Reliability-based phasor measurement unit placement in power systems considering transmission line-外文文献.doc

Reliability-based phasor measurement unit placementin power systems considering transmission lineoutages and channel limitsOscar Gomez1,2, Mario A. Rios1, George Anders31Department of Electrical Engineering and Electronics, School of Engineering, Universidad de los Andes, Bogot,Colombia2Department of Technology, School of Electrical Technology, Universidad Tecnolgica de Pereira, Pereira, Colombia3Electrical Engineering, Technical University of Lodz, Lodz, PolandE-mail: .coAbstract: Since phasor measurement unit (PMU) was invented, there has been growing interest in developing methodologiesfor finding the minimum number of PMUs for complete system observability. The methods for the PMU placement mustconsider the fact that the network topology may change when the power system is affected by a contingency event.Therefore the PMU placement problem can be stated as finding the minimum number of PMUs for complete systemobservability considering the failure probability of transmission lines. In this study, the authors propose a new reliabilitybasedmodel for the contingency constrained PMUs placement. Initially, a methodology, that considers the probability offailure of the power system components, is proposed. Next, an algorithm is presented for selecting the minimal number ofPMUs and their locations to monitor the system under normal operation and the most credible contingencies. A probabilisticindex is introduced to select a desired level of reliability for the wide-area monitoring system. Finally, the availability ofPMU measuring channels is incorporated in the model, so more realistic and useful results can be obtained. The problem isformulated and solved as a binary integer linear programming model and tested on the IEEE 9-bus, IEEE 57-bus andRTS96 test systems.1 IntroductionA phasor measurement unit (PMU) provides synchronisedphasor measurements of voltages and currents from widelydispersed locations in an electric power grid. Since PMUwas invented, there has been growing interest in developingmethodologies for finding the minimum number of PMUsfor complete system observability.The problem was initially introduced in 1; then, severalapproaches, that can be categorised into two groups, themeta-heuristic optimisation methods and the conventionaldeterministic techniques, have been proposed.Examples of the meta-heuristic methods include canonicalgenetic algorithm 2, non-dominated sorting geneticalgorithm 3, Tabu search 4, simulated annealingcombined with Tabu search 5, particle swarm optimisation6, adaptive clonal algorithm 7, differential evolutionalgorithm 8 and immunity genetic algorithm 9. Thedisadvantage of these methods is the long execution times,which can restrict their applications to large power systems,and the possibility of obtaining a non-optimal solution.On the other hand, numerous research studies based ondeterministic approaches have been developed. For instance,in 10, the integer programming approach is applied to thePMU placement problem. A method, using integer linearprogramming for power networks with and withoutconventional measurements, was proposed in 11. Themodel presented in 11 was extended in 12 to considerthe zero-injection effect, incomplete observability andmeasurement redundancy. In 13, a formulation wasproposed which applies integer linear programming, andincorporates the effect of zero-injection; in addition, amultistage scheduling framework for PMU placement in agiven time horizon was suggested. PMUs placement andconventional flow measurements location aresimultaneously considered as decision variables in 14. Theformulation is initially posed as a non-linear integerprogramming problem and then transformed into anequivalent integer linear programming. The PMU placementproblem using integer quadratic programming wasdiscussed in 15 without consideration of the effect of thezero-injection buses. In 16, it is presented a participationfactor-based approach to optimally allocate a predefinednumber of PMUs throughout an observable system in orderto maximise the accuracy of the estimated state.The objective of these papers was to find the minimalnumber of PMUs that ensures full observability withoutconsideration of transmission line outages. Consequently, theresulting optimal placement of PMUs may not guaranteecomplete system observability in case of any IET Gener. Transm. Distrib., 2014, Vol. 8, Iss. 1, pp. 121130doi: 10.1049/iet-gtd.2013.0251121 The Institution of Engineering and Technology 2013In order to design a robust wide-area monitoring system(WAMS), which can ensure complete system observabilityunder the failure of any transmission line or even a PMU,some works have considered power system contingenciesand loss of measurements (failure of a PMU or itscommunication links).For instance, in 17 Sodhi et al. presented a method foroptimal placement of PMUs that ensures systemobservability under a pre-specified number of criticalcontingencies, which are identified by performingbeforehand a voltage stability analysis. Although thesecontingencies are critical for the system stability, they couldhave small probability of occurrence; thereforecontingencies with higher probability of occurrence andhighly negative effect on the system observability could beomitted. In 18, a method for the optimal placement ofPMUs that considers two types of contingencies (singlemeasurement loss and single-branch outage) was presented.The methodology uses a sequential addition approach tosearch for necessary candidates for single measurement lossand single-branch outage conditions, which are optimisedby binary integer programming and a heuristic technique. In15, the integer quadratic programming approach was usedto minimise the total number of PMUs under an outage of asingle transmission line or one PMU; however, a list ofbranch outages to be considered is prepared beforehand.This model, which was based on numerical observabilityanalyses, is computationally expensive. In 3, an optimalset of PMUs, which maximise the measurementredundancy, was found using a non-dominated sortinggenetic algorithm and topological observability. Thealgorithm starts with a set of PMUs that ensures completeobservability of the system, and the additional PMUs areadded in an iterative way until a predefined measurementredundancy has been achieved. In 19, integer linearprogramming was proposed for solving the optimalplacement of PMU anticipating the loss of a PMU or a lineoutage. The effect of a single line outage is added directlyto the model by using auxiliary variables. A technique forplacing the PMUs in multiple stages over a given timeperiod that ensures complete power system observabilityeven under a branch outage or a PMU failure was presentedin 20. The approach proposed in 3, 15, 1720 does nottake into account the stochastic nature of power systembehaviour, so the WAMS could be designed for ensureobservability of either the system under unlikelycontingencies or all N 1 contingencies.Although the monitoring system may be robust enough tomaintain the system observability anticipating all possiblecontingencies, the number of PMUs could be very high andthe implementation of the system monitoring would beexpensive. On the other hand, the random nature ofcontingencies causes that some transmission lines havehigher probability of failure than others. Therefore it isnecessary to design a methodology that considers therandom nature of the transmission line outages and WAMScomponent failures.PMU placement considering random operating scenariosand random topologies was initially proposed in 21. Theauthors proposed a methodology to find the optimallocation of PMUs for wide-area monitoring and control oflarge disturbances; the methodology places a minimumnumber of PMUs that maximises the useful information tomonitor the system dynamic performance. In 22, Aminifaret al. find the optimal number of PMUs to enhance thesystem observability by considering random componentoutages. Through an iterative process, authors find theprobability of observability associated with all buses, whichare averaged to get a system index. This index is posteriorlyused to select the best solution from all the possible ones.Although authors consider random outages of the WAMScomponents, and analytical reliability evaluation methods tocalculate the probability of observability, the algorithmrequires finding all the optimal solutions of the PMUplacement problem, which might be very large for relativelylarge-scale systems with thousands of buses. The approachproposed in our paper avoids finding all optimal solutions,it defines the WAMS reliability as the probability ofobserving all the buses under N 1 contingencies and itfinds the optimal solution without an exhaustive search ofthe possible PMU placements.Aminifar et al. 23 developed a methodology for thestaged PMU placement in a multiyear planning horizon,where the average probability of observability is maximisedat the intermediate planning stages. Initially, they calculatethe minimum number of PMUs for the last stage; then, themultistage scheduling is determined in the context of thefinal solution by solving a subsidiary optimisation modelfor each stage. The minimum number of PMUs for the finalstage must satisfy the criterion that the probability ofobservability associated with all buses would be equal to orgreater than a set of values that must be estimated orcalculated a priori. The model for the probability ofobservability is a non-linear function which must belinearised. Our proposal is based on the system state space,so all relations are already linear, and an integer linearprogramming model can be applied.On the other hand, one should remember that placing aPMU at a given bus can measure the phasor voltage at thatbus and the phasor currents along all lines incident to thatbus; however, every PMU comes with a limited number ofchannels, so a more realistic and useful model should takeinto account the limited channel capacities. PMU placementconsidering channel capacity was initially addressed in 24,where the placement problem was formulated and solvedusing a binary integer programming approach. In 25, afour-step algorithm, that minimises the number of addedPMUs with minimum number of channels, was proposed.The steps include: inspecting the existence ofmeasurements, identifying a set of buses that satisfyconditions for PMU placement, identifying buses that PMUplacement on them makes system observable with minimumcost and determining currents and voltages that should bemeasured. In 26, both integer linear programming andgenetic algorithm were implemented to optimise the PMUplacement considering the number of analogue channels.The methodology initially solves the classical integer linearprogramming model for PMUs placement in order to get allthe multiple solutions. Then, the genetic algorithm is usedto find the configuration that uses the minimum number ofchannels. Finally, Miljanic et al. 27 presents a cellulargenetic algorithm for solving the PMU placement problemtaking into account the availability of PMU measuringchannels.Najafabadi and Alouani 25, Zhao and Makram 26 andMiljanic et al. 27, use meta-heuristic algorithms forfinding the optimal placement of PMUs considering channellimits. Although those algorithms can search very largespaces of candidate solutions, they do not guaranteereaching an optimal one. On the other hand, althoughKorkali and Abur 24 propose an integer linearprogramming model, it makes a change of the 122 The Institution of Engineering and Technology 2013IET Gener. Transm. Distrib., 2014, Vol. 8, Iss. 1, pp. 121130doi: 10.1049/iet-gtd.2013.0251variables and uses the transpose of observability matrix fordeveloping the optimisation model; therefore it cannot beused in the approach discussed in this paper. Therefore anew integer linear model of the channel capacity isproposed to incorporate the channel limits in thereliability-based PMU placement.In this paper, we propose a new reliability-based model forthe contingency-constrained PMUs placement. Initially, theprobability of failure of the transmission lines is consideredfor placing the PMUs at the most reliable buses. Reliabilityof a bus for the monitoring system is defined as theavailability of the basic components for the operation of thePMU and the availability of the adjacent lines to a bus, insuch a way that the PMU can correctly observe itsneighbourhood buses. Therefore, the transmission linesprobability of failure is considered during the selection ofthe minimal number of PMUs, and their location to monitorthe system under normal operation and the most likelycontingencies. A probabilistic index will be presented toselect the level of reliability that the system operator wantsits WAMS to meet. The problem is formulated and solvedusing a binary integer linear programming model. Thus, thepaper simultaneously considers the reliability of the buses,lines and WAMS, as well as, allowing for only someimportant contingencies to be considered by an introductionof the desired system reliability index. In addition, thelimitation in the number of channels will be considered inorder to achieve a more realistic placement of PMUs. Thezero-injection effect will not be considered because ourobjective is to improve the WAMS reliability, which isdegraded when many components have to be available tomake one zero-injection effect applicable. Since the effectof zero-injection will be excluded in the PMU placementprocess, each bus is made observable either by its ownPMU or by PMUs at the adjacent buses.The paper is organised as follows. In Section 2, theconventional integer linear model for completeobservability is presented; next, the state-space enumerationmethod is discussed in Section 3 to select the most reliablebuses for the PMU placement. Then, a probabilistic-basedmethodology is presented in Section 4 to select the locationof the PMUs to ensure full observability under the mostcredible contingencies. Section 5 shows the incorporation ofchannel limitation in the developed model. Finally,numerical results of the proposed model are presented inSection 6, and conclusions are provided in Section 7.2 Integer linear model for completeobservabilityA PMU placed at a given bus can measure the voltage phasorof the bus as well as the phasor currents for all lines incidentto that bus. Consequently, bus voltage along with all adjacentbus voltages will also be available (solvable).The objective of the PMU placement problem is toaccomplish this task by using a minimum number of PMUs.For an n-bus system, the PMU placement problem can beformulated as followsmin_Ni=1xis.t.fi(x) =_kVixk 1(1)where xi is a binary decision variable vector, whosecomponents are defined asxi= 1, if a PMU is placed at bus i0, otherwise_and f (x)i is the observability constraint for each bus i, whoseelements are the sum of the variable that represents the bus iand the set of variables that represent the buses connected tothe bus i (i).For example, let us consider a bus connected to other threebuses, as shown in Fig. 1.For the topology shown in Fig. 1, the constrain f (x)1 isf1(x) = x1+ x2+ x3+ x4 1 (2)To improve the observability of a specific bus in such a waythat it can be monitored by at least two PMUs, the right-handside of the inequality (2) must be multiplied by 2.This mathematical model is well known in the specialisedliterature, and it is highly dependent on the system topology;hence, network observability will be drastically affected bytopology changes. Therefore the PMU location shouldpreferably be selected at the more reliable buses in order todecrease the probability of losing observability in the system.3 PMU placement based on bus reliabilityThe first step in evaluating the reliability of WAMS is toassess the PMU reliability based on the availability of itsbasic components. Reliability analysis of PMUs has beenaddressed in 2831, where hierarchical Markov, Markovprocess with fuzzy sets, fuzzy Markov and Monte Carlodynamic fault tree, respectively, were used.However, from the standpoint of a location in the powersystem, not only the availability of the PMU but also theavailabilities of the transmission lines are necessary for theproper operation of the WAMS; in fact, transmission linesare indispensable for observing the neighbouring buses of abus with an installed PMU. Therefore, in order to select themost reliable buses, transmission line failures must beconsidered as a crucial element for the mission of the PMU.The transmission line failures will be modelled as anindependent single outage; that is, only first-ordercontingencies will be considered, which is not related interms of its cause to any other failures that may occur at thesame time. According to the number of circuits betweenbuses, transmission line failures can be modelled as a singlecomponent, which can have either in service (up) or out ofservice (down) modes (Fig. 2), or as a two (or more)repairable independent components with dependent outagesFig. 1 Three bus configuration (Fig. 3).IET Gener. Transm. Distrib., 2014, Vol. 8, I