AC Induction Motor Control Using the Constant V/f Principle and a Space-vector PWM Algorithm

• Cost-effective and energy efficient 3-phase induction motor drive

• Interrupt driven

• Low memory and computing requirements

1. AT90PWM3 Key Features
2. Principle of the Space-Vector Modulation
3. Efficient Implementation of the SV-PWM
4. Sector Determination Algorithm
5. Hardware Description (ATAVRMC200)
6. Software Description
7. Project Description
8. Experimentation

Resources; Code Size : 2 584 bytes ,RAM Size : 217 bytes, CPU Load : 33% @ 8MHz

AT90PWM3 Key Features

The control algorithms have been implemented on the AT90PWM3, a low-cost lowpower single-chip microcontroller, achieving up to 16 MIPS and suitable for the control of DC-DC buck-boost converters, permanent magnet synchronous machines, threephase induction motors and brushless DC motors. This device integrates:

• 8-bit AVR advanced RISC architecture microcontroller (core similar to the ATmega 88)
• 8K Bytes of In-System-Programmable Flash memory
• 512 Bytes of static RAM to store variables and lookup tables dedicated to the application program
• 512 bytes of EEPROM to store configuration data and look-up tables
• one 8-bit timer and one 16-bit timer
• 6 PWM channels optimized for Half-Bridge Power Control
• an 11-channel 10-bit ADC and a 10-bit DAC
• 3 on-chip comparators
• a programmable watchdog timer with an internal oscillator

Principle of the Space-Vector Modulation

Figure 1. shows the typical structure of a three-phase induction motor connected to a VSI (Voltage Source Inverter). Since the motor is considered as a balanced load with an unconnected neutral ,Vn=(Va+Vb+Vc)/3 , Van=Va-Vn=(Vab-Vac) /3 , Vbn=Vb-Vn=(Vbc-Vac) /3 and Vcn=Vc-Vn=(Vca-Vbc) /3 . Since the upper power switches can only be On or Off, and since the lower ones are supposed to always be in the opposed state (the dead-times of the inverter legs are neglected), there are only eight possible switching states, as shown on Figure 2. Six of voltages.them lead to non-zero phase voltages, and two interchangeable states lead to zero phase When mapped in a 2D-frame fixed to the stator using a Concordia transformation, the six non-zero phase voltages form the vertices of a hexagon. (See Figure 3.)

As shown on Figure 3. , the angle between two successive non-zero voltages is always 60 degrees.

In complex form, these non-zero phase voltages can be written as Vk , with k = 1..6 and Vo-v7=0V. Table 1. shows the line-to-line and line-to-neutral voltages in each of the 8 possible configurations of the inverter.



In the Concordia frame, any stator voltage Vs = Vα + jVβ =Vsm cos(θ) + jVsm sin(θ) located insidethis hexagon belongs to one of the six sectors, and can be expressed as a linear combination of the two non-zero phase voltages which delimit this sector: Vs=dkVk+(dk+1)(Vk+1). Equating dkVk+(dk+1)(Vk+1) to Vsm cos(θ) + jVsm sin(θ) in each sector leads to the expressions of the dutycycles shown in Table 2. Since the inverter cannot instantaneously generate Vs the spacevector PWM principle consists in producing a Ts-periodic voltage whose average value equal Vs by generating Vk during Tk=dkTs and Vk+1 during Tk+1 = (dk+1)Ts.

Since dk+(dk+1) these voltages must be completed over the switching period To by Vo and/or V7 . Several solutions are possible , and the one which minimizes the total harmonic distorsion of the stator current consists i applying Vo and V7 during the same duration To=T7 is equally applied at the beginning and at the end of the switching period, whereas is applied at the middle. As an illustration, the upper side of
Figure 4 . shows the waveforms obtained in sector 1

Efficient Implementation of the SV-PWM

Table 2. seems to show that the duty cycles have different expressions in each sector. A thorough study of these expressions show that since sin(x)=sin(π-x) , all these duty cycles can be written in a unified way as dk and dk+1 with θ''=(π/3)- θ' and θ'= θ -(k-1)π/3. Since these expressions no longer depend on the sector number, they can be denoted as da and db . Since θ' is always between 0 and π/3, computing da and db requires a sine table for angles inside this interval only. This greatly reduces the amount of memory required to store this sine table. The AT90PWM3 provides the 3 power stage controllers (PSC) to generate the switching waveforms computed from the Space Vector algorythms. The counters will count from zero to a value corresponding to one half of the switching period (as shown on the lower side of Fig. 4), and then count down to zero. The values that must be stored in the three compare registers are given in Table 3.

Sector Determination Algorithm

To determine the sector which a given stator voltage belongs Vs to, some algorithms have been proposed in the literature which generally require many arithmetic operations and are based on the coordinates of Vs in the Concordia plane or in the a-b-c phase space. When this voltage is deduced from a V/f control principle, its modulus Vsm is computed by the V/f law recalled i the previous application note, and its phase θ is deduced from ωs by a discrete-time integrator. To implement this sector determination algorithm efficiently, we manage θ' and k instead of θ in a dedicated integrator shown on Fig. 6. The sector number is the output of a modulo six counter activated each time θ' exceeds π/3 , and θ' is confined to lie between 0 and π/3 (see Fig. 7).

The resulting dataflow diagram, shown on Fig. 8, can be used to build a speed control loop (Figure 8.), in which the difference between the desired speed and the measured speed feeds a PI controller that determines the stator voltage frequency. To decrease the complexity of the controller, the input of the V/f law and of the space vector PWM algorithm is the absolute value of the stator voltage frequency. If the output of the PI controller is a negative number, two of the switching variables driving the power transistors of the inverter are interchanged.

Hardware Description (ATAVRMC200)

This application is available on the ATAVRMC200 evaluation board. This board provides a way to start and experiment asynchronous motor control.

ATAVRMC200 main features:

• AT90PWM3 microcontroller
• 110-230VAC motor drive
• Intelligent Power Module (230V / 400W board sized)
• ISP & Emulator interface
• RS232 interface
• Isolated I/O for sensors
• 0-10V input for command or sensor

Software Description

All algorithms have been written in the C language using IAR's embedded workbench and AVR Studio as development tools. For the space vector PWM algorithm, a table of the rounded values of for k between 0 and 80 is used. The length of this table (81 bytes) is a better trade-off between the size of the available internal memory and the quantification of the rotor shaft speed. For bi-directional speed control, the values stored in two of the comparators are interchanged when the output of the PI regulator is a negative number Figure 8.

Project Description

The software is available in the attached project on the Atmel web Site. The project to use is Project_Vector.

Experimentation

Figure 9. shows the speed response and the stator voltages obtained with the microcontroller for speed reference steps between +700 and -700 rpm. These experimental results were obtained with a 750 W induction machine. This figure shows that the desired speed is reached after a 1.2 s long transient, and that when the stator frequency ωs obtained at the output of the PI regulator nears zero, the stator voltage magnitude is equal to the boost voltage. These figures also confirm that transient obtained with a a space vector PWM is smoother but also longer.