An Integrated Electricity–Gas–Heat Energy System Based on the Synergy of Long- and Short-Term Energy Storage

New energy sources, such as wind and solar energy, have been widely adopted; however, their volatility and instability have become the key issues restricting their utilization. To cope with this challenge, hybrid energy storage systems, as flexible regulation schemes, are capable of balancing the supply and demand of the power system according to different timescales and power demands, and enhancing the efficiency and utilization of new energy sources. Therefore, this paper proposes an integrated energy system planning and optimization method based on hybrid energy storage. Firstly, an adaptive noise integration empirical modal decomposition method based on the optimization improvement of the grey wolf algorithm is designed for the power allocation strategy of the hybrid energy storage system; secondly, for the electric–gas system, an energy management strategy for the hybrid electric–gas energy storage system, taking into account the operating characteristics of the alkaline electrolyzer, is proposed in order to strengthen the complementary mechanism between electric energy storage and gas energy storage. Finally, a multi-objective planning and optimization model for a comprehensive energy system based on a hybrid energy storage system is constructed. The combined configuration of long-term and short-term energy equipment can flexibly adjust energy supply and storage strategies according to demand changes on different timescales, achieve optimal resource allocation, and ensure the stability, economy, and reliability of the system. This paper uses a park in Shanxi, China, as a case study to validate the effectiveness of the methodology proposed in this paper. The example shows that the configuration of the electrical–thermal hybrid energy storage system proposed in this paper leads to a significant improvement in the economy, with an increase in annual profit of CNY 3.78 million, or 22.96%. At the same time, environmental protection is significantly enhanced, and total annual carbon emissions are reduced by 7.4 tons, with a reduction of 19.23%.