1. Introduction The balance of capacitor voltage in a three-level inverter is a crucial indicator for ensuring the safe and efficient operation of the motor. If the DC-side capacitor voltage of the three-level inverter is not balanced, the output voltage will contain second-order or higher even-order harmonics, which can cause significant damage to AC drives. Therefore, midpoint potential drift is a problem that must be addressed in three-level inverters. This paper uses a three-level SVPWM algorithm based on the dq coordinate system to implement the main algorithm of the three-level system. Based on this, two midpoint balance control strategies are proposed to solve the midpoint balance problem, and the two algorithms are compared and analyzed. 2. Implementation of the Algorithm Based on the dq Coordinate System A three-level inverter has 27 basic vectors to choose from. The entire spatial voltage vector distribution diagram can be divided into 6 sectors and 24 triangular regions (see Figure 1). The sector position of the reference voltage vector can be determined based on the angle of the reference voltage vector. As shown in Figure 2, any 60° sector is divided into four small triangles: a, b, c, and d. When a reference vector v of a certain length rotates within a sector, it may cross different triangular regions. Based on this, the vector operating modes are divided into four types: mode A, mode AC, mode BCD, and mode BD. At the boundary between different regions, there exists a vector switching angle, as shown in Figure 2. θ1 and θ2 can be obtained through simple trigonometric operations. Thus, the triangular region where the reference vector is located can be clearly determined using the vector switching angles θ1 and θ2. According to the NTV (nearest triangle vectors) principle, the reference vector is synthesized using the three intrinsic vectors constituting the triangle. The action time of each vector can then be obtained. The action time of each vector within different triangular regions is shown in Figure 3. [img=340,293]http://www.ca800.com/uploadfile/maga/inv2008-6/weizhenxing-1.jpg[/img] Figure 1 Three-level inverter space voltage vector diagram [img=283,244]http://www.ca800.com/uploadfile/maga/inv2008-6/weizhenxing-2.jpg[/img] Figure 2 Vector switching angle diagram [align=center] [img=283,243]http://www.ca800.com/uploadfile/maga/inv2008-6/weizhenxing-3.jpg[/img][/align] Figure 3 Vector action time distribution diagram 3 Midpoint potential balance control [b]3.1 Hysteresis comparison method based on control factor m[/b] The current direction is defined as follows: the direction flowing into the load neutral point n is the positive direction of the load current, and the direction flowing out of the DC side midpoint is the positive direction of the midpoint current. Of the 27 voltage vectors, only 18 affect the midpoint potential. At any given moment when these 18 vectors are in effect, the absolute value of the current flowing into (or out of) the midpoint is always equal to the absolute value of the current in a certain phase, i[sub]x[/sub] (x=a, b, c). For the small vector, when the load current of that phase is directly connected to the DC side midpoint, the small vector is defined as a positive small vector, and the midpoint current i[sub]0[/sub]=i[sub]x[/sub]; when the load current of that phase is not directly connected to the midpoint, the small vector is defined as a negative small vector, and the midpoint current i[sub]0[/sub]=-i[sub]x[/sub]. For the medium vector, i[sub]0[/sub]=i[sub]x[/sub]. Let the switching state of a certain vector be (a, b, c), where a, b, c = 1, 0, -1. Then the relationship between the midpoint current and the load current can be summarized as follows: i[sub]0[/sub]=i[sub]a[/sub]（a+1)(1-a）+i[sub]b[/sub]（b+1)(1-b）+i[sub]c[/sub]（c+1)(1-c） (1) Under the same load conditions, the effects of a pair of positive and negative small vectors on the midpoint potential are completely opposite. Therefore, by properly allocating the action time of these two vectors, the drift of the midpoint can be controlled. This is the core idea of ​​this midpoint balancing strategy. [img=283,208]http://www.ca800.com/uploadfile/maga/inv2008-6/weizhenxing-4.jpg[/img] Figure 4 The hysteresis comparison method for vector region division and vector action time allocation takes the first sector as an example, as shown in Figure 4. In order to enhance the control capability of a pair of positive and negative small vectors on the midpoint potential, the small vectors are used in triangles a1, c1, and d; and the small vectors are used in triangles a2, c2, and b. When the vector is located in region c1, as shown in the figure, the duration of action of the small vector v2 is t2. Define the control factor m (m∈(0,1)). Let the duration of action of the negative small vector be t2-=mt2, and the duration of action of the positive small vector be t2+=(1-m)t2. Define the offset of the midpoint potential δv=vc2-vdc/2, where vc2 is the voltage of the lower arm capacitor c2, and vdc is the DC bus voltage. Based on the above definitions, the specific regulation is as follows: (1) When δv>0, i0>0 or δv<0, i0<0, i.e. δvi0>0, increase the duration of action of the negative small vectors, i.e. keep m∈(0.5,1); (2) When δv>0, i0<0 or δv<0, i0>0, i.e. δvi0<0, increase the duration of action of the positive small vectors, i.e. keep m∈[0,0.5]; (3) When δvi0=0, m=0.5. [b]3.2 Accurate Calculation Method Based on Control Factor ms[sub]0[/sub] In fact, the fundamental reason for midpoint potential drift is the non-conservation of charge flowing into or out of the midpoint within a switching cycle. Based on this idea, if the total charge flowing into the midpoint within each switching cycle can be guaranteed to be zero, then the midpoint potential can be precisely controlled, or in other words, the fluctuation of the midpoint potential can be minimized. For simplicity, we continue to use the PWM output sequence rule of the previous method. Observing the appendix, we can find that in each cycle, the pulse sequence always begins with a negative (or positive) small vector of a certain small vector and ends with a negative (or positive) small vector of that small vector. For the convenience of explaining the problem later, this small vector is called the main control small vector. In addition to the main control small vector, in a PWM cycle, adjacent small vectors are also used in some regions, which are called auxiliary control small vectors. As shown in Figure 5, the main control small vector in the (0°, 30°) region is v[sub]1[/sub], and the auxiliary control small vector is v[sub]2[/sub]; The primary control vector (30°, 60°) is v2, and the secondary control vector is v1. The definitions of the intermediate and large vectors remain unchanged. Let the duration of action of the primary control vector in a certain region be tms0, the duration of action of the secondary control vector be tm, and the duration of action of the intermediate vector be tm. Introduce the time allocation coefficient ms0 of the primary control vector (ms0 ∈ [-1, 1]), and define... The duration of the positive small vector is t_ms0 + t_ms0 = (1 + t_ms0)t_ms0/2, and the duration of the negative small vector is t_ms0 - t_ms0 = (1 - t_ms0)t_ms0/2. Therefore, the total charge flowing into the midpoint from both positive and negative small vectors is q_ms0 = t_ms0 + ix₀ - t_ms0 - ix₀ = q_ms0 ms0ix0tms0, where ix0 represents the phase current corresponding to this small vector, i.e., ix0 = (ia, ib, ic); further observing Table 1, we can obtain the charge flowing into the midpoint from the adjacent small vectors as: qms = -ix1tms1, where ix1 represents the phase current corresponding to this adjacent small vector as ix1 = (ia, ib, ic); the charge flowing into the midpoint from the medium vector is: qm = imtm; the large vector has no effect on the midpoint potential. To ensure that the midpoint potential does not fluctuate, the total charge flowing into the midpoint must be zero: qms0. +q[sub]ms1[/sub]+q[sub]m[/sub]=0 that is: ms[sub]0[/sub]i[sub]x0[/sub]t[sub]ms0[/sub]-i[sub]x1[/sub]t[sub]ms1[/sub]+i[sub]m[/sub]t[sub]m[/sub]=0 (2) [img=283,236]http://www.ca800.com/uploadfile/maga/inv2008-6/weizhenxing-5.jpg[/img] Figure 5 The vector region division and application time allocation, including the magnitude and direction of the midpoint current, are determined by the following: Since ms[sub]0[/sub]∈[-1,1], the solved ms[sub]0[/sub] should be limited: when ms[sub]0[/sub]＞1, ms[sub]0[/sub]=1; when ms[sub]0[/sub]＜-1, ms[sub]0[/sub]=-1. This maximizes the balancing ability of the positive and negative small vectors on the midpoint potential. The drawback of this algorithm is that it lacks the ability to pull the midpoint potential back to the equilibrium point once the midpoint deviates. To compensate for this, the first method can be combined with this method, specifically as follows: Set a voltage error hysteresis loop δu[sub]set[/sub]. If the actual deviation of the midpoint potential δu<δu[sub]set[/sub], the second method is used; if the actual deviation of the midpoint potential δu>δu[sub]set[/sub], the first method is used. This allows for accurate control of the midpoint potential. [img=567,242]http://www.ca800.com/uploadfile/maga/inv2008-6/weizhenxing-b1.jpg[/img] 4 Simulation and Result Analysis For this algorithm, the system simulation parameters are set as follows: a three-phase asynchronous squirrel-cage motor is selected, with rated power p[sub]n[/sub]=4kW, rated line voltage u[sub]n[/sub]=400V, rated frequency f[sub]n[/sub]=50Hz, and rated speed ω[sub]r[/sub]= 1430 r/min, stator resistance rs = 1.405 ω, rotor resistance rr = 1.395 ω, stator leakage inductance lsl = 0.005839 h, rotor leakage inductance lrl = 0.005839 h, stator-rotor mutual inductance lm = 0.1722 h, moment of inertia j = 0.0131 kg·m², number of pole pairs p = 2, switching frequency f = 10 kHz, DC bus voltage vdc = 600 V, DC side capacitance c1 = c2 = 1200 μF, flux linkage amplitude given |ψs＊| = 0.8 Wb. [b]4.1 Hysteresis Midpoint Control Strategy Based on Control Factor m[/b] To verify the algorithm, the system's operating state is set as follows: at t=0s, the given speed ωr=1200rpm＝125.6rad/s, no-load start; at t=0.2s, a sudden load torque tl=15n·m is applied. Figures 6 and 7 show the waveforms obtained under this control strategy. [img=283,254]http://www.ca800.com/uploadfile/maga/inv2008-6/weizhenxing-6.jpg[/img] Figure 6 Deviation between the DC side lower capacitor voltage and the ideal voltage: vc2-vdc/2 (based on control factor m) [img=283,243]http://www.ca800.com/uploadfile/maga/inv2008-6/weizhenxing-7.jpg[/img] Figure 7 Line voltage waveform (based on control factor m) [b]4.2 Midpoint control strategy based on accurate calculation method of control factor ms[sub]0[/sub] System operating state setting: At t=0s, the given speed ω[sub]r[/sub]=700rpm＝73.3rad/s, no-load start, at t=0.15s, the given speed ω[sub]r[/sub]=1200rpm＝125.6rad/s, at t=0.24s, the sudden load torque t[sub]l[/sub]=15n·m. The deviation voltage hysteresis setting value δu=1v. Figures 8 and 9 are the waveforms of this control strategy. [img=340,138]http://www.ca800.com/uploadfile/maga/inv2008-6/weizhenxing-8.jpg[/img] Figure 8. Deviation between DC-side lower capacitor voltage and ideal voltage: v[sub]c2[/sub]-v[sub]dc[/sub]/2 (based on control factor ms[sub]0[/sub]) [img=340,341]http://www.ca800.com/uploadfile/maga/inv2008-6/weizhenxing-9.jpg[/img] Figure 9. Line voltage and phase voltage waveforms (based on control factor ms[sub]0[/sub]) 5. Comparison of two midpoint control strategies The idea of ​​the first midpoint control method is very simple. Since it uses hysteresis comparison, it cannot make accurate compensation for the midpoint potential in terms of quantity, or it does not give full play to the compensation effect of positive and negative small vectors on the midpoint potential. The calculation of the balance strategy based on control factor ms[sub]0[/sub] is much greater than that of the balance strategy based on control factor m. This cost is exchanged for the improvement of the midpoint potential control accuracy. By setting the hysteresis width of the deviation voltage, the midpoint drift can be limited to a certain range and will not be affected by load changes. This is exactly what the strategy based on control factor m cannot do. As for which of these two control strategies to choose, it depends on the accuracy of the system. About the author Wei Zhenxing (1982-) Male Master's student Research direction: power system and its automation. References [1] Ma Xiaoliang. High power AC-AC frequency conversion speed regulation and vector control technology. Beijing: Machinery Industry Press [2] Bimal K. Bose. Modern power electronics and AC drive. Translated by Wang Cong, Zhao Jin, Yu Qingguang, Cheng Hong et al. Beijing: Machinery Industry Press, 2005 [3] Huang Jun, Wang Zhaoan. Power Electronic Converter Technology. Beijing: Machinery Industry Press, 1999 [4] Steffen Bernet. Recent developments of high power converters for industry and traction application. 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