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Harmonic Load Flow Analysis

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Contents 1. INTRODUCTION – HARMONIC LAOD FLOW ANALYSIS SOFTWARE 3 2. POWER SYSTEM HARMONICS 4 2.1 Concept of Power System Harmonics 4 2.1.1Fourier Series and Harmonics 4 2.1.2 Distortion Indices 6 2.1.3 Characteristics of Harmonics in Power Systems 7 2.2 HARMONIC SOURCES 8 2.3 EFFECT OF HARMONICS 9 2.3.1 Thermal losses in harmonic environment 10 2.3.2 Effects on power system equipment 10 2.3.3 Capacitor banks 10 2.3.4 Transformers 11 2.3.5 Rotating machines 11 3. HARMONIC LOAD FLOW ANALYSIS 12 3.1 LOAD FLOW ANALYSIS 12 3.1.1 Load flow problem formulation 12 3.1.2 Backward forward sweep method 14 3.2 THREE PHASE HARMONIC ANALYSIS 17 3.2.1 Components model 18 3.2.2 Algorithm 18 4. INTERNAL FUNCTIONING OF HARMONIC LOAD …show more content…

The Fourier series for a periodic function f(t) with fundamental frequency ω can be presented as: ft= C0+ n=1∞Cncos(nωt+θn) Equation 1 Fourier series for a periodic function The coefficients Cn and phase angles n for n-th harmonic are given by: Cn= An2+ Bn2 Equation 2 θn= tan-1-BnAn Equation 3 where T=2π/ω and C0 is the dc component of the function. The rms value of ft is defined as: An= 2T0Tf(t)cos(nωt)dt Equation 4 Bn= 2T0Tf(t)sin(nωt)dt Equation 5 C0= 1T0Tf(t)dt Equation 6 RMS= C02+ n=1∞Cn22 Equation 7 RMS value In general, one can think of devices that produce distortion as exhibiting a nonlinear relationship between voltage and current. Such nonlinear relationships can lead to several forms of distortion as summarized below: * A periodic steady state exists and the distorted waveform can be expressed as a Fourier series with a fundamental frequency equal to the power frequency. * A periodic steady state exists and the distorted waveform can be expressed as a Fourier series with fundamental frequency that is a sub multiple of power frequency. * The waveform is aperiodic but perhaps almost periodic. A trigonometric series expansion may still exist (as an exact representation or as an approximation). The first case is commonly encountered in harmonic studies. There are several advantages to decomposing

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