Distribution Network Reconfiguration With Reliability Constraints

2004 Internattonal Conference on

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Power System Technology POWERCON 2004 Slngapon, 21-24 November 2004

Distribution Network Reconfiguration with Reliability Constraints A. Coelho , A. B. Rodrigues, M. G . Da Silva, Member, IEEE

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Abstract Electric Distribution Networks Reconfiguration is carried out by the openlnglclosing of switching devices while keeping the feeder’s radial topology. Traditionally, the reconfiguration of distribution networks bas been implemented aiming to: dnimize electric losses in the conductors, to enhance voltage profiles and balance the feeder’s loads. However, the proposed methodologiesfor acbievhg these objectives do not include the reconfiguration impacts on the system reliability indices. The main aim of this paper i s to present a methodology for recon6gurating a distribution network with the objective of minimizing the electric losses taking into account constraints assodated with: overloads, voltage drops and violation of the targets for reliability indices. The proposed methodology for solving this problem is based on the Parallel Simulated Annealing algorithm. This methodology allows the generation of candidate solutions without violating topological constraintr,.The proposed model has been validated and t&ed in standard distribution systems.

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Index Terms Reconfiguration, Optimization, Reliability, Parallel Simulated Annealing, Simulated Annealing.

I. INTRODUCIlON N general, overhead distribution systems have radial topology. This topology is used due to the following advantages: minimization of fault currents, equipment costs reduction and simplification of protection coordination procedures. The distribution network reconfiguration is carried out by the opening and closing cif switching devices but keeping feeder’s radial topology. Traditionally, distribution network reconfiguration has been implemented aiming to: minimize electric losses, to enhance the voltage profiles and to balance the feeder’s loads. These objectives have been achieved using methodologies such as Simulated Annealing, Genetic Algorithms and Tabu Search. Yet, the application of these

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AU the authors are with the Elecrricity Engineer D e p m e n i of ihe Federal University of Maranh5o (UFMA). Corresponding author: M. G. Da Silva (e-mail: p i a @ dee.ufma.br).

0-7803-8610-8/04/$20.00 0 2004 IEEE

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methodologies in reconfiguration problems does not consider the inclusion of the reconfiguration impacts on the system’s reliability indices. Furthermore, in the current deregulated structure of the electric sector, the distribution utilities are forced to increase their profits to guarantee their survival within a competitive environment and to achieve the reliability targets stablished by regulatory agencies. In this context, the network distribution reconfiguration may become an attractive alternative for electric distribution utilities, The interest in network reconfiguration is due to the fact that the opening and closing of switching devices does not result in additional costs for distribution utilities. Therefore, it is extremely important to develop methodologies that account for aspects related to electric losses, voltage profiles, load balancing and reliability during the distribution network reconfiguration. The main aim of this paper is to present a methodology for reconfigmating a distribution network with the objective of minimizing electric losses considering constraints associated with: overloads, voltage drops and violations of reliability indices targets. The proposed methodology to solve this problem is based on the Intensified Simulated Annealing Algorithm. It yields candidate solutions without violating topological constraints, that is, meshed and disconnected networks are not generated in the optimization process. The proposed models and techniques have been validated and tested in standard distribution systems. This paper is organized in the following way: section II presents a general formulation of the electric losses. Section III presents a tool developed for the load flow, used for the evaluation of losses, voltage drops and feeder’s loading. Section IV deals with a methodology for reliability indices evaluation. In section V an optimization technique for the solution of the distribution network reconfiguration problem is presented. Results with the proposed method applied in a test system are shown in section VI. Finally, in section VII, the conclusions and the final comments are presented.

II.

GENERAL FORMULATION OF THE ELECTRICLOSSES MINIMIZATION PROBLEM

Active power losses on distribution networks are composed of the following parts: Losses by Joule effect in the conductors, tranformer's coils, etc.; Error in the billing of supplied power; Frauds The first loss in the above list constitutes the technical losses while the last two are called commercial losses. The acceptable level of technical losses varies according to the utility and it depends on several factors, such as load density in the supplied region. Technical losses due to line and equipment electric resistance, are continuosly dissipated, decreasing the electric power available for consumption in distribution and transmission systems. Reference values in the field's point 2% of technical losses for transmission and 5% for distribution [l]. In Brazil, very often, technical losses for distribution networks are far beyond those values [2], thus identifying a promising area for power gains by reducing losses. Line electric losses minimization problem due to resistances can he formulated as follows[3]:

example of Back-Forward Sweep [4], where formulations are based on Kirchhofrs Iaws. This method presents optimal convergence characteristics for radial distribution networks. From Figure 1, in following are the voltages and currents equations for the load flow evaluation:

+

E4'

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Figure 1-Circuit Currents and Voltages Representation.

(3) (4)

where :

1, e l , are the currents in bus k and m.

I , is the current in branch km. F,,,is the set of bus fed by bus m.

iE S

subject to : Radiality. Voltage drops. Feeder's loading. System's reliability. Where: S is the set of the system line sections; k and m are the terminal nodes for the section i; Ek (E,,,) complex voltages for the node k (m); giis the series conductance for the section i. The voltages and are evaluated by means of load flow recursive equations, which structurally are favorable to schemes of computational solutions. There are several methods that can be used to minimize losses in distribution systems. Among them we can mention: reconductoring (using lower resistance conductors), capacitors optimal placement, network reconfiguration (changes in the distribution network topology) fixed regulators and transformer's taps.

LIL

LOADFLOW

The method used to solve the load Bow problem was the Current Summation Method, which is an

s, is the complex power in bus k. E , is the complex voitage in bus k. 2, is the impedance for the branch k-m.

Y;h is the admittance of the shunt element connected to bus k. This method is specific for radid networks and it is based on back-forward sweep. In the back-forward algorithm the bus and branches enumeration scheme is extremely important, and it can affect the global method's efficiency.

N.PROBABILISTIC EVALUATION OF b L L 4 B I u T y Basically there are two techniques to evaluate a distribution system's reliability: the Analytical Methods and the Stochastic Simulation Methods[5,6]. In this paper, the State Enumeration AnalyticaI Method has been used (SEAM) to estimate the reliability in distribution networks while taking into account voltage and loading constraints. The SEAM method was used

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due to its low computational cost, required to estimate the reliabikty indices. The SEAM method evaluates the impact of each system's contingency (faults in the lines, transformers or protection devices) and weight this impact based on the duration and frequency of this contingency to obtain reliability indices. Impact estimation of a contingency on distribution networks is associated with the fctllowing operational aspects [7]: 1) Switching of Protection Devices: Protection devices (breakers, fuses) operate to eliminate the fault; 2) Restauration of load point upstream the fault: sectioning devices upstream the fault, such as normally closed switches(NC), isolators and fuses are opened to clear a fault. This procedure allows the re-initialization of the protection devices used to eliminate the fault and also iillows the restoration of power supply to all the consumers upstream the fault; 3) Restoration of load points downstream to the fault: opening the sectioning devices downstream the fault isolates other sections that remain de-energized, This procedure allows that some consumers located downstream the fault being restored through alternative paths by closing the NO switches: 4) Repairing: the component that suffered the fault is repaired and the system returns to its pre-fault state.

The protection devices operated in a contingency are illustrated in Fig.2. The evaluation of predictive reliability of a distribution network is usually associated with the system's performance in the consumers load points. The most used reliability indices to estimate the reliability of system load points are: failure rate (Ai ), annual unavailability (vi)and the average restoration time (c). These indices are important from the individual consumer point of view, but they do not provide information that characterizes the total distribution system performance. Hence, it is necessary to use additional indices to evaluate the reliability of a distribution networks. These indices must reflect the severity and amplitude of the component's faults for the whole distribution network.

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Fig. 2- Sequencing of protection devices operation during the event of a contingency (fault) An additional set of indices can be evaluated using the basic indices A i , CJi, and n' for each system load point, including the aspects previously mentioned . The indices used in this paper to evaluate the distribution systems reliability indices are [7]: 1. ASIFI- Average System Interruption Frequency Index. 2. ASIDI - Average System Interruption Duration Index.

V. PARALLEL SIMULATED A " E A L I N G METHOD In this work, the proposed algorithm for solving the distribution network reconfiguration problem is the Parallel Simulated Annealing (PSA) [SI method, which is an extension of the Simulated Annealing (SA) [9] method. Even though the SA method is an attractive technique for this sort of optimization, it has some disadvantages with respect to the PSA method. The SA method frequently yields small transition states that stay in a minimum local for multimodal non convex, non linear problems, and other problems with a huge solution space. To overcome these drawbacks, the SAI method intensifies the routine of the transition states in the original SA method to obtain better solutions, that is, it increases the number of neighboring states to be searched. Basically, the PSA method uses point searching in a similar way to the SA method, but the PSA method generates states of multiple neighboring states instead of only one, as it is shown in Figure 3. This procedure increases the possibilities in getting an optimal solution close to the objective function optimal global value.

A. Neighbours Generation SA r

0

I

1 I

2I

i

3 I.

l+ration m.

PSA

Figure 3-Difference between the searches of both, the SA and PSA methods. The PSA algorithm is presented in following: Step 1 ) Initialization Start an initial state (base-case). Define the temperature ti and t h , the reduction factor r and perform an evaluation of the base case. Step 2) Generation of Neighbouring Stares The generation of neighboring states is carried out to obtain a better number of searching areas in the solution space, so as to discover a solution close to a global optimum.

The neighbour states generation is done by producing new configurations of the electric network through the opening and closing of switches normally closed and normally opened, respectively. In this work, a new topology is obtained by identifying, initiaIly all NO switches of the distribution network. Next, the normally closed (NC) switches belonging to the paths in between the terminals of each NO switch and the substation bus, are also identified. In this way, each generated neighbor will correspond to the pair composed by one NO switch and one NC switch belonging to the paths in between the terminals of the NO switch and the substation bus. For real electric power distribuition systems, it will be computationally unfeasible to estimate all neighbors associated to a given configuration. For this reason, in this work, a random selection of NC switches has been proposed, in which only a NC switch associated with each terminal (initial and final sides) of the NO switch is selected. In other words, the number of closed switches (neighbors) for the optimization process will double the number of NO switches. B. Objective Funcrion Estimation To estimate the adequacy of each configuration, aspects concerning electric losses in the feeders, voltage profile and the impact of the reliability indices are considered. Next, the analysis proceeds with a program to evaluate the reliability indices and the load flow. By using the results, the adequacy for a given configuration is obtained from equation (7).

Step 3 ) Neighbours Assessment Each configuration (neighbour) will have its objective function assessed (fitness). (7)

Step 4 ) Generurion ofrhe Next State

In order to make it so that one of the neighbors is accepted, this must attend the following conditions:

Where:

N is the set of system nodes; R is the set of reliability indices (R={ASIFI,ASIDI]);

Step 5 ) Cooling Process The temperature control parameter is decreased using geometric progression ti = r * t d Step 6 ) Stop Crirerium When the temperature becomes higher than the minimum temperature, the process returns to step 2.

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Pflv(i), Pfiv(i), pfri(r) are the penalty factors for violations in the: loading of the section i, voltage of the node i and reliability index r,

* Case

1: Estimation of losses and reliability indices considering loading constraints in the lines and voltage profile. * Case 2: Estimation of losses and reliability indices considering constraints of case 2 and the system reliability.

Vj2V&,0.

TABLEI TEST SYSTEM CHARACERISTICS.

Zi and lim: are the evaluated and the maximum values for the current in the section i, respectively; Vi is the magnitude of the nodal voltage in the node i; Vmin minimum voltage limit; ?is the target value for a reliability index r; W, Wv and Wr are the weights associated with violations of loading, voltage and reliability

W.

RESULTS

The proposed algorithm for reconfigurating the distribution networks with reliability constraints has been applied to the te’st system proposed in reference [lo]. This system has no protection devices along its lines or switching along its lines. Thus, changes have been made in that system to allow the modeling of reliability constraints in the reconfiguration of the distribution network. The criteria used in the allocation of the protection devices and in the system’s switching

Load Peak Voltage MVA Base Number of Load Points Number of Components Number of NO switches

I 3715 kW

1 12,66 kV 1 10MVA I 32 I 69 1 5

Reliability data of the overhead transmission lines used in the tests with the system shown in Figure 5 are presented in Table II, where: is the permanent

apem

is the repair time, and failure rate; Trrprir switching time.

TShis the

TABLE II TEST SYSTEM R E L I A B W DATA.

are:

I) Reconnectors: a reconnector has been inserted just at the begining of the feeder; 2) Fuses: fuses have been allocated at the beginning of the section with greater load density and at the section that would act as the branch start points. 3) Closed Switches: it has been added an NC switch at the beginning of each section. This criterium was used to obtain a higher possible number of configurations and, consequently, it increases the probability to get a solution close to the global optimum. The test system is shown in Figure 4, and the main characteristics of this system are presented in Table I. The analysis of the reliability constraints for the minimizaiion of losses in distribution networks has been performed considering the following casesstudies:

* Case D (Base Case): Estimation of losses and reliability indices of the base-case (initial configuration), without considering constraints.

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T ch [hours]

I .oo

Figures 5 and 6 show the results of the analysis of losses and reliability indices for the test system’s casestudies. Results presented in these figures have been obtained considering the following values of S A I method parameters: Inicial Temperature 1,0 Freedng Temperature: 0,Ol Annealing Rate: 0.99

Figure 4-On-line Diagram of the test system with their protection and switching devices. upon the loading constraints in the feeders and voltage profile. These results point out that reliability constraints must be modeled over the losses minimization through the electric network reconfiguration.

The impact of reliability constraints on the loss minimization can be estimared comparing the case studies 1 and 2 with respect to the base-case. The result presented in Figure 5 showed that losses reduction is small when the reliability constraints are modeled on the distribution network reconfiguration. For example, for the test system, the reduction in the losses for study-case 1 and 2 compared with base-case are 30.68% and 22.63%, respectively. Besides that, it can be noted that when a reliability constraint is activated, the reliability indices for case 2 have been improved. Therefore, the developed methodology tries to minimize losses as much as possible and, at the same time, it lets the system to operate under more reasonable reliability levels. For example, in Figure 6, the ASIDI index for case 2 suffered a 24.08% reduction compared with case 1.

Figure 5 - Total Loss of the Test System

Finally, Table 111 illustrates the generated topologies, represented by the initial and ending node of the open switches for studies-cases 1 and 2, after the application of' the losses reduction algorithm with reliability constraints.

Figure 6 -Test System Reliability Indices The result presented in Figure 5 shows that for case 1 a 30.68% loss reduction ocurred with respect to the base-case. Meanwhile, this reduction gives a meaningful decay in the reliability indices. For example, in Figure 6, for case 1, the A S D I index increase was 33.26% when compared with the base case. This effect is due to the fact that the losses minimization is done only based

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For the optimal configuration of cases I and 2, in Figure 7 are presented the voltages in all the buses. It can be noted that the voltages in all buses meet a minimum voltage limit (Vmin = 0.92p.u.) allowed for the feeders.

According to the results, the reconfiguration of electric distribution networks provides the utilities to become more competitive by reducing the electric losses and offering to their users, at the same time, higher reliability levels. Wr. REFERENCES

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Case 2

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120-7;8-14;10-43;24-28;32-171156,8

12 16 20 24

28 U

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36 40 44 48 “52 56 60 W

[l] Bunch, J. B.,Miller, R. D.e Wheeler, J. E. Diswibution system integrated voltage and reactive power control. JEEE Transactions on POWUAppi~atU~ and Systms, PAS-101:284-289, 1982. [2] Cavellucci, C. “Informed Search Based on Graphs for Lasses Minimizadon in Elecnic Disrribution Systems”. P h D Thesis presented at UNICAMF’, Campinas. S%oPaulo, 1998 (in portugnese). [3] MonticeUi, A. “ b a d Flow in Elechical Networks”. Ed. Edgard Blucher, 1983. (in Portuguese). [4] D.Shirmohammadi, H. W.Hong, A. Semlyen. G. X. Luo, “A compesation-Based Power Flow Method for Weakly Meshed Disnibution and Transmission Network, IEEE Trans. Power Spt, Vo1.3 (Z), May, pp.753-762,1988. [ 5 ] Roy Billinton, Ronald N. Man. “Reliability Evaluation of Engineering Systems: Concepts and Techniques”, 2nd ed,,Plenum Press, 1992. New York, USA. [6] Roy Billinton, Wenyuan Li, “Reliability Assessment of Ekecmc Power systems Using Monte Carla M e b d s ” . Plenum Press, 1994, New York, USA. [7] Roy Billinton, Ronald N. AUan, “Reliability Evaluation of Power Systems”. 2nd ed., Plenum Press, 1996, New York, USA. [SI H. Mori et al., ‘ ‘ P d e l Simulated Annealing for power sysrem decomposition.” IEEE Trans. Power Syst., vo1.9, May 1994. [9] Kirkpatrick S., Gelan Jr.. C. D., Vecchi, M. P., Optimization by Simulated Annealing, Science. 220 N.4598, pp.671-680, 1983. [lo] S. K. Goswami, S. K. Basu; “A New Algorithm for the Reconfiguration of Disnibution Feeders for Loss Minimization”, EEE Trans. on Power Delivery, vo1.7, No.3, July, pp. 1484 1491. 1992. ~

Figure ‘7 - Bus Voltage for the cases under study

IX.BiOGwms

VU.CONCLUSION In this paper an algorithm was presented for electric power distribution network reconfiguration considering reliability constraints. The proposed optimization method was Parallel Simulated Anmaling. A method has been included for the evaluation of the reliability indices (State Enumeration Analyhcal Method) and another one for the load flow (Current Summation) in order to estimate voltage drops and feeder overloading. Results obtained with this technique in a distribution network test system have showed that: Reliability constraints can be taken into account in a distribution network reconfiguration at low computational cost and acceptable accuracy. The inclusion of reliability constraints in the distribution network reconfiguration have significant impacts in the reliability indices associated with the duration and frequency of electric interruptions (ASIDI and ASET).

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A. Coelho is a post-graduate student in Electrical Engineering at Federal University of Maranhiio (UFMA) - Brazil. He obtained his first degree in Electrical Engineering from UFMA, in 2004. M. G. Da Silva is professor of Electrical Energy Systems in DEE at UFMA, SI0 Luis, Brazil. She has MSc and PhD degrees in power engineering from UFF’BBrazil and UMISTNK, respectively. Her primary research interest is the modelling, evaluation and application of probabilistic techniques to power systems problems, particularly those concerned with reliability. She is a member of the IEEE. A. B. Rodrigues is assistent research in Electrical Energy Systems in the Power System Team, UFMA. He obtained his first degree in Electrical Engineering and MSc in power engineering from UFMA in 1998 and 2003, respectively. His primary research interest is the reliability assessment in composite and distribution systems.