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This paper presents a new method for solving the multi-area power system economic dispatch (MAED) problem with tie line constraints. This formulation extends the traditional economic dispatch methods used in study applications such as unit commitment to include area demand constraints, area reserve constraints, and tie line capacity constraints between the modeled areas. The MAED is formulated as a capacitated nonlinear network flow problem which is solved using a high-speed network load flow code. The MAED determines the amount of power that can be economically generated in one area and transferred to another area to displace generation in the second area. The network flow model does not compute the actual power transfer between areas. The paper demonstrates that a significant number of the problem constraints may be formulated as network-type, and as a result, the method provides a robust, high-speed solution method for surprisingly large class of electric utility problems including the ability to analyze potential purchases and sales in a multi-area power system environment.