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4c : Single Phase VSI with Sine-Triangular PWM
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Inverter in Power-Electronics refers to a class of power conversion circuits that operate from a dc voltage source or a dc current source and convert it into a symmetric ac voltage or current. It does reverse of what ac-to-dc ‘converter’ does. The input to the inverter is a direct dc source or dc source derived from an ac source. For example, the primary source of input power may be utility ac voltage supply that is converted to dc by an ac - dc rectifier with filter capacitor and then ‘inverted’ back to ac using an inverter. Here, the final ac output may be of a different frequency and magnitude than the input ac of the utility supply.

If the input dc is a voltage source, the inverter is called a Voltage Source Inverter (VSI). One can similarly think of a Current Source Inverter (CSI), where the input to the circuit is a current source. The VSI circuit has direct control over ‘output (ac) voltage’ whereas the CSI directly controls ‘output (ac) current’.

The simplest dc voltage source for a VSI may be a battery bank or a solar photovoltaic cells stack. An ac voltage supply, after rectification into dc can also serve as a dc voltage source. A voltage source is called stiff, if the source voltage magnitude does not depend on load connected to it. All voltage source inverters assume stiff voltage supply at the input.

Output of voltage waveforms of ideal inverters should be sinusoidal. However practical inverter waveforms are non sinusoidal and contain certain harmonics. For low and medium power applications square wave or quasi square wave voltages are acceptable.

A variable voltage can be obtained by varying the input dc voltage and maintaining the gain of the inverter constant. On the other hand, if the dc input voltage is fixed then variable output voltage can be obtained by varying the gain of the inverter. This can be accomplished by Pulse Width Modulation-PWM control within the inverter. PWM means the width of the square pulse in positive and negative halves can be adjusted according to the rms of the output required. The inverter gain may be defined as ratio of the ac output (rms) voltage to dc input voltage. In Square Wave PWM technique the output ac rms voltage is fixed when input dc voltage is fixed.
 

Single Phase Bridge VSI
 

Fig 4(a) shows the power circuit diagram for single phase bridge voltage source inverter. In this four switches (in 2 legs) are used to generate the ac waveform at the output. Any semiconductor switch like IGBT, MOSFET or BJT can be used. Four switches are sufficient for resistive load because load current io is in phase with output voltage vo. However this is not true in case of RL load where the io is not in phase with vo and diodes connected in anti-parallel with switch will allow the conduction of the current when the main switch is turned off. These diodes are called as Feedback Diodes since the energy is fed back to the dc source.


Fig 4(a) IGBT based Single phase bridge voltage source inverter power circuit diagram.


Fig 4(a) IGBT based Single phase bridge voltage source inverter power circuit diagram.
 

Square Wave PWM

In full bridge inverter, when T1, T2 conduct the output voltage is Vs and when T3, T4 conducts the output voltage is -Vs. The switches T1, T2 conducts for period of 0<t≤T/2 and the switches T3, T4 conducts for period of T/2<t≤T where ‘T’ is the time period of the gate pulses to the devices. The frequency of output ac voltage can be varied by varying the T of the gate signal. The root mean square (rms) value of output ac voltage:



PWM techniques for voltage control of Single Phase Inverters


The following PWM techniques are used for controlling the output ac rms voltage and frequency in an inverter:

•    Single-Pulse-Width-Modulation
•    Multiple-Pulse-Width-Modulation
•    Sinusoidal-Pulse-Width-Modulation (SPWM)

Single-Pulse-Width-Modulation


In single pulse width modulation control, there is only one pulse per half cycle and the output rms voltage is changed by varying the width of the pulse. The gating signals and output voltages of single pulse-width modulation are shown in fig 4(b). The gating signals are generated by comparing the rectangular control signal of amplitude Vc with triangular carrier signal Vcar. The frequency of the control signal determines the fundamental frequency of ac output voltage. The amplitude modulation index is defined as:


The rms ac output voltage

where

By varying the control signal amplitude Vc from 0 to Vcar the pulse width ton can be modified from 0 secs to T/2 secs and the rms output voltage Vo from 0 to Vs.

In multiple PWM control, instead of having a single pulse per half cycle, there will be multiple number of pulses per half cycle, all of them being of equal width.

Sinusoidal-Pulse-Width-Modulation (SPWM)

In sinusoidal pulse width modulation there are multiple pulses per half-cycle and the width of the each pulse is varied with respect to the sine wave magnitude. Fig 4(c) shows the gating signals and output voltage of SPWM with unipolar switching. In this scheme, the switches in the two legs of the full-bridge inverter are not switched simultaneously, as in the bi-polar scheme.



Fig 4(b) Gating signals and output voltage of Single pulse-width modulation


In this unipolar scheme the legs A and B of the full-bridge inverter are controlled separately by comparing carrier triangular wave vcar with control sinusoidal signal vc and -vc respectively. This SPWM is generally used in industrial applications. The number of pulses per half-cycle depends upon the ratio of the frequency of carrier signal (fc) to the modulating sinusoidal signal. The frequency of control signal or the modulating signal sets the inverter output frequency (fo) and the peak magnitude of control signal controls the modulation index ma which in turn controls the rms output voltage. The area of each pulse corresponds approximately to the area under the sine wave between the adjacent midpoints of off periods on the gating signals. If ton is the width of nth pulse, the rms output voltage can be determined by:



The amplitude modulation index is defined as:





where, = peak magnitude of control signal (modulating sine wave)
             = peak magnitude of carrier signal (triangular signal)

The frequency modulation ratio is defined as:

where, = frequency of control signal (sine signal)
            = frequency of carrier signal (triangular signal)


Applications

•    Uninterruptible Power Supply (UPS),
•    Adjustable Speed Drives (ASD) for ac motors,
•    Electronic frequency changer circuits used in induction heating, welding etc.,
•    HVDC transmission at lower power levels
•    Renewable Energy such as solar, fuel cell to AC conversion
•    Electronic Ballast and Compact Fluorescent lamps
•    Active Filters for power quality improvement
•    Custom power devices: DSTACTCOM, DVR, UPQC,
•    FACTS: STATCOM, SSSC, UPFC, etc.

 

 

 

 

 

 

 

 

 

 

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