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Find optimal capacity and location of distributed generation units in radial distribution networks by using enhanced coyote optimization algorithm

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Abstract

This paper proposes a novel effective optimization algorithm called enhanced coyote optimization algorithm (ECOA). This proposed method is applied to optimally select the position and capacity of distributed generators (DGs) in radial distribution networks. It is a multi-objective optimization problem where properly installing DGs should simultaneously reduce the power loss, operating costs as well as improve voltage stability. Based on the original coyote optimization algorithm (COA), ECOA is developed to be able to expand the search area and retain a good solution group in each generation. It includes two modifications to improve the efficiency of the original COA approach where the first one is replacing the central solution by the best current solution in the first new solution generation technique and the second focuses on reducing the computation burden and process time in the second new solution generation step. In this research, various experiments have been implemented by applying ECOA, COA as well as salp swarm algorithm (SSA), Sunflower optimization (SOA) for three IEEE radial distribution power networks with 33, 69 and 85 buses. Obtained results have been statistically analyzed to investigate the appropriate control parameters and to verify the performance of the proposed ECOA method. In addition, the performance of ECOA is also compared to various similar meta-heuristic methods such as genetic algorithm (GA), particle swarm optimization (PSO), hybrid genetic algorithm and particle swarm optimization (HGA-PSO), simulated annealing, bacterial foraging optimization algorithm, backtracking search optimization algorithm, harmony search algorithm, whale optimization algorithm (WOA) and combined power loss index-whale optimization algorithm (PLI-WOA). Detailed comparisons show that ECOA can determine more effective location and size of DGs with faster speed than other methods. Specifically, the improvement levels of the proposed method over compared to SFO, SSA, and COA can be up to 2.1978%, 0.7858% and 0.2348%. Furthermore, as compared to other existing methods in references, ECOA achieves the significant improvements which are up to 31.7491%, 20.2143% and 22.7213% for the three test systems, respectively. Thus, the proposed method is a favorable method in solving the optimal determination of DGs in radial distribution networks.

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Abbreviations

\( AP_{Dg,k}^{{}} \) :

Active power of the kth DG

\( {\text{AP}}_{\text{Gr}} \) :

Active power which is supplied from grid through substation

\( {\text{AP}}_{k}^{\hbox{min} } ,{\text{AP}}_{k}^{\hbox{max} } \) :

The lower and upper bounds of the capacity of the kth DG

APLo,l :

Active power at the lth load

\( {\text{AP}}_{\text{Dg}}^{\hbox{min} } ,{\text{AP}}_{\text{Dg}}^{\hbox{max} } \) :

The lower and upper bounds of capacity of DG

\( CV_{k}^{\hbox{min} } ,CV_{k}^{\hbox{max} } \) :

The lowest and highest values of the kth control variable

\( \Delta I_{b,q,p} \) :

The penalty for current violation of the bth line corresponding to the qth solution in the pth pack

\( \Delta V_{j,q,p} \) :

The penalty for current violation of the jth bus corresponding to the qth solution in the pth pack

\( \varepsilon_{i} ,\varepsilon_{v} \) :

Penalty factors of current and voltage in fitness function

\( F_{A} \) :

Objective function of total power loss

\( F_{B} \) :

Objective function of voltage deviation index

\( F_{C} \) :

Objective function of total operation cost

\( {\text{FF}}_{q,p}^{{}} ,{\text{FF}}_{q,p}^{\text{new}} \) :

Fitness function of the qth old and new solution in the pth pack

\( F_{\text{OF}}^{{}} \) :

Multi-objective function

\( F_{i}^{{}} \) :

The food source position of the ith dimension corresponding to the salp position

\( I_{b} \) :

Current magnitude in the bth branch without DGs

\( I_{b}^{\hbox{max} } \) :

Maximum limitation of the current magnitude in the bth branch

\( I_{b,q,p} \) :

The current magnitude in the bth line of the qth solution in the pth pack

\( I_{{{\text{Dg}},b}} \) :

Current magnitude in the bth branch with DGs

It:

Current iteration

ItMax :

Maximum iteration

\( N_{\text{Br}}^{{}} \) :

Number of branches in the distribution network

\( N_{\text{Bu}}^{{}} \) :

Number of buses in the distribution network

N c :

Number of coyotes in each pack

\( N_{\text{Dg}}^{{}} \) :

Number of DGs in the integrated distribution network

N Lo :

Number of all loads

N p :

Number of packs

N ps :

Population size

N c :

Number of coyotes in each pack

\( O_{\text{cv}} \) :

The number of control variables

\( {\text{OF}}_{q,p} \) :

Objective function of the qth solution in the pth pack

\( \omega_{A} ,\omega_{B} ,\omega_{C} \) :

The coefficients of the multi-objective function

\( {\text{Pos}}_{{{\text{Dg}},k}}^{{}} \) :

The position of the kth DG

\( {\text{Pos}}_{k}^{\hbox{min} } ,{\text{Pos}}_{k}^{\hbox{max} } \) :

The lower and upper bounds of the position of the kth DG

P :

The number of individuals in the sunflower population

r, r 2, r 3 :

Random numbers in range from 0 to 1

\( R_{b}^{{}} \) :

Resistance of the bth branch

S best,p, S worst,p :

The best solution and the worst solution in the pth pack

S best,rd1, S best,rd2, S best,rd3, S best,rd4 :

The best solutions picked up randomly from different packs

S cent,p :

The center solution in the pth pack

S g_best :

The best solution in the population

\( S_{q,p}^{{}} ,S_{q,p}^{\text{new}} \) :

The current and new solution of the qth coyote in the pth pack

S rd1,p, S rd2,p, S rd3,p, S rd4,p :

The randomly picked up solutions from the pth pack

\( S_{i}^{1} \) :

The leader salp position corresponding to the ith dimension

\( S_{i}^{k} \) :

The position of the kth salp corresponding to the ith dimension

TAPL:

Total active power loss of the network without any DG

TAPLDg :

Total active power loss of the network with DGs

ubi, lbi :

The upper bound and lower bound of the ith dimension in determining the salp position

\( V_{j}^{{}} \) :

Voltage at the jth bus

\( V_{j}^{\hbox{max} } \), \( V_{j}^{\hbox{min} } \) :

Lower and upper limitations of bus voltage magnitude

\( V_{j,q,p} \) :

The voltage magnitude at the jth bus of the qth solution in the pth pack

\( X_{i}^{{}} ,X_{{}}^{*} \) :

The ith current position and the best position of the current sunflower population

ABC:

Artificial bee colony algorithm

BB-BC:

Big bang-big crunch

BFOA:

Bacterial foraging optimization algorithm

BSOA:

Backtracking search optimization algorithm

COA:

Coyote optimization algorithm

DG:

Distributed generation unit

DGs:

Distributed generation units

GA:

Genetic algorithm

GA/PSO:

Hybrid genetic algorithm and particle swarm optimization

HAS:

Harmony search algorithm

PSO:

Particle swarm optimization

PLI-WOA:

Combined power loss index-whale optimization algorithm

Pu:

Per unit

SA:

Simulated annealing

SFO:

Sunflower optimization

SSA:

Salp swarm algorithm

WOA:

Whale optimization algorithm

TAPL:

Total active power losses

TOC:

Total operation cost

VDI:

Voltage deviation index

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Authors and Affiliations

  1. Institute of Research and Development, Duy Tan University, Danang, 550000, Vietnam

    Thai Dinh Pham

  2. Power System Optimization Research Group, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Thang Trung Nguyen & Bach Hoang Dinh

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Appendix

Appendix

See Tables 10, 11 and 12.

Table 10 The best location and capacity of DGs found by the proposed method and other methods for the IEEE 33-bus distribution network
Full size table
Table 11 The best location and capacity of DGs found by the proposed method and other methods for the IEEE 69-bus distribution network
Full size table
Table 12 The best location and capacity of DGs found by the proposed method and other methods for the IEEE 85-bus distribution network
Full size table

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Pham, T.D., Nguyen, T.T. & Dinh, B.H. Find optimal capacity and location of distributed generation units in radial distribution networks by using enhanced coyote optimization algorithm. Neural Comput & Applic 33, 4343–4371 (2021). https://doi.org/10.1007/s00521-020-05239-1

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