This thesis explores how to best choose data when curve fitting using power exponential functions. The power exponential functions used are μ(b; x)=(xe1-x)b and Φ(ρ; x)=((1-x)ex)ρ . We use a number of designs such as the equidistant design, the Chebyshev design and the the D-optimal design to compare which design gives the best fit. A few examples including the logistic and the heidler function are looked at during the comparison. The measurement of the errors were made based on the sum of least squares errors in the first part and the maximum error in the second part. MATLAB was used in this comparison.

The proliferation of Electric Vehicles (EVs) poses new challenges for the Distribution System Operator (DSO). For example, the rectifiers that are used for charging EV batteries could significantly influence Power Quality (PQ), in terms of harmonic distortion. The emissions from individual EV, are well regulated by current harmonic emission standards. But what the aggregation of multiple EV loads will look like is still uncertain and the research being made in this area is still in its early stage.  The DSO responsibilities include ensuring grid code compliance confirmed by PQ metering.  In general, 10 minute RMS values are sufficient. However, the large scale integration of non-linear loads, like EVs, could lead to new dynamic phenomena, possibly lost in the process of time aggregation. In this thesis PQ and, in more detail, the concept of harmonics, and how this is related to EVs, is presented. A current-harmonic load model using power exponential functions and built from actual measurement data during the individual charging of four different fully electric vehicles was constructed. The model was based on individual emitted current harmonics as a function of state of charge (SOC), and was used to deterministically simulate the simultaneous charging of six vehicles fed from the same bus. The aggregation of current harmonics up to the 11th was simulated while randomizing battery SOC, the start of charging, and the kind of vehicle. Additionally, an investigation of the impact on aggregation in time was conducted. The analysis clearly shows the importance of phase angle information, its correlation to SOC, and how the aggregation of EV loads is influenced by these factors. The analysis also shows that 10 minute RMS aggregation could lead to significant deviations from the “actual” (200ms) data.  This indicates that 10 minute value monitoring could lead to information losses.

This thesis examines how to find the best fit to a series of data points when curve fitting using power-exponential models. We describe the different numerical methods such as the Gauss-Newton and Levenberg-Marquardt methods to compare them for solving non-linear least squares of curve fitting using different power-exponential functions. In addition, we show the results of numerical experiments that illustrate the effectiveness of this approach.Furthermore, we show its application to the practical problems by using different sets of data such as death rates and rocket-triggered lightning return strokes based on the transmission line model.