A neutral-point potential balance control strategy for three-level inverter based on VSVPWM

CHENG Dong-liang, WANG Xiao-peng, ZHU Tian-liang, MA Wen-gang

(School of Electronic and Information Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China)

Abstract： The topology of diode neutral-point-clamped (NPC) three-level inverter is prone to neutral-point potential offset. When the sum of three-phase current is zero, the virtual space vector pulse width modulation (VSVPWM) scheme does not cause the neutral-point voltage offset, but it lacks the ability to balance the deviation. For this reason, a neutral-point potential control strategy combining virtual space vector modulation and loop width control is proposed. The neutral-point potential is balanced by introducing the distribution factor for the regions with redundant vectors. For other regions, the potential is controlled by selecting a suitable switching sequence. Meanwhile, the effect on the virtual vector modulation is reduced within the loop width by setting an appropriate loop width, thereby improving the balance effect. The simulation results show that the proposed method has a strong ability to control the offset and has excellent potential balance performance under the conditions of balanced load, unbalanced load and asymmetric capacitance parameters.

Key words： three-level inverter; virtual space vector pulse width modulation (VSVPWM); neutral-point potential balance; switching sequence

0 Introduction

Compared to the two-level inverter， the switching stress of the three-level neutral-point-clamped (NPC) inverter is reduced by half, and the harmonic distortion of the output waveform is even smaller[1]. At present, it has been widely used in the field of flexible AC transmission, reactive power compensation and absorption, and so on[2-3]. But the three-level NPC inverter has the problem of neutral-point potential imbalance， which will increase the harmonic content of the output voltage, reduce the lifetime of the switch device, and even cause the breakdown of DC link capacitors[4]. Therefore, it is significant to study the neutral-point potential balance problem of three-level inverters.

The method of controlling the neutral-point potential balance can be divided into hardware control and software control. The former requires additional costs, so software methods are widely used. Ref.[5] was based on space vector pulse modulation(SVPWM), and the neutral-point potential was balanced by changing the action time of redundant small vectors. However, when the modulation index was high, the control effect was not satisfactory. In Refs.[6-7], the virtonal space vector pulse width modulation (VSVPWM) theoretically balanced the neutral-point potential completely, but it did not effectively balance the offset caused by unbalanced load parameters and element parameters. Gui, et al. proposed the concept of variable virtual vector pulse width modulation (VVSVPWM)[8]. According to the value of the neutral-point potential, changing the length of virtual middle vector could better achieve the neutral-point potential balance. Jiang, et al. proposed some hybrid modulation schemes, and different modulation methods were switched to control the potential under different situations, but the complexity of the algorithm was also increased[9-11].

Based on the above analysis, a neutral-point potential balance method based on VSVPWM is proposed. The neutral-point potential balance is achieved by adjusting the action time of positive and negative small vectors. In region 5, the neutral-point potential is controlled by selecting an appropriate switching sequence, which greatly improves the ability to control the balance of potential in this small region. Finally, a simulation model is built based on Matlab/Simulink to verify the performance of the proposed algorithm under different conditions.

1 Principle of potential imbalance for three-level inverter

The topology of NPC three-level inverter is shown in Fig.1. Take phaseAas an example. Each phase has three level states: whenQ1andQ2are on, the state is marked “p”; whenQ2andQ3are on, the state is marked “o”; whenQ3andQ4are on, the state is marked “n”. The other two phases also obey this rule.

Fig.1 Topology of NPC three-level inverter

As shown in Fig.1, the relationship between the voltage and current of DC link capacitor is

(1)

(2)

whereiC1,iC2andioare the currents of capacitanceC1,C2 and neutral-point, respectively;UC10andUC20are the capacitor voltages at the initial time, and the asymmetry of capacitance parameters and load parameters may causeUC10≠UC20.

From Fig.1, it can be known thatiC1-iC2=i0. Assuming thatC1=C2=CandUC10=UC20, we can get

(3)

As known from Eq.(3), if the charge of inflow and outflow is not zero during a switching period, it will cause the neutral-point potential imbalance. In addition, ifUC1is not equal toUC2, the neutral-point potential can be balanced by adjusting the charge flowing out of the neutral-point.

The three-level inverter has 27 switching states, corresponding to 27 basic space voltage vectors, and the space voltage vectors diagram is shown in Fig.2.

Fig.2 Space voltage vectors diagram of three-level NPC inverter

The different vectors correspond to different neutral-point currents that will have different effects on the neutral-point potential. The neutral-point currentiocan be expressed as[12]

(4)

whereSjis the switching function and is defined as

(5)

The neutral-point currents for different voltage vectors can be obtained according to Eq.(4). Table 1 shows the neutral-point currents for the voltage vectors in sector Ⅰ.

Table 1 Neutral-point current for different voltage vectors

2 Traditional VSVPWM

The VSVPWM introduces a virtual middle vector on the basis of the traditional SVPWM, which divides a sector into 5 small regions. Taking the first sector as an example, the virtual space vectors diagram is shown in Fig.3.

Fig.3 Virtual space vectors diagram in sector Ⅰ

The virtual middle vector in sector Ⅰ is defined as

(6)

As known from Table 1, the vectorsV0,VL1andVL2do not affect the neutral-point potential. Since the switching periodTSis very short, the three-phase current can be considered a constant value during a switching cycle[6]. When the three-phase current satisfiesia+ib+ic=0, the action time ofVMis equally distributed to its three component vectors, which can ensure that the charge flowing out of the neutral-point within one switching cycle is zero, thus it will not affect the neutral-point potential. Similarly,VS1andVS2also do not cause potential shifts by dividing the action time equally.

The VSVPWM is proposed under the conditions that the three-phase current satisfiesia+ib+ic=0, but the three-phase current in the actual operation will not always meet the conditions. Meanwhile, it is difficult to balance the offset caused by unbalanced load parameters and element parameters.

For VSVPWM, the switching sequences of voltage vectors in sector Ⅰ are shown in Table 2.

Table 2 Switching sequences of vectors in sector Ⅰ

3 Neutral-point potential balance control strategy

3.1 Potential control based on time distribution factor

From Table 2, it can be seen that there are redundant small vectors in regions 1-4, and the neutral-point potential can be controlled by introducing the distribution factor. Assuming that the voltages of the two capacitors areUC1andUC2respectively at the end of the last switching cycle, the voltage difference between the two capacitors can be defined as

ΔU=UC1-UC2.

(7)

The charge that needs to be compensated for the current switching cycle can be expressed as

(8)

Taking the region 1 as an example, there are two pairs of redundant small vectors. Two time distribution factors,k1andk2, are introduced, corresponding to the first and second pairs of redundant vectors, respectively. If the action time of the vectorsVS2,VS1andV0are represented byT1,T2andT3, respectively, the switching sequence and the action time are shown in Table 3.

Table 3 Switching sequence and action time in region 1

Combined with Table 3 and Table 1, it can be calculated that the charge flowing out of the neutral-point during a switching cycle is

ΔQ=ick1T1-iak2T2.

(9)

In order to achieve the balance of neutral-point potential, it is necessary to satisfy ΔQ=Q0. Let the absolute values of the two factors be equal, if the direction of neutral-point current is the same when the two P-type small vectors work,k2is equal tok1. The value of the distribution factork1is

(10)

Otherwise,k2=-k1, the value ofk1is

(11)

It should be noted that the time distribution factorsk1andk2need to satisfy -1≤(k1,k2)≤1. Ifk1≥1,k1=1; ifk1≤-1,k1=-1. This indicates that when the potential difference is relatively large, accurate compensation cannot be achieved within one switching cycle, and the neutral-point potential can be balanced after several switching cycles. Considering that the traditional VSVPWM does not cause potential offset in some cases, a loop width,h, is introduced. And the neutral-point potential difference ΔUsatisfies

(12)

It can be seen from Eq.(12) that when |ΔU|≤hand the current satisfiesia+ib+ic=0, the calculated value of distribution factor is 0, which has no effect on the neutral-point potential. That is to say, only the VSVPWM scheme works. Similarly, there are redundant small vectors for the regions 2, 3 and 4, and the same method can be used to balance the neutral-point potential.

3.2 Switching sequence selection control

As known from Table 2, when the reference vector is in region 5 for the traditional VSVPWM, there is no a pair of redundant small vector in the switching sequence. Therefore, the neutral-point potential that has been shifted cannot be balanced by introducing the distribution factor. The paper proposes that the neutral-point potential in region 5 can be controlled by selecting the appropriate sequence.

It is known from Eq.(6) that the traditional virtual middle vector contains two small vectors, and all of them have redundant vectors. Therefore, without changing the amplitude of the virtual middle vector, it can be expressed as two other forms besides the original sequence. The effects of the three virtual middle vectors on the output voltage are the same, but they correspond to different neutral-point currents. Therefore, the neutral point potential can be controlled by selecting the appropriate switching sequence. Taking the first sector as an example, the virtual middle vector can be expressed as the following two forms, namely

(13)

The switching sequence needs to satisfy the condition that only two switching devices can act between two switching states. At the same time, in order to reduce the harmonic distortion, the switching sequence should be symmetrical. On the premise of satisfying the above requirements, two other switching sequences are available, as shown in Table 4.

Table 4 Switching sequences in region 5

When the switching sequence 1 and the switching sequence 2 are applied respectively, if the operation time of the virtual middle vector isT1, the charge flowing out of the neutral-point in one switching period is ΔQ1and ΔQ2, respectively, namely

(14)

When the three-phase current meetsia+ib+ic=0, simplifying Eq.(14), we can obtain

(15)

The appropriate switching sequence can be selected to balance the neutral-point potential according to the value of the currentsia,icand potential difference ΔU. But if ΔUfloats up and down near to 0, it may cause frequent switching of the sequences and violent fluctuation of the neutral-point potential waveform, which is not conducive to the balance control of neutral-point voltage. Considering the loop widthh, in combination with Eq.(15), the sequence selection rules for the region 5 in the first sector are as follows:

1) When ΔU>handia>0, switching sequence 1 is selected.

2) When ΔU<-handic<0, switching sequence 2 is selected.

3) In other cases, the original switching sequence is selected.

4 Simulation results and analysis

In order to verify the performance of the proposed method, a simulation model of three-level inverter is built with Matlab/Simulink software, as shown in Fig.4. And some of the parameters have been labeled in the diagram.

Fig.4 Main circuit of simulation model

Fig.5 gives the circuit model for the selection of switching sequence. The simulation is carried out under the three conditions: balanced load, unbalanced load and asymmetric capacitance parameters. The simulation parameters are as follows: the DC link voltageUdc=600 V, DC link capacitorsC1=C2=1 000 μF, filter inductanceL=1.26 mH, filter capacitorC=40 μF, switching frequency is 5 kHz, fundamental frequency is 50 Hz, modulation index is 0.9, and loop widthh=1. The loads are different under the three conditions.

Fig.5 Circuit diagram of selecting switch sequence

4.1 Three-phase balanced load

When each phase load meets the conditions thatR=9 Ω andL=30 mH, the simulation waveforms of VSVPWM under three-phase balanced load conditions are shown in Fig.6.

It can be seen from Fig.6(a)that the line voltage waveform is good under balanced load conditions. Due to the influence of sampling time of the solver, the neutral-point potential may be offset, but it cannot be effectively controlled by traditional VSVPWM, as shown in Fig.6(b).

After introducing the distribution factor, the simulation waveform is improved obviously, as shown in Fig.6(c). Since the balance control is only in regions 3 and 4, there is a large fluctuation at the initial stage of the balance, and accordingly a longer balance time is needed (about 0.1 s).

By comparing Figs.6(c) and (d), it can be observed that the ability to control the neutral-point potential is obviously improved after taking the sequence control. The balance is achieved within only 0.05 s, and the initial fluctuations are also smaller.

Fig.6 Simulation waveforms of balanced load

4.2 Three-phase unbalanced load

Changing the load of phaseAtoR=12 Ω,L=10 mH, the other two phase loads remain unchanged. The simulation waveforms of neutral-point potential are shown in Fig.7. From Fig.7(a), it can be seen that the neutral-point potential deviation is more obvious under unbalanced load condition than under the balanced load, while the VSVPWM scheme is difficult to balance the deviation. After the distribution factor and sequence control are applied, the neutral point potential is quickly balanced, as shown in Fig.7(b). At the same time, the fluctuation is smaller than before.

Fig.7 Simulation waveforms of unbalanced load

4.3 Asymmetric capacitance parameters

When the load of each phase isR=9 Ω,l=30 mH, the capacitorC2 is changed to 1 150 μF, and the neutral-point control is applied at 0.05 s, the simulation waveform of the capacitor voltage is shown in Fig.8. It can be seen that the capacitor voltage difference is about 40 V in the initial period due to the asymmetry of the capacitance parameters. After the control strategy is used at 0.05 s, the neutral-point potential gradually tends to balance. Comparing Fig.8(a) with Fig.8(b), it can be seen that when only the distribution factor is adopted, it takes 0.03 s to achieve the balance. After applying the sequence control to region 5, only 0.01 s is needed to achieve the balance. Compared with the virtual space vector modulation, the proposed method can greatly improve the ability to control the neutral-point potential and achieve the balance control more quickly.

Fig.8 Simulation waveforms of asymmetric capacitance parameters

5 Conclusion

Since the traditional VSVPWM cannot effectively balance the potential offset caused by asymmetric parameters, a new neutral-point potential control strategy based on VSVPWM under three-phase balanced load condition are proposed. By introducing the distribution factors and selecting the appropriate switching sequence, the neutral-point potential can be controlled in every small region. The simulation is performed under the conditions of balanced load, unbalanced load and asymmetric capacitance parameters, respectively. The results show that the neutral-point potential can be rapidly balanced under the above conditions, and it still has a good performance when the modulation index is high.