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Synchronous generator models for the simulation of electromagnetic transients Brandwajn, Vladimir

Abstract

Techniques for modelling of synchronous generators in the simulation of electromagnetic transients are described. First of all, an adequate mathematical model of the generator is established. It uses the conventional set of generator data only, which are readily available, but it is flexible enough to accommodate additional data, if and when such become available. The resulting differential equations of the generator are then transformed into linear algebraic equations, with a time varying coefficient matrix, by using the numerically stable trapezoidal rule of integration. These equations can be interfaced with the equations of an electromagnetic transients program in one of two ways: (a) Solve the equations of the generator simultaneously with the equations of a three-phase Thevenin equivalent circuit of the transmission network seen from the generator terminals. (b) Replace the generator model with a modified Thevenin equivalent circuit and solve the network equations with the generator treated as known voltage sources e[sup red][sub ph] (t-Δt) behind constant resistances [R [sup red][sub ph]]. After the network solution at each time step, the stator quantities are known and used to solve the equations for the rotor windings. These two methods cover, in principle, all possible interfacing techniques. They are not tied to the trapezoidal rule of integration, but can be used with any other implicit integration technique. The results obtained with these two techniques are practically identical. Interfacing by method (b), however, is more general since it does not require a Thevenin equivalent circuit of the network seen from the generator terminals. The numerical examples used in this thesis contain comparisons with field test results in order to verify the adequacy of the generator model as well as the correctness of the numerical procedures. A short discussion of nonlinear saturation effects is also presented. A method of including these effects into the model of the generator is then proposed. Typical applications of the developed numerical procedures include dynamic overvoltages, torsional vibrations of the turbine-generator shaft system, resynchronization of the generator after pole slipping and detailed assessment of generator damping terms in transient stability simulations.

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