The realization of "thermoelectric decoupling" through thermal storage technology is considered the most feasible technical route to improve the peaking capacity of CHP units. However, the evolutionary characteristics of the thermocline in the limited space within the hot water storage tank are influenced by the coupling of structural and operational parameters, making it difficult for comprehensive performance experiments. Therefore, it is difficult to form an analysis system from the structural design to the experimental verification of the hot water storage tank. In order to explore the similar laws in the operating characteristics of different sizes of hot water storage tanks and to realize the transition from large-size structural design to small-scale experiments, the theoretical design equations of the simplified hot water storage tank model are first derived in the moving coordinate system. According to the control equations and boundary conditions, the similarity conditions of operating characteristics of different sizes of hot water storage tanks are analyzed theoretically. The study concludes that tanks with the same operating characteristics should ensure equal Reynolds number, similar structural parameters, and other boundary conditions are otherwise consistent. It is further concluded that the ratio of the operating time of a hot water storage tank is equal to the square of the ratio of its geometric dimensions. Moreover, the accuracy of the numerical model is verified experimentally and the operating characteristics of different sizes of hot water storage tanks are simulated. The simulation results show that the method in this paper has high accuracy in predicting the heat release time and designing the hot water storage tank size. The dimensionless temperature profiles of hot water storage tanks satisfying the similarity condition have very high similarity in dimensionless time, and the maximum difference in capacity utilization accumulation is only 0.06%. The findings of this study can provide some theoretical references for the theoretical design and optimization process of thermal storage tanks.