The calculation of power system harmonic voltages and currents and analyzing power quality problems can be classified into frequency- and time-domain methods. Frequency-domain techniques are widely used for harmonic problem formulation. They are a reformulation of the fundamental load flow problem in the presence of nonlinear loads and/or distorted utility voltages. This complicated, nonlinear, and harmonically coupled problem has been solved in several ways in order to reach a compromise between simplicity and reliability of the formulation. Time-domain techniques can accurately model system nonlinearities and are mostly used for power quality problems such as transient and stability issues under nonsinusoidal operating conditions. They require more computation time than frequency-domain approaches but can accurately model nonlinearities (e.g., saturation and hysteresis), transients, and stability associated with transformers, nonlinear loads, and synchronous generators. Some techniques are based on a combination of frequency- and time-domain methods. In the frequency domain, the power system is linearly modeled while nonlinear simulation of components and loads can be accurately performed in the time domain. Hybrid time- and frequency-domain techniques result in moderate computational speed and accuracy.

This chapter starts with a review of power system matrices and the fundamental Newton Raphson load flow algorithm. In Section 7.4, the Newton Raphson harmonic power flow formulation is presented and explained in detail. In the last part of this chapter, a survey and classification of harmonic power flow approaches are addressed. All phasors are in per unit (pu) and all phase angles are assumed to be in radians.