Distribution Network Reconfiguration together with Distributed Generator and Shunt Capacitor allocation for Loss Minimization Partha P. Biswas, P.N. Suganthan
Gehan A. J. Amaratunga
School of Electrical and Electronic Engineering Nanyang Technological University, Singapore
[email protected],
[email protected]
Department of Engineering University of Cambridge, United Kingdom
[email protected]
Abstract—Distribution network accounts for a significant amount of real power loss in the power system. Minimization of losses in the network is desirable for economical and efficient operation of the system. One way of loss minimization is the optimal reconfiguration of the distribution network by selecting appropriate network switches to open. These open switches are termed as tie switches. As distribution network construction is closed loop, the open tie switches ensure that the radial nature of distribution network is maintained. The power loss can also be reduced by adding distributed generators (DGs) and shunt capacitors (SCs) locally near to the load points. This paper proposes an approach to simultaneously reconfigure the network, size and place both DGs and SCs in the network to minimize real power loss. LSHADE-EpSin algorithm is employed to perform the optimization task. Success history based parameter adaptation technique of differential evolution (DE) is termed as SHADE. LSHADE is the linear population size reduction technique of SHADE. LSHADE-EpSin introduces an additional adaptation technique for a control parameter during initial search stage to improve exploration capability. Standard IEEE-33 and IEEE-69 bus systems are tested with the algorithms. The results are found to be encouraging when compared with some of the recent studies. Keywords—Distribution network, real power loss, optimal reconfiguration, distributed generator, shunt capacitor.
I. INTRODUCTION Distribution network acts as the interface between transmission network and consumer load points. The configuration of the distribution network is usually closed-loop, though the operation is radial. The distribution network contains both sectionalizing and tie switches. Although fundamentally both switches are same, tie switches in the network are the switches that remain open to maintain radial nature of the network. Any sectionalizing switch (normally closed) of base configuration of the network can be opened during reconfiguration so that it becomes a tie switch. The optimal reconfiguration decides the appropriate switches, opening of which effect the minimum power loss. The process must ensure that no consumer is isolated and radiality of the network is retained. Distributed generators (DGs) like diesel generators, solar photovoltaics (PV), small wind turbines etc. and shunt capacitors (SCs) are also added to the radial distribution network (RDN) to boost capacity, reduce losses and improve voltage profile of the network. However, DGs and SCs need to be optimally placed and sized for efficient operation of the
distribution network. In summary, network reconfiguration and compensation must be optimal to minimize power loss while maintaining power balance and adhering to the limits on line capacities and bus voltages. Several literatures performed loss minimization with only reconfiguration of the network. Some metaheuristics recently applied to the problem include runner root algorithm (RRA) [1], cuckoo search algorithm (CSA) [2], modified bacterial foraging optimization algorithm (MBFOA) [3] and modified particle swarm optimization (MPSO) [4]. Many works concentrate on allocation of DGs and SCs to minimize system real power loss. Ref. [5] applies hybrid of harmony search and particle artificial bee colony algorithms to optimally place and size both DGs and SCs. Real and reactive power losses are minimized using decomposition based multi-objective evolutionary algorithm (MOEA/D) in [6]. In recent times, optimal sizing and siting of DGs and SCs are also performed using metaheuristics intersect mutation differential evolution (IMDE) [7] and back-tracking search algorithm (BSA) [8]. A limited number of studies [9-12] are available for simultaneous reconfiguration and allocation of DGs using fireworks algorithm (FWA) [9], adaptive cuckoo search algorithm (ACSA) [10], LSHADE algorithm [11] and heuristic method of uniform voltage distribution based constructive reconfiguration algorithm (UVDA) [12]. Though, to our best knowledge no literature performed optimal network reconfiguration together with optimal sizing and placement of both DGs and SCs. Our research presented in this paper uses LSHADE-EpSin algorithm for simultaneous reconfiguration and allocation of DGs and SCs. LSHADE-EpSin was a joint winner in realparameter single objective optimization competition in CEC 2016 on CEC 2014 benchmark problems [13]. DE and SHADE have successfully been implemented in optimal power flow problems [14,15]. The performance of LSHADE is found to be highly competitive in discrete location optimization problem of windfarm layout [16] and continuous variable optimization in hybrid active filter design [17]. LSHADE-EpSin has also been successfully applied to the problem of minimizing total harmonic distortion (THD) of multilevel inverters [18]. The current problem of RDN involves optimization of both discrete (bus no., switch no.) and continuous variables. As SHADE and variants of LSHADE are already proven to be effective in
optimizing both discrete and continuous variables, we adopt LSHADE-EpSin for the optimization task. In rest of the paper, problem formulation for simultaneous network reconfiguration is included in section II. Section III provides details of the power flow calculations performed in this work. The algorithm and its application are explained in section IV. Case studies, results and comparisons are included in section V, and finally conclusion is drawn in section VI. II. NETWORK RECONFIGURATION Fig. 1 and Fig. 2 show the base configurations for IEEE-33 and IEEE-69 bus systems, respectively. Bus (node) numbers are circled; normally closed sectionalizing switches are indicated with solid lines while normally open tie switches are with dotted lines. The numbers of closed sectionalizing switches and open tie switches must remain same before and after reconfiguration of the network. Therefore, opening of a closed switch must be
accompanied by closing of an open switch [11]. The opened sectionalizing switch naturally becomes the tie switch. As a first step of optimal reconfiguration, loops (assuming closing of all switches) are identified in the network. As can be observed from the diagrams, both the networks have 5 loops (Loop1 to Loop5). Now, from each loop one switch is to be opened to reinstate radial nature of the network. The disconnected switch must be unique for each loop and opening of the switch must not isolate any bus. The algorithm performs checks of all such possible switches to identify the best combination of tie switches. The process of identifying the tie switches, deciding locations and ratings of all DGs and SCs are simultaneous so that network loss is minimized. Outputs of the optimization algorithm are the identification numbers (labels) of tie switches, the bus numbers for allocating DGs and SCs and the ratings of DGs and SCs. III. POWER FLOW FORMULATION A simple radial feeder configuration is represented by the single line diagram in Fig. 3. Power flow is computed with the aid of following set of equations [6]:
Fig. 1: Base configuration of IEEE-33 bus distribution network
Fig. 2: Base configuration of IEEE-69 bus distribution network
0
1
k-1
P0 ,Q0
P1 ,Q1
k Pk-1 ,Qk-1
PL1 ,QL1
k+1 Pk ,Qk
PLk-1 ,QLk-1
N
Pk+1 ,Qk+1
PLk ,QLk
PN ,QN
PLk+1 ,QLk+1
PLN ,QLN
Fig. 3: Single line diagram of a radial feeder
= = |
−
−
−
−
| = | | −2 +
,
.
,
(1)
+ . | |
(2)
+
+
,
+ | |
.
,
. + . | | ,
,
(3)
is the real power and is the reactive power flowing where out of bus ; is the real load demand and is the reactive load demand at bus + 1. Resistance and reactance of and the line section between buses and + 1 are , , respectively. Bus has voltage magnitude of | |. The , ) in the line section connecting buses and power loss ( + 1 is calculated by: ( , + 1) =
.
,
+ | |
=
( , + 1)
(5)
It is assumed that the DG units can deliver active (real) power if only (e.g. solar PV). Therefore, a DG delivering power added to -th bus, loading of bus changes from to ( − ). The shunt capacitor of rating at -th bus is modelled as a reactive power injection device to that bus. During the optimization process, following constraints must be satisfied: ≤| |≤ ,
≤
,
Differential Evolution (DE) algorithm has mainly 3 control parameters: scale factor ( ), crossover rate ( ) and population size ( ). The parameters and are adapted in SHADE [19] based on historical memory of successful control parameters. The remaining control parameter population size ( ) is dynamically reduced following a linear function in LSHDAE [20]. LSHADE-EpSin [21] implements ensemble sinusoidal approach to adapt the parameter during initial search stage. The algorithm is briefly described herein. A. Initialization The DE process starts with initialization of candidate solutions within the feasible bounds [ , ] . E.g. -th component of the -th decision vector is initialized as: ( ) ,
(4)
) in the network is sum of all the line
Total power loss ( losses computed by:
IV. APPLICATION OF LSHADE-EPSIN ALGORITHM
=
+
,
[0,1](
,
−
,
)
(8)
where = 1 to and = 1 to with being the dimension of [0,1] is a random number between 0 and 1 the problem. and superscript ‘0’ denotes initialization. B. Mutation ( )
Mutation creates a donor/mutant vector at current generation corresponding to each population member ( ) . The algorithm implements referred to as the target vector ‘current-to-pbest/1’ mutation strategy: ( )
=
( )
+
( )
.
( )
−
( )
+
( )
.(
( )
−
( )
) (9)
(6) (
)
(7)
In this study, we consider = 0.90 p.u. and = 1.05 p.u., the minimum and maximum allowable voltage ranges for the system buses, respectively. Equation (7) defines the limits on current carrying capability of the line section between buses and + 1. It may be noted that current limits of the branches are not explicit and definite for IEEE bus systems. Moreover, as addition of DG and SC improve the voltage profile throughout the system, the current is reduced from the base configuration. Hence, check of the constraint in equation (7) is not essential by the algorithm.
& are mutually exclusive and selected The indices ( ) randomly from the range [1, Np]. refers to best × ( ∊ [0,1]) individuals of current generation. The scaling ( ) factor is a positive control parameter to scale the difference vectors in generation for the -th individual. If an ( ) element , of the mutant vector fails to satisfy the boundary conditions specified by [ , , , ], it is corrected as: ( ) ,
=
(
,
+
(
,
+
( ) ( ) , )/2 if , ( ) ( ) , )/2 if ,
< >
,
(10) ,
C. Parameter Adaptation In LSHADE-EpSin, an ensemble of decreasing and increasing sinusoidal adaptation techniques (in equations (11) ( ) and (12)) is used for for first half of total generations (i.e. ≤ /2): − ( ) = 0.5 ∗ sin(2 ∗ ∗ + )∗ +1 (11) ( )
∗ )∗
= 0.5 ∗ sin(2 ∗ =
and,
(μ
+1
(12)
, 0.1)
(13)
is adaptive and sampled from where is fixed, randomly Cauchy distribution with location parameter chosen from successful mean frequencies of previous generations. 0.1 is the scale parameter for Cauchy distribution. ( )
/2), is For second half of the generations (i.e. > adapted following same technique as in LSHADE. Throughout ( ) the generations, follows uniform adaptation strategy. Therefore, ( )
=
(μ ( )
=
( )
, 0.1) for (μ
>
( )
/2
(14)
, 0.1)
where is the initial population size, NFE is the current number of fitness evaluations, is the maximum is set to 4 because the number of fitness evaluations. mutation strategy of LSHADE requires minimum 4 individuals. ( + 1) < ( + 1)] numbers of If ( ), [ ( )− worst ranked individuals are deleted from the population [20]. A summary of the steps involved in the algorithm is provided herein: A. Input and initialization: 1. Input , 2. Define decision vector and range of all its elements. such vectors 3. Generate initial population of defined as in equation (8). 4. Set generation counter = 0, dynamic population size ( )= , evaluation counter = 1, control ( ) ( ) parameters μ =μ = 0.5 and = 0.5. B. Algorithm loop: 1.
where ( , 0.1) is the value sampled form normal ( ) distribution with mean and variance 0.1; ( ) , 0.1) is sampled from Cauchy distribution with ( ( ) ( ) and scale parameter 0.1. Both location parameter ( ) and are initialized to 0.5 and updated thereafter based on successful mean and location parameter values using weighted Lehmer mean [19,20].
2. 3. 4. 5. 6. 7.
trial or offspring vector
( )
( ) , ,
=(
( )
( ) , ,…..,
combining its elements with the target vector
forms the ( ) , ) ( )
.
by The
( )
controls the probability of crossover. crossover rate Binomial crossover scheme for an element is expressed as: ( ) ,
where [1, ].
=
( ) , if
=
or
,
[0,1] ≤
( ) , otherwise
( )
,
(16)
is a randomly selected natural number in the range
E. Linear population size reduction (LPSR) The concept of population size reduction following a linear function was introduced in LSHADE. After each generation , the population size in next generation + 1 is computed by: ( + 1) =
−
.
+
(17)
, i.e.
as per equation (5) for
where = 1 to . Increase counter NFE by i.e. NFE = NFE + . do while termination criteria < for = 1 to do --------------( ) ( ) Adapt control parameters and as per equations (11) to (15). ( ) Perform mutation to generate vector as per equation (9). ( ) Perform crossover to generate element , as per equation (16). Evaluate
( )
i.e.
as per equation (5) for
( )
D. Crossover Through crossover operation, donor vector
( )
( )
(15)
( )
Evaluate
8.
. Increase evaluation counter NFE by 1 i.e. NFE = NFE+1. Select best fit individuals for next generation. If, ( ) ( ) ( ) ( ) u( ) ≤ , = . Else = ( )
.
End for loop. -----------------( + 1) 9. Update population size for next generation as per LPSR strategy in equation (17). 10. Increase generation counter = + 1. Go to step 2 of algorithm loop. The dimensions of various case studies for the problem and other useful parameters are listed in Table I. Case 11 and Case 21 are for network reconfiguration only for IEEE-33 and IEEE69 bus systems, respectively. As 5 switches are to be identified for each loop of a network, the number of decision variables for these cases is 5. Selected population size here is 100. It is assumed that maximum 3 DGs and 3 SCs can be added to the network. Case 12 and Case 22 deal with optimal sizing and siting of these added components. Therefore, a total of 12
TABLE I. LSHADE-EPSIN ALGORITHM PARAMETERS Parameter Dimension of optimization problem, d Initial population size, Maximum no. of fitness evaluations,
Network and case no. IEEE-33 bus IEEE-69 bus Case 11 Case 21 Case 12 Case 22 Case 13 Case 23 Case 11 Case 21 Cases 12 & 13 Cases 22 & 23 Cases 11, 12 & Cases 21, 22 & 13 23
Value 5 12 17 100 150 50000
variables (6 locations + 6 ratings) are to be optimized for these cases. As Case 13 and Case 23 are for simultaneous reconfiguration and allocation of the components, the number of variables in each case is 17. The selected population size for Cases 12, 13, 22 and 23 is 150. Maximum 50,000 fitness evaluations are performed for each study case. V. CASE STUDIES, RESULTS AND COMPARISONS The study cases are discussed, results are summarized, analyzed and compared with equivalent past studies in this section. Each study case is run for 5 times and results are found to be consistent with negligible variations among different runs. IEEE-33 bus system has a total load of 3.72 MW and 2.30 MVAR; while IEEE-69 bus has the loading of 3.80 MW and 2.69 MVAR. Line and load data for the networks can be referred in [22]. In the study cases of network reconfiguration (Case 11 and Case 21), LSHADE-EpSin achieves the lowest loss data alongwith some other algorithms listed in Table II. The minor variation in results for Case 21 is due to approximation of some network data. As observed from the results of Case 21, any switch among 55, 56, 57 and 58 can be opened in the corresponding loop without notable change in network loss value. TABLE II. SIMULATION RESULTS AND COMPARISON FOR NETWORK RECONFIGURATION ONLY Case no. Case 11 (33-bus)
Algorithm
LSHADEEpSin RRA [1] CSA [2] FWA [9] ACSA [10] UVDA [12] Case 21 LSHADE(69-bus) EpSin CSA [2] FWA [9] ACSA [10] UVDA [12] [a] recalculated values
Open switches 7, 9, 14, 32, 37
Power loss (kW) 139.55
Min. voltage, p.u. (bus no.) 0.9378 (32)
7, 9, 14, 32, 37 7, 9, 14, 32, 37 7, 9, 14, 28, 32 7, 9, 14, 28, 32 7, 9, 14, 32, 37 14, 55, 61, 69, 70
139.55 139.55[a] 139.98 139.98 139.55 98.60
0.9378 (32) 0.9378 (32) 0.9413 (32) 0.9413 (32) 0.9378 (32) 0.9495 (61)
14, 57, 61, 69, 70 14, 56, 61, 69, 70 14, 57, 61, 69, 70 14, 58, 61, 69, 70
98.59[a] 98.59 98.59 98.58
0.9495 (61) 0.9495 (61) 0.9495 (61) 0.9495 (61)
In Case 12 and Case 22, both DGs and SCs are optimally sized and placed in the networks to minimize real power loss. To compare with past results, the penetration of DG is limited to 2 MW for 33-bus system and 2.25 MW for 69-bus system [6]. For SC, the total cumulative ratings are restricted to 2.3 MVAR
and 2.69 MVAR for 33-bus and 69-bus systems, respectively [6]. Further, we consider that the network can be augmented with 3 DGs and 3 SCs for the objective of loss minimization. In Case 12, LSHADE-EpSin attains power loss of 19.37 kW, least when compared with other algorithms listed in Table III. Lowest loss of 5.81 kW is achieved in Case 22 with LSHADE-EpSin algorithm for 69-bus network. It may be noted that total installed capacity of DG is almost same for LSHADE-EpSin, MOEA/D [6] and IMDE [7]. However, higher numbers of evenly distributed components are more effective in reducing losses. It is worthwhile to note that due to physical limitations of installation and sometimes for economic viability, the total number of added components is restricted. The last column indicates minimum voltage in the system and the bus that experiences it. Alongwith lowest loss value, recommended allocation of compensating components by LSHADE-EpSin leads to minimum voltage deviation from 1 p.u. TABLE III. SIMULATION RESULTS AND COMPARISON FOR DG AND SC ALLOCATION ONLY Case no. Algorithm
Case 12 (33-bus)
LSHADEEpSin MOEA/D [6] IMDE [7]
Case 22 (69-bus)
Hybrid [5] BSA [8] LSHADEEpSin MOEA/D [6] IMDE [7]
DG rating in kW (bus no.) 665 (14) 446 (25) 889 (30) 840 (13) 1140 (30) 1080 (10) 896.4 (31) 2531 (6) 2500 (6) 310 (12) 313 (21) 1627 (61) 520 (17) 1731 (61) 479 (24) 1738 (62)
SC rating in kVAR (bus no.) 950 (3) 341 (14) 1009 (30) 453 (12) 1040 (30) 254.8 (16) 932.3 (30) 1250 (30) 1243.6 (6) 582 (12) 881 (49) 1227 (61) 353 (17) 1239 (61) 1192 (61) 109 (63)
Power loss (kW) 19.37
Min. voltage, p.u. (bus no.) 0.9863 (8)
28.47
0.9800 (25)
32.08
0.979 (25)
58.45 58.37 5.81
0.9536 (18) 0.9943 (65)
7.20
0.9943 (69)
13.83
0.9915 (68)
The performance and results of LSHADE algorithm on case study of simultaneous reconfiguration and only DG allocation have been presented in ref. [11]. Here, Case 13 and Case 23 deal with simultaneous reconfiguration and allocation of two types of components – DG and SC. The numbers and maximum cumulative ratings of added DGs and SCs are same as in Case 12 for 33-bus system and Case 22 for 69-bus system. The network operation is most efficient when allocations of DGs and SCs are accompanied by network reconfiguration as seen in Table IV. In Case 13, LSHADE-EpSin attains minimum power loss of 15.63 kW by network reconfiguration together with optimal addition of total 2 MW of DGs and 2.3 MVAR of SCs. Like 33-bus system, Case 23 of 69-bus system incurs minimum power loss of 4.82 kW when simultaneous network reconfiguration and optimum addition of total 2.25 MW of DGs and 2.69 MVAR of SCs are executed. The voltage profiles for various case studies of IEEE-33 bus system are portrayed in Fig. 4. The profile is best for Case 13 when network reconfiguration is accompanied by allocation of DGs and SCs. Voltage profile is also acceptably uniform in
Case no. Parameter Case 13 Open switches (33-bus) Real power loss (kW) DG rating in kW (bus no.) SC rating in kVAR (bus no.) Min. voltage, p.u. (bus no.) Case 23 Open switches (69-bus) Real power loss (kW) DG rating in kW (bus no.) SC rating in kVAR (bus no.) Min. voltage, p.u. (bus no.)
LSHADE-EpSin results 7, 11, 12, 17, 26 15.63 557 (15), 813 (25), 630 (32) 703 (3), 399 (9), 1198 (30) 0.9891 (12) 14, 17, 69, 72, 73 4.82 394 (12), 200 (21), 1656 (61) 528 (12), 934 (49), 1228 (61) 0.9956 (17)
Case 12 with selected distribution of DGs and SCs. Fig. 5 shows bus voltage profiles for case studies pertaining to IEEE 69-bus system. Similar to 33-bus system, voltage profile is the best in Case 23 of simultaneous reconfiguration, DG and SC allocation. Both the diagrams also establish that the voltage constraint (from 0.90 p.u. to 1.05 p.u.) is duly satisfied in all the study cases involving the two distribution networks.
can still be observed beyond half of the total fitness evaluations. Further, one complete run of Case 13 for 33-bus system with 50,000 fitness evaluations takes about 5-6 minutes to complete in MATLAB on a personal computer with Intel Core i5 CPU @2.7GHz and 4GB RAM. 60 Case 13 50 Power loss (kW)
TABLE IV. RESULTS FOR SIMULTANEOUS RECONFIGURATION, DG AND SC ALLOCATION
Case 23
40 30 20 10 0 0
10000
20000 30000 40000 Number of fitness evaluations
50000
Fig. 6: Convergence of LSHADE-EpSin for Case 13 and Case 23
1.01
VI. CONCLUSION
1
Voltage (in p.u.)
0.99 0.98 0.97 0.96 Case 11 Case 12 Case 13
0.95 0.94 0.93 1
5
9
13
17 Bus no.
21
25
29
33
Fig. 4: Bus voltage profiles for various case studies of 33-bus system 1.01
ACKNOWLEDGMENT
1
This project is funded by the National Research Foundation Singapore under its Campus for Research Excellence and Technological Enterprise (CREATE) program.
0.99 Voltage (in p.u.)
This paper discusses an application approach of LSHADEEpSin algorithm in minimizing real power loss in the distribution network. The mixed integer non-linear problem with both discrete and continuous variables has been successfully optimized by the algorithm. Further, network operation is found to be most efficient when reconfiguration is simultaneously accompanied by DG and SC allocation. The suggested approach in this study leads to the lowest real power loss among comparable algorithms. The total allowable installed capacities of DGs and SCs have been fully and effectively utilized. In future, the effectiveness of the algorithm can further be explored on networks with even larger number of buses.
0.98 0.97
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0.96
[1]
Case 21 Case 22 Case 23
0.95 0.94 1
7
13
19
25
31 37 43 Bus no.
49
55
61
67
Fig. 5: Bus voltage profiles for various case studies of 69-bus system
Fig. 6 indicates convergence of the algorithm for Case 13 and Case 23. In first half of the generations (i.e. upto 25000 fitness evaluations), the adaptation technique of scale factor is designed to perform exploration in the search space. During second half of the generations, the algorithm exploits the solutions obtained to arrive at global optima. The convergence of the algorithm thus
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