Introduction to Phasors

Complex Numbers and Phasors

1. Abstract (you’re reading this now) 2. Complex numbers: Magnitude, phase, real and imaginary parts 3. Complex numbers: Polar-to-Rectangular conversion and vice-versa 4. Complex numbers: Addition, subtraction, multiplication, division 5. Complex numbers: More complex manipulations 6. Phasors: Phasor-to-sinusoid conversions and vice-versa 7. Phasors: Real-world applications (borrowing from EECS...

Fundamental Relations Between the LMS Algorithm and the DFT

The digital Fourier transform (DFT) and the adaptive least mean square (LMS) algorithm have existed for some time. This paper establishes a connection between them. The result is the “LMS spectrum analyzer,” a new means for the calculation of the DFT. The method uses a set of N periodic complex phasors whose frequencies are equally spaced from dc to the sampling frequency. The phasors are weigh...

Using Frequency-Matched Numerical Integration Methods for the Simulation of Dynamic Phasor Models in Power Systems

In this paper the use of frequency-matched linear numerical integration techniques for the simulation of systems modelled by the dynamic phasors approach (DPA) is proposed and investigated. Such methods show an increased accuracy and computational efficiency around the matched frequency. Such frequency matched methods are derived by analyzing the local truncation error in the frequency domain a...

Power System Stability Monitoring and Control using Dynamic Phasors

Artificial neural network model of photovoltaic generator for power flow analysis in PSSSINCAL

Output of a three-phase photovoltaic generator (PVG) is a function of sunlight irradiance, temperature, and three-phase terminal voltage phasors. Three-phase PVGs are largely connected to rural distribution systems feeders that are predominantly unbalanced. Models of PVGs that are only a function of sunlight irradiance and temperature disregarding unbalanced three-phase terminal voltages phasor...