1 Introduction

The matrix converter is a new type of AC-AC converter with excellent input and output characteristics. It allows single-stage frequency conversion, without the need for large-capacity energy storage components such as large capacitors. And the voltage is adjustable, the output frequency can be higher or lower than the input frequency, especially its power can flow in both directions, with four-quadrant operation capability. Based on the space vector control of matrix converters, this paper presents a scheme based on DSP+PLD. Experiments show that this scheme can improve the reliability of commutation under high frequency and large current, and simplify the control system.

2 Space vector modulation of matrix converters

A matrix converter used to realize the AC-AC transformation is shown in Figure 1. It can be replaced by an equivalent AC-DC-AC structure composed of a virtual rectifier and a virtual inverter, as shown in Figure 2. Using such an equivalent structure can make full use of the mature PWM control technology in AC-DC-AC conversion, and can analyze the switching control law of the actual matrix converter through the switching function.

When analyzing Figures 1 and 2, first define the switching function.

Figure 1 Matrix converter structure

Figure 2 Equivalent intersection-straight-intersection structure

For the equivalent intersection-ortho-intersection structure of Figure 2, j∈{a,b,c,A,B,C,},k∈{P,N}. According to the principle that the input voltage cannot be short-circuited and the output circuit cannot be suddenly opened, there must be one and only one switch on the same DC bus P or N of the virtual rectifier, that is,

Sak＋Sbk＋Sck=1，k∈{P，N} （1）

The virtual inverter must have one and only one switch on the same output phase A, B or C, that is,

SjP＋SjN=1，j∈{A，B，C，} （2）

For the actual structure of the matrix converter in Fig. 1, j∈{A,B,C,}, k∈{a,b,c}. According to the principle that the input voltage cannot be short-circuited and the output circuit cannot be suddenly opened, each output phase can only be connected to and must be connected to one input phase, and the switching function must satisfy

Sja＋Sjb＋Sjc=1，j∈{A，B，C，} （3）

There are 27 switch combinations that can satisfy equation (3), but there are 6 types of switch combinations that cannot be found in the equivalent AC-DC-AC structure, so there are 21 valid switch combinations and vectors, see Table 1.

After derivation, the switching function relationship between the equivalent AC-DC-AC structure and the matrix converter can be obtained as:

Sjk=SjPSkP＋SjNSkN， j∈{A，B，C，}，k∈{a，b，c} （4）

Constraints are

1≤SGm＋SJn＋SKI≤2 （5）

Where: G, J, K∈{A,B,C,}, m,n,1∈{a,b,c}, and G≠J≠K, m≠n≠1.

According to formula (4), the corresponding relationship between the vectors formed by the 21 effective switch combinations of the matrix converter and the 6 input phase current vectors and 6 output line voltage vectors of the equivalent AC-DC-AC structure can be obtained, as shown in Figure 3 and Table 1 , so that the AC-AC direct transform space vector modulation strategy of the matrix converter is obtained from the double space vector modulation strategy of the equivalent AC-DC-AC structure.

Figure 3. Vector diagram of input phase current and output line voltage

In the equivalent AC-DC-AC structure, the ideal output line voltage reference vector circle of the inverter part and the ideal input phase current reference vector circle of the rectifier part are divided into 6 sectors, so there are 36 possible sectors Area combination, taking the virtual rectifier and inverter both working in the first sector as an example, can be used for the space current of vector synthesis, the voltage vectors are I6, I1 and U6, U1 respectively. The comprehensive modulation of the two space vectors adopts mutual nested approach to achieve. The entire input phase current and output line voltage vector synthesis process has a total of I6-U6, I6-U1, I1-U6, I1-U1 and zero vector I0-U05 combinations. The action time of each vector combination, expressed as a duty cycle, is the product of the duty cycles of the vectors within that combination. which is

I6－U6：

Dxα=Dx·Dα=msin（60°－θi）sin（60°－θv） （6）

I6—U1：

Dxβ=Dx·Dβ=msin（60°－θi）sinθv （7）

I1－U6：

Dα=Dy·Dα=msinθisin（60°－θv） （8）

I1－U1：

Dyβ=Dy·Dβ=msinθisinθv （9）

I0－U0：

D0=1－Dxα－Dxβ－Dyα－Dyβ （10）

Where: θi is the phase angle of the input phase current;

θv is the phase angle of the output line voltage.

After the duty cycle is calculated above, the corresponding vector and switch combination of the real matrix converter is found through the switch function. The selection steps and principles of the switch combination are as follows: Assuming that the output line voltage vector and the input phase current are both located in the first sector, the fixed vectors U1, U6, I1, and I6 of the combined sum are obtained according to Figure 3, and the corresponding matrix converter is obtained. 8 vectors 1P, 3P, 4P, 6P, 1N, 3N, 4N, 6N, and then select 4 vectors from the above 8 vectors according to the principle of obtaining the maximum voltage transfer ratio and unity power factor. To obtain unity power factor, the phase angle difference between the input phase voltage and the input phase current should be 0, noting that the input line voltage vector leads the input phase current by 30°, the input line voltage vector may be located in the 1st sector or the 2nd sector Therefore, the maximum value of the input line voltage is Uab and -Uca, then 4 vectors need to be selected from the above 8 vectors to make the output line voltage UOAB equal to Uab or -Uca, the selected 4 vectors are 1P, 3N, 4N, 6P, and 4 vectors determine the switching sequence as 1P, 3N, 4N, and 6P according to the principle of the least number of switches. With the addition of zero vector, the duty cycle of the 5 vectors is determined by equations (6), (7), (8) , (9), (10) are determined. The output line voltage vector and the input phase current have a total of 36 sector combinations, which correspond to the 36 vector modulation switch combinations of the matrix transformation.

3 Safe commutation strategy

This system adopts the reverse series IGBT combination switch of common collector to form a bidirectional power switch. According to the condition that the input voltage cannot be short-circuited and the output circuit cannot be suddenly opened, safe switching requires that any two groups of switches of the same phase output cannot be turned on at the same time. Group switches cannot be turned off at the same time. Due to the differences in the turn-on time, turn-off time of the device, and the time delay of the drive circuit, strict simultaneous switching cannot be achieved. To solve this problem, N. Burany proposed the famous four-quadrant switch multi-step switching control method, and its commutation process can be illustrated by the one-phase output circuit shown in Figure 4 and Figure 5. Taking the commutation from the a input phase to the b input phase as an example, when the load current iL > 0, the first step is to turn off the negative conduction part SlN, the second step is to turn on S2P, the third step is to turn off S1P, and the fourth step is to turn on S2N, thereby completing the successful commutation of the two bidirectional switches, not only prohibits the switch combination that may short-circuit the power supply, but also ensures that at least one circulation path is provided to the load at any time.

Figure 4 Schematic diagram of one-phase output circuit

Figure 5 Schematic diagram of the driving signal of the 4-step commutation strategy

4 Control system design and experimental results

Figure 6 is a block diagram of the matrix converter system with DSP as the control core. After the DSP detects the input phase voltage sector and obtains the desired output line voltage sector, through the space vector modulation strategy, the DSP sends 6 channels of drive signals and protection signals to the The logic of PLD, four-step commutation, and driving is completed by the internal logic device PLD of the module. The PLD sends 18 driving signals to the 18 discrete switches of the main circuit.

Figure 6. The block diagram of the matrix converter experiment system

The waveforms are shown in Figures 7, 8, and 9, the sampling frequency is 10kHz, the modulation ratio M=0.866, and the input filter parameters: L=30mH, C=15μF.

Figure 7 Input phase voltage ua waveform and input phase current ia waveform

Figure 8 Waveforms of output line voltage uL and output line current iL

(a) Input phase current

(b) Output line voltage

Figure 9 FET analysis

5 Conclusion

The matrix converter control system composed of DSP+PLD has a simple structure, less system wiring, and simple control circuit and software. The reliability of the system is improved, which lays the foundation for the matrix converter to develop to high power, digitalization and industrial application.

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