A Rule-Based Approach for Parameter Estimation in Variable Rank Environments

In the past, the important set of parameters for power transmission engineers contained frequency, phase offset and amplitude of the fundamental system frequency. It was used to identify overload and underload as well as the power flow in the grid. Moreover, abnormal variations in these parameters were used to identify events and faults. From a signal processing point-of-view, such treatment is commonly compared with a narrow bandpass around the system frequency and a set of parameter estimators for the desired three parameters which might be based on e.g. DFT or zero-crossing.

However, the grid becomes highly dynamic as the generation becomes more diverse. It becomes more challenging to monitor this grid sufficiently as not only the time constants shorten. The mechanisms influencing the operation complicate. One might try to utilize information that is hidden in the spectrum and lost after the bandpass. This thesis investigates the possibilities of subspace-based parameter estimation in the context of power system measurement. The signal model is derived to consist of superposed, partly damped sinusoids in white Gaussian noise. Moreover, it can be assumed that the amplitudes of the signal components range from the nominal system frequency amplitude down to amplitudes near the noise level. Some components can also be very close in case of a modulation occurring.

From a collaborating work, it is known that the power system signal can be segmented into different quasi-stationary segments each describable by a different instance of the signal model. This implies not only varying parameters but also a changeing signal order. As subspace-based algorithms are based on by averaging estimated autocorrelation matrices, it becomes necessary to handle the model instance changes. This especially holds for the rank which, therefore, has to be estimated. The special signal characteristics prove challenging for established rank estimators. In consequence, a framework called DaPT was developed utilizing a slightly over-assumed rank to keep track of newly emerging components. The framework rates the estimates and provides a stabilized set of estimates as output.

Interestingly, the framework (although developed for power system measurement) is also applicable to music. In a few examples, it is demonstrated the same framework can be used to identify the tones played by their names and, in addition, interprets their context, which means chord identification.