## 1 Introduction  
With the increasing penetration of renewable energy sources, the need for flexibility in distribution networks (DN) over multiple time scales has increased [1]. In this context, flexible resources such as battery energy storage systems (BESS) and district heat networks (DHN) have become an important instrument for smoothing out power fluctuations of renewable energy sources and improving power quality due to their ability to transfer energy over time [2]. Therefore, it is important to study the cooperative operation method of DN with different types of flexible resources in order to improve the flexible regulation capability of the system and thus improve the operation economy of the system [3]. With the characteristics of fast power regulation and storage of electricity, battery energy storage systems play a large role in smoothing power fluctuations of intermittent energy sources, shaving peaks and filling valleys, improving voltage quality, and providing backup power sources, etc. It is the key to realizing flexible regulation of widely accessed distributed energy sources in DN. There have been more references on the cooperative dispatch of DN and BESS. In [4], an optimal dispatch method of BESS in unbalanced distribution networks is proposed so as to minimize power losses and simultaneously ensure that the network satisfies current and voltage constraints. In [5], an optimal dispatch method for BESS in DN considering peak-load transfer is proposed to improve the voltage distribution in DN. In order to mitigate the adverse effects of renewable energy sources in active distribution networks, energy management and the optimal dispatch method of BESS have been proposed in [6] to reduce operation costs, power losses, and voltage fluctuations in unbalanced distribution networks. In [7], a joint day-ahead and intraday optimal dispatch method for active distribution networks is proposed, which is capable of dispatching centralized and distributed energy storage based on their differences in capacity and responsiveness. DHN is a potential flexible resource that can break the rigid constraints of real-time balance between heat supply and heat load by adjusting the water supply temperature [8; 9; 10]. This type of energy storage effect provides additional flexible regulation capability to DN to consume renewable energy. Several references have studied the cooperative dispatch of DN and DHN. In order to improve the absorption capacity of DN for wind power, an integrated electric-heat dispatch model considering the heat inertia of the DHN has been developed in [11], in which an integrated model for fully simulating the dynamic distribution of the district heat network has been proposed for the first time. In [12], a centralized optimal dispatch model for an integrated electric-heat energy system is developed by considering the use of electric boilers and heat storage tanks to improve the flexibility of combined heating and power (CHP) units for better consumption of wind power. In [13; 14], pipelines in the DHN and buildings are further utilized as heat storage to provide flexibility in order to solve the problem of wind curtailment in the DN, and a dispatch model for CHP that takes into account the heat storage capacity of pipelines and buildings is developed. In [15], a coordinated operation strategy based on model predictive control for a multi-area integrated electric-heat energy system is proposed, which takes into account the heat storage capacity of DHN by taking into account the transmission delay of the pipelines and the heat inertia of the buildings. All of the above references adopt the centralized cooperative dispatch methods, whereas the DN, DHN, and BESS are managed by the distribution network operator, the district heat network operator, and the energy storage aggregator, respectively, and the centralized cooperative dispatch of them is difficult to achieve in this context.