The high penetration of distributed photovoltaic generation in distribution networks is prone to causing frequent overvoltage problems. However

traditional centralized optimal scheduling methods suffer from high communication requirements and slow response speeds

making it difficult to meet the demands of real-time voltage regulation. To address this issue

a distributed fast voltage regulation method for energy storage in distribution networks based on linear quadratic optimal control is proposed. First

to reduce communication burden

the distribution network is partitioned into clusters according to the electrical-distance-based modularity index. Second

an optimal control model for the active distribution network is established

with voltage recovery and energy storage power balance as the control objective. A distributed controller based on a novel observer is then designed

in which the observer gain is optimally selected to enhance the voltage control speed. Finally

simulations are conducted on the IEEE33-bus and IEEE69-bus systems. The results show that the proposed distributed optimal control method for energy storage can effectively eliminate node voltage violations while ensuring power balance among the energy storage units

thereby improving the voltage profile of the distribution network.