Determining Optimum Location and Sizing of Distributed Generation Systems in a Real Radial Distribution Network

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Determining optimum location and aizing of DGs

Kaya and Bozkurt

Corresponding Author:

Altuğ Bozkurt E-mail:

[email protected] Received: April 8,2021 Accepted: May 8, 2021

Available Online Date: August 5, 2021

DOI: 10.5152/electrica.2021.21038

ORIGINAL ARTICLE

Determining Optimum Location and Sizing of Distributed Generation Systems in a Real Radial Distribution Network

Anıl Kaya

, Altuğ Bozkurt

1Department of Electrical Engineering, Graduate School of Science and Engineering, Yıldız Technical University, İstanbul, Turkey

2Department of Electrical Engineering, Yıldız Technical University, İstanbul, Turkey

Cite this article as: A. Kaya, A. Bozkurt. "Determining Optimum Location and Sizing of Distributed Generation Systems in a Real Radial Distribution Network", Electrica, vol. 21, no. 3, pp. 342-351, Sep. 2021.

ABSTRACT

In recent years, with the changing concept of electrical energy, distributed generation systems have gained more importance. Distributed generation systems can contribute to distribution networks by increasing energy supply security, reducing power losses, and improving voltage stability. Optimal locations and sizes should be determined to obtain maximum benefit from distributed generation systems that will be connected to distribution networks.

This paper presents a multi-objective placement and sizing optimization model of distributed generation systems to minimize power losses and voltage deviations. The proposed model is implemented on a 40-bus real radial network using particle swarm algorithm and whale optimization algorithm. The obtained results on different load scenarios using particle swarm algorithm and whale optimization algorithm algorithms are presented comparatively.

Index Terms—Distributed generation systems, particle swarm optimization, whale optimization algorithm

Electrica 2021; 21(3): 342-351

Nomenclature

The sets, indices, parameters, and variables that are used in this paper are alphabetically listed in Tables I–II. Other symbols and abbreviations are defined where they first appear.

I. INTRODUCTION A. Motivation

The classical central system structure, which consists of the generation, transmission, distribu- tion, and consumption of electrical energy, is undergoing a long-term transformation due to reasons such as sustainability and environmental policies, global warming concerns, techno- logical developments, and the strengthening of local governments. In addition, energy trans- formation, which has a very important place in the Sustainable Development Goals of the United Nations, is expected to accelerate in the 2020s, which have been declared as an action period within the scope of the development goals [1].

In particular, renewable energy source-based distributed generation sysytems (RES-DGs), which are directly connected to distribution networks, are an important part of the energy transformation concept.

DGs have some benefits on distribution networks such as increasing energy supply security, reducing power losses, and improving voltage stability. In recent years, DGs, which have been also included in the problem areas of network planning and expansion, are considered as a cost-cutting opportunity [2-4].

The optimization of location and capacity is required to obtain maximum benefit from DGs in terms of system operation. In order to fulfill this requirement, this paper proposes an approach where the position and capacity optimizations of the DGs to be connected to the network are provided in a way that minimizes the power losses and voltage drops occurring in the distribu- tion network.

B. Literature Overview

There are many studies on the problems of connecting DGs to distribution networks, in the literature. These studies mostly revolve around the use of different numerical and heuristic algorithms that deal with the problem of determining the opti- mal allocations and capacities of DGs in order to minimize the power losses in the distribution networks, and to improve the system voltage stability. The authors of [5] demonstrated the determination of the optimal allocation and capacity for DGs on a radial distribution network to minimize power losses and maximize savings in energy distribution costs using the satin bowerbird optimization and the ant lion optimizer algorithms.

In [6], the DG position and capacity optimization problem are considered by taking the fault current limit into account, using a nondominated sorting genetic algorithm. In [7-9], position and capacity optimizations are applied by considering sun-based DG generation profiles in real local networks using PSO, the genetic algorithm, and the improved PSO algorithm, respec- tively. In the literature, there are also studies in which hybrid algorithms are used to obtain better results on the DG optimi- zation problem. In [10], a novel methodology is proposed to solve the problem of RES-DGs planning optimization based on the improved Harris hawks optimizer using PSO. Authors of [11] proposed a multi-objective optimization method based on the sine cosine algorithm combined with fuzzy logic decision making for optimal installation of multiple distribution static compensators in distribution networks. In [12], the optimal allo- cation of DGs to minimize power losses using the hybrid grey wolf optimizer algorithm is demonstrated. In [13], a novel GA/

PSO hybrid algorithm is used for the optimal location and sizing of DGs in the distribution network, to minimize network power losses and improve voltage regulation. In [14], a comprehen- sive optimization model for the sizing and siting of RES-DGs, electric vehicle charging stations, and energy storage systems within the distribution system is proposed, which is formulated as a second-order conic programming problem by considering time-varying DG generation and load consumption.

More detailed reviews on the DG optimization problem can be found in [15-18] where different methods and algorithms are shown.

In this study, the position and capacity optimization of the DGs to be connected to a real radial distribution network is per- formed using PSO and WOA algorithms to minimize the total system power loss and voltage drops.

The remainder of this paper is organized as Section 2, where the mathematical programming and algorithms are explained, Section 3, where the proposed methodology is tested and the results are shown, and Section 4, where the conclusion is presented.

II. METHODOLOGY

In this section, the mathematical programming of the pro- posed model is demonstrated. In addition to this, two different

heuristic algorithms to be used in this optimization problem are explained.

A. Objective Function

In the DG optimization problem, the objective function can be formulated as a single-objective or multi-objective problem.

In this optimization problem, the objective function is a multi- objective function formulated as the minimization of the total active power loss and the weighted sum of the voltage drops:

f min w P { 1 lossw VDI2 (1) Active power loss and voltage deviation index, which are the components of the objective function defined in (1), are given in (2) and (3), respectively:

Ploss I R

l L

l l

2 (2)

VDI V V

i B

ref i MV

(3)

B. Constraints

Some technical and regulatory constraints for the solution of the objective function are defined below.

• Active and reactive power balances are explained in (4) and (5):

Pslack PDG P P

i B

L i loss i h

MV

, ,

1

(4)

Qslack QDG Q Q

i B

L i loss i h

MV

, ,

1

(5)

• Voltage limit values on each bus are specified in (6):

Vmin≤ ≤V Vi max (6)

• DG capacity limits are explained in (7), (8), and (9). The DG capacity limit to be connected to a low voltage (LV) bus where defined in (8) is detected over a related medium voltage (MV)/

LV transformer capacity. In Turkey, this rate is restricted as 50%

of the capacity of the related distribution transformer by the regulation:

P_DG^cap P P

i B

DGMV h B

DGLV

MV LV

h B

DGLV

h icap LV

P K TR

PDG PDGcap

i h, ≤ (9)

C. Solution Methods

In this section, the algorithms that will be used in the solution of the objective function are mentioned.

1) Particle Swarm Optimization (PSO)

The PSO algorithm is an intuitive method developed by Kennedy and Eberhart [19], inspired by the social movement of animals moving in a herd. The particle swarm theorem has two main purposes. The first is to locate the best-placed particle in the flock; the second is to ensure that other particles also move according to this position. The PSO flowchart is shown in Fig. 1.

The next positions of the particles are determined according to past movements and updates on the individuals which have the best position. The PSO algorithm, which corresponds to a solution for each particle, tries to reach the best result by updat- ing the velocity and position criteria. Here, (10) and (11) are the equations of speed and position update criteria:

v_m^k1 z v_m^k c rand pbest¹









xmk x v

mk mk

^{1  1} (11)

where, xmk is the current position of particle, vm is the veloc- ity value, rand represents random value, c1 and c2 are scale factors, k is the iteration number, pbest and gbest are the best local and global position values,and z is the inertia coefficient.

The PSO flowchart is shown in Fig. 2.

2) Whale Optimization Algorithm (WOA)

The WOA, first presented by Mirjalili and Lewis [20], is an intuitive solution method inspired by the hunting strate- gies of humpback whales. When hunting, humpback whales encircle their prey with air bubbles of a particular shape, depending on the location of their prey. This special behavior of hunting can be expressed with a two-phase mathemati- cal model. The first stage is searching for prey and encircling the prey with air bubbles, which is given in (12) and (13) respectively:

D C X t  ^*

X t

where, t represents current iteration, and 

X^* represents the best value of the position vector so far. 

A ve 

C are e coeffi- cient vectors which are given in (14) and (15):

A2a r a  (14)

C= 2r (15)

where, a is linearly decreasing vector from 2 to 0 and r is the random vector between [0, 1]. Whether or not to perform the global search is decided by the value of 

A. If A ≥ 1, it means that the search for prey continues, and if A <1, it means that the prey can be attacked by the air bubble method. The search mechanism of WOA is shown in Fig. 2. Equations (16) and (17) are used for case A ≥ 1, and (12) and (13) are used for case A < 1:

D C X  randX (16)

X t

where 

Xrand represents the random value of the position vector in current iteration.

Fig. 1. Flowcart of proposed PSO.

Fig. 2. Bubble net searching mechanisim in WOA [20].

The second part of WOA, the spiral position update, is given in (18) and (19):

X t

D X t’ ^*

where, 

D’ indicates the distance between the target position and the solution candidate, b is constant value, and l is a ran- dom number between [-1, 1].

The definition of whether the position update will be spiral or linear while searching is given in (20):

X t X t A D p

D e cos^bl l X t p

 



1  0 5

2 0 5

*

*

, ,

’  , ,



(20)

where p is a random number between [0, 1]. The WOA flow- chart is shown in Fig. 3.

III. RESULTS AND DISCUSSIONS A. Input Data

The proposed model is implemented on a real radial distribu- tion network located in Şile district, operated by the İstanbul Anadolu Yakası Elektrik Dağıtım A.Ş. (AYEDAŞ). There are 40 MV bus and 20 MV/LV distribution transformers on the feeder, as can be seen from the one-line diagram in Fig. 4. The line param- eters and transformer data related to the distribution network are shown in Table III.

The total energy consumption of the feeder in February is given in Fig. 5. Throughout the year, the feeder has a similar energy demand curve, which has a peak value of around 0.45–

0.5 MWh.

Fig. 3. Flowchart of proposed WOA.

Fig. 4. One-Line diagram of the distribution feeder.

B. Simulation and Results

The proposed model and load flow are applied via MATLAB R2019b software running on a personal computer with Intel Core i5-6300u processor, 2.40 GHz, 4GB RAM, x64-bit based operating system. The assigned values for the simulation ini- tialization parameters are given in Table IV.

The implementation is carried out on three different load pro- file scenarios considering two DGs to be connected to the distribution network. Due to the low-rated powers of the dis- tribution transformers in the distribution network, the imple- mentation is carried out at the MV level.

PSO and WOA algorithms are used to determine the optimum location and capacity of DGs in the implementation.

a) First ScenarioReal Life Profile

In the first case, the simulation is carried out by considering the peak load of the system according to the real consump- tion graph in Fig. 5. In the solution of both algorithms, the total active power loss is reduced by 78.95%. The optimal bus location numbers of DGs are 18/31 in PSO and 20/31 in WOA. The voltage values of the system buses in with and without DGs cases are shown in Fig. 6. In this scenario, the voltage values of the system buses without DGs are already very close to the reference bus value because of the low consumption.

b) Second Scenario50% Load Profile

In the second scenario, the load profile is adjusted to be 50%

of the total installed power of the transformer. While power loss without DG is 8.6kW, the placements of DGs using PSO and WOA leads to reductions in the power losses by 94.68%

and 94.21%, respectively, to 0.45 kW and 0.49 kW. The opti- mal bus numbers for placements of DGs are found to be 20/31 and 20/37, with PSO and WOA respectively. The volt- age profile of the system buses in the second scenario are shown in Fig. 7.

Comparing in terms of minimum voltage values, PSO approaches the reference bus voltage value more than WOA.

c) Third Scenario 100% Load Profile

In the third scenario, the optimization is carried out assuming a consumption amount of 100% of the power of the total trans- former. The results obtained show that the reductions of the total power losses compared to the base case are 95.53% and 94.47%, respectively, in PSO and WOA. The optimal bus num- bers for placements of DGs are found to be 20/31 and 22/37, in PSO and WOA respectively. The voltage profile of the system buses is shown Fig. 8.

Detailed results are presented in Table V. In all three load sce- narios, the performance score of the objective function in PSO is better than the results obtained with WOA. When the simu- lation run times are examined, it is clearly seen that the PSO TABLE I. INDICES AND SETS

l Index of lines İ Index of MV buses

H Index of LV buses and relevant MV/LV transformer units L Set of lines

BMV Set of MV buses BLV Set of LV buses

TABLE II. PARAMETERS AND VARIABLES F The objective function

Il The current flowing through line l [p.u.]

K The ratio of allowed installed DG capacity with respect to the MV/LV transformer-rated power PDGcap The total allowable DG capacity [p.u]

PDGLV The active power injected by DG at LV level PDGMV The active power injected by DG at MV level PDG h i,,

QDG h i,

The active and reactive power injected by DG at bus i or h [p.u.]

P Qloss, loss The total active and reactive power loss [p.u.]

PL i,, QL i, The active and reactive power load at bus i [p.u.]

Pslack, . The active and reactive power injected by the slack bus [p.u.]

RL The resistance of line l [p.u.]

Sb The base apparent power [MVA]

TR_{h i}^cap_, Rated power of MV/LV transformers between MV bus i and LV bus h [p.u.]

Usys The base voltage value of the system [kV]

Vi Voltage magnitude at bus i [p.u.]

Vmax,Vmin The maximum allowable voltage value [p.u]

Vref Voltage magnitude of reference bus [p.u.]

VDI Voltage deviation index

w w1, 2 Weighted coefficients in multi-objective function

TABLE III. THE LINE PARAMETERS AND TRANSFORMER DATA

Index (i , l) Bus Type Load [kW] Transformer Power [kVA] R [p.u.] X [p.u.] Z [p.u.]

1 Slack - - 0.0019 0.0012 0.00

2 PQ - - 0.0143 0.0096 0.02

3 PQ - - 0.0116 0.0077 0.01

4 PQ 29 400 0.0353 0.0088 0.03

5 PQ 6 40 0.1084 0.0287 0.11

6 PQ - - 0.074 0.0494 0.09

7 PQ 40 250 0.0712 0.0475 0.09

8 PQ - - 0.1393 0.0928 0.17

9 PQ - - 0.0148 0.0039 0.02

10 PQ 4 25 0.0585 0.0155 0.06

11 PQ 0 - 0.0037 0.001 0.00

12 PQ 27 250 0.0419 0.0111 0.04

13 PQ 29 50 0.2514 0.0665 0.26

14 PQ - - 0.043 0.0287 0.05

15 PQ 22 160 0.0308 0.0082 0.03

16 PQ - - 0.0833 0.0555 0.10

17 PQ 29 250 0.0222 0.0059 0.02

18 PQ - - 0.043 0.0287 0.05

19 PQ 24 160 0.0197 0.0052 0.02

20 PQ - - 0.0278 0.0185 0.03

21 PQ 24 250 0.0222 0.0059 0.02

22 PQ - - 0.0136 0.0036 0.01

23 PQ - - 0.0068 0.0018 0.01

24 PQ 36 250 0.3537 0.0936 0.37

25 PQ 8 50 0.0638 0.0426 0.08

26 PQ - - 0.0368 0.0245 0.04

27 PQ 11 100 0.0136 0.0036 0.01

28 PQ - - 0.0372 0.0248 0.04

29 PQ 8 50 0.0521 0.0138 0.05

30 PQ - - 0.0388 0.0103 0.04

31 PQ - - 0.1023 0.0271 0.11

32 PQ - - 0.0271 0.0072 0.03

33 PQ 24 160 0.0037 0.001 0.00

34 PQ - - 0.1023 0.0271 0.11

35 PQ 36 250 0.0037 0.001 0.00

36 PQ 12 100 0.0949 0.0251 0.10

37 PQ - - 0.0678 0.0179 0.07

38 PQ 30 250 0.016 0.0042 0.02

39 PQ 27 400 0.0037 0.001 0.00

40 PQ 27 250

algorithm converges to the solution in a much shorter time than WOA.

IV. CONCLUSION

DGs can be planned to eliminate some of the weaknesses of distribution networks. In order to obtain maximum benefit from this planning, the placement and capacity of the DGs should be optimized. In this study, DGs allocation and siting are optimized to minimize the system power losses and volt- age deviations, using PSO and WOA algorithms. The proposed model is implemented on a real radial distribution network considering three different constant time–load scenarios. The results indicated that the optimization of DGs can be very effective in reducing active power losses and limiting volt- age deviations. In addition to this, it was found that PSO has a better performance compared to WOA in this optimization problem.

Fig. 5. Energy consumption graph of the feeder.

TABLE IV. SIMULATION INITIALIZATION PARAMETERS

BMV 40

Sb 100

Usys 34.5

N (Max. Iteration) 100

G (Number of DGs) 2

Vmin [p.u.] 0.95

Vmax [p.u.] 1.05

w1 0.7

w2 0.3

Fig. 6. Voltage profile in the first scenario.

Peer-review: Externally peer-reviewed.

Author Contributions: Concept – A.K., A.B.; Design – A.K., A.B.;

Supervision – A.K., A.B.; Resources – A.K., A.B.; Materials – A.K., A.B.; Data Collection and/or Processing – A.K., A.B.; Analysis and/or Interpretation – A.K., A.B.; Literature Search – A.K., A.B.; Writing Manuscript – A.K., A.B.;

Critical Review – A.K., A.B.

Acknowledgements: The authors would like to thank AYEDAŞ for pro- viding the necessary data on the feeder used in this study.

Conflict of Interest: The authors have no conflicts of interest to declare.

Financial Disclosure: The authors declared that this study has received no financial support.

Fig. 7. Voltage profile in the second scenario.

Fig. 8. Voltage profile results in the third scenerio.

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TABLE V. SIMULATION RESULTS

Load Capacity Real Load 50% 100%

Method PSO WOA PSO WOA PSO WOA

Total Power Loss [kW] 0.12 0.12 0.45 0.49 1.52 1.54

Power loss reduction (%) 78.95% 78.95% 94.68% 94.21% 95.53% 95.47%

Minimum Voltage [p.u.] 0.9999 0.9999 0.9998 0.9996 0.9994 0.999

DG Size [kW] 156.5/163.6 126.81/165.1 539.4/758.6 751/564.5 1062.9/1533.1 982.5/1463,8

DG Location 18/31 20/31 20/31 20/37 20/31 22/37

Objective Function Score 0.0004383 0.00044539 0.0020564 0.0022393 0.0047568 0.0052308

Run Time (s) 171.6 440.4 175.5 384.3 189.2 358.6

Without DGTotal Power Loss 0.57

kWVmin 0.9987 Without DGTotal Power Loss 8.46

kWVmin 0.9931 Without DGTotal Power Loss 34 kWVmin 0.9857

Altuğ Bozkurt received the M.Sc. and Ph.D. degrees in Electrical Engineering from Yildiz Technical University in 2005 and in 2012, respectively. He has been working as an Assistant Professor at the in Electrical Engineering Department of Yildiz Technical University. His research interests include analysis of power systems, wind energy systems, and power quality.

Anıl Kaya received a bachelor’s degree in Electrical Engineering from Yildiz Technical University in 2016. He is pursuing his M.Sc. degree in Electrical Power Systems, Yildiz Technical University. He has been working in a specialist position at İstanbul Anadolu Yakası Electricity Distribution Company for more than 2 years. His research interests include distributed renewable generation, grid management, and data analytics.