Abstract: Insufficient capacity and output of black-start power supply for micro-grid will lead to its frequency and voltage instability.Therefore，a hybrid energy storage system（HESS）within lithium batteries and lead acid batteries is proposed as the coordinated control method of the black-start power supply for photovoltaic and energy storage micro-grid.In order to improve the long-term operation of island micro-grid，the low-frequency component of an HESS dispatching command is taken as the power command of a lead-acid battery.Lead-acid batteries provide capacity and power support for the HESS for their high cost performance，while lithium batteries provide voltage and frequency support for the micro-grid for their long service lives. According to the characteristics of the batteries，the cost model including investment，operation and maintenance cost of an HESS is established.Power systems computer aided design（PSCAD）simulation tests can verify the effectiveness of the method proposed.

Key words: photovoltaic and energy storage micro-grid, hybrid energy storage system, island operation, black start, coordinated control, lead-acid batter, lithium battery, photovoltaic power, wind powe