## 4 Node Sensitivity Analysis and Calculation Method  
For power networks with a small number of nodes, the optimal configuration scheme for the location and capacity of ETSHE can be easily calculated by exhaustive methods. When the power network is complicated, there are many installation nodes available for installing energy storage at this time. If the optimal node is still selected according to the exhaustive method, the calculation of the optimal allocation scheme is large, which cannot be solved or the result falls into a local optimum. For this reason, the sensitivity analysis method was proposed to calculate the sensitivity coefficient of electric regenerative heating equipment installed at the node, and the node with higher sensitivity was selected as the alternative set of the installation node of ETHSE, which will greatly improve the optimal allocation efficiency of electrical thermal storage. Sensitivity coefficient refers to the degree of sensitivity of the system, represented by state variables to changes in the control variables and disturbance variables [28]. For the electric storage thermal heating equipment location and capacity optimization configuration model, it refers to the sensitivity of the objective function of the optimal configuration to changes in energy storage installation capacity. The optimization objective of this paper is multi-objective function and the fundamental purpose of  
Figure 1: Optimization configuration model. installing energy storage is to effectively control the power quality problem of the distribution system. When a large number of single-phase photovoltaic power sources are connected to the system, it will cause voltage three-phase imbalance problems. However, as single-phase photovoltaic power generation has not been widely used, it has little influence on the three-phase unbalance degree of power grid voltage. Therefore, only the three-phase imbalance is considered when defining sensitivity. In a three-phase three-wire system, there is no zero-sequence component. For a three-phase system without a zero-sequence component, the simplified calculation method of the three-phase imbalance recommended by the national standard is as follows [29]:  
\[f_{\epsilon 2}=\sqrt{\frac{1-\sqrt{3-6L}}{1+\sqrt{3-6L}}}\times 100\% \tag{24}\]  
\[L=\frac{a^{4}+b^{4}+c^{4}}{\left(a^{2}+b^{2}+c^{2}\right)^  
storage system is installed at this node, the higher the value, the better the power quality will be. Therefore, by calculating the sensitivity coefficients of all nodes in the system, it is possible to find in advance a set of alternative nodes that are better at improving the power quality of the system, which can effectively reduce the number of computing nodes, greatly reduce the amount of calculations, and improve the optimization of the economy and efficiency of configuration. Nodes are ranked according to the sensitivity coefficient, and higher-sensitivity nodes are preferentially selected to form an initial optimized candidate set. Subsequently, the heuristic optimization algorithm can be applied to solve the model quickly. This paper used the adaptive inertial weight IMOPSO algorithm to solve the model. The main steps of the adaptive inertia weight IMOPSO algorithm are as follows:  
1. The network topology, switch state, node voltage range, distributed photovoltaic, wind parameters, and parameters of ETSHE in the distribution network system are initialized. The sensitivity coefficients of each node are calculated and sorted separately. The top 40% of the sorted nodes are selected to form a candidate set of installation nodes. 2. The parameters such as the size of the particle swarm, the maximum number of iterations of the algorithm, the acceleration factor, the value range of the adaptive inertia weight, and the speed range of the particles are set in the improved particle swarm optimization. 3. The particles in the candidate set are evaluated, and the fitness function value of each particle is calculated.