Salp swarm optimizer to solve optimal power flow comprising voltage stability analysis

  • Attia A. El-FerganyEmail author
  • Hany M. Hasanien
Original Article


A new attempt of employing salp swarm algorithm (SSA) to tackle the optimal power flow (OPF) problem is demonstrated in the current study. This aforementioned problem has four fitness functions to be optimized such as (1) the sum of generating units’ fuel costs, (2) total network real power losses, (3) entire sum of voltage deviation of load buses, and (4) static voltage stability (VS) of electric power systems. At initial stage, these objective are solved one by one, and at a later stage, different vector objective functions are solved simultaneously by the SSA. The VS study based on a modal analysis is taken into consideration as an objective function. In this issue, the eigenvalues and eigenvectors of a reduced Jacobian matrix due to the reactive power change are figured. The smaller magnitude of eigenvalues indicates the vicinity to system voltage instability. As the magnitude of eigenvalues increases, the incremental voltage decreases, which means strong VS. The output active power of generating units, their voltages, transformers tap setting, and capacitor devices represent the search field. Two electric grids such as IEEE 57- and 118-bus electric networks are demonstrated to examine the performance of the SSA. The effectiveness of the SSA–OPF methodology is compared with that obtained by using other competing optimization methods. Furthermore, statistical performance measures comprising parametric and nonparametric tests are made and the simulation results are extensively verified which indicate a competition of the SSA with others algorithms in solving the OPF problem.


Power system operations Optimization approaches Voltage stability Modal analysis 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interests.


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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.Electrical Power and Machines Department, Faculty of EngineeringZagazig UniversityZagazigEgypt
  2. 2.Electrical Power and Machines Department, Faculty of EngineeringAin Shams UniversityCairoEgypt

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