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Space vector modulation using 8-bit ST7MC microcontroller and ST7MC-KIT/BLDC starter kit

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Last Updated: 21/11/2007

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AN2154 Application note
Space vector modulation using 8-bit ST7MC microcontroller and ST7MC-KIT/BLDC starter kit
Introduction
Due to its compatibility for use in vector control (field orientation) of AC motors, Space Vector Modulation (SVPWM) is one of the most widely utilized techniques to generate sinusoidal line-to-line voltages and currents with a three-phase inverter. This application note first illustrates the theory of Space Vector Modulation and then describes an algorithm which can be utilized to implement SVPWM using the 8-bit microcontroller ST7MC.

November 2007

Rev 3

1/16
www.st.com

Contents

AN2154

Contents
1 2 Space vector modulation theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 The PWM generator block of ST7MC motor control peripheral for SVPWM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1 Symmetrical space vector modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3

ST7MC implementation of symmetrical SVPWM . . . . . . . . . . . . . . . . . 10
3.1 3.2 Fixed settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Symmetrical SVPWM algorithm description . . . . . . . . . . . . . . . . . . . . . . . 11

4

Conclusions and experimental results . . . . . . . . . . . . . . . . . . . . . . . . . 13
4.1 4.2 The CPU load evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 The output waveform captures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

5

Revision history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

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List of figures

List of figures
Figure 1. Figure 2. Figure 3. Figure 4. Figure 5. Figure 6. Figure 7. Figure 8. Figure 9. Figure 10. Motor connected to a three-phase inverter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Space vector diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 The 12-bit PWM block generator of ST7MC motor control peripheral . . . . . . . . . . . . . . . . . 8 Center-aligned PWM waveform: compare 0 register = 8, compare register value = 4 . . . . . 8 Edge-aligned PWM waveform: compare 0 register = 8, compare register value = 4 . . . . . . 8 Edge-aligned SVPWM patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Center-aligned SVPWM patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 The update interrupt service routine block diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Phase voltage, line-to-ground voltage and neutral point-to-ground voltage . . . . . . . . . . . . 14 Magnitude spectrum of the motor phase voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

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Space vector modulation theory

AN2154

1

Space vector modulation theory
Figure 1 shows a three-phase inverter connected to a star connected motor. Figure 1. Motor connected to a three-phase inverter

Obviously, to avoid shorting the DC source Vdc, only one transistor for each leg must be switched on at one time. There are only eight possible switching states depending on the transistors that are turned on: Table 1. Three-phase Inverter allowed states
State 000 001 010 011 100 101 110 111 Conducting transistor T2, T4, T6 T2, T4, T5 T2, T3, T6 T2, T3, T5 T1, T4, T6 T1, T4, T5 T1, T3, T6 T1, T3, T5

Please note that in states 000 and 111 (null states), points A, B, and C are shortened to the negative and positive DC bus links respectively through low side and high side transistors so there are no line-to-line voltages applied to the motor. On the contrary, in the remaining six states, a voltage is present across the motor phases, causing a current to flow through statorical windings and flux to be produced by this current. It is very useful to express the states reported in Table 1 as space vectors. The six active vectors and the two null states can be plotted on the complex plane as shown in Figure 2:

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AN2154 Figure 2. Space vector diagram

Space vector modulation theory

Each one of the reference voltages V100, V110,... corresponds to one of the switching states reported in Table 1. In order to obtain sine wave voltages on the motor phases, a continuously rotating vector V must be produced so that one complete turn of the vector V on the complex plan represents one electrical turn of the motor (coincident with one mechanical turn in case of one pole pair motor). As it will be subsequently demonstrated, when linear modulation is applied, the circumference described by the rotating vector must stay inside the hexagon shown in Figure 2. The goal of space vector modulation is exactly to generate the appropriate PWM signals so that any vector V inside the hexagon can be produced by "time weighting" the two reference vectors that bound the sector in which V lies. Considering Figure 2, vector V can be expressed as: Equation 1
V = Va + Vb

where Va and Vb, are respectively components of vector V , with respect to V001 and V 011 . As mentioned earlier, vectors V a and V b will be generated by applying respectively the reference vectors V 001 and V 011 for a well-defined percentage of PWM period T0. Therefore, by defining ta, tb and t0 as the permanency time of vectors, V 001, V011 and V 111 (or V 000) inside the PWM period, it is possible to write: Equation 2
ta tb t0 V = V a + V b = ----- V 001 + ----- V 011 + ----- ( V 111 o r V 000 ) T0 T0 T0

with Equation 3
Va t a = ----------- T 0 V 001

5/16

Space vector modulation theory Equation 4
Vb t b = ----------- T 0 V 001

AN2154

Equation 5
t0 = T0 ta tb

Moreover, referring to Figure 2 it is easy to demonstrate that: Equation 6
V sin -- = V a sin -3 3 V sin = V b sin -3

Equation 7

from which it is possible to get: Equation 8
2 v a = ------ V sin -- 3 3

Equation 9
2 V b = ------ V sin 3

If we now substitute Equation 8 and 9 into Equation 3 and 4, it is possible to compute times ta, tb and t0 as a function of angle á and of modulation index mi=V/Vxxx: Equation 10
2 t a = ------ T 0 m i sin -- 3 3 0 -3

Equation 11
2 t b = ------ T 0 m i sin 3

0 -3

Equation 12
t0 = T0 ta tb

Please note that when the modulation index exceeds 3/2, the value of t0 can become negative for certain values of . Since this does not have a physical meaning, it can be affirmed that the maximum value of mi guaranteeing the proper working for space vector modulation in linear region is exactly 3/2. Higher values of mi would lead to overmodulation, where Equation 10 - 12 are no longer valid. Graphically, this means that for space vector modulation to work properly, the magnitude of the vector V must be small enough to ensure that the vector is totally contained inside the hexagon shown in Figure 2.

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AN2154

The PWM generator block of ST7MC motor control peripheral for SVPWM

2

The PWM generator block of ST7MC motor control peripheral for SVPWM
This section provides a basic functional description of the 12 bit PWM generator embedded into the ST7MC motor control peripheral. Figure 3 schematizes the block diagram of the PWM generator. The 3 PWM signals are generated using a freerunning 12-bit PWM Counter and three 13-bit Compare registers for phase U, V and W: MCMPU, MCMPV and MCMPW registers. A fourth 12-bit register (MCMP0) is needed to set up the PWM carrier frequency. All three PWM signals (Phases U, V and W) are then directed to the channel manager, in which dead time may be added. The 12-bit PWM Counter clock is supplied through a 3-bit prescaler to allow the generation of lower PWM carrier frequencies. It divides Fmtc by 1, 2, 3,..., 8 to get Fcounter. The PWM generator can work in center-aligned or edge-aligned mode, depending on the CMS bit setting in the MPCR register:

Center-aligned Mode (CMS bit = 1): In this operating mode, the PWM Counter counts up to the value loaded in the 12-bit Compare 0 register (MCMP0). Subsequently it counts down until it reaches zero and restarts counting up. The PWM signals are set to '0' when the PWM Counter reaches, in counting up, the corresponding 13-bit Compare register value, and they are set to '1' when the PWM Counter reaches the 13-bit Compare value again in counting down. Figure 4 shows a center-aligned PWM waveform, where the Compare 0 register value is equal to 8. Edge-aligned Mode (CMS bit = 0): In this operating mode, the PWM Counter counts up to the value loaded in the 12-bit Compare Register. Then the PWM Counter is cleared and it restarts counting up. The PWM signals are set to '0' when the PWM Counter reaches, in counting up, the corresponding 13-bit Compare register value, and they are set to '1' when the PWM Counter is cleared. Figure 5 shows an edge-aligned PWM waveform, where the Compare 0 register value is equal to 8. Both in center-aligned and edge-aligned modes, the four Compare registers (one Compare 0 and three for the U, V and W phases) are updated (and an Update 'U' event interrupt is generated if enabled) when the PWM counter underflows or overflows, and the 8-bit Repetition countdown has reached zero.This means that data is transferred from the preload compare registers to the compare registers every N cycles of the PWM Counter, where N is the value of the 8-bit Repetition register in edge-aligned mode. When using centeraligned mode, the repetition countdown is decremented every time the PWM counter overflows or underflows. Although this limits the maximum number of repetitions to 128 PWM cycles, this makes it possible to update the duty cycle twice per PWM period.

7/16

The PWM generator block of ST7MC motor control peripheral for SVPWM Figure 3.

AN2154

The 12-bit PWM block generator of ST7MC motor control peripheral

l

eP et

du ro

(s) ct

Ob -

ol s

Figure 4.

Center-aligned PWM waveform: compare 0 register = 8, compare register value = 4

Figure 5.

Edge-aligned PWM waveform: compare 0 register = 8, compare register value = 4

2.1

Symmetrical space vector modulation
As discussed in Chapter 2 , the goal of SVPWM is to generate three appropriate PWM signals in order to create, on the phases of the motor, three vectors V shifted (by 120 between each other) and continuously rotating inside the space vector hexagon on the complex plane. Moreover, it has been also discussed that, to create vectors V inside one of the six sectors, the reference vectors which bound that sector have to be "time weighted" using Equation 10 - 12.

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AN2154

The PWM generator block of ST7MC motor control peripheral for SVPWM There are several possible ways to distribute time t0 (associated to one of the two null sectors) inside the PWM period. The first possibility is shown in Figure 6. It utilizes ST7MC Motor control peripheral 12-bit PWM generator in edge-aligned mode. Please note that the edge alignment implies the presence of the passage between the null state 000 and the null state 111 and, then, the need of three contemporary switches commutation. Literature demonstrates that, in order to reduce the number of commutation and switching losses, it is preferable to utilize a states sequence where successive states are also adjacent. This means that passing from one state to the successive one should occur with only one switch commutation. This implies that the null state 111 must be always situated after one of the states 110, 101, 011, and null state 000 must be always situated after one of the states 100, 001, 010. Figure 7 shows a typical switching pattern generated by ST7MC Motor control peripheral 12 bit PWM generator in "center-aligned" mode. It can be observed that the above rules are respected. Please be aware that, to be coherent with what has been stated in the previous paragraph, the PWM period should be reported as T0, while in Figure 7 it has been indicated as 1/fs. It is convenient, in fact, from this point on, to indicate with T0 only a half of the PWM period. It is easy to understand that Equation 10 - 12 are still valid in the case that ta, tb are taken as shown in Figure 7. Please observe that time t0, associated with the null states, has been divided into two parts: t0` is relative to the permanency time of state 111 and t0`` is relative to the permanency time of state 000. Since Equation 12 does not give any information about the values of these two times, their choice could be arbitrary. Nevertheless, literature demonstrates that the best total harmonic distortion on line to neutral voltage and on motor current is achieved when: Equation 13
t t`0 = t`0 = --0 ` 2

In this case the modulation is called symmetrical SVPWM. Figure 6. Edge-aligned SVPWM patterns

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ST7MC implementation of symmetrical SVPWM Figure 7. Center-aligned SVPWM patterns

A N2154

3

ST7MC implementation of symmetrical SVPWM
A practical implementation of symmetrical SVPWM has been implemented using ST7MC, the STMicroelectronics 8-bit microcontroller dedicated to Motor Control. Thanks to its embedded Motor control peripheral, the space vector modulation can be easily implemented without excessive computational load for the CPU. The firmware developed is strongly based on the three-phase AC Induction Motor Control Software Library, downloadable from the web site: www.st.com and widely described in application note AN1904 (downloadable from the same web page). This library can handle AC asynchronous motor control in open loop and closed loop for optimum slip regulation using sinusoidal modulation with 3rd harmonic injection. Starting from the mentioned library, the symmetrical SVPWM has been generated mainly by modifying the 'U' event interrupt service routine dedicated to the sinus plus 3rd harmonic waveform generation.

3.1

Fixed settings
The aim of this paragraph is to illustrate which of the parameters defined in AC Induction Motor control library have been fixed during the symmetrical SVPWM algorithm development. All these settings are not mandatory, but a modification of one of them could require some firmware modification in order to restore the full firmware functioning. Relating to AC asynchronous motor control library, the main parameters which have been set are:

Speed regulation: open loop operation has been selected. PWM pattern: center-aligned PWM must be chosen for symmetrical SVPWM. PWM frequency: it has been set equal to 15.625 kHz. This has been achieved by fixing MCMP0 register at 255 and by setting the prescaler to 1 (Fcounter=Fmtc/2). This choice allows both the elimination of the acoustical noise introduced by the switches and to perform all the necessary computations for PWM patterns generation in 8-bit format. Repetition counter: it has been fixed at 2 so that a U event is generated every 1.5 PWM periods. Accordingly with ST7MC Starter Kit schematic rev. C-6, the index modulation is adjustable from potentiometer RV2 in the range between 0 to 0.866, and the output waveform frequency is adjustable from potentiometer RV1 in the range between 3 and 225 Hz. Maximum and minimum frequency can be eventually varied by changing HIGHEST_FREQ and LOWEST_FREQ parameters values in MTC_param.h header file.

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AN2154

ST7MC implementation of symmetrical SVPWM

3.2

Symmetrical SVPWM algorithm description
As discussed in Chapter 1, in order to generate SVPWM, vector V must rotate continuously inside the space vector hexagon. This implies that time ta, tb and t0 must continuously vary following Equation 10 - 12. Since these equations are only valid for in the range between 0 and /3, it could be very convenient to represent angle á by an 11-bit variable. This way, the most significant 3 bits can be used to indicate the sector, and the least significant 8-bits can contain the angle of vector V inside the identified sector. The resolution is given by /(3.256) radians equivalent to 0.234 degrees. In practical implementation, to keep the frequency resolution high, it is necessary to store angle in a 16-bit variable. According to the previous discussion, the most significant 3 bits identify the sector, the successive 8 bits are used to identify the angle inside the sector and the least significant 5 bits are not used for ta, tb and t0 computation. In order to reduce the CPU computational load, a look-up table has been used for storing time ta and tb using Equation 10 and 11 with the maximum admissible value of modulation index mi (that is 0.866). Moreover, comparing Equation 10 and 11 it is possible to note that the ta table is exactly the same as the tb table in reverse. This means that only one look-up table is necessary. During runtime, the look-up times ta and tb must be scaled accordingly with the value of modulation index imposed from the user. This is achieved in two steps: first, times ta and tb are multiplied by an 8-bit variable (SineMag) read from potentiometer RV2 and, therefore, only the result of the most significant byte is considered (that is the equivalent of a division by 256). After ta and tb scaling, the three values to be loaded into the compare registers must be calculated to generate the waveform shown in Figure 7. Let us suppose, for example, that vector V is, in a well known instant, situated in sector 0 and, therefore, it has to be "time weighted" between state 001 and 011 (this situation is exposed in Figure 7). The values to be loaded into the compare registers are: Equation 14
0 Phase U compare register (MCMPU)= --- F counter 2

t

Equation 15
t0 Phase V compare register (MCMPV)= --- + t F counter 2 a

Equation 16
t0 Phase W compare register (MCMPW)= --- + t a + t b = T 0 2 t 0 --- F c o u n t e r 2

Moreover, as it is: Equation 17
1 1T 0 = ------------------ = --------------------------------- = 32 s ( 2 f s ) ( 2 15.625 )

and Equation 18
M C M P 0 = T 0 F c o u n t e r 1 = 255

11/16

ST7MC implementation of symmetrical SVPWM it follows that T0-t0 is simply equal to ~t0 (i.e. NOT(t0)). In addition, considering the equation: Equation 19
( T 0 ( t a + t b ) ) ( t a t b) t0 --- = ---------------------------------- = ----------------2 2 2

A N2154

it is possible to express Phase X compare registers (X=U, V, W) as function of only ta and tb (Fcounter dependency will be omitted from this point on): Equation 20
a b Phase U compare register = -------------------------- -

( t +t ) 2

Equation 21
Phase V compare register = -------------------------- + t a 2

( t a + t b)

Equation 22
a b Phase W compare register = -------------------------- -

( t + t ) 2

A similar line of reasoning can be followed for the other sectors.Table 2 shows the values to be loaded into the Phase U, V and W compare registers depending on the sector in which vector V is located. Table 3 lists and shortly describes the variables utilized in SVPWM algorithm, while Figure 8 shows the algorithm block diagram. Table 2.
Sector

Compare registers values
Phase U compare register (MCPUH) ( ( t a + t b )) ------------------------------2 ( ( t a + t b )) ------------------------------2 ( ( t a + t b )) ------------------------------- + t a 2 ( t a + t b) -------------------------- 2 ( t a + t b) -------------------------- 2 ( t a + t b) -------------------------- + t b 2 Phase V compare register (MCPVH) ( t a + t b) -------------------------- + t a 2 ( t a + t b) -------------------------- 2 ( t a + t b) -------------------------- 2 ( ta + tb ) -------------------------- + t b 2 ( ( t a + t b )) ------------------------------2 ( ( t a + t b )) ------------------------------2 Phase W compare register (MCPWH) ( t a + t b) -------------------------- 2 ( t a + t b) -------------------------- 2 ( ( t a + t b )) ------------------------------2 ( ( t a + t b )) ------------------------------2 ( t a + t b) -------------------------- + t a 2 ( t a + t b ) -------------------------- 2

0

1

2

3

4

5

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AN2154

Conclusions and experimental results

Table 3.

Variables utilized in SVPWM algorithm
Variable size 16 bit (0x0 0 0xBFFF) 16 bit 8 bit 8 bit 8 bit Physical meaning Angle d/dt ta tb mi*256 Resolution

Variable name Phase SineFreq Ta Tb SineMag
t0 T0

0.234 degrees
0.212 Hz 12 bit timer resolution (125 ns) 12 bit timer resolution (125 ns) 0.0039

It is not a defined variable. It is always computed as T0- ta- tb T0 is not a defined variable. It is constant at 15.625 kHz carrier frequency

4

Conclusions and experimental results
Star ting from the ST7MC three-phase asynchronous motor control library, an algorithm for symmetrical SVPWM has been developed. This section illustrates the measurement carried out for CPU load evaluation and shows the oscilloscope capture of obtained output waveforms.

4.1

The CPU load evaluation
The contribution of the implemented algorithm to the CPU load has been estimated measuring the U interrupt routine execution time at 8 MHz clock frequency with the usage of ST7MC emulator (ST7MDT50-EMU3). The average execution time of the above mentioned routine turned out to be equal to: Equation 23
t e x = 23.1 sec

The contribution of SVPWM implementation to the CPU load has been, therefore, computed in the exposed situation using relationship: Equation 24
te x C P U L O A D = ----------------------------------------------------------------------------------------- = 24.1% 0.5 t P W M ( R E P C O U N T E R + 1 )

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Conclusions and experimental results Figure 8. The update interrupt service routine block diagram

AN2154

4.2

The output waveform captures
Referring to Figure 2, Figure 9 illustrates the voltage of neutral point N with respect to ground (Channel 1), the voltage of point A with respect to ground (Channel 2), and the phase voltage of one of the three phases of the motor (VAN, Channel 3). Figure 10 shows the magnitude spectrum of the motor phase voltage. Figure 9. Phase voltage, line-to-ground voltage and neutral point-to-ground voltage

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AN2154 Figure 10. Magnitude spectrum of the motor phase voltage

Revision history

5

Revision history
Table 4.
Date 24-May-2005 19-Nov-2007 21-Nov-2007

Document revision history
Revision 1 2 3 Initial release Removed references to obsolete products Watermark removed, no content change Changes

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AN2154

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