Solution to security constrained pumped-storage hydraulic unit scheduling problem by using modified subgradient algorithm based on feasible values

A lossy electric power system that contains thermal units and a pumped-storage (p-s) hydraulic unit is considered in this paper. The total fuel cost of the thermal units in an operation cycle is minimized under some possible electric and hydraulic constraints by means of a power dispatch method proposed by us and based on modified subgradient method operating on feasible values. The proposed dispatch technique considers minimum and maximum reservoir storage limits of the p-s unit, upper and lower generation limits of the thermal units, upper and lower pumping/generation power limits of the p-s unit, maximum transmission capacities of the transmission lines, upper and lower limits of the bus voltage magnitudes and off-nominal tap ratios in a considered power system. A nonlinear programming model is set up for the problem solution. Power system transmission loss is inserted into this model as equality constraints via the load flow equations. Since all constraints in the nonlinear programming model are functions of complex bus voltages and off-nominal tap ratios (once there are off-nominal tap changing transformers in the power system), they are taken as independent variables. The proposed dispatch technique was tested on an example power system that has 12 buses with five thermal units and a p-s hydraulic unit. Optimal total cost value for the power system without any p-s unit is calculated first. Later on, the same optimal total cost value for the power system with a p-s unit is recalculated and the obtained saving in the optimal total cost value, due to the employment of the p-s unit, is presented. The numeric example, which is considered in this paper, was also solved by means of other dispatch technique that uses pseudo spot price electricity algorithm. Results obtained from the proposed method and from the other method are compared.