Reactive power allocation through the modified Z-bus and Aumann-Shapley method

This paper presents a new method based on the circuit theory and game theory for the allocation of reactive power. The allocation is calculated for each load, identifying and quantifying the responsibility of each reactive source. In the proposed method: the generators, line shunt, and bus shunt are modeled as current sources and loads are modeled as constant admittance, and obtained modified Z-bus matrix using circuit theory, which was coupled to the Aumann-Shapley method for calculating the unitary participation of each current source in the reactive power consumed by each load, considering each one as an independent player of the "reactive power allocation" game. The properties of the Aumann-Shapley method ensure equitable allocation and recovery of the total reactive power. Numerical results applied to the 5-bus and IEEE 30-bus systems are presented, discussed and compared with the other methods to demonstrate the applicability of the proposed method.