TRANSMISSION EXPANSION PLANNING

Abstract

The basic consideration in power system planning is to provide a cheap and high quality power supply to the consumers. As the investments associated with the power projects and transmission network expansions are enormous, a careful investigation of the expansion of these facilities is required so as to minimize the revenue requirements. Moreover as the demand for electric power is ever increasing, it may be required to evolve a suitable expansion strategy for a planning period of ten, twenty or thirty years. In such cases the planning horizon has to be subdivided into stages and the decisions regarding the necessary expansions at every stage may be made. The decision at one stage is influenced by the decisions already taken and will influence the future decisions. Another important point to be decided is the basis on which alternative expansion policies are to be evaluated - This is because, a system requiring less capital investments may prove to be more expensive in the long run due to higher recurring expenditure associated with operating costs includ ing fuel and maintenance and system losses. This calls for a proper assessment of the various expenditure involved, namely the capital costs for construction and expansion of the facilitiesj the operating costs and cost due to system losses. Models are developed in the present work for determining the future expansions of the transmission network along with

generation facilities in power system. A model is developed for the single stage expansion planning of transmission network and power plants to meet a given future demand. These two subsystems are treated as the parts of an integrated system as their expansion plannings are interdependent. The expansions of the facilities are determined by minimizing the total annual revenue requirements consisting of annual capital and recurr ing costs subject to constraints based on future demand, system security and bounds on power plant expansion. The mathematical formulation results in a minimization problem which falls in the category of mixed integer linear programm ing problems. The discrete variables are those representing the network and power plant expansions and the continuous variables represent the power plant additional capacities and power outputs. This problem is solved by a decomposition technique. The algorithm developed for the solution incor porates screening logic which considerably reduces the computer memory and time requirements required for large scale system problems. The model can accommodate various cost functions associated with the types of power plants and network expansions. A model has been developed to include the effect of network losses in the planning studies. The losses in the network are represented as functions of fuel costs and network

expansion costs. This formulation enables the inclusion of the losses in the model developed for the expansion planning. The planning of networks are generally made by consider ing the active power flows in the system. This may sometimes result in the violation of reactive power generation and voltage specifications at one or more buses in the system. Static capacitor installations or tapchanging transformers together with the generator bus voltages have been considered in the past for controlling the reactive power and system bus voltages. A model has been presented wherein static capacitors, tap settings of transformers and generator bus voltages have been simultaneously considered for controlling the system bus voltages and reactive power generation. In this model the variables representing the static capacitors and tap settings are discrete variables and the generator voltages are represented by continuous variables. The size of the problem is reduced by eliminating some of the variables from the problem formula tion by using a sensitivity relationship. The long term expansion of the power system is formulated as a multistage expansion problem. The total planning horizon is subdivided into stages and decisions regarding the expan sion of the network and powerplant and operating schedule for the power plants and transmission lines are determined at every stage. A new approach for the solution of the problem has been developed using preference order dynamic programming technique. In this approach, the power plant expansions are

considered to be discrete valued and selected from a set of avialble power plant sizes or generator units. In one of the models, the transmission network expansions are consi dered to be linear. In a second model, the transmission net work expansions are considered as discrete valued. Associated with every feasible power plant expansions, a set of partial policies corresponding to possible network configurations in the neighbourhood of a minimum cost policy, is constructed. Some skipping rules are developed to reduce the number of alter native policies to be evaluated. In a third approach, the multistage expansion planning problem is formulated as a static optimization problem. This can accommodate the various types of cost models representing the types of power plants available in the system. A method is developed to decompose this large problem,time -intervalwise into subproblems by absorbing the coupling constraints into the objective function. Exploiting the structure of the main problem a sequential solution procedure is developed for the solution of these smaller subproblems. A strategy is evolved to coordinate the subproblem solutions in determining the saddle point. Uncertainties associated with future demand, generator and transmission line outages etc. have an impact on the planning decisions for future. If these are not properly taken care of in the planning studies, the resulting design may prove to be either unreliable or costly. A model is developed for determining the long term generation expansion policy in electric utility systems considering the uncertain ties in demand forecast and generator outages. The formula tion of the problem is based on the preference order dynamic programming. System failure is defined in terms of the total probability for the demand to exceed the installed generation capacity. Utility of the system is calculated by assigning penalty cost for the failure of the system. The decisions at every stage is obtained by minimizing an objective function consisting of expected values of capital and operat ing costs, the penalty costs associated with the system overdesign and failure and the deviation of the cost. The model aims at a trade off between capital costs and utility of the system. The algorithm developed for the solution of the problem consists of skipping rules which considerably reduce the number of alternatives to be evaluated at every stage. A method is presented for solving the load flow problem for planning studies. The problem is formulated as an unconstrained minimization problem in which the objective function represents the active and reactive power mis matches at every bus and penalty functions associated with the violation of voltage and system security requirements. The problem is decomposed into subproblems using P-Q decoupling. An iterative technique has been evolved for the solution of the subproblems exploiting the sparsity and symmetry of the first and second order derivative matrices. A method is presented for the post optimality analysis

of the technique developed for the solution of system expansion planning problem consisting of mixed variables. This enables the reoptimization of the problem for variations in the planning data. In short, mathematical models have been developed for the planning of transmission network and power plant expan sions and. allied problems in power system engineering. The models presented are for short and long term planning studies under deterministic or stochastic conditions.