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Authors: Kumar, S. Pushpa
Issue Date: 1988
Abstract: Present day power systems are complex and have grown very large. It is now more important to design and operate systems with high degree of practical efficiency, security and reliability. In recent years, the main emphasis of power system engineering has been on the improvement of service quality. It is noted that increase in capacity of interconnection systems, allow a reduction in the capacity of generation, means a more economic management of the system. This increase, especially in the case of long distances can be obtained more economically by the use of more complex technological devices. The resulting reliability of the electric system and the consequences on system operation are the subject of in-depth study; these phenomena are sometimes difficult to represent at the planning stage and then concern more particularly the implicit or explicit margins required by operators and the performance of the control system at his disposal./The modern reactive power control concerns not only the regulation of system voltage, but also the co-ordinated operation of the reactive power sources within the system. In other words, the reac tive power control is aimed at the realization of the so-called rational system operation. Further, reactive power optimization has gained more importance due to exploitation of power generating sources at remote places and inclusion of long EHV ac as well as long dc transmission networks in the system. The objective of reactive power dispatch is to control all controllable reactive power sources in the system in a co-ordinated manner to improve the system voltage profile and to minimize the system losses. The reactive power dispatch problem is a non-linear constrained mathematical programming problem, and most of the currently available non-linear programming methods are applicable to only small power systems. The difficulty is in both the tasks of formulation and solution of optimization problems. Improvements in these tasks, therefore would make the application of optimiza tion methods to large size power system problems a practical reali zation. Hence an attempt has been made to develop improved algorithm for reactive power management. In normal practice, the reactive generation of generators alone may not be sufficient for meeting the reactive requirement of the system. In such cases external reactive sources must be switched on in various load buses. Also these reactive sources are available in most of the load buses. Hence for a particular load condition, the selection of optimal buses - an optimal bus is defined as one that causes maximum overall voltage correction when a unit capacitor is added to it - for reactive injection will reduce the number of problem variables in reactive power optimization. A method is proposed for the selection of optimal buses for reactive power injection. The system loss for a given load and generation condition is a function of reactive power flow in the lines. Therefore, minimum loss condition is an optimum reactive power dispatch. Hence the first model developed for reactive power control, used the minimization of net real power losses as objective function, power balance equations as equality constraint and bounds on variables as inequality constraints. The problem is solved using a recursive quadratic programming algorithm. The non-linear prog ramming problem is transformed into a quadratic approximation problem based upon an augmented Lagrangian function which include both Lagrange and Penalty parameter. Active Set Strategy is used to convert the problem into an equality constrained quadratic programming problem. A new approach is used for automatic selec tion of penalty parameter in each iteration allowing the penalty parameter to decrease rapidly in order to get fast convergence and retaining large enough to avoid 'Maratos effect*. The devel oped algorithm is found to be very effective for small and medium size problems. The major justification for reactive supplies on a power system, other than voltage control, is to release system capabi lity for additional power handling capability. Loss reduction is secondary. Systems normally operate their reactive supplies on the basis of acceptable voltage, not losses. (Reactive losses in the system play an important role to maintain suitable voltage profile.^ Hence the model developed for this purpose included the minimization of both real and reactive power losses in the network The advantages obtained by this new formulation are the unloading of system and equipment resulting from the reduction of reactive flows, and corresponding reduction in active and reactive losses. The power factor of the generators are improved and the system security is enhanced by retaining the reactive generation capa bility in reserve for use during emergency. To reduce the size of the problem,the variables are divided into basic and nonbasic variables and a modified reduced gradient algorithm is used for the solution. An efficient method is applied for resolving degeneracy, that normally present in reduced gradient algorithm, by solving a linear programming problem of smaller dimension. LP problem need to be solved only if any basic variable violates, its limit. The developed algorithm is found to be robust and takes less time compared with other GRG methods available. The aim of a system operator is to assure the maximum conti nuity and regularity of service. The guarantee that the system will be able to cope with particular contingencies, and emergency situations, can be attained if suitable margins of reactive power are available on the generating units. Reactive margin and their distribution are critical during heavy load hours, so it is essen tial, to maintain as much as possible a uniform distribution of reactive power among synchronous generators. To achieve this goal,a new model has been developed in terms of system real power losses, reactive power reserve, and proper sharing of reactive generation among generators. The advantage of this model is that power system security can be improved by the reduced loadings of the power faci lities, improved voltage profile of transmission system and improved power factor of generators. The solution method employed here is simple one using the second order optimality conditions of the Lagrangian function and Newton's method is used for the solution of unknown variables. Quadratic penalty function method is used to enforce the bounds on the violated variables. Another improve ment in this solution method is,a superior way of organising the optimality conditions for efficiently exploiting sparsity of the network. Recent advancement in sparse matrix analysis is fully utilised to reduce storage requirement and solution time. This method is found to be very efficient and well adaptive for large (v) scale system analysis. A comparative study of various methods used in this investi gation for reactive power control reveals that the explicit Newton method is superior in terms of both convergence characteristics as well as execution time compared with the recursive quadratic programming method and the modified reduced gradient method. A new model is developed for the reactive power control in an integrated AC-DC system. Even though dc transmission lines carry no reactive power, real power flow into the converters is accompanied by some reactive power flow because of the phase control. Net reactive power absorption by the converter can be varied by the converter controls. Generator voltages, and on-load transformer taps, are the reactive power control variables in ac systems. In AC-DC system these control variables have to be optimized in a co-ordinated manner including the reactive require ments at the dc terminals. The model minimises the real and reac tive losses in the AC-DC system network. The solution method described in the previous model, the Hessian and Jacobian terms are to be evaluated in each iteration. Since this calculation is costly especially in large systems, the algorithm used in this model instead of calculating these terms in each iteration, their values are updated using a sparse updating method. The efficacy of this method is tested on integrated AC-DC systems. A comparative study of the explicit Newton method with the evaluation of Hessian and Jacobian of the coefficient matrix in each iteration and the sparse LDU updation of the coefficient matrix shows that the LDU updation procedure is superior in terms of convergence characteristics and solution time. The algorithms described are theoretically sound, convergent algorithms that are able to trade-off overhead per iteration and asymptotic convergence rate. All the developed methods are tested on realistic systems, results presented and discussed in detail.
Other Identifiers: Ph.D
Appears in Collections:DOCTORAL THESES (Electrical Engg)

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