New approach to steady-state and dynamic nonlinear modelling of laminated salient-pole alternator systems
A complete mathematical model for a generator system consisting of an isolated laminated salient-pole alternator, exciter and prime mover is presented, with emphasis on the inherent electromagnetic nonlinearities in the alternator and its exciter. An equivalent circuit, representing the rotor circuits accurately, has been adopted to model the al ternator in the dqo reference frame. A computer program has been developed to calculate the unsaturated parameters of the model using the machine design data. A new approach has been developed to account for the electromagnetic saturation effects on the model reactances. Consequently new saturation factors, based on the machine design particulars have been deri ved. The advantages of these saturation factors, compared with conventional factors, are that both mutual saturation effects between the main and leakage fluxes, and between the direct- and quadratureaxis fluxes are considered. A mathematical nonlinear model, utilising the new saturation factors, is presented for a system containing an isolated laminated salientpole alternator and a direct thyristor static exciter. A digital computer program has been developed to simulate the system. The predicted results, for some steady state and dynamic candi tions, showgood agreement with test results and clear improvement over those obtained if saturation is either neglected or considered using the conventional saturation factors. At high saturation levels, the conventional method of calculating the machine transformer voltages, using static saturated reactances, gives unacceptable errors. A method for calculating these voltages correctly, in models utilising the currents as state space variables, is presented using new derived dynamic saturated reactances. This dynamic reactance concept is presented in a generalised form so that it can be applied to any machine with different saturation factors. The previous mathematical model of the alternator system has been modified according to the dynamic reactance concept, and the computer program has been developed accordingly. The predicted results confirm the need to apply this concept especially to dynamic conditions characterised by high saturation levels. To extend the analysis to a wider range of loading conditions, the alternator has been modelled in the abc reference frame. The unsaturated, static and dynamic saturated reactances of the machine in this reference frame have been obtained using conventional dqo-abc transformation techniques. Starting from the fundamental machine relations, a new set of equations, in the phase reference frame, has been derived employing the new dynamic reactance concept. A comprehensive system consisting of an isolated laminated salientpole alternator, brushless exciter, thyristor divert automatic voltage regulator and a diesel prime mover has been studied. Both the alternator and the exciter have been modelled in the abc frame to comply with the nature of rectifier loading associated with the exci ter. A complete steady state and dynamic mathematical model is presented where the t~r technique has been applied to the dynamic variable topology of the system electrical circuits. The model presented covers all the possible modes of operation associated with the exciter rotating bridge rectifier circuit. A digital computer program has been developed to simUlate the system. The predicted results obtained using the new set of saturation factors in conjunction with the dynamic reactance concept show good agreement with the test results. The study presented confirms the validity of the mathematical models developed for the alternator systems. Also, it supports the metlxxi by which the electromagnetic nonlinearity has been accounted for.