Decentralised conic optimisation of reactive power considering uncertainty of renewable energy sources

This study proposes a decentralised reactive power optimisation of capacitors in distribution system with uncertain renewable energy sources (RES). The optimisation problem is modelled as minimising the active power loss and installed capacitors costs, subject to power flow constraints and other operation conditions. In view of the non-linear power flow equality constraints with uncertain power of the RES, the optimisation problem is hard to be solved efficiently due to the non-linear and stochastic issues. To this end, the discrete probability model of RES has been utilised to build the multi-scenario deterministic formulation of the stochastic problem, which further changes to a mixed integer conic optimisation (CO) model by relaxing the non-linear power flow equations. Besides, in keeping with the growing complexity of modern distribution system, a decentralised CO algorithm for large-scale problem is developed to separate the problem into smaller subproblems. The sufficient conditions which guarantee the exactness of the conic relaxed power flow equalities in subproblems are discussed as well. Simulations verify the effectiveness of the proposed algorithm.