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Multi-objective optimal power flow solutions using a constraint handling technique of evolutionary algorithms

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Abstract

In power systems, optimal power flow (OPF) is a complex and constrained optimization problem in which quite often multiple and conflicting objectives are required to be optimized. The traditional way of dealing with multi-objective OPF (MOOPF) is the weighted sum method which converts the multi-objective OPF into a single-objective problem and provides a single solution from the set of Pareto solutions. This paper presents MOOPF study applying multi-objective evolutionary algorithm based on decomposition (MOEA/D) where a set of non-dominated solutions (Pareto solutions) can be obtained in a single run of the algorithm. OPF is formulated with two or more objectives among fuel (generation) cost, emission, power loss and voltage deviation. The other important aspect in OPF problem is about satisfying power system constraints. As the search process adopted by evolutionary algorithms is unconstrained, for a constrained optimization problem like OPF, static penalty function approach has been extensively employed to discard infeasible solutions. This approach requires selection of a suitable penalty coefficient, largely done by trial-and-error, and an improper selection may often lead to violation of system constraints. In this paper, an effective constraint handling method, superiority of feasible solutions (SF), is used in conjunction with MOEA/D to handle network constraints in MOOPF study. The algorithm MOEA/D-SF is applied to standard IEEE 30-bus and IEEE 57-bus test systems. Simulation results are analyzed, especially for constraint violation and compared with recently reported results on OPF.

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Abbreviations

CH:

Constraint handling

EA:

Evolutionary algorithm

HV:

Hypervolume

MOEA/D:

Multi-objective evolutionary algorithm based on decomposition

MOOPF:

Multi-objective optimal power flow

MOP:

Multi-objective optimization problem

PF:

Pareto front

p.u.:

Per unit

SF:

Superiority of feasible solutions

VAR:

Volt-ampere reactive

nl:

Number of transmission lines

NB:

Total number of buses

NC:

Number of shunt (VAR) compensators

NG:

Number of generators

NL:

Number of load buses

NT:

Number of tap-regulated transformers

ai, bi, ci :

Cost coefficients of generator i

B ij :

Susceptance between buses i and j

G ij :

Transfer conductance between buses i and j

P Di :

Active power demand at bus i

P Gi :

Active power of generator at i-th bus

Q Ck :

Shunt (VAR) compensation at k-th bus

Q Di :

Reactive power demand at bus i

Q Gi :

Reactive power of generator at i-th bus

S lq :

Loading of q-th line

T j :

j-th branch transformer tap

V j :

Voltage magnitude of j-th bus (either generator or load)

VD:

Aggregate voltage deviation of load buses in the network

V Gi :

Voltage magnitude of i-th generator bus

V Lp :

Voltage magnitude of p-th load bus

\( \alpha_{i} , \beta_{i} , \gamma_{i} ,\omega_{i} , \mu_{i} \) :

Emission coefficients of generator i

δ j :

Voltage angle at bus j

δ ij :

Voltage angle difference between buses i and j

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Funding

This work is supported by the Singapore National Research Foundation (NRF) under its Campus for Research Excellence and Technological Enterprise (CREATE) program.

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Authors and Affiliations

  1. School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, Singapore

    Partha P. Biswas & P. N. Suganthan

  2. Kyungpook National University, Daegu, South Korea

    R. Mallipeddi

  3. Department of Engineering, University of Cambridge, Cambridge, UK

    Gehan A. J. Amaratunga

Authors
  1. Partha P. Biswas
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  2. P. N. Suganthan
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  3. R. Mallipeddi
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  4. Gehan A. J. Amaratunga
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Correspondence to R. Mallipeddi.

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Communicated by V. Loia.

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Appendix

Appendix

See Table 18.

Table 18 Cost and emission coefficients of generators for IEEE 30-bus (Chaib et al. 2016; Shabanpour-Haghighi et al. 2014) and IEEE 57-bus (Yuan et al. 2017; Biswas et al. 2018c) systems
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Biswas, P.P., Suganthan, P.N., Mallipeddi, R. et al. Multi-objective optimal power flow solutions using a constraint handling technique of evolutionary algorithms. Soft Comput 24, 2999–3023 (2020). https://doi.org/10.1007/s00500-019-04077-1

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