Introduction to Power Inverters | What Is 3-Phase Power?, Part 6 - MATLAB & Simulink
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    Introduction to Power Inverters | What Is 3-Phase Power?, Part 6

    From the series: What Is 3-Phase Power?

    In 3-phase electrical power systems, the AC system is commonly connected to a DC system. The process of converting DC to AC is known as inversion.

    You will learn:

    1. The operating principle of a single controllable power electronic switch
    2. How an H-bridge inverter converts a DC voltage to an AC voltage
    3. The value of null vectors in a switching sequence and what switching sequences should be avoided
    4. Why pulse-width modulation (PWM) is used to control an inverter
    5. How a 3-phase inverter converts DC to 3-phase AC

    Published: 12 Jun 2022

    Hello, everyone. My name is Graham Dudgeon, and welcome to part 6 in a series of tutorials on 3-phase power. The aim of the video series is to build up our engineering knowledge on the design, analysis, and operation of 3-phase electrical power systems. Today, we'll explore the fundamentals of converting DC power to AC power using inverters.

    The process of converting a DC waveform, which has only one polarity, to an AC waveform, which has both positive and negative polarity, is known as inversion. An inverter requires a controllable switch. That is a switch which we can turn on and off with a control signal. Note that controls signals are also referred to as gate signals.

    Here, we have an ideal controllable switch, which connects an ideal DC source with voltage V1 to a resistive load with voltage V2. The switch will conduct when it's turned on and will stop conducting when it's turned off. Typically, a positive signal will turn the device on, and setting the gate signal to 0 will turn a device off.

    In practice, ideal switches do not exist, and switches such as IGBTs and MOSFETs are used. But for the purpose of this tutorial, we will assume we have ideal switches. Note that when a switch changes its conduction state, we refer to that as commutation. Also note that a single switch cannot reverse the polarity of the DC source.

    To develop the DC source so that positive voltage and negative voltage appears on the AC side, we can configure an architecture known as an H-bridge. The aim of an H-bridge is to allow separate paths for the DC voltage to be passed through as a positive voltage and also to be converted into a negative voltage.

    The H-bridge achieves this by allowing a connection between the negative AC terminal to the positive DC terminal and the positive AC terminal to the negative DC terminal. In the animation, you can see that during positive conduction the switches 1 and 4 conduct, and during the negative conduction, the switches 2 and 3 conduct. The AC waveform is a square wave that flips between plus VDC and minus VDC. Note that DC voltage and DC current remain constant from the switching pattern.

    This is a good place to talk about forbidden switching states. It's a bad idea to turn on switches 1 and 2 at the same time or switches 3 and 4 at the same time. If we do that, we short circuit our supply. However, we do have two additional switching sequences at our disposal that do not cause problems and can, in fact, benefit operation. They are the so-called null vectors, where we turn on switches 1 and 3 together or switches 2 and 4 together. Let's take a look at why null vectors are useful.

    Null factors will set AC voltage to 0. You can see that when we do this that the AC voltage is a little closer to a sinusoidal shape than our previous waveform, as we now have three states to choose from, plus VDC, 0, and minus VDC. We still have work to do to emulate a sinusoidal, but we're making progress. Because the AC voltage is not a pure sinusoidal, we're introducing harmonics onto the system. That is frequency components that are higher than our AC frequency. We'll cover harmonic analysis in the next tutorial.

    On the AC waveform, note that the null period lasts for 60 degrees and the positive or negative periods lasts for 120 degrees relative to the period of the AC waveform. Also note that DC current drops to 0 amps during a null sequence.

    Next, we'll consider this switching sequence for a 3-phase inverter. You can see that we are able to generate three line voltages that have the same shape as our H-bridge example and are phase shifted by 120 degrees as required.

    Here are our good and bad switching sequences. As with the H-bridge, we want to avoid switching sequences that will short circuit our supply. I have also shown the null vectors for a 3-phase inverter, where we can either turn on switches 1, 3, and 5, or turn on switches 2, 4, and 6.

    Now notice that the null vectors for the 3-phase system are not being used in the switching sequence we're showing here. We can actually achieve zero voltage in a phase by connecting two upper or two lower switches together. But notice that when this happens in a 3-phase system, we do not achieve zero current.

    So why do we need null vectors in a 3-phase inverter? The answer relates to pulse width modulation. It needs more flexibility in achieving zero voltage than we can achieve with the simple switching sequence we see here. Support is pulsed with modulation. As we are able only to turn switches on and off, we need a way to emulate a sinusoidal using discrete switching states. We do this with pulse-width modulation or PWM.

    Pulse-width modulation includes a sinusoidal onto a high frequency binary signal. It does this by comparing a high frequency carrier wave, which, in this case, is a triangular wave shown in black, with the sinusoidal we want to emulate known as the modulation wave. You can see that when the modulation wave is greater than the carrier wave, the binary signal is on, and when the modulation wave is lower than the carrier wave, that the binary signal is off.

    On the right, you can see the effect of increasing the carrier frequency by a factor of 4 in this case. Higher carrier frequencies are more desirable, as they provide more resolution in the encoding of the sinusoid. In practice, much higher carrier frequencies are used than I'm showing here. I'm keeping the carrier frequency relatively low for visualization reasons.

    Let's take a look at pulse-width modulation in action on our H-bridge. Note that the null vectors are used regularly in our PWM switching strategy. You may be wondering how each PWM signal is generated for the four devices. Let's revisit the PWM signal to clarify this.

    You can see that for arm one, which has switches 1 and 2, that the S2 PWM signal is the logical NOT of the S1 PWM signal. For arm two, which has switches S3 and S4, the signal for S3 is generated by using a carrier wave that is flipped relative to the carrier for arm one. The S4 PWM signal is the logical NOT of the S3 PWM signal. We now have the four gate signals we need.

    With a 3-phase system, we compare the three waveforms we want to encode with the single carrier wave. As we saw before with our single phase example, when the modulation wave is greater than the carrier wave, the binary signal is on. And when the modulation wave is lower than the carrier wave, the binary signal is off.

    What you're seeing here is the generation of the PWM signals for switches 1, 3, and 5. The PWM signals for switches 2, 4, and 6 are the logical NOT of the PWM signals for switches S1, S3, and S5. On the right, you can see the effect of increasing the carrier frequency by a factor of 4. As I noted before, higher carrier frequencies are more desirable, as they provide more resolution in the encoding of the sinusiods.

    Here is our 3-phase inverter operating with PWM. If you watch carefully, you'll see that null sequences are being used. During a null sequence, all voltages drop to 0 volts and DC current drops to 0 amps. Let me actually pause the animation. So we'll freeze this, and we'll just go to one of the null sequences. So bang on 12 seconds of the video is a null sequence.

    So here you can see that the voltages all drop to 0, and our DC current also drops to 0. So we confirm that we have a null sequence. In this case, switch 2, 4, and 6 are on.

    So in summary, inversion is the process of converting a DC waveform, which has only one polarity, into an AC waveform, which has both positive and negative polarity. Inversion requires power electronic switches that can be turned on and off by a gate signal. Switching combinations that short circuit the DC source must be avoided. Null vectors bring all AC voltages and DC current to 0, and they're important for enabling pulse-width modulation, or PWM. PWM encodes a sinusoid onto a high frequency binary signal, and so allows the emulation of sinusoids from high frequency switching. Inverters introduce harmonics onto the system.

    One more thing before we go-- for more information on pulse-width modulation and inverter control, please view these videos from my colleague Melda. Search YouTube for Motor Control MATLAB. The application is motor control, but Melda has valuable information on the details of how PWM is implemented, particularly in part 3 and part 5. I hope you find this information useful. Thank you for listening.