Research on Space Voltage Vector PWM Control Method Based on PIC Microcontroller

0 Introduction
PWM technology is widely used in motor variable frequency speed regulation systems. PWM control uses the on and off of semiconductor switching devices to convert rectified DC into a pulse sequence, and controls the pulse width and pulse train period to achieve voltage and frequency conversion control, while reducing output voltage and current harmonics. Early SPWM control mainly focused on making the inverter output voltage waveform as close to a sine wave as possible, hoping that the fundamental component of the output PWM voltage waveform is as large as possible and the harmonic component is as small as possible, without considering the influence of the rotating magnetic field of the motor itself. Space voltage vector PWM technology is a hot topic in current research. It considers the inverter and AC motor as a whole. Its control goal is to make the magnetic flux trajectory approximate to a circle, which is also called flux tracking PWM control. Based on the analysis of the principle of space voltage vector PWM, this paper proposes a method for implementing SVPWM control based on a 16-bit PIC24FJ64GA microcontroller.

1 Principle of space voltage vector PWM control
Space voltage vector PWM control is based on the ideal magnetic flux circle of the AC motor under the three-phase symmetrical sinusoidal voltage supply state. Different combinations of the switch control signals of each bridge arm of the inverter are used to make the actual magnetic flux running trajectory formed by the output working voltage vector of the inverter approach the reference circle magnetic flux running trajectory.
The basic stator voltage vector is defined as:

where ua, ub and uc are the phase voltages of the three-phase stator windings respectively. In the variable frequency speed regulation system, the schematic diagram of a typical three-phase voltage type inverter circuit is shown in Figure 1. Udc represents the DC side voltage. The phase voltage on the stator side of the motor is determined by the switching states of the three power devices SA, SB and SC. SA, SB and SC represent the switching states of the two power devices under the same bridge arm respectively. If SA is 1, it means that the upper bridge arm is connected, the lower bridge arm is disconnected, and ua is connected to Udc; otherwise, SA is 0, which means that the lower bridge arm is connected, the upper bridge arm is disconnected, and ua is connected to 0. Similarly, the relationship between the state of switch SA and ub, and the relationship between the state of switch SC and uc can be obtained.

According to the 8 combinations of the switching states of the power devices SA, SB and SC, 8 space voltage vectors can be formed, as shown in Figure 2. For the external load, the output voltage including 6 non-zero vectors V1 (100), V2 (010), V3 (110), V4 (001), V5 (101), V6 (011), and 2 zero voltage vectors V0 (000), V7 (111) is zero. The six non-zero voltage vectors are spaced apart from each other in space. The
three-phase input voltage of the motor with Y-type stator winding is:

According to the principle of keeping the amplitude unchanged when transforming the three-phase system to the two-phase system, the synthetic space vector of the three-phase voltage can be expressed in the α, β coordinate system as:

Wherein, Uα and Uβ are the components of the space voltage vector on the stationary αβ axis of the stator.
1.1 Synthesis of spatial voltage vectors
According to the parallelogram law of vector synthesis and the PWM equivalent area principle, the above eight vectors can be used to synthesize an output voltage vector with a finite modulus length at any angle. The maximum modulus length determines the maximum amplitude of the output voltage, as shown in Figure 3.

In the figure, θ is the angle between Uref and the space voltage vector Uθ. Uref falls between vectors Uα and Uβ, and is the output voltage vector synthesized from the two.

In the formula, Ts is the sampling period, and t1 and t2 are the action time of voltage vectors Uα and Uβ respectively.
According to the trigonometric sine theorem,

the amplitudes of the six space voltage vectors are equal and equal to 2Udc/3. From formulas (5) and (6), it can be obtained

that the action time of adjacent basic vectors is changed within a PWM cycle Ts, and the amplitudes of the synthesized voltage space vectors are guaranteed to be equal. Therefore, when Ts is small enough, the trajectory of the voltage vector is a regular polygon that is approximately circular. In order to minimize the number of switches at each state transition, it is necessary to be at t0=Ts-t1-t2. In order to make the movement speed of the magnetic flux smooth, the zero vector is not inserted centrally, but the zero vector is evenly divided into several parts and inserted into the magnetic flux trajectory at multiple points.
1.2 Determine the sector
Divide Figure 2 into 6 sectors, and the sector numbers are marked in the figure. The following introduces the method of determining the sector number. Let,, respectively:

Define three variables: m, n and p. If X>0, then m=1, otherwise m=0; y>0, then n=1, otherwise n=0: Z>0, then p=1, otherwise p=0. Suppose the sector number N=4p+2n+m, the corresponding relationship between N and the sector where the output voltage vector is located is shown in Table 1,

2 Implementation of SVPWM based on PIC microcontroller
Space voltage vector PWM control is implemented using the PIC24FJ64GA chip produced by Microchip, which is a powerful architecture developed on the basis of the existing RISC microcontroller series architecture. This architecture enables users to upgrade their applications by providing them with stronger computing capabilities and a richer set of peripherals. At the same time, this architecture is strictly designed to be
as consistent as possible with the existing PIC MCU functions and instruction mnemonics, thereby simplifying the upgrade of applications.
The PIC24FJ64GA004 uses an improved Harvard structure with independent program and data storage space and independent program and data buses. The architecture also allows direct access to the program space through the data space during code execution. The program address space can store 4M instruction words. The highest running speed can reach 16MIPS, with 8MHz internal oscillator with 4×PLL option and multiple frequency division options, 17-bit×17-bit single-cycle hardware multiplier, 32-bit/16-bit working register, and optimized C compiler instruction architecture. PIC24FJ64GA004 also has a series of functions that can significantly reduce power consumption during operation, including: dynamic clock switching, doze mode operation, and instruction-based energy-saving mode. In terms of analog characteristics, it has up to 13 channels of 10-bit analog DAC, which is used for motor speed feedback, and the use of analog signals such as voltage and current to achieve various motor controls. It also has a fault protection clock monitor operation function, which can protect the circuit well.
2.1 Hardware Circuit Block Diagram
PIC24FJ64GA has 5 16-bit timers/counters with programmed prescalers, 5 16-bit input captures, and 5 16-bit comparison/PWM outputs. In terms of speed measurement, this paper adopts the photoelectric code disk measurement method, combined with the timer/counter and related interfaces of the PIC24F microcontroller, and uses the M/T method to program the speed calculation. The encoder model E6B2-CWZ6C produced by Omron is powered by a 5-24V power supply and has three outputs, namely phase A, phase B, and phase Z. A and B are used for speed measurement. Their phase difference is 90°, and 1500 pulses are output for each turn; while the Z pulse outputs one pulse for each turn, which is used for system positioning. In the circuit design, the inverter drive uses the IR2130 integrated chip. The inverter driven by this chip has the advantages of simple structure, stable operation, and reliable over-current and short-circuit protection. The hardware structure is shown in Figure 4.

． 2 Implementation of SVPWM algorithm software programming
Figure 5 Initialization flow chart Figure 6 SVPWM interrupt subroutine The SVPWM algorithm can be implemented by programming the PIC software. The program writing mainly includes the main program and the SVPWM interrupt subroutine. The main program mainly completes the initialization of the PIC24FJ64GA system and configures the on-chip peripheral resources. The interrupt subroutine mainly completes the function of outputting the required PWM waveform. The specific flow charts are shown in Figures 5 and 6.

3 Result Analysis
The control chip uses a 16-bit single-chip microcomputer PIC24FJ64GA. The space voltage PWM algorithm is written in the AC motor vector control system and downloaded to the control chip. The motor parameters of the simulation experiment are: rated power of 6kW, rated voltage of 310V, number of pole pairs of 2, moment of inertia of 0.0085, and rated speed of 3600r/min. The phase current and line voltage waveforms output by the simulation experiment are shown in Figures 7 and 8.

As can be seen from Figures 7 and 8, the SVPWM algorithm has a better current sinusoidality and a small stator output voltage and current harmonic, which verifies the effectiveness of the system design.

4 Conclusions
Space voltage vector PWM control has the characteristics of high DC bus voltage utilization, small switching device loss, and easy digital implementation. It has been widely used in AC motor variable frequency speed regulation systems. This paper uses PIC microcontrollers to implement the SVPWM algorithm in AC motor variable frequency speed regulation control systems. It has the characteristics of low cost, simple circuit design, and few current harmonic components. It has a certain application space in some occasions where the control accuracy requirements are not high, such as electric furnace temperature regulation, water level regulation, wind power regulation, etc.