs are to be placed. To restore system observability both zero pivots (columns 2 and 4) should be transformed into nonzeros in . Since the linear decoupled model is used to create the Jacobian matrix each branch PMU will contribute a phase angle at the sending-end bus and a phase angle difference between the sending and receiving-end buses. Each PMU will be modeled by these two measurements. If any pair of measurements corresponding to a PMU can remove both zero pivots in the matrix, that PMU will be chosen to restore system observability. The procedure to choose candidate PMUs to replace zero pivots is as follows: 1) Set candidate PMU counter . 2) Apply Peters-Wilkinson factorization to the H matrix by limiting the row pivoting to the two rows corresponding to candidate branch PMU “k”. 3) If no zero pivots are encountered, then PMU “k” will be flagged as capable of removing both zero pivots and therefore restoring network observability. Create a new flag array F and set , where nz is the number of zero pivots eliminated. If all of the zero pivots remain, then let . 4) Increment PMU counter, . 5) If , stop. Else, go to step 2). For the four-bus example system, the flag array F will be given by

Now an integer programming problem can be formulated as follows:

where cost of installation of PMU at bus ; binary variable indicating whether or not a PMU is placed in branch ; number of zero pivots encountered in when using only the existing measurements.

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IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 25, NO. 1, FEBRUARY 2010

For the four-bus example, since two zero pivots exist in lower . PMUs in branches 2–4 and 4–2 can triangular matrix, therefore restore the observability of the system in the case of the considered contingency. Repeating the above described procedure for each contingency yields a set of candidates for each contingency and a contingency to candidate incident matrix can be formed. V. LOSS OF PMU AND MULTIPLE CONTINGENCIES The problem of optimal placement of branch PMUs to have a fully observable system is discussed earlier in this paper. However, the possibility of a PMU failure is not considered. The failure of any PMU may result in loss of network observability or it may decrease the capability to detect bad data in the system. Another concern is the possibility of multiple contingencies occurring either simultaneously or in cascade within a short period of time. When such possibilities are taken into account, a robust PMU placement can be accomplished. The proposed method can increase the reliability of the system in such a way that failure of even several PMUs and multiple simultaneous contingencies can be handled. In general, the proposed method will work unless both original and backup PMUs that are incident to a given bus are simultaneously lost either due to the multiple contingencies or PMU failure. The proposed method to find the backup set of PMUs for an already installed set of PMUs is as follows: 1) Find the optimal set of PMUs to have an observable system as discussed in Section II. 2) Remove all branches with PMU placements in step 1. Let all the columns of the matrix that correspond to PMU assigned branches be stored in a new matrix called . Let be stored as matrix . Each the remainder of matrix column of matrix corresponds to a branch with no PMU at either ends. 3) If there is no null row in , no further action is required. matrix can be replaced as in (1) and the solution of integer programming will yield the optimal solution for backup PMUs of those found in step 2. Else, let row of be null. Find all columns of whose th row is nonzero. If only one column is found, simply augment by attaching this column to . If more than one column with nonzero entries in row is found, choose the one whose receiving end bus is least repeated in matrix. 4) Replace matrix by the modified . Solve the integer programming problem and obtain the new set of backup PMUs for the previous set. For illustration, the method is applied to a simple seven-bus system shown in Fig. 5. The branch to bus incident matrix for this system is

Fig. 5. Seven-bus system.

The optimal original set of PMUs to have a fully observable so and modified matrices can system is be written as

matrix represents those branches of the system where matrix correspond to no PMU is assigned. Null rows in buses which cannot be reached by placing PMUs on remaining branches. This may happen if all of the branches incident to a given bus are already chosen in the original set of PMUs (Bus 2). Removing all those branches from the branch to bus incident matrix creates a null row for that bus in . A special case is when there is a radial branch (4–6) which can only become observable by assigning a PMU to the branch. Since this branch will also belong to the original PMU set and there is no other connection to that bus, the row corresponding to the remote end bus (4) in will be null. In these two cases, columns corresponding to added branches are moved from to and hence integer programming solution will assign repeated PMUs to these branches, i.e., these branches will appear in both the primary and backup branch PMU sets. In the above seven-bus system example, second and fourth rows of are null. Therefore columns are to be added to from . Both columns 1 and 2 of have nonzero entries in their 2nd row. Column 1 of represents branch 1–2, the receiving end of which is bus 1. Column 2 of D corresponds to branch 2–3, receiving end of which is bus 3. Since bus 1 is repeated less in , branch 2–1 is chosen to be added to P. Such a choice is not required for row 4 since there is only one candidate column with a nonzero row 4. Hence first and third columns are added to P. The new P will then look like

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EMAMI AND ABUR: ROBUST MEASUREMENT DESIGN

TABLE II ORIGINAL AND BACKUP PMU PLACEMENTS FOR THE 30-BUS SYSTEM

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paper considers the so-called branch PMUs which monitor a single branch by measuring the associated current and terminal voltage phasors. The study also takes into account PMU failures and network contingencies that involve topology changes. Furthermore, bad data detectability of PMU measurements is also addressed. An optimal PMU placement strategy is developed for this purpose. The developed method is applied to small test systems as well as to a large utility system and results are presented. ACKNOWLEDGMENT The authors would like to thank Mr. F. Galvan of Entergy Corporation for the contributions during the course of this project. REFERENCES

: shows the repeated branches in both original and backup location.

IP solution will be given as . Hence, there are only two additional PMUs to be installed in the system as backups since PMUs in branches 1–2 and 4–6 are already installed as part of the primary set. Clearly for those cases when a PMU that is assigned to a radial branch fails, it will not be possible to avoid creation of observable islands. On the other hand, duplicate PMUs can be installed at opposite ends of such lines. While this will account for PMU failures, it can still not avoid unobservability if the line is disconnected due to a fault. This method is tested on the IEEE 30-bus test system. Table II shows the results of original and backup PMUs obtained for this case. VI. CASE STUDY The method is applied to a large utility system with 2285 buses. It is found that 1291 branch PMUs will be needed for a fully observable system. Considering the existing 649 zero injections in the system decreases the number of required branch PMUs to 1005. Also, 165 critical measurements are found for this system and 135 branch PMUs are required to transform these critical measurements. Also, the optimal placement of branch PMUs for top 20 contingencies of this system are obtained. VII. CONCLUSIONS Placement of synchronized phasor measurements has so far been investigated utilizing multi channel PMUs. This

[1] A. G. Phadke, “Synchronized phasor measurements in power system,” IEEE Comput. Appl. Power, vol. 6, no. 2, pp. 10–15, Apr. 1993. [2] D. Novosel, K. Vu, V. Centeno, S. Skok, and M. Begovic, “Benefits of synchronized measurement technology for power grid applications,” in Proc. 40th Annu. Hawaii Int. Conf. System Sciences, Jan. 2007, pp. 118–120. [3] T. L. Baldwin, L. Mili, M. B. Boisen, and R. Adapa, “Power system observability with minimal phasor measurement placement,” IEEE Trans. Power Syst., vol. 8, no. 2, pp. 707–715, May 1993. [4] B. Xu and A. Abur, “Observability analysis and measurement placement for systems with PMUs,” in Proc. IEEE PES Power Systems Conf. Expo., New York, Oct. 10–12, 2004. [5] F. Galvan, The Eastern Interconnect Phasor Project-Modernizing America’s Electric Grid, PES TD 2005/2006, May 21–24, 2006, pp. 1343–1345. [6] R. Emami, A. Abur, and F. Galvan, “Optimal placement of phasor measurements for enhanced state estimation: A case study,” in Proc. PSCC, Glasgow, U.K., 2008. [7] R. F. Nuqui and A. G. Phadke, “Phasor measurement unit placement techniques for complete and incomplete observability,” IEEE Trans. Power Del., vol. 20, no. 4, pp. 2381–2388, Oct. 2005. [8] J. Chen and A. Abur, “Placement of PMUs to enable bad data detection in state estimation,” IEEE Trans. Power Syst., vol. 21, no. 4, pp. 1608–1615, Nov. 2006. [9] G. Peters and J. H. Wilkinson, “The least-squares problem and pseudoinverses,” Comput. J., vol. 13, no. 4, pp. 309–316, Aug. 1970. [10] Power System Test Case Archive, Univ. Washington. [Online]. Available: http://www.ee.washington.edu/research/pstca/pf30/pg_tca30bus. htm. [11] A. G. Exposito and A. Abur, “Generalized observability analysis and measurement classification,” IEEE Trans. Power Syst., vol. 13, no. 3, pp. 1090–1096, Aug. 1998.

Roozbeh Emami (S’07) received the B.S. degree from Khajed Nassir University of Technology, Tehran, Iran, in 2003 and the M.S. degree from Iran University of Science and Technology, Tehran, in 2006. He is currently pursuing the Ph.D. degree in the Department of Electrical and Computer Engineering at Northeastern University, Boston, MA.

Ali Abur (F’03) received the B.S. degree from Orta Dogu Teknik Universitesi, Ankara, Turkey, in 1979 and the M.S. and Ph.D. degrees from The Ohio State University, Columbus, in 1981 and 1985, respectively. He was a Professor at the Department of Electrical Engineering, Texas A&M University, College Station, until November 2005, when he moved to Northeastern University, Boston, MA, as the Chair of the Electrical and Computer Engineering Department. His research interests are in computational methods for the solution of power system monitoring, operation, and control problems.

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