Optimal allocation of multi-type distributed generators using backtracking search optimization algorithm

Electrical Power and Energy Systems 64 (2015) 1197–1205

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Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes

Optimal allocation of multi-type distributed generators using backtracking search optimization algorithm Attia El-Fergany ⇑ Department of Electric Power and Machines, Faculty of Engineering, Zagazig University, P. O. Box 44519, Zagazig, Egypt

a r t i c l e

i n f o

Article history: Received 25 November 2013 Received in revised form 6 September 2014 Accepted 12 September 2014

Keywords: Distributed generation Loss minimization Cumulative voltage deviations Loss sensitivity factors Backtracking search optimization algorithm

a b s t r a c t In this article, a very recently swarm optimization technique namely a backtracking search optimization algorithm (BSOA) is addressed to assign the distributed generators (DGs) along radial distribution networks. One of the main features of the BSOA is a single control parameter and not over sensitive to the initial value of this factor. The objective function is adapted with weighting factor to reduce the network real loss and enhance the voltage profile with the purpose of improving the operating performance. In addition, the combined power factor and reduction in network reactive power loss are spotted. Set of fuzzy expert rules using loss sensitivity factors and bus voltages are employed to identify the initial DG’s locations. The proposed approach is attuned to tackle the shortfall of loss sensitivity factors and to decide the final placement of the DGs. Two types of the DGs are studied and investigated. The proposed method is demonstrated and validated thru many radial distribution networks with different sizes and complexities. The BSOA-based methodology can efficiently generate high-quality solutions compared to other competitive techniques in the literature. Ó 2014 Elsevier Ltd. All rights reserved.

Introduction Installations of the distributed generations (DGs) can be purposefully implemented in power systems for grid strengthening, reducing network power losses (active and reactive), peak load shaving, improving voltage profiles, and load factors, reducing for system upgrade investments, and improving system security, dependability, and efficacy [1–3]. The network loss minimization is one of the significant points in operating the power system networks. In a typical distribution system, particularly, in developing countries, network losses are as much as 20% of total power generated is wasted in the form of power losses [4–7], which would cost millions of dollars every year. The losses in a distribution area are mainly of two types; technical and non-technical either active or reactive types. The two bus system depicted in Fig. 1 represents a distribution level feeder between buses i and j. The active and reactive power losses in line i–j are given by Eqs. (1) and (2), respectively:

Ploss ¼ Rij : ij

ðP 2j þ Q 2j Þ

¼ X ij : Q loss ij

jV j j2 ðP2j þ Q 2j Þ jV j j2

⇑ Tel.: +20 100 5705526; fax: +20 55 2304987. E-mail address: [email protected] http://dx.doi.org/10.1016/j.ijepes.2014.09.020 0142-0615/Ó 2014 Elsevier Ltd. All rights reserved.

ð1Þ ð2Þ

According to Eqs. (1) and (2), the feeder power loss is closely related to the active and reactive power flows. This concludes that the reductions of these power flows will certainly lead to reduce network losses accordingly. The DG is anticipated to become more essential in the future power system deregulations. The main reason of using DG units in power system is technical and economic benefits that have presented in [1,2,8–10]. Placement of DG on the system might lead to reduce losses (DG impact on losses is similar to placement of capacitors). The only big difference is that some types of DGs have both real and reactive power flow loss impacts, and a capacitor affects only the reactive flow loss. Like Capacitors, too much DG at the wrong placement will increase losses on the lines. It is crucially important to determine the size and location of DG unit to be placed. Studies indicate that poor selection of location and size would lead to higher losses than the losses without DG [11,12]. In the last few years various techniques have been developed to find for the optimal location and size of the DG. Different analytical approaches minimizing line losses were utilized and proposed for the DG allocation [11–17] and optimal power flow [18,19]. Many different evolutionary algorithms (EAs) with different search operators have been reported in literature and exhaustively used in solving numerical optimization problems [20]. However, No single algorithm is consistently able to solve all types of optimization problems [20,21]. Unlike classical optimization techniques, the EAs do not guarantee finding the optimum solutions for

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Nomenclatures PLoss QLoss Ploss ij

total network active power loss total network reactive power loss active power losses of the line between the nodes i and j

Q loss ij

reactive power losses of the line between the nodes i and j resistance of the line between the nodes i and j reactance of the line between the nodes i and j voltage magnitude of bus i voltage magnitude of bus j total effective real power load fed through bus j total effective reactive power fed through bus j number of network buses total number of lines weighting factor (ranges from 0 to 1) number of distributed generators (DGs) number of connected loads active power supplied by slack bus reactive power supplied by slack bus injected active power of ith DG injected active power of ith DG active power demand of load at bus i reactive power demand of load at bus i active power loss of branch i reactive power loss of branch i short circuit level at bus i

Rij Xij |Vi| |Vj| Pj Qj NB nbr

x NDG NL PSlack QSlack PDG,i QDG,i PD,i QD,i PLoss(i) QLoss(i) ISC(i)

a problem, only close to optimal solutions. However, the EAs are sufficiently flexible to solve different types of optimization problems without going in depth to the problem. The EAs should have global exploration and local exploitation abilities [21,22]. For the same purpose of DG allocation, an EA uses genetic algorithm [23,24] and other heuristic algorithm methods through goal programming [25], harmony search algorithm [26], cat swarm optimization [27], particle swarm optimization (PSO) [28,29], artificial bee colony (ABC) algorithm [30], and differential evolution (DE) [31] have been applied to place single and/or multi-DGs for various objectives. A wide variety of DG technologies and types exists [17]: (i) non-renewable energy technologies, and (ii) renewable energy technologies. The first group consists of internal combustion engines, gas turbines, micro-turbines, etc. The second group produces electricity using renewable energy sources, i.e solar energy, wind energy, tidal energy, wave energy, geothermal energy, biomass, etc. Although DG has relatively small size compared with central generation, it is large enough to satisfy electricity requests of a group of local customers. The DG resources are classified into four categories [17,29] as depicted in Table 1. The backtracking search optimization algorithm (BSOA) is a new meta-heuristic algorithm developed in 2013 [32]. The BSOA has a unique mechanism for generating a trial individual enables it to solve numerical optimization problems successfully and quickly. The BSOA uses three basic genetic operators: selection, mutation and crossover to generate trial individuals. The BSOA

W/DG WO/DG PDG,min PDG,max PFDG,min PFDG,max Si Srated i

with DG’s installations without DG’s installations lower limit of DG active output power upper limit of DG active output power lower limit of DG power factor upper limit of DG power factor actual line flow of line i rated line i transfer capacity l penetration level kVC penalty function for the voltage constraints kLFC penalty function for the line flow constraint kPtC penalty function for the maximum allowable DG penetration kSC penalty function for the bus short level LSF(j) loss sensitivity factor (LSF) of bus j LSFmax maximum value of LSFs LSFmin minimum value of LSFs LF load flow LR loss reduction N population size D problem dimension rand(. . .) uniform distribution LBj lower bound of the optimised parameter j UBj upper bound of the optimised parameter j Pi target individual i in the population P

has a random mutation scheme that uses only one direction individual for each target individual, in contrast with many genetic algorithms such as differential evolution. The BSOA randomly picks the direction individual from individuals of a randomly chosen previous generation [32]. The development of an optimization methodology capable of defining the DG unit placement and sizing that improves the system operation characteristics when dealing with the avalanche of DG penetration is a necessity. This work proposes the solution of DG allocation (bus number and size) using the BSOA-based approach. One of main interests of the article is to examine the performance of the BSOA in defining the optimal locations and sizes of DGs. LSFs and bus voltages are utilized for the initial identification of locations using fuzzy expert rules. DG types (A) and (C) are considered and analysed; their effects on network performance in terms of the loss reduction and voltage profile enhancement. The proposed methodology is applied to the 33-bus and the 94-bus radial distribution networks to examine its viability. Comparisons to the analytical and other heuristic methods in the literature validate the cropped results. Objective function formulation and constraints Great attention should be paid to the problem of DG allocation. For this reason, the formulation of objective function and specific constraints should be modelled carefully. The objective function is adapted to reduce the system active losses and improving the bus voltage profile with a weighting factor. The cumulative voltage deviation (CVD) at each bus must be made as small as possible. The CVD is utilized to indicate the voltage profile improvement and calculated using:

8 0 if 0:95 6 jV i j 6 1:05 > < NB X CVD ¼ > j1  V i j else : i¼1

Fig. 1. Portion of a radial distribution network of i–j bus.

ð3Þ

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A. El-Fergany / Electrical Power and Energy Systems 64 (2015) 1197–1205 N DG NL X X PDG;i 6 l: PD;j

Table 1 Various types of the DG technologies.

i¼1

Type of DG

P

Q

Example

(A) (B) (C)

+ 0 +

0 + +

(D)

+



Photovoltaic arrays and fuel cells Synchronous condensers and capacitors Diesel synchronous generators and wind turbines Wind turbines/induction generators at fixed speed

+ Produces

 Absorbs

ð12Þ

j¼1

The penetration is a measure of the amount of power injected in the network by the DG sources compared with the total load demands of the system. The penetration level can be calculated using:

PNDG

l ¼ Pi¼1 NL

PDG;i

ð13Þ

i¼j P D;j

Network active power loss

The bi-objective weighted function can be defined as a constrained optimization problem as given in Eq. (4):

8 > <

  i¼1 P Loss ðiÞ W Minimise x: P  nbr > : i¼1 P loss ðiÞ Pnbr

DG

þ ð1  xÞ:

WO DG

9 > =

CVDjW DG CVDjWO DG > ;

ð4Þ

The system loss with DGs should be less than system loss without DGs. nbr X Ploss ðiÞjW

DG

<

nbr X

Ploss ðmÞjWO

ð14Þ

DG

m¼1

i¼1

Network short circuit level

Subject to set of equality and inequality constraints that should be satisfied while achieving the minimization of the proposed objective function:

The system short levels with DGs should be less than or equal the pre-values without DGs.

Power balance

ISC ðiÞjW

Active and reactive power balance can be expressed as defined in Eqs. (5) and (6), respectively.

PSlack þ

N DG NL nbr X X X PDG;i ¼ PD;i þ PLoss ðiÞ i¼1

Q Slack þ

i¼1

NDG NL nbr X X X Q DG;i ¼ Q D;i þ Q Loss ðiÞ i¼1

ð5Þ

i¼1

ð6Þ

i¼1

i¼1

Bus voltage limits In order to have quality supply, the voltage profile of the network should be supported to an acceptable range. The voltage limits can be expressed:

jV min j 6 jV i j 6 jV max j i 8 N B

ð7Þ

DG sizing limits

6 ISC ðiÞjWO

DG

DG

i 8 NB

A penalty factors associated with each violated constraint are burdened to the objective function in order to force a solution to stay away from the infeasible solution space. Therefore, the optimal solution is found when no constraint is violated and the objective function is minimized. The penalty functions method can be seen as penalizing infeasible solutions. It is worthy to state that: (1) Active and reactive power balances are achieved using LF calculations. (2) The inequality constraints of DG’s active power limits, PF limits {DG type (C)} and voltages are bounded within the lower and upper bounds of the BSOA (self-constrained). (3) Other constraints (line flow, load’s bus voltage, maximum allowable DG penetration and short circuit) are penalised the objective function as follows:

"

# NB NB X X kVC ¼ wv : maxð0;hjV i j  jV max jiÞ þ maxð0; hjV min j  jV i jiÞ ð16Þ i¼1 i¼1 " # nbr X ð17Þ maxð0; Si  Srated Þ kLFC ¼ wL : i "

i¼1

N DG NL X X kPtC ¼ wp : max 0; h PDG;i  l PD;j i i¼1

PDG;min 6 PDG;i 6 PDG;max

i 8 NDG

PF DG;min 6 PF DG;i 6 PF DG;max i 8 NDG   Q DG;i ¼ PDG;i :tan cos1 ðPF DG;i Þ

ð8Þ ð9Þ ð10Þ

In the case of DG type (A): PFDG,min = PFDG,max = 1.

All the branch apparent power flows would be maintained below their thermal capacities to avoid lack of line security.

Si 6 Srated i

i 8 nbr

ð11Þ

Maximum level of DG penetration The total power generated by DGs should be limited to a specific penetration level (l) to maintain the quality of the network.

!# ð18Þ

j¼1

" # NB X kSC ¼ wS : maxð0; hISC ðiÞjW DG  ISC ðiÞjWO DG iÞ

ð19Þ

i¼1

where wv, wp, wS and wp are the penalty function weights having large positive value. The sum of penalties is given by:

Penalties ¼ kVC þ kLFC þ kPtC þ kSC

Line flow

ð15Þ

ð20Þ

Finally, the problem mathematical model can be formulated as constrained optimization problem as follows:

MinimizefFðX; UÞ þ Penaltiesg  gðX; UÞ ¼ 0 S:t: hðX; UÞ 6 0

ð21Þ

F(X, U) is the weighted objective function to be minimized; g(X, U) and h(X, U) are the set of equality and inequality constraints, respectively. X is the state variables and U is the vector of control variables. The control variables are DG active output power and

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DG PF for type (C) and only DG active output power for DG type (A). The state variables are bus voltage, line power flow and bus short circuit current. Initial identifications of DG placement and Fuzzy expert rules The initial identification of high potential nodes for DG placement aims to reduce the search space for the optimization procedure. In this proposed work, the LSF is utilized for this purpose [33]. The LSF may be able to predict which bus will have the greatest loss reduction when active and reactive injections are put in place. With reference to Fig. 1 and Eq. (1), the LSF is computed using:

LSFðjÞ ¼ ¼

@Pijloss @Pj 2Pj jV j j2

:Rij

j 8 f2 . . . :NB g;

i 8 f1 . . . :NB  1g

ð22Þ

Set of fuzzy expert rules are proposed to determine appropriate initial DG locations [34]. The normalised LSFs and bus voltages are modelled by fuzzy membership functions (MFs) (see Fig. 2). The normalised LSF for values between [0,1] is defined as:

LSFðjÞ ¼

LSFðjÞ  LSF min LSF max  LSF min

j 8 f2 . . . NB g

ð23Þ

After calculating the suitability MF, the centroid method is used to de-fuzzify in order to conclude the optimal DG locations (see Fig. 3). The DGs would be placed on the buses with the highest suitability values which involve LSF and voltage indicators. The rules are summarized in the fuzzy decision matrix presented in Table 2. It is worthy to state that the membership functions utilized are trapezoidal and triangular shapes as shown in Figs. 2 and 3. The surface graph of compiled rules stated in Table 2 is shown in Fig. 4 It is well-known that LSF observations may not lead to the optimum locations due to the fact the LSF calculations depend on the network topology, configurations, and loading [12,35]. To tackle

Degree of membership

L

LL

1

M

H

this restriction, the proposed approach will search within pre-identified search space of high potential buses defined by fuzzy expert rules for the optimum DG placement. After ranking buses, 15–25% of buses (depends on the size of the given network) could be initially identified as the search space for the BSOA-based approach. Undoubtedly, larger search space will increase the CPU processing time and make LF to diverge.

Overview of the BSOA The BSOA is a population-based iterative EA designed to be a global minimizer. The BSOA can be explained by dividing its functions into five procedures: (i) initialization, (ii) selection-I, (iii) mutation, (iv) crossover, and (v) selection-II. The structure of BSOA is quite simple; thus, it can be easily adapted to different numerical engineering optimization problems. The BSOA’s general structure is revealed in Fig. 5. The BSOA’s strategy for generating a trial population includes two new crossover and mutation operators. The BSOA’s strategies for generating trial populations and controlling the amplitude of the search-direction matrix and search-space boundaries give it very powerful exploration and exploitation capabilities. In particular, the BSOA possesses a memory in which it stores a population from a randomly chosen previous generation for use in generating the search-direction matrix. The BSOA has strong strategy for both a global exploration and local exploitation with good feature of avoiding local minima. More details about the BSOA procedures would be referred to [32]. The BSOA five main procedures are outlined below: BSOA Initialization The BSOA initializes the population P as defined in Eq. (24).

Pi;j ¼ LBj þ randð. . .Þ:ðUBj  LBj Þ i 8 N & j 8 D

ð24Þ

Selection-I The BSOA’s Selection-I stage determines the historical population oldP to be used for calculating the search direction. The initial historical population is determined using Eq. (25).

HH

0.8

oldPi;j ¼ LBj þ randð. . .Þ:ðUBj  LBj Þ i 8 N &j 8 D

0.6

After oldP is determined, the permuting function is applied to randomly change the order of the individuals in oldP using random shuffling function as formulated in Eq. (26).

0.4

oldP :¼ permutingðoldPÞ

0.2 0

ð25Þ

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

ð26Þ

1

LSF LL

L

N

H

HH

0.8 0.6 0.4 0.2 0 0.9

0.94

0.96

0.98

1

1.02

1.04

1.06

1.08

1.1

|V| Fig. 2. MFs plot for the normalised LSF and the p.u bus voltage magnitude (inputs).

M

H

HH

0.8 0.6 0.4 0.2 0

0.92

L

1 LL

Degree of membership

Degree of membership

1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Suitability Fig. 3. MF plot for suitability factor of DG placement priority (output).

1

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DE and its variants. The mix rate parameter (mixrate) in the BSOA’s crossover process controls the number of elements of individuals that will mutate in a trial by using [mixrate.rand(. . .).D]. The function of the mixrate is quite unlike the crossover rate used in DE. Two strategies are randomly used to define the BSOA’s map: (i) mixrate, and (ii) allows only one randomly chosen individual to mutate in each. The BSOA’s crossover process is more complex than the processes used in the DE.

Table 2 Rules of Fuzzy decision matrix for DG suitability factors [34].

Selection-II In selection-II stage, the trial populations Tis that have better fitness values than the corresponding Pis are used to update the Pis based on a greedy selection. If the best individual of P (Pbest) has a better fitness value than the global minimum value obtained, the global minimizer is updated to be Pbest, and the global minimum value is updated to be the fitness value of Pbest. The procedure of the BSOA-based methodology to allocate DG can be summarized in the flow-chart diagram shown in Fig. 6.

Suitability

0.8 0.6 0.4

Numerical results and simulations

0.2 1.1 1.05 1

|V|

0.95 0.9

0

0.4

0.2

0.6

0.8

1

LSF

Fig. 4. Plot of fuzzy expert rules in surface view.

Intialisation

Mutation

Cycle=1

Crossover

Selection-I

Selection-II

Generate trialpopulations

Cycle=Cycle+1

The proposed algorithm is illustrated and applied to the 33- and the 94-node radial distribution systems. The line and load data for these two systems are obtained from [36,37], respectively. The single line diagrams of the 33- and 94-bus test cases are shown in Figs. 7 and 8, respectively. The constraint of short circuit defined in Eq. (15) is disabled in the study. The proposed approach is encoded and implemented using MATLAB release 2011a/Ò7.12 [38]. Simulations are executed on a Dell Laptop with Processor IntelÒ Core i5 CPU 2.40 GHz having 4.0 GB of RAM with 32-bit operating system. The backward/forward sweep distribution LF method [12] is employed to solve the equations iteratively and update the bus voltages. The outcome of initial LF without introducing DGs and with 100% loading is depicted in Table 3 for the test cases of the 33-and the 94-node radial networks. After intensive trails and errors; parameters adopted for the BSOA-based algorithm for the test cases of the 33-bus and the

No Stopping? Crop the optimal solutions

Yes

Network data, set constraints, no. of DGs required, and type of DGs

Fig. 5. General structure of the BSOA.

Mutation The BSOA’s mutation process generates the initial form of the trial population mutant. The historical population is used in the calculation of the search-direction matrix; the BSOA generates a trial population, taking partial advantage of its experiences from previous generations. Crossover The BSOA uses a non-uniform crossover strategy that is more complex than the crossover strategies used in many genetic algorithms. The BSOA’s crossover process produces the final arrangement of the trial population T. The initial value of the trial population is Mutant, as set in the mutation process. Trial individuals with better fitness values for the optimization problem are used to evolve the target population individuals. The BSOA’s crossover approach is quite dissimilar to the crossover strategies used in

Run initial distribution LF, short circuit and get initial bus voltages, losses, overall PF, line flows, etc...

Fuzzy expert rules for bus’s ranking

Run distribution LF and perform short circuit

Estimate the objective function & penalties

Selection-I, Generate trialpopulations: Mutation, Crossover and Selection-II Cycle=Cycle+1

Set the BSOA control parameters (Mixrate, population size and maximum cycles) Cycle=1

Generate the BSOA populations

No Stopping? Yes Record optimal DG(s) sizes and placement, active and reactive network losses and bus voltages

Fig. 6. Overall flow-chart of the BSOA-based method and optimal DGs allocation.

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19

20

Slack 2

1

3

21

22

26

27

4

5

Table 4 The control parameters of the proposed BSOA-based method and the constraints.

28

30

29

24

32

15

6 7

23

31

25

16

8

14

9

13

10

11

33

Parameter

17 18

No. of nominated buses Weighting factor (x) Population size (N) Mix rate parameter (mixrate) Maximum iteration Penetration level (l) Penalty weights (wv, wp, wS and wp) Voltage limits PDG,min 6 PDG,i 6 PDG,max PFDG,min 6 PFDG,i 6 PFDG,max

12

Fig. 7. Single line diagram of the 33-node radial distribution system.

Slack

1

2

3

4

34

38

5

6

7

45

49

50

44

48

68

47

67

69

70

8

9

10

11

12

13

39

52

40

53

37

41

59

55

18

19

75

77

20 83 78

21

22

23

84

85

86

79

80

81

88

89

24

25

60

56

14 61

62

26 90

57

74

15

16

28

Test case-2 (94-node)

9 0.5 13 0.5 150 50% 1000

14 0.5 18 0.9 200 50% 1000

0.90 6 |Vi| 6 1.05PU 0.95 6 |Vi| 6 1.05PU 0 6 PDG,i 6 5MW 1 6 PFDG,i 6 1 for type (A) 0.65 6 PFDG,i 6 1 for type (C)

94-bus radial distribution networks, and the required inequality constraints are organised in Table 4.

17

63

65

Test Case-1: thirty three-bus radial distribution network 66

94

27 91

72

64

93

Test case-1 (33-node)

73

58

54

42

87

71

46

36

76

51

43

35

Proposed Value(s)

29

30

92

31 32

33

82

Fig. 8. Single line diagram of an actual Portuguese 94-node radial distribution system.

This is a 12.66 kV radial distribution system having 33 buses, 32 branches and total loads of (3715 + j 2300) kVA. The combined load PF of this system at slack bus is 0.85 (lagging). After applying the proposed approach to define the optimal DG locations and sizes; the obtained results are organised in Table 5. The network voltage profile with single and multiple DGs type (A) is publicized in Fig. 9. Whenever the number of DGs increased, the voltage profile is improved which is attested by the values of CVD (see Table 5). However, it is obvious that the losses are slightly reduced, as in

Table 3 Initial LF run without the DG installations for the two test cases. Item

Base LF without DGs

Minimum voltagea Maximum voltagea Total CVDa PLoss (kW) QLoss (kVAr) Combined system PF High potential buses for DG placement a

Test case-1 (33-bus)

Test case-2 (94-bus)

0.9040 @ bus 18 0.9970 @ bus 2 1.621 210.84 143.12 0.8490 6, 8, 13, 10, 28, 9, 29, 3, 31, 30, 14, 17, ...

0.8485 @ bus 92 0.9951 @ bus 2 8.697 362.86 504.04 0.8769 10, 18, 21, 54, 11, 90, 94, 29, 31, 91, 32, 30, 33, 92, 52, 15, 16, . . .

Excluding the slack bus.

Table 5 Summaries for the 33-node radial network after applying the proposed approach. Item

(Bus, DG size (MW)) for DG type (A) (Bus, DG size (MW)/DGPF) for DG type (C) Minimum voltagea Maximum voltagea Total CVDa PLoss (kW) QLoss (kVAr) Combined system PF Average elapsed time (s)b a b

One-DG

Two-DGs

Three-DGs

Type (A)

Type (C)

Type (A)

Type (C)

Type (A)

Type (C)

(8, 1.8575)

(8, 1.8575/0.82)

(13, 0.880) (31, 0.924)

(13, 0.777/0.89) (29, 1.032/0.70)

(13, 0.632) (28, 0.487) (31, 0.550)

(13, 0.698/0.86) (29, 0.402/0.71) (31, 0.658/0.70)

0.9441 0.9982 0.217 118.12 83.48 0.638 20.40

0.9549 1.006 0 82.78 61.97 0.876 36.87

0.9665 0.9981 0 89.34 60.90 0.647 23.54

0.9796 0.9986 0 31.98 22.03 0.914 49.80

0.9554 0.9981 0 89.05 60.56 0.671 24.95

0.9795 0.9993 0 29.65 21.23 0.922 56.50

Excluding the slack bus. This CPU processing time includes the time consumed in LF runs.

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The optimal DG allocation is planning aspect in nature (off-line application) and the processing time is not considered a concern. Nevertheless, the CPU time exhausted to reach the optimal solution by the proposed BSOA-based method is counted (including LF runs which, is estimated to be 70% of the total time) and depicted in Table 5. Table 6 arranges the numerical results of the analytical methods using golden and grid searches [12], LSF and exhaustive LF (ELF) [13,17] and other evolutionary techniques [29,30] compared to the proposed BSOA-based method to allocate DG’s type (A). The robustness and efficacy of the proposed algorithms are verified based on some statistical factors because of the randomness of the meta-heuristic algorithms, many trials have been made. The proposed BSOA has been run 50 times and the minimum, the maximum, the mean, the median, the standard deviation (SD) and the variance (VR) of the objective function are obtained as offered in Table 7. It can be noticed that the algorithm has the ability to reach either to the final optimum value of objective function or very close to it in every run with minimum VR and SD (refer Table 7).

Bus Voltage in PU

1 0.98 0.96 0.94 3 DGs 2 DGs 1 DG Without DG

0.92 0.9

5

10

15

20

25

30

Bus Number Fig. 9. Bus voltage profile with single and multiple DGs type (A) in the 33-bus radial system.

1.02

Bus Voltage in PU

1 0.98 0.96 0.94 0.92 0.9

Test Case-2: ninety four-bus actual radial distribution feeder

3 DGs 2 DGs 1 DG Without DG 5

10

15

20

25

This second test case is an actual Portuguese radial distribution system with 94 nodes and 22 lateral buses with total loads of (4797 + j 2323.9) kVA. This electric distribution network has some demanding characteristics which imposes heavier operating conditions to the network: the load is heavy and the length of the distribution branches is high; and the voltage profile does not respect the acceptable voltage boundaries. Two scenarios of one DG of type (A) and type (C) are considered for this test case. After applying the proposed optimization method to identify only one DG of each type (14 nodes are initially nominated as initial search space), the cropped results are summarized in Table 8. Significant reductions in network losses (active and reactive) have been reinforced and an observable improvement in voltage profile is shown in Fig. 11. On the other hand, the combined network PF with DG type (A) is low. However, whereas DG type

30

Bus Number Fig. 10. Bus voltage profile without and with DG’s type (C) installations for the 33bus network.

the case of using 2 DGs and 3 DGs or even insignificant (i.e. more DGs would not guarantee minimum network losses). Whereas DG type (C) is capable to supply reactive power in addition to real power are optimally allocated would result in the considerable improvement in the bus voltage profile along the feeder as shown in Fig. 10. In addition, DGs type (C) gives better voltage profile compared to DGs type (A) (realise Figs. 9 and 10).

Table 6 Comparisons of the optimal results of different approaches (DG’s type (A)). Method

Optimal location & DG capacity (MW) of type (A) One-DG

a b

Two-DGs

Three-DGs

(Bus, Size)

LR% (%)

(Bus, Size)

LR%

(Bus, Size)

LR%

Golden search [12] Grid search [12] Analytical [13] Analytical [13] LSF Analytical [17] LSF

(6, 2.590) (6, 2.600) (6, 2.490) (10, 1.400) (18, 0.743)

47.60 47.85 47.33 41.55 30.48

– – – – (18, 0.720) (33, 0.900)

– – – – 52.32%

– – – – 59.72%

Analytical [17] ELF

(6, 2.600)

47.39

(12, 1.020) (30, 1.020)

58.51%

PSO [29]

(6, 2.567)

47.40

(13, 0.849) (30, 1.152)

58.68%

ABC [30] BSOA

(6, 3.380) (8, 1.858)

44.83 43.98a

– (13, 0.880) (31, 0.924)

– 57.62%a

(6, 2.460)

47.30b

(13, 0.730) (29, 1.355)

58.22%b

– – – – (18, 0.720) (33, 0.810) (25, 0.900) (13, 0.900) (30, 0.900) (24, 0.900) (24, 1.099) (30, 1.064) (14, 0.753) – (13, 0.632) (28, 0.486) (31, 0.550) (3, 1.030) (13, 0.807) (29, 1.106)

All proposed constraints are respected with the proposed BSOA-based approach. All proposed constraints are obeyed except the penetration level.

64.83%

65.51%

– 57.76%a

62.07%b

1204

A. El-Fergany / Electrical Power and Energy Systems 64 (2015) 1197–1205

Table 7 Statistical measures and efficacy of the BSOA performance after 50 runs. Factor (PU)

1 DG

Minimum Maximum Average Median SD VR

2 DGs

3 DGs

PV

PQ

PV

PQ

PV

PQ

0.3471 0.3523 0.3492 0.3481 6.823e04 4.656e07

0.1965 0.2105 0.1975 0.1983 5.654e4 6.435e8

0.2119 0.2180 0.2153 0.2144 7.345e5 4.567e7

0.0758 0.0799 0.0779 0.0765 8.934e6 3.876e8

0.2117 0.2186 0.2160 0.2172 6.934e5 5.653e7

0.0703 0.0745 0.0724 0.0711 7.634e6 6.879e9

Table 8 Summaries after applying the proposed method to define one DG of each type (best results). Item

DG scenario

(Bus, DG size (MW))/type (A) and (Bus, DG size (MW)/DGPF)/type (C) Minimum voltagea Maximum voltagea Total CVDa PLoss (kW) QLoss (kVAr) Combined system PF Average elapsed time (s)b a b

Type (A)

Type (C)

(21, 2.3985) 0.9276 0.9967 3.2356 153.86 (57.60% reduction) 177.46 (62.79% reduction) 0.714 118.00

(18, 2.3985/0.853) 0.9519 0.9980 0 85.13 (76.54% reduction) 97.18 (80.72% reduction) 0.934 234.00

Excluding the slack bus. This processing time comprises the time consumed in LF runs.

The numerical results and simulations validate the efficacy and applicability of the proposed approach in comparisons with the analytical and other heuristic methods reported in the literature.

Bus Voltage in PU

1.05 1 0.95

References

0.9 1 DG type (C) 1 DG type (A) Without DG

0.85 0.8

10

20

30

40

50

60

70

80

90

Bus Number Fig. 11. Bus voltage profile before and after applying optimization (1 DG types (A) and (C)).

(C) is proposed, the combined system PF is rectified as revealed in Table 8. The BSOA is competent of producing results close to the optimal solutions as validated by the comparisons with other methods and with steadily smooth convergence characteristics. In addition, all constraints have been checked and found within pre-defined allowable specified ranges.

Conclusions The article is addressed an application of the recently BSOA technique to define the optimal locations and sizes of multi-type DGs. Fuzzy expert rules employed both LSFs and voltage indicators are proposed for the initial identifications of DG’s placement. However, the final decision is taken by the proposed BSOA methodology. The BSOA-based approach needs very little effort in tuning the algorithm control parameters, which is an advantageous for the implementation perspective. The combined power factor of the network is deteriorated whereas the DG type (A) is introduced. However, with proposing DG type (C), the power factor and voltage profile are considerably improved. Regardless, significant reductions in the network technical losses are remarked and cropped.

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