On the direct solution of power system optimisation problems

Nonlinear, quadratic, flexible and linear programming techniques have been applied to solve the optimal power flow and transmission system expansion problems to ensure that the power system is operating at minimum cost with all security constraints satisfied and to determine the minimum-cost additions required to accommodate known changes in demands and generation respectively. These methods are generally slow and computationally expensive, and hence cannot be applied for power system operational planning. Though the linear programming approach is generally accepted and widely used, least squares methods have been shown to have good convergence properties with speed advantages, lower computer storage requirements, and wide applications for short-term operational planning of power systems Kabe (1984) presented a simple, straight-forward and elegant mathematical technique for obtaining direct solutions to LP problems. The paper illustrates the use of Kabe´s algorithm for power rescheduling and transmission system expansion using a 4-bus system with emphasis on computational techniques, and critically examines the efficiency of the method and why it is particularly useful for power system optimisation problems