The main research objective is power grid and phasor measurement units. It is posited that the act of measuring the various parameters of signal is the same to solving the equation for the chosen mathematical model. Essentially is a fitting problem in mathematics. The equation is a model of what metrologists term the measurand, the name given to the quantity to be measured, and the measurement equipment must be designed around it. The equation being fit is a model based on the “physics” of the signal and natural phenomenon behind it. Regardless of exactly how the measurement is made, a metric defined and called the Goodness of Fit allows the measuring system to comment on the match between the signal it is observing and the model. The metric is based on the residuals, the differences between the signal itself and the value calculated from the result of measurement. Results from real-word phasor measurement units and real-world signals illustrate that the equation of the PMU is well solved during steady conditions. The effects of a fault in the transmission system is analyzed on the Goodness of Fit metric for a PMU. This work addresses how to deal with non-stationary power signals. Firstly, to measure a time varying signal, in a world of digital measurements, the relationship between the sampling window of the measurement system and the rate at which the signal is varying must be addressed. In this work several changing-frequency cases are examined. It is shown that the parameters of the AC signal can be found by curve-fitting. A working proof-of-concept signal estimator is shown and realized in the MATLAB environment. Lessons can be drawn about the role of different noises in measurement and about the very meaning of the result. Statistical tools, such as Allan variance are used to examine the stability of performance for estimator, as well as noise influence on estimation process. A new statistical analysis tool is experimentally shown to be applicable to digital measurements, called “sampling variance”. By varying sampling rate, it is shown that an optimum exists for smallest parameter variance depending on noise type. The Doctoral Thesis has been written in English. It consists of an Introduction; 5 Chapters; Conclusion; 58 figures; 2 tables; 3 annexes; the total number of pages is 91. The Bibliography contains 60 titles