The three-phase half-bridge SPWM inverter is the most widely used inverter in three-phase UPS. Regardless of whether it is a power frequency UPS or a high frequency UPS, whether it is a UPS with an isolation transformer or a UPS without an isolation transformer, this inverter is used as the output of the UPS.

**1. Composition and working principle of three-phase half-bridge SPWM inverter**The three-phase half-bridge SPWM inverter with dead zone is shown in Figure 1, where Figure (a) is the main circuit, and Figure (b) is the working waveform. It can be seen from Figure (a) that the three-phase half-bridge SPWM inverter is composed of three single-phase two-level SPWM inverters as shown in Figure 2. In order to ensure the symmetry of the three-phase output voltage, the carrier ratio F should be an odd multiple of 3. This not only ensures the same three-phase SPWM waveform, but also the zero sequence harmonics in the upper and lower frequencies of the carrier and carrier harmonics. eliminated. When the value of F is large enough, the AC filter can be omitted. When the carrier u

_{c}is a common triangular wave and the modulation wave u

_{s}is a three-phase sine wave, the output voltage of each phase of the three-phase inverter is a two-level SPWM waveform, and the line voltage is a three-level SPWM waveform, as shown in Figure 1 (b ) As shown. Since the three single-phase SPWM inverters in the three-phase inverter use a common DC power supply E, the DC power supply voltage of each bridge arm is E/2. In this way, the double Fourier series expression of the phase voltage and two-level SPWM waveform of the three-phase half-bridge SPWM inverter can be obtained by the method. If you consider the existence of the dead zone, the double Fourier series expression of the two-level SPWM waveform of the phase voltage is obtained by equation (2-5) (assuming the initial phase angle φ=0). In Figure 1, there are

Because the line voltage u_{AB}=u_{AO’}-u_{BO’}, there is

Note that sin(2π/6)=(√3/2), F= an integer multiple of 3, sin (mF·2π)/6=0, then we get

The above formula can also be simplified as

because

So have

If the dead zone is not considered, that is, when Δt=0, 1+e^{jmΔt}=2, then the above formula becomes

In the same way, the double Fourier series expressions of u_{BC} and u_{CA} can be obtained.

Obviously, in the spectrum of the online voltages u_{AB}, u_{BC}, and u_{CA}, the fundamental wave amplitude is √3 times the phase voltage amplitude. The carrier components with very high amplitudes are eliminated, the harmonics of the carrier are also eliminated, and the zero-sequence harmonic components in their upper and lower side frequencies no longer exist.

The sin[(m+n)π/2] in formula (7) is to eliminate those terms when m and n are both even numbers or both odd numbers.

The general harmonic value of the output voltage of the three-phase SPWM inverter (when F is large) and the output voltage spectrum are shown in Figure 3 and Figure 4, respectively.

**2. The influence of dead zone on output voltage**The three-phase half-bridge SPWM inverter is affected by the inherent storage time ts of the switching tube used, and the turn-on time ton is often less than the turn-off time toff. Therefore, it is prone to simultaneous conduction of the upper and lower switching tubes of the same bridge arm. The short-circuit fault. In order to avoid this phenomenon, it is usually necessary to set the switching time lag Δt, which is commonly referred to as the “dead zone”. The purpose of setting the dead zone Δt is to ensure that after one switch tube on the bridge arm is reliably turned off, the other switch tube can be turned on. There are two ways to set the dead zone: one is to turn off in advance by Δt/2, and to turn on after Δt/2, which is called bilateral symmetrical setting; the other is to turn off on time and turn on after Δt, which is called unilateral asymmetric setting. . The following only takes a symmetrical setting as an example to illustrate the influence of the dead zone on the output voltage of a three-phase half-bridge SPWM inverter.

A typical voltage-type three-phase half-bridge SPWM inverter and its working waveform are shown in Figure 5. The figure (a) is the main circuit, and the figure (b) is the working waveform when the dead zone is set bilaterally symmetrically. In the working waveform, u_{AO} is the ideal voltage waveform (carrier ratio F=ωc/ωs=9) between the A phase and the midpoint “O” of the DC power supply voltage, and u’_{AO} is the voltage waveform when the dead zone is set. In the inductive load, when Sap is on, point A is +E/2, and when San is on, point A is -E/2. In the dead zone Δt, when S_{ap} and S_{an} are not conducting, the inductive load makes the feedback diode VD_{ap} or VD_{an }freewheel to keep the phase A current i_{A} continuous. In the positive half cycle recognized by i_{A}, VDan continues to flow, point A is connected to the negative pole of the DC power supply, and the voltage at point A is -E/2; in the negative half cycle recognized by i_{A}, VD_{ap }continues to flow, and point A is connected to the positive pole of the DC power supply. The point voltage is +E/2, so that the waveform of the actual output voltage u”_{AO} of the inverter is distorted compared with the ideal waveform u_{AO}. In the positive half cycle of i_{A}, all positive pulse widths are reduced by △t, and all negative pulse widths are increased by △t; in the negative half cycle recognized by iA, all negative pulse widths are reduced by △t, and all positive pulse widths are increased by △t . This is due to the feedback diodes VD_{ap} and VD_{an} in the dead zone Δt. Caused by the freewheeling. The actual voltage waveform after distortion is shown as the u’’_{AO }waveform in Figure 5(b). Since the feedback diodes VD_{ap} and VD_{an} are in the dead zone Δt. The error waveform caused by freewheeling is u_{Dap.Dan} in the figure. Shown. Through the above analysis, it can be known that the actual waveform u’’AO is caused. There are three factors that cause distortion:

①Dead zone and dead zone setting method;

② Freewheeling of feedback diode when inductive load;

③Load power factor.

The dead zone and diode freewheeling are the fundamental reasons for the actual leaping of u’’_{AO}. The effect of the setting method and load cosφ is only to change the pulse distribution state of the error waveform u_{Dap.Dan}. What must be pointed out here is that cosφ is to u’’_{AO}. The influence of the waveform is discontinuous, as shown in Figure 6. Although φ1 and φ2 represent two different power factor angles, the error waves they produce are the same, which shows that only when the change of φ angle exceeds the pulse width does it have an effect. Therefore, the influence of cosφ on u’’_{AO} is discontinuous. That is to say, it is very difficult to find a common solution for the above three factors affecting u’’_{AO} distortion. For this reason, it can be approximately considered that the influence of cosφ is continuous (when F is relatively large, the error caused by this influence is very small), which can be derived from inductive load (cosφ<1) and no-load (i_{A}= 0), the influence of the dead zone Δt on the output voltage of the SPWM voltage three-phase half-bridge inverter.

1). For the harmonic analysis of the dead zone wave u’_{AO }in Figure 5(b)

In Figure 5(b), the dead zone wave u’_{AO} is obtained when the diode is not freewheeling when there is no load (i_{A}=0). u’_{AO} is mirror symmetry and is a function of odd harmonics. Therefore, the time function equation for the two-level SPWM wave with the dead zone wave u’_{AO} in Figure 5(b) is

For the fundamental wave and the harmonics of the fundamental wave, m=0, e^{j(mX+nY)}=e^{jnY}, then the method can be derived according to the above formula

Since ∫^{π}_{0}sinY·cosnY.dY=0, A_{0n}+jB_{0n}=(ME/π)∫^{π}_{0}sinY·sinnYdY.

When n=1, A_{01}+jB_{01}=j(ME/π)∫^{π}_{0}sin²Y·dY=j(ME/2)

For the harmonics of the fundamental wave, when n≠1, there is ∫^{π}_{0} (sinY·sinnY·dY=0, A_{0n} + jB_{0n}=0, which means that there is no harmonic of the fundamental wave.

For the carrier and the harmonics of the carrier, if n=0, then

Because sinmπ=0, so A_{m0}=0,

When m=even, cosmπ=1, cosmπ-1=0, B_{m0}=0;

When m=odd number, cosmπ=-1, cosmπ-1=-2,

For the carrier and the m-th harmonic of the carrier and its upper and lower side frequencies, there are

When one of m and n is odd and the other is even, cos(m+n)π=-1, so

Through the above analysis, the u’_{AO} double Fourier series expression when the dead zone is bilaterally symmetrically set at no load (i_{A}=0) (without feedback diode freewheeling) is expressed as

2). Harmonic analysis of the error wave u_{Dap.Dan} in Figure 5

The error wave u_{Dap.Dan} in Figure 5 is a general harmonic function. In its double Fourier series expression, there are

Known from Bessel Theory

and

So have

For fundamental wave and fundamental wave harmonics, if m=0, then

For the fundamental wave, there is n=1, there is

Then there is

For the harmonics of the fundamental wave, n≠1, then

For the carrier and the harmonics of the carrier, if n=0, then

When m=odd,cosmπ+1=0,Am0=0;

When m=even number, cosmπ+1=2,Am0=-(2E/mπ)J0(mMπ/2)sinm△tωc/2

For the upper and lower side frequencies of the carrier and the m-th harmonic of the carrier, there are

When m and n are both odd or even, there are

From the above analysis, the double Fourier series of the error wave u_{Dap.Dan} in Figure 5(b) can be expressed as

3). Analysis of the equation of the actual wave u’’_{AO }and the influence of the dead zone

(1) The equation of the actual wave u’’_{AO}:

From Figure 5(b), it is known that the actual wave u’’_{AO} is equal to the sum of the dead zone wave u’_{AO} and the error wave u_{Dap.Dan}. In order to facilitate the addition of u’_{AO}, u_{Dap.Dan}, the phase relationship between u’’_{AO}, u’_{AO}, u_{Dap.D}an must be found first, and then added according to their phase relationship.

It can be seen from Figure 5(b) that since the dead zone is bilaterally symmetrically arranged, and the learned dead zone is set on the front and rear edges of the pulse, u’_{AO} is in phase with the modulating wave us. The current iA is considered to lag behind the u’_{AO} wave φ angle, and the error waves u_{Dap.Dan} and i_{A} have opposite phases, so u_{Dap.Dan.} The phase of the wave is ahead of the u’_{AO} wave by 180°-φ, as shown in Figure 7. Therefore, when taking the phase of u’_{AO} wave as the reference, we can get

Substituting formula (15) and formula (25) into the above formula, and noting that the phases of u_{Dap.Dan} in formula (25) are opposite to u’_{AO}, we can get

When u”_{AO}‘s fundamental wave amplitude U’_{AO(1)}=ME/2, u_{Dap.Dan} fundamental wave amplitude U_{Dap.Dant(1)}=(2E/π²)△toωc, we can see u”_{AO} The amplitude of

The initial phase angle of u’’_{AO} fundamental wave φ’ is

Substitute the values of U’’_{AO}(1) and φ’ into the equation of u’’_{AO} to get

Since the influence of cosφ is not continuous, it can be seen from Figure 7 that when the angle φ is less than a pulse width, it can be regarded as the u’’_{AO }when the equation (29) and φ=0. The equations are the same, so the equations (15) and (25) are directly added together to get

(2) The influence of dead zone on output voltage

The influence of the dead zone Δt on the output voltage of the SPWM inverter is related to the setting method of the dead zone, the size of the dead zone Δt, the carrier ratio F, the operation mode of the inverter or the power factor of the load.

① The influence of operating mode or load cosφ: when running at no load or cosφ=1, the feedback diode does not freewheel, the error wave u_{Dap.Dan}=0, the actual wave u”_{AO} equals the dead zone wave u’_{AO} ; When running under inductive load, cosφ<1, feedback diode freewheeling, error wave u_{Dap.Dan}≠0, actual wave u”_{AO} is equal to dead zone wave u’_{AO} error wave u_{Dap.Dan}

②dead zone Influence of setting mode: when no load or cosφ=1, symmetrical setting mode does not appear cosine wave term, total harmonic content is less, asymmetric setting mode has cosine term, total harmonic content is larger; when it is inductive load (Cosφ<1), the effects of the two setting methods are basically the same, but the total harmonic content of the asymmetric setting method is larger. Therefore, the symmetric setting method should be selected as far as possible when conditions permit.

③ The influence of the dead zone Δt: When there is no load, the feedback diode does not freewheel, the dead zone has no effect on the fundamental wave, and does not generate new low-order harmonics, only has some influence on the original harmonic amplitude; In the case of an inductive load, the feedback diode freewheels and generates an error wave, so that the fundamental wave amplitude of the output voltage decreases with the increase of Δt, as shown in Figure 8. The phase of the fundamental wave is ahead of the φ’angle, and 3, 5, 7, … harmonics with amplitude (2E/π²) (1/n) △tωc appear. The larger the Δt, the 3, 5, 7, … harmonics The larger the amplitude, the higher the distortion rate of the output voltage, as shown in Figure 9.

④ The influence of carrier ratio F: When it is an inductive load, the feedback diode freewheels, and the actual wave u”_{AO}. The first two terms in the equation are

In this formula, ωc=Fωs. Therefore, when F increases, the fundamental wave amplitude decreases, and the 3, 5, 7, … sub-harmonic amplitude ratio increases, and the lower side frequency of the carrier in the u”_{AO} equation produces 3, 5, 7, …The subharmonics decrease with increasing F. The result of the combined effects of these two parts of low-order harmonics is that the amplitude of the low-order harmonics first decreases and then increases significantly with the increase of F. There is a best way to minimize the content of low-order harmonics. The carrier ratio F, which is greater or less than the optimal carrier ratio F, will increase the 3, 5, 7, … sub-harmonic content, as shown in Figure 10. This feature breaks the theory that the SPWM inverter reduces the content of low-order harmonics as F increases.

Setting the dead zone Δt in the SPWM inverter can avoid short-circuit faults in which the switch tubes of the same bridge arm are turned on at the same time. At the same time, in the case of inductive load, the diode freewheeling caused by the dead zone can turn on the switch tube ZVT, so the turn-on loss can be reduced. This is the benefit of setting a dead zone. The negative effect is to reduce the amplitude of the fundamental wave of the output voltage, lead the phase of φ’, and produce 3, 5, 7, … sub-harmonics. This shortcoming has a greater impact on the frequency conversion speed control system. When the frequency conversion speed regulation system is running at low speed, ωs decreases, which is equivalent to the increase of carrier ratio F=ωc/ωs, which reduces the influence of the fundamental wave amplitude and makes the 3, 5, 7, … sub-harmonic ratio The impact of the increase is more serious. In this case, in order to ensure the good operation of the variable frequency speed regulation system, it is necessary to repair the negative effects of the dead zone, or adopt a special protection circuit to prevent the same bridge arm switches from being turned on at the same time, as shown in Figure 11. Show. It uses blocking diodes to prevent series and short circuits, as shown in the diodes VD_{a} and VD_{b} in Figure 11 (a) and VD_{a}, VD_{b} and VD_{c} in Figure 11 (b). When the two switching tubes on the same bridge arm are turned on at the same time, the forward voltage drop on the blocking diode can be used to turn off the above switching tubes.

**3. Compensation for the influence of dead zone**The following introduces two compensation methods for the influence of the dead zone: one is current feedback compensation; the other is voltage feedback compensation.

1).Current feedback compensation

The circuit using current feedback compensation is shown in Figure 12. By detecting the three-phase output current of the inverter, and turning it into a three-phase square wave voltage and adding them to their respective modulation waves u_{s}, such as changing the detected phase A current i_{A} into a square wave voltage u_{i} and adding it to the phase A modulation On the wave u_{s}, the square wave voltage u_{i} will make the inverter produce a compensation voltage u_{com} that has the same phase as the current i_{A}, similar to the error wave u_{Dap .Dan}, but opposite in phase to u_{Dap.Dan}, as shown in Figure 13.

The phase of the compensation voltage u_{com} is the same as the phase of the current i_{A}, and is opposite to the phase of the error wave voltage u_{Dap.Dan}. Since each side of the carrier triangle wave is linear, so u_{s}+u_{i} the modulated waveform is equal to the sum of u_{s} and u_{i} modulated waveforms. The dead zone modulation wave generated by u_{s }is u’_{AO}, the error wave generated by the feedback diode is u_{Dap.Dan}, and the modulation wave generated by u_{i} is u_{com}. Therefore, the output voltage equation of the inverter is

Using the current feedback compensation circuit as shown in Figure 12, the purpose of eliminating the error wave u_{Dap.Dan}, reducing the fundamental wave amplitude and generating the adverse effects of 3, 5, 7, … sub-harmonics is well achieved.

2).Voltage feedback compensation

The circuit using voltage feedback compensation is shown in Figure 14. The SPWM output voltage waveform u”_{AO} of each phase. It is detected by the step-down converter T, and the phase is reversed to -u’’_{AO}, and -u’’_{AO} is used. Add the given SPWM signal u”_{AO} with dead zone to get the compensation voltage u_{com}. The phase of u_{com} is the same as the current i_{A}, which is opposite to the phase of the error waves u_{Dap.Dan}, which can be used to offset the bad effects of the error waves u_{Dap.Dan}.

The voltage feedback compensation circuit shown in Figure 14 can completely eliminate the adverse effects caused by the error waves u_{Dap.Dan}, but its circuit is more complicated than the current feedback compensation circuit.