This paper proposes an optimization method of demand resource capacities to manage the voltage in the distribution network with photovoltaic generations (PV). The proposed method is within the cooperative voltage management system based on the cooperative game theory in which an imputation in a non-empty core is guaranteed. In the proposed method, the optimization problem is formulated as a bi-level programming problem in which a leader, who is a distribution network operator, optimizes the demand resource capacities of consumers and followers, who are consumers in the distribution network, determine the amount of controlled resources under the optimized resource capacities. In order to solve the bi-level programming problem by a commercial solver efficiently, it is converted to a mixed-integer linear programming problem. The imputation in the core is computed based on a dual solution of the lower level problem. The proposed method is validated by computational experiments using a large scale distribution network model with multiple feeders and PVs.
