1 Introduction Due to the fact that voltage space vector pulse width modulation (SVPWM) can reduce the number of switching devices by 1/3 and increase the utilization rate of DC voltage by 15.47% compared with traditional sinusoidal pulse width modulation (SPWM), it can significantly reduce the harmonic components of the inverter output current and the harmonic losses of the motor and reduce the pulsating torque, and is therefore widely used in motor control. However, conventional SVPWM methods require complex trigonometric function and coordinate rotation calculations, as well as the judgment of the sector where the output voltage vector is located. The complex calculations have an undeniable impact on high-precision real-time control. In view of this, this paper will use the switching function method to realize SVPWM inverter control based on the equivalence principle of SVPWM and SPWM [1]. The switching function method can greatly simplify the calculation process, improve the calculation accuracy, and has achieved good control results in the product development of industrial frequency converters. 2. Switching Function SVPWM 2.1 Equivalence Principle of SVPWM and SWPM Based on the equivalence principle of SVPWM and SWPM, the modulation function of the SVPWM control method is actually a piecewise continuous function obtained by superimposing a special zero-sequence component on the sinusoidal modulation function of SWPM. The zero-sequence component is half of the phase with the smallest instantaneous absolute value in the three-phase symmetrical sinusoidal modulation function, as shown in Figure 1 (uo). In this figure, ua, ub, and uc are three-phase symmetrical sinusoidal modulation functions. For the sinusoidal modulation function ua with an initial phase of zero, superimposing uo yields one phase modulation function of SVPWM, as shown in Figure 2 (ua′). Similarly, shifting ua′ by 120° and 240° respectively yields the waveforms of the other two phase modulation functions of SVPWM, ub′ and uc′. From the above, it can be considered that an equivalent transformation relationship has been established between SVPWM and SWPM from the perspective of modulation function. The SVPWM control method can directly adopt the existing SWPM control method, greatly increasing the number of SVPWM control methods. Since the maximum value of the SVPWM modulation function is 1/3 the maximum value of the SWPM modulation function (see Figure 2), it is clear that the equivalent SVPWM control method still has the characteristic that the maximum voltage utilization rate is 1.1547 times that of the SWPM control method. [align=center] Figure 1 SVPWM zero-sequence component waveform Figure 2 SVPWM one-phase target modulation waveform[/align] 2.2 SVPWM switching function representation Switching function refers to a continuous function or piecewise continuous function used to describe the duty cycle of a set of related power switches in the converter under given input voltage function, desired output voltage function and various constraints. The general expression of the switching function of the upper and lower power switches of the same bridge arm in the inverter[2] is as follows: (1) Where, f upper switch and f lower switch are the switching functions describing the instantaneous duty cycle of the upper and lower switches of any bridge arm, respectively, q is the modulation index, and the DC side voltage does not exclude a certain degree of fluctuation. Specifically, in the SVPWM control method, the inverter's switching function matrix can be described as (2) where f[sub]1[/sub] and f[sub]4[/sub], f[sub]3[/sub] and f[sub]6[/sub], f[sub]5[/sub] and f[sub]2[/sub] represent the instantaneous duty cycle functions of the upper and lower transistors of the first, second, and third bridge arms of the inverter, respectively. According to the physical meaning described by the switching function, each function element in the switching function matrix must satisfy the following relationship: f[sub]i[/sub]≥0[sub] i[/sub]=1…6, f[sub]1[/sub]+f[sub]4[/sub]=1, f[sub]3[/sub]+ f[sub]6[/sub]=1, f[sub]5[/sub]+ f[sub]2[/sub]=1. According to Figure 2, after analysis, the piecewise modulation function of SVPWM can be obtained by the envelope composed of the following three basic sine functions [3] (3) Specifically, the interval [0, 2π] can be divided into 7 sub-intervals, and the three-phase symmetrical modulation functions of SVPWM, eu, ev and ew are used in each interval [align=center] (4) (5) (6) [/align] Thus, the three-phase phase voltages expected to be output in the SVPWM control method can be expressed as vom·eu, vom·ev and vom·ew respectively, where vom is the amplitude of the expected output phase voltage. Assuming that the DC side voltage of the inverter is a constant value vdc, the specific expressions of each function element in the SVPWM switching function matrix can be obtained from the general switching function expression of the inverter. The modulation function of SVPWM in the interval [0, 2π] consists of 7 segments, and the corresponding switching function matrices should be given according to the intervals respectively. Without loss of generality, the specific expressions of each switching function are given below, taking the first interval 0≤ω0t≤π/6 as an example: [align=center] (7) (8) (9)[/align] Where q is the modulation index, q∈[0,1], q=2v[sub]om[/sub]/ v[sub]dc[/sub]. Similarly, the switching function matrix of other intervals can be derived. 3 Implementation method and experimental results The principle of the svpwm switching function seems very complicated, but the implementation method is very simple. The following is the usage method of the svpwm switching function. First, it is only necessary to calculate the function value of the unit modulation function eu in the interval [0,2π] and make it into a table and store it in the flash memory of the microcontroller for reference; then, based on the switching function and the stored eu table, the duty cycle of the first bridge arm transistor in each carrier cycle is calculated; finally, the actual conduction pulse width of the first bridge arm transistor is calculated according to the duty cycle, carrier cycle and voltage frequency relationship. Similarly, by shifting the EU table by 120° and 240° respectively during the lookup, the conduction pulse widths of the upper transistors in the second and third bridge arms can be calculated. Since a complementary triggering method is used, the conduction pulse widths of the three lower transistors do not need to be calculated repeatedly. In the inverter design, the Motorola microcontroller 68HC908MR16 is selected. Because it has complementary triggering function for upper and lower transistors and automatic dead-time insertion capability, only the pulse width of the upper transistor needs to be calculated, greatly simplifying the computation and improving reliability. On the other hand, the 68HC908MR16 has a frequency multiplier function, which can increase the switching frequency according to actual needs, overcoming the limitation that it is difficult for a typical 8-bit microcontroller to achieve a very high switching frequency. An AC-DC-AC inverter product platform based on an IPM was established in the laboratory. The experimental motor was a Y90S-4TH, 1.1kW, Y-connected, and the load was an electromagnetic speed-regulating motor YCT160-4B. The IPM was a PM20CTM060, and the switching frequency was 3.0kHz, without frequency multiplication. The motor line current waveforms at various frequencies were tested under the above conditions, and some test results are given below. The motor line current waveforms at output frequencies of 1.75 Hz, 9.64 Hz, 49.5 Hz, and 101.0 Hz are shown in Figures 3, 4, 5, and 6, respectively. It can be seen that the sinusoidal nature of the inverter output current waveform is very high within a wide frequency range, indicating that the SVPWM inverter control method based on the switching function is effective. Under the above experimental conditions, the actual measured effective value of the fundamental line voltage of the SPWM control method at a modulation depth of 1 and an output frequency of 50 Hz was 193.5 V, while the effective value of the fundamental line voltage of the SVPWM control method based on the switching function was 223.7 V. This indicates that the voltage utilization rate of the SVPWM control method is about 15% higher than that of the SPWM method. Regarding the harmonic distribution of SVPWM, due to space limitations, it will not be discussed in this paper. [align=center] Figure 3 Motor line current waveform (1.75 Hz) Figure 4 Motor line current waveform (9.64 Hz) Figure 5 Motor line current waveform (49.5 Hz) Figure 6 Motor line current waveform (101.0 Hz)[/align] 4 Conclusion The SVPWM control method based on switching functions achieves excellent inverter control performance. It is easy to program, exhibits high sinusoidal strength of the motor line current, and improves voltage utilization by approximately 15% compared to the traditional SPWM control method. Furthermore, the introduction of switching functions makes the control technology clearer in its concept, easier to adjust parameters, and more convenient for microcomputer implementation, making it worthy of promotion. This control method has been successfully applied to the development of industrial frequency converters and has been commercialized. About the Author: Chen Hui (1973-) Male, Lecturer/Master's Thesis. Research direction: Power Electronics Technology and Computer Control Technology. References [1] g-myong lee and dong-choon lee, implementation of naturally sampled space vector modulation elimination microprocessors, tsinghua, ipemc'2000:803-807 [2] yang xijun, gong youmin. application of single-to-single phase matrix conversion in conventional rectifier-inverter, journal of shanghai university, sept. 2000, 5 (3):211-216 [3] Chen Guocheng. PWM variable frequency speed regulation and soft switching power conversion technology. Beijing: Machinery Industry Press, 2001 [4] Yi Longqiang, Dai Yuxing. Application of SVPWM technology in single-phase inverter power supply. Journal of Electrical Engineering, 2007, 22 (9) [5] Li Yi, Fan Pangguo. Design of digital AC variable frequency speed regulation system based on SVPWM. Electrical Drive, 2007, 37 (9)