Probabilistic Operation of Electric Power Systems Considering Environmental Constraint (Part 5)* -A Strict Method for Transmission Capacity-

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An optimum operation scheduling method is reported using quadratic programming. In this report, the optimum operation is considered as that which economically satisfiers all line capacities and environmental constraint. This method is developed in order to extend another method whose schedule satisfies many of the constraints of a faulty state in an electric power system. The limit of NO_x pollution is considered as a typical environmental constraint. Kuhn-Tucker conditions are shown for this problem. Except for the NO_x pollution constraint, the Kuhn-Tucker conditions are solved using quadratic programming. The kinds of artificial variables introduced, which are necessary for an initial feasible solution, are kept to a minimum so that the calculation can be done compactly. The cost function of the quadratic programming is constituted by the quadratic equations which are selected from Kuhn-Tucker conditions. The cost function is modified to a linear equation. The results of the model system simulations are compared with the quadratic programming method and LaGrange’s multipliers method. Investigating them, the following is shown :　LaGrange’s method is very fast for calculating time, but it is weak if there are many and severe constraint. The quadratic method can estimate the optimum operation strictly even when the constraints are many and severe.
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