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A multi-period optimal power dispatching problem is considered for a network of energy utilities connected via multiple transmission lines, where the goal is to find the lowest operational-cost dispatching of diverse generation sources to satisfy demand over a time horizon comprised of multiple periods, and consisting of varying power and demand conditions. Our model captures various interactions among the time-varying periods including which generators should be allocated, when they should be brought into use, and the operational costs associated with each. An efficient algorithm is derived that exploits the structure inherent in this multi-period economic dispatch problem. The control options of our optimization model consist of the dispatching order and dispatching amount of available power generators. Our solutions are shown to be globally optimal under conditions that often arise in practice. Numerical experiments based on these solutions and analysis are presented to illustrate our findings.