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

•The proposed method is based on Circuit Theory in combination with Aumann-Shapley Method.•It quantifies the individual contribution of each agent, even when connected to the same bus.•It shows that the line shunt injects a significant part of reactive power required by the load.•It fully allocates the reactive power, thanks to the additive property of the Aumann-Shapley Method.•The results show that the proposed method doesnt require strong computational effort. 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.