ON SOME ASPECTS OF POWER SYSTEM PLANNING PROBLEMS

Abstract

There is continuous increase in demand of electrical energy due to the growth of population and expansion of industry. To meet this increase in demand the generation of the power system has to be planned suitably. Consequent to the increase in demand and generation, there will be change in the power flow pattern in the network transmitting power from generating station to the load centres. This may result in overloading of some of the network branches. From the thermal and stability considerations, it is essential to take into consideration transmission network planning also into account together with generation expansion planning. In addition to the generation-transmission planning, it is necessary to see that for the expanded power systems, the voltages at the load centres are within the limits. The other factors to be considered in planning are reserves to be provided due to reliability considerations, maximum power available, limits on line additions etc. There have been a number of models developed for gene ration planning and generation- transmission planning. Most of these assume that the voltages are maintained at 1 p.u. As the voltages at the load centres also affect the loading of transmission lines, it is necessary to take into consideration the voltages also. Amathematical model for generation-transmission planning has been developed using the Tellegan's theorem. In this,

sensitivities of the line currents due to the changes in load and generation at load and generation buses respectively (using the adjoint network) are calculated. The generation transmission planning problem is formulated as a mixed integer programming problem with increase in the generation and generation capacity expansion variables considered as continuous variables and the line additions as integer variables. The cost function consists of cost of generation expansion and cost of line additions. The constraints consist of maximun limits on generation, and maximum current in the transmission lines. The problem is solved by modified mixed integer pro gramming in which the integer variables are treated as continuous variables for some iterations (which results in reduction in C.P.U. time). In cases where generation expansion planning has already been decided upon, it is necessary to plan the network to remove the anticipated overloading of lines. It is also necessary to plan the voltage correction by use of shunt capacitors at load buses and tapsetting transformers. Amathematical model has been developed for the above purpose. The sensitivities of line currents due to line additions and capacitor locations are determined. Aline addition which has the maximum effect in removing overloading of lines and in bringing the voltages at load buses back into the prescribed limits is decided upon. When the overbadings are removed similar steps are followed to alleviate voltage violations by using the shunt capacitors at the load buses. A load flow is carried out to find out the Ill actual effect of this decision. This process is continued till overloading is completely removed and voltages are within limits. Another mathematical formulation is made treating the transmission expansion planning and voltage correction problem as an integer programming problem. The constraints, considered are maximum limit on current in transmission lines and limits en load bus voltages. Tellegan's theorem is used to find out the sensitivities of line currents and load bus voltages due to the line additions and static capacitor locations. The power system configurations have become very complex due to interconnections between different geographical areas. A deficit area buys surplus power from other areas. Energy trade also takes place between subsystems to meet the demand economically. Due to these reasons it is necessary to plan the generation expansion in the interconnected systems. By integrated planning of the interconnected power system, total installed capacity can be reduced and there is reduction in overall cost of expansion. A two level generation planning expansion algorithm is developed for interconnected systems. In the first level of optimal generation planning, optimal expansion of unit additions and increase in generation is determined for each subsystem independently assuming the flow in the interconnections. The second level of optimization consists of modifying the flow in the interconnections. With modified interconnection power flows the expansion schedules of subsystems are also modified.

The process is continued till overall optimal cost of expansion is obtained. The constraints considered are maximum power limits on each type of generation, minimum reserve limit on each type of generation and minimum reserve required in each subsystem. The power generation and reserves are considered as continuous variables and generating unit (capacity) additions as integer variables. For each subsystem the expansion schedule is determined using modified Mixed integer programming. A mathematical model is developed for the transmissiongeneration planning of interconnected systems. In addition to the constraints considered in generation planning of inter connected systems, the security constraints for the trans mission lines are included. The maximum phase angle across each branch is specified. 'The optimization procedure is same as that of generation expansion planning of interconnected systems. To design the interconnections each interconnection is included in one of the subsystems. An algorithm is developed to include pumped storage plants in generation planning for a power systaa. For an assumed annual load duration curve, optimal scheduling is determined for the power system modifying the load duration curve. The gene rating unit additions required to meet the given future demand are calculated using a mixed integer programming formulation. The pumping energy and the energy to be generated by the pumped storage scheme are calculated by solving a subproblem using linear programming. The generation schedule for each part of the modified load duration curve is obtained to determine the total operating costs. The saving in cost due to the inclusion of pumped storage plants is determined. In short, mathematical models have been developed for expansion planning of the power systems. The models presented consider the effect of interconnections and the pumped storage type of plants. Models are also developed taking into account the resistances of transmission lines and voltages at the nodes.