| Inadequacy in voltage stability in power systems is one of the major concerns to utilities. The voltage stability problem is primarily due to the lack of reactive power reserves, and this thesis is to investigate an optimal reactive power planning problem. The planning problem is divided into two parts, the short-term and long-term planning problems. In the short-term reactive power planning the problem is decomposed into real power (P) and reactive power (Q) optimization modules. The advantage of this is that it uses the same cost objective function for P and Q unlike other conventional methods, which use the power loss function for the Q module.; Load flow for the base case is run to get the initial operating point. Linear Programming formulation is used in the P and Q optimization modules utilizing the revised simplex method. The control variables are the generator real power outputs for the real power module, bus voltages, and transformer tap-settings for reactive power module, with their limits as the constraints. Unlike the other methods this formulation uses the piece-wise linear function to represent quadratic cost function.; The long-term planning is to determine the optimal investment in the reactive power compensation devices. The method determines the optimal compensation to keep the system voltage profile within the prescribed range which may change due to load increase over a number of years. This is done by forming the long-term problem as an optimal control problem and decomposing the problem into a three-level hierarchical optimization problem. The long-term is decomposed into a number of yearly Hamiltonian minimization problems using the maximum principle. Each Hamiltonian minimization problem is then decomposed into investment and the short-term (operation) subproblems via the Bender's decomposition technique. The operation is solved by decomposing into P-Q subproblems. |
