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Authors: Palaniswamy, K. A.
Issue Date: 1981
Abstract: As we know today, the demand for the electric energy is in creasing exponentially with time. Due to unavoidable delays in increasing the generation, transmission and distribution capa-» bilities to meet the demand, power systems are operated near critical limits for comparatively larger periods. In such a case any disturbance may lead the system to emergency operating state. A power system is said to be in emergency mode of operation when one or more of the security constraints are being violated. The emergency operating state comes about when some component emergency ratings are exceeded or when the voltage for a customer cannot be maintained at a safe minimum. In modern power systems, it is not uncommon to install generators with a capacity of from 25 to *t0 percent of the system or area demand. In such instances, it is uneconomical to operate sufficient spinning reserve, even.if avail able, to protect against the loss of such units. The net result is that loss of so large a unit overloads interconnections or other supplemental power sources to the extent that they are tripped out, leaving the area or system deficient in generating capacity. The continued operation of a system under emergency conditions may result in forced outages or damage to the equipment unless appropriate emergency control actions are taken within a given time limit after the constraints violations have occurred- The corrective measures to be taken to improve the operating conditions are: • generation rescheduling • reduction of system voltage . opening of tie-lines . load shedding When a particular system or a component part thereof, does not have sufficient reserve generation (either generating units or transmission connections), load shedding may then become mandatory. Load shedding minimizes the extent and duration of inter ruption that may result from disturbances that are more severe than the system design criteria. The corrective measures, except the generation rescheduling, may cause inconvenience to electric energy consumers. In this thesis, the control of a povtsr system under emergency condition is viewed as an optimization problem in which customer inconvenience is minimized subject to the steady state operating constraints of the system. The inconvenience is modelled by a scalar function which may consist of terms depending on the load actually curtailed, deviations from scheduled voltage, deviation from area interchange schedule, equipment overload resulting in reduced life, etc. The problem of minimizing the inconvenience subject to the equality and inequality constraints of the system has been attempted by many authors. Mostly linear programming has been applied for the solution of the problem. The linear programming tends to provide solution at the extremities of the operating region, which usually leads to increased transmission losses and an uneven distribution of spare capacities. The quadratic programming (Q.P.) provides a more uniform voltage profile, reduced transmission losses and uniform power distribution. The q* formulation enables the optimal solution iii to be obtained in a finite number of simplex-type exchange steps, thus avoiding the complex nesting of iterative loops, necessitated by the Lagrangian method of solution. However, the QP. approach has the difficulty of storage requirement in solving real large size system problems. The storage requirement difficulty is not that serious, as it could be overcome with the latest techniques available to exploit the sparsity. So an humble attempt has been made by the author for the first time to exploit the advantages of the quadratic programming in minimizing the load curtailment. The method has been illustrated on sample system for both generation and line outages. Fast optimal load-flow under emergency operating conditions will enable one to decide on one of the appropriate actions so as to prevent further violation of constraints and/or return the system to normal state, with second-order method, the optimal loadflow problem becomes a problem of the same type as the normal loadflow problem. Several papers are available in the literature for the optimal load-flow solution using Hessian method. However, in all the methods, the Hessian matrix is to be computed explicitly in each iteration. For large systems it would take considerable computer time. In this thesis a method is presented which overcomes this difficulty. The explicit calculation of the Hessian is avoided using a quasi-Newton method. Amongst the updates that can be used for the quasi-Newton method, the complementary Davidon-Fletcher- Lowell (CDFP) update gives good approximation to the Hessian. The method is found to be very effective especially for large systems. It is observed that the saving in C.P.U. time using this update iv is about 30 percent. The Hessian matrix is updated in each iteration and triangular factorization is employed to solve for the correction in the variables. Gill and Murray proposed methods to incorporate modification in the CDFP update to obtain directly the elements of the unit-lower triangular and diagonal matrices from the corres ponding elements in the previous iteration. An important property of the methods is that whatever the rounding error incurred, the Hessian matrix remains positive-definite. This method works well for small systems. The computer time and memory requirement increases for large systems. It is also shown that the accuracy can be improved by using variable multiplication factor for voltage correction. Farther improvements are also attempted. The simulation results on IEEE l*f-bus, 30-bus, 57-bus and 118-bus test systems are presented. Generation rescheduling and optimal load shedding problem has been formulated as an optimal load-flow problem. The generation violating constraints are incorporated into the objective function by means of penalty terms. The problem is solved using the secondorder load-flow technique developed. Another contribution of this thesis is a fast and efficient solution algorithm for the above problem. Simulation results on sample systems for generation outage, with and without maintaining constant power factor at load buses, are presented. Line outages cause overloading of other transmission lines, violation of voltage limits at load buses and violation of reactive power generation limits at generator buses. By incorporating the violating constraints in the generation rescheduling and load shedding model using penalty terms, secure operating conditions for line outages are obtained. Test results on sample systems have been very encouraging and are presented in this thesis. Under normal conditions, system frequency is maintained constant and generators are operated at a scheduled voltage and output. Following a major supply outage or tripping of tie-line breakers, the frequency does not remain constant. The rate at which the frequency falls depends on the generation/demand imbalance caused by the emergency. With change in frequency, the generation is varied by the generator control devices and net load reflected on to system also changes depending on the composition of loads. It becomes, therefore, necessary to take account of generator control effects and voltage and frequency characteristics of loads in calculating the optimal load curtailment under emergency conditions. This thesis presents a model in which frequency is also taken as a variable. The model is very effective not only for finding optimal load shedding but also for other control actions such as Flat frequency control, Tie-line control and Tie-line bias control. The simulation results on sample systems show that the method can be used for on-line control of power systems during an emergency. To summarize, the objective of the thesis, that is to make an humble attempt to formulate and investigate the feasibility of control actions under emergency conditions in a co-ordinated manner so as to be able to use for on-line computer control applications, have been successfully analyzed.
Other Identifiers: Ph.D
Appears in Collections:DOCTORAL THESES (Electrical Engg)

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