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AVR Microcontrollers Application Note AVR495: AC Induction Motor Control Using the Constant V/f Principle and a Space-vector PWM Algorithm 1. Features • Cost-effective and energy efficient 3-phase induction motor drive • Interrupt driven • Low memory and computing requirements 2. Introduction In a previous application note [AVR494], the implementation on an AT90PWM3 of an induction motor speed control loop using the constant Volts per Hertz principle and a natural pulse-width modulation (PWM) technique was described. A more sophisti- cated approach using a space vector PWM instead of the natur...
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AVR Microcontrollers Application Note AVR495: AC Induction Motor Control Using the Constant V/f Principle and a Space-vector PWM Algorithm

1. Features • Cost-effective and energy efficient 3-phase induction motor drive • Interrupt driven • Low memory and computing requirements 2. Introduction In a previous application note [AVR494], the implementation on an AT90PWM3 of an induction motor speed control loop using the constant Volts per Hertz principle and a natural pulse-width modulation (PWM) technique was described. A more sophisti- cated approach using a space vector PWM instead of the natural PWM technique is known to provide lower energy consumption and improved transient responses. The aim of this application note is to show that this approach, though more computation- ally intensive, can also be implemented on an AT90PWM3. 3. AT90PWM3 Key Features The control algorithms have been implemented on the AT90PWM3, a low-cost low- power single-chip microcontroller, achieving up to 16 MIPS and suitable for the control of DC-DC buck-boost converters, permanent magnet synchronous machines, three- phase 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, 4. Theory of Operation 4.1 Principle of the Space-Vector Modulation Figure 4-1. Typical structure of an inverter-fed induction motor. Figure 4-1.shows the typical structure of a three-phase induction motor connected to a VSI (Volt- age Source Inverter). Since the motor is considered as a balanced load with an unconnected neu t ra l , Vn = 〈Va + Vb + Vc〉 ⁄ 3 , Van =Va −Vn = (Vab −Vca) /3 , Vbn =Vb −Vn =(Vbc −Vab)/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 4-2. Six of them lead to non-zero phase voltages, and two interchangeable states lead to zero phase volt- ages. When mapped in a 2D-frame fixed to the stator using a Concordia transformation [1,2], the six non-zero phase voltages form the vertices of a hexagon. (See Figure 4-3.)

V

⎡Vα ⎤ ⎡1 −1/ 2 −1/ 2 ⎡ ⎤ ⎤ an⎢ ⎥ ⎢ ⎥ = ⎢ ⎥ V ⎣Vβ ⎦ ⎣⎢0 3 / 2 − 3 / 2⎥ ⎢ bn ⎥ ⎦ ⎢⎣Vcn ⎥⎦ Figure 4-2. Possible switching configurations of a 3-phase inverter 2 Application Note,

Application Note

As shown on Figure 4-3., the angle between two successive non-zero voltages is always 60 degrees. j(k 1)π− In complex form, these non-zero phase voltages can be written as V = E e 3k , with k = 1..6 and V0 = V7 = 0 V. Table 4-1. shows the line-to-line and line-to-neutral voltages in each of the 8 pos- sible configurations of the inverter. Figure 4-3. Representation of the eight possible switching configurations in the Concordia reference frame Table 4-1. Switching configurations and output voltages of a 3-phase inverter Sa+ Sb+ Sc+ Si Vab Vbc Vca Van Vbn Vcn Vα Vβ Vi000S000000000V0001S1 0 -E E -E/3 -E/3 +2E/3 -E/2 –E 3 ⁄ 2 V5010S2 -EE0-E/3 +2E/3 -E/3 -E/2E3⁄ 2 V3011S3 -E0E-2E/3 -E/3 -E/3 -E 0 V4100S4E0-E +2E/3 -E/3 -E/3E0V1101S5 E -E 0 E/3 -2E/3 E/3 E/2 –E 3 ⁄ 2 V6110S60E-E E/3 E/3 -2E/3 E/2E3⁄ 2 V2111S700000000V7, Table 4-2. Expressions of the duty cycles in each sector In the Concordia frame, any stator voltage Vs =Vα + jVβ = Vsm cos(θ ) + jVsm sin(θ ) located inside this 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 = dk Vk + dk+1Vk+1 . Equating dk Vk +dk+1Vk+1 to Vsm cos(θ ) + jVsm sin(θ ) in each sector leads to the expressions of the duty cycles shown in Table 4-2. Since the inverter cannot instantaneously generate Vs , the space- vector PWM principle consists in producing a Ts -periodic voltage whose average value equals Vs ,by generating Vk during Tk = d kTs and Vk +1 during Tk +1 = dk +1Ts . Since dk + dk +1 ≤ 1 , these voltages must be completed over the switching period Ts by V0 and/or V7 . Several solutions are possible [3,4], and the one which minimizes the total harmonic distorsion of the stator current 1− d − d T = T = k k +1 T consists in applying V0 and V7 during the same duration072s. V0 is equally applied at the beginning and at the end of the switching period, whereas V7 is applied at the middle. As an illustration, the upper side of Figure 4-4. shows the waveforms obtained in sector 1. 4 Application Note,

Application Note

4.2 Efficient Implementation of the SV-PWM Table 4-2. seems to show that the duty cycles have different expressions in each sector. A thor- ough study of these expressions show that since sin(x) = sin(π − x) , all these duty cycles can be 2V 2V written in a unified way as d = smk sin(θ ′′) and d smk +1 = sin(θ ′) π , with θ ′′ = −θ ′ andE3E33θ′ θ (k π= − −1) 3 . Since these expressions no longer depend on the sector number, they can be π denoted as da and db . Since θ ′ is always between 0 and 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 wave- forms 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 4-3. Figure 4-4. Inverter switch waveforms and corresponding compare register values, Table 4-3. Compare Register Values vs Sector Number 4.3 Sector Determination Algorithm To determine the sector which a given stator voltage Vs belongs 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 in 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 k is the output of a modulo six counterππactivated each time θ ′ exceeds 3 , and θ ′ is confined to lie between 0 and (see Fig. 7). Figure 4-5. Sector determination algorithm 6 Application Note,

Application Note

Figure 4-6. Sector determination The resulting dataflow diagram, shown on Fig. 8, can be used to build a speed control loop (Fig- ure 4-8.), 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 con- troller, 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. Figure 4-7. Space Vector PWM data flow diagram, Figure 4-8. Block diagram of the complete control system. 5. 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 6. 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 2πk values of 127 sin( )480 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 (see Figure 4-8.). 6.1 Project Description The software is available in the attached project on the Atmel web Site. The project to use is Project_Vector. The Project_Natural corresponds to the AVR494 Application Note. 8 Application Note,

Application Note

Table 6-1. List of Files used in the “Project_Vector”.IAR project. File Description main_space_vector_PWM.c main upper level of the application space_vector_PWM2.c sector and theta determination controlVF.c Compute a constant V/F ratio mc_control.c regulation loop (PI) read_acquisitionADC.c return the ADC result init.c CPU initialization (IO ports, timers) psc_initialisation2.c PSC initialization adc.c ADC functions dac.c DAC functions 6.2 Experimentation Figure 6-1. 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 withaaspace vector PWM is smoother but also longer. Figure 6-1. Measured speed (in rpm) and line-to-neutral stator voltage (in Volts) obtained with the microcontroller during speed reference steps (a) −500 −1012345678(b) −50 −1012345678(c) −50 3 3.02 3.04 3.06 3.08 3.1 3.12 3.14 3.16 3.18 3.2 time [s] 7. Resources Code Size : 2 584 bytes RAM Size : 217 bytes stator voltage [V] stator voltage [V] speed [rpm], CPU Load : 33% @ 8MHz 8. References 1. Atmel AVR494, AC Induction Motor Control Using the constant V/f Principle and a Natural PWM Algorithm. 2. W. Leonhard, “Control of electrical drives”, 2nd Ed, Springer, 1996. 3. F.A. Toliyat, S.G. Campbell, “DSP-based electromechanical motion control”, CRC Press, 2004. 4. Y.Y. Tzou, H.J. Hsu, “FPGA realisation of space-vector PWM control IC for three-phase PWM inverters”, IEEE Transactions on Power Electronics, Vol 12, No 6, pp 953-963, 1997. 5. K. Zhou, D. Wang, “Relation between space-vector modulation and three-phase carrier-based PWM”, IEEE Transactions on Industrial Electronics, Vol. 49, No. 1, pp 186-196, February 2002. 10 Application Note,

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