Electrical Power and Energy Systems 52 (2013) 34–41

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Electr ical Power and Energy Systems

journal homepage: www.elsevier .com/locate / i jepes

Planning high quality metering systems for state estimation through aconstructive heuristic

0142-0615/$ - see front matter � 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijepes.2013.03.019

⇑ Corresponding author. Tel.: +55 21 26295472; fax: +55 21 26295627. E-mail address: julio@ic.uff.br (J.C.S. de Souza).

Helder Roberto de Oliveira Rocha, Julio Cesar Stacchini de Souza ⇑, Milton Brown Do Coutto Filho Fluminense Federal University, Rua Passo da Pátria, 156, São Domingos, 24210-240 Niteroi, Rio de Janeiro, Brazil

a r t i c l e i n f o

Article history: Received 4 April 2012 Received in revised form 20 March 2013 Accepted 25 March 2013

Keywords:Power system state estimation HeuristicsOptimization

a b s t r a c t

The design of metering plans for power system state estimation is a classical, complex, combinato rial optimi zation problem, many times solved by a family of metaheuristic algorithms. This paper presents a methodol ogy for designing reliable and robust metering systems, taking into account aspects, such as: observabilit y; absence of critical data; possibl e changes in network configuration; loss of remote ter- minal units. To accomp lish this task, a simple, practical value, constructive heuristic that considers inher- ent characteristics of the meter placement problem is proposed. Simulations with the IEEE 14, 30, and 118-b us test systems, as well as with part of a real Brazilian system, illustrate the performance of the pro- posed constructive approach. Regarding redundan cy requisites, high quality metering plans are obtained without requiring a formal optimization technique. It is also shown that the proposed heuristic can be employed in conjunction with an optimization tool (a popular metaheuristic, e.g. ant colony optimiza- tion) to achieve even better results. Test results obtained in the paper are encouraging, as compared with those found in the technical literature.

� 2013 Elsevier Ltd. All rights reserved.

1. Introductio n Several methods have been proposed for meter placemen t in

Power system state estimation (SE) is responsible for processin greal-time measurements and providing a complete and reliable database, to be accessed by advanced analysis tools in an Energy Management System [1,2]. Data redundancy is crucial for the success of the SE process. With an adequate redundan cy level, SE can effectively process, detect, and identify bad data (BD), facing a possible temporary loss of measurements without compromising the reliability of the estimate d values. Data redundancy for SE is evaluated considering the number, type, and topologic al distribu- tion of measure ments in the electrical network. It is also necessary to consider that during power system operation, network configu-ration changes, loss of remote terminal units (RTUs) or temporary malfunction of the data acquisition system may occur, reducing data redundancy available for SE [3]. Even critical redundancy lev- els may be achieved [4], leading to inadequate performanc e of BD processing routines. Therefore, when planning metering systems it is necessar y to adopt redundancy requisites, so as to: allow observ- ability of the entire network of interest; avoid critical data; assure reliability of the SE results (BD detection, identification and suppression is possible); provide robustness to deal with loss of measureme nts and network configuration changes. Although highly redundant metering systems are desirable , they are not usu- ally attained due to financial constraints.

electric power systems. In [5], a method that takes into account technical and financial issues is proposed. However, the optimiza- tion process adopted involves an exhaustiv e search procedure. In [6,7], a method to reinforce an existing metering system is pre- sented, based on the topological observability of the monitore dnetwork. In [8], an algorithm for the identification of observable islands and selection of additional measurements to restore net- work observabi lity is considered . Methods that take into account observabi lity, reliability, and robustness are presented in [9,10].However , the minimizatio n of investment costs is not explicitly considered . In [11], costs are incorporate d, but an exhaustive search procedure is employed . In [12,13], a metering system is de- signed for a primary network, including the occurrence of network changes or measurement losses. Nevertheles s, only the observabil- ity requisite is established. In [14] practical aspects are considered for placing RTUs in distribut ion systems.

Methods based on intelligent system techniques have also been proposed for obtaining optimal metering systems [15–17]. How- ever, the reliability requiremen t is not explicitly considered, thus compromi sing BD suppressi on capability of the estimation process. In [18], a genetic algorithm (GA) is employed to design metering systems without critical data, regardles s of correspondi ng costs. On the other hand, investment costs are explicitly considered in [19], but SE reliability can be assured only for a single topologic al scenario. In [20,21], low cost metering systems are obtained through a GA, assuring SE reliability for different topological sce- narios. A steady-st ate GA [22] and an evolutionary algorithm [23]

H.R. de Oliveira Rocha et al. / Electrical Power and Energy Systems 52 (2013) 34–41 35

have been employed to obtain metering systems that do not pres- ent critical RTUs. An RTU is said to be critical when its loss leads to network unobservab ility.

Although metaheu ristics have been successfu lly applied to the meter placement problem, they require the formulation of puzzling objective functions and fine-tuning of key parameters, usually problem- dependent. These aspects can difficult the direct application of such techniqu es to solve practical (real-world)problems. On the other hand, the use of heuristic methods can be beneficial to the optimization process [24,25].

The main contribution of this paper is a practical, efficientprocedure that employs a probabili stic constructive heuristic to obtain low cost, reliable, robust metering plans for SE. The avoid- ance of critical redundancy levels for a primary network ensures SE reliability , whereas for different topological scenarios and even- tually losses of RTUs accounts for robustness. The proposed heuris- tic is simple, easy to implement and does not require the use of complex objective functions nor adjustment s in parameter values of optimization algorithms (pathway in which no optimizati on technique is exploited). Tests with the IEEE 14, 30, and 118-bus systems, as well as with part of a real Brazilian system, are per- formed. The results obtained by the proposed heuristic procedure (although suboptimal ) are very close to those attained when sophisticated optimization techniques are used. It is also shown that improved solutions can be obtained, if the proposed probabi- listic constructive heuristic is employed in conjunct ion with an optimization tool (e.g. ant colony optimizati on). Test results are promising as compared with to those experimental reported in the technical literature.

2. Meter placement problem

Data redundan cy is essential to a successful SE process. A well- planned metering system is the one in which a compromise between redundancy and cost (conflicting objectives) is achieved. Thus, the meter placemen t problem can be viewed as a combinato- rial optimization problem: investment cost minimized, while adequate data redundancy (no critical conditions to the SE process)assured. In this section, data redundancy requiremen ts are stated and the optimization problem is formulated.

Traditional ly, SE uses the magnitude and angle of bus voltages as the system state and measurements of active/react ive power flows and injections along with some voltage magnitud e measure- ments, all of them acquired by RTUs. Synchronized measure ments provided by phasor measure ment units (PMUs) are gradually becoming available for many applicati ons, SE included. A PMU in- stalled at a given bus can provide the voltage phasor at the bus and phasor currents on branches incident to that bus.

Some methods for optimal PMU placemen t have also been pro- posed [26–28]. Owing to the high costs involving PMU infrastruc- ture, it is believed that few PMUs will be strategically placed to reinforce existing metering systems. The incorporati on of PMU measureme nts to design metering plans will be subject of a future paper.

2.1. Redundancy requirement s

An adequate data redundancy is assessed through a metering system design in which not only the number, but also the type and location of measureme nts are considered, bearing in mind the following requiremen ts:

� Observabilit y—SE is accomplished for the entire network. � Reliability—BD detection, identification, and suppression is

possible.

� Robustnes s—In the event of network configuration changes or temporary malfuncti on of the data acquisition system (imply-ing in redundancy deterioration) observabi lity and reliability requiremen ts are still met. � Cost—Investment cost for data acquisition is minimized.

Usually, the linearized and decoupled SE is adopted to perform observabi lity analysis, taking into account the Ph (active power-an- gle) model [6].

Let G be the gain matrix of the SE process, obtained by:

G ¼ HtR�1H ð1Þ

where H is the Jacobian matrix obtained from the lineariza tion of the load-flow equations for the current network configuration and R is the diagonal covariance matrix of the measurem ent noise vector.

A system is said to be observabl e, if G is nonsingular, which can be verified during its triangula r factorization (no zero pivots, if the reference bus angle is not included).

Reliability can be guaranteed if BD can be effectively handled by SE residual analysis, which means that critical measureme nts and sets should not be allowed in the metering plan. The residual vec- tor r, defined as being the difference between the measure ment vector z and the corresponding filtered quantities z, is normalized and submitted to a validation test [1,2]:

rNðiÞ ¼ jrðiÞj=rEðiÞ 6 threshold ð2Þ

E ¼ R �HG�1Ht ð3Þ

where rEðiÞ ¼ffiffiffiffiffiffiffiffiffiffiffiffiEði; iÞ

pis the standard deviatio n of the ith compo-

nent of the residual vector. Threshold violations indicate the presen ce of BD.A critical measureme nt (Cmeas) is a non-redund ant measureme nt, for which the filtering process is useless. Thus, the residua l and standard deviatio n associated with a Cmeas always equals zero [4]:

rðiÞ ¼ zðiÞ � zðiÞ ¼ 0 ð4Þ

rEðiÞ ¼ffiffiffiffiffiffiffiffiffiffiffiffiEði; iÞ

q¼ 0 ð5Þ

Normalized residuals of measureme nts pertaining to a critical set (Cset) are equal, and their correlation coefficients present maxi- mum values. Suppose that measureme nts i and j belong to the same Cset. Then, it follows that [4]:

qði; jÞ ¼ rNðiÞrNðjÞ

¼ 1 ð6Þ

cði; jÞ ¼ Eði; jÞffiffiffiffiffiffiffiffiffiffiffiffiEði; iÞ

p ffiffiffiffiffiffiffiffiffiffiffiffiEðj; jÞ

p ¼ 1 ð7Þ

It can be seen from (4) that BD in Cmeas are not detectable . On the other hand, although bad measurem ents in Csets are detectable ,they cannot be identified, as shown in (6). Besides, the loss of aCmeas leads to unobserva bility, while the loss of any measureme nt of a Cset makes the remaining ones Cmeas [8]. Several metho ds for identifying Cmeas and Csets can be found in the technical literature [4,29–32]. In this work, the detection/ identification of such critical- ities is done by employin g the method presented in [4].

Meter placement is of primary importance and one of the most difficult problems in SE. This is due not only to its combinatori al nature, but also to the need of establishi ng a trade-off between SE performanc e and metering system cost. The formulation of the optimal meter placement problem is presented next.

36 H.R. de Oliveira Rocha et al. / Electrical Power and Energy Systems 52 (2013) 34–41

2.2. Problem formulation

The combinatorial optimization problem can be formulated as follows:

Min ðmetering system cost Þs:t: observability

reliability

robustness

ð8Þ

2.2.1. Observability As previously stated, the observabi lity requiremen t can be eval-

uated by checking the non-singula rity of the SE gain matrix G.Thus, the problem formulation becomes:

MinXNbRTU

i¼1

ðCostRTUi� ci þ

XNmeteri

j¼1

CostMeterij� dijÞ

" #

s:t: detðGÞ–0ci and dij 2 f0;1g

ð9Þ

where Nb RTU is the number of buses eligible for RTU allocation; Nmeteri the number of meter s that can be allocated in the ithRTU; Cost RTUi

the cost of the ith RTU; Cost Meterijthe cost of the jth

meter of the ith RTU; ci = 1, if the ith RTU is alloca ted; ci = 0, other- wise; dij = 1, if the jth measureme nt is installed in the ith RTU; and dij = 0, otherwise.

2.2.2. Reliability This requiremen t can be taken into account by adding con-

straints in (9) that impose the absence of Cmeas and Csets in the aimed metering plan. The problem can be formulated now as:

MinXNbRTU

i¼1

ðCostRTUi� ci þ

XNmeteri

j¼1

CostMeterij� dijÞ

" #

s:t: detðGÞ–0Eðk; kÞ–0; k ¼ 1; . . . ;m

qðk; ‘Þ–1 _ cðk; ‘Þ–1; k ¼ 1; . . . ;m; ‘ ¼ 1; . . . ;m; k–‘

ci; dij 2 f0;1gð10Þ

where m is the total number of measureme nts of the meter ing plan. Accordin g to (5)–(7), the new constraints guarant ee the absence of Cmeas and Csets.

2.2.3. Robustness During power system operation, situation s such as the tempo-

rary unavailability of groups of measureme nts (loss of an RTU) or changes in network configuration may reduce data redundan cy for SE. Conseque ntly, observability and reliability requirements cannot be guaranteed anymore. To avoid such situations, it is nec- essary to plan robust metering systems, capable of withstand ing

1 2

4

13 2 3

4 observable islands

Fig. 1. Observability of state variables ( power injection; d power flow).

configuration changes and RTU losses, still preserving observabi lity and reliability of the SE process. Thus, the problem formulat ion consideri ng different network configurations is given by:

MinXNbRTU

i¼1

ðCostRTUi�ciþXNmeteri

j¼1

CostMeterij�dijÞ

" #

s:t: detðGtÞ–0; t¼1; . . . ;NConfig

Etðk;kÞ–0; k¼1; . . . ;mt ; t¼1; . . . ;NConfig

qtðk; ‘Þ–1_ctðk; ‘Þ–1; k¼1; . . . ;mt ; ‘¼1; . . . ;mt ; k–‘; t¼1; . . . ;NConfig

ci;dij 2f0;1gð11Þ

where NConfig is the number of network configurations being consid- ered when planning the metering system; mt is the number of mea- surement s presen t in the tth configuration. The same constra ints in (10) are now considered in (11), for each network configuration of intere st.

Now consideri ng the unavailability of a group of measureme nts, assume that network observabi lity should be preserved, even in case of loss of any RTU. This means that critical RTUs should not be allowed. It is also possible to have a metering system for which the loss of any RTU does not cause the presence of Cmeas. For this sake, the concept of a critical set of RTUs is introduce d and definedin this work as: the one that contains RTUs whose loss will not lead the system to unobservabilit y and no Cmeas will arise. So, if ametering system is free from a critical set of RTUs, this means that besides preserving system observability, no Cmeas will be present if any RTU is lost. The problem formulation for such situation is presente d in (12).

MinXNbRTU

i¼1

CostRTUi�ciþXNmeteri

j¼1

CostMeterij�dij

!" #

s:t: detðGsÞ–0; s ¼ 1; . . . ;NRTU

Esðk; kÞ–0; k ¼ 1; . . . ;ms; s ¼ 1; . . . ;NRTU

q0ðk; ‘Þ–1 _ c0ðk; ‘Þ–1; k ¼ 1; . . . ;m; ‘ ¼ 1; . . . ;m; k–‘

ci;dij 2 f0;1gð12Þ

where NRTU is the number of RTUs in a given metering plan; ms thenumber of measureme nts remaining when the sth RTU is lost; coef- ficients q0ðk; ‘Þ and c0ðk; ‘Þ are compute d for the basic scenario, i.e., when all RTUs are present. It is importan t to mention that observ- ability and absence of Cmeas are required, even when an RTU is lost, which guarantees that the meter ing plan is free from critical RTUs and from a critical set of RTUs.

For the sake of simplicity, robustness has been considered in (11) and (12). However, these formulation s can be integrated, con- sidering the constrain ts related to configuration changes and RTU losses in conjunction .

3. Extractio n of problem characte ristics

The constructive heuristic proposed in this paper takes into ac- count some characterist ics that have been observed in metering systems designed for SE, regarding observabi lity and reliability requiremen ts. It is assumed here that the allocation of any RTU implies the use of all measureme nts associated with it. Using the active power-angle observabi lity model, these measurements are active power flows/injections. Then, the following statement can be made:

Statement: An RTU placed at a given bus with many incident branches will observe more state variables than at one with few connected branches.

In the illustrative example of Fig. 1, it can be seen that all the state variables are able to be reached through the equations of

1 2 4 3

Fig. 3. Observable network without Csets - radial network.

1 2 4 3

irrelevant branch

Fig. 4. Unobservable network.

1 2 4 3

6 5

Fig. 5. Observable network without Cmeas - meshed network.

1 2 3 4

6 5

Fig. 6. Observable network without Csets - meshed network.

H.R. de Oliveira Rocha et al. / Electrical Power and Energy Systems 52 (2013) 34–41 37

measureme nts, if an RTU is allocated at bus 2. But it will not hap- pen, if an RTU is placed at bus 4. A state variable is said to be ac- cessed by a given measure ment, if it is present in the correspondi ng measurement equation.

Clearly, power network topology also influences the placemen tof meters to meet these requiremen ts. Depending on the network characterist ics, the conditions that guarante e SE observability and reliability can be stated as follows.

3.1. Radial networks

In radial networks it is important to avoid the presence of irrel- evant branches, which would lead to system unobservab ility.

Condition#1: Radial networks are observable and free from Cmeas if the state of each bus is accessed by at least two mea- surements from an RTU placed at the bus or from two RTUs placed at its adjacent buses. Condition#2: Radial networks are free from Csets if RTUs are allocated in all buses.

Figs. 2 and 3 illustrate such situations, whereas Fig. 4 shows an unobservab le network.

3.2. Meshed networks

Regarding meshed networks the following conditions can be established.

Condition#3: Meshed networks are observable and free from Cmeas if the state of each bus is accessed by measurements from an RTU placed at this bus or at one adjacent to it. Condition#4: Meshed networks are observable and free from Csets if the state of each bus is accessed by measurements from at least two RTUs.

Condition s 3 and 4 are exemplified by Figs. 5 and 6.Usually, power systems are composed by a combination of ra-

dial and meshed networks. The practical guidelines presented here can be conjugated to establish a heuristic procedure for designing high quality metering plans.

4. Proposed methodology

Here, by means of inherent characteri stics of the meter place- ment problem, a constructi ve heuristic is develope d to reduce the effort to obtain good solutions, regarding SE data redundancy requiremen ts introduced in Section 2. Although one cannot guarantee that optimal solutions will be obtained via heuristic procedures, it is possible to achieve high quality solutions with re- spect to investment costs and to the attendan ce of reliability and robustness requiremen ts.

4.1. Probabilistic constructive heuristic

Based on the guidelines described in Section 3, a probabilistic constructive heuristic (PCH) has been developed. Three dynamic lists, modified during the construction of a metering plan, are built:

1 2 4 3

Fig. 2. Observable network without Cmeas - radial network.

L1: contains all system buses eligible for RTU allocation . In this list, buses are sorted (in descending order) according to the number branches incident to them. L2: contains buses at which the allocation of an RTU is proposed .L3: contains buses at which the allocation of an RTU is discarded.

Next, the main steps of the proposed PCH algorithm are de- scribed, considering SE observability and reliability requiremen ts.

4.1.1. PCH algorithm

(i) Create L1; it starts from the bus that presents more incident branches. At this point, L1 contains all system buses, L2 and L3 are empty.

(ii) Select next bus i in L1 and allocate an RTU (and all associated measurements ) at this bus. Move bus i to L2.

38 H.R. de Oliveira Rocha et al. / Electrical Power and Energy Systems 52 (2013) 34–41

(iii) Create a roulette wheel in which the number of cavities equals the number of incident branches n, at bus i. Each cav- ity represents an integer number between 1 and n, being the cavity area proportional to this number. Rotate the roulette wheel in order to obtain a given number r.

(iv) Check if it is possible to discard the allocation of RTUs at buses connected to bus i, based on the information stored in L2 and on the results obtained at step (iii) after rotating the roulette wheel:

(1) If only observabi lity and absence of Cmeas are of inter-

est, the allocation of an RTU will be discarded for every bus adjacent to i that is part of a meshed network and whose number of incident branches is less or equal to the number r obtained by the roulette wheel at step (iii). If bus i pertains to a radial part of the network, the allocation of an RTU is discarded for every bus adja- cent to i for which there are RTUs already allocated at two (at least) adjacent buses. If a bus adjacent to i is aterminal bus, the allocation of an RTU is also discarded.

(2) If the absence of Csets is also of interest, the allocation of an RTU will be discarded at every bus adjacent to i that is part of a meshed network, for which there are RTUs already allocated at two (at least) adjacent buses and whose number of incident branches is less or equal to r.

(v) The buses adjacent to i for which the allocation of an RTU has been discarded at step (iv) are transferred to L3, whereas the others remain in L1.

(vi) If L1 is empty, end the constructive algorithm. The metering plan consists of RTUs installed at the buses in L2. Otherwise, return to step (ii).

The presente d algorithm leads to low cost metering systems that are always feasible with respect to observability and/or reliability requirements. It is also important to remark that the probabilistic nature of the proposed heuristic is embedded in the algorithm at step (iii). The roulette wheel makes probabilistic the choice of the buses at which the allocation of RTUs is discarded in step (iv). Otherwise, the choice of the buses in which the alloca- tion of RTUs is discarded would be determinist ic and the execution of the proposed algorithm would always produce the same result. The PCH may obtain different metering plans each time it is exe- cuted. The value of r may allow the allocation of RTUs at buses with many incident branches even if they are adjacent to buses in which the allocation of RTUs has already been proposed. The diversity of solutions is an important feature for population based metaheuris- tics, such as the one presente d in Section 4.4.

4.2. Robustness requirem ent

To take into account that a metering plan has to meet SE requi- sites of observability and/or reliability under different topologie s of interest, the PCH algorithm of Section 4.1 is employed, but consid- ering now that: a given bus is said to pertain to a meshed network, if this happens for all topology scenarios; it is said to pertain to aradial network, when this condition is verified for at least one topology. Thus, at step (iv), the decisions are taken based on how each bus has been classified with respect to the type of network it is inserted in.

Regarding the absence of critical RTUs or a critical set of RTUs, the solutions provided by the algorithm of Section 4.1 (when the absence of Csets is aimed) can be already considered good solutions. In many cases, these solutions will also be feasible with respect to the absence of such criticalities of RTUs. If not feasible, these will be good enough to be refined during the evolution pro- cess guided by a population based metaheurist ic, such as the one proposed in the methodology presented in the next section.

4.3. Local search

The PCH proposed in Section 4.1 can be executed several times and each time it is executed a new high quality metering plan is obtained. Note that when executing the PCH, the dimension of the solution vector correspond s to the number of system buses (or to the number of buses in which the allocation of an RTU is al- lowed, if there is any restriction for the allocation at some buses). It is assumed that all possible measure ments are present in each allo- cated RTU. After executing the PCH a pre-defined number of times, the best solution found can be refined by performing a simple local search. The dimension of the solution vector now corresponds to the total number of meters allocated in the best solution found by the PCH and each element of this vector represents one of these meters. The local search consists of a simple algorithm that tries to find more economic solutions by removing the surplus of measure -ments, i.e. those which the removal will not cause violation of any constrain t presente d in (12). For example, when the PCH is used to obtain metering plans that satisfy network observabi lity and absence of Cmeas constraints (always simultaneou sly met by the PCH solutions), the local search can be employed to eliminate the surplus of measureme nts so that only the observability require- ment is attended (reducing investme nt costs).

4.4. Integrating PCH into ant colony optimization algorithm

In order to show how the proposed PCH can be employed as part of an optimization process, this section presents the combina- tion of the PCH with an ant colony optimizati on (ACO) algorithm. The ACO reinforces the best solutions obtained by the PCH, provid- ing a memory feature that allows the generation of solutions that tend to be better than the previous ones.

The ACO [33] is a population-based metaheuristic, founded on the structure and behavior of ant colonies. Ants can deal with complex tasks by acting in a collective manner. When moving from one location to another, ants deposit a chemical substance, called pheromo ne, in their path. The presence of pheromo ne in a given path attracts other ants, which will reinforce the concentratio n of pheromo ne in that path. Then, the pheromone is a key element for informat ion exchange among ants, making possible the execu- tion of important and complex tasks. Theoretical and practical aspects of the ACO can be found in [33].

At each step of the ACO-based algorithm, a population of solu- tions is obtained by employing the PCH. It is important to stress that the probabili stic nature of the PCH is based on the use of aroulette wheel at step (iv) of the algorithm (Section 4.1), which will allow different decisions on the allocation of RTUs every time this algorithm is executed. However, the choice of the first bus at which an RTU will be allocated remains determini stic, as can be seen at step (ii) of the PCH algorithm. In order to introduce more diversity in each population generated by the proposed ACO-based approach , the choice of the first bus to allocate an RTU becomes also probabilistic when using the PCH. Then, step (ii) of the con- structive algorithm presente d in Section 4.1 is modified so that the selection of each bus in L1 becomes nondetermi nistic. A rou- lette wheel is now employed at this step, in which each cavity rep- resents a given bus, being its area proportional to the amount of pheromo ne and to the number of incident branches at that bus. The probabili ty of selecting a given bus is:

piðtÞ ¼½siðtÞ�a½uigi�

b

XNBarras

j¼1

½sjðtÞ�a½uigj�b

ð13Þ

where siðtÞ is the amount of pherom one at bus i; ui is the number of incident branches at bus i; gi represe nts the permission to allocate

H.R. de Oliveira Rocha et al. / Electrical Power and Energy Systems 52 (2013) 34–41 39

an RTU at bus i (heuristic: equal to 1, if allowed; otherwise, set to 0);a is the sensitivit y to the trail of pheromon e and b is the sensitivity to the heuristic information . si(t) – amount of pheromone at bus i.

In the first iteration of the ACO process a set of ns solutions is generated by employing ns times the constructive algorithm. The best solution is declared the current solution and the amount of pheromone is updated (at each bus in which the allocation of an RTU is proposed). These buses are more likely to be selected, when performing the roulette wheel in the next iteration. The best solu- tion is compared with the best solution obtained so far (currentsolution). The current solution is updated, whenever a better solution is found. Each proposed solution is evaluated through the following fitness function (FF):

FF ¼XNR

i¼1

CostRTUiþXNM

j¼1

CostMeteriþXNConfig

t¼1

½Obst � Pobs þ NCmeast

� PCmeast þ NmCsett � PCsett � þXNR

s¼1

½Obss � Pobs� ð14Þ

where NR and NM are the number of RTUs and meters to be in- stalled, respective ly; Obs t indicates whether the tth network config-uration is observabl e (Obst = 0) or not (Obst = 1), whereas Pobs is apenalty factor for unobserva ble scenarios; NCmeast is the number of Cmeas in the tth network configuration, whereas PCmeast is a penalty factor for the occurren ce of Cmeas in such scenario; similarly, NmCsett is the number of measureme nts that pertain to Csets and PCsett is a penalty factor impose d for the occurren ce of Csets in the tth network configuration. The third line of (14) refers to scenarios (index s) derived from the loss of RTUs, instead of network config-uration chang es.

The first two terms of FF refer to the metering system cost. The third aims to guarante e network observability, as well as SE reli- ability, for all network scenarios of interest. Finally, the fourth ac- counts for the absence of critical RTUs.

The FF built in (14) is simple and flexible, allowing the planner to easily represent the objectives to be achieved. For instance, if the metering plan should guarantee SE reliability for a single network configuration scenario and the loss of RTUs is not of concern, the fourth term of (14) is neglected and NConfig is set to 1 in the third term. Also, if there are NConfig topologie s of interest and SE reliabil- ity should be guaranteed for only one of them (all the other config-urations will be barely observabl e), PCsett is set to zero for (NConfig � 1) topology scenarios.

Table 1Results with the IEEE 30-bus system.

Method Constraint Meters RTUs Cost ($)

PCH Observability 29 10 1130.5 ACO-PCH Observability 29 10 1130.5 GA [20] Observability 29 10 1130.5

PCH No Cmeas 37 10 1166.5 ACO-PCH No Cmeas 37 10 1166.5 GA [20] No Cmeas 37 10 1166.5

PCH No Csets 38 19 2071.0 ACO-PCH No Csets 43 18 1993.5 GA [20] No Csets 45 18 2002.5

4.4.1. ACO–PCH algorithm

(i) Define ACO parameters, such as the maximum number of iteration s and the number of ants (number of solutions con- structed at each iteration). The initial amount of pheromo ne at each bus is equal to 1.

(ii) If the maximum number of iterations is achieved, end the algorithm and the current solution is declared the problem solution. Otherwise, go to step (iii).

(iii) Construct ns solutions using the PCH of Section 3 (but now considering a roulette wheel to select each bus at step (ii)of that heuristic accordin g to (13)). Evaluate each solution using the FF (14).

(iv) Update the amount of pheromone at buses that take part in the best solution found after performi ng step (iii).

(v) If the best solution obtained at step (iii) is better than the current problem solution, it becomes the current solution. At the first iteration, the best solution found will be declared the current problem solution.

(vi) Return to step (ii).

The pheromone update occurs according to (15):

siðt þ 1Þ ¼ ð1� qÞsiðtÞ þ DsiðtÞ ð15Þ

where q is the pheromone evaporat ion rate and DsiðtÞ is the pher- omone deposited at bus i.

The first term in (15) is responsible for the pheromone evapora- tion [33], whereas the second term accounts for the pheromone incremen t.

5. Test results

The proposed methodol ogy has been tested using the IEEE 14, 30, 118-bus test systems, and part of a real Brazilian system [20,23]. Details on the performed simulatio ns and the results ob- tained are given. The results attained only through the PCH are compare d to those when it is combined with a metaheuristic. Also, comparis ons with results found in the technical literature in which an optimization process has been carried out are provided. The objective of these comparisons is to show that, despite of being simple, easy to implement and use, the proposed heuristic proce- dure obtains high quality metering plans, similar to those obtained by sophisticated optimization algorithms.

5.1. Description of simulation

Many tests have been performed with the proposed methodol- ogy to plan low cost, reliable, robust metering systems for SE. Among them, some results are presente d here showing the benefitsof the proposed approach. Tests have been carried out using a1.88 GHz Intel Core 2 Duo PC, with 1 GB of RAM. The proposed methodol ogy has been implemented in FORTRAN programm ing language .

The relative costs adopted for meters and RTUs were, respec- tively, $4.50 and $100.00. These costs are expresse d in monetary units and have been commonl y adopted in previous works [16,20–23]. The following parameters were used when executing the ACO algorithm: a = 1.0; b = 2.0; q = 0.8; Dsi = 1.

The results illustrate the metering systems costs, as well as the number of meters and RTUs, necessar y to meet the established requiremen ts in each case. Computi ng times are shown whenever such a comparison is possible.

5.2. Observability and reliability requirements

Tables 1 and 2 show results obtained when requiremen ts of observabi lity and reliability (absence of Cmeas and Csets) are con- sidered. Although tests with all systems have been performed, only the results obtained for the IEEE 30-bus and part of a Brazilian 61- bus system are presented, as in such cases comparisons with other results reported in the technical literature (GAs proposed in [20,21]) are possible. The PCH solutions shown in Tables 1 and 2are the best among those obtained after performi ng independen t

Table 2Results with the Brazilian 61-bus system.

Method Constraint Meters RTUs Cost ($)

PCH Observability 60 23 2570.5 ACO-PCH Observability 60 23 2570.5 GA [21] Observability 68 30 3306.0

PCH No Cmeas 80 23 2660.0 ACO-PCH No Cmeas 80 23 2660.5 GA [21] No Cmeas 84 35 3878.0

PCH No Csets 91 48 5209.5 ACO-PCH No Csets 95 45 4927.5 GA [21] No Csets 107 49 5381.5

Table 4No critical RTUs.

System Method Meters RTUs Cost ($) Time (sec)

IEEE 14 PCH 34 9 1053.0 0.6 IEEE 14 ACO-PCH 17 9 976.5 0.6 IEEE 14 EA [23] 23 9 1003.5 15.0 IEEE 14 SSGA [22] 17 10 1076.5 –

IEEE 30 PCH 74 21 2433.0 8.7 IEEE 30 ACO-PCH 40 21 2280.0 8.7 IEEE 30 EA [23] 53 21 2338.5 64.0 IEEE 30 SSGA [22] 40 28 2980.0 –

Brazilian 61 PCH 160 48 5520.0 333.0 Brazilian 61 ACO-PCH 73 48 5128.5 333.0 Brazilian 61 EA [23] 115 42 4381.5 –

IEEE 118 PCH 162 75 8229.0 6270.0 IEEE 118 ACO-PCH 152 70 7684.0 6270.0 IEEE 118 EA [23] 206 70 7927.0 7590.0

40 H.R. de Oliveira Rocha et al. / Electrical Power and Energy Systems 52 (2013) 34–41

runs of the proposed constructive heuristic. For comparison pur- poses, the number of independent runs of the PCH corresponded to the number of times it was executed by the ACO–PCH method to obtain the results shown in Tables 1 and 2. It is also important to remark that the number of RTUs found in the other solutions ob- tained by executing only the PCH is not significantly different from those presented in Tables 1 and 2.

The results in Tables 1 and 2 show that high quality solutions were obtained when employing only the PCH, with no optimiza- tion process involved . As expected , improved results have been obtained with ACO–PCH, as the PCH is employed throughout the optimization process driven by the ACO. Similar results have also been observed for tests performed with the IEEE 14 and 118-bus test systems.

5.3. Robustness requirem ent

Tests considering the possibilit y of topology changes and loss of RTUs have also been performed . This accounts for the requiremen tof robustness and results obtained when employin g only the PCH and others obtained by different optimization methods are pre- sented in Tables 3 and 4.

Table 3 presents results considering that reliability require- ments must be observed not only for the base case topology but also for scenarios derived from the outage of any branch of the IEEE 14-bus system. The results are compare d to those obtained with aGA reported in [21]. Table 4 shows metering plans for different test systems, obtained when the absence of critical RTUs is required. Comparisons with a steady-state genetic algorithm (SSGA) and an evolutionary algorithm (EA) reported in [22] and [23], respec- tively, are presente d. Again, low cost metering systems are obtained. The metering plans are free from Csets and can now withstand the loss of any RTU, without compromising observability .

It should be noted that the best performanc e presente d by the ACO is due to its combination with the proposed PCH. A fair com- parison among the metaheu ristics would require the combination of each of them with the proposed PCH, which is out of the scope of

Table 3Results with the IEEE 14-bus system (different topologies).

Method Constraint Meters RTUs Cost ($)

PCH Observability 14 8 863.0 ACO-PCH Observability 14 6 663.0 GA [21] Observability 14 8 863.0

PCH No Cmeas 20 8 890.0 ACO-PCH No Cmeas 21 7 794.5 GA [21] No Cmeas 20 8 890.0

PCH No Csets 28 14 1526.0 ACO-PCH No Csets 27 14 1521.5 GA [21] No Csets 27 14 1521.5

this work. Rather than that, the objective here is to show that high quality metering plans, quite as good as those obtained through sophistic ated optimization methods, can be obtained by employing the simple and easy to implement PCH as a stand-alone tool. To obtain the results presented in Tables 3 and 4, the number of inde- pendent runs of the PCH corresponded to the number of times it was executed by the ACO–PCH. This explains the same computa- tional time achieved by PCH and ACO–PCH in Table 4. Once more, the number of RTUs found in the other solutions generate d by the PCH is similar to those presented in Tables 3 and 4.

5.4. Comments

The proposed PCH is a simple heuristic procedure to obtain low cost metering plans, which are always feasible with respect to SE observabi lity and reliability requiremen ts. It can be executed sev- eral times and, due to its probabilistic nature, different high quality solutions are found. It is important to emphasize that most of the PCH solutions also meet the robustness requiremen ts described in this work.

The PCH may be employed as a very simple, efficient, effective stand-alone tool to obtain low cost, reliable, robust metering plans. The simplicity of the proposed approach lies on the fact that high quality metering plans are obtained without the need to carry out any optimizati on process, avoiding intricate algorithms whose success requires the fine-tuning of some parameters, usually prob- lem-depe ndent. The PCH can find applicati on in the industry as asimple tool, of easy offline implementati on, for the design/expan- sion of metering systems that preserve SE observability and reliability .

Although high quality solutions are obtained without the need of employing any optimization technique, the combination of the PCH with an optimization tool can ameliorate the results. The pro- posed heuristic is suited for the combination with any metaheuris- tic and the application of an ACO–PCH was developed to illustrate such a possibility.

6. Conclusi on

This work presented a methodology for the design of metering systems for SE that satisfy requisites such as observabi lity, reliabil- ity, and robustness, considering the possibility of topology changes and loss of RTUs. A simple, efficient, effective constructi ve heuristic has been proposed to obtain low cost, reliable, robust metering systems. Test results have shown that the proposed heuristic procedure is capable of finding solutions of high quality when compare d to those obtained by refined optimizati on methods . It

H.R. de Oliveira Rocha et al. / Electrical Power and Energy Systems 52 (2013) 34–41 41

has also been shown how the proposed heuristic can be integrated into an optimizati on technique so as to obtain an even more pow- erful planning tool. However , due to its simplicity and to the high quality solutions it generate s, the proposed heuristic is also appeal- ing as a stand-alone instrument for the design of metering plans.

Acknowled gements

The authors gratefully acknowledge the financial assistance Granted by CNPq and FAPERJ in support of this research.

References

[1] Monticelli A. Power system state estimation: a generalized approach. Kluwer Academic Publishers; 1999 .

[2] Abur A, Expósito AG. Power system state estimation: theory and implementation. Marcel Decker 2004 .

[3] Do Coutto Filho MB, Souza JCS, Matos RSG, Schilling MTh. Strategies for preserving data redundancy in power system state estimation. In: 13th Power systems computation conference; 1999. p. 1–7.

[4] Do Coutto Filho MB, Souza JCS, Schilling MTh. Handling critical data and observability. Elect Power Compon Syst 2007;35(5):553–73.

[5] Koglin HJ. Optimal measuring system for state estimation. In: 5th Power systems computation conference; 1975, paper 2.3/12.

[6] Clements KA, Krumpholz GR, Davis PW. State estimation measurement system reliability evaluation – an efficient algorithm based on topological observability theory. IEEE Trans Power App Syst 1982;PAS-101(4):997–1004.

[7] Clements KA, Krumpholz GR, Davis PW. Power system state estimation with measurement deficiency: an observability/measurement placement algorithm. IEEE Trans Power App Syst 1983;PAS-102(7):2012–20.

[8] Monticelli A, Wu F F. Network observability: identification of observable islands and measurement placement. IEEE Trans Power App Syst 1985;PAS- 104(5):1035–41.

[9] Korres GN, Contaxis GC. A tool for the evaluation and selection of state estimation measurement schemes. IEEE Trans Power Syst 1994;9(2):1110–6.

[10] Yehia M, Jabr R, El-Bitar I, Waked R. A PC based state estimator interfaced with a remote terminal unit placement algorithm. IEEE Trans Power Syst 2001;16(2):210–5.

[11] Baran ME, Zhu J, Zhu H, Garren KE. A meter placement method for state estimation. IEEE Trans Power Syst 1995;10(3):1704–10.

[12] Abur A, Magnago FH. Optimal meter placement for maintaining observability during single branch outages. IEEE Trans Power Syst 1999;14(4):1273–8.

[13] Magnago FH, Abur A. A unified approach to robust meter placement against loss of measurements and branch outages. IEEE Trans Power Syst 2000;15(3):945–9.

[14] Razi Kazemi AA, Dehghanian P. A practical approach on optimal RTU placement in power distribution systems incorporating fuzzy sets theory. Int J Eng Intell Syst 2012;37(1):31–42.

[15] Mori, H, Matsuzaki O. A tabu search based approach to meter placement in static state estimation. In: Intelligent systems application to power systems conference, Rio de Janeiro, Brazil, April 1999. p. 365–9.

[16] Riccieri, OF, Falcão DM. A meter placement method for state estimation using genetic algorithms. In: Intelligent systems application to power systems conference, Rio de Janeiro, Brazil, April 1999. p. 360–4.

[17] Antonio AB, Torreão JRA, Do Coutto Filho M.B. Meter placement for power system state estimation using simulated annealing. In: IEEE porto powertech conference, Porto, Portugal, September 2001, paper 146.

[18] Coser J, Rolim JG, Simões Costa, AJA. Meter placement for power state estimation: an approach based on genetic algorithm and topological observability analysis. In: Intelligent systems application to power systems conference, Budapest, Hungary, June 2001. p. 1–6.

[19] Souza, JCS, Do Coutto Filho MB, Meza EM, Schilling MTh. Optimal meter placement for reliable state estimation. In: Intelligent systems application to power systems conference, Lemnos, Greece, August 2003. p. 1–6.

[20] Do Coutto Filho MB, Meza EBM, Souza JCS, Schilling MTh., Capdeville, C. Application of genetic algorithms for planning metering systems in state estimation. In: 15th Power systems computation conference, Liege, Belgium, August 2005. p. 1–7.

[21] Souza JCS, Do Coutto Filho MB, Schilling MTh, Capdeville C. Optimal metering systems for monitoring power networks under multiple topological scenarios. IEEE Trans Power Syst 2005;20(4):1700–8.

[22] Coser J, Simões Costa AJA, Rolim JG. Metering scheme optimization with emphasis on ensuring bad-data processing capability. IEEE Trans Power Syst 2006;21(4):1903–11.

[23] Vigliassi MP, London Jr. JBA, Delbem ACB, Bretas NG. Metering system planning for state estimation via evolutionary algorithm and HD matrix. In: IEEE bucharest powertech conference, Bucharest, Romania, July 2009. p. 1–6.

[24] Hamouda A, Sayah S. Optimal capacitors sizing in distribution feeders using heuristic search based node stability-indices. Int J Eng Intell Syst 2013;46(1):56–64.

[25] Mahmudabadi A, Rashidinejad M. An application of hybrid heuristic method to solve concurrent transmission network expansion and reactive power planning. Int J Eng Intell Syst 2013;45(1):71–7.

[26] Chen J, Abur A. Placement of PMUs to enable bad data detection in state estimation. IEEE Trans Power Syst 2006;21(4):1608–15.

[27] Emami R, Abur A, Galvan F. Optimal placement of phasor measurements for enhanced state estimation: a case study. In: 16th Power systems computation conference, Glasgow, Scotland, July 2008. p. 1–7.

[28] Saha Roy BK, Sinha AK, Pradhan AK. An optimal PMU placement technique for power system observability. Int J Eng Intell Syst 2012;42(1):71–7.

[29] Simões Costa A, Piazza TS, Mandel A. Qualitative methods to solve qualitative problems in power system state estimation. IEEE Trans Power Syst 1990;5(3):941–9.

[30] Korres GN, Contaxis GC. Identification and updating of minimally dependent sets of measurements in state estimation. IEEE Trans Power Syst 1991;6(3):999–1005.

[31] Almeida, MC, Asada EN, Garcia, AV. Identifying critical sets in state estimation using Gram matrix. In: IEEE bucharest powertech conference, Bucharest, Romania, July 2009. p. 1–6.

[32] London Jr JBA, Alberto LFC, Bretas NG. Analysis of measurement-set qualitative characteristics for state-estimation purposes. IET Gen Transm Distrib 2007;1(1):39–45.

[33] Dorigo M, Maniezzo V, Colorni A. The ant system: optimization by a colony of cooperating agents. IEEE Trans Syst Man Cyber Part B 1996;26(1):29–41.