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Certain single input, linearised extremum controllers of the empirical type described in the literature have been designed and their performances have been compared to that of an approximately optimal controller. The plant is subject to disturbances, lags and measurement noise. A dimensionless performance criterion and description of the plant have been used to present the results. A design procedure for a sinusoidal perturbation controller in connection with the above plant has been obtained, using a linear equivalent circuit for the system together with an experimentally obtained estimate of the equivalent circuit validity. Experimental results have shown that the resulting design is the best, and that the system is likely to remain stable, when the performance of the system is limited mainly by the measurement noise. This empirical controller has been compared with Roberts approximately optimal controller and has been shown to perform equally well if the effect of the lag is small. The performances of three different types of extremum controller have been compared when the plant lags can be neglected. The three controllers use sine wave perturbation, square wave perturbation, and square wave perturbation with a sample and hold unit in the controller. It has been shown that all three the perturbation frequency is infinite. When the perturbation frequency is limited, as in a practical system, the controllers without the sample and hold unit give better performance, at the expense of requiring the adjustment of an additional controller parameter.

Various computer programs are currently used by electric utilities to determine if potential subsynchronous resonance problems exist which can impact turbine-generators. One of the most popular of these is the frequency scanning program. The representative transmission system input data for these programs are generally based on constant temperature and frequency. However, as conductor temperatures and applied frequencies fluctuate, the resistances also change. This thesis investigates the effects that resistance variations, due to temperature and frequency, have on frequency scanning results. The maximum resistance change (increased and decreased) from the standard value is determined and applied to the transmission lines in four study system cases. The frequency scan output for the modified cases is used to determine if torsional interaction has become more severe. It is found that, under extreme conditions, the net system damping can decrease by over one hundred percent.

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