A hierarchical time-varying optimization algorithm for Photovoltaic-energy storage to suppress three-phase imbalances in active distribution networks

• An index for evaluating three-phase voltage imbalance degree is established. • An online optimization model for three-phase unbalanced distribution network is established. • The sensitivity associated with the three-phase unbalance is decoupled. • An online optimization method based on voltage measurement feedback is designed. • The method only depends on local measurements and boundary information for each distribution area. For three-phase unbalance problems due to excessive single-phase loads, unbalanced load connections and ground faults, etc. This paper proposes a hierarchical time-varying optimization algorithm for active distribution networks to suppress three-phase voltage imbalance. First, an evaluation index of three-phase voltage unbalance is established, and a time-varying optimization model of the distribution network that includes three-phase unbalance constraints is developed by taking into account the regulation of photovoltaic (PV) and energy storage systems; second, a time-varying optimization method for distribution networks based on voltage measurement feedback is designed, in this method, the sensitivity of PV and energy storage regulation to mitigate three-phase imbalance is calculated based on voltage measurements, the sensitivity related to the three-phase imbalance is decoupled at the boundaries of different zones within the distribution network, this sensitivity can be obtained by combining voltage measurement feedback from within the zones and information exchange between zones; finally, the results are iteratively refined using the distribution network information obtained through measurements, this iterative process achieves a time-varying optimization tracking effect that suppresses three-phase imbalance. The effectiveness and superiority of the proposed algorithm were validated through an IEEE 123–101 node medium–low voltage distribution network case study. The case study results demonstrate that the algorithm can effectively reduce system three-phase voltage imbalance degree.