SECURE OPERATION OF POWER SYSTEM UNDER CRITICAL LOADING CONDITIONS

Abstract

In recent years, increased attention has been given to improve the power- system performance by enhanced utilization of existing equipment, thus deferring construction of new transmission lines and transferring power over greater distances. This increased loading of power system and exploitation of power transmission system in particular, may jeopardize security of the system which is of utmost concern to both system operators and planners. In the past, operators maintained reliable performance of the power system using their experience and on-the-spot assessment of network conditions. However, power networks are now large, complex and highly interlinked. The increased number of possible operating scenarios can lead to situations where the operator's analytical ability may even fail. The remedy to such situations is the centralized control over power resources and more dependence on computers to assist the operator in system monitoring, control and economic dispatch. Security is the most important aspect for the satisfactory operation of the power system. The power system should be operated in such a way that it furnishes electrical energy as required by the customers without interruption while maintaining the quality of service in terms of proper voltage and frequency. The security of the power system is influenced by the line loading, bus voltage magnitudes, reactive power compensating devices, transient stability, faster protective relaying schemes and various controls available at the automatic load dispatch centers. Voltage related problems of the power system, if not attended to immediately may prove to be fatal. From a secure operation point of view, the objective of power system operation is to keep bus voltage magnitudes and angles, and the real and reactive power flows in lines within acceptable limits despite changes in load or available resources. The present scenario of the heavily loaded power system demands understanding of the nature of, and conditions for security that must be explored and strengthened in order to obtain the reliable electric energy supply that can be maintained under new, unprecedented conditions and requirements. In the past, much emphasis was laid on preserving system synchronism, as voltage magnitudes did not change significantly. Of late, voltage related operational problems of power systems have become of prime concern as it is one of the potential causes of system disruption leading to failures and blackouts. The frequency of occurrence of such events are on increase because the increased transmission line loading has departed from the energy flow patterns that it was designed to support. There is as yet no accepted theory or practical understanding fully adequate to meet the needs of the power system planners and operators for dealing with such problems. There are various control strategies adopted for the secure operation of a power system when critical loading conditions are taken into account. Under such situations, the various parameters of the system such as generation adjustment (Real and Reactive), generator bus voltage adjustment, transformer tap adjustment, switched capacitors/reactors, load transfer and interchange adjustments are required to be monitored and controlled.

In the present work, the objective is to evaluate the power system performance under steady state conditions. The emphasis has been laid on the voltage security of the power system experiencing heavy loading conditions. The heavy loading conditions are defined in terms of voltage limit violation at the buses and the thermal limit violation of the transmission lines. The loading conditions under which power balance constraints are not satisfied for any bus in the system are termed as critical loading conditions. The economy is of secondary importance during the critical operation, although, balance between economy and security needs to be maintained. An algorithm has been developed for assessing the voltage security of the power system under steady state. In the algorithm developed, new indices have been suggested and these indices have been evaluated starting from base case loading to critical loading point for the three cases, namely (i) real power varied at all the load buses with reactive power held constant(ii) reactive power varied at all the load buses with real power held constant and (iii) loading each bus to its critical limit keeping the power factor constant at all the load buses. The indices developed allow some obscure properties of the system to appear and thus act as a tool to check the collapse of the system under heavy loading conditions. The appropriate Jacobian elements at the solution point are used for calculating the indices. The three indices suggested are named as; diagonal element dependent index - the ratio of the maximum diagonal element value to the minimum diagonal element of the Jacobian; maximum row sum dependent index - the maximum row sum of the Jacobian and Euclidean norm dependent index - given by the Euclidean norm of the Jacobian.

The indices defined are simple, elegant and easy to interpret in indicating the voltage security of the power system. For obtaining the diagonal element dependent index the diagonal element of the Jacobian must be prominent and for the other two indices the Jacobian should be nonsingular. An effort has also been made to find the optimal load margin at the buses of the systems keeping load power factor constant. The objective therefore is to maximize the real load at the buses and minimize the reactive power generation, thus satisfying the power balance equations and generator output without violating the limits on bus voltage magnitudes. For this purpose the problem has been formulated as an optimization problem to identify the weak points/areas in the system from voltage security point of view and it has been solved using the Reduced Gradient Method. The problem has been formulated in two parts. In the first part, the objective function to be maximized consists of summation of the real load at all the buses with real load and real generation as independent variables and the bus angles at all buses except slack bus as dependent variables. In the second part of the problem, reactive generation at generator buses and the losses in the system are minimized by taking the reactive generation at generator buses and the transformer tap ratio as an independent variable and the bus voltage magnitudes as dependent variables. The two problems have been solved repeatedly in a sequential manner, till the load flow solution is obtained. The weak areas have been identified under maximal loading of the system with losses minimized (or in terms of the load shared by different buses as a percentage of the total load increase). The problem formulated as iv above tests the overloading capability of the power system with minimum reactive generation so that the losses are minimized. Further, the weak areas identified by way of voltage limit violations at the various buses in the system have been alleviated by using the local optimization technique. The local optimization technique is useful because few buses in the vicinity of limit violating buses need to be processed rather than the complete system. It saves lot of computational effort. The controls exercised to alleviate the bus voltage magnitudes are (i) reactive power generation of generator buses (ii) reactive power generation of switchable reactors/capacitors (iii) turns ratio of tap changing transformer and (iv) the load shedding. The above controls lead to minimization of the voltage limit violation at the buses. The problem of alleviation of voltage limit violation has also been formulated as an optimization problem. The objective function to be minimized is taken as the weighted sum of the squares of the limit violation of bus voltages. The voltages at all buses have been considered as dependent variables with a constraint on the upper and lower limit except the slack bus voltage. The independent variables are generator reactive power, generation or absorption of reactive power from the switchable capacitor or reactor, tap changing transformer ratio and load to be shedded. While operating the transformer in the local area, proper care has been taken so that its operation does not deteriorate the bus voltage controlled by it. The continuous variation of transformer tap is assured in the local optimization procedure. The transformers are modelled by their pi-equivalent network. Switchable reactors and capacitors are modelled as reactive power sources varying continuously at the buses to which they are connected. Thorough understanding of the bulk power transmission system is essential when it is heavily utilized, to ensure reliable and economic service to customers. As transmission lines become overloaded, the system operators are faced with increasingly difficult reactive and voltage control problems. In the light of the difficulties faced by the operators, new indices have been developed under steady state conditions to demonstrate the detection of voltage instability in the system in terms of the changes experienced by Jacobian elements as loading progresses and reaches the critical point where no convergence is possible. The Reduced Gradient Method has been used to load the system to its full capability and the weak areas in the system have been identified from voltage security point of view. The alleviation of voltage limit violations is very important for operational planning, security studies and reliability evaluation of the power system. The concept of local optimization has been used for alleviating voltage limit violations which results in an efficient, reliable and direct method that may prove to be suitable for on-line applications. The algorithms developed have been tested on 6-Bus, 24-Bus, 26-Bus and 57-Bus systems.