The three-level SPWM wave can be obtained by the two-level SPWM wave through the phase-shifting and superposition method, as shown in Figure 1. There are two phase-shifting and superposition methods: one is to first shift the phase of the sinusoidal modulation wave by 360°/2=180°, as shown in Figure 1(b), and then compare it with the same carrier triangle wave to obtain two two-phase Flat SP WM wave. And uAa and uAb, use uAa-uAb=uA to get the three-level SPWM wave; the other is to first shift the carrier triangle wave by 360°/2=180°, as shown in Figure 1(c), and then the same The sinusoidal modulation wave is compared, and two two-level SPWM waves uAa and uAb are obtained. Use uAa-uAb=uA to obtain the three-level SPWM wave. Comparing Figure 1 (b) and (c), we can see that the three-level SPWM waveforms obtained by these two phase-shifting and superposition methods are exactly the same.
The following specifically introduces an application example of using a sine modulation wave to shift the phase by 180° to obtain a three-level SPWM wave with a dead zone. The working waveform is shown in Figure 2. In order to simplify the analysis, equation (1) can be used, when φ=0, we can get
The Fourier series expression of uAb is derived as follows.
because
So have
When n=0, there is
When m=0, it is the same as the two-level SPWM wave derivation, when n>1, there is A0n+jB0n=0.
When n=1, there are A01=0, B01=-ME, and we get
because
also because
When n=0 is an odd number, cos(nπ/2)=0, so
Obviously, when n is an even number, sin²(nπ/2)=0; when n is an odd number, sin²(nπ/2)=1. When m is an even number, cos(mπ/2)=(﹣1)(m/2); when m is an odd number, cos(mπ/2)=0.
It should be noted here that: since the frequency fc single of the unipolar carrier triangle wave is twice as large as the frequency fc double of the bipolar carrier triangle wave, that is, fc single = 2fc double, so the F single, m single and double of the unipolar SPWM The relationship between F double and m double of the polarity SPWM is F single = 2F double, m single = (1/2) m double. Substituting the value of F into the above formula can obtain the double Fourier series expression of the unipolar SPWM three-level SPWM wave as
This formula shows: by the phase-shifting superposition method of subtracting two two-level SPWM waves with a sine modulation wave 180°, one fc single = 2fc double, that is, F single = F double, m single = (1/2) m double (that is, F single is an even number) three-level SPWM wave. In the two two-level SPWM waves, the carrier harmonics, the odd multiples of the carrier harmonics, and their upper and lower side frequencies are all eliminated.
The sine modulation wave is phase-shifted by 180° and superimposed to obtain the control circuit of the three-level SPWM wave, as shown in Figure 3.
If you use a subtractor to output, you use the drive signal for phase-shifting and superposition; if you use a high-speed comparator to output, you use the two bridge arms of the inverter’s main circuit for phase-shifting and superimposing.
In order to obtain the three-level SPWM wave by the phase-shifting and superposition method, the carrier ratio F single must be an even number. Because F single = 2F double, F double is an integer, so F single is even.
Equation (10) is an expression of the three-level SPWM wave double Fourier series obtained by the phase-shifting and superposition method considering the existence of the dead zone. Among them, 1+ejm△t increases with the increase of m and △t. When the existence of the dead zone is not considered, △t=0,1+ejm△t=2 in the formula, and substituting this result into the formula (10), the double Fourier series expression without dead zone uA can be obtained as
