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Analysis and control of subsynchronous resonance in the presence of thyristor controlled series compensation Kabiri, Khosro


In this thesis, the problem of subsynchronous mechanical oscillations in the shaft assembly of a turbo-generator with its steam turbine stages is studied, when the generator is connected to a Thyristor Controlled Series Capacitor (TCSC) compensated transmission line. The first three-phase thyristor controlled series capacitor was installed in 1992. The usefulness of this device for mitigating subsynchronous resonance has been established. There are, however, issues remaining to be investigated. A point of contention is the nature of the behaviour of TCSC towards subsynchronous frequencies. Although TCSC does not have resistive components as such, it puts up significant resistance to the subsynchronous current flow when in open-loop operation. This characteristic, known as passive damping, has been observed both on network analyzers and in simulations. Here, with the aid of analytical relations and discrete Fourier analysis, a physical explanation is provided for this behaviour. The average steady-state linearization, although an efficient method for obtaining linear models for switching circuits, fails to capture the passive damping of TCSC. The Poincaré mapping technique, on the other hand, provides the state matrix of the discrete linear time-invariant system that is equivalent to the linearized time-periodic model of the switching circuit in the sense of Lyapunov. Therefore it is accurate in the eigenvalue analysis for stability studies. Poincaré mapping together with a perturbation method is used here to find a linearized discrete model for a TCSC compensated system, in which the small signal variation of the state is explicitly given in terms of the small signal variation of the TCSC firing angles. The model is used first for the eigenvalue analysis and then for the design of an all-stabilizing closed-loop controller for small signal control of the thyristor firing angles in order to damp subsynchronous mechanical oscillations. In the past, Poincaré mapping has been used to derive continuous dynamic models for the TCSC alone, by first finding the discrete advance map, and then by converting the equations to the continuous domain. Here, we discretize the generator, line and TCSC equations together to arrive at a state space model for the entire system. The First IEEE Subsynchronous Resonance Benchmark Model is our case study. The method is general enough, however, to be used for other configurations as well. Finally, the steady-state relations of TCSC in non-equidistant firing are developed, and its dynamic behaviour with the new open-loop firing scheme is studied using transient simulation.

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