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This is the first paper in a two-part report on linear programming (LP) applied to power system security control calculations. The advantages of an LP approach are complete computational reliabilit and very high speed, making it suitable for real-time or study-mode purposes. Both corrective and preventive security control strategies are dealt with. Active- power control is exercised over generators, phase shifters and hvdc links. Load shedding and emergency start-up of plant are included. Part I presents the basic LP formulation and algorithm, and gives the computational details necessary to obtain very fast solutions. Specific applications to practical power systems are described in Part II1.