There also exist “side-bands” around the main harmonic frequencies. where f m is the frequency of the modulation (sine) waveform. Main harmonics located at : f = kp (f m ) k =1,2,3. PWM spectra observations The harmonics appear in “clusters” at multiple of the carrier frequencies. Highly mathematical in nature Space-vector modulation (SVM) A simple technique based on volt-second that is normally used with three-phase inverter motor-drive Īsymmetric and symmetric regular samplingīipolar PWM switching: Pulse-width characterizationĭetermination of switching angles for kth PWM pulse (1)Įxample For the PWM shown below, calculate the switching angles pulses no. Harmonic elimination/minimisation PWM PWM waveforms are constructed to eliminate some undesirable harmonics from the output waveform spectra. Regular sampling simplified version of natural sampling that results in simple digital implementation Optimised PWM PWM waveform are constructed based on certain performance criteria, e.g. PWM types Natural (sinusoidal) sampling (as shown on previous slide) Problems with analogue circuitry, e.g. Its digital version, known as REGULAR sampling is widely used in industry. Pulse Width Modulation (PWM) Triangulation method (Natural sampling) Amplitudes of the triangular wave (carrier) and sine wave (modulating) are compared to obtain PWM waveform. A three-phase inverter with star connected load is shown below Three-phase inverter Each leg (Red, Yellow, Blue) is delayed by 120 degrees. The switching in the second leg is “delayed by 180 degrees” from the first leg.
FOURIER COEFFICIENTS BIPOLAR SQUARE WAVE FULL
Single-phase, full-bridge (1) Full bridge (single phase) is built from two half-bridge leg. This is the main source of distortion for high-quality sine wave inverter. Dead time creates “low frequency envelope”. Shoot through fault and “Dead-time” In practical, a dead time as shown below is required to avoid “shoot-through” faults, i.e. If the top switch is closed (on), the bottom must be off, and vice-versa. The top and bottom switch has to be “complementary”, i.e. Thus the DC link is equally “spilt” into two. Basic building block for full bridge, three phase and higher order inverters. Half-bridge inverter (1) Also known as the “inverter leg”. Due to the small separation between the fundamental an harmonics, output low-pass filter design can be very difficult. If fundamental is 50Hz, then nearest harmonic is 150Hz. Even harmonics are absent Nearest harmonics is the 3rd. Spectra of square wave Spectra (harmonics) characteristics: Harmonic decreases with a factor of (1/ n ).
FOURIER COEFFICIENTS BIPOLAR SQUARE WAVE SERIES
Fourier Series is a tool to analyse wave shapes. įourier Series Study of harmonics requires understanding of wave shapes. Total Harmonic Distortion (THD) is a measure to determine the “quality” of a given waveform. Harmonics may cause degradation of equipment. Why need to consider harmonics? Sinusoidal waveform quality must match TNB supply. They can cause serious voltage distortion. Lower order harmonics (3 rd, 5 th etc) are very difficult to filter, due to the filter size and high filter order. Output voltage harmonics/ distortion Harmonics cause distortion on the output voltage. Output voltage amplitude can be varied by varying the “magnitude” of the DC input voltage. Variable Voltage Variable Frequency Capability Output voltage frequency can be varied by “period” of the square-wave pulse. In some applications such as AC motor drive, filtering is not required. In some applications such as UPS, “ high purity ” sine wave output is required. An LC section low-pass filter is normally fitted at the inverter output to reduce the high frequency harmonics. Harmonics Filtering Output of the inverter is “chopped AC voltage with zero DC component”. Simple square-wave inverter (1) To illustrate the concept of AC waveform generation General block diagram TYPICAL APPLICATIONS: Un-interruptible power supply (UPS), Industrial (induction motor) drives, Traction, HVDC
Chapter 4 DC to AC Conversion (INVERTER) General concept Single-phase inverter Harmonics Modulation Three-phase inverter ĭC to AC Converter (Inverter) DEFINITION: Converts DC to AC power by switching the DC input voltage (or current) in a pre-determined sequence so as to generate AC voltage (or current) output.
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