The Interarea Matrix: A Tie Line Flow Model for Power Pools

This paper presents a method of modeling the ties and lines in a power pool for use in dispatch, pool costing, and security- related functions. External pool ties, as well as ties and lines, within the pool are modeled. The networks of all pool members as well as those external to the pool are incorporated in the model. The model consists of a matrix whose rows represent ties and lines and whose columns represent generators, loads if explicitly represented, and net interchanges. Both current and power models are given. The current model yields tie currents when postmultiplied by a current vector and the power model yields tie powers when postmultiplied by a power vector. The model allows loads to be treated explicitly, as mentioned above or implicitly, where the load currents or powers are not required for tie flow determinations. Lines within the areas of the pool are included under the tie designation. Off-nominal autotransformers and phase shifters, which represent a difficult case, are rigorously considered.