Multi-Mode Damping of Power System Oscillations

In maintaining power system stability; especially that of large interconnected systems, in the face of large disturbances it is desirable to have a non-linear control technique that is simple and inexpensive to implement. This thesis presents a non-linear control technique which relies on angle measurements taken at strategic points in the power system with the aid of the G.P.S. ( Global Positioning System ) timing signal. A method for estimating these bus angles which is faster than previous methods is developed as well as a technique for choosing the locations of these transducers. This transducer placement algorithm aims to place transducers at locations whose bus voltage response to the less well damped inter-area modes is maximised and whose response to the better damped local modes is minimised. Since the control techniques are based on aggregated classical models of coherent generators it is important to be able to estimate the internal voltages of these aggregate machines. The placement algorithm ensures maximally precise angle estimates in the presence of noise by minimising the condition number of the observation matrix relating transducer bus voltages to internal aggregated machine voltages. The non-linear control techniques presented rely on an energy function developed in this thesis which is based on the physical circuit energy of the system. One technique; the Direct Energy technique looks at maximising the negativity of the time rate of change of the energy function, assuming that the energy function is positive during the time frame of interest. It is shown that should the number of controllers be less than the number of modes, excluding the centre of area mode, then sustained oscillations appear which will only be damped by the natural damping of the system. This may be overcome by using techniques which rely on reducing the entire system energy over the time frame of interest. These so-called Lookahead techniques can rely on higher order time derivatives of the energy function or on co-states, the latter being the principal focus of this thesis. The Lookahead control technique developed is based on co-states which are estimated by the using the solution to the time independent Ricatti equation for a LQ model of the system. It is shown to produce good damping in a number of case studies. Furthermore it is shown to perform well in the presence of both static and dynamic load models. Also it is shown that the path dependent terms introduce some ambiguity as to whether or not the system will converge to a stable equilibrium point. It is shown that it is possible to put a bound on the region to which the power system can be assured to converge. Furthermore the addition of the above-mentioned control strategies has the effect of overcoming the effect of the path dependent terms and, should the control action be strong enough, completely swamping them and ensuring system convergence to a stable operating point. In any case the energy function could be directly monitored since all the data needed is being collected anyway for control purposes.PhD Doctorat