A Multi-Objective PMU Placement Method Considering Measurement Redundancy and Observability Value...

8/10/2019 A Multi-Objective PMU Placement Method Considering Measurement Redundancy and Observability Value Under Contingencies.pdf

1/11

2136 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 28, NO. 3, AUGUST 2013

A Multi-Objective PMU Placement MethodConsidering Measurement Redundancy and

Observability Value Under ContingenciesSeyed Mahdi Mazhari, Student Member, IEEE, Hassan Monsef, Hamid Lesani, and

Alireza Fereidunian, Member, IEEE

AbstractThis paper proposes a multi-objective phasor

measurement units (PMUs) placement method in electric trans-mission grids. Further consideration is devoted to the early PMUplacement formulations, to simultaneously determine minimumnumber of PMUs, as well as maximum measurement redun-

dancy. Moreover, a new methodology is presented for valuationof observability under contingencies, including line outages and

loss of PMUs. Furthermore, a generalized observability functionis introduced to allocate the PMUs in presence of conventional

non-synchronous measurements. The resultant optimizationproblem is solved using Cellular Learning Automata (CLA),

introducing new CLA local rules to improve the optimizationprocess. The developed method is conducted on IEEE standardtest systems as well as the Iranian 230- and 400-kV transmissiongrids, followed by a discussion on results.

Index TermsCellular learning automata (CLA), measurementredundancy, observability, optimal placement, phasor measure-

ment unit (PMU), power system contingencies.

NOTATION

The notation used throughout this paper is reproduced below

for quick reference.Sets:

Set of network buses.

Set of network lines.

Set of lines which would be unobservable whenline is out.

Set of lines which would be unobservable whenPMU is lost.

Set of buses which have PMU.

Set of costs for placing PMUs at .

Manuscript received October 12, 2011; revised February 08, 2012, May 24,2012, and September 06, 2012; accepted October 17, 2012. Date of publicationFebruary 01, 2013; date of current version July 18, 2013. Paper no. TPWRS-00907-2011.

S. M. Mazhari, H. Monsef, and H. Lesani are with the School of Electricaland Computer Engineering, University of Tehran, Tehran, Iran (e-mail:[email protected]; [email protected]; [email protected]).

A. Fereidunian is with the Electrical Engineering Faculty, K. N. ToosiUniversity of Technology and also with the School of Electrical andComputer Engineering, University of Tehran, Tehran, Iran (e-mail: [email protected]; [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TPWRS.2012.2234147

Set of neighboring lines of bus .

Set of union of bus and neighboring buses ofthe th bus.

Set of lines incident to bus .

Set of actions of the th learning automaton.

Set of inputs of the th learning automaton.

Set of actions probability vector of the th learningautomaton.

Constants:

Total costs imposed for placing PMU at bus ($).

Maximum project budget ($).

Minimum number of redundancy requirementsof bus .

Failure rate of PMU (fr/year).

Failure rate of line (fr/year).Disturbance rate of line including events whichcaused a failure in line or ones which are cleared

by the protective devices (fr/year).

Total number of network buses .

Average outage time of PMU (hr).

Average outage time of line (hr).

Reward parameter of the CLA algorithm.

Penalty parameter of the CLA algorithm.

Monetary factor of observability value of line .Very large number.

Small number.

Functions:

Objective function of the PMU placementproblem.

Observability function of bus .

Observability function of bus due tonon-synchronous measurements of bus (or

between buses ).

0885-8950/$31.00 2013 IEEE


2/11

MAZHARIet al.: MULTI-OBJECTIVE PMU PLACEMENT METHOD CONSIDERING MEASUREMENT REDUNDANCY 2137

Penalty function of PMUs unreliability.

Penalty function of lines unreliability.

Penalty function of buses redundancies.

Penalty function of buses unobservability.

Probability of selecting action at the th iteration.

Observability value of each disturbance.

Variables:

Binary decision variable that is equal to 1 if PMUis installed at bus and 0 otherwise.

Binary decision variable that is equal to 1 if busis observed and 0 otherwise.

Binary decision variable that is equal to 1 if busis zero-injection bus or there is a power injectionmeasurement at bus and 0 otherwise.

Binary decision variable that is equal to 1 if thereis a voltage measurement at bus and 0 otherwise.

Binary decision variable that is equal to 1 if thereis a flow injection measurement between buses

and 0 otherwise.

Binary decision variable that is equal to 0 if theth power injection measurement has observed a

network bus and 1 otherwise.

I. INTRODUCTION

P HASOR measurement units (PMUs) are crucial elementsof wide-area state estimation systems in transmissiongrids, as they maintain a high quality observability on electricalquantities of power system [1].

Power system operators should ensure that electrical quanti-ties lie within their normal limits. They utilize state estimationto observe the system conditions. Since full observability of thesystem is a prerequisite to the state estimation, measurementsare distributed throughout the network and joined to the stateestimators [2]. Based on these measurements, state estimatorsobtain an estimate of the state of the power system, while en-suring consistency of the estimates with the measurement set[3]. It is said that a system is topologically observable, if all ofits bus voltage phasors can be estimated [2].

The PMUs are intelligent electronic devices (IEDs), whichprovide synchronized real-time measurements of voltage pha-sors, as well as predetermined number of incident current pha-sors at the buses where they are located [4]. PMUs are synchro-nized in a wide-area interconnected network using global posi-tioning systems (GPS). According to Ohms Law, when a PMUis placed at a bus, neighboring buses also become observable.Furthermore, if voltage phasors at both ends of a branch are ob-served, the branch current can be calculated using the Kirch-hoffs Voltage Law (KVL) [5]. Accordingly, it is neither eco-nomical (due to PMU cost) nor possible (due to nonexistence of

communication facilities in some substations) and even nor nec-essary (due to Ohms and Kirchhoffs Laws) to install a PMU

at every node of a wide-area interconnected network. Hence,optimal PMU placement is formulated as a power system opti-mization problem andis investigated in various studies [5][18].

Considerable research has been devoted to PMU placementproblem in literature. The performance of genetic algorithmand simulated annealing is investigated for solving the PMU

placement problem in [5] and [6], respectively. In [7], immunitygenetic algorithm is applied to a standard test system. Whilesatisfactory results are presented, obtained results may hardlymeet the topological observability constraints [15]. Althoughthese methods can find minimum number of PMUs, measure-ment redundancy, as a conflicting and progressive objective,is rarely considered. Non-dominated sorting genetic algorithm(NSGA) is proposed in [8] for simultaneous minimization ofnumber of PMUs and maximization of measurement redun-dancy; however, this method may not lead to the minimumnumber of PMUs that can make the system observable [9]. A

binary search algorithm is proposed in [9] for system observ-ability, which is capable offinding the global optimum, yet it is

computationally expensive.Moreover, integer programming has been widely used for

PMU placement [10][13]. In [10], integer quadratic program-ming is proposed, considering single line outages and loss ofPMUs. However, effects of zero-injection buses are not consid-ered in the developed algorithm. A generalized integer linear

programming is also used in [11]. The method considers powernetwork with and without conventional measurements; never-theless, it needs some modifications to be used in multistage

planning. Moreover, it is not studied the contingencies. A newinteger linear programming based formulation is proposed formulti-stage scheduling of PMU placement in [12]. Although the

method considers PMU losses, line outage contingencies are notincorporated. Reference [13] conducts a binary integer linearprogramming, considering system observability and minimummetering economy as objectives. It proposes a new method tomodel the conventional measurements and studies the effectsof unequal PMU costs and PMU outages, yet line outage con-tingencies are not considered there. In [14], a contingency-con-strained PMU placement model is proposed, presenting a newformulation for the problem, considering the effects of PMUlosses and line outages. Although, solution time is substantiallydecreased, their proposed formulation may not meet topolog-ical observability constraints, while two or more zero-injection

buses are interconnected in the system [15]. Hence, infeasibleresults are reported in some cases (see Section V-A).

Despite aforementioned literature, some researchers havestudied the PMU placement for purposes other than full ob-servability [16], [17]. In [16], a gradual PMU placement is

proposed, considering depth of unobservability. Moreover, [17]developed an algorithm in which PMU placement is studied for

bad data processing in state estimation.To the best of our knowledge, worth of observability under

contingencies is not considered in previous studies yet, since itis assumed that the network remains full observable in contin-gencies. However, meeting the mentioned constraint in presenceof PMU losses and line outages needs excessive PMUs, leading

to proposing PMUs for almost half of network buses [10], [12]and [14], [15].


3/11


This paper reports a modified multi-objective PMU place-ment method. First, worth of observability is calculated for aset of PMUs in contingency, by ranking the prospective contin-gencies. As the most note-worthy contribution of this paper, the

prevalent PMU placement problem formulation is extended andnew concepts are considered, as for maximizing measurementredundancy and observability valuation under contingencies, allin presence of conventional measurements. The contingenciesconsidered in this paper include line outages and PMU losses.Moreover, as the second contribution of this paper, the optimiza-tion problem is tackled by Cellular Learning Automata (CLA),introducing new CLA local rules to enhance the optimization

process. Finally, the developed method is applied to the IEEEstandard test systems as well as the Iranian 230- and 400-kVtransmission network, followed by presenting the results andcomparing them to those of previous research.

II. PROBLEMFORMULATION

A. Mathematical Modeling

In this paper, the multi-objective PMU placement problem isformulated as in (1)(12). Equation (1) represents the objectivefunction of the PMU placement problem, in which, thefirst termrepresents total cost of PMUs installed throughout the network.The second term represents a penalty factor for observability re-dundancies in normal operation; and the third and fourth terms

provide penalty functions for buses unobservability under con-tingencies. Finally, the fifth term is a penalty function which ac-counts for the network unobservability in normal operation. ThePMU placement problem constraints are represented in (2)(3).

While (2) assures that whole buses possess their least prede-fined redundancies, and (3) guarantees that total project cost isless than the project budget:

(1)

Subject to:

(2)

(3)

where:

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

B. Description on the Employed Terms

In the first term of (1), the total costs imposed for placing aPMU at a bus are affected by its geographical position, type of

PMU, and status of the existing telecommunication system atthat bus [13].

The second term of (1), guarantees the achievement of max-imum measurement redundancy while minimizing the numberof PMUs during the optimization process. In this term,shows penalty function of buses redundancy and is calculatedthrough (4). In this equation, is the maximum number ofnetwork redundancies, which appears when PMUs are installedat all of the network buses. Equation (5) shows how iscalculated for a network. Accordingly, minimizing a penaltyfunction as , can guarantee the achievementof maximum measurement redundancy. Since, the mentioned

penalty parameter and the first term of (1) are not as the sametype, simultaneous optimization of these terms by a singleobjective function cannot lead to the optimal solution [8]. Toovercome this deficiency, the penalty function is divided bymaximum network redundancy and the obtained result is mul-tiplied by minimum PMU cost as shown in (1) and (4). In (4),is a small quantity, which ensures that in all situations.It is empirically seen in simulations that if ,the optimization algorithm always converges to the optimalsolution. In (1), the redundancy penalty function, , is multi-

plied by PMU cost to increase the worth of redundancy duringoptimization process. Moreover, is selected, in order

to ensure that is always less than a PMU costHence, although an increase in number of PMUs decreasesthe , increases in the first term of (1) would be more thandecrease of the second term, thus leading to an increase in theobjective function. Therefore, the possibility of entrapping inlocal minima is reduced, while the first two terms of (1) areminimized.

Third and fourth terms of (1) show effects of PMU losses andline outages, respectively; considering worth of observabilityin contingencies. The aim of PMU placement is to make thesystem topologically observable. Therefore, the system opera-tors expect to observe all networkdisturbances (includingfaults,

blackouts, or ones which are cleared by the protective devicesand etc.) by efficient utilization of a number of PMUs at proper

buses. However, PMU losses and line outages may cause a set of


4/11


disturbances not to be observed in contingency situations. To re-solve this issue, the researchers have solved the PMU placement

problem with respect to contingency criterion [10][15].This criterion guarantees that the system is observable undersingle contingencies. Although the criterion substan-tially improves the system reliability, it may be economicallyinefficient as it proposes excessive PMUs, comparing to the situ-ation without this criterion [14], [15]. Similarly, observability ofsome lines may have little significance [19]. On the other hand,from the technical point of view, the system operator may tendto observe the current flows through a corridor in any situation,thusneedto considerhigherordersof reliabilitylike andso on. Therefore, it is not reasonable to limit the observabilitylevel of such lines by criterion [20], [21]. Addressingthese concerns is the motivation behind proposing the observ-ability value in this work, i.e., the third and fourth terms of theobjective function.

Therefore, worth of observability in contingencies is evalu-ated and the PMU placement is conducted based upon an eco-

nomic objective function. Third and fourth terms of (1) showeffects of PMU losses and line outages, respectively. It is as-sumed that a PMU is the main element for sensing a set of linedisturbances which are observed directly or by the aid of thisPMU. Therefore, it can be said that the PMU cost is depreci-ated to sense a set of disturbance during its lifecycle. Hence,each disturbance has a monetary value like (8). Since some ofnetwork disturbance may be missed without PMUs within con-tingencies, it would be economical to place a PMU at a bus, ifthat helps a considerable number of disturbances to be sensedin such situation. Thus the financial benefit of installing a PMUis significant comparing to its cost.

Worth of un-sensed disturbances due to PMU losses and lineoutages are formulated through (6) and (7), respectively. In (6),the annual PMU outage time is multiplied by theset of disturbances which are not sensed during its outage time.It should be noted that the set of disturbance that are senseddirectly or by the aid of PMU is calculated as .

Since the cost of PMU is depreciated to observe these distur-bances, (6) is able to calculate worth of disturbances which arenot sensed because of the PMU outages. In this equation, theunion operator is used to represent the simultaneous occur-rence of disturbances in contingencies.

A monetary factor for observability value of line is consid-

ered in the penalty function, to represent the criticality of theline. A line may have strategic role regarding its usage, the pathwhich it construct, and so on. For instance, transmission lineswhich export electrical energy between two countries or two re-gions might have more importance for the system operator. Inorder to meet these constraints in the proposed penalty function,

, which shows the monetary factor for observability value ofline , is added to (6). The factor can be set equal to 1 fora simple network or when the actual value of is not deter-mined. However, if is set to , the optimization algorithmtries to find the PMU layout in which line shall be observedunder contingencies.

In (7), similar to (6), the annual line outage time

is multiplied by the set of disturbances whichare not sensed during its outage time. Worth of each distur-

bance is calculated by dividing the total PMU costs bytotal number of network disturbances as formulated in (8).It must be noted that, (6) and (7) are formed based on singlecontingencies [12][14]. However, they can easily be extendedto consider multiple simultaneous contingencies. Nevertheless,unlike [12][14] in which power network remains observableduring contingencies, that might not be necessarily economical,our proposed method may not lead to complete observabilityin contingencies unless it is economically efficient. Since thethird and fourth terms of (1) represents the monetary worth ofobservability in contingencies, the first four terms of (1) havethe same unit ($); hence, they can be simultaneously optimizedthrough a single objective function as reported in (1).

The fifth term of (1) shows penalty parameter of network un-observability in which is the penalty function of bus un-observability and is calculated through (9). In this equation,is a binary decision variable that is equal to 1 if bus i is ob-servable and is set to 0 otherwise. Moreover, as illustrated inthe fifth term of (1), the unobservability penalty function

is multiplied by a very large number . If all of the networkbuses are observed, the will return zero and no penalty isadded to the objective function. Hence, the objective functionwill return the least value for the feasible solutions, comparingto those of infeasible ones. It is empirically seen in simulationsthat if ), the optimization algorithm alwaysconverges to the optimal solution.

C. Proposed Observability Function

A new observability function is proposed in (10). This

equation remains unchanged in presence of conventionalnon-synchronous measurements and zero-injection buses.While the first term represents direct observability from neigh-

boring PMUs, the effects of conventional measurements areconsidered within the second and third terms. In the third term,

shows observability due to installation of a conventionalvoltage phasor measurement at bus . If a voltage measurementis installed on a bus, it measures voltage phasor of that bus, andthe bus becomes observable [15], [22].

In addition, which is calculated as (11) represents thetimes by which the th bus is observed due to the effects of zero-injection buses or conventional measurements that are placedat bus (or between buses and ). Since a branch flow mea-surement can easily measure the branch current, if the voltage

phasor at one end of the branch is observed, the voltage phasorat the other end becomes observable according to Ohms Law[15], [16], [22]. This effect is considered in thefirst term of (11).For a set of buses that coincide to a zero-injection bus, plus thatzero-injection bus, if the voltage phasors are all observable ex-cept one, the unobservable bus also will be observed via KCL[11][16]. This situation is modeled through the second termof (11). In this term, is a floor square bracket function andguarantees the second term of (11) to be binary. Assume busas a zero-injection bus. If members of the set are all ob-servable except one, would equal to

1 and the remaining bus also became observable, otherwise thesecond term of (11) would equal to 0.


5/11


Fig. 1. Interaction between learning automata and environment [24][26].

Since (10)(12) are dependent, in order to calculate observ-abilityfunction for the entire buses of a network, a pseudo-repet-itive procedure is conducted as follows:Step 1) Initialize for using (13):

other

(13)

Step 2) Calculate (12) for the entire network buses.Step 3) Update using (10)(11).

Step 4) Repeat steps (2)(3) until for all buses.

III. CELLULARLEARNINGAUTOMATA

Cellular automata are dynamically discrete systems whichtheir behavior relies on their local relevance [23], [24]. Cellularautomata are composed of a regular array of cells and each fol-lows a simple rule. While each cell can assume a state froma finite set of states, they act together to improve themselvesand to express complicated behavioral patterns [25]. The timegoes discrete and the cells update their states synchronously ac-cording to a local rule. The present state of each cell depends on

the previous states of a set of cells, including the cell itself, andconstitutes its neighborhood [26]. A cell is called a neighboringof another cell if they can affect each other in a period of time[25].

Cellular automata can be reinforced by learning automata tobe used as a powerful mathematical model for various problems[26]. Learning automata are adaptive decision-making unitswhich select their current action based on past experiencesearned from the environment. Their performances are im-

proved by learning how to choose the best action from a finiteset of allowed actions through repeated interactions with theirenvironment [24].

Automata are guided to the optimal actions considering in-teractions between automata and the adaptive unit, which iscalled random environment. Fig. 1 illustrates how a stochasticautomaton works in feedback connected with a random envi-ronment. Accordingly, an action is chosen at random based on a

probability distribution kept over the action-set. Then, the givenaction is sent as the input to the random environment. The en-vironment responds the listed actions proportional to reinforce-ment signals, and the action probability vector is updated con-sidering feedback from the environment [24][26]. Prevalentlearning automata try to find the optimal actions, so that average

penalty received from the environment is minimized. The objec-tive of a learning automaton can be changed by maximizing av-erage reward received from the environment or other multi-ob-

jective approaches [25].

Variable structure learning automata (VSLA) are representedby a quartet , where is the set of in-puts, is the set of actions, is the set of actions prob-ability vector and is learning algorithm. The learning algo-rithm is a recurrence relation which is used to modify the ac-tion probability vector. At each instant , the action probabilityvector is updated by the linear learning algorithm given in (14),if the selected action is rewarded by the random environment,and it is updated as given in (15) if the taken action is penalized[24][26]:

(14)

(15)

In the above equation, represents total number ofactions for each automaton. If , the recurrence (14)

and (15) are called linear reward-penalty algorithm,if , the given equations are called linear reward-penalty , and finally if they are called linearreward-inaction .

The overall procedure of the CLA can be described as fol-lows: each cell contains a learning automaton which initially se-lects an action in random, from afinite set of its allowed actions.Then, the selected actions are rewarded or penalized accordingto the actions selected by their neighbors (local rules) and alsothe new state of the CLA (an environmental rule). Afterwards,the entire learning automata update their probability function

based on the amount of received rewards or penalties. In the nextstep, the same process is repeated except that the probability ofchoosing a particular action is increased more than the others foreach automaton. By repeating the algorithm for several times,convergence to the optimal solution is achieved [24][26].

IV. SOLUTIONAPPROACH

CLA is a robust algorithm, established on a network struc-ture, where its cells cooperate to achieve a unique aim [25],[28]. Hence, it can easily be adapted to the transmission net-work and PMU placement problem. In CLA, state of each celldepends on the state of neighboring cells. Similarly, in the PMU

placement problem, installing a PMU at a bus depends on the

state of neighboring buses. Therefore, a CLA based algorithmis completely consistent with the PMU placement problem, as itstructurally emulates the PMU placement problem. Moreover,implementing the proposed reliability model needs to create aset of sub-graphs which are similar to the neighboringcells of each automaton. Therefore, the CLA based algorithmreduces the computational burden while solvingthe PMU place-ment problem. Moreover, the CLA algorithm has been used forsolving various problems so far and satisfactory results werereported [26][31]. According to the above discussion, in this

paper the PMU placement problem is modeled through CLA;though it could also be solved using other evolutionary algo-rithms.

Each network bus is considered as a cell which reinforcedby an automaton. The motivations behind employing


6/11


Fig. 2. Neighboring lines of a CLA cell and CLA local rules. (a) First CLA local rule. (b) Second CLA local rule. (c) Third CLA local rule.

the automata are as follows: As it is mathematicallyproven that the automata are -optimal [24], [25],enlisting proper learning rate guarantees the achievement of theoptimal solutions [32]. Moreover, the significant performanceof the learning algorithms illustrated in (14)(15) for theautomata is reported in several studies [26][33].

Each automaton contains two allowed actions: expressing aPMU to either be installed in the cell or not. Environmentalrule is defined based on (1) and all members of the setare assumed as neighbors of the bus (CLA cell) . Local ruleswhich show local improvement of neighboring cells is achieved

by applying (1) to the set of neighboring buses and neighboringlines which are defined as follows:

(16)

Neighboring lines for a simple case is shown in Fig. 2. Ac-

cordingly, in any iteration, CLA cells select proper actions basedon their actions probability vector. Then, the observability func-tion is determined for all buses using (10)(12) in a pseudo-repetitive procedure. Afterwards, objective function of the PMU

placement problem is calculated using (1). If the current CLAstatus improved the objective function, the response sent fromthe environment is positive and all the selected actions are pri-marily rewarded, otherwise penalized. Then, CLA local rulesare investigated for each cell using (1) and (16). According tothe local rules, the CLA cell is again rewarded or penalized. Byrepeating the mentioned process for several times, the algorithmconverges to the optimal solution. In this paper, the CLA local

rules are defi

ned as follows: If the present action of a cell differs to that of the previousone: If the cell action differs to that of the previous actions of

some of its neighbors, and if at least one action amongitsneighbors equals to that of the cell previous action, thereward or penalty is based on local rule. Thus, if localrule is improved, the cell action is rewarded, otherwise

penalized. This is schematically shown in Fig. 2(a). If the cell action equals to that of all previous actions

of its neighbors, and if the number of neighbors whichhave changed their action is more than those that havenot changed, the reward or penalty is based on local rule.This is schematically shown in Fig. 2(b).

If the present action of a cell equals to the previous one:

If the cell action equals to the previous actions of someof its neighbors, and if none have changed their actions,the reward or penalty is based on local rule. This isschematically shown in Fig. 2(c).

If a cell action has not received any reward or penalty by ap-plying the local rules, it does not receive any secondarily reward

or penalty.It must be noted that CLA local rules change in a wide range

and could be changed according to the problem statement. Nev-ertheless, the aim of these rules is to prepare a suitable way togive reward or penalty to an action in which the cell be ableto find the optimal action through repeated interactions with itsneighbors and the environment. Accordingly, these rules are notlimited to the above mentioned ones, and new rules can be of-fered and tested. A set of CLA local rules and their applicationsare investigated in [25][31]. Moreover, [33] presents a set of

publications regarding cellular automata, learning automata andthe CLA.

V. NUMERICALSTUDIES ANDRESULTS

Aimed at solving the problem of PMU placement by the pro-posed method, software is developed within a user-friendly en-vironment. The user can see the results by providing the GISready map (or presenting complete network information) andentering technical and economic data. To evaluate the perfor-mance of the proposed method, the problem is solved for IEEEstandard test systems [34] as well as for the Iranian 230- and400-kV transmission networks [35] and compared to that of

previous research. The technical specifications of the computerused for simulations are Centrino 1.8-GHz CPU with a 1 GB of

RAM.

A. First Scenario

In this scenario the solution is conducted for the IEEE stan-dard test systems, and the obtained results are compared to thoseof previous research.

As it can be seen in Table I, the proposed method couldachieve the best existing solution from the minimization ofPMU numbers viewpoint. Moreover, as shown in Table II, incomparison with the previous methods, the proposed solutionhas improved the measurement redundancy for the 30-bus testsystem (19%). Accordingly, the second term of (1) which isadded to the objective function to find the maximum measure-ment redundancy has improved the obtained solutions. The


7/11


TABLE IOBTAINEDRESULTS OF THEPMU PLACEMENT FORIEEE STANDARDTESTSYSTEMS

TABLE IICOMPARISON OFOBTAINEDRESULTS BYSEVERALMETHODS FORIEEE STANDARDTESTSYSTEMS

TABLE III

PMU PLACEMENT INPRESENCE OFNON-SYNCHRONOUS CONVENTIONALMEASUREMENTS FORIEEE 57-BUSTESTSYSTEM

Fig. 3. Part of the IEEE 118-bus test system.

execution times for test systems are 1.61, 19.19, 43.45, 337.09and 1691.27 seconds, respectively.

The obtained results of [14] for 118-bus test system are betterthan this paper proposed solutions in terms of minimization ofnumber of PMUs. Moreover, the results obtained in [14] are in-feasible, as they cannot meet the topological observability ofthe system due to buses 63 and 64 [15]. This part of the network

is shown in Fig. 3. In thisfi

gure, according to the results pre-sented by [14], no PMU is installed in buses 59, 61, 63, 64 and65; yet buses 59, 61 and 65 are observable due to the adjacentPMUs or effects of zero-injection buses. Moreover, according to[34], buses 63 and 64 are zero-injection buses. Since buses coin-ciding to an unobservable zero-injection bus (buses 63 or 64) arenot all observable, the zero-injection bus cannot be identifiedas observable by applying the KCL at zero-injection bus [14].Hence, the IEEE 118-bus test system cannot be completely ob-served using these PMUs formation. These authors have foundthat the modeling proposed by [14] for zero-injection buses mayachieve infeasible solutions when two or more zero-injection

buses are connected together [15]. Accordingly, buses 13, 14and 32 of the 39-bus test system reported in [14] are not topolog-ically observable, while PMU can be installed in zero-injection

buses. Besides, the results of the IEEE 118-bus system reportedin [15] are also infeasible due to unobservability of buses 33 and35. It should be noted that [7] has presented two results for the118-bus test system including and excluding a new observabilityrule proposed in [36]. Since this paper deals with the prevalent

observability rules, the corresponding results are reported from[7].

B. Second Scenario

In this scenario, effects of conventional measurements are in-vestigated in various situations for the IEEE 57-bus test systemand obtained results are presented in Table III. As shown inthis table, while power injection measurements could reducethe number of PMUs, average measurements redundancy is in-creased (3%). Besides, combination of power injection and cur-rent flow measurements has produced better solutions (10%).Moreover, while effects of voltage measurements in a number

of PMUs are negligible for this case, they could properly im-prove measurement redundancies (9.5%). According to theseresults, effects of non-synchronous conventional measurementsin PMU placement are non-negligible, but change according toconventional measurement locations and situation of the zero-injection buses.

The binary search algorithm that is proposed in [9] is im-plemented to solve the PMU placement problem in presenceof non-synchronous measurements. Obtained results of theimplemented direct search algorithm for the IEEE 57-bus testsystemwhich is achieved after approximately two hours ofcomputationare completely consistent with results presentedin Table III. Accordingly, the proposed observability func-tion results appropriate solutions in presence of conventionalnon-synchronous measurements.


8/11


TABLE IVPMU PLACEMENTUNDERSINGLECONTINGENCY FORIEEE 57-BUSTESTSYSTEM

TABLE VPMU PLACEMENTCONSIDERING WORTH OFSTATEESTIMATIONUNDERCONTINGENCIES FORIEEE 57-BUSTESTSYSTEM

C. Third Scenario

In this scenario, PMU placement is conducted under singlecontingencies including line outages and loss of PMUs [14]. Inorder to meet the full observability under single line outages,no line must be unobservable when a line is out. Hence, the setof in (7) should be null for the entire line outages, whichleads to . To do so, the monetary factor of observabilityvalue of each line is set equal to a very large number .By minimizing the objective function (1), the optimization al-gorithm tends to choose the layouts in which to de-crease the fitness level. In addition, since the algorithm does nottackle with the PMU outages, the is set equal to zero. Sim-ilarly, to meet the full observability under single loss of PMUs,

is set to zero and . The mentioned model is con-ducted on the IEEE 57-bus test system and obtained results arecompared to those of [14]. As it can be seen in Table IV, thetotal number of required PMUs under single contingencies isreported, beside average measurement redundancies. As shownin the first row of this table that the CLA solution requires 19PMUs under single line outages which is the same as the re-sult reported in [14] from the number of PMUs point of view.However, the proposed algorithm has improved the measure-ment redundancy by 8% which demonstrates the performanceof the second term of (1). Moreover, the second row of Table IVcompares the CLA results with those of [14] under single loss

of PMUs. According to these results, while the CLA proposed asolution with 25 PMUs, the associated result in [14] requires 26PMUs. In addition, the CLA solution has better measurement re-dundancy (5%). Hence, the proposed model has achieved bettersolution for single loss of PMUs which shows the quality of theCLA algorithm form the optimization viewpoint. Moreover, thecomparisons presented in Tables II and IV illustrate that the pro-

posed worth of state estimation formulated in (6) and (7) resultsproper solutions under boundary conditions.

In order to investigate the PMU placement under the pro-posed contingency model, the problem is conducted for thesame test case and obtained results are presented in Table V.For this reason, rate of line outages and rate of PMU losses areset equal to 0.08 (fr/year/km) and 20 (fr/year), respectively.In addition, average fault clearance time for lines and PMUs

plus PMU costs are set equal to 5 , 2 and 5000 (US$),

respectively. Disturbance rate of transmission lines is assumedtwice of the failure rate.

As it can be seen in Tables IV and V, while total number ofPMUs in normal condition is 11, 19 PMUs are needed to coverthe single line outage condition [14]. However, the proposedcontingency approach needs 12 PMUs for line outage condi-tion. According to this table, almost similar results are achievedfor other contingences including single PMU losses and simul-taneous line and PMU outages. In addition, while disturbanceworth is doubled, total required PMUs are increased almost29%. Based on this Table, since the PMUs are located in almosthalf of network buses, it seems that excessive PMUs are needed

through contingency PMU placement. On the other hand,the proposed contingency approach has proposed more reason-able solutions in which worth of network disturbances is partic-ipated in PMU placement during contingencies.

D. Fourth Scenario

In this scenario, the PMU placement problem is investigatedfor real Iranian 230- and 400-kV transmission network. The Ira-nian transmission grids are highly interconnected and managed

by 16 regional utilities owned by a holder state owned company(Tavanir).

The 230- and 400-kV transmission lines have roughly lengths

of 24 000 and 15 000 km, respectively, all of them monitoredby Tavanir. The under-study network which is shown in Fig. 4,contains 242 buses and 364 corridors. While contingency dataare set the same as third scenario, complete data listing can befound in [35].

Obtained results are shown in Tables VI and VII. As it can beseen, while the under-study network needs 71 PMUs in normalcondition, required PMUs are increased almost 35% to coverthe contingencies. In addition, sensitivity analysis presented inTable VIII shows that in the most critical condition in which dis-turbances worth are quadrupled comparing to normal condition,almost 58% of network buses need PMU. On contrary, whiledisturbances worth are set as normal condition, required PMUsare increased almost 35% comparing to normal operation. Thisshows that exact values of disturbance worth are required for


9/11


TABLE VIOBTAINEDRESULTS OFPMU PLACEMENT FOR THEIRANIAN230- AND 400- KV TRANSMISSION NETWORK

TABLE VIIOBTAINEDRESULTS OFPMU PLACEMENT FOR THEIRANIAN230-AND 400-KV TRANSMISSION NETWORKUNDERVARIOUSWORTH OFCONTINGENCIES

Fig. 4. Iranian 230- and 400-kV transmission network.

TABLE VIIIRESULTS OF THEPROPOSEDPMU PLACEMENTMODEL FOR THEIRANIANTRANSMISSIONNETWORKUSINGEVOLUTIONARYALGORITHMS

optimal planning. Hence, the authors propose that PMU place-ment be studied in two phases for practical networks: In the firstphase, PMU placement by the proposed approach be investi-gated using . Then, PMUs be installed throughout thenetwork considering results of the first phase. Afterwards, net-work disturbances are stored during state estimation for a periodof time. In the second phase, theproblem would be conducted bythe proposed approach using actual worth of disturbances basedon obtained informationof real operational periods. Final outputof the mentioned phases leads to a PMUs placement which hasoptimal performance in both normal and contingency situations.

In order to investigate optimality of the CLA solutions for theIranian transmission grid, the proposed objective function of (1)is minimized by means of a binary particle swarm optimization

Fig. 5. Trajectory of best solution for the BPSO, CLA, and GA.

(BPSO) algorithm proposed in [32] as well as theGA introducedin [5]. Moreover, as an initial solution, PMU is selected for the

entire network buses. Each algorithm is conducted for 10 inde-pendent runs and obtained results are shown in Table VIII. As itcan be seen in this table, average results of the CLA algorithmare better than those of the BPSO and GA. In addition, trajec-tory of the best solution for each algorithm is shown in Fig. 5.According to these comparisons, optimal solution of the CLA is

better than the mentioned evolutionary algorithms and has beenachieved in less execution time.

E. Fifth Scenario

In learning automata-based algorithms, choosing the properlearning rate is the most challenging issue. However, from

the learning automata theory, it is concluded that solutionoptimality is inversely proportional to the learning rate [24],[25]. Although, it is common to assume inthis sort of problems [24][28], for confidence, IEEE standardtest systems which are investigated in [9] are assumed. Then,the percentage of the converged runs (PCR) to the expectedresults (or better than them) for different values of learningrate is calculated for 100 independent runs. Table IX showsthe obtained results. In this table, (LR) is the learning rate,(PRT) is running time of the algorithm which is divided by themaximum running time of the algorithm when and(PSR) is the algorithm sampling rate which is divided by themaximum sampling rate of the algorithm when . Itcan be observed that the proposed algorithm always convergesto the minimal solution if the learning rate set to .


10/11


TABLE IXPERFORMANCE EVALUATION OF THEPROPOSEDALGORITHM FORDIFFERENTLEARNINGRATES

TABLE XSENSITIVITYANALYSIS OF THEPROPOSEDCLA LOCALRULES FOR THEIRANIAN 230-AND 400-KV TRANSMISSION NETWORK

Since the proposed algorithm aims at finding the minimumsolution, in this paper the learning rate is set to .

In addition, effects of the proposed CLA local rules are in-vestigated in this scenario and obtained results are shown inTable X. For this reason, the fourth scenario is repeated foreach Test of Table X for 10 independent runs. As it can beseen in this table, while probability of achieving optimal solu-tions is increased, computational burden is almost doubled byapplying these rules to the optimization algorithm. Although itis hard to highlight exact effects of each CLA local rule basedon these slight tests, it can be concluded that local rules have

properly improved rewarding strategy so that better solutionsare achieved in Test 2-Test 8 rather than Test 1. It should

be noted that, although in Test 8 computer executive opera-

tions are increased, the solution time is decreased since learningautomata could find their proper actions sooner.

VI. CONCLUSION

The multi-objective PMU placement problem was investi-gated as an optimization problem using CLA. The prevalentPMU placement problem formulation is extended and new con-cepts of measurement redundancy and observability value incontingencies were defined and added to the model. A new

observability function was proposed in which effects of con-ventional measurements and zero-injection buses were consid-ered during a pseudo-repetitive process. Furthermore, effects ofconventional measurements on PMU placement were studiedin various situations. Finally, the problem was conducted forthe IEEE standard test systems as well as the Iranian 230- and400-kV transmission network and compared to those of the pre-vious research. The obtained results revealed that the proposedapproach can be used as an effective tool for optimal PMU

placement of a practical network under contingencies.Further research may be conducted on preparing an integer

linear programming based formulation for the proposed objec-tive function, and investigating the effects of installing redun-dant PMUs at a bus on the worth of observability in contingen-cies.

ACKNOWLEDGMENT

The authors would like to thank Prof. M. R. Meybodi andDr. J. Akbari-Torkestani for their valuable help, comments, andsuggestions.

The insightful and constructive comments of the editors andthe anonymous refereesthat greatly improved the content and

presentation of this manuscriptare thankfully acknowledged.

REFERENCES[1] A. G. Phadke,Synchronizedphasor measurements in power systems,

IEEE C omput. Appl. Power, vol. 6, no. 2, pp. 1015, Apr. 1993.[2] A. Abur and A. G. Esposito, Power System State Estimation: Theory

and Implementation. New York: Marcel Dekker, 2004.[3] A. S. Debs, Modern Power Sys tems Control and Operation. London,

U.K.: Kluwer, 1998.

[4] R. E. Wilson, Satellite synchronized measurements confi

rm powerequation, IEEE Potentials, vol. 13, no. 2, pp. 2628, Apr. 1994.[5] F. J. Marn, F. Garca-Lagos, G. Joya, and F. Sandoval, Genetic algo-

rithms for optimal placement of phasor measurement units in electricnetworks,Electron. Lett., vol. 39, no. 19, pp. 14031405, Sep. 2003.

[6] T.L. Baldwin, L. Mili, M.B. Boisen, and R.Adapa,Powersystem ob-servability with minimalphasor measurement placement,IEEE Trans.

Power Syst., vol. 8, no. 2, pp. 707715, May 1993.[7] F. Aminifar,C. Lucas, A. Khodaei, and M. Fotuhi-Firuzabad, Optimal

placement of phasor measurement units using immunity genetic algo-rithm, IEEE Trans. Power Del., vol. 24, no. 3, pp. 10141020, Jul.2009.

[8] B. Milosevic and M. Begovic, Nondominated sorting genetic algo-rithm for optimal phasor measurementplacement,IEEE Trans. PowerSyst., vol. 18, no. 1, pp. 6975, Feb. 2003.

[9] S. Chakrabarti and E. Kyriakides, Optimal placement of phasor mea-surement units for power system observability, IEEE Trans. PowerSyst., vol. 23, no. 3, pp. 14331440, Aug. 2008.

[10] S. Chakrabarti, E. Kyriakides, and D. G. Eliades, Placement of syn-chronized measurements for power system observability,IEEE Trans.

Power Del., vol. 24, no. 1, pp. 1219, Jan. 2009.[11] J. B. Gou, Generalized integer linear programming formulation for

optimal PMU placement,IEEE Trans. Power Syst., vol. 23, no. 3, pp.10991104, Aug. 2008.

[12] D. Dua, S. Dambhare, R. K. Gajbhiye, and S. A. Soman, Optimalmultistage scheduling of PMU placement: An ILP approach, IEEETrans. Power Del., vol. 23, no. 4, pp. 18121820, Oct. 2006.

[13] N. H. Abbasy and H. M. Ismail, A unified approach for the optimalPMU location for power system state estimation, IEEE Trans. PowerSyst., vol. 24, no. 2, pp. 806813, May 2009.

[14] F. Aminifar, A. Khodaei, M. Fotuhi-Firuzabad, and M. Shahideh-pour,Contingency-constrained PMU placement in power networks,IEEETrans. Power Syst., vol. 25, no. 1, pp. 516523, Feb. 2010.

[15] S. M. Mahaei and M. Tarafdar-Hagh, Minimizing the number ofPMUs and their optimal placement in power systems, Elect. PowerSyst. Res., vol. 83, pp. 6672, 2012.


11/11


[16] R. F. Nuqui and A. G. Phadke, Phasor measurement unit placementtechniques for complete and incomplete observability, IEEE Trans.

Power Del., vol. 20, no. 4, pp. 23812388, Oct. 2005.[17] J. Chen and A. Abur, Placement of PMUs to enable bad data detec-

tion in state estimation, IEEE Trans. Power Syst., vol. 21, no. 4, pp.16081615, Nov. 2006.

[18] B. Xu and A. Abur, Observability analysis and measurement place-ment for system with PMUs, in Proc. IEEE Power Syst. Conf. Expo.,Oct. 2004, vol. 2, pp. 943946.

[19] S. Almeida, R. Pestana, and F. M. Barbosa, Severe contingenciesanalysis in Portuguese transmission system, in Proc. 41st Universi-ties Power Engineering Int. Conf., 2006, pp. 462466.

[20] Y. Sun and T. J. Overbye, Visualizations for power system contin-gency analysis data, IEEE Trans. Power Syst., vol. 19, no. 4, pp.18591866, Nov. 2004.

[21] B. L. Silverstein and D. M. Porter, Contingency ranking for bulksystem reliability criterion, IEEE Trans. Power Syst., vol. 7, no. 3,

pp. 956964, Aug. 1992.[22] F. Aminifar, M. Fotuhi-Firuzabad, M. Shahidehpour, and A. Khodaei,

Observability enhancement by optimal PMU placement consideringrandom power system outages,Energy Syst., no. 2, pp. 4565, 2011.

[23] E. M. Carreno, R. M. Rochaand, and A. Padilha-Feltrin, A cellularautomaton approach to spatial electric load forecasting, IEEE Trans.

Power Syst., vol. 26, no. 2, pp. 532540, May 2011.[24] K. S. Narendra and K. S. Thathachar, Learning Automata: An Intro-

duction. New York: Printice-Hall, 1989.[25] M. R. Meybodi and H. Beigy, A mathematical framework for cellularlearning automata,J. Adv. Complex Syst., vol. 7, no. 3, pp. 295320,2004.

[26] J. A. Torkestani and M. R. Meybodi, A cellular learning automata-based algorithm for solving the vertex coloring problem, Expert Syst.Appl., vol. 38, pp. 92379247, 2011.

[27] A. Enami-Eraghi, J. Akbari-Torkestani, M. R. Meybodi, and A. H.Fathy-Navid, Cellular learning automata-based channel assignmentalgorithms for wireless mobile ad hoc networks, in Proc. Int. Conf.

Machine Learning and Computing, 2011, pp. 173177.[28] M. Saheb-Zamani, F. Mehdipour, and M. R. Meybodi, Implementa-

tion of cellular learning automata on reconfigurable computing sys-tems, inProc. Canadian Conf. Electrical and Computer Engineering,2003, vol. 2, pp. 11391142.

[29] H. Beigy and M. R. Meybodi, Cellular learning automata with mul-tiple learning automata in each cell and its applications, IEEE Trans.Syst., Man, Cybern., vol. 40, no. 1, pp. 5465, 2010.

[30] H. Beigy and M. R. Meybodi, A self-organizing channel assignmentalgorithm: A cellular learning automata approach,Intell. Data Eng.

Autom. Learn., vol. 26, no. 90, pp. 119126, 2003.[31] R. Rastegar and M. R. Meybodi, A new evolutionary computing

model based on cellular learning automata, in Proc. IEEE Conf.Cybernetics and Intelligent Systems, 2004, vol. 1, pp. 433438.

[32] C. nsal, Intelligent navigation of autonomous vehicles in an auto-mated highway system: Learning methods and interacting vehicles ap-

proach, Ph.D. dissertation, Virginia Polytechnic Institute and StateUniversity, Blacksburg, Virginia, 1996.

[33] [Online]. Available: http://ce.aut.ac.ir/~meybodi/index.htm#publica-tion.

[34] R. Christie, Power System Test Archive, Aug. 1999. [Online]. Avail-able: http://www.ee.washington.edu/research/pstca.

[35] [Online]. Available: http://mazhariac.persiangig.com/.

[36] M. Hajian, A. M. Ranjbar, T. Amraee, and B. Mozafari, Optimalplacement of PMUs to maintain network observability using a modi-fied BPSO algorithm,Int. J. Elect. Power Energy Syst. , vol. 33, no.1, pp. 2834, 2011.

Seyed Mahdi Mazhari (S12) received the B.S.(Hon.) degree from the University of Birjand, Bir-

jand, Iran, in 2010 and the M.S. (Hon.) degree fromthe University of Tehran, Tehran, Iran, 2012, both inelectrical engineering.

Currently, he is working as a research associate atthe research Center of power system operation and

planning studies, University of Tehran. His researchinterest includesplanning of the electric power distri-

bution and transmission systems, power system oper-ation, and artificial intelligence applications to power

system optimization problems.

Hassan Monsef received the B.Sc. degree fromSharif University of Technology, Tehran, Iran,in 1986, the M.Sc. degree with honor from theUniversity of Tehran in 1989, and the Ph.D. degreefrom Sharif University of Technology in 1996, all in

power engineering.He has been with the University College of En-

gineering, School of Electrical and Computer Engi-neering, University of Tehran, since 1996, where hecurrently is an Associate Professor. His research in-

terests are power system operation under deregula-tion, reliability of power system, power systems economics, renewable energysystems, and its integration in smart grid.

Hamid Lesani received the M.S. degree in powerengineering from the University of Tehran, Tehran,Iran, in 1975 and the Ph.D. degree in electrical en-gineering from the University of Dundee, Dundee,U.K., in 1987.

Then, he joined the Department of Electrical andComputer Engineering, University of Tehran, wherehe currently serves as a Professor at the Center of Ex-cellence for Control and Intelligent Processing. Histeaching and research interests is focused on design

and modeling of electrical machines and power sys-tems.

Prof. Lesani is a member of the IEEE PES and the IEEE Iran Section.

Alireza Fereidunian(M08) received the M.Sc. andPh.D. degrees from the University of Tehran, Tehran,Iran, in 1997 and 2009, respectively.

He is an Assistant Professor at the K. N. ToosiUniversity of Technology, Tehran. He is a Post-Doc-toral Research Associate at the University of Tehran.His research interests include Smart Grid, energydistribution systems, and application of IT and AIin power systems. Moreover, he works in complexsystems, systems reliability and human-automation

interactions areas, where he has invented the Adap-tive Autonomy Expert System (AAES).

Dr. Fereidunian is an IEEE-SMC-HCI TC member and a member of INCOSE(as INCOSE Iran point of contact).

A Multi-Objective PMU Placement Method Considering Measurement Redundancy and Observability Value...

Documents

Transcript of A Multi-Objective PMU Placement Method Considering Measurement Redundancy and Observability Value...