Abstract: Energy storage is a key component in mitigating power fluctuations of renewable energy sources and supporting the construction of new power systems. However, existing energy storage planning methods do not consider the potential dynamic changes in unit energy construction costs during the planning period, but only rely on a constant unit energy construction cost, which is not conducive for power system planners to comprehensively assess energy storage planning strategies. Therefore, this paper proposes an analytical methodology for energy storage planning considering variable unit energy construction costs, aiming to analyze the relationship between the energy storage unit energy construction costs and the energy storage planning results so that power system planners can get more comprehensive and effective information. Firstly, to address the nonlinear characteristics of the energy storage planning model caused by energy storage charging/discharging complementary constraints, a constraint relaxation-based linearization framework for energy storage planning models was proposed, transforming the original nonlinear optimization problem into a precise linear optimization problem. Furthermore, based on the linear optimization formulation of the energy storage planning models, the unit energy construction cost was treated as a variable parameter. Using the multi-parameter planning theory, an analytical mapping function between the unit energy construction costs and the energy storage planning results was derived, enabling quantitative analysis of the relationship. The proposed method was verified through numerical experiments in the IEEE 118-bus test system. The results show that the proposed method can solve the original nonlinear energy storage planning problem with reduced computational burden while maintaining high precision, enabling accurate quantification of the energy storage planning results.