# Distribution Network Reconfiguration

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<ul><li><p>398 IEEE Transactions on Power Systems, Vol. 12, No. 1, February 1997 </p><p>UTION NETWORK RECONFIGURATION FOR ENERGY LOSS REDUCTION </p><p>Kubin Taleski, Member IEEE Dragoslav RajiCid, Member IEEE University "Sv. Kiril i Metodij," Faculty of Electrical Engineering Skopje </p><p>Skopje, Republic of Macedonia </p><p>Abstract A new method for energy loss reduction for distribution networks is presented. It is based on known techniques and algo- rithms for radial network analysis -- oriented element ordering, power summation method for power flow, statistical representation of load variations, and a recently developed energy summation method for computation of energy losses. These methods, com- bined with the heuristic rules developed to lead the iterative proc- ess, make the energy loss minimization method effective, robust and fast. It presents an altemative to the power minimization methods for operation and planning purposes. </p><p>Keywords: Daily load curve, Energy losses, Energy loss reduction, Energy summation, Oriented ordering, Power losses, Power loss reduction, Power summation, Radial network, Reconfiguration. </p><p>INTRQDUCTION </p><p>Radial networks have some advantages over meshed net- works such as lower short circuit currents and simpler switching and protecting equipment. On the other hand, the radial structure provides lower overall reliability. Therefore, to use the benefits of the radial structure, and at the same time to overcome the difficulties, distribution systems are planned and built as weakly meshed networks, but operated as radial networks. </p><p>The radial structure of distribution networks is achieved by placing a number of sectionalizing switches in the net- work (usually referred to as tie switches) used to open the loops that would otherwise exist. These switches, together with the circuit breakers at the beginning of each feeder, are used for reconfiguration of the network when needed. Obvi- ously, the greater the number of switches, the greater are the possibilities for reconfiguration and the better are the effects. </p><p>Generally, network reconfiguration is needed to: i) provide service to as many customers as possible following a fault condition, or during planned outages for maintenance purposes, ii) reduce system losses, and balance the loads to avoid overload of network elements [l]. </p><p>There have been a number of works concerning resistive line losses reduction in distribution networks through recon- figuration [ 1-91. Generally there are two approaches to the </p><p>96 WM 305-3 PWRS A paper recommended and approved by the IEEE Power System Engineering Committee of the IEEE Power Engineering Society for presentation at the 1996 IEEE/PES Winter Meeting, January 21- 25, 1996, Baltimore, MD. Manuscript submitted July 25, 1994; made available for printing December 15, 1995. </p><p>reconfiguration problem. The first approach would be to de- termine the status of all switches in the network simultane- ously. Due to the combinatorial nature of the problem, very complicated mathematical techniques should be used and large computational time is needed. Usually, the solution ob- tained by methods using this approach represents a global optimum of the loss optimization problem. </p><p>The second approach would be to deal with each possible loop (determined by an open tie switch) one at a time. Methods based on this approach are simpler and faster. The simplicity and speed are achieved by introducing heuristic techniques and approximations. Sometimes these methods lead to a local optimum that closely approximates the global optimum. </p><p>Traditionally optimal configurations are obtained by minimizing power losses. For a given period, a moment of time is chosen as a representative state of the load conditions in the network (usually the system peak) and a power loss optimization method is used to determine the configuration of the network. </p><p>The problem of loss minimization becomes very complex if energy losses are to be optimized. Since loads change on an hourly basis or even shorter, configuration of the network may need to be changed accordingly. In [7,8,9] the problem of non-coincidence of peak loads, and diversity of load c gories was addressed and implemented in energy loss mini- mization methods. </p><p>To provide operation with minimum power and energy losses, the network should be equipped with remotely oper- ated tie switches, preferably in every line of the network to accomplish the highest level of flexibility. Even though such an operation can provide significant savings [7], it requires increased investment and operational costs needed for highly automated control and monitoring system. </p><p>The method proposed in this paper can be used to deter- mine the configuration with minimum energy losses for a given period. It is based on several favorable characteristics of methods and techniques specially developed for radial network analysis -- oriented ordering of the network ele- ments, power summation method for power flow, and statis- tical representation of load variations, all together combined in the energy summation method for computation of energy losses [lo]. </p><p>Basically, the method belongs to the methods known as "branch exchange techniques." Possible loops in the net- work (or feeder pairs) are analyzed and reconfigured one at a time. The reconfiguration is performed by closing the open tie switch that defines the loop, and opening the switch in the branch that produces maximum savings in energy losses. </p><p>0885-8950/97/$10.00 0 1996 IEEE </p><p>Authorized licensed use limited to: The National Institute of Engineering. Downloaded on August 24, 2009 at 02:36 from IEEE Xplore. Restrictions apply. </p></li><li><p>399 </p><p>' _ _ _ _ ) I </p><p>The candidate branch to be opened is chosen using a similar approximate technique found in [3], but applied for energy losses, rather than power losses. The order by which the loops are analyzed and reconfigured is determined by heu- ristic rules. A number of power loss minimization methods based on the branch exchange technique have used heuristics to determine the open switch to be closed, for example [ 1,3,5,6]. However, since those methods deal with a particu- lar moment of time, the same heuristic rules can not be ap- plied, as loads and voltages vary with time. </p><p>The proposed method may have advantages over tradi- tional methods that take into account only power losses. On the other hand, it requires more input data to describe varia- tions of loads, daily load curves (DLC) for typical consumer types in particular. However, it is not necessary to know DLCs for every load point in the network. Usually there are arbitrary number of different typical consumer types, much less than the number of load points. Consumers of a certain type have DLCs of equal or similar shape, but with different magnitude (peak active and reactive power). If DLCs are expressed in p.u. of their peak active power, the only data needed to represent the load at a load point is the maximum active and reactive powers, and the DLC type. Furthermore, the proposed method allows the load at a load point to be expressed as a combination of different consumer types. </p><p>GLOSSARY OF SYMBOLS </p><p>- Branch </p><p>T - duration of the load curves; nt - number of time intervals in T; n - number of consumer types in the network; </p><p>P and Q - active and reactive power, respectively; p and q - active and reactive power in p.u. of peak load for </p><p>load curves, respectively; I and V - current and voltage, respectively; </p><p>R - line resistance; W - energy; </p><p>e,f- components of typical loads at load points (in P.u.) for active and reactive power, respectively; </p><p>- second statistical moment of a random variable. The following symbols are used combined with the gen- </p><p>eral symbols: A - denotes energy or power losses, or time interval; </p><p>'I - denotes a quantity at the receiving end of an ele- ment; </p><p>P and Q - as superscript denote that the variable is associ- ated with active and reactive power or energy, re- spectively; </p><p>m - lower case letter as subscript denotes that the vari- able is associated with an element; </p><p>M - upper case letter as subscript denotes that the vari- able is associated with a node; </p><p>i, j and k - as sub-subscripts denote that the variable is asso- ciated with load curve of type i, j or k; </p><p>t - as sub-subscript denote that the variable is associ- ated with a particular moment of time (interval) t; </p><p>- bar over a variable denotes average value (power); - - bar under a variable denotes a complex quantity. - </p><p>orientation </p><p>Z' A </p><p>Link b _ _ _ </p><p>Lx </p><p>Fig. 1 Two feeder (one loop) distribution network </p><p>We will assume that every branch in the network is equipped with a switch. To maintain the radiality of the net- work the switch in one of the branches (branch a in Fig. 1) is open. Network elements are numbered using the oriented ordering algorithm described in [lo]. As a result of the or- dering, a branch (and its receiving node) is assigned a num- ber (index) in the ordered list that is always greater than the index of the sending end. The orientation of branches in the network is positive fi-om the sending node (lower index) to the receiving node (higher index). </p><p>If the open switch in line a is at the side of node Z, intro- ducing the fictitious node Z', branch a can be treated as a branch of the network with no load flowing in it. The posi- tive orientation af the loop is defined fi-om the node with lower index (Z) to the node with higher index (2'). Through- out the paper we will use the term loop as a synonym for an open tie line. The same terminology will be used instead of the termfeederpair, because a single feeder may have a loop within. </p><p>It is assumed that peak loads and corresponding typical DLCs are known at each load point, and that there are n dif- ferent consumer types. We will also assume that at each load point the resulting load can be represented as a sum of n dif- ferent consumer types (1). Furthermore, each load can be of constant power, constant current, or constant impedance type [lo]. Similarly, the proposed method in this paper assumes balanced three-phase loads and network elements, but it can be adapted for use in case of unbalanced networks. </p><p>n n </p><p>t = 1, ..., nt . </p><p>The purpose of the reconfiguration is to determine which branch in the loop should be opened, instead of branch A-2, to obtain minimum energy losses. Let us assume that branch x is the branch we are looking for. If the network is analyzed only at a particular moment, the effect of the reconfiguration (change in power losses in the loop) can be estimated by us- ing (2), as in [3]: </p><p>The reconfiguration, or in other words the load transfer from feeder a-nl to feeder z-n2, can be simulated by injec- </p><p>Authorized licensed use limited to: The National Institute of Engineering. Downloaded on August 24, 2009 at 02:36 from IEEE Xplore. Restrictions apply. </p></li><li><p>400 </p><p>tion of complex current equal to the current flowing through branch x at nodes Z and Z', with directions shown on Fig. 1. By doing this, the current in branch x will become zero -- which is equivalent to the effect of closing the switch in branch a, and opening the switch in linex. </p><p>However, (2) can not be applied if energy losses are to be estimated. But, a similar formula can be derived if the en- ergy summation method [lo] is used. Briefly, if statistical characteristics of the DLCs are calculated (second moments of random variables that compose DLCs), the average power losses in a particular branch m (defined as a quotient of ac- tive energy losses and period r ) can be calculated from (3): </p><p>According to [IO], voltage magnitude V, in (3) is the av- erage voltage at the receiving end of line m, obtained from a power flow calculation with average loads (average power) applied at load points. </p><p>Let us, for the time being, assume that (average) node voltages will not change significantly due to the load transfer performed by the reconfiguration. By analogy, the recon- figuration can be simulated if an average complex power, equal to the average complex power at the receiving end of branch x, is injected at nodes 2 and 2'. But the location of the switch to be opened is not known, so we will fmd the amount of complex energy (average complex power) needed to achieve minimum energy losses in the network. The branch to be opened will be the one whose average complex power flow equals the average complex power oktained. </p><p>Since there can be n different load types in the network, the injected average complex power 6P+ j6e can be decom- posed into n different components: </p><p>The active energy losses (or the average active power losses) in branch m, after the injection of the complex power sP+ J ~ Q at nodes Z and Z', can approximately be calculated using (5). </p><p>According to the use tation, the plus sign in (5) is orientation coincides with the </p><p>The apount of average power loss change in line m can be </p><p>applied for branches orientation of the loop (branches hom n2 to z in Fig. 1). </p><p>estimated from (5) and (3), resulting into (6): change - upnew - upold = - </p><p>M m - m m </p><p>and the amount of average power loss change for the loop can be calculated from (7): </p><p>Function (7) reaches extreme if its first partial derivatives, with respect to 6P and @ , are equal to zero: </p><p>, Equations (8) represent two sets of n linear equations and, </p><p>after rearranging, they can be written as (9.a) and (9.b). I </p><p>m=a V& </p><p>k = l , ..., n ; ( 9 4 </p><p>- 2 m=a V , </p><p>k = l , ,n. (9.b) Right hand sides of (9.a) and (9.b) can be calculated fiom </p><p>the average power flows in branches of the loop. Note that the positive sign indicates a branch with opposite orientation in respect to the loop orientation, and that (9.a) needed only for those consumer types that are loop -- the remaining c complex power are set t </p><p>matical solution of the problem. minimized if a branch in the loo power flow satisfies relation (10). </p><p>Linear equations (9.a) and (9.b) losses can be </p><p>Obviously, it would be very hard, if not impossible, to find a branch whose all n components meet the requirements from (10). Therefore, the solution obtained fiom (9.a) and (9.b) has little practical implementation, and it is presented only to justify the technique proposed in this paper. </p><p>Since the direct solution of the problem is very compli- cated to obtain, we will apply the technique used in [3]. With respect to (I I), eq. (7) can be rewritten as in (12). </p><p>Authorized licensed use limited to: The National Institute of Engineering. Downloaded on August 24, 2009 at 02:36 from IEEE Xplore. Restrictions apply. </p></li><li><p>401 </p><p>Element ordering Set al l LOFs to .FALSE. </p><p>Optimize independent loops </p><p>The similarity between (2) and (12) is obvious. Equation (12) can be used to estimate the amount of energy loss changes over period T, achieved by closing branch a and opening the branch with average complex power at the re- ceiving end equal to 6P + j6Q. </p><p>The change in configuration will alter the power flows in branches affected by that change. At this point it would be rational...</p></li></ul>

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