Distribution Network Reconfiguration For Loss Reduction With Variable Demands

2004 IEEElPES Transmission & Distribution Conference 8 Exposition: Latin America

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Distribution Network Reconfiguration for Loss Reduction with Variable Demands E. A. Bueno, C. Lyra, Senior Member IEEE, and C.Cavellucci

period of time [8-131. Although loss reductions is achieved when the in distribution systems, considering variable demands. codguration of distribution system is changed to adjust to the Formulations for both fixed and variable demands are presented. demand variations, is important to consider that switch Simple examples illustrate significant aspects of the problem with operations imply some risk, due to transitory disturbances on variabte demands. Two algorithms are proposed to solve the loss the network. reduction problem with fixed configuration for the whole The purpose of this paper is to discuss the impact on loss planning period. reduction due to load variations during the planning period. Index Terms-Distribution system, loss minimization, network Their contributions are a careful analysis of the loss reduction reconfiguration. problem with variable demands and two heuristic approaches to solve the problem, considering an unchanged configuration I. INTRODUCTION during the whole planning period. all electric power systems energy is continuously The next section presents the mathematical formulation for dissipated in the lines and equipments - these losses are the loss reductions problems, with fEed and variable named “technical losses”. In Brazil, losses amount to around demands. Section I11 discusses simple case studies to illustrate 15% of total energy production [l]; in the distribution systems the main aspect of the problem. Section IV and V propose losses frequently achieve levels above 8% [2]. approaches to deal with the problem of loss reduction under Distributions networks usually operate with a radial variable demands and fxed network configurations. configuration. Neighbor feeders are linked through Conclusions fallow. interconnection switches (open switches). A network 11. PROBLEM CHARACTERISTICS reconfiguration can be achieved by changing the opedclosed status of switches, keeping the radial topology of the network. Figure 1 presents a simplified diagram of a primary electric In 1975, the French engineers Merlin and Back [3] proposed power distribution network, distinguishing the principal to use network recodlguration procedures for loss reductions entities for the loss reduction problem: substations (SE), lines in distribution systems. (L), switches (SW)and consumption in the load blocks (LB). The number of passible configurations on a distribution system is associated to the number of switch state combinations, which increases in a factorial relation with the number of switches existing in the network. Thus, evaluation of all possible configurations is not possible, even with state of the art computers. Heuristic techniques are adapted to deal t 4 with the problem [4]; among them “Sequential Switch L B I SW, . Opening” [3,5] and “Branch Exchange” [6,7] are probably the most popular approaches. The majority of the methodologies applied to the loss reduction problem consider fixed demands. However, some works already identified the benefits of approaching the U 2 6 problem considering the load variations throughout a given Absrract- This paper presents a contribution to loss reduction

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Fig. 1. Electric power distribution network This work was supported by the CNPq - entity from Govem of Brazil to support study and research. E. A. Bueno is a Ph.D. student at the School of Elecbical and Computer Engineering (EEC), University of Campinas (UNICAMF), Campinas, Sa0 Paulo, Brazil (e-mail: [email protected]). C. Lyra is with FEECRMICAMP, Campinas, S b Paulo, Brazil (e-m$l: [email protected]). C. Cavellucci is with THOTH Solutions, Campinas, Sao Paulo, Brazil (email: [email protected]).

0-7803-8775-91041$20.00 02004 lEEE

The distribution network can be represented by a graph G = [N, A], where N is the set of nodes and A the set of arcs [14], Fig. 2 presents a graph representation for the primary distribution network of Fig. 1.

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usually be approximated to one per unit (5 x 1 P.u.). In such cases it is possible to simplify the (l), becoming unnecessary the voltage magnitude comtraints in problem P [7]. Also, in well compensated networks, the reactivate power can be considered approximately proportional to the active power, (e. g., Q, a,Pj for V j ), Under this assumption, both power flow equations are equivalent. Also, the objective function, represented by (4), can be expressed as follows. N

f:

f ( ~ =) (I+ a z ) ~ r P P i J=l

(2

1

Note that the optimization result is not altered by the term 1 + a in (2). So, it needs to be considered just for the losses calculation, after the problem resolution.

with closed switch Transmission network

-9- Line _____"_""_

k=1

Fig. 2. Graph representation of distributionnetwork

The nodes are associated with load blocks or substations (a node root, R, is also included to prevent difficulties in the treatment of network connectivity). The arcs are associated with either lines or switches - the arcs thai connect the substations to the node root represent the transmission network.

B. Formulation for Uniform Remand Variation Figure 3 presents a load curve with uniform demand variation.

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Demands

11

,

A . Fixed Demand Formulation "he electric losses (dssipated power) through the lines are proportional to the square of the currents, They can be expressed in terms of the active and reactivate power flows in the network arcs [7]. So the total losses in the network are defmed by the fimctionf(P, Q) as following.

Fig. 3. Load Curve with Uniform Demands Variations

where the q k is the resistance of the line. The active power (PJk), the reactivate power (Q,,t), and the voltage magnitudes (4)can be calculated by an approximate power flow method [7]. The reconfiguration problem for a set of known demands (in a given moment), can be characterized as

The energy losses considering the uniform demand variation can be defmed by the functionf(P, T),

(j=l

k-l

Considering that hi is a constant, the fhction f (P, T ) can be expressed as

s.t. - Powerjlows;

- Muximumflows constraints;

- Voltage magniiude constraints; - Network radial operation.

To solve the problem P it is necessary to find the arcs (switches) that must be (closed switches) or not (open switches) in a radial configuration for the network. The vector C,., with dimension of the number of arcs, is composed of binary components (0 defining open switches and 1 defining closed switches). The voltage magnitudes of the distribution systems can

Since multiplication by a constant does not alter the result of the optimization, (4) shows that to solve the losses reduction problem with uniform demand variation is equivalent to solving the problem for fixed demands. The constant K

=[$

A,J;)

should be considered just for the calculation of

the losses, after the problem solution.

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C. Formulationfor Non Uniform Demand Variation In practice, the load variation is not uniform. For example, during a given period of a day, an industrial area can reduce consumption while a residential area increases consumption. In this section we propose formulations for the loss reduction problem with non-uniformdemand variations. Two scenarios are considered: allowing changes in configurations after each significant modification in demand profiles and keeping configurations fixed for the whole planning period. These two scenarios can be formulated as follows.

d,

d,

4

4

Fig.4. Fictitious distribution network

Suppose three levels of load values: low, medium and high. Table I shows the consumption in each load block di (in Fig. 4), for the three load levels. S.t.

pvd

Pvd,

TABLE 1

Without Fked Configuration Constraint

Wizh Fixed Configururion Comtruint

DEMAIVDSDVL~CHCONSUMPTION BLOCK

A.Ci.Pi=br

A.C.Pi=bi

ippPpF 9,= [ x A ’ 1~it is a tree

P SF SF ij= [ xjf’)it is atree

Low @hours) Medim(10 hours)

High (6hours)

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2.5 12,O 4,O

di 3,O

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dj 1,5 2,O

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2,5

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Consider the resistance for all ms 1 ohm. The optimal where T is the number of the time intervals considered; C is a radial configurations for the low, medium, and high load square diagonal matrix, where the diagonal is the vector of levels are, respectively, the configurations 1, 2 and 3, states of switches in the network (Cy); P is the vector of presented in Fig, 5 . power flows; b is the vector of demands in nodes and power are bounds on flows;,Ti injected at the root node; P and “ F I G 1” is the group of arcs that represent closed switches in the Optimal for “low l d ’ interval i and is the group of arcs that represent closed switches during the whole planning period. Solving problem Pvd is equivalent to solving several MNFlG 2 uncoupled problems, one for each time interval Ai. optimalEar “nzedhmlaclb‘ h problem P V d c just one network configration is allowed for the whole planning period. Because of this assumption, problem Pvdrcis much larger (and difficult) than problem P v d . CONFIG 3 Actually, problem PVdrchas not been previousIy approached by other researchers. In this paper, two approaches for the solution of the problem Pvap are proposed. The f i t approach, named Fig. 5. optimalRadial Cofigurations “Mini” Energy Losses”, is based on the algorithm of The losses for each configuration shown h Fig. 5 are “Sequential Switch Opening”, developed by Merlin and Back (1975). ?‘he second approach, named ‘%eneralized Branch present in Table II. The last line (Optimal Losses) gives the Exchange”, is inspired in the algorithm “Branch Exchange’’ best values for losses, supposing that the network is allowed [ 6 ] . Those methods will be discussed in the Sections IV and to change configuration in order to adapt to the demands V, respectively. Next section presents simple case studies to variations. Column “Total 24h” presents the total network losses for a one day planning period. The first three lines of illustrate sigruficant aspects of the problem. this column consider that the system operates with fmed configurations, respectively, the configurations 1, 2, and 3. The last line (of the same column) informs the losses for the 111. CASESTUDIES Figure 4 shows a reduce distribution network with 9 nodes one day period, when the system operates with the best and 11 arcs. It will be used to study the behavior of the configuration for each load profile. The last column in same Table II (Increase) indicates the increase in losses with electrical losses under demand variations. respect to the optimal situation (when the network is modified to adapt its configuration to the load).

386

TABLE U

TABLE III

LOSSESIN OPTLMUMCONFIGCIRATION

TOTALLOSSESEE~~ERGY VALUES

I

I

Losses Low Load Power

0

Energy

ww

High Load

Power

(kw)

Energy (kw

Total

Energy

&w4

Another radial configuration is presented in Fig, 7. Its Results shown in Table I1 allow the following conclusions: power and energy losses for low and high load are presented [)The best loss reductions are achieved when network in Table IV. configurations are altered to adapt to load variations; iQ When it is imposed that network configurations should be fixed, the best operation alternatives would not necessarily be the best configuration for the high load; iii) In some situations the constraint that the configuration remain fixed will not lead to a significant increment in total losses - note in Table I1 that if the system operates Fig. 7. An alternative configuration with Configuration 2 losses will increase only 1,5%, with respect to the optimal condition. TABLE lV iv) A small change in the configuration can lead to ENERGYLOSSESVALUESINALTE~VATIVE CONFIGURATTON significant reduction in losses - for instance, switching from Configuration 3 to Configuration 2 leads to a loss I Losses reduction of approximately 38%. High Load Total Low Load ~~_________

In the example, Configuration 2 (best configuration for Power Energy Power Energy Energy medium level loads) corresponds the best alternative to (kw) WW 0 (kwh) operate the network with a fxed configuration. However, the Duration I 12hours 12 hours I 24hours optimal fixed network configuration is not necessarily the best configuration for a given period. This situation will be illustrated in the following example. Consider the same network shown in Fig. 4. To simplify The Configuration C is not the best alternative for either exposition, consider only two segments of the load curve, both the low or high loads. However, it is better than with a 12 hours interval. Consumption in each node is Configurations A and B under the constraint of operation with presented in Table I. The optimal configurations for each load a fixed configuration for a day. profile are present io Fig. 6. Next sections propose alternatives approaches to find Table III presents the losses in power (kW) and energy optimal fmed configurations, for operation during a given (kwh) for the two load situations. Last column shows energy planning period. In other words, they propose methods to losses during a one day period. solve problem Pvdlc.

-

CONFIG A optimal far “low l o d

CONFIG B

-

Fig. 6 . Optimal Configurationsfor Low and High Loads

IV.M”M ENERGYLOSSES(MEL) In their pioneering work, Merlin and Back (1975) proposed the method of “Sequential Switch Opening” for loss reduction problem with fixed demands. In short, the method consists of the successive application of two procedures, until a radial solution is found: 9 Find the best distribution of flows for a network with cycles ii)Open the switch with the smallest power flow. The MEL algorithm is an extension of these ideas for solving problem PvdfF.It can be summarized in the following sequence of steps.

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flows for all the considering different degrees of freedom for the network situations of loads, without the constraint of radial operation. In the ideal case, networks can change operation; configurations freely, in order to better adapt to demand Step U2 Calculate the total energy associated with each arc variations. In a case more realistic, and difficult, networks for the whole planning period (the total energy associated should operate with fixed configuration; analysis of this case with one arc is the sum of the energies that circulate in the is the main contribution of the paper. arc, considering all intervals); The mathematical formulations were simplified to Srep 03 Verify if the network has cycles; if yes, remove the emphasize the most important characteristics of the problem. arc in a cycle (open the switch) with the smallest energy Simple examples were designed to illustrate the various value and r e m to Step 01;otherwise, STOP and show aspecb of the problem. the solution. The case studies showed the importance of developing methods that lead to good solutions of the problem with variable demands and fixed configurations. The “Minimum V. BRANCH EXCHANGE BY ENERGY (BEE) Energy Losses” and “Branch Exchange by Energy” methods The Branch Exchange method proposed by Civanlar et al. were proposed in this direction. [6] starts witch a radial configuration. Through branch exchanges, the configuration is modified successively in the attempt to reduce resistive losses, without losing the radial VII. BFEFtENCES network topology. Good branches for exchanges can be [l] C. Cavellucci, “Buscas Informadas baseadas em Grafos para a identified with the following conditions: MinimizaGb das Perdas em Sistemas de DistribuiqBo de Energia EUtrica’*, PhD. dissertation, Electrical Engineering and Computation i 1 if there is a significantvoltage difference between the Faculty, Unicamp, 1998. terminals (nodes) of an open switch, then there are (21 J. B. Buch, R D. Miller and J. E. Wheeler, “Distrbutiou System possibilities of losses reduction; Integrated Voltage and Reactive Power Control”. IEEE Transactions on loss reduction is achieved with load tsansfer from the Power Apparam and Systems, pp. 284 - 289, 1982. low voltage terminal to the high voltage terminal. [3] A. Merlin and H. Back,“Search for a Minimal-LossOperating Spanning The following algorithm adapts the Branch Exchange ideas Tree Coniiguration in an Urban Power Distribution System”. Proc. 1975 PSCC 5th Power System Compulation Conference, Cambridge (VK), to deal with problem Pvdrf Step01 Calculate the optimal power

io

step U1 Consider a radial network configuration; calculate voltages for all nodes; Step 02 If there are no switches with significant voltage drop between terminals, STOP (the process of Branch Exchange is fmished); Step 03 For each open switch, For all load profile, calculate the voltage differences between terminals; - multiply the value of the voltage difference for each profile by the interval duration; - calculate the voltuge direreme extended, corresponding to the sum of the product of voltage difference by the duration of the intervals; Step U4 Close the switch that shows the largest voltage drflerence extended - identify the cycle formed in the network; - fmd the switch whose opening will provide the largest energy losses reduction; Step 05 Return to the radial configuration, by opening the switch of the cycle that provides the largest energy losses reduction; Step 06 Update the values of voltages and return to Step 02.

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VI. CONCLUSIONS paper brings in a contribution to the problem of This ~technical losses reduction by reconfiguration in electric power distribution system, with variable demands. A mathematical formulation for the problem was presented,

paper 1.2/6. C. Lyra, C. Pissarra and C. Cavellucci, ‘Xdu@o de Padas na Distribuiqilo de E n e p Elktrica”, CBA 2000 h i s do Xm Congressp Brasileiro de Autodtica. [SI D. Siurmohammadl and H. Hang, “Reconfiguration of Electric Distribution Networks for Resistive Line Losses Reduction”. IEEE. 1989. [6] S. Civanlar, J.J. Grainger; H. Ym and S.S.H. Lee.“Distribution Feeder Reconfiguration for Loss Reduction”. IEEE. Transaclions on Power Delivery, vol. 3, pp. 1217-1223, 1988. [7] M. Baran and F. Wu ‘Wetwork Reconl?ption in Distribution System for Lass Reduction and Load Balancing”.IEEE. Trunsactions on Power Delivery, vol. 4, pp. 1401-1407,1989. [SI R E. Lee attd C. L. Brooks, “A Method and Its Application to Evaluate Automated Distribution Control”. IEEE Transactions on Power Delivery, vol. 3, pp: 1232 - 1238, 1988. [9] C. S. Chen and M. Y. Cho, Tnergy Loss Reduction by Critical Switches”, IEEE Transactions on Power Delivery, vol. 8, pp. 1246-1253, 1993. [lo] Q. Zhou, D. Shmohammadi and W. H. E. Liu, ‘?)ismibution F d a Reconfiguration for Operation Cost Reduction”. IEEE, Transactions OR Power Systems, vo1.12,pp. 730-735,1997. Ill] R Taleski and 0. RajiEiE, “Distribution Network Reconfiguration for Energy Loss Reduction” IEEE Transacrions on Power System, vol. 12, pp. 398 - 406, 1997. [12] K. Y. Huang and H. C. Chin, “DistributionFeeder Energy Conservation by using Heuristics Fuzzy Approach” Electrical Power and Energy Systems, vol. 24, pp, 43945,2002. [13] P. A. Vargas, C. Lyra, and F. J. Von Zuben, "Learning Classifiers on Guard Against Losses in DistributionNetworks”. IEEE/PES T&D 2002 Latin Americo, 2002. [I41 R.K. Ahuja, T.L.Mapanti and J. B. Orlin, ‘Wetwork Flows: Theory, Algorithms, and Applications”. Prentice Hall, Engtewood Cliffs, NJ. 1993. [ 151 Luemberg, D.G. Linear and Nonlinear Programming. Addison-Wesley, 1984 [16] Lyra, C. and Tavares, H. “A contribution to the midterm scheduling of large scale hydrothermal power systems”. IEEE Transactions on Power Systems, 3,1988, pp. 852-857 [4]

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Christian0 Lyra is a professor of Electrical Engineering at the School of Electrical and Computer hgineering of the University of Campinas (UNICAMF'), in Sit0 Paulo, Brazil. Born in 1951 in Pemambuco (Brazil), he 6nished high school as an AFS exchange student in Philadelphia, United States in 1970. He graduated from the Federal University of Pemambuco (Brazil) in 1975 with a B.S. degree in electrical engineerhg. His M.S. and Ph.D. degrees in electrical engineering were received from UNICAMP, in 1979 and 1984, respectively. Following a brief career at the Power Company of the S b Francisco River, he joined the Faculty of UNICAMP in 1978 where he has been head of the Department of Systems Engineering and Director of Graduate Program in Electrical Engineering;presently he is the Dean of the School of Electrical and Computer Engineering. His research interests include power systems optlnization, energy systems analysis, planning and operation of dLFtrbution systems and infelhgentcomputing. He is a Senior Member of LEEE. Celso Cavellucci manages Thoth Solutions. He graduated in 1974 from the University of Mackenzie in SS0 Paulo (Brazil) with a B.S. in electrical engineering. His M.S.and PhD. degrees in electtical engineering were received from UNICAMP, in 1989 and 1999, respectively. M e r working for VASP airlines and Olivetti of Brazil, he joined the Power Company of Sib Paul0 (CPFL)in 1976, where he has coordinated the areas of information analysis and systems analysis and developed methodology to assess planning, project and operation of dwtribution networks. He left CPFL in 2000 to start moth Solutions. His research interests include planning and operation of distribution systems, artificial intelligence and combinatorial optimization.

Edilson Ap. Bueno received in 1996 the 3.S. degree in electrical engineering from S3o Paul0 State University (UNESP) in Ilha Solteira. His M.S. degree in electrical engineering was received from University of Campinas o]NICAMF') in 2000. Currently, he is a PbD. student ai UNlCAMP. His research interest5 include planning and o p e d o n of distribution systems and operational research.

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