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An improved version of salp swarm algorithm for solving optimal power flow problem

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Abstract

Salp swarm algorithm (SSA) is a recent optimization technique inspired by behavior of the salp chains in deep oceans. However, the SSA is efficient, simple and easy to implement, it is susceptible to stagnation at local optima for some cases. The main contribution of this paper is proposing an improved salp swarm algorithm algorithm (ISSA) for enhancing the search capabilities of the original SSA to solve the optimal power flow (OPF) problem. In the proposed ISSA, both of exploration and the exploitation processes are enhanced. The exploration process is achieved by applying a random mutation to find new searching areas while an adaptive process is developed to enhance the exploitation process by focusing on the most promising search area. This strategy will balance the transformation between exploration and exploitation. The ISSA is employed to achieve OPF with non-smooth and non-convex generator fuel cost functions such as; minimizing quadratic fuel cost, piecewise quadratic cost, quadratic fuel cost considering the valve-point effect and prohibited zones. The main advantages of the ISSA are avoiding stagnation at local optima and can solve nonlinear and non-smooth optimization problems where its adaptive operators balance between the exploration and exploitation phases of this algorithm. However, the parameters of ISSA need to be carefully defined before application of algorithm. The proposed algorithm is validated using the standard IEEE 30-bus, IEEE 57-bus and IEEE 118-bus test systems. The performance of proposed algorithm is comprehensively compared with moth-flame optimization algorithm, improved harmony search algorithm, genetic algorithm and other reported optimization techniques. The results prove the effectiveness and superiority of the proposed algorithm compared with other optimization techniques.

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Abbreviations

\( x_{j}^{1} \) :

The position of the leader in the jth dimension

\( x_{j}^{i} \) :

The position of ith follower salp in jth dimension

\( F_{j} \) :

The position of the food source in the jth dimension

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

The lower and upper bound of jth dimension

C 2, C 3, C 4 :

Random numbers in the interval of [0,1]

C 1 :

Time varying coefficient

t :

The current iteration

\( T_{\hbox{max} } \) :

The maximum number of iterations

\( v_{\text{final}} \) :

The final speed

v 0 :

The initial speed

\( V_{\text{L}} \) :

The voltage of load bus

\( Q_{\text{G}} \) :

The reactive power output of generators

\( S_{\text{TL}} \) :

The apparent power flow in transmission line

NPQ:

Number of load buses

NPV:

Number of generators PV buses

NTL:

Number of transmission lines

\( \lambda_{p} ,\lambda_{v} ,\lambda_{Q} ,\lambda_{s} \) :

Penalty factors

\( \delta_{j} , \delta_{i} \) :

Voltage angles bus i and j

A :

Time varying parameter

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

The minimum and the maximum voltage limits of load bus, respectively

\( T_{i}^{\hbox{min} } ,T_{i}^{\hbox{max} } \) :

The minimum and the maximum limits tap setting of transformers, respectively

\( P_{\text{Gi}}^{\hbox{min} } ,P_{\text{Gi}}^{\hbox{max} } \) :

The minimum and the maximum generated active limits ith generator, respectively

\( S_{{{\text{TL}},i}}^{\hbox{max} } \) :

The maximum apparent power flow limit of line i

x 0 :

The initial position of salp

E :

Time varying coefficient

F :

The objective function

x :

The state variables vector

u :

The control variables vector

\( g_{i} , h_{j} \) :

The equality and inequality constraints,

m, n :

Number of equality and inequality constraints

POZs:

Prohibited operating zones

\( P_{G1} \) :

The generated power of slack bus

\( P_{\text{G}} \) :

The output active power of generator

\( V_{\text{G}} \) :

The voltage of generating bus

\( Q_{\text{C}} \) :

The injected reactive power of shunt compensator

T :

Tap setting of transformer

NG:

Number of generators

NC:

Number of shunt compensator

NT:

Number of transformers

\( X_{j}^{\text{new}} \) :

The new position of the salp swarm

a i, b i, c i :

The cost coefficients of ith generator

d i, e i :

The fuel cost coefficients of the ith generator unit with valve-point effects

P D, Q D :

Active and reactive load demand

G, B :

Conductance, substance of transmission line

\( Q_{\text{ci}}^{\hbox{min} } ,Q_{\text{ci}}^{\hbox{max} } \) :

The minimum and the maximum limits of compensator reactive power, respectively

\( A_{\hbox{max} } ,A_{\hbox{min} } \) :

The minimum and the maximum A limit of the parameter, respectively

\( Q_{\text{Gi}}^{\hbox{min} } ,Q_{\text{Gi}}^{\hbox{max} } \) :

The minimum and the maximum generated reactive limits ith generator, respectively

\( K_{\hbox{min} } ,K_{\hbox{max} } \) :

The minimum and the maximum K limiter respectively

a :

The slap’s acceleration

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Acknowledgements

The authors thank the support of the National Research and Development Agency of Chile (ANID), ANID/Fondap/15110019.

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Authors and Affiliations

  1. Electrical Engineering Department, Faculty of Engineering, Aswan University, Aswan, 81542, Egypt

    Salma Abd el-sattar & Salah Kamel

  2. Electrical Engineering Department, Faculty of Engineering, Sohag University, Sohag, Egypt

    Mohamed Ebeed

  3. Department of Electrical Engineering, University of Jaén, 23700 EPS Linares, Jaén, Spain

    Francisco Jurado

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Abd el-sattar, S., Kamel, S., Ebeed, M. et al. An improved version of salp swarm algorithm for solving optimal power flow problem. Soft Comput 25, 4027–4052 (2021). https://doi.org/10.1007/s00500-020-05431-4

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