Voltage security constrained minimization of power losses in an electric power system

Matjaž Dolinar (Faculty of Electrical Engineering, University of Ljubljana, Ljubljana, Slovenia)
Miloš Pantoš (Faculty of Electrical Engineering, University of Ljubljana, Ljubljana, Slovenia)
Drago Dolinar (FERI, University of Maribor, Maribor, Slovenia)



The purpose of this paper is to present an improved approach to reactive power planning in electric power systems (EPS). It is based on minimization of a transmission network's active power losses. Several operating conditions have to be fulfilled to ensure stable operation of an EPS with minimal power losses. Some new limitations such as voltage instability detection and generator capability curve limit have been added to the existing method in order to improve the reliability of reactive power planning. The proposed method was tested on a model of the Slovenian power system. The results show the achievement of significant reduction in active power losses, while maintaining adequate EPS security.


Optimal voltage profile has to be found in order to determine minimal possible active power losses of EPS. The objective function, used to find the optimal voltage profile, has integer and floating point variables and is non‐differentiable with several local minima. Additionally, to ensure secure operation of EPS, several equality and inequality boundaries and limitations have to be applied. Differential evolution (DE) was used to solve the optimization problem.


Corresponding reactive power planning can significantly reduce active power losses in EPS. However, such planning can affect the security of EPS, therefore, several additional constrains have to be considered. The presented constrains considerably improve the operational security of EPS.

Research limitations/implications

DE was used to solve the minimization problem. Although this method has proven to be fast and reliable, it is theoretically possible that the obtained solution is not global minimum.


Novel approach to voltage security constrained reactive power planning with additional nonlinear constrains, such as generator capability curves and voltage instability detection.



Dolinar, M., Pantoš, M. and Dolinar, D. (2009), "Voltage security constrained minimization of power losses in an electric power system", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 28 No. 3, pp. 613-625. https://doi.org/10.1108/03321640910940882

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