Optimal power flow for the Kenya power system using the steepest descent method

Abstract

Economy and reliability of service are important considerations in power system operation and planning. The primary objective in power system planning and operation is to minimise the cost of meeting the power requirements of the system over some appropriate period of time and in a manner consistent with reliable service. The appropriate time could be short ( say afew minutes) or long ( say one year) depending on the nature of the energy resources available to the system. Obviously, the aim in the utilization of energy resources is to realise the greatest possible value during the period of operation in terms of fuel usage. Thermal or gas stations rely on fossil fuels like coal, diesel, gas etc for their operation. In addition to being expensive, fossil fuels are exhaustible and therefore thermal stations should be set to operate with minimum cost so as to reduce fuel usage. Hydro and geothermal stations have negligible operating costs but should nonetheless be operated efficiently if the available hydro and geothermal resources are to be exploited to the maximum. The limiting factor is of course system constraints like voltage levels, power flow on transmission lines, generator output limits, etc., which should be maintained within an acceptable operating range to ensure reliability of supply. An optimal power flow problem formulates an appropriate objective function ( cost, real power loss, load shedding etc.) which is then minimised subject to satisfying system constraints like voltage levels, transformer taps, line flows etc. The solution can be obtained using several non - linear programming techniques which include the steepest descent method, Quadratic Programming Method ( QPM) and the Gradient Projection Method (GPM) among others. In this thesis, the optimization problem is solved using the steepest descent method and targets the Kenya Power System. The solution technique is based on the Newton Raphson load flow formulation, a first order gradient adjustment algorithm for minimising the objective function and use of penalty functions to account for violation of dependent variables. These include system security constraints such as voltage levels on load buses and real and reactive power flows on transmission lines which, when satisfied, ensure a reliable and secure supply of power. Only the short term operational problem is addressed. The long term hydro-thermal co-ordination planning problem is recommended for future research.