The Solutions Of The Switching Angles For Half-Wave Symmetry SHEPWM

As one of the most basic core contents in modern Power Electronic techniques, Pulse Width Modulation (PWM) technique is studied deeply and used widely in the last decades, it can be applied in the area of united power flow controller, superconducting magnetic energy storage, static var compensation, electric drive, high voltage direct current transmission, grid-connected of renewable source, active power filter, novel uninterrupted power supply, and so on.By taking half-wave symmetry SHEPWM as the research object, this paper discusses the characteristics of switching angles, how to obtain initial values, iterative algorithm of switching angles under DC ripple of VSC and Neural Network algorithm of switching angles.This paper compared half-wave symmetry SHEPWM with non-symmetrical SHEPWM and quarter-wave symmetry SHEPWM, then concluded that half-wave symmetry SHEPWM had best waveform characteristics of all. The half-wave symmetry waveform did not contain even-order harmonic and DC component naturally compared to non-symmetrical waveform, and could control harmonic phasing and amplitude at the same time compared to quarter-wave symmetry waveform at the same frequency. Then this paper presented D-STATCOM controller based on half-wave symmetry SHEPWM and phase-shift strategy and tested this controller by simulation. D-STATCOM could compensate both harmonic current and reactive power under this controller. The results improved validity of half-wave symmetry SHEPWM method.Half-wave symmetry waveform has more freedom than quarter-wave symmetry at same switching frequency, so it is more difficult to seek initial value of switching angle. This paper provide that initial values based on quarter-wave symmetry SHEPWM has the best iterative effect. This paper discusses different iteration result of different initial values under different conditions of modulation waveform. These initial values are obtained by experience, by triangular carrier waveform comparing with modulation waveform, by the theory of center of gravity coincidence and by quarter-wave symmetry SHEPWM formulations. Simulation results reported that it is useful for rapid convergence to keep phase of fundamental component zero. In addition, initial value based on triangular carrier waveform with injecting zero sequence harmonics technique and based on quarter-wave symmetry SHEPWM had least number of iteration. Comprehensive consideration, it is best to use initial value based on quarter-wave symmetry SHEPWM.Usually, DC voltage of VSC is assumed to be constant and the ac network is assumed to be balance. However, voltage punctuations often occur on the DC side due to the unbalanced voltage of power system. This paper presented a half-wave symmetry SHEPWM based on improved switching function modulation used to eliminate these parasitic harmonic. The simulation results presented three conclusions. First, improved half-wave symmetry SHEPWM can effectively cut out all parasitic harmonics in line voltage even though notable double line-frequency ripples on DC side voltage existed. The second result was that different switch angles caused different unbalance of phase voltage. It was best to chose angles causing the smallest unbalance. At last, the improved half-wave symmetry SHEPWM was also effective for a DC bus with a ripple of4th harmonics. Simulation results proved the validity and practicability of the proposed method.It is a very complex process that using the traditional iterative algorithm for obtaining the switching angle of improved half-wave symmetry SHEPWM method. Because, each switching angle of each phase must be calculated separately. In order to obtain angles as fast as possible, this paper established BP neural network to fit SHEPWM formulations. First, introducing variation factor into PSO algorithm to avoid early maturity phenomenon and overcome a local optimal solution. Then, searching initial weight values and threshold values with PSO algorithm for propose of accelerating training. Because a multiple outputs BP neural network didn’t has enough fit precision, this paper used a array of single output BP network to replace of the multiple outputs BP network. Also, the orthogonal test was used to confirm the array BP networks performance during the whole independent variables space with a12factors,11levels orthogonal table. Simulation result provided this method outperforms the traditional multiple outputs network.At last, this paper validated the methods and solution algorithms on the real time digital simulation experimental platform.