The paper presents a phenomenon of directional change in the case of a LQR controller applied to multivariable plants with amplitude and rate constraints imposed on the control vector, as well as the impact of the latter on control performance, with the indirect observation of the windup phenomenon effect via frequency of consecutive resat- urations. The interplay of directional change of the computed control vector with control performance has been thoroughly investigated, and it is a result of the presence of con- straints imposed on the applied control vector for different ratios of the number of control inputs to plant outputs. The impact of the directional change phenomenon on the control performance (and also on the windup phenomenon) has been defined, stating that performance deterioration is not tightly coupled with preservation of direction of the computed control vector. This conjecture has been supported by numerous simulation results for different types of plants with different LQR controller parameters.
The influence of wrong information about transition and measurement models on estimation quality has been presented in the paper. Two methods of a particle filter, with and without the Population Monte Carlo modification, and also the extended and unscented Kalman filters methods have been compared. A small 5-bus power system has been used in simulations, which have been performed based on one data set, and this data set has been chosen from among 100 different – to draw the most general conclusions. Based on the obtained results it has been found that for the particle filter methods the implementation of the slightly higher standard deviation than the true value, usually increases the estimation quality. For the Kalman filters methods it has been concluded that optimal values of variances are equal to the true values.
An approach to power system state estimation using a particle filter has been proposed in the paper. Two problems have been taken into account during research, namely bad measurements data and a network structure modification with rapid changes of the state variables. For each case the modification of the algorithm has been proposed. It has also been observed that anti-zero bias modification has a very positive influence on the obtained results (few orders of magnitude, in comparison to the standard particle filter), and additional calculations are quite symbolic. In the second problem, used modification also improved estimation quality of the state variables. The obtained results have been compared to the extended Kalman filter method.