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
The sound waves are produced by a random oscillating crystal, and are inaudible to humans. A instrument called a
Jitter and shimmer are measures of the cycle-to-cycle variations of fundamental frequency and amplitude, respectively, which have been largely used for the description of pathological voice
Answer: As we know, we can calculate the period, if the frequency of the signal is given by the formula
In this experiment, the signal generator was set so that the frequency meter showed a reading of 1,803 Hz. The microphone was moved to a distance from the speaker so that the oscilloscope displayed a straight diagonal line. This position was of the microphone was recorded as the initial position, or beginning of a wavelength. The microphone was then moved farther in the same direction until the oscilloscope displays the same horizontal line. This position was recorded as final position, or the end of the wavelength. The distance between the two positions represents one wavelength for this frequency. This was repeated for frequencies of 2,402 Hz, 3,002, Hz, 3,602 Hz, and 4,201 Hz.
In elecronic, broadcast, transportation, filters are used to select the desired signal, and deny or block unwanted signals. Or put in other words, they may be the only way we have to block.The doing so, we want to signal and other frequency or with a device, is frequency-selective - it behave different towards different frequencies. Such device is called a filter. (Bertrand, 2002)
This process of Fourier transform and back-transform establishes the essential frequency components of the temporal data while eliminating high-frequency noise. This is a powerful technique to:
Fig.7-a) Total harmonic distortion versus input currents at 1 MHz. b) Total harmonic distortion versus input currents at 100 MHz. c) Total harmonic distortion versus input currents at 1 GHz (various amplitudes of I_x signal and a fixed amplitude of I_y signal).
Alpha waves are thought to indicate a relaxed but awake state. They have a frequency of 8-13 Hz and an
where V_c (t) is the voltage across the capacitor as a function of time and V_b is the input voltage. We then linearize the data by manipulating the
A composite signal can be decomposed into individual sine waves called harmonies.Fourier analsis is done to decompose a signal.the decomposed signals have different amplitude,frequency and phase.A periodic signal has
Print out the image of a clock and open the spreadsheet called Grapher. You will find both of
strating the energy transformations involved in the process * outlines what frequency modulation or amplitude modulation is
The red bar on the left acts as the driving piston. If it moves in a sinusoidal manner from left to right, then the wave that is produced will be a sinusoidal wave. Since the wave is sinusoidal, the wavelength, amplitude and frequency are constant. This is seen in nature as a tuning fork, which produces a periodic sound wave. In a one dimensional tube as shown above, each particle undergoes simple harmonic motion. The volume that is contained in one wavelength also undergoes this same motion. We can represent the displacement of this volume as:
The system is characterized by the relationships of its components and the non-linearity that exists between these components.
amplitude for each segment as in real room .This system uses a key to generate a