[align=center]Research and Simulation on SVPWM flux track generation CHEN Shi-hao, FENG Xiao-yun, JIANG Wei, XIE Fang School of Electrical Engineering, Southwest Jiaotong University, Chengdu, Sichuan 610031, China 陈世浩，冯晓云，蒋威，谢方 西南交大学電電工程学院，四川成都610031, China[/align] Abstract : This paper provides a detailed analysis and derivation of the basic principles of space vector pulse width modulation (SVPWM). Six conventional flux linkage circle approximation methods for SVPWM control are presented, and a method for simulating an isosceles flux linkage circle is proposed. Simulation results based on MATLAB/SIMULINK show that the new method approximates the flux linkage circle more closely and has better symmetry. Keywords : SVPWM; inverter; approximation method; SIMULINK ABSTRACT : This paper analyzes and deduces the theory of SVPWM. Six kinds of normal methods of tracking the flux circle are presented, and a new method of approaching the flux circle is proposed. It is proved to be a closer approximation of the flux circle and has more symmetric performance through the simulation of MATLAB/SIMULINK. KEY WORDS: SVPWM; inverter; approximation method; SIMULINK 1 Introduction The SVPWM algorithm can achieve an inverter output line voltage amplitude of up to U[sub]d[/sub], which is about 15.47% higher than the conventional SPWM algorithm. SVPWM has multiple modulation methods. By changing its modulation method, the number of switching operations of the inverter power devices can be reduced, thereby reducing the switching losses of the power devices and improving the control performance of the system. At the same sampling frequency, the number of switching operations of the inverter power devices using the switching loss mode SVPWM algorithm is reduced by 1/3 compared with the conventional SVPWM algorithm, which greatly reduces the switching losses of the power devices. SVPWM is essentially a modified SPWM based on the regular sampling of a modulation wave with zero-sequence components injected into a three-phase sine wave by a space vector. It is an optimized PWM method that can significantly reduce the harmonic components of the inverter output current and the harmonic losses of the motor, and reduce the pulsating torque of the motor. Moreover, SVPWM has a clear physical concept and a simple control algorithm, making it suitable for digital implementation. [2] [3] 2 Working principle of space voltage vector pulse width modulation technology The SVPWM algorithm takes the ideal flux linkage circle of the stator of a three-phase symmetrical motor when powered by a three-phase symmetrical sine wave voltage as the reference. The actual flux linkage vector formed by different switching modes of the three-phase inverter is used to track the reference flux linkage circle. During the tracking process, the switching mode of the inverter is switched appropriately to form a PWM wave. [align=center]Fig.1 The main circuit of two-level inverter[/align] 3 Seven methods for approximating the flux linkage circle: SVPWM synthesizes the terminal voltage states of the three-phase inverter into space voltage vectors on the complex plane, and forms eight space vectors through different switching states. These eight space vectors are used to approximate the flux linkage circle, thus forming the SVPWM wave. In the SVPWM algorithm, different approximation methods will produce different PWM waveforms. In the process of tracking the flux linkage circle using eight space vectors, the angle bisectors of the six non-zero vectors divide the complex plane into six sectors, denoted as I, II, III, IV, V, and VI, as shown in Figure 2. Any edge of a polygon can be approximated by two non-zero vectors of its sector. Clearly, the polygon in sector I is best approximated by U4 and U6; in sector II, U6 and U2 are best approximated, and so on, yielding the optimal approximation vector set as shown in Table 1. There are multiple ways to approximate the flux linkage circle using eight space vectors. Different methods generate PWM waveforms with different harmonic components, and the number of switching operations within one sampling period Tr also differs. Seven approximation methods are discussed below (taking the first sector as an example, N=36). In the first approximation method, the zero vector U0 is evenly distributed between the starting and ending points of vector U1, first moving through vector U4, and then through vector U6. It can be seen that within one sampling period, the upper bridge arm device has four on/off actions. [align=center] Fig.3 Method 1 vector approach mode and switch action[/align] The second approximation method inserts a zero vector U[sub]0[/sub] at the starting point of the first segment, first moves through vector U[sub]4[/sub], and inserts a zero vector U[sub]7[/sub] at the ending point; inserts a zero vector U[sub]7[/sub] at the starting point of the second segment, first moves through vector U[sub]6[/sub], and inserts a zero vector U[sub]0[/sub] at the ending point. It can be seen that this is the method with the lowest bridge arm switching frequency. Within one sampling period, the upper bridge arm device has 3 on or off actions. [align=center]Fig. 4 Method 2 vector approach mode and switch motion[/align] In the third approximation method, the zero vector U[sub]0[/sub] is evenly distributed at the starting and ending points of vector U[sub]I[/sub], and the non-zero vector U[sub]6[/sub] passes through the midpoint of U[sub]I[/sub], with U[sub]6[/sub] being evenly distributed on both sides. It can be seen that the upper bridge arm device has 4 switching actions within one sampling period. [align=center]Fig. 5 Method 3 vector approach mode and switch motion[/align] The fourth approximation method is basically the same as the third, except that a zero vector is inserted when vector U[sub]6[/sub] passes through the midpoint of U[sub]I[/sub], as shown in Fig. 6. It can be seen that the upper bridge arm device has 6 switching actions within one sampling period. [align=center]Fig.6 Method 4 vector approach mode and switch motion[/align] The fifth approximation mode is basically the same as the first, except that the zero vector U[sub]0[/sub] is further subdivided into 4 parts, which are evenly distributed at the starting and ending points of vector U[sub]1[/sub] and the midpoints of U[sub]4[/sub] and U[sub]6[/sub]. First, the zero vector U[sub]0[/sub] is moved, then vector U[sub]4[/sub], and then vector U[sub]6[/sub]. It can be seen that the upper bridge arm device has 10 switching actions within one sampling period. [align=center] Fig.7 Method 5 vector approach mode and switch motion[/align] The sixth approximation mode is basically the same as the first, except that the zero vector is taken over by U[sub]7[/sub], the vector U[sub]4[/sub] is used first, then the zero vector is inserted by U[sub]7[/sub], and then the vector U[sub]6[/sub] is used. It can be seen that the upper bridge arm device has 4 switching actions within one sampling period. [align=center] Fig.8 Method 6 vector approach mode and switch motion[/align] The seventh approximation mode is a simulated isosceles approximation mode. Since the better the circular symmetry of the magnetic flux of the polygon approximation, the lower the harmonics. Imagine that if all the two-sided approximation vectors are isosceles triangles €ABC, then the magnetic flux polygon will have good symmetry. As shown in Figure 9, the isosceles triangle has a BC that is not a standard effective vector. Therefore, BE and EC are used to synthesize BC, which means taking a part of the long side to synthesize the other leg. This is equivalent to using three sides to approximate two sides of the isosceles triangle. Taking the first sector as an example, if N equals 36, the first sector is divided into 6 parts. The first 3 parts, U[sub]4[/sub], are the long sides, and the last 3 parts, U[sub]6[/sub], are the long sides. Method 7 is similar to Method 3 in form, which is a three-side approximation. [align=center] Fig.9 Method 7 vector approach mode and switch motion[/align] Methods 1 to 6 can all be calculated using conventional formulas, but Method 7 requires dividing the long side into two unequal parts, so further calculation is required. [align=center] Fig.10 Calculation of the voltage vector duration in Method 7[/align] 4 Simulation Results and Analysis This paper uses the Matlab/Simulink platform to build a simulation system for SVPWM control of a three-level inverter to power an asynchronous motor. The following are the spectrum diagrams of various approximation methods at f=40Hz: [align=center] Fig.11 The spectrum of Method 1 Fig.12 The spectrum of Method 2 Fig.12 The spectrum of Method 2 Fig.13 The spectrum of Method 3 Fig.13 The spectrum of Method 3 Fig.14 The spectrum of Method 4 Fig.14 The spectrum of Method 4 Fig.15 The spectrum of Method 5 Fig.15 The spectrum of Method 5 Fig.16 The spectrum of Method 6 Fig.16 The spectrum of Method 6 Fig.17 The spectrum of Method 7 [/align] As can be seen from the figures, Method 1 has large harmonics at the 4th and 18th harmonics. Since the three-phase induction motor has no neutral line, the 3nth harmonic can be ignored. Therefore, the 18th harmonic can be ignored. The (6n-1)th harmonic is greater than the (6n+1)th harmonic. THD=24.04% is the lowest among the six approximation methods. Method 2 exhibits low low-order harmonics but significant even-order harmonics in the high-frequency band. Method 3 shows the highest 12th harmonic, which has no impact on the motor; followed by the 22nd harmonic, accounting for 13.00% of the fundamental frequency. Method 4 shows the highest 18th harmonic, which has no impact on the motor; followed by the 19th harmonic, accounting for 15.89% of the fundamental frequency. The 13th harmonic accounts for 11.32% of the fundamental frequency. The THD of 42.94% is the highest among the six approximation methods. Method 5 has relatively large low-order harmonics, which will affect the sinusoidal nature of the input current. Method 6 shows low low-order harmonics, but relatively high 17th and 19th harmonics. Since Method 7 is similar to Method 3, both using trilateration and the same zero-vector interpolation method, a comparative analysis of their simulation results is presented. The current and torque fluctuations of the two methods are comparable, but Method 7 has a lower THD than Method 3. 5. Conclusion As the above analysis shows, the two-stage approximation method has better suppression capability for low-order harmonics than other methods. This is because the two-stage approximation method has good output voltage waveform symmetry; each phase voltage waveform has exactly one wavefront in each carrier cycle, and the two switches on each bridge arm switch only once, a feature not found in other methods. The new method proposed in this paper approximates the flux linkage circle more closely, has better symmetry, and exhibits lower THD. References [1] JIANG Shi-jun. Application of track control of flux linkage to locomotive auxiliary inverter supply. Electric Drive For Locomotives, 2003.1(1):15-18 [2] ZHANG Chun-jiang et al. Simulation research of harmonics of space vector PWM waves. Journal of Yanshan University. 2004.4(2):141-144 [3] XIONG Jian et al. Comparison Study of Voltage Space Vector PWM and Conventional SPWM. Electric Power Electronics Technology. 1999.2(1):25-28 Power Electronics, 1999.2(1):25-28 Received Date: Author Biographies: Chen Shihao (1983-), male, Xinye, Henan, Master's student, research direction: power electronics and AC drives; Feng Xiaoyun (1962-), female, Xiayi, Henan, Professor/Doctoral Supervisor, research direction: power electronics and AC drives, Automatic Train Control (ATC) and Automatic Train Operation (ATO) Contact Information: Chen Shihao, 392#, Jiuli Campus, Southwest Jiaotong University, Sichuan Province (610031) 13518153745 [email protected]