Although the instantaneous value analysis method makes it easier to clarify the instantaneous current and power distribution relationships between electrical sources and flows, if it is directly applied to analyze the source-flow Energy Distribution Relationship (EDR) of a large AC/DC power grid, there remain problems such as a large amount of calculation and incompatibility with common gateway energy metering modes. Therefore, a new method of analyzing EDR is proposed. For AC branch source-flow pairs, the distribution relationships of instantaneous current, instantaneous power and periodic energy are derived, and a method for calculating through-energy components and energy loss is proposed. This method is extended to DC branch source-flow pairs with virtual AC technology. Forward and backward tracking algorithms of EDR for all associated path chains of any network source-flow pair are proposed. The cases show that the method can calculate the grid-level EDRs, and provide theoretical support to further develop an integrated analysis system of energy-flow and non-energy flow for a smart grid. This work is supported by the Science and Technology Project of State Grid Corporation of China (No. SGTYHT/18-JS-206).