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Modified soccer game optimization and its application on power flow and distribution generation placement problems of distribution systems

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Abstract

Distribution power flow (DPF) and distribution generation (DG) placement are important problems in modern distribution systems (DSs). The DPF problem is modelled as an optimization problem of minimizing the node power mismatches, while considering the corrections of node voltages as solution variables. The node locations and DG ratings of DG placement (DGP) problem are considered as optimization parameters with an objective of minimizing the network loss (NL). The soccer game optimization (SGO) models the movements of soccer game players by "move-off" and "move-forward" phases, and has the drawback of performing simple arithmetic average for representing random stochastic movements of players during its "move-forward" phase. This paper endeavours to first remodel the move-forward phase by adapting Levy Flight mechanism to simulate the random jumping action of players to a long distance in getting the ball and scoring a goal, and then develop new modified SGO (MSGO) based methods for solving the formulated DPF and DGP problems. The simulation study exhibited that the proposed DPF method is 751 and 666 times faster than the NR PF technique and the DGP method is able to save the NL by 65% and 69% for 33 and 69 node systems respectively.

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Abbreviations

BBO:

Biogeography based optimization

DDPF:

Decoupled DPF

DG:

Distribution generation

DGP:

DG placement

DPF:

Distribution PF

DS:

Distribution systems

FACTS:

Flexible AC transmission systems

FBS:

Forward and backward sweeps

FCPF:

Feeder current based PF

FDGPS:

Flower pollination based DGP scheme

FF:

Fitness function

HCACO:

Hyper cube-ant colony optimization

MPGSA:

Modified plant growth simulation algorithm

MSGO:

Modified SGO

MSGO-DPF:

MSGO based DPF

MSGO-DGP:

MSGO based DGP

NL:

Network loss

NR:

Newton-Raphson

PF:

Power flow

SA-HSO:

Sensitivity analysis and harmony search optimization

SFLO:

Shuffled frog leap optimization

SGO:

Soccer game optimization

TL-GWO:

Teaching–learning and grey wolf based optimization

UVDA:

Uniform voltage distribution based algorithm

VRDPF:

Voltage regulation based DPF

A:

Active team

B:

Substitute team

\(D\) :

Ball dribbler

\(i_{qp}\) and \(i_{qp}^{\max }\) :

Feeder current from node-q to node-p and its limit respectively

\(na\) and \(nb\) :

Number of active and substitute players respectively

\(ng\) :

Number of DG units

\(nn\) :

Number of nodes

\(N_{p}\) :

Node location of pth DG unit

\(nsv\) :

Number of solution variables

\(P_{G,p}\) :

Real power generation of pth DG unit

\(P_{L,p}\) :

Real power load at node-p

\(P_{i}^{sp}\) and \(Q_{i}^{sp}\) :

Specified real and reactive powers at node-i respectively

\(P_{i}^{cal}\) and \(Q_{i}^{cal}\) :

Calculated real and reactive node powers at node-i respectively

\(rand\) :

Random number (0, 1)

\(S^{D}\) :

Position of ball dribbler

\(S^{D} (t)\) :

Position of the ball dribbler at instant-t

\(S^{i}\) :

Position ith soccer game player

\(S^{i} (t)\) :

\(S^{i}\) At instant-t

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

Best memorized position of \(S^{i}\)

\(S_{mem}^{i} (t)\) :

\(S_{mem}^{i}\) At instant-t

T :

Maximum number of iterations

\(t\) :

Iteration counter

\(U_{j}\) and \(L_{j}\) :

Upper and lower limits of jth solution variable respectively

\(V\) :

Vector of node voltage magnitudes

\(V^{o}\) :

Initial values for \(V\)

\(Y_{ij} \angle \theta_{ij}\) :

Element of node admittance matrix corresponding to ith row and jth column

\(\beta_{1} ,\;\beta_{2} ,\;{\text{and}}\;\beta_{3}\) :

Weight parameters

\(\gamma\) :

A scaling factor that controls the step size \(ss\)

\(\sigma\) :

A Constant

\(\eta\) :

Probability factor for replacing an active player by a substitute player

\(\theta\) :

A constant

\(\rho_{1} ,\rho_{2}\) :

Switch probability parameters

\(\delta\) :

Vector of node voltage angles

\(\delta^{o}\) :

Vector of initial node voltage angles

\(\Im\) :

Levy flight

\(\Phi (\sigma )\) :

A gamma function

\(\Psi^{DPF}\) :

Cost function of the DPF problem

\(\Psi^{DGP}\) :

Cost function of the DGP problem

\(\psi_{1}\) and \(\psi_{2}\) :

Penalty factors

\(\Im\) :

A set of feeders, whose currents violate the respective limit

\(\Delta P_{i}\) and \(\Delta Q_{i}\) :

Real and reactive power mismatches at node-i respectively

\(\Delta V\) :

Correction vector of node voltage magnitudes

\(\Delta V_{i}\) :

Voltage magnitude of ith node

\(\Delta \delta\) :

Correction vector of node voltage angles

\(\Delta \delta_{i}\) :

Voltage angle of ith node

\(\Delta \delta^{net}\) and \(\Delta V^{net}\) :

Vector of net required corrections of node voltage angles and node voltage magnitudes respectively

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Authors and Affiliations

  1. Department of Electrical Engineering, Annamalai University, Annamalainagar, Tamil Nadu, India

    Yogambari Venkatesan & Aravindhababu Palanivelu

  2. Department of Electrical Engineering, Sreenidhi Institute of Science and Technology, Hyderabad, India

    Koganti Srilakshmi

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  1. Yogambari Venkatesan
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  2. Koganti Srilakshmi
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Correspondence to Yogambari Venkatesan.

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Venkatesan, Y., Srilakshmi, K. & Palanivelu, A. Modified soccer game optimization and its application on power flow and distribution generation placement problems of distribution systems. Evol. Intel. 16, 539–552 (2023). https://doi.org/10.1007/s12065-021-00677-9

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