Pulse Width Modulation

The PWM modulators are open-loop voltage controllers, and the commonly used techniques for PWM modulation is carrier based PWM, space vector modulation and random PWM. However, other methods of PWM are included in the classification below. The only technique to be described here will be sinusoidal carrier based PWM, since only this PWM is used in this work.

PWM CLASSIFICATION

There are various techniques of PWM proposed in literature, namely;

 Sinusoidal PWM (SPWM)

 Random PWM

 Minimum ripple current PWM

 Space-Vector PWM (SVM)

 Selected harmonic elimination (SHE) PWM

 Sigma-delta modulation

 Sinusoidal PWM with instantaneous current control

 Delta modulation

 Hysteresis band current control PWM

Conventional inverter utilizes pulse width modulated (PWM) as control strategy. PWM inverters can control their output voltage and frequency at the same time. The harmonic components in the load currents can also be decreased when PWM is implemented. Due to these characteristics, they have become a major practice in several industrial applications such as variable speed drives, uninterruptible power supplies, and other power conversion systems. Although, the major concern is to mitigate the harmonic components in output currents, in order to reduce the influences of electromagnetic interferences or noise and vibrations. In the three-phase inverter, there is significant reduction of the harmonic currents compared to the single-phase PWM inverter. Nowadays, the standard single-phase inverters implement the full- bridge system whereby the power circuits used is approximate sinusoidal modulation technique. Then the three output voltage values are zero, positive (+Vdc) and negative supply dc voltage levels (-Vdc). Hence, the carrier frequency and switching functions determines the harmonic components of their output voltage. Therefore, the harmonic is reduced only to a certain level.

(Selvaraj & Rahim 2009; Park et al. 2003) proposed an inverter topology that uses two reference signals, in place of one reference signal, to produce PWM signals for the switches. A proportional-integral (PI) current control technique is used to maintain the output current sinusoidal, to have high dynamic performance when the atmospheric conditions is changing rapidly and to maintain the power factor close to unity since the inverter is used in a PV system.

2.22.1 Sinusoidal Pulse Width Modulation (SPWM)

The current injected into the grid is filtered by a filtering inductance Lf and it must be

producing sinusoidal current is sinusoidal PWM. A high-frequency carrier and a low- frequency sinusoid are compared to achieve sinusoidal PWM, which is the modulating or reference signal. The switches have constant switching frequency due to the constant period of the carrier. the crossing of the carrier and the modulating signal determines the switching constant(Selvaraj & Rahim 2009; Park et al. 2003).

The sinusoidal PWM technique is easy to apply resulting in the widespread use of the technique for industrial converters. The PWM technique of controlling the output voltage is described in Fig. 2.22a below. The basic principle of SPWM is described as the comparison between high frequency isosceles triangular waveform which is the carrier signal and slow-varying sinusoidal waveform which is the modulating signal at the fundamental frequency and the switching points of power devices is determined by the points of intersection of the waves. The periodic waveform of the carrier signal has a period of Ts and varies between −1 and 1. This technique can alternatively be

identified as triangulation, sub oscillation or sub harmonic procedure. The pulse widths of 𝑉𝑎𝑜 wave vary in a sinusoidal way in order to have the fundamental component frequency average and the modulating signal frequency to be equal and its amplitude is proportional to the command modulating voltage (Reznik 2012; Yazdani & Iravani 2010; Marwali & Keyhani 2004). The same carrier wave can be used for all three phases, as shown on Figure 2.22b and 2.22c below.

The PWM process is shown in Figure 2.22 below, where the switch has its switching function defined as:

s(t) = 1, if the switch is commanded to conduct s(t) = 0, if the switch is turned off.

Therefore, as Figure 2.22c shows when the modulating signal is greater than the carrier signal, a turn-on command is issued for one switch, and the turn-on command is cancelled for the other switch. The reverse of this happens when the modulating signal is lesser than the carrier signal. However, when a switch is ordered to turn on, it does not imply that it has to conduct; the switch conducts on the condition that the turn-on command is provided and the current direction agrees with the characteristics of the switch. For instance, an IGBT can only conduct when the current flow is from the collector to the emitter, in response to a turn-on command.

Similarly, the periodic saw-tooth waveform can also be used as a carrier signal. Although, for high-power converters, a triangular carrier signal is frequently used (Panda et al. 2009; Yazdani & Iravani 2010).

Figure 2.22a: Schematic representation of the mechanism of generating PWM gating pulses for inverter switches in Simulink

Figure 2.22b: Three-phase VSI system with SPWM

The maximum output voltage in the linear region when modulation index q is between 0 and 1 for SPWM is:

𝑉

=

2

= 0.612𝑉

𝑚 =

𝑉𝑇 (2.27)

Where 𝑉𝑝 peak value of the modulating wave and 𝑉𝑇 peak value of the carrier wave

Figure 2.22c: Sinusoidal PWM for three phase VSI V V Vb Va V V Vb Va