This paper is the beginning part of the discussion on the multi-scale energy interactions in the Meiyu front rainstorm. The kinetic energy equations and potential energy equations of large scale background field, meso-α scale and meso-micro-β scale are derived from motion equations and thermodynamic equations in the z coordinate system using the anelastic approximation by dividing the basic physical quantity into three scales for the purpose to analyze the multi-scale energy interactions. Various energy conversions are presented in the energy equations. The kinetic energy equations mainly include kinetic energy transportation or conversion, the work of horizontal pressure gradient force, vertical perturbation pressure gradient force, buoyancy, Coriolis force and friction. The potential energy equations mainly include potential energy transportation or conversion, and the effects of buoyancy and diabetic heating. Among them, the effect of buoyancy is substantially the energy conversion term between the potential energy and kinetic energy, and thus is the most critical energy conversion term in the process of rainstorm development. In the future study, the energy equations will be applied to the Meiyu front rainstorm, and the physical mechanism for the diagnosed energy interaction, which affects the development and disappearance of rainstorm, will be given.