Transcript
  • 398 IEEE Transactions on Power Systems, Vol. 12, No. 1, February 1997

    UTION NETWORK RECONFIGURATION FOR ENERGY LOSS REDUCTION

    Kubin Taleski, Member IEEE Dragoslav RajiCid, Member IEEE University "Sv. Kiril i Metodij," Faculty of Electrical Engineering Skopje

    Skopje, Republic of Macedonia

    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.

    Keywords: Daily load curve, Energy losses, Energy loss reduction, Energy summation, Oriented ordering, Power losses, Power loss reduction, Power summation, Radial network, Reconfiguration.

    INTRQDUCTION

    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.

    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.

    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].

    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

    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.

    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.

    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.

    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.

    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.

    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.

    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].

    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.

    0885-8950/97/$10.00 0 1996 IEEE

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    ' _ _ _ _ ) I

    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.

    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.

    GLOSSARY OF SYMBOLS

    - Branch

    T - duration of the load curves; nt - number of time intervals in T; n - number of consumer types in the network;

    P and Q - active and reactive power, respectively; p and q - active and reactive power in p.u. of peak load for

    load curves, respectively; I and V - current and voltage, respectively;

    R - line resistance; W - energy;

    e,f- components of typical loads at load points (in P.u.) for active and reactive power, respectively;

    - second statistical moment of a random variable. The following symbols are used combined with the gen-

    eral symbols: A - denotes energy or power losses, or time interval;

    'I - denotes a quantity at the receiving end of an ele- ment;

    P and Q - as superscript denote that the variable is associ- ated with active and reactive power or energy, re- spectively;

    m - lower case letter as subscript denotes that the vari- able is associated with an element;

    M - upper case letter as subscript denotes that the vari- able is associated with a node;

    i, j and k - as sub-subscripts denote that the variable is asso- ciated with load curve of type i, j or k;

    t - as sub-subscript denote that the variable is associ- ated with a particular moment of time (interval) t;

    - bar over a variable denotes average value (power); - - bar under a variable denotes a complex quantity. -

    orientation

    Z' A

    Link b _ _ _

    Lx

    Fig. 1 Two feeder (one loop) distribution network

    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).

    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.

    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.

    n n

    t = 1, ..., nt .

    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]:

    The reconfiguration, or in other words the load transfer from feeder a-nl to feeder z-n2, can be simulated by injec-

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    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.

    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):

    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.

    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.

    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:

    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).

    According to the use tation, the plus sign in (5) is orientation coincides with the

    The apount of average power loss change in line m can be

    applied for branches orientation of the loop (branches hom n2 to z in Fig. 1).

    estimated from (5) and (3), resulting into (6): change - upnew - upold = -

    M m - m m

    and the amount of average power loss change for the loop can be calculated from (7):

    Function (7) reaches extreme if its first partial derivatives, with respect to 6P and @ , are equal to zero:

    , Equations (8) represent two sets of n linear equations and,

    after rearranging, they can be written as (9.a) and (9.b). I

    m=a V&

    k = l , ..., n ; ( 9 4

    - 2 m=a V ,

    k = l , ,n. (9.b) Right hand sides of (9.a) and (9.b) can be calculated fiom

    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

    matical solution of the problem. minimized if a branch in the loo power flow satisfies relation (10).

    Linear equations (9.a) and (9.b) losses can be

    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.

    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).

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    Element ordering Set al l LOFs to .FALSE.

    Optimize independent loops

    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.

    The change in configuration will alter the power flows in branches affected by that change. At this point it would be rational to test branches for possible overloads. For exam- ple, current magnitude in branch n2 in every interval At can be approximately calculated with (1 3) using average power flow at its receiving end (14). Furthermore, if all branches in the feeder have equal current limits, only the first branch should be tested (branch n2 in Fig. 1).

    Since node voltages are not known for every interval At, we can use average node voltages, similarly to ( 3 ) . Tests showed that errors produced by approximate formula (1 3) are of the same magnitude as errors produced by (3) when branch energy losses are calculated. According to [ 101 those errors are less than 5%, even for heavily loaded networks.

    THE ENERGY LOSS MINIMIZATION METHOD

    The procedure described in the previous section would be sufficient if applied simultaneously to all loops in the net- work, but only if the loops do not have mutual branches. The problem becomes more complicated if some branches in the network belong to more than one loop. It is because load transfer in one loop can affect power flows in the loops that share mutual branches.

    The simplified flow-chart of the energy loss minimization method is shown in Fig. 2.

    At the beginning of the procedure, after the oriented or- dering, loops (open tie switches) are identified, and for each loop a loop optimality flag (LOF) is assigned. LOF when TRUE indicates that the loop has been optimized. Then, the

    ~

    I

    Calculate average node voltages and average power flows Set LOFs to .FALSE. for loops with changed power flows

    i

    I

    r Select next loop for optimizaaon ' Estimate energy loss changes Select a branch to be opened

    I / \

    _ _ _ _ ~ i.

    ~ Change configuration and reorder network elements I I

    17- ,:L-- Optimal configuration found 1

    L

    Fig 2 Simplified flow-chart for the proposed algorithm

    independent loops are identified -- we will use the term inde- pendent loops for those loops that do not have any mutual branches. For these loops the procedure for selection of a branch to be opened is applied simultaneously, and the loops are marked as optimized (their LOFs set to TRUE), because they do not have to be further analyzed.

    The remaining of the procedure is iterative. At the be- ginning of each iteration a power flow is performed to calcu- late average node voltages needed for the energy loss calcu- lation that follows. (Note that energy loss calculation is also performed in the previous step for optimization of the inde- pendent loops.) Then, the active energy losses for each loop are tested to determine which loops were affected by the re- configuration in the previous iteration. If such loops exist, their LOFs are set to FALSE. At this stage branch current limits can be tested, and if necessary take appropriate action.

    The process continues by selection of the next loop to be optimized. At this point it should be noted that the order by which loops are selected and optimized may significantly af- fect the efficiency of the method. To avoid unnecessary it- erations efficient criteria for loop selection must be estab- lished.

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    Various power loss minimization methods based on the branch exchange technique use different criteria to determine the order by which the loops are analyzed. Usually, it is the voltage difference across the open switches, or the power loss difference across the two sub paths of the loop -- branches with coincident orientation with the loop orienta- tion and the branches with oppmite orientation.

    For this method a set of specific heuristic rules was set up. These rules are based on the analysis of the network topol- ogy and the active energy losses for each loop. Parts of a complex radial distribution network shown in Fig. 3 and Fig. 4 will be used to explain the basic principles for selec- tion of the switch to be closed.

    The part of the network in Fig. 3 has one open tie switch (loop Ll). A characteristic of loop L1 is that one of the sub paths does not contain any branches. Let us assume, for the moment, that all network elements are with identical parame- ters and that loads are uniformly distributed. If this were true, the configuration with minimum losses for a single loop could have been achieved by opening the switch in the branch at the middle sf the loop. Even if none of the as- sumptions above is true, it is normal to expect that, eventu- ally, id the minimization process, the open switch A-A would have to be moved on sub path A'-M-A, towards node A . Therefore, loops like loop L1 should have priority for opti- mization in the reconfiguration process.

    The part of the network shown in Fig. 4 includes two open tie switches: consequently, there are two loops (L2 and L3), oriented as indicated by the arrows. Both loops have same root (node B), and they overlap -- a part of loop L2 (branches between nodes B and N> i s a subset of loop L3. We will refer to loops L2 and L3 as an inner-outer loop pair (IOLP).

    The relation between loops L2 and L3 (inner and outer loop) is also used for construction of the heuristic rules. In most cases, as tests showed, it is more efficient to optimize the inner loop first. If the relation between those two loops has not changed (the open switch in the new configuration is on the path B-C-C'-N), then optimize the outer loop. The oriented ordering technique used for the element ordering provides an efficient and fast detection of IOLPs.

    Note that, generally, more than two loops may have simi- lar relationship. If more than two loops have at least one mu- tual branch, they are considered as an innedouter loop group. Furthermore, the identification of the most inner and the most outer loop is accomplished by comparison of the energy losses associated with the loops. The Ioop with the lowest energy losses is declared as the most inner loop, while the loop with the highest losses, as the most outer loop. For ex- ample, if loop L2 in Fig. 4 has lower energy losses than loop L3, L2 is an inner loop, whileL3 is an outer loop.

    The selection of the loop to be optimized (or the open tie switch to be closed) is performed by the following rules, listed by descending order of precedence:

    Select and optimize first loops with characteristics like loop L1 in Fig. 3 (highly unbalanced energy losses over both loop's sub paths). As described ear- lier, these loops are the most likely candidates for op- timization. If these loops are not optimized at this

    Fig 3 Part of a radial distribution network with one loop

    To substation Loop L3

    Fig. 4 Part of a radial distribution network with two loops

    early stage of the process, their later optimization can affect the configuration in loops, thus requiring extra iterations.

    exists, the se1 trary. When a pair or group is or group is not selected until all optimized. The or mized in the group is from outer loop. Due to the app (12), the accuracy o higher if the chan modest changes in energy losses. Therefore, by op- timizing the loops with lower losses (inner loops) the possibilities for false estimates are lower. Select the next loop in the list of ordered elements.

    The application of these rules provides fewer iterations to be performed. However, for networks in which many loops overlap, some loops need to be optimized more than once.

    The next step in the minimization procedure is to deter- mine the branch to be opened. To avoid testing all the branches in the loop, the first two branches adjacent to the open switch are tested. If there are no power sources in the network (other than at the slack ) the results of the tests will have opposite signs. Equati the active energy loss change if branches z and b are opened (Fig. 1). This is accomplished by substituting in (1 1):

    Detect all IOL

    Then, the branches on the path on which the first branch has negative changes are checked. The energy loss changes become positive, or i The branch with highest negative energy loss changes so far is selected to be opened. sources at nodes other than the slack nod energy and power flows in parts of the network can be dis- turbed. If this is the case, the swi to be opened is deter- mined by testing all branches in th

    Finally, the last step in the procedure is the reordering of the network elements. oted before, the proposed method, as well as the pro s it uses (power and energy

    However,

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  • 403

    lem of non-coincident peak loads is solved simpler -- their magnitude is what counts, not the timing.

    The problem of network reconfiguration is not solely a technical problem. Usually it is a matter of utility compa- nies' policies. Some utilities change their network configu- rations on a seasonal basis, while other utilities reconfigure their networks more fiequently. The methodology presented in this paper allows to evaluate the benefits of more fiequent reconfiguration, for example on weekdaylweekend basis, in addition to seasonal changes. Even periods shorter than 24 hours can be used, for example off-peak and peak load peri- ods [7].

    TEST RESULTS

    summation methods), are based on the oriented ordering of the network elements. After a change in the configuration is performed, it is necessary to update the indices in the list of ordered elements.

    The reordering can be simply accomplished by a full or- dering such as the one performed at the top of the procedure. However, for large networks this task could be time consum- ing. On the other hand, only small segments of the ordered list are affected by the reconfiguration, and it is rational to take advantage of that fact. Therefore, a special technique for partial reordering was developed. Tests performed on a 150-node (28 loops) radial network suggest that speed gains over a full ordering are 5 to 10 times, depending on the scale of the changes in the configuration.

    A special characteristic of the proposed method is that it can be used, with minor modifications in (12), as a power loss minimization method as well. Note that if n=1, and the DLC is flat ( F&,) = Q = 1 ), average power losses become

    power losses. Hence, equation (12) can be considered as a general form of equation (2). Both minimization versions of the method were tested on numerous networks, and they pro- duced configurations with lowest energy or power losses, re- spectively.

    The proposed method for energy loss reduction is very simple and fast. Both characteristics are achieved by the as- sumption that average node voltages do not change much with each load transfer. However, there are situations when this assumption can produce false estimates in (12) and lead to a change in configuration with higher energy losses. But, since energy losses are recalculated in every iteration, such situations are easily detected, and the changes are ignored by marking the current loop as optimized and proceeding with the next one. The price to pay for that is an extra iteration.

    At this point it must be emphasized that the configuration of the network with minimum energy losses over a period does not necessarily mean it provides the most cost savings. There are several issues to be considered, among them costs for switching. For example, there are cases, as it happens with power loss optimization methods, when expected sav- ings are marginal and overwhelmed by switching costs. In addition, there are situations when savings in energy losses may not be greater than the price difference between lost power and lost energy.

    On the other hand, the proposed method is capable of dealing with networks and loading conditions in which maximum power losses do not occur at system peak (example network in AppendixA), or when maximum (energy) savings are expected during off-peak periods [7,9].

    Even though the proposed method deals with energy, it does not require load curves for all load points. At most load points there will be only one consumer category. Once typi- cal consumer groups are determined, and they are assigned to load points, only additional data, except peak loads, are the types of DLCs at load points. Loads that do not conform to a single consumer category can be mathematically decom- posed into n typical consumer load curves (l), requiring knowledge of components e andfonly. Likewise, the prob-

    %,l)

    The effectiveness of the proposed method for energy loss reduction was tested for convergence and ability to provide configuration with lowest energy losses. The method has not been compared with other methods, since, by the authors' knowledge, there are no similar methods suitable for com- parison.

    Computer programs, Written in FORTRAN, were devel- oped and ran on a 66MHz 486DX2 PC/AT compatible per- sonal computer. The power and energy summation methods [lo] were used for all power flow and energy loss calcula- tions. The nominal voltage was chosen as a base voltage and as the voltage at the slack bus. In all cases (power summa- tion method) the iterative process finishes if, in two con- secutive iterations, changes in both network active and reac- tive power losses are lower than 0.01 kWkvar.

    Test results presented in this paper include two networks. The first test network (10 kV, 16-nodes and 2 loops) is non existent, but was constructed for demonstration purposes using realistic data. Two types of consumer were adopted fi-om [ l 11: Urban Residential Load (URL,), and Commercial Load (CL). The data for the network elements, as well as for the loads, is presented in Table I.

    The results of the optimization for both energy and power losses at system peak are presented in Table 11, and complex network load and loss curves are presented in Figs. A.2 and A.3. The results show that two optimal configurations differ significantly. Power losses at system peak (8 p.m.) for both configurations are almost identical. But, the configuration obtained for minimum power losses at system peak has 6% higher energy losses, and 14% higher maximum power, losses (10 a.m.) than the configuration obtained for minimum en- ergy losses. However, not always the two minimization methods result in configurations that differ that much, as proven with the second test network.

    The second test network (12.66 kV, 32-nodes and 5 loops) was used in [IO], but originally found in [l]. Since the network in [l] was used for power loss reduction, it had to be modified. Two consumer types were assigned to the load points in the following way: every odd node was as- signed URL type, while every even node, CL type. Loads fiom [l] were used as peak loads. Also, nodes were given names with the letter N preceding the number.

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    TABLE I DATA FOR THE 10 KV TEST NETWORK

    Branch Sending Receiving

    node node I 0 0.00 0 55

    030 012 025 010 025 010 0.25 0.10 025 010 0.30 0 12 025 010 030 012 050 020

    Load at receiving node E G 7 G F E - I

    kW h a r type

    500 200 URL 500 200 URL 500 200 URL 500 200 URL 400 150 CL 450 150 CL 500 200 CL 400 150 CL 400 150 CL 400 150 CL 500 200 CL 400 150 CL 600 200 URL 600 200 URL 600 200 URL 600 200 CL

    0 0

    TABLE II COMPARISON OF BOTH OPTIMAL. CONFIGURATIONS

    If the power loss minimization algorithm is applied (for the moment when system peak occuss -- 8 p.m.), it leads to the configuration defined by the following open lines: N6-N7, N8-N9, N13-Nl4, N27-N28 and N31-N32. The number of iterations varies depending on the starting con- figuration, but the final (optimal) configuration is always identical. The power losses for the optimal configuration are 105.6 kW, while energy losses over a 24 hour period, are 1735.9 kWh. In this case, the same configuration is achieved if the energy minimization algorithm is applied.

    Many factors influence the differences between confgu- rations obtained by the power and energy loss minimization methods, such as: loads and types of loads, voltage variation at the slack node, variances and covariance of DLCs, and network element parameters. Since it is almost impossible to predict the outcome of both minimization methods, the fmal decision about which configuration should be used for most economical operation should consider factors such as costs for power, energy, and switching.

    To illustrate the effects of the heuristic rules used for se- lection of the switch to be closed, the intermediate results of the energy minimization algorithm for the second test net- work are presented in Table 111. The starting configuration for this test is defined by the following open lines: N7-N20, NS-Nl4, Nll-N21, N17-N32 and N24-N28. The energy losses for this configuration are 2477.8 kWh. The results ob- tained using the heuristic rules are presented in the first half of the table. The second half of the table shows the results when no rules are applied -- the order by which loops are

    TABLE J l l INFLUENCE OF THE HEURISTIC RULES ON SELECTION OF SWITCH TO BE OPENED

    Iteration/ I Closeline I Open line I Energy losses (no ofloops tested) I kWh

    1 /(I) 1 N8 - N14 I N13 - N14 [ 2411.3 Loop selection by heuristic rules

    2 / (1) N7 - N20 N6 - N7 1897 9 3 /(1) N11 - N21 N8 - N9 1779.9 4 IC31 N17 - N32 N31 - N32 1744.1 5 l(4) N24 - N28 N27 - N28 1735.9

    Loop selection by thelr position in the ordered list N24 - N28 N27 - N28 2141 0

    1809 8 1 /(I) 2 I (2.) N21 - N11 N9 - N10

    1795 8 1812 6 1780 5 1772 0 1753 2 1761 9 1735 9

    selected is determined by their position in the list of ordered elements. The numbers in parentheses show how many loops were tested in each iteration before a decrease in the energy losses was achieved.

    Results in Table 111 show that the order by which loops are optimized directly affects the performance of the pro- posed algorithm. Note that if no heuristic is applied, the number of iterations depends on the positions of the loops in the ordered list of elements. Also note that in the 4. iteration and 7. iteration there are false estimates resulting into energy loss increase, requiring repetition with another loop.

    Finally, some remarks about the speed of the energy loss ization method. Most of the computational time in each iteration is used for calculation of the energy losses. The number of loops tested and the number of branches tested for (1 2) does not significantly affect the time required for one iteration. For example, for the second test network when heuristic rules are used, the average time was 0.050 seconds per iteration.

    CONCLUSIONS

    A method for distribution network reconfiguration for en- ergy loss reduction is presented. The method can be used to obtain the configuration with minimum active energy losses over a period of time and can be used as an advantageous al- ternative to the power loss minimization methods. Its ro- bustness, effectiveness and accuracy are inherited &om the energy summation method and further improved by the heu- ristic rules used to lead the minimization process. The com- putational time is almost identical to the time needed by power loss minimization methods that makes this method suitable for operation, as well for planning purposes.

    ACKNOWLEDGMENT

    This work was supported in part by the Ministry of Sci- ence, Republic of Macedonia.

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  • APPENDIX A: NUMERICAL EXAMPLE

    LOOP LOF Awloop AW+ AW- AW+/AW- kWh kWh kWh

    I

    405

    MI0 MI1 MI2 In this section we will present a brief numerical example for optimization of the first test network (Table1 and Fig. A.l). There are two loops in the network and they can be considered as a loop pair, similar to the example in Fig. 4 (same root -- M, and mutual line M-M6). Second moments p2 for DLCs (URI, and CL) used in the tests are calculated fiom (A. 1) [ l I] and are presented in Table A.1 in p.u. of av- erage power for the corresponding DLC.

    I = 1 ,..., n;/= 1 ,..., n , (A. 1 ) where all quantities in the right hand sides of (A.l) are ex- pressed in p.u. of peak active power for the corresponding DLC.

    The next step is to determine the loop to be optimized first. Active energy losses for each loop, as well as energy losses for branches on the positive and negative path ( AW+ and AW- ), are calculated and they are shown in Table A.11 (1. iteration).

    Loop M15-Ml6 is chosen to be optimized first for the following reasons: it is considered as an inner loop (lower energy losses, 47.8 kwh) and it has higher unbalanced losses across both paths (0.281 11).

    TABLE A.1 SECOND MOMENTS FOR DLCS USED IN THE TESTS h 1

    1. Iteration Active network losses: 1729.2 kWh M15-Ml6 I FALSE I 47.8 I 10.5 I 37.3 I 0.28111 M5 -M9 I FALSE I 49.2 I 20.1 I 29.1 I 0.68920

    2. Iteration Active network losses: 1632.2 kWh

    Next, it should be determined which branch in the loop provides highest energy loss reductions if opened. Estimates for energy loss reductions if adjacent lines to line M15-Ml6 are opened, are calculated using (12):

    Open line Estimates for energy loss reduction (kWh) M12 - MI6 96.0 MI4 - MI5 -318.3

    lese L MI M2 M3 M4 M5

    Fig. A.l Graph of the 10 kV test network

    Estimates show that branches on the path M15-M if opened would produce increase in energy losses. Next, line Mll-M12 is tested and the test shows that, if opened, that line will produce energy loss reduction equal to 9.3 kwh. Line M12-Ml6 is the best candidate since it yields to highest reduction if opened.

    The next iteration starts with calculation of energy losses for the new configuration. Results of the calculations are shown in Table A.11 (2. iteration). Note that loop M12-Ml6 is marked as optimized (LOF'TRUE). Estimates for energy loss reduction for adjacent lines to line M5-M9 are:

    Open line Estimates for energy loss reduction (kWh) M8 - M9 -77.6 M4 - M5 -56.1

    Since opening neither line produces energy loss reduction, this loop is marked as optimized, leaving us with no loop to be further optimized.

    In the configuration determined for minimum power losses at system peak, the most loaded branch is M-M6. At 10 a.m. it is loaded at 93% of its thermal limit (255 A), while at 8 p.m. (system peak) it is loaded at 64% (Fig. A.4). In the final configuration obtained for mi&" energy losses the same branch is loaded at 77% of its limit (10 a.m. Fig. AS). Minimal voltages for both configurations are 0.9543 and 0.9636 P.u., respectively.

    S (kVA) 8000

    AP (kW) S,,=7247.1 kVA 2oo

    2000 50

    1000 t t O

    0 2 4 6 8 10 12 14 16 18 20 22 24 Time

    Fig. A.2 Apparent load and active power loss curves for the network in the configuration with minimum power losses at system peak

    Authorized licensed use limited to: The National Institute of Engineering. Downloaded on August 24, 2009 at 02:36 from IEEE Xplore. Restrictions apply.

  • 406

    S (kVA)

    8ooo i AP (kW

    S,,=7247.5 W A T 2oo

    0 2 4 6 8 10 12 14 16 18 20 22 24 Time

    Fig A 3 Apparent load and active power loss curves for the network in the configuration with minimum energy losses

    kW, kvar 4000 T

    Line M-M6

    3000

    2000

    1000

    -P -Q 0 - 9 : , / # : I / 8 I 8 ; 8 : # I > l , I > : I /

    0 2 4 6 8 10 12 14 16 18 20 22 24 Time

    Fig A 4 Load curves for the most loaded branch in the network in the configuration with minimum power losses

    kW, kvar

    4000 i Line M-M6

    P -Q - i 07-3 : ' I , I ' I ' : ' I , I , I , ~, I I : I I 0 2 4 6 8 10 12 14 16 18 20 22 24

    Time

    REFERENCES

    [ l ] M. E. Baran, and F. F. Wu, "Network Reconfiguration In Dis- tribution Systems For Loss Reduction And Load Balancing," IEEE Trans on PWRD, Vol. 4, No. 2, pp. 1401-1407, April 1989.

    [2] C. S. Chen, and M. Y. Cho, "Determination of Critical Switches in Distribution Systems," IEEE Trans. on PWRD,

    [3] S. Civanlar, J. J. Grainger, H. Yin, and S. S. H. Lee, "Distribution Feeder Reconfiguration For Loss Reduction," IEEE Trans on PWRD, Vol. 3, No. 3, pp. 1217-1223, July 1988.

    [4] D. Shirmohammadi, and H. W. Hong, "Reconfiguration Of Electric Distribution Networks For Resistive Line Losses Re- duction," IEEE Trans on PWRD, Vol. 4, No. 2, pp. 1492- 1498, April 1989.

    [5] C-C. Liu, S. J. Lee, and K. Vu, "Loss Minimization Of Distri- bution Feeders: Optimality And Algorithm," IEEE Trans. on PWRD, Vol. 4, No. 2, pp. 1281-1289, April 1989.

    [6] S. K. Goswami, and S. K. Basu, "A New Algorithm For The Reconfiguration Of Distribution Feeders For Loss Minimiza- tion," IEEE Trans. on PWRD, Vol. 7, No. 3, pp. 1484-1491, July 1992.

    [7] R. E. Lee, and C. L. Brooks, "A Method And Its Application To Evaluate Automated Distribution Control," IEEE Trans on PWRD, Vol. 3, No. 3, pp. 1232-1240, October 1988.

    [XI R. P. Broadwater, A. H. Khan, H. E. Shaalan, and R. E. Lee, "Time Varying Load Analysis To Reduce Distribution Losses Through Reconfiguration," IEEE Trans on PWRLI, Vol. 8,

    [9] C. S. Chen, and M. Y. Cho, "Energy Loss Reduction by Criti- cal Switches," IEEE Trans on PWRD, Vol. 8 , No. 3, pp.

    [lo] R. Taleski, and D. RajiCiC, "Energy Summation Method For Energy Loss Computation In Radial Distribution Networks," Paper no. 95SM601-5 PWRS presented at the EEEPES 1995 Summer Meeting, Portland, OR, July 23-27, 1995.

    [ 111 A. L. Shenkman, "Energy Loss Computation By Using Statis- tical Techniques," IEEE Trans on PWRD, Vol. 5, No. 1, pp.

    Vol. 7, NO. 3, pp. 1443-1449, July 1992.

    NO. 1, pp. 294-300, January 1993.

    1246-1253, July 1993.

    254-258, January 1990.

    Rubin Taleski (M '90) was born in 1957. He received his B.S. and M.S. degrees, both in Electrical Engineering, from the University "Sv. Kiril i Metodij" in Skopje in 1980 and 1990, respectively. During the period 1981-1987 he worked at the Institute for Energy in Skopje. In 1987 he joined the Faculty of Electrical Engineering in Skopje, and presently he is a teaching assistant in Power Systems at the same University. His subjects of interest are computer appli- cations in power and distribution system analysis.

    Drugoslav Rujicic (M '86) was born in 1935. He received his B.S. from University "Sv. Kiril i Metodij" in Skopje and M.S. and Ph.D. from the University of Belgrade, all in Electrical Engineering. Presently he is a Professor at the Faculty of Electrical Engineering at the University "Sv. Kiril i Metodij" in Skopje. His current area of interest is analysis of transmission and distribution systems.

    Fig. A.5 Load curves for the most loaded branch in the network in the configuration with minimum energy losses

    Authorized licensed use limited to: The National Institute of Engineering. Downloaded on August 24, 2009 at 02:36 from IEEE Xplore. Restrictions apply.


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