ECONOMY AND SECURITY BASED LOAD FLOW SOLUTION OF LARGE SCALE POWER SYSTEMS

Abstract

With the rapid increase in demand for electrical energy, the size and complexity of power networks have grown tremen - dously. It therefore becomes necessary to install large size ..ge nerators with increased number of interconnections due to economic aspects. Bulk power is transported over large and complex transmission system. Therefore it is essential to generate and transport the power in the most efficient and economic manner. Security is another important aspect for the satisfactory operation of the power system. The power system should be operated such that it furnishes the electrical energy as required by the customers and for as long as required, at the.same time maintaining the quality of the service charac - terized by stable electrical frequency and voltage, and keeping the continuity with time. As the size of the network increases it becomes difficult and time consuming to analyse the complete network. This study is directed towards the deve lopment of efficient decomposition method which can be used for load Gov; solution, contingency analysis and optimal load flow solutions. A very efficient and robust method has been introduced for the solution of the optimal load flow problem- The decomposition method presented in this study, decom - poses the large size network into number of blocks from the weak coupling point such that the effect on the boundary nodes is minimum. In the presented technique, each block contains, iii total number of its existing buses plus the external boundary buses. Each block for the purpose of solution includes its boundary lines. The buses connecting boundary lines and present in the remaining network termed as exter nal boundary buses are modelled as swing buses. The blocks along with their boundary lines are solved in a sequential manner such that the successive block has maximum number of interconnections from the preceeding block. The blocks are solved for varying convergence from lower accuracy to high er accuracy. The boundary bus- voltages are updated after solving each block. The proposed decomposition method is used to assess the security of the system with various contingencies, as well as for the base case load flow solu tions. The next objective of the presented work has been to solve the optimal power flow problem such that it minimizes the system operating cost, real power losses and reactive power generation such that the power flow equations and limit constraints, imposed upon the variables by the system ope - rating conditions and design considerations are satisfied. All problem variables are decomposed into two sets i.e. control cad state variables which reduces the complexity of the problem. In order to reduce the size of the problem, the complete problem of optimal load flow has been decomposed into two subproblems i.e. real power optimization and reactive power

optimization, on the basis of decoupling principle. This simplifies the formulation, reduces computational efforts, storage and provides certain flexibility in the types of calculations desired. The sub- problem of real power optimization is solved • in view of minimizing the total generation cost. The objective function used in this study minimizes the real power genera - tion cost, deviation from scheduled reactive power. The com plexity and size of the optimal power dispatch problem has motivated the decomposition of problem variables into state and control variables. The swing bus real power generation and generator bus voltage phase angles are taken as state variables. Real power generation from various generating sources (excluding swing bus) and line loadings are consi dered as control variables. The reduced gradients are then calculated using sensitivity relationship between state and control variables. The problem of reactive power optimization has been solved in view of economics and system security considera - tions. The objective function used in this study minimizes the real power losses, the deviation from optimal active power despatch and the difference between percentage sharing of reactive power among generators. The reactive power is minimized such that the generators operate well within their capability limit. Such reactive power sharing will improve the stability limit of the machine which are likely to go out of step due to excessive under excited operation. The objective function is optimized such that the power flow equations and the limits imposed upon the variables due "to system operating conditions and design considerations are satisfied. The problem variables are decomposed into con - trol and state variables to reduce the complexity of the problem. Generator terminal voltage magnitudes, transfor mer tap positions and setting of reactive power sources available in the system are taken as control variables. Voltage magnitudes of the load buses and reactive power generation from various generating sources are considered as state variables. Then reduced gradients are calculated using sensitivity relationship. The optimal power flow (both sub-problems; problem is a constrained non -linear programming problem. Existing methods for solving optimal load flow problems have several deficiencies starting from their use of penalty functions to handle constraints, which makes the convergence slow, feasible point algorithm requires the initial point to satisfy all the constraints. Also the existing methods are lacking robustness and under stressful conditions they often fail to converge. The Han Powell algorithm has been proved to be extremely fast and robust for optimal power flow problems. However, it has two serious disadvantages, that the cycling can occur in the technique of adjusting line search para - meters and the maratos effect causes slow convergence.

A new approach based on modified Kan-powell method has been suggested to solve the optimal load flow sub - problems. The developed method includes the watchdog technique which overcomes the cycling and maratos effect. This method is fast, robust and reliable. It is logically straight forward. Moreover it is not essential to begin with a feasible point nor it is strictly necessary to converge the constraints at each iterations. Even with starting point outside the feasible region, the method converges rapidly to an optimum solution. For very large power systems, the size of optimal load flow sub-problems become large. The decomposition approach developed for load flow studies of a very large power system has been used to solve optimal load flow problem. The network is decomposed into number of blocks, zone wise. The subnetworks are optimized along with their external boundary buses in a sequence with varying conver gence tolerance. The coordination is carried out after optimizing each block. The external boundary feMBfl are modelled such that the power variation of these buses are monitored and. are not allowed to have large variation. The practical networks are solved as a whole and with the pro - posed decomposition technique, and results are compared.