An algorithm based on the hypervolume indicator and its application to voltage coordinated control

•Defined ε-hypervolume indicator and proved its monotonicity with Pareto set.•An algorithm based the ε-hypervolume indicator was proposed.•A coordinated voltage control model was established.

Voltage coordinated control involves the coordinated control of multiple time scales and multi-objective space, which is one of the key technologies of the smart grid. This paper focuses on the physical nature of voltage coordinated control in multi-objective space and proposes a method of coordinated control based on the ε-hypervolume indicator to search for solutions in the multi-objective space partitioned by the ε-dominated domain. The method was compared with several mainstream multi-objective optimization methods on several grid models to verify its effectiveness.