Optimal Placement of Phasor Measurement Units for State Estimation

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1 PSERC Optimal Placement o Phasor Measurement Units or State Estimation Final Project Report Power Systems Engineering Research Center A National Science Foundation Industry/University Cooperative Research Center since

2 Power Systems Engineering Research Center Optimal Placement o Phasor Measurement Units or State Estimation Final Project Report Report Authors Bei Xu Ali Abur Teas A&M University PSERC Publication - October

3 Inormation about this project For inormation about this project contact: Ali Abur, Ph.D. Teas A&M University Department o Electrical Engineering College Station, TX - Phone: -- Fa: -- abur@ee.tamu.edu Power Systems Engineering Research Center This is a project report rom the Power Systems Engineering Research Center (PSERC). PSERC is a multi-university Center conducting research on challenges acing a restructuring electric power industry and educating the net generation o power engineers. More inormation about PSERC can be ound at the Center s website: For additional inormation, contact: Power Systems Engineering Research Center Cornell University Phillips Hall Ithaca, New York Phone: -- Fa: -- Notice Concerning Copyright Material PSERC members are given permission to copy without ee all or part o this publication or internal use i appropriate attribution is given to this document as the source material. This report is available or downloading rom the PSERC website. Teas A&M University. All rights reserved.

4 Acknowledgements The Power Systems Engineering Research Center (PSERC) sponsored this project as a targeted project through supplemental unding rom Tennessee Valley Authority (TVA) as a research project titled Optimal Placement o Phasor Measurement Units or State Estimation. The project began in September and is completed in July. We epress our appreciation or the support provided by TVA. We also epress our appreciation or the support provided by PSERC s industrial members and by the National Science Foundation under grant NSF EEC- received under the Industry / University Cooperative Research Center program. The authors thank all PSERC members or their technical advice on the project. Special thanks to Wai-Ran Wu, Lisa Beard, Joshua Shultz, Ian Grant, Armando Rodriguez, Gary Bullock, Clay DeLoach, Gregory Dooley, and Mike Ingram rom TVA, and Jay Giri rom AREVA T&D or their assistance in providing the two versions o the system and measurement data or the TVA system. i

5 Eecutive Summary This report describes a study undertaken to determine the optimal locations o phasor measurement units () or a given power system. Power systems are rapidly becoming populated by. have multiple uses at substations. They provide valuable phasor inormation or protection and control o power systems during abnormal operation. Under normal operations, they also help in monitoring the system state. This project ocuses on the use o PMU measurements in state estimators. The principle objective was to investigate methods o determining optimal locations or so that the system state o an entire power system can be observable. Several actors aect how this can be accomplished, such as the available data rom eisting conventional measurements, the number and location o zero injection buses, the number and location o installed, and, o course, the system topology. Two new procedures were used to solve the problem o optimally locating. One is a numerical procedure where the problem is ormulated as an integer optimization problem. The solution algorithm was implemented in a computer program. Several case studies were conducted to evaluate the algorithm s perormance. The other procedure is a topology-based method which inds the strategic locations or by merging observable islands. Standard test systems were irst used to validate the sotware program or simple cases using the topology-based method. Subsequently, TVA s internal system data were used to obtain results or a large system. We ound that the entire system can be made observable by strategically placing at one-third o the system buses or a given system. Fewer may be needed i there are zero injection buses in the system. The sotware is developed in Matlab using an eternal optimization program (TomLab) which is used to implement the integer programming solution. The results o the project can be etended to investigate the beneits o adding a small number o at strategic locations to improve bad data detection and identiication capability in the system. Similarly, it may be worthwhile to investigate the placement o a ew or purposes o eliminating the possibility o unobservable states during epected topology changes or contingencies. ii

6 Table o Contents. State Estimation and Network Observability.... Introduction.... Project Objectives and Description.... Developed Methods.... Integer Programming Based Procedure.... Topology Based Procedure.... Placement Strategy Against Loss o a Single PMU.... Illustrative Eamples.... IEEE -bus system.... IEEE -bus system.... IEEE -bus system.... IEEE -bus system.... TVA System Case Studies.... TVA System (version ).... TVA System (version ).... Conclusions and Future Work... Reerences... Project Publications... iii

7 Table o Figures Figure.. PMU placement on IEEE -Bus System... Figure.. IEEE -bus system with conventional measurements... Figure.. System diagram ater the merger o buses and... Figure.. Observable islands o IEEE -bus system... Figure.. IEEE -bus system... Figure.. IEEE -bus system... Figure.. IEEE -bus system... Figure.. IEEE -bus system... iv

8 Table o Tables Table. System inormation o IEEE -bus system... Table. Simulation results or -bus system without considering single PMU loss... Table. Simulation results or -bus system considering single PMU loss... Table. System inormation o IEEE -bus system... Table. Simulation results or -bus system without considering single PMU loss... Table. Simulation results or -bus system considering single PMU loss... Table. System inormation o IEEE -bus system... Table. Simulation results or -bus system without considering single PMU loss... Table. Simulation results or -bus system considering single PMU loss... Table. System inormation o IEEE -bus system... Table. Simulation results or -bus system without considering single PMU loss Table. Simulation results or -bus system considering single PMU loss... Table. Measurements inormation or IEEE -bus system... Table. Simulation results or -bus system considering conventional measurements... Table. Brie inormation o TVA system (version )... Table. Bus names and numbers with installed... Table. Bus names and numbers where are scheduled to be installed... Table. Results o case studies or the TVA data (version )... Table. Detailed results or case... Table. Detailed results or case... Table. Detailed results or case... Table. Detailed results or case... Table. System inormation o TVA system (version )... Table. Inormation o installed in TVA system (version )... Table. Simulation results o TVA system (version ) without considering conventional measurement, zero injections or... Table. Simulation results o TVA system (version ) considering conventional measurement and zero injections... Table. Simulation results o TVA system (version ) considering conventional measurement and zero injections... v

9 . State Estimation and Network Observability. Introduction Secure operation o power systems requires close monitoring o the system operating conditions. This is traditionally accomplished by the state estimator which resides in the control center computer and has access to the measurements received rom numerous substations in the monitored system. By collecting analog measurements and the status data o the circuit breakers rom remotely monitored and controlled substations and eeding them as input into state estimation unction, state estimation can provide an estimate or all metered and un-metered electrical quantities and network parameters o the power system, detect and ilter out gross errors in the measurement set and detect the topology errors in the network coniguration. Until recently, available measurement sets did not contain phase angle measurements due to the technical diiculties associated with the synchronization o measurements at remote locations. Global positioning satellite (GPS) technology alleviated these diiculties and lead to the development o phasor measurement units (PMU). Synchronized Phase Measurement Unit (PMU) is a monitoring device, which was irst introduced in mid-s. Phasor measurement units (PMU) are devices, which use synchronization signals rom the global positioning system (GPS) satellites and provide the phasors o voltage and currents measured at a given substation. As the become more and more aordable, their utilization will increase not only or substation applications but also at the control centers or the EMS applications. One o the applications, which will be signiicantly aected by the introduction o, is the state estimator. TVA is in the process o installing phasor measurement units (PMU) or enhanced monitoring o the TVA system. In order to avoid redundant use o, the optimal locations or the new must be determined. The objective this project is to make use o a minimum number o in order to make the system ully observable. Installation o will be a gradual process, requiring decisions on the best possible locations or a limited number o at the beginning. Hence, a systematic method is needed or inding the best locations or new in the presence o other already placed and/or conventional measurements. This project investigates this issue and provides a practical solution or the PMU placement problem.. Project Objectives and Description State estimators provide optimal estimates o bus voltage phasors based on the available measurements and knowledge about the network topology. These measurements are commonly provided by the remote terminal units (RTU) at the substations and include real/reactive power lows, power injections, and magnitudes o bus voltages and branch currents. More recently, synchronized phasor measurements have started to become available at selected substations in the system. One o the issues aced by the planning engineers is how to select the best locations to install new.

10 The idea o using direct phasor measurements or system monitoring applications including the speciic case o state estimation is not new. Earlier work done by Phadke and his co-workers [-] introduces the use o or such applications. This work is later etended to the investigation o optimal location o where each PMU is assumed to provide voltage and current phasors at its associated bus and all incident branches []. It is thereore possible to ully monitor the system by using relatively small number o much less than the number o buses in the system. This problem is ormulated and solved by using a graph theoretic observability analysis and an optimization method based on Simulated Annealing in []. Possible loss or ailure o is not considered in that study. This project is concerned about the optimal placement o so that they can provide the maimum beneit or the state estimation unction. It is understood that these devices have multiple uses and thereore their placement may have to be based on considerations related to several other applications, however this study limits its scope to the speciic application o state estimation. Hence, the objective o the placement problem is to ensure that the entire system remains a single observable island or the given measurement set. In this report, two dierent procedures are proposed to solve the PMU placement problem. First, a numerical method based on integer programming will be presented. The ormulation o the problem acilitates analysis o network observability and is general enough to account or the eistence o zero and non-zero power injections and power low measurements. There are two dierent ways to treat zero and non-zero power injection measurements using this method. One is via the use o non-linear constraints, and the other one is based on a special topology transormation. These two methods will be illustrated in this report using the IEEE -bus as an eample. The procedure can also be etended to account or loss o single. Net, an alternative procedure o PMU placement or systems with a large number o conventional measurements and ew observable islands is also developed. The eiciency o this method increases with the number o already eisting measurements. By placing at the strategic boundary buses and merging the ew eisting observable islands, an observable system will be quickly rendered. This report is organized in our sections. Section contains the details o the developed methods or the solution o the optimal PMU placement problem. The two alternative methods, which are mentioned above, are described irst, ollowed by the discussion o the case where loss o single PMU is considered as an added reliability criterion. Section presents numerical results obtained by applying the developed methods to standard IEEE test systems with typical measurement conigurations. Finally, the optimal PMU placement results obtained or two dierent sets o network and measurement data received rom TVA are presented in section. Conclusions and inal remarks are added at the end o the report.

11 . Developed Methods provide two types o measurements: bus voltage phasors and branch current phasors. Depending on the type o used the number o channels used or measuring voltage and current phasors will vary. In this report, it is assumed that each PMU has enough channels to record the bus voltage phasor at its associated bus and current phasors along all branches that are incident to this bus. The objective o the PMU placement problem is to render an observable system by using a minimum number o. An eample o an optimally placed set o in a -bus system is shown below in Figure.. Figure.. Optimal PMU placement or a -bus test system

12 In this system, there are three placed at buses, and respectively. Bus is the only zero injection bus. The PMU at bus can not only measure the voltage phasor o bus, but also the current phasors o branches -, -, - and -. Using Ohm s law, the voltage phasors at buses,, and can be obtained rom the branch currents and the voltage at bus. Having determined voltage phasors at buses,,,, and, the current phasors o branches -, - and - can be calculated. Following the same logic, PMU at bus can measure the voltage phasor at bus and the current phasors o branches -, -, - and -, thus allowing the calculation o the voltage phasors at buses,,, and the current phasor o branch -. PMU at bus can measure the voltage phasor at bus and the current phasors o branches -, -, -, - and allow the calculation o the voltage phasors at buses,,,, and the current phasors o branches -. As voltage phasors o buses,,, are known, current phasors o branches - and - can now also be calculated. Using the known current phasors o branches - and -, and the zero injection at bus, the current phasor o branch - can be derived using the Kirchho s Current Law. The only remaining unknown voltage phasor at bus can now be calculated by using the voltage phasor at bus and the current phasor o branch -. Thus the entire system becomes observable by placing only three at buses,, and by considering the zero injection at bus. In this report, two dierent procedures are introduced to solve the PMU placement problem. One is an integer based programming method, and the other one is a topologybased method. Both o these methods will be discussed in detail via the use o the IEEE -bus eample in the ollowing sections.. Integer Programming Based Procedure In this section, a numerical method based on Integer Programming will be presented to solve the optimal PMU placement problem. The ormulation o problem is shown as below. For an n-bus system, the PMU placement problem can be ormulated as ollows: min n i w s. t. ( X ) ˆ i i (.) where X is a binary decision variable vector, whose entries are deined as: i i a PMU is installed otherwise at bus i

13 w i is the cost o the PMU installed at bus i. (X ) is a vector unction, whose entries are non-zero i the corresponding bus voltage is solvable using the given measurement set and zero otherwise. ˆ is a vector whose entries are all ones. Inner product o the binary decision variable vector and the cost vector represents the total installation costs o the selected. Constraint unctions ensure ull network observability while minimizing the total installation cost o the. The procedure or building the constraint equations will be described or three possible cases where there are () no conventional measurement or zero injections, () low measurements or () low measurements as well as injection measurements (they may be zero injections or measured injections). Description o the procedure or each case will be given using IEEE -bus system eample or clariication. However, the entire procedure is actually programmed and successully tested on dierent size systems with diverse measurement conigurations. Consider the IEEE -bus system and its measurement coniguration shown in Figure.. The black dot near bus represents that bus is a zero injection bus (or has a injection measurement installed) while the black bo on line - represents a paired low measurement on line -. Figure.. IEEE -bus system with conventional measurements Case. A system with no conventional measurements and/or zero injections In this case, the low measurement and the zero injection are ignored. In order to orm the constraint set, the binary connectivity matri A, whose entries are deined below, will be ormed irst: i k m or k i otherwise A k, m and m are connedted Matri A can be directly obtained rom the bus admittance matri by transorming its entries into binary orm. Building the A matri or the -bus system yields:

14 A (.) The constraints or this case can be ormed as: ) ( X A X (.) The operator serves as the logical OR and the use o in the right hand side o the inequality ensures that at least one o the variables appearing in the sum will be non-zero. For eample, consider the constraints associated with bus and as given below:

15 The irst constraint implies that at least one PMU must be placed at either one o buses, or in order to make bus observable. Similarly, the second constraint indicates that at least one PMU should be installed at any one o the buses,,,, or in order to make bus observable. Case : A system with some low measurements. This case considers the situation where some low measurements may be present. Flow measurement on branch - in the -bus eample system will be used to illustrate the approach on how to deal with eisting low measurements. Eistence o this low measurement will lead to the modiication o the constraints or buses and accordingly. Modiication ollows the observation that having a low measurement along a given branch allows the calculation o one o the terminal bus voltage phasors when the other one is known. Hence, the constraint equations associated with the terminal buses o the measured branch can be merged into a single constraint. In the case o the eample system, the constraints or buses and are merged into a joint constraint as ollows. _ new which implies that i either one o the voltage phasors at bus or is observable, the other one will be observable. Applying this modiication to the constraints or the -bus system, the ollowing set o constraints will be obtained: ) ( _ X new (.)

16 Case : A system with both injection measurements (some o which may be zero injection pseudo-measurements) and low measurements. This case considers the most general situation where both injection and low measurements may be present, but not enough to make the entire system observable. Injection measurements whether they are zero injections or not, are treated the same way. Consider again the same -bus system, where bus is a zero injection bus. It is easy to see that i the phasor voltages at any three out o the our buses,, and are known, then the ourth one can be calculated using the Kirchho s Current Law applied at bus where the net injected current is known. There are two dierent ways to treat the injection measurements and orm the constraints. One is to orm non-linear constraints or the neighbors o the buses, which have injection measurements installed. The alternative approach involves a topology transormation. These will be discussed separately net. a) Forming non-linear constraints One way to treat the injection buses is to modiy the constraints associated with the neighboring buses o these buses and orm a set o non-linear constraints. This is accomplished as shown below. To treat the zero injection bus in the IEEE -bus system, constraints associate with its neighboring buses, and will be modiied as ollows, Note that the operator. serves as the logical AND in the above equations. The epressions or i can be urther simpliied by using the ollowing properties o the logical AND (.) and OR () operators: Given two sets A and B, where set A is a subset o set B, then B B A and A B A. For instance, substituting the epression or in the epression or, can be written as: ) (

17 The product is eliminated because it is the subset o, which already eists in the epression. Using similar reasoning, and are also eliminated. Note that the epression or should also include an etra product term given by, however this higher order term will be neglected. In all our simulated cases, this approimation is ound to have no eect on the optimization. Then, substituting the epression o yields: ) ( Substituting or : ) ( Finally, the epression or simpliies to the ollowing:. Applying similar simpliication logic to all other epressions, the constraint set can be written as ollows: Note that the constraints corresponding to all other buses will remain the same as given in equation (.). One eception to this is the constraint or bus where the injection is measured (or known). This constraint will be eliminated rom the constraint set. The reason or removing the constraints associated with injection buses is that their eects are indirectly taken into account by the product terms augmented to the constraints associated with the neighboring buses. The constraints or this case are shown in (.).

18 ) ( _ X new (.) This way o orming constraints or zero injection buses or buses which have injection measurements is complicated and time consuming. It is also noticed that nonlinear part will be introduced in the constraints and it will urther slow down the integer programming. Hence, the ollowing alternative method is developed or systems with a large number o injections to process. b) Topology transormation This alternative method reerred here as the topology transormation is developed or handling injection measurements. The main idea is to merge the bus which has the injection measurement, with any one o its neighbors. This is based on the observation that i the voltage phasors o all its neighbors are known, the voltage phasor o this injection bus can be calculated by the Kirchho s Current Law. Figure. shows the updated system diagram ater the merger o buses and into a new bus. The newly created branch - relects the original connection between buses and. Hence, the constraints vector unction can be ormed as shown in (.).

19 ) ( ' ' ' _ ' X new (.) Topology transormation is aster and will not introduce any nonlinear part in constraint set. Yet a word o caution needs to be added here in that, i the optimal solution chooses the newly ormed ictitious bus (merger o two actual buses) as a candidate bus, it may place one PMU on one o these two buses or two on both. In this case, a topology analysis needs to be applied to check the observability o the system. This also assures that the minimum number o will be placed. Figure.. System diagram ater the merger o buses and

20 . Topology Based Procedure Figure.. Observable islands or the IEEE -bus system The integer programming based procedure is quite eective in systematically placing in a system where there are very ew eisting measurements. It can also be used or placing in a system which is to be eclusively monitored by PMUS only. However, most o today s power systems already have a signiicant number o conventional measurements and are planned to be installed to enhance the eisting measurement system. For such systems which may be unobservable and have ew observable islands, a topology based method can be easier to apply. The method will ind the strategic locations o by merging the observable islands. Since only boundaries buses contribute to the process o merging observable islands, these will be the strategic locations or placing. First a numerical observability analysis is carried out to determine the observable islands. Then the boundary bus, which connects to the maimum number o other islands or the one which has the maimum number o branches connected to other islands will be chosen to place a PMU. In order to take advantage o the injection measurements, ater the selection o one PMU location, the numerical observability analysis will be re-applied to update the observable islands. Consider the IEEE -bus system eample shown in Figure., where there are initially observable islands. Boundary buses are identiied as buses,,,,,,, and. Among them bus, and are connected two dierent observable islands respectively, and have the maimum number o neighbor islands. Bus is chosen to install a PMU. Numerical observability analysis is eecuted and the system is ound to become observable. This implies that installing one PMU at bus merges all o the ive observable islands into one observable system. The logic is simple and easy to implement, provided that there are ew observable islands and consequently ew boundary buses. Eective utilization o this method will be illustrated in section on the TVA system.

21 . Placement Strategy Against Loss o a Single PMU So ar it is assumed that those which are placed by the proposed method, will unction perectly. While are highly reliable, they are prone to ailure just like any other measuring device. In order to guard against such unepected ailures o, the above placement strategy is etended to account or single PMU loss. In this study, this objective is achieved by choosing two independent PMU sets, a primary set and a backup set, each o which can make the system observable on its own. I any PMU is lost, the other set o will guarantee the observability o the system. The primary set o is chosen by building the constraint unctions according to the procedures described in subsections above and solving the integer-programming problem. The backup set is chosen by removing all the i terms in the constraint unctions, where bus i is in the primary set, in order to avoid picking up the same bus which appears in primary set. Then the integer-programming problem is solved to obtain the backup set.

22 . Illustrative Eamples This section contains various simulation eamples, which are carried out using the IEEE -bus, -bus, -bus and -bus systems. TOMLAB/MINLP and MILP [] sotware package is used to solve the Integer Linear/Nonlinear Programming problem. Detailed system inormation and simulation results are given in the ollowing sub-sections.. IEEE -bus system Figure.. IEEE -bus system IEEE -bus system is shown in Figure.. The Inormation o the system and zero injections are given in the Table.. System Table. System inormation o IEEE -bus system # o branches # o zero injections Zero injection buses IEEE -bus Case. Eect o considering zero injections In this case, Integer Programming method is used to solve the optimal PMU placement problem without considering the loss o single PMU. Simulations are carried out with and without considering zero injections. Results are given in Table..

23 Table. Simulation results or the -bus system without considering single PMU loss Consider zero injections Ignore zero injections Non-linear constraints Topology transormation # o # o # o,,,,,,, Case. Considering single PMU loss This case determines the optimal PMU locations that will maintain observability under the loss o any single PMU. Integer Programming is used, simulations are carried out with and without considering zero injections. Results are given in Table.. # o Table. Simulation results or -bus system considering single PMU loss Consider zero injections Ignore zero injections Non-linear constraints Topology transormation # o # o,,,,,,,,,,,,,,,,,,,,. IEEE -bus system IEEE -bus system is shown in Figure.. The Inormation o the system and zero injections are given in the Table.. System Table. System inormation o IEEE -bus system # o branches # o zero injections Zero injection buses IEEE -bus,,,, Case. Eect o considering zero injection In this case, Integer Programming method is used to solve the optimal PMU placement problem without considering the loss o single PMU. Simulations are carried out with and without considering zero injections. Results are given in Table..

24 Table. Simulation results or -bus system without considering single PMU loss Consider zero injections Ignore zero injections Non-linear constraints Topology transormation # o # o # o,,,,,,,,,,,,,,,,,,,,,, Figure.. IEEE -bus system

25 Case. Considering single PMU loss In this case, single PMU loss is considered. Integer Programming is used, simulations are carried out with and without considering zero injections. Results are given in Table.. # o Table. Simulation results or -bus system considering single PMU loss Consider zero injections Ignore zero injections Non-linear constraints Topology transormation # o # o,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,. IEEE -bus system Figure.. IEEE -bus system

26 IEEE -bus system is shown in Figure.. The Inormation o the system and zero injections are given in the Table.. System Table. System inormation o IEEE -bus system # o branches # o zero injections IEEE -bus Zero injection buses,,,,,,,,,,,,,, Case. Eect o considering zero injection In this case, Integer Programming method is used to solve the optimal PMU placement problem without considering the loss o single PMU. Simulations are carried out with and without considering zero injections. Results are given in Table.. Table. Simulation results or -bus system without considering single PMU loss Consider zero injections Ignore zero injections Non-linear constraints Topology transormation # o # o # o,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, Case. Considering single PMU loss In this case, single PMU loss is considered. Integer Programming is used, simulations are carried out with and without considering zero injections. Results are given in Table.. # o Table. Simulation results or -bus system considering single PMU loss Consider zero injections Ignore zero injections Non-linear constraints Topology transormation # o # o,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

27 . IEEE -bus system IEEE -bus system is shown in Figure.. The Inormation o the system and zero injections are given in the Table.. System Table. System inormation o IEEE -bus system # o branches # o zero injections Zero injection buses IEEE -bus,,,,,,,,, Case. Eect o considering zero injection In this case, Integer Programming method is used to solve the optimal PMU placement problem without considering the loss o single PMU. Simulations are carried out with and without considering zero injections. Results are given in Table.. Figure.. IEEE -bus system

28 Table. Simulation results or -bus system without considering single PMU loss Consider zero injections Ignore zero injections Non-linear constraints Topology transormation # o # o # o,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, Case. Considering single PMU loss In this case, single PMU loss is considered. Integer Programming is used, simulations are carried out with and without considering zero injections. Results are given in Table.. Table. Simulation results or -bus system considering single PMU loss Consider zero injections Ignore zero injections Non-linear constraints Topology transormation # o # o # o,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

29 Case. System having several conventional measurements In this case, several conventional measurements are introduced into IEEE -bus system and several observable islands are ormed. The list o low and injection measurements is given in Table.. Zero injections shown in Table. are also considered and treated the same as injection measurements. Topology based method to merge observable islands is used and results are shown in Table.. Loss o single PMU is not considered in this case. Table. Measurements inormation or IEEE -bus system Flow measurements Injection measurements No. Locations No. -, -, -, -, -, -, -, -, -, -, -, -, -, -, -, -, -, -, -, -, -, -, -, -, -, -, -, -, -, -, -, -, -, -, -, -, -, -, -, -, -, -, -, -, -, -, -, -, -,,,,,,,,,,,,,,,,,,,,,,,,,,,, # o observable islands Table. Simulation results or -bus system considering conventional measurements # o Loc.(bus #),,,,,,,,,,,,,,,,,,

30 . TVA System Case Studies. TVA System (version ) a. System inormation version At the beginning o the project, TVA network data, along with a list o buses where were installed or planned to be installed, are received rom TVA. The data also revealed several buses where the net injected power was zero. Such buses, reerred as zero injection buses, allow urther reductions in the required number o in making the overall system observable. Initial PMU placement algorithm is then modiied to account or these zero injection buses, as well as or those already installed. The developed algorithm is applied to TVA data, based on various assumptions and PMU placement results are obtained. TVA data which are received in August rom TVA contain buses out o which are zero injection buses. Inormation about the already installed and scheduled to be installed is provided as a list o bus names. For several o the bus names in this list, it is ound that more than one bus number (o dierent voltage levels) correspond to the same bus name in the TVA data ile. Thus, it is assumed that all such buses have. Also, it is noted that some o these buses have zero injections, which allow urther reductions in the required to be placed in the system. There are a total o installed in this system and scheduled to be installed. A brie inormation o TVA system is listed in Table.. The lists o installed and scheduled to be installed are shown in Tables. and. respectively. Table. Brie inormation o TVA system (version ) Number o buses Number o branches Number o zero injections Table. Bus names and numbers with installed Bus Name Number o Bus Number Cordova,, Shelby,, Freeport, Volunteer, Summer Shade Total Installed * o them are zero injections buses

31 Table. Bus names and numbers where are scheduled to be installed Bus Name Number o Bus Number Paradise, Shawnee,,,,, Marshall, Widows Creek,, Davidson, Weakley, Cumberland, Sullivan, Bull Run, Lowndes,, (,, ) West Point, Johnsonville,,,, PMU Scheduled: * o them are zero injection buses b. Studied cases version All simulations are carried out using the Integer Programming method. TOMLAB/MINLP [] sotware package is used to solve the Integer Nonlinear Programming problem. Four cases that relect dierent possibilities are investigated. Case : This case does not involve any assumptions and it does not try to take advantage o any eisting zero injection buses. Hence, this can be considered as the worst case scenario. In this case, out o the total system buses, o them are chosen or PMU installations. When these suggested locations are checked against those listed in Table., o them match the chosen bus numbers as shown in Table.. This result ought to be evaluated by keeping in mind the act that the developed PMU placement algorithm does not yield a unique answer. Depending on the initialization, several equally good (yielding the same number o ) solutions can be obtained. The one presented here happens to be one o them.

32 Case : This case is the same as case, ecept the solution is orced to include those already installed rom Table.. Note that, compared to case, the total number o is increased by one as indicated in Table.. This implies that those already installed are located at airly optimal locations, requiring only one etra PMU with respect to the optimal case. Case : This case ollows case, where in addition to the already installed, those, which are scheduled to be installed, are also orced into the solution. In this case, as given in Table., the total number o required jumped to, a signiicant deviation rom the optimal value o. Based on this inormation, the simple conclusion will be that the scheduled PMU installations are not the best rom the point o view o observability. Naturally, this conclusion carries a lot o uncertainty due to the act that our interpretation o Table. or the scheduled PMU locations may not be correct. Furthermore, observability may not be the primary concern behind the decisions or the scheduled locations. They may be planned to be placed or other important concerns such as angle or voltage stability monitoring. Case : This case is similar to case, ecept or the act that all buses with zero injections are assumed passive (no generation and no load) and are placed accordingly. As shown in Table., including these constraints ( buses are identiied as zero injection buses) reduced the optimal PMU locations signiicantly down to. It should be noted that the solution ound in this case matches buses rom Table.. Table. Results o case studies or the TVA data (version ) Ignore zero-inj. Consider zero-inj. No Number o : Matched Locations:(),,,,,,,,,,,,,,,, Installed Total : New Installed & Total : Scheduled New Number o : No Matched,,,,, Locations:(),, Detailed list o bus numbers indicating the locations or or the our cases described above, are given in Tables. through. below.

33 Table. Detailed results or case Total No. o,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

34 Table. Detailed results or case Total No. o Installed Number o Locations (Bus No.),,,,,,,,,, Newly Selected Buses,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

35 Table. Detailed results or case Total No. o Installed Number o Locations (Bus No.),,,,,,,,,, Scheduled Pmus Newly Selected Buses,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

36 Table. Detailed results or case Total No. o,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,. TVA System (version ) a. System inormation version An new set o network and measurement data are received rom TVA via Areva in late June. This data will be reerred as version in the report. The inormation o TVA system (version ) is shown in Table.. There are installed in the system. The inormation o is given in Table.. Table. System inormation o TVA system (version ) Number o buses Number o branches Number o zero injections Number o paired inj. meas. Number o paired low meas.

37 Table. Inormation o installed in TVA system (version ) Number o Bus No. with V-Phasor Branches with I-Phasor -, -, -, - -, -, - - -, -, - b. Simulation results o TVA system version Three case studies are conducted using the new version o TVA data. In all these studies, the problem is ormulated and solved using Integer Programming method. TOMLAB/MINLP sotware package is used to solve the Integer Nonlinear Programming problem. Brie description o these cases are given below ollowed by their respective simulation results. Case This case assumes no eisting and disregards all conventional measurements including zero injections. Hence, the results relect the worst case scenario where the entire system is made observable by newly placed only. Case In this case, all eisting conventional measurements, namely the bus power injections (zero as well as non-zero) and line power lows are incorporated into the optimization ormulation. Case This case is the same as Case, ecept it also includes already installed (which are shown in Table.). As can be seen rom the optimization results, these do not make any dierence in the optimal placement solution with respect to Case. The simulation results showing the number o required and their locations (bus numbers) are given below in Tables.. or cases - respectively.

38 Table. Simulation results o TVA system (version ) or Case Total No. o,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

39 Table. Simulation results o TVA system (version ) or Case Total No. o,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

40 Table. Simulation results o TVA system (version ) or Case Total No. o,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

41 . Conclusions and Future Work This project accomplished two objectives. First, two practical methods or determining optimal locations or are developed. Second, the developed methods are implemented and applied to several test systems, including the internal TVA system. Placement o can be carried out using dierent criteria depending on the objective o the investigator. In this project, the main ocus is on the state estimation unction and thereore the objective is to make the entire system observable by optimal placement o. The project considered various scenarios where the system is irst assumed to be observed by only. While this appears impractical today, it may very well be the case in a ew years when these devices become standard equipment at substations. Net, the placement problem is considered or a system with eisting measurements, some o which may be. Case studies which are carried out on test systems as well as the TVA s internal system indicate that strategically placing at roughly one third o the system buses, the entire system can be made observable with only. Furthermore, zero injections, which can be considered ree measurements, can signiicantly reduce the required number o or a given system. PMU placement problem does not have a unique solution. Depending upon the starting point, the developed optimization scheme may yield dierent sets o optimal solutions, each one providing the same minimum number o but at dierent locations. On the other hand, it is not unusual to have additional considerations apart rom strict observability criterion, when deciding on the location o. These considerations can be taken into account by appropriately modiying the optimization problem which is ormulated in this project. This can be done as an etension to this project in the uture. One o the important unctions o state estimators is to detect and eliminate bad measurements in the system. Bad data processing is strongly dependent upon the measurement redundancy as well as accuracy o the measurements used. Even or ully observable systems, strategic placement o ew can signiicantly improve bad data detection and identiication capability. This aspect o PMU placement can also be investigated in the uture so that the operation o the eisting state estimators can be improved via PMU placement.

42 Reerences [] A. G. Phadke, Synchronized phasor measurements in power systems, IEEE Computer Applications in Power, Vol., Issue, pp. -, April. [] A. G. Phadke, J. S. Thorp, and K. J. Karimi, State Estimation with Phasor Measurements, IEEE Transactions on Power Systems, Vol., No., pp. -, February. [] T. L. Baldwin, L. Mili, M. B. Boisen, and R. Adapa, Power System Observability With Minimal Phasor Measurement Placement, IEEE Transactions on Power Systems, Vol., No., pp. -, May. [] The TOMLAB Optimization Environment, Web page URL: Project Publications [] Bei Xu and A. Abur, Observability Analysis and Measurement Placement or Systems with, Proceedings o the IEEE PES Power Systems Conerence and Eposition, October, New York, NY. [] Bei Xu, Y. J. Yoon and A. Abur, Optimal Placement and Utilization o Phasor Measurements or State Estimation, Power System Computation Conerence, August, Liege, Belgium.

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