PERFORMANCE OF DIVIDED WINDING ROTOR SYNCHRONOUS GENERATOR UNDER ABNORMAL OPERATING CONDITIONS

Abstract

The work pertains to the study of a divided-winding-rotor (d.w.r.) synchronous generator under abnormal operating conditions The system considered is a single d.w.r. machine feeding power to an infinite busbar through a transformer and a short transmission line. Amathematical model of the d.w.r. system, amenable to computer solution, is developed in state variable form with actual field currents, and other stator and rotor currents taken in Park's reference frame as state variables. The mathematical model so developed appears to be superior over previous models, as available in published literature, since no transformation of currents and voltages from actual field winding system to ficti tious field winding system or vice versa is needed and thus mak«s a saving in computation time. The model can easily take into account the effect of symmetric 3-phase fault, any type of field fault and a multiple fault comprising of 3-phase fault and field fault. The work describes an investigation on the transient performance of the d.w.r. synchronous generator both with and without excitation controls. The contribution of field regulators, both separately and in combination, are described. The field regulators considered are essentially of proportional type with derivative stabilising feedback around the amplifiers as employed by previous authors, The analysis illustrates the positional change in resultant rotor m.m.f. on the transient performance. Behaviour of d.w.r. generator, equipped with automatic angle and

voltage regulators and speed governor, has been studied under abnormal operating conditions such as (a) external fault and (b) sustained loss of excitation, caused due to short circuiting or open circuiting of field terminals, in either of the field windings. Two types of transmission line vis. (a) low-impedance line and (b) high-impedance line are taken into consideration to observe the effects of transmission line parameters on transient stability of the system. 5th order Kutta Merson technique is employed for the numerical solution done with a time-step of 2 ms. The digital simulation shows that the quick reversal of reactivefield- winding current during an external fault is responsible in bringing the rotor m.m.f. back towards the pole-axis and thus helps to maintain transient stability especially for faults of long duration. It is also found that the quick reversal of reactive-field-winding current is not absolutely essential for external faults of shorter duration as the angle regulator, located on the torque-field-winding, alone is quite capable of maintaining stability. It is also found that permanent loss of excitation of the reactive-field-winding does not affect stability, whereas similar loss of excitation in torque-field-winding is catastrophic. Although transient performance of synchronous generator under unbalanced conditions had been studied by many authors, but hardly any literature is available on d.w.r. generator simulating unsymmetrical faults occuring on the transmission line through which the generator is connected to the infinite busbar. This type of fault is more common in nature than symmetric 3-phase fault occuring at machine terminals. The work describes a mathematical model, using direct phase quantities, of a d.w.r. generator assumed to be equipped with all its controls and connec ted to an infinite busbar through a transformer and a short trans mission line. The mathematical model developed can take into account the speed variation of the rotor under transient conditions and needs no further transformation of system parameters as is required in d-q-o or a-p-o models. The model can be used to simulate both symmetric and unsymmetric fault conditions at ease thus facilitating the exact performance of the system. Numerical solution using digital computer has been described and a timestep of 0.2 ms is chosen for the numerical solution made. The faults simulated are (a) symmetrical 3-phase short circuit, (b) double line to ground short circuit, (c) line to line short circuit and (d) single line to ground short circuit. The studies revealed that the d.w.r. system, which has already exhibited superior transient performance under balanced fault conditions, also exhibits similar improved transient performance under all types of unbalanced fault conditions. A system has to encounter line to line and single line to ground short circuits more frequently than symmetric 3-phase short circuit. The improvement with the d.w.r. system is particularly marked under these fault conditions. The system can withstand sustained single line to ground short circuit. In rectifier excitation system the rectifier unit in each field circuit usually consists of reversible double-bridge arrangement with automatic-change-over-system from forward bridge

to reverse bridge and vice versa to permit field currents to flow in either direction. Therefore there exists a possibility of the failure of the automatic-change-over-systems of both field circuits constraining field current either not to flow or to flow in one particular direction only. There are two types of severe multiple fault that can probably occur in a d.w.r. generator equipped with rectifier excitation system. These are (a) 'simul taneous fault' comprising of temporary external 3-phase short circuit together with a fault in the automatic change over system located at the reactive field circuit causing a permanent opening of the reactive field circuit and Cb) 'double fault' comprising of temporary external 3-phase short circuit accompanied by faults in the automatic change over systems of the field circuits restricting both field currents to flow in one particular direction only. This type of fault is most severe when an under-excited d.w.r. generator undergoes 3-phase short circuit and a detailed study of this type of multiple fault is reported in this work. It is found that to study the effect of this type of multiple fault, the mathematical models as developed by previous authors are inadequate because of inherent difficulties in representing current-blocking conditions. Daring the blocking period the particular field winding is effectively open circuited; the excitation source is isolated and the machine equations are modified to take into account the corresponding field current constrained to zero. The machine response is calculated by a step by step numerical solution of the modified equations considering the discontinuity in the field

circuit. Two sets of state variable equations are therefore needed-one for normal forward directions of field currents and the other for blocking condition. The studies revealed the indispensibility of the torque-field-winding during transient disturbances especially when the machine is operating at leading power factor and a d.w.r. generator while undergoing any type of multiple fault is more prone to instability than when under the effects of external disturbances alone. Furthermore transient stability is minimum when leading reactive power of the generator becomes equal to the active power since the probability of the torque-field-winding current getting blocked is maximum under this condition. Though d.w.r. generator had been investigated by various authors, but the field regulators chosen for their studies were mostly of proportional type with derivative stabilising feedback. For better transient performance excitation regulators comprising of proportional, first and second derivative gain settings have been considered for both the field windings of the d.w.r. genera tor. The angle regulator located on torque-field-winding is assumedto be energised by means of a feedback signal proportional to system rotor angle and on its first and second derivatives. The voltage regulator located on reactive-field-winding is assumed to work on proportional signals of machine terminal voltage and load current together with the first and second derivatives of the load current.

The work describes a systematic analytical approach to the selection of regulator gains in various channels. Proportional current gain setting is chosen from the consideration of normal compounding so that no load voltage of the generator becomes equal to its rated voltage. Proportional voltage gain setting is so selected as to provide a good voltage regulation and the height of the power angle characteristic curve is substantially high. Incorporation of proportional angle gain in conjunction with proportional voltage and current gains further increases the height of power angle characteristic curve. After selecting the proper values of proportional gain settings from the considera tions of voltage regulation and aperiodic stability, the method of ^decomposition technique is applied to optimise the derivative gain settings of automatic angle and voltage regulators for best steady state performance. It is found that the derivative gain settings of the angle and voltage regulators are to be changed non-linearly to achieve best dynamic performance under all credible operating conditions of the system. After determining best gain settings under steady state conditions for all regulator channels, the d.w.r. system is completely reinvestigated for various transient disturbances such as (a) sudden 3-phase short circuit, (b) sustained loss of excitation in either of the field windings, Cc) all types of unsymmetric faults and (d) both types of multiple fault e.g. (i) simultaneous fault and (ii) double fault. It is found that the d.w.r. generator when equipped with this new type of exci tation scheme, exhibits better transient performance in terms of

maximum swing in rotor angle, recovery of machine terminal voltage etc. than when equipped with proportional regulators having constant gain settings as developed by previous authors. The reason for this superior transient performance is due to the incorporation of first and second derivatives of system operating variables in the dynamics of regulators which play a great role during transient disturbances.