0 Introduction
With the rapid development of power electronics technology, microcomputer technology, rare earth permanent magnet materials and control theory, PMSM has advantages such as small size, light weight, high efficiency, small moment of inertia and high reliability, and has been increasingly widely used [1]. DTC is a new method after vector control technology. It adopts stator flux orientation, uses discrete two-point adjustment, and directly controls the flux and torque of the motor, so that the motor torque response is fast [2]. Compared with vector control, DTC system has advantages such as simple control system structure, fast torque dynamic response, less dependence on motor parameters, and good robustness to changes in motor parameters [3], and has received widespread attention. SVPWM control strategy was proposed by Japanese scholars in the 1980s for AC motor frequency conversion speed regulation. Its main idea is to use the switching of inverter space vector voltage to obtain a quasi-circular magnetic field, so that the inverter outputs a voltage with appropriate waveform [4-7]. Its theoretical basis is the average value equivalence principle, that is, by combining the basic voltage vectors in one switching cycle, the average value is equal to the given voltage vector. At a certain moment, the voltage vector rotates into a certain region, which can be obtained by different combinations of the time of two adjacent non-zero vectors and zero vectors that make up this region. The action time of the two vectors is applied multiple times within a sampling period, thereby controlling the action time of each voltage vector, so that the voltage space vector rotates approximately along a circular trajectory. The actual magnetic flux generated by the different switching states of the inverter approximates the ideal magnetic flux circle, and the switching state of the inverter is determined by the comparison between the two, thus forming a PWM waveform. In this paper, the PMSM DTC system based on SVPWM is simulated using the Matlab/Simulink simulation tool. The establishment of the unit models in the SVPWM module is described in detail, and the combination of DTC system and SVPWM technology is specifically explained, i.e., the expected voltage vector model; and the performance of the control system is analyzed, providing a theoretical basis for better realization of digital control of PMSM DTC system based on SVPWM. 1 SVPWM Principle SVPWM approximates the reference circle by generating an effective voltage vector through different switching modes of inverter power devices. Figure 1 is a typical structure diagram of a three-phase voltage source inverter frequency conversion speed regulation system, which is the DC bus voltage. Six switching transistors are used to form three bridge arms a, b, and c, respectively, using ideal switches 1 to 6. The upper and lower switches in each bridge arm are interlocked for conduction. The switching states of the three bridge arms are represented by switching variables s <sub>a </sub> , s <sub> b</sub>, and s<sub>c</sub>. If the upper bridge arm conduction is represented by "1" and the lower bridge arm conduction by "0", then the inverter has eight possible three-phase state combinations, including six non-zero voltage vectors and two zero voltage vectors. From the perspective of normal inverter operation, the first six states are valid, while the last two states are invalid because the inverter has no voltage output in these states. Assume the six switching transistors cycle in the following pattern: 456, 561, 612, 123, 234, 345. Taking operating state (100) as an example, at this time, power switching devices "1", "3", and "2" are turned on, the potentials at points A and B of the motor stator are positive, and point C is negative. The voltages relative to the midpoint O of the DC power supply are all DC voltages with an amplitude of . The three-phase voltage space vectors are located on the three-phase axes A, B, and C, respectively. The three-phase combined voltage space vector is , with an amplitude of and a direction on the C-axis. Similarly, the voltage space vectors combined in other operating states can be obtained. The voltage space vectors generated by these eight operating states are called the basic voltage space vectors, and their distribution is shown in Figure 2.Figure 1. Structure diagram of a three-phase voltage source inverter variable frequency speed control system. Figure 2. Basic voltage space vector distribution diagram.
Simulink simulation of 2 SVPWM
As can be seen from the principle of SVPWM, the establishment of the SVPWM module mainly includes: sector judgment module, calculation of basic vector action time module, calculation of switching action time module, SVPWM waveform generation module, inverter voltage module, etc. [9]. 2.1 Sector judgment When applying SVPWM technology, the sector where the synthesized voltage vector is located must be determined first. Here, we use the following method to determine the sector. The relationship between sector and sector is: Let N=A+2B+4C. It can be seen that the correspondence between sector and N is shown in Table 1, and the model is shown in Figure 3. Table 1 Correspondence between sector and NFigure 3 Sector Judgment Model
2.2 Calculate the duration of action of the basic vectors
After determining the sector where the voltage composite vector is located, the conduction of the composite voltage vector into two adjacent voltage vectors in this sector should be calculated.
Figure 5. Calculation model for basic vector action time
2.3 Calculation model for switching action time
Formula (2):
Based on the transmission order, action time, and switching point patterns of the above vectors, the desired voltage space vector can be synthesized to achieve flux tracking.
2.4 Generation of SVPWM waveform
Figure 6 Simulation model of vector switching point
Figure 7. Generation model of PWM waveform
2.5 Inverter Voltage Model
Taking the A-phase voltage of the inverter as an example, its simulation model is shown in Figure 8.
Figure 8 Inverter A-phase voltage module
The simulation model of SVPWM can be established from the above sub-models, as shown in Figure 9:
Figure 9 SVPWM simulation model
2.6 SVPWM Simulation Waveform Analysis
Figure 12 Simulation waveform at the switching point
Figure 13 SVPWM three-phase output voltage waveform
As can be seen from Figure 13, the voltage output is equidistant and of equal amplitude in half a cycle, with a wide pulse in the middle and narrow pulses on both sides. This is beneficial for the low-order harmonic components in the motor output voltage.
3. Implementation of SVPWM-based DTC System 3.1 Composition of SVPWM-based DTC SystemThe structure of the PMSM DTC system based on SVPWM is shown in Figure 14. This control system includes two PI regulators: speed regulator (ASR) and torque regulator (ATR), a expected voltage vector calculation model, an SVPWM model, a voltage source inverter model, a 3s/2s conversion model, a flux linkage estimation model, a torque estimation model, and other modules. The modeling of the DTC system has been described in detail in reference [10], and will not be repeated here. How to combine the DTC principle and SVPWM technology is the focus of this paper, namely the expected voltage vector model.
Figure 14 Block diagram of PMSM DTC system based on SVPWM
3.2 Expected Voltage Vector Calculation Model
The mathematical model of PMSM in the dq0 rotating coordinate system is:
Therefore there is
4 System Simulation Analysis
The torque response curves are somewhat similar. At the beginning, the current value is relatively large, but it quickly reaches the set value. The sinusoidal nature of the two-phase current is very good, and the stator flux linkage trajectory is also very smooth. Under sudden changes in speed and load, the dynamic and static characteristics of the system are both good.
5. Conclusion Based on the analysis of SVPWM technology, this paper implements a PMSM DTC system based on the SVPWM strategy, combined with the DTC principle. In the Matlab/Simulink simulation environment, the construction of the SVPWM module is described in detail, and the simulation results are briefly analyzed. The combination of SVPWM technology and the DTC system is explained in detail. Simulation results show that the waveform is consistent with the theoretical analysis, the system can operate smoothly, and has good dynamic and static characteristics, laying a theoretical foundation for the digital implementation of PMSM DTC based on SVPWM. Contact Address: Zhang Ping, Postgraduate Student, Class of 2010, P.O. Box 76, School of Automation, Qingdao University of Science and Technology, No. 53 Zhengzhou Road, Qingdao, Shandong Province, China. E-mail: [email protected] TEL: 13165011308 Postcode: 266042
