Optimal Reconfiguration and Distributed Generator ...

Optimal Reconfiguration and Distributed Generator allocation in Distribution Network using an advanced Adaptive Differential Evolution Partha P Biswas1, R. Mallipeddi2

P.N. Suganthan1, Gehan A J Amaratunga3

Nanyang Technological University, Singapore Kyungpook National University, South Korea [email protected], [email protected]

3 University of Cambridge, United Kingdom [email protected], [email protected]

1

2

Abstract—Power loss in an electrical network is unavoidable due to its inherent resistance. However, for economical and efficient operation, the network loss shall be minimized to the extent possible. Construction of the distribution network is usually closed loop, though operation is radial with opening of a suitable sectionalizing switch that disconnects a branch in the loop. This process of reconfiguration i.e. selection of sectionalizing switch is done in a way such that system loss in minimized. Another effective way of reducing power loss is addition of distributed generators (DGs) locally to the system nodes (buses). DG size and location also need to be optimized for minimization of real power loss. This paper presents an application of a metaheuristic to simultaneously allocate DGs and perform reconfiguration of a couple of standard radial distribution networks. Both location and placement of the DG are optimized by the algorithm. As an obvious fact, the optimization problem is a combination of discrete (location) and continuous (rating) variables. Linear population size reduction technique of success history based adaptive differential evolution (L-SHADE) is implemented to perform the optimization task with objective of minimizing network real power loss. The algorithm is tested on standard IEEE 33-bus and 69-bus radial distribution networks. The simulation results are found to be promising and highly competitive when compared with results of other equivalent algorithms. Keywords—Distribution network, real power loss, distributed generator, optimal reconfiguration, L-SHADE algorithm.

I. INTRODUCTION The distribution system network accounts for a significant amount of power loss, sometimes in the order of 10-13% of the generated output [1]. High distribution loss means inefficiency and poor voltage regulation of the network. To increase efficiency and enhance voltage regulation of the system, network is to be properly reconfigured. In addition, locally added distributed generations (DGs) in the form of a diesel generator, solar photovoltaics (PV), a wind turbine etc. can reduce losses, improve voltage profile and boost capacity of the system. However, reconfiguration of the network or allotment of the DG cannot be random as it might result in inefficient performance and unintended operation of the network. Radial arrangements of the feeders in the network must be maintained after reconfiguration. Size and placement of the DG shall be optimized such that power loss is minimized satisfying system constraints on power balance, line capacity and bus voltage.

Loss minimization by only reconfiguration of the networks is performed in many literatures. Some of the recent studies that implement evolutionary algorithms (EAs) for the optimization task are with fireworks algorithm (FWA) [2], cuckoo search algorithm (CSA) [3], modified bacterial foraging optimization algorithm (MBFOA) [4] and modified particle swarm optimization (MPSO) [5]. Further, several works concentrate on optimization of DGs only to minimize system loss. Handpicked studies in recent times focus only on allotment of DGs are ref. [6] where analytical approach is taken, ref. [7] where genetic algorithm (GA) is adopted and ref. [8] where hybrid method with ant colony optimization (ACO) and artificial bee colony (ABC) is applied. A limited number of studies have been performed for simultaneous system reconfiguration and allocation of DGs. Incidentally maximum reduction in loss can be achieved with this approach. Reference [9] employed fireworks algorithm (FWA) to perform the optimization task. Adaptive cuckoo search algorithm (ACSA) [10] improved the past results by FWA. A heuristic method named uniform voltage distribution based constructive reconfiguration algorithm (UVDA) [11] reported some of the best results on the problem of network reconfiguration accompanied by DG allocation. Our research presented in this paper uses L-SHADE algorithm, a well-established optimization algorithm for the constrained, multimodal non-linear problems. L-SHADE improves the performance of success history based adaptive differential evolution (SHADE) with progressive linear reduction of population size. The algorithm performed best among non-hybrid algorithms for the optimization of real parameter single-objective function in CEC 2014 competition [12]. L-SHADE has successfully been applied to the problems of discrete location optimization of wind turbines in a windfarm [13], total harmonic distortion minimization in multilevel inverters [14] and hybrid active power filter parameter optimization [15]. Motivated by the growing application and encouraging performance of the algorithm in power domain, we further investigate its usefulness on the problem of distribution network. Minimization of power loss in the distribution network is set as the objective with optimal reconfiguration and DG allocation. The algorithm simultaneously optimizes DG size and location (bus no.) and reconfigures the network. IEEE standard 33-bus and 69-bus radial distribution networks are studied under

the purview of this literature and simulation results are found to be among the best. In rest of the paper, problem formulation for simultaneous network reconfiguration and power flow are included in section II. Section III provides detail of the study cases performed in this work. The algorithm and its application are explained in section IV. Simulation results and comparisons are included in section V, finally ending with conclusion in section VI. II. MATHEMATICAL FORMULATION The aim of this paper is to decide optimal reconfiguration alongwith DG allocation in the radial distribution network. In following sub-sections, the approach to maintain the radial nature of the network after reconfiguration and power flow equations are described. A. Network reconfiguration Fig. 1 and Fig. 2 show the base configurations for 33-bus and 69-bus systems respectively with dotted lines representing

normally open tie switches. Nodes (buses) are numbered within the circles. As a first step to apply the algorithm for optimal reconfiguration, all sectionalizing and tie switches of the network are closed. This process creates certain loops in the network marked as Loop1 to Loop5 in the diagrams. Thereafter, any one switch (either tie or sectionalizing) in the loop is opened to maintain the radial nature of the network. The switch must be unique for each loop and opening of the switch should not isolate any node (bus) in the network. The algorithm performs several iterations to come up with the switch numbers, opening of which minimizes the power loss. It must be noted that this operation and allocation of DG are simultaneous. Output solutions of the algorithm are the suggested switches for opening together with optimal sizes and locations of DGs that minimize network loss. B. Power flow formulation Fig. 3 represents single line diagram of a radial feeder configuration. Computation of power flow is performed using a set of recursive equations on active power, reactive power and bus voltages [16]:

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

PLk ,QLk

N

Pk+1 ,Qk+1

PLk+1 ,QLk+1

PN ,QN

PLN ,QLN

Fig. 3: Single line diagram of a radial feeder

|

=

−

−

=

−

−

| = | | −2 +

,

,

.

,

+ | |

(1)

.

+ | |

(2)

+

+

,

.

. + . | |

III. STUDY CASES

,

,

(3)

and are the real and reactive power flowing out of where, bus ; and are the real load and reactive load at bus + 1. The line section between buses and + 1 has a and a reactance of , . Magnitude of resistance of , ) in the line voltage of bus is | |. The power loss ( section connecting buses and + 1 is computed by: ( , + 1) =

.

,

+ | |

(4)

Total power loss ( ) in the network is summation of all the line losses calculated by: =

( , + 1)

(5)

This study considers that the DG units supply only real power with unity power factor (e.g. solar PV). Hence, a DG delivering when added to -th bus, the loading of that output power bus changes from to ( − ). The algorithm checks all possible locations with all probable ratings of the DGs during the search process to find the most optimum allocation. During the process of network reconfiguration and DG addition, following constraints of the network must be satisfied: ≤| |≤ ,

≤

,

(6) (

)

the currents in base case. Therefore, it is not essential to check this constraint during optimization.

(7)

where, equation (6) is for allowable voltage magnitude range of and . In this study, we consider bus between = 0.90 p.u. and = 1.05 p.u. Equation (7) defines the constraint on current carrying capacity of the line between buses and + 1. Branch current limits of the standard IEEE bus systems are not definite and explicit. Further, as voltage profile is improved throughout the network with network reconfiguration and DG allocation, branch currents reduce from

The study cases performed for the two distribution networks are discussed in this section. Scenarios of only reconfiguration, only DG allocation and simultaneous reconfiguration and DG allocation are considered in case studies. It is worthwhile to note that number and total power of the added DGs play vital roles in the obtained final loss of the network. Increase in number of DGs beyond a certain value may not be technically and/or commercially feasible. Again, DG penetration cannot be too high; else the network might turn into an active network. Too large cumulative rating of added DGs might increase short circuit levels of the components connected to the system. Therefore, we judiciously limit the number and penetration of the DGs in line with some past literatures for fair and valid comparison of current results with previously reported results. TABLE I. SUMMARY OF STUDY CASES Network

Case no. Case description

33-bus

Case 1 Case 2 Case 3

69-bus

Case 4 Case 5 Case 6

Only reconfiguration Only DG allocation Simultaneous reconfiguration and DG allocation Only reconfiguration Only DG allocation Simultaneous reconfiguration and DG allocation

No. of DGs 3 3

Max DG penetration 2.5 MW 2.5 MW

3 3

2.5 MW 2.5 MW

Total load of 33-bus network is 3.72 MW and 2.30 MVAr, while that of 69-bus network is 3.80 MW and 2.69 MVAr. Line parameters and detailed data on load demands for the networks are provided in [17]. A summary of the case studies is presented in Table I, where it can be observed that the number of DGs is limited to 3. Minimum rating of DG is set to 200 kW for practicability of application with cumulative rating of all DGs in the network not to exceed 2.5 MW. IV. APPLICATION OF L-SHADE ALGORITHM During the last decade, Differential evolution (DE) evolved as an efficient and powerful population-based stochastic search technique for solving optimization problems over continuous search spaces [18]. As the performance of conventional DE is highly dependent on the settings of the scaling factor (F), the crossover rate (CR), the population size (Np), and the chosen

mutation/crossover strategies [19], different ideas have been proposed. In SHADE [20], the control parameters F and CR are adapted during evolution based on success history of the parameters. As a further improvement, in addition to F and CR, control parameter population size (Np) is reduced linearly over successive generations in L-SHADE [21]. A brief description of L-SHADE and its application to distribution network problem are presented in this section.

0.1 signifies variance and scale parameter for the corresponding ( ) ( ) distributions. μ & μ are randomly chosen from the memory where the scale factors and crossover rates of successful candidates of previous generations are stored. These two values are initialized to 0.5 and subsequently modified by weighted Lehmer mean, the detail is in reference [20,21]. D. Crossover ( )

A. Initialization The process of DE starts with an initial population (Np vectors with d dimensions) of randomly generated candidate solutions within the search space specified by lower and upper bounds. In the population, the jth component of the ith decision vector is initialized as: ( ) ,

=

,

+

[0,1](

,

−

,

)

(8)

[0,1] is a random where i = 1 to Np and j = 1 to d. number between 0 and 1 and superscript ‘0’ signifies initialization. B. Mutation After initialization, corresponding to each member in the ( ) population referred to as target vector , a donor/mutant ( ) is generated at current generation t through mutation vector operation. In the current work, the mutation strategy adopted is referred as ‘current-to-pbest/1’: ( )

=

( )

+

( )

.

( )

−

( )

+

( )

.(

( )

−

( )

In the crossover operation, donor vector combines its ( ) to form the trial/offspring elements with the target vector ( ) ( ) ( ) ( ) = ( , , , , … . . , , ) . Binomial crossover is vector commonly adopted to operate on each variable. The binomial ( ) is expressed as: crossover with crossover rate ( ) ,

=

( ) , if

=

or

,

( )

[0,1] ≤

( ) , otherwise

,

(13)

where K is any randomly chosen natural number in the range [1, ], where d is the dimension of the problem. E. Selection Selection process determines if the trial (offspring) vector is going to replace the target vector at next generation t+1 by performing the following comparison: (

)

=

u

( )

if

u ( )

( )

≤

( )

,

otherwise

(14)

) (9) where f(.) is the objective function to be minimized.

& are randomly selected from the range The indices ( ) [1, Np] and are mutually exclusive; is chosen from the top × ( ∊ [0,1]) individuals of current generation. The ( ) scaling factor is a positive control parameter for scaling the difference vectors corresponding to the ith individual at the tth ( ) generation. If an element , of the mutant vector fails to satisfy the boundary conditions specified by [ , , , ], it is corrected as: ( ) ( ) ( , + , )/2 if , < , ( ) = (10) , ( ) ( ) ( , + , )/2 if , > , C. Parameter Adaptation At a given generation t, each individual generates a new trial ( ) ( ) (offspring) vector with its associated parameters and which are adapted using – ( ) ( ) ( )

= =

(μ (μ

( )

, 0.1) , 0.1)

( )

( )

(11) (12)

, 0.1) & (μ , 0.1) are sampled where (μ values from Normal and Cauchy distributions with mean ( ) ( ) μ and location parameter μ , respectively. The value

F. Linear population size reduction (LPSR) The achievement of SHADE that employs success history based adaptation technique of scaling factor F and crossover rate CR has been demonstrated in [20]. In addition, it has been also discovered that dynamic reduction of population size (Np) accelerates the performance of SHADE. Therefore, L-SHADE was proposed where the population is reduced over generation and the size of population reductions is determined by a linear function given in equation (15). After each generation t, the population size in the next generation t+1 is calculated by – ( + 1) =

.

+

(15)

is set to 4 because the selected mutation strategy requires minimum 4 individuals. is the initially selected population size while and NFE are the maximum number of fitness evaluations and current number of fitness ( + 1) < evaluations, respectively. If ( ) , a total of [ ( )− ( + 1)] worst individuals are deleted from the population [21]. A summary of steps involved in the algorithm is described herein -

A. Input and initialization: 1. Input , 2. Define vector and range of all its elements. such vectors 3. Create random initial population of defined as as per equation (8). 4. Set generation counter t = 0, dynamic population size ( )= , evaluation counter = 1 and ( ) ( ) control parameters μ =μ = 0.5. B. Algorithm loop: ( ) , i.e. as per equation (5) for 1. Evaluate ( ) where i = 1 to Np. Increase counter NFE by Np i.e. NFE = NFE + Np. 2. while termination criteria < do 3. for i = 1 to Np do --------------( ) ( ) 4. Adapt control parameters and as per equations (11) & (12). ( ) 5. Perform mutation to generate vector as per equation (9). ( ) 6. Perform crossover to generate element , as per equation (13). ( ) 7. Evaluate i.e. as per equation (5) for ( ) . Increase evaluation counter NFE by 1 i.e. NFE = NFE+1. 8. 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 (15). 10. Increase generation counter t = t+1. Go to step 2 of algorithm loop. TABLE II. L-SHADE ALGORITHM PARAMETER Parameter

Case no.

Value

Dimension of optimization problem, d

Case 1 & 4 Case 2 & 5 Case 3 & 6 Case 1, 2, 4 & 5 Case 3 & 6 Case 1, 2, 4 & 5 Case 3 & 6

5 6 11 100 120 20,000 25,000

Initial population size, Maximum no. of fitness evaluations,

Table II lists the dimensions of the optimization problem for various study cases and also applied parameters for L-SHADE algorithm. Cases 1 and 4 are for network reconfiguration only. As mentioned before, 5 loops are recognized for each network. A unique sectionalizing switch is to be identified in each loop for opening. Therefore, a total of 5 decision variables are to be optimized in these cases. Cases 2 and 5 are for allotment of suitably rated 3-DGs. The candidate bus for allocation of a DG can be any bus in the network. 3 variables represent 3 locations (buses) in the network while remaining 3 signify ratings of all

the 3-DGs. As cases 3 and 6 are for both reconfiguration and DG allocation, the number of decision variables in these cases is 11. Due to higher number of variables in cases 3 and 6, initial population sizes are selected a little larger than the remaining cases. Increasing the population size beyond 120 does not have notable impact in the outcome as number of fitness evaluations performed for these cases is also higher. It may be noted that initial population size and maximum number of fitness evaluations are selected after several trials of the algorithm. V. RESULTS AND COMPARISONS Simulation results with application of L-SHADE algorithm are analyzed in this section. Each study case is run 5 times and results are found to be consistent with negligible variations among different runs. Table III summarizes the results together with comparison of present study with similar past studies. The best loss values among comparable algorithms are highlighted in bold fonts. Selected DG ratings are included in the tables with bus nos. to allocate the DGs are provided in parentheses next to the selected optimal ratings. In case 1 of network reconfiguration for 33-bus system, algorithm L-SHADE achieves lowest loss value alongwith UVDA [11]. Results of similar study case 4 for 69-bus system are same for all the algorithms. Little variation in decimal places is observed possibly due to rounding off some numerical values of network parameters. Change in opening of any switch among 55, 56, 57 and 58 in corresponding loop does not affect the final output results. In study case 2 of DG siting and sizing for 33-bus system, algorithm L-SHADE attains real power loss value of 72.90 kW, least among all. Another important aspect to note on this study result is cumulative rating for the DGs. While L-SHADE limits the total rating to 2.5 MW, ACSA [10] selected more than 3.2 MW. The difference is significant as larger DG rating incurs higher cost of installation. Output results of UVDA [11] with a total cumulative DG rating of about 2.7 MW are better than ACSA [10]. On voltage regulation front, high DG rating helps to maintain slightly better voltage profile as can be observed from results of ACSA [10]. However, voltage regulation is not the primary objective of this optimization. Study case of DG allotment for 69-bus system is case 5 where remarkably low loss figure of 69.60 kW is realized in present study. Like case 2, ACSA [10] selects largest total rating for the DGs. In case 3 of simultaneous reconfiguration and DG allocation in 33-bus network, present study reports a loss value of 53.15 kW, almost same as reported by ACSA [10]. However, total selected DG rating by ACSA [10] is about 3.3 MW, close to 90% loading of the network. L-SHADE optimally distributes a total of 2.5 MW of DG power and suitably reconfigures the network such that lowest loss can be achieved with minimum rating of the DG. It may be noted that reference [9] adopted sequential approach in placing and sizing the DGs. After network reconfiguration, candidate buses are identified for DG allocation followed by DG capacity optimization. However, as

TABLE III. SIMULATION RESULTS AND COMPARISON WITH PAST STUDIES

33-bus

69-bus

a. DG

Case no. Case 1

Case description Only reconfiguration

Case 2

Only DG allocation

Case 3

Simultaneous reconfiguration and DG allocation

Case 4

Only reconfiguration

Case 5

Only DG allocation

Case 6

Simultaneous reconfiguration and DG allocation

Parameter Open switches Real power loss (kW) Min. bus voltage, p.u. (bus no.) Open switches Real power loss (kW) DG sizes in kW (bus no.) Min. bus voltage, p.u. (bus no.) Open switches Real power loss (kW) DG sizes in kW (bus no.) Min. bus voltage, p.u. (bus no.) Open switches Real power loss (kW) Min. bus voltage, p.u. (bus no.) Open switches Real power loss (kW) DG sizes in kW (bus no.) Min. bus voltage, p.u. (bus no.) Open switches Real power loss (kW) DG sizes in kW (bus no.)

Min. bus voltage, p.u. (bus no.) location and size are optimized sequentially

observed from results of other methods, simultaneous siting and sizing of DGs are more effective in reducing system losses. In case 6 for 69-bus system, the minimum real power loss of 35.54 kW is achieved by L-SHADE algorithm with total added capacity for the DGs is capped at 2.5 MW. When compared with UVDA [11], the loss is about 1.5 kW lower with about 200 kW less total proposed capacity of the DGs. Fig. 4 shows voltage profiles of the network buses for various study cases performed for IEEE 33-bus system. Voltage profile is the best when network reconfiguration is accompanied by optimal sizing and placement of the DGs. 1

UVDA [11] 7, 9, 14, 32, 37 139.55 0.9378 (32) 33, 34, 35, 36, 37 74.21 875 (11), 931 (24), 925 (29) 0.962 (33) 7, 10, 13, 27, 32 57.29 649 (15), 486 (21), 1554 (29) 0.976 (32) 14, 58, 61, 69, 70 98.58 0.9495 (61) 69, 70, 71, 72, 73 72.63 604 (11), 417 (17), 1410 (61) 0.9688 (65) 14, 58, 63, 69, 70 37.11 538 (11), 673 (17), 1472 (61) 0.9816 (63)

1.01 1 0.99 0.98 0.97 0.96 Case-4

0.95

Case-5

Case-6

0.94 1

1.01

Various optimization algorithm FWA [9] ACSA [10] 7, 9, 14, 28, 32 7, 9, 14, 28, 32 139.98 139.98 0.9413 (32) 0.9413 (32) 33, 34, 35, 36, 37 33, 34, 35, 36, 37 88.68 74.26 589.7 (14), 779.8 (14), 189.5 (18), 1125.1 (24), 1014.6 (32) 1349.6 (30) 0.9680 (30) 0.9778 (33) 7, 11, 14, 28, 32 11, 28, 31, 33, 34 53.21 67.11a 531.5 (18), 964.6 (7), 615.8 (29), 896.8 (18), 536.7 (32) 1438.1 (25) 0.9713 (14) 0.9806 (31) 14, 56, 61, 69, 70 14, 57, 61, 69, 70 98.59 98.59 0.9495 (61) 0.9495 (61) 69, 70, 71, 72, 73 69, 70, 71, 72, 73 77.85 72.44 225.8 (27), 602.2 (11), 1198.6 (61), 380.4 (18), 408.5 (65) 2000 (61) 0.9740 (62) 0.9890 (65) 13, 55, 63, 69, 70 14, 58, 61, 69, 70 37.02 39.25a 1127.2 (61), 541.3 (11), 275.0 (62), 1724.0 (61), 415.9 (65) 553.6 (65) 0.9796 (61) 0.9869 (50)

L-SHADE 7, 9, 14, 32, 37 139.55 0.9378 (32) 33, 34, 35, 36, 37 72.90 733.9 (14), 733.5 (25), 1032.6 (30) 0.9658 (33) 7, 9, 14, 27, 30 53.15 523.8 (12), 779.6 (18), 1196.6 (25) 0.9688 (31) 14, 55, 61, 69, 70 98.60 0.9495 (61) 69, 70, 71, 72, 73 69.60 423.1 (11), 380.4 (18), 1696.5 (61) 0.9776 (65) 14, 58, 61, 69, 70 35.54 517.6 (11), 559.4 (27) 1423.0 (61) 0.9811 (61)

Voltage (in p.u.)

Network

7

13

19

25

31 37 43 Bus no.

49

55

61

67

Fig. 5: Bus voltage profiles of 69-bus system for various case studies

Voltage (in p.u.)

0.99

Fig. 5 is for bus voltage profiles of various study cases for IEEE 69-bus system. Justifiably best profile is observed in case 6 of simultaneous reconfiguration and DG allocation. In both the diagrams of voltage profiles, clearly voltage limits (0.90 p.u. – 1.05 p.u.) for the network buses are duly compiled in all study cases.

0.98 0.97 0.96 0.95

Case-1 Case-2 Case-3

0.94

VI. CONCLUSION

0.93 1

5

9

13

17 Bus no.

21

25

29

Fig. 4: Bus voltage profiles of 33-bus system for various case studies

33

This paper presents a useful and effective application of LSHADE algorithm for optimization of simultaneous discrete and continuous variables in a real-world problem of distribution

network. With selection of more appropriate network switches for opening, with little reshuffle of DG location, and with more accurate distribution of DG capacity, L-SHADE achieves the lowest real power loss in any study case among equivalent algorithms. Lowering loss by any margin is both technically and commercially beneficial. The proposed algorithm is highly efficient and productive in finding most optimal solutions for the single objective optimization problem discussed in this literature. Application of the algorithm on a larger network with higher number of buses and on a network with added VAR compensators remains the topic for future study.

[9]

[10]

[11]

[12]

ACKNOWLEDGMENT This project is funded by the National Research Foundation Singapore under its Campus for Research Excellence and Technological Enterprise (CREATE) program.

[13]

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