A particle swarm optimization-based approach for pricing VAR providers in the electricity market with the consideration of voltage security

This paper introduces an integration of particle swarm optimization "PSO" and successive linear programming "SLP" for dealing with VAR ancillary service problem in a competitive market-based environment. The main target of the developed market is to enable transmission operator "TO" to procure VAR service in a minimum payment while maintaining the system security in normal states and emergency state. In order to achieve this purpose, the problem is stated as large-scale highly nonlinear constrained optimization problem with a non-differentiable objective function representing VAR payment and operational costs. This type of problem is hard to be treated straightforwardly by the classical optimization methods. Therefore, we propose here a two layer hybrid PSO/SLP approach, which is suited for carrying out the difficulties associated with non-differentiable and discontinuous objective functions. The PSO is used in the first layer to find the global minimum payment of VAR contracts that maintain all the constraints including voltage security in all the transition states. The SLP is used in the second layer to minimize the power losses cost in the normal state and control costs in the emergency states. The proposed method has been examined on the standard IEEE 57 bus-system and compared with GA/SLP method to demonstrate its capability