Perfect Harmonics High Voltage IGBT Inverter

1 Introduction

A foreign company has used a new high-voltage frequency conversion technology to produce a perfect harmonic-free high-voltage frequency converter (PERFECTHARMONY) with a power of 315kW to 10,000kW. It can achieve direct 3kV or 6kV high-voltage output without an additional output transformer; it is the first company to use advanced IGBT switching devices in high-voltage frequency converters; it has achieved perfect input and output waveforms, and can meet the strict requirements of power supply departments in various countries on harmonics without adding any filters; the input power factor reaches more than 0.95; the overall efficiency (including input isolation transformation) is as high as 97%. The reason for achieving such high indicators is that three new high-voltage frequency conversion technologies are used: first, the direct series superposition of single-phase bridge SPWM inverters with independent power supply is used in the output inverter part; second, the multi-phase multiple superposition rectification technology is used in the input rectification part; and third, the power unit modularization technology is used in the structure.

2 Direct series superposition of single-phase bridge SPWM inverters

The direct series superposition method of single-phase bridge SPWM inverter is formed by directly connecting N single-phase bridge SPWM inverters with independent DC power supplies in series. This is a series superposition method specially used for high-voltage and high-power inverters. This method uses N carrier triangle waves with 2π/N phase angles shifted in sequence to compare with the same sinusoidal modulation wave to generate N groups of control signals. These N groups of control signals (N groups of signals differ by 2π/N phase angles in sequence) are used to control N single-phase bridge SPWM inverters with independent DC power supplies in sequence, so that each single-phase bridge inverter outputs the same fundamental voltage, and then the output voltages of N single-phase bridge inverters are connected in series to obtain a multi-level SPWM harmonic-free voltage output. This series connection does not have a voltage balancing problem.

2.1 Series superposition of two single-phase bridge SPWM inverters

A direct series superposition circuit of a single-phase bridge SPWM inverter with an independent DC power supply is shown in Figure 1. Since N=2, the phase shift angle of the carrier triangle wave α==π(=180°). For a three-phase output inverter, its A phase circuit is composed of two single-phase bridge SPWM inverters A1 and A2 connected in series. The phase shift angle of the carrier triangle wave of A1 is α=0; the phase shift angle of the carrier triangle wave of A2 is α=(=180°). The carrier triangle waves of A1 and A2 are modulated with the same A-phase sine wave. In this way, the output voltage up1 of A1 and the output voltage up2 of A2 can be obtained. Up1 and up2 have the same fundamental voltage. The output voltage uA=up1+up2 after A1 and A2 are connected in series is a harmonic-free voltage output as a sine wave, and its waveform is shown in Figure 2.

Figure 1 Series superposition of two single-phase bridge SPWM inverters

Figure 2 Waveform after A1 and A2 are superimposed in series

In order to obtain the SPWM waveform of the output voltage up1 and up2 of the single-phase bridge SPWM inverter A1 and A2, the coordinates of the leading and trailing edges a and b of each pulse in the SPWM waveform must be obtained first. For this purpose, the equation of the carrier triangle wave is listed first:

For single-phase inverter A1α=0

（1）

For single-phase inverter A2α=180° (2)

K=0，±1，±2…

The equation of the modulated wave is: us(t)=Ussinωst (3) Assuming the carrier ratio, modulation ratio.

For the waveform of the output voltage up2 of the single-phase inverter A2,

At sampling point a: Ussinωst=－

令ωst=Y；ωct=X，

则X=2πK＋π－α－πMsinY

At sampling point b: X = 2πK + π - α + πMsinY

From the up2 waveform of A2 in Figure 2, we can see that: X=ωct In the range of 2πK＋α to 2π(K＋1)＋α, the positive pulse of up2 is obtained between points a and b, so the time function of the SPWM wave of up2 can be obtained as: up2(X, Y)=(4)Y=X

The function up2(X, Y) can be expressed by a double Fourier series: up2(X, Y) = Aoo + (AoncosnY + BonsinnY) + (AmocosmX + BmosinmY) + {Amncos(mX + nY) + Bmnsin(mX + nY)}

Source: Amn＋jBmn=up2(X，Y)

Substituting equation (4) into the above equation, we get: Amn+jBmn==

From Bessel function we get: So: Amn + jBmn =

·〔〕=j(5)

When n is zero or an even number, =0, Amn+jBmn=0,

When n is an odd number, =2, so: Amn + jBmn = jJn (mMπ)

·〔cosm(π－α)＋jsinm(π－α)〕Amn=－Jn(mMπ)sinm(π－α)；Bmn=Jn(mMπ)cosm(π－α)当m=0时=1Aon＋Bon=up2 (X, Y)

Because up2(X, Y) is an odd function, we have:

Year=0Good=up2(X,Y)=

When n=1, Bo1=ME; when n≠1, Bon=0

Therefore, the double Fourier series formula of the SPWM waveform of up2 is: up2(t)=MEsinωst＋cosm(π－α)·sin〔(mF＋n)ωst〕－sinm(π－α)

·cos〔(mF＋n)ωst〕(6)

Since the carrier triangle wave of A1 has α=0 and the carrier triangle wave of A2 has α=π, and A1 and A2 use the same sinusoidal modulation wave, we can get from equation (6): up1(t)=MEsinωst＋cosm(π－0)·sin〔(mF＋n)ωst〕－sinm(π－0)

cos〔(mF＋n)ωst〕(7)up2（t）=MEsinωst＋cosm(π－π)·sin〔(mF＋n)ωst〕－sinm(π－π)

·cos〔(mF＋n)ωst〕(8)

Since the fundamental voltages of up1(t) and up2(t) are the same, and sinm(π-0)+sinm(π-π)=0, for cosm(π-0)+coom(π-π): when m is an even number, it is equal to 2; when m is an odd number, it is equal to zero. Therefore, the double Fourier series formula of uA obtained by adding equation (7) and equation (8) is: uA=up1(t)+up2(t)=2MEsinωst+sin〔(mF+n)ωst〕(9)

From formula (9), we can know that the five-level voltage output is obtained by superimposing the series connection of N=2 in the inverter A phase output voltage. uA no longer contains harmonics below 2F±1, but only contains harmonics above 2F±1. The waveform of uA=up1(t)+up2(t) is shown in Figure 2.

2.2N single-phase bridge SPWM inverters in series

When N is any natural number equal to or greater than 2, the above direct series superposition method can be used, and the circuit is shown in Figure 3 to eliminate the harmonic components less than NF±1 in the SPWM waveform. The phase shift angle of its carrier triangle wave is shifted by 2π/N in sequence. For phase A, the α of single-phase inverter A1 is 0, the α of A2 is 2π/N, the α of A3 is ·(3-1)…the α of AN is ·(N-1), and A1~AN use the same A-phase sine wave as the modulation wave to obtain the output voltage up1(t)~upN(t) of A1~AN: up1(t)=MEsinωst＋cosm(π-0)·sin〔(mF＋n)ωst〕－sinm(π-0)

·cos〔(mF＋n)ωst〕(10)up2(t)=MEsinωst＋cosm(π－)·sin〔(mF＋n)ωst〕－sinm(π－)

cosm(π－G)

Figure 3 N independent power supplies are directly connected in series

·cos〔(mF＋n)ωst〕(11)

……upN(t)=MEsinωst＋cosm〔π－〕·sin〔(mF＋n)ωst〕－sin〔π－〕

cos〔(mF＋n)ωst〕(12) Since up1(t)～upN(t) have the same fundamental voltage, sinm(π－0)＋sinm(π－)＋…sinm〔π－〕=0; for the value of cosm(π－0)＋cosm(π－)＋…＋cosm〔π－〕=cosm(π－G), it and the values ​​of N and m are shown in Table 1. Table 1 Relationship between cosm(π－G) and N, m

Therefore: The output voltage uA of phase A is equal to:

uA=up1(t)＋up2(t)＋…＋upN(t)=NMEsinωst±sin〔(mF＋n)ωst〕(13)

For example, when N=5: u5=5MEsinωst－sin〔(mF＋n)ωst〕(14)

When N=5, an 11-level voltage output will be obtained in the A-phase output voltage after series superposition. The uA will no longer contain harmonics below 5F±1, but only harmonics above 5F±1, and its waveform is shown in Figure 4.

From formula (13), it can be seen that: after the direct series superposition of N single-phase bridge SPWM inverters with independent power supplies, (2N+1) levels of voltage output will be obtained in the A-phase output voltage, and harmonics below NF±1 can be eliminated in the double Fourier series of uA. For example, when the switching frequency fs=6000Hz, the carrier ratio F==120, and N=5, in the Fourier series of the A-phase output voltage, harmonics below 5×120±1=600±1 can be eliminated, so it is called a harmonic-free inverter (meaning no low-order harmonics).

n=±1,±3

n=±1,±3

Figure 4 Output voltage waveform of series superposition when N=5

Figure 518-phase triple superposition rectifier circuit

3. Multi-phase multiple superposition rectification

The input rectifier part of the perfect harmonic-free high-voltage inverter mainly adopts 18-phase three-phase superposition rectification method and 30-phase five-phase superposition rectification method.

3.1 18-phase triple superposition rectification The 18-phase triple superposition rectification circuit and waveform are shown in Figure 5. The input transformer adopts an 18-phase rectification circuit with Y/ΔΔΔ connection. The three sets of secondary windings of the input transformer lag in turn by a phase angle of = 20°, and each supplies power to a three-phase bridge rectifier. The three three-phase bridge rectifiers output separately, and the output DC current is Id. The primary input current ia of the transformer is ++, and , and are the primary supply currents corresponding to the three secondary windings. After the triple superposition of , and , the primary current ia becomes a ten-step equal-step wide step wave, so the Biriger formula can be used to calculate the amplitude of the fundamental wave and each harmonic of ia: Where: n is the harmonic amplitude: n*=n() is the harmonic number corresponding to n;

δi is the jump value at point ti, n=1,2,3…m;

T is the function repetition period.

Using Biriger's formula to calculate the fundamental wave and harmonic amplitude of the ten-step equal-width ladder of ia, we can get

Imn=〔〕=()〔〕(15)

Use this formula to calculate the amplitude of the fundamental wave and each harmonic:

Im1=3.175Id；Im5=0.144Id；Im7=0.0838IdIm11=0.053Id；Im13=0.0554Id…

Therefore, the Fourier series formula of the input current ia is:

it=()

〔sinωt＋0.045sin5ωt＋0.0264sin7ωt＋0.0167sin11ωt

＋0.0174sin13ωt＋0.0588sin17ωt0.034sin19ωt〕

(16)

From this formula, we can see that the low-order harmonic content of ia is greatly reduced.

3. 230-phase five-phase superposition rectification

The waveform of the 30-phase quintuple superimposed rectifier circuit and the input current ia of the Y/ΔΔΔΔΔ connected input transformer is shown in Figure 6. The five sets of secondary windings of the input transformer lag the phase angle in turn. Each set of secondary windings supplies power to a three-phase bridge rectifier. The five three-phase bridge rectifiers output separately, and the output DC current is Id. The primary input currents corresponding to the five secondary windings are,,, and, and the transformer primary input current ia=++++. The waveform of the input current ia after quintuple superimposition is a 16-step equal-order wide step wave. The fundamental wave and the amplitude of each harmonic are calculated using the Biriger formula:

Imn=()〔〕

Figure 630 Phase 5 Superposition Rectification Circuit

Figure 7 Schematic diagram of power unit module circuit

Use this formula to calculate the amplitude of the fundamental wave and each harmonic:

Im1=5.274Id; Im5=0.220Id; Im7=0.118IdIm11=0.055Id; Im13=0.0433Id; Im17=0.033IdIm19=0.0317Id; Im23=0.0358Id; Im25=0.0026IdThe Fourier series formula of input current ia is:

ia=(＋)(sinωt＋0.0417sin5ωt

＋0.0223sin7ωt＋0.0104sin11ωt＋0.0082sin13ωt

＋0.0063sin17ωt＋0.006sin19ωt＋0.0067sin23ωt

＋0.00048sin25ωt＋…）（18）

From this formula, we can see that harmonics below the 25th order are greatly reduced.

4Power unit modularization

In order to facilitate production and maintenance, the perfect harmonic-free high-voltage inverter adopts a modular power unit. The circuit of the power unit module is shown in Figure 7. It is a voltage-type power unit composed of a fuse, a three-phase bridge rectifier, a DC filter capacitor, and an IGBT single-phase full-bridge inverter. The DC filter capacitor in the unit must be large enough to allow the inverter to withstand a 30% power supply voltage drop and a 5-cycle power supply voltage loss.

The power unit composed of 3.3kV IGBT switching devices can output 4160V medium voltage. The SPWM voltage source inverter with two power units in series is shown in Figure 8. Due to the small number of power units in series, in order to obtain excellent performance, an output AC filter can be added to the output end of the inverter. The input rectifier power supply uses an 18-phase triple superposition rectifier.

The circuit of the voltage source inverter with an output voltage of 6000V is shown in Figure 9, using five IGBT power units with a voltage of 690V in series. Since the power unit modules with independent DC power supplies are connected in series, there is no voltage balancing problem. The switching frequency of the IGBT in the power unit is 600Hz, and there are five power units in series in each phase, so the equivalent switching frequency of the output phase voltage is 6000Hz. The input rectifier circuit uses a 6000V voltage source inverter 30-phase five-phase superposition rectifier circuit, with an input current distortion of 0.8% and an input voltage distortion of 1.2%. The waveforms of the input and output voltages and currents are very close to sinusoidal.

Figure 8 SPWM voltage source inverter with two power units in series (output voltage 4160V)

Figure 9 The output voltage of five power units in series is

5 Conclusion

This perfect harmonic-free high-voltage IGBT inverter solves the three major problems of series voltage balancing of switch devices, harmonics and efficiency in high-voltage inverters. The direct series superposition technology of single-phase bridge SPWM inverters with independent DC power supply is adopted to reduce the low-order harmonics of the output voltage, facilitate the adjustment of the output voltage, eliminate the steady-state and dynamic voltage balancing problems of series connection of switch devices, reduce the switching frequency of a single switch device, and improve the inverter efficiency; the multi-phase multi-superposition rectification technology is adopted to reduce the input current harmonics, reduce the pollution to the mains power grid, and improve the input power factor; the modular technology of power units is adopted to facilitate installation and maintenance and improve the reliability of the inverter.