The application relates to an combined heating power and cooling apparatus with energy storage for an active distribution network and its operating method. The apparatus is comprised of a generation apparatus, a generator, a waste heat recovering and absorbing heat pump, a high temperature flue gas-water heat exchanger, a medium temperature flue gas-water heat exchanger, a low temperature flue gas-water heat exchanger, a energy storing electric heat pump, a high temperature energy storing canister, a low temperature energy storing canister, a cooling tower a number of circulating water pumps and a number of valves. The operating method changes the traditional operation modes of the system “determining electricity based on heat” and “determining electricity based on cooling”, causes the system to regulate power of the generated electricity on grid, participate in the regulation of grid load, solve the problem of a limited ability of generation peak regulation due to the inter-coupling of power generation, heat supply and cooling supply.