Distribution Network Reconfiguration To Minimize Resistive Line Losses

1338

IEEE Transactions on Power Delivery, Vol. 10, No. 3, July 1995

DISTRIBUTION NETWORK RECONFIGURATION TO MINIMIZE RESISTIVE LINE LOSSES G.J. Peponis

M.P. Papadopoulos Member IEEE

N.D. Hatziargyriou Senior Member IEEE

Electric Power Division Department of Electrical and Computer Engineering National Technical University, Athens, Greece Abstract The oblective of the analysls presented is to outlme and vahdate a methodology for the optmumnon of MV distribution networks operatlon, so that vanable loads are fed under minmum energy losses Loss mrurruzatlon 1s acheved by the installation of shunt capacitors and reconfiguration of the network The impact of load vanatlon and load modelling on the optimizing decisions is examined Two different reconfiguraaon methods are applied and compared

have been developed In the flrst U], a simple formula IS used for the esnmanon of the loss redumon obtamed by a partlcular switchmg optlon, that 1s closmg a s w t c h and operung another m the loop formed C'Swtch Exchange Method - SEM) In the second C231,all ne w t c h e s are mtially closed, and an o p m a l load flow IS obtamed The system 1s returned to a r a d a l configuration by s u c c e m v e operungs of the smtches h a m g the lowest current flow, untll network radahty 1s obtamed C'Sequennal Swtch Operung Method - SSOM) Many papers uslng the above ideas have been presented m recent years

1. INTRODUCTION Most electric dstnbution networks are operated radally Nevertheless, there are usually several interconnecting tie switches avalable, especially in the underground medium voltage networks Configuration alteratlons may be performed by changes of the state of network switches, in such a way that radiality is always reestablished after the end of the manipulations The optimal operating condition of distnbutlon networks 1s usually considered to b e obtamed when line losses are minimized, without any violations of branches loading and voltage limits Other service quality critena can be further used, like service continuity or voltage stabihty

Loss minmization problem was formerly faced as a part of distribution networks planning studes Recent advances m distribution automanon technology have substantially unproved control and network management capabllihes Consequently, the general problem of loss minimizatlon has greater effect on distribution operation declsions Practically, loss minimmtion 1s obtaned in two ways installation of capacitors, when thls 1s economically lustdied, - network reconfiguration, that IS the selection of the proper topological structure of the network for mnimum losses Determination of the optimum size and placement of capaators is an old problem for distributlon engineers and several papers have been publlshed on this subpct The reconfiguratlon problem has been relatively recently tackled, because of the advanced computing and control capabihtles required for its study This is due to the fact that in real distnbution networks the number of switchmg options to be tested and controlled for loss minimization is very large

In t h paper, ~ a combmed method for the approach to the optunal operatmg conditlon of M r b u t l o n networks 1s presented Its two mam steps are: - Optunum or near optmum network configuranon is obtamed uslng one of the two baslc methods mennoned above, takmg into account loadmg and voltage constrants A voltage quahty index [41 1s also calculated - Optmum capaator me and locatlon are deterrmned T ~ E 1s obtamed w t h the method developed in [51, based on dynarmc programmmg techmques This procedure IS repeated untll the two steps produce the same configuratlon and capaator arrangements The computer program developed 1s apphed on a typical 20 kV network conslstlng of five feeders The m p a c t of load variatlon and load modelling on loss m m m n o n and voltage quahty mdex improvement 1s exammed

2. GENERAL ALGORITHM The proposed method conslsts of the following s t e p s 1 Determine the operatlng condtlon and energy losses of the exlstlng system 2 Reconfigure the system to mmimue energy losses and determme the new operanng condinon 3 Remove the installed capaators and connect the ones resulUng in the m u m u m net benefit on the reconfigured system 4 Repeat steps 2 and 3 until reconfiguratlon and capacitor mstallanon steps produce the m e configuratlon and capaator arrangements 5 Perform a fmal load flow analysls and evaluate energy losses

In the five steps outlined above, load i s modeled as follows Heuristic rather than analytical methods appear to be more effective for feeder reconfiguratlon studies Two bam methods

This paper was presented at the 1993 Athens Power Tech Conference held in Athens, Greece, September 5-8. 1993.

Generally, the total load at each node conslsts of five types (eg , residential, industrial, etcJ Typical load varianon wth hme 1s determmed by a given proflle for each characterlstic day (eg , m t e r workmg day, summer weekend day, etc) Given the total power installed and the load composition at each node, active and reactlve load curves can be obtamed Loads can be represented by dfferent models as constant current (voltage independent current injemons) - CJ, constant power (inversely proportional to voltage value current injections) - CS, constant impedance (directly propornonal to voltage value) - CZ and mixed - MX that is any combinanon of the previous models

0885-8977/95/$04.00 Q 1993 IEEE

1339 3. NETWORK RECONFIGURATION PROCESS

d) A switching option leading to energy loss redumon can be

The two basic reconfiguratlon methods have been improved and generalized in order to account for variable loads

m e d out if no branch flow constrants are violated Refernng to Figl, the checks r e q w e d are defined Superscripts refer to the network configurations before and after the switchmg action

3.1 SWITCH EXCHANGE METHOD (SEMI This method, described m U], is applied for CJ loads It 1s based on the estimabon of loss reduction resultmg from a partlcular switching option from (1). A swtching option 1s defined as t h ~ of closing one open switch and openmg one of the switches m the loop formed

where: D set of buses w h c h are &connected from Feeder-I1 and connected to Feeder-I with this m t c h m g optlon, m,n buses connected to branch m-n, where the m t c h to be closed is installed Bus m 1s connected on Feeder-I and bus n on Feeder-11, JI complex load current at bus 1, Rloop series reslstance of the loop formed by closmg the switch of branch m-n,

-

-

-

-

E m component of E = RBu, . JBus corresponding to bus m R B Uis~ the 'reslstance matrix' of Feeder-I before the lsad transfer, found using the substation bus as reference JBus is the vector of bus currents for Feeder-I, E n similar to E m but defined for bus n on Feeder-11, Re[l,*,I I real part, complex conlugate and magnitude operators, respectively

-

-

After considermg all possible swtching options, the one which provides the largest loss reducnon 1s carried out This set of actions is called 'step' Successlve steps are followed untll no further loss reducuon E posslble This method does not ensure convergence to the optimum configuration, while it E dependent on the initlal state of the network switches

3.2 IMPROVED SWITCH EXCHANGE METHOD (ISEM)

<+&

Let us consider the network of Figl and examine the effects of closing the switch of branch m-n and opening h s of branch k-l Figure 1:

Switching option : closing smtch of opemngm-n, branch smtch

FEEDER-I

of branch k-1.

Equation (1) can b e more efficiently applied, if w e take mto account the following general remarks

TI =

a)

where

-I

On the path (start - m) : On the path (start - n):

-loop 1,

=

I,

-loop

+I,

T'OOp = -bef - -loop

1,

1,

In both reconfiguration methods, branches are numbered after each step in layers away from the root, as presented in t31 3.3 SEQUENTIAL SWITCH OPENING METHOD (SSOM) In thls method, developed in E1 and modified in [31. a low loss configuration 1s determined by applymg an opnmal power flow analysls to the system with all switches closed The system 1s lead to a radml configuration by operung the m t c h e s of the branches with the lowest current, the optlmal flow pattern bemg determined after each switch operung operanon, called "step" Branch current flows should be checked for constramt wolanons after each step Optunal flow at each meshed network E determined as the branch current flowing in the resistive network (with branch reactances neglected), the load nodal current i n p a o n s c o m d e r e d constant W e tius 1s true for CJ loads, as proved in [31, it can not be generahzed for all load models This is due to the fact that load dependence on voltage does not allow the direct transfer of the load current in~ectionscalculated for the complex network to its r e m t w e part Mathemancally, the denvations required by the Lagrange optimlzanon method do not give a m p l e results slmilar to those for CJ loads illustrated in t31 However, SSOM can be applied for all load models and g v e s satlsfactory results Load variation complicates further the choice of the switch to be opened at each step Various tests have shown that the s w t c h to be opened corresponds to the branch with

mhzlF (til2 , where 7, (t) the complex current flowing on t

branch k at time t 1s

the load current flowmg through

itD

the switch whose operung is being exammed

-

-

In practice, changes in the state of the two switches (closmg, operung) are not slmultaneous, and the loop formed r e m m for several minutes Dunng t h s operatmg con&tlon constramt wolatlons on the following branches should be exanuned :

b) E, = RB-, . A(], m). I BRANCH where: R B R ~ N C-Hdiagonal matnx of branch resistances, A(iM - m column of the branch mcidence maadapted to the radml operation of dlstnbutlon networks [61 and

-

I BRANCH - branch current vector Avoiding constructlon of R B Umatrix ~ is very advantageous for reconfiguration processes c) Lost energy can be estimated by addmg AP(t) for all dlfferent network loadings (hme points) T h s summation prevents us from the use of the heunstlc rule that loss reductlon may OCCUT for the swtches where I&,[ < IF&[,which reduces the number of switching options [ll

However, t h method presents the advantage of being independent from the initlal configuratlon and so it 1s more hkely to o b t a n the absolute optimum rather than a local "mum

Power flow solution of meshed networks. U m g diacoptics [?1, it can be proven, that a branch h a m g a normally open switch can be presented in closed positlon as nodal current inpctions on the nodes connected

-

U

Ill

Current I,, is calculated

-d-

from :

i'

4oop

1340 If more than one normally open switches e x s t , closmg of each one affects current injectlons representmg the others through

- v, , v,

In such configuratlons, iterative power the voltages flows are required to determine branch flows accurately, as accuracy highly affects the results of SSOM

of them are open. M a n lines conductors are of ACSR-95 and ACSR-50 types and laterals of ACSR-50 and ACSR-16 types (Aluminium Cable Steel Reinforced - 95/90/16 mma copper equivalent) INFEED

This power flow method may result in voltage instabllity for CS or CZ loads for c e r t a n poor inihal network configuratlons In general, however it is computatlonally effiaent and accurate

4. CAPACITOR INSTALLATION PROCESS A3

Reactive power compensation IS the most widely accepted mean of improvmg voltage profile and energy losses in distribuhon networks With this approach next to voltage/var control other operahonal parameters are also Improved, h e the peak current flows on network branches and the total peak MVA of the system The total peak MW reduction however, IS queshonable and it depends on the type of load For CJ loads power loss reductlon results in an equal mcrease of power consumption and constant incoming MW fed to the network Reductlon is observed for CS loads and increase, in most cases, for CZ loads Voltage improvement cannot be directly financially m a t e d , while the profit resultlng from total MVA and branch current flow reductions depends as well on other operatlon parameters and long term planning decmons On the contrary, loss reduction can b e dlrectly fmancially estimated The objective cost function of this problem

1s

where : summation mcludes all network branches, SL&k) the profit due to annual energy loss reductlon on branch k, resulting from the flow of capaatlve current k k on it CXick) annual cost (depreciatlon plus operatlonal cost) of the capacitor klrinstalled at bus k Power loss reductlon on branch k

1s

proven to be:

APk = 3Rk(2ILkI,, - I & ) where : Rk the k-th branch resistance and ILk the reactlve load current flow on branch k

(4)

Summing up energy losses for all different network loadmg conditions over one year, gives the annual energy loss reduction Dynamic programmng techmques, are proven to be very efficient in the solutlon of t h s optmuation problem [5,Bl and have been used in our approach

t closed switch

\

openswitch

Figure 2 Application network For CJ load model the mind annual m a m u m load of each feeder 1s Feeder A B C D E 242 51 296 311 52 LoadcMVA) : Ihstrlbutlon substahon mts or groups a r e connected at each node Loadmg has been d e t e m e d takmg mto account the load composlhon (resldentlal, industnal etcJ of each feeder and the correspondmg load profiles Estlmatlon of network voltage quahty 1s obtamed using Cw mdex Tfus 1s evaluated as the summatlon of node voltage variances : 0 Each variance is calculated based on the nommal voltage and the summatlon 1s weighted by the contrbutlon of the node's load to the total The results of the h e u r m c methods are compared to the absolute optlmum for each load model The latter 1s obtamed from the exammation of all posslble configuratlons and the evaluanon of energy losses for those techrucally accepted The tune r e q u r e d for tfus d e t d e d search IS, of course, prohbihve for actual system apphcatlons

51 APPLICATION OF RECONFIGURATION METHODS

Sll Constant current loads The optlmal configuration found by the d e t d e d search of all posslble configuratlons, 1s lllustrated m Fig 3 INFEED

An heuristic method for the applicatlon of fixed capaators on networks m t h load models dlfferent than CJ conmts of the following steps: d, Determine the operahng condmon of the network talang into account load voltage dependence (capacitors are modelled as CZ loads) b) Remove the capaators m a l l e d c) For the current flows d e t e m e d m step a, fmd the capacitor set that rnmnuzes operahon cost d) Repeat steps a-c untll the capaator set installed 1s not altered

\ \\

El

S. STUDY CASE The overhead system illustrated in Fig2 was selected for the application of the methods presented It corns of five 20kV feeders, with 63 nodes and 80 branches There are 50 branch switches installed At the initlal configuratlon, shown m Rg2, 17

Figure 3 Optimum configuration for CJ loads. The steps followed applymg the two h e u r m c methods are flustrated m Fig4 ISEM gives succeSSlve radial configurahons

1341 with decreasing losses after each step Cw index is also continuously unproved SSOM begm from the meshed network (all switches closed) and by sequential switch o p e m g s radiahty is a c h e v e d The change of m i m u m losses after the optlmal flow at each step is illustrated in Fig 4 Lost energy / year (MWh) 3200-h

I

-

4 cw

-

200

- - - - _ _ - _

31001-

0

3000

-cs g

2 2800 0 -SSOM

2

4

-ISEM

6

8

10

12

*

Optlmum

16

14

2

4

-CZ

6

8

*

+MX

10

12

14

16 Steps

Optlmums

Figure 5 Reconfiguration results for other load models.

steps

--

Cw

Figure 4 Reconfiguration results for CJloads. From Fig4 it is clear that voltage improvement 1s also obtaned by network reconfiguratlon a m m g at loss redumon The numerical results are summarlzed in Table 1 Maxlmum voltage drop (AV,& 1s also presented

Configur ation

I

Cw

+ 1043 1043

2,77770 2B575 2,68752

1462 U70 U70

334483 3,08708 3,08708

1263

677 677

I

0 00 0 00

0 07 0 00

4 86 4 86

0 00 0 00

Table 2 Reconfiguration numerical results for other load models.

51.3 Initial state effects Table 1 Reconfiguration numerical results for CJloads The execution time of the two algorithms depends highly on the management of the data files required to account for the loads variation However, it should be noted that ISEM appears much faster (105 secs on a PC 386, 33 MHz for 16 different network loadings, while SSOM requires 477 secs)

51.2 Other load models The different load models are conadered and results are compared with those for CJ loads In particular, m x e d loads are considered consisting of 30% CJ loads, 25% CS and 45% CZ for the winter period and 30%, 4546, 25% respectively for the summer period The optimum configuration for CS and MX loads is the one illustrated in Fig3 (same with that for CJ loads) For CZ loads minimum energy loss 1s achieved by closlng branches C2-D7 and B4-Bl4 and opening branches D2-D7 and C9-Bl4 m R g 3

In order to examine the dependence of the heme methods on the initial status of the network swtches, both methods are apphed on a partlcularly poor initial configuratlon, resultlng in mtlal losses of 6,87356 MWh and CW = 781 Application of ISEM provides the optimum network configuratlon of R g 3 The mtial state conadered r e q u r e s 28% more time than the irutial state of Fig2 SSOM g v e s the Same results for CJ loads but 125% more tlme 1s r e q u r e d due to the meshed power flow method used For other load models SSOM g v e s no results, as voltage instabihty is noted

It can be concluded that irutial configuratlon affects ISEM results and SSOM computlng time Alternabve power flow methods could be used with SSOM for CS, CZ and MX loads when needed for special initial configuratlons

5.2 APPLICATION OF RECONFIGURATION AND CAPACITOR INSTALLATION METHODS

SSOM was applied and convergence to the optlmum for each load model 1s lllustrated in Fig6 The effect of those models on the network losses presents particular mteresi

In t& section, the mstallation of fixed capacltor banks at the network after reconfiguratlon 1s exarmned The general algorithm presented in sectlon 2 is applied

The numerical results are summanzed in Table 2

As mentloned, capacitor installatlon takes mto conaderatlon energy loss reduction, as well as capacltor cost to maxlrmze the net economical profit, and can be mplemented for all load models

It can b e noticed that load model hghly affects calculated losses The MX load model, w h c h can be conadered the most accurate, gives almost the Same results with CJ model However, load model does not seriously affect convergence to optunum configuration

In the followmg applicatlons installation of 300, 450, 600 and 900 CkVA capacitors is exarmned

1342 5.2.1 Constant current loads The ISEM is chosen for network reconfiguranon as the effects of capacitor installation can be more clearly illustrated After reconfiguration, capacitors are optunally installed at nodes (sizes in CkVA): A2 900, 83 900, B4 450, C2 900, D2 900, E2 600 and E3 900 (5550 CkVA in total) Configuration is slightly altered after this installation The results a r e given in Fig6 The final annual energy losses are 2,25093 MWh, which gives a total 2943% reduction of the initial losses Maximum voltage drop becomes 10 07%

i ; - - - p

3300 Lost energy

I

year

(MWh)

:I

3100

27001

Cepscllor lnslallallon

I

-190

2500

2100 '

"

-Losses

0

°

-c w

10 7

12/13 14 : Steps

Figure 6 Reconfiguration and capacitor installation for CJ

loads. 5.2.2 Other load models For CS loads the initial energy loss 1s 3,78811 MWh After reconfiguration, the following capamtors are installed: A2 900, B3 900, B4 600, C2 900, D2 900, D4 300, E2 600 and E3 900 CkVA (6000 CkVA in total) The resulting energy loss 1s reduced by 38 43% For CZ loads, the capacitors installed are: A2 900, E3 900, B4 450, C2 900, D2 900, E 2 600 and E3 900 CkVA (9550 CkVA in total), resulting in total energy loss reduction 1607% For MX loads, the capacitors mstalled are: A2 900, B3 900, B4 600, C2 900, D2 900, E2 600 and E 3 900 CkVA (5700 CkVA m total). resulting in total energy loss reduction 27 89% We observe that energy losses are seriously affected by the load model used, although there are not important differences in the proposed capacitors It is also interestmg that the results obtaned for CJ and MX loads are approximately the same This concluslon is in agreement with expenmental results publlshed in [91

6. CONCLUSIONS In this paper, a combined reactive power control and network reconfiguration method is presented and applied on a typical 20kV overhead network The effectiveness of the most widely used network reconfiguration methods for loss m i n i m t i o n is investigated taking into account the load modelling alternatives The most important conclusions are the followmg: -

-

In the cases considered, the same fmal configuranon is practically obtamed by any of the two methods, "Switch Exchange - SEM, o r "Sequential Switch Opening' - SSOM However, the first method requires substantially less computer time while the second method is independent from the initial configuration and thus more likely leads to the actual optimum Voltage quality is in general improved with loss reduction Load model substantially affects line losses, but has no

-

signlficant influence on the switching actions optimizmg network configuranon and on reactive power control by shunt capacitors Constant current load model appears to give the most accurate calculation results

REFERENCES U1. SCivanlar, J J G r a n g e r , H Yin, S H Lee, 'Dstnbution feeder

reconfiguration for loss reduction", IEEE Trans on Power Delivery, Vo13, July 1988 I21 A MerlinB Back, 'Search for a Minimal-Loss Operating SDannina Tree Confiauration for an Urban Power 6stribuGon System, Proc PSCC, Cambridge 1975, Paper 12/6 DSkmohammadi, H W Hong, 'Reconfiguration of Electric bstribunon Networks for Resistive Line Losses Reduction', IEEE Trans on Power Delivery, Vo14, April 1989 J B Bunch, R D Miller, J E Wheeler, 'Dstribunon System Integrated Voltage and Reactive Power Control", IEEE Trans on PAS, Vol PAS-101, No 2, Feb 1982 M Papadopoulos, P Polysos, A Facaros, K Mariolis, 'Selection of the Optimum Size and Location of Capacitor Banks on Medium Voltage Networks', CIRED 1983 M Papadopoulos, N D Hatuargyriou, M E Papadakis Graphics Aided Interactive Analysls of Radial Dmribution Networks , IEFE Trans on Power Delivery, Vol PWRD-2, Nr4, October 1987 A Brameller, R N Allan, Y M Hamam, Sparsity, Pitman Publlshmg Ltd, London, 1976 HDuran, 'Ophmum Number, Location, and Size of Shunt Capacltors in Radial Dstribution Feeders A Dynamic Programming Approach', IEEE Trans on Power Apparatus and Systems, Vol PAS-87, September 1968 E F Gorzelnik, Switching in Capacitors does not Reduce Real Power on Feeders, Electncal World, March 1988

AUTHOR BIOGRAPHIES G J Peponis was born in Preveza, Greece in 1961 He received the Dploma in Electrical Engineering from the Natlonal Technical Universlty of Athens, Greece in 1991 At present he is pursung postgraduate studies leading to the doctorate degree HE research deals with planning and design of h t r i b u t i o n systems and renewable energy sources M P Papadopoulos was born in Ioannina, Greece in 1932 He received the Dploma in Electrical and Mechanical Ehgineering in 1956 and the PhD degree in 1974 from the National Technical University of Athens, Greece In 1956 h e loined the Pubhc Power Corporation of Greece He has been engaged in the planning, deslgn, operation and control of rural and urban distribution networks, as well as in the utflization of electric energy From 1965 to 1970 and from 1972 to 1985 h e was also employed as a part-nme Assistant in the Electrical Ehgineering Department of NTUA He is currently Associate Professor in the same Department His m a n research interests concern distribution systems and renewable energy sources ND Hatziarayriou was born in Athens, Greece in 1954 He received the Dlploma in Electncal and Mechanical Ehgineermg from the National Technical University of Athens (NTUA), Greece in 1976 and MSc and PhD degrees from the University of Manchester Institute of Science and Technology (UMIST), Manchester, England in 1979 and 1982, respectwely He is currently Assoclate Professor at the Power Dvlsion of the Electrical Engmeering Department of NTUA His research interests mclude Modelling and Dgital Techniques for Power System Analysis and Control Dr Hatziargyriou is a senior member of IEEE and member of CIGRE and the Technical Chamber of Greece