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AN706-00036-1v0-E
32-BIT MICROCONTROLLER
MB9B100A/MB9B300A/MB9B400A/MB9B500A Series
Space Vector Pulse Width Modulation
TM
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AN706-00036-1v0-E
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AN706-00036-1v0-E
Revision History
Rev
Date
Remark
1.0
Jul. 04, 2011
First Edition
2
AN706-00036-1v0-E
Table of Contents
Revision History.................................................................................................................... 2
Table of Contents.................................................................................................................. 3
1
Introduction.................................................................................................................... 4
2
SVPWM Theory ............................................................................................................. 4
2.1
Overview ................................................................................................................ 4
2.1
Theory .................................................................................................................... 6
2.2
SVPWM Actualize................................................................................................. 10
2.3
SVPWM Arithmetic in FM3 family......................................................................... 12
2.3.1
Make sure the Uref belong to which sector..................................................... 12
2.3.1
Determine open time of 2 adjacent basic vector............................................ 13
2.3.2
Calculate conduction time ............................................................................. 14
2.3.3
Create SVPWM waveform ............................................................................ 15
3
AN706-00036-1v0-E
1
Introduction
This application note describes SVPWM function Theory, Block, Function, Flow, Sample,
Parameter in FM3 family Inverter Platform.
2
SVPWM Theory
Technical Background
2.1
Overview
In motor theory, motor speed is defined by the formula:
(1)
Where f-Power frequency,p-pole pairs
Through the formula ,speed
regulate need change
the power frequency or the motor
pole pairs, and change power frequency easier than change motor pole pairs, so, at present,
the great mass of motor speed regulate use frequency convert.
How to change power frequency? Currently, use the type of: AC-DC-AC. It’s means,
convert
3-phase power AC into DC, then, invert the DC into 3-phase AC and change
frequency. First, define the 3-phase power AC interphase voltage is:
√2 cos
2π/3
√2 cos
4π/3
√2 cos
(2)
Take this 3-phase AC voltage into stationary system (α-β):
(The formulae deduce please reference the [AN] coordinate transform Clarke Transform
formulae (12))
2
3
ua
2
3
0.5ub
√3
u
2 b
0.5uc
√3
u
2 c
√2 cos
√2 sin
(3)
Take this into voltage space vector:
us
(4)
In sine power:
us
√2
cos
sin
4
√2
(5)
AN706-00036-1v0-E
This equation is a circularity in plural plane. So, in motor theory, invariableness’ voltage(U)
and frequency, stator voltage space vector in plural plane move along with a circularity , and
space vector move
a cycle in a power frequency cycle.
Figure 2-1, the line voltage space vector will move other circularity , it’s radius more than
phase voltage circularity √3 ,and they have 30° phase angle.
In stator 3-phase voltage space vector will move along with a circularity (start) into another
circularity (stabile).
The SVPWM use to regulate power frequency and draw a nice circularity
part.
Figure 2-1
5
through DC–AC
AN706-00036-1v0-E
2.1
Theory
SVPWM: Space Vector Pulse Width Modulation.
Purpose: SVPWM can directly transform the stator voltage vectors from the two-phase
α,β-coordinate system into pulse-width modulation (PWM) signals (duty cycle values).
proverbial motor formulae is :
U1
dψ1
dt
R1 i1
(6)
U1 is stator voltage vector, Ψ1 is stator flux vector, i1 is stator current vector.
When U1 is a standard sine wave, that is the same size and direction continuous change,
the trajectory is an ideal circle. So,
U1
ψ1
R1 i1 dt
(7)
When R1 *i1<<U1:
ψ1
U1 dt
(8)
Flux trajectory depends on voltage vector.
So we can design the circuit of DC to 3-phase AC
Figure 2-2
As shown in figure 2-2, in the circuit diagram, have 6 power switch a, b, c, a’, b’, c’ plot out
they into 2 groups, S[ a,b,c] , S’[a’, b’, c’], they control the switch ON/OFF, and they mutex,
Sx
S
S′
1
0
It’s means each voltage vector is coded by the three-digit number and have eight possible
switching states (vectors) are feasible.
For example: Sx = [1, 0, 0].
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AN706-00036-1v0-E
The point [a], [b’], [c’] switch ON, and [a’], [b], [c] switch OFF.
UaN
Udc ,
UbN
UcN
0
UaN
UbN
Udc
In motor theory,
b
c
Take
UaN
Udc , UbN
UcN
b
0
c
Udc
0
into the formula,
Similarly, can calculate other switching states, below in Table 2-1.
Table 1
Sa
Sa
Sa
Vector
UaN
UbN
UcN
Ua
Ub
Uc
0
0
0
U0
0
0
0
0
0
0
1
0
0
U4
Udc
0
0
2Udc/3
- Udc/3
- Udc/3
1
1
0
U6
Udc
Udc
0
Udc/3
Udc/3
- 2Udc/3
0
1
0
U2
0
Udc
0
- Udc/3
2Udc/3
- Udc/3
0
1
1
U3
0
Udc
Udc
- 2Udc/3
Udc/3
Udc/3
0
0
1
U1
0
0
Udc
- Udc/3
- Udc/3
2Udc/3
1
0
1
U5
Udc
0
Udc
Udc/3
- 2Udc/3
Udc/3
1
1
1
U7
0
0
0
0
0
0
Form formula (3) and (4), the voltage space vector formula:
2
3
us
a
Where
exp j
ua
aub
a2 uc
a2
exp j
2π
3
(9)
4π
3
Take table 2-1 vector:
U4
2
U 3 dc U2
2
2π
Udc exp j
3
3
U1
2
π
Udc exp j
3
3
U6
2
4π
Udc exp j
3
3
U3
2
U exp jπ
3 dc
2
5π
Udc exp j
3
3
U5
All of non-zero vectors have the same amplitude
vectors
angle
is
π
, 3
60° for
(10)
example,
7
2
U
3 dc , and between
f=50Hz,
the
vector
border two
change
time:
AN706-00036-1v0-E
t
60 1
360 50
3.33ms
.
8
AN706-00036-1v0-E
Graphical representation of all combinations is the hexagon shown in Figure 2-3. There are
six non-zero vectors, U0, U60, U120, U180, U240, U300, and two zero vectors, O000 and
O111, defined in α, β coordinates.
Figure 2-3
In figure 2-3, the red line
plot out the hexagon into six sectors, every between
border
two vectors angle is 60°, the border two vectors and zero vector could compose random
voltage vector.
T
0
Uref dt
Tx
0
Ux dt
Tx Ty
Tx
T
Uy dt
Tx Ty
U0 dt
(11)
Or
Uref T
Ux Tx
Uy Ty
U0 T0
(12)
This formula means, in sector the voltage vector rotating course could plot out many small
part , it’s have the same effect.
So, in the interest of bring 3-phase sine AC voltage, use the voltage vector compose,
begin from U4(100),every time
compose from between
increase a little increment, every increment could
border two vectors and zero vector. Then the enactment voltage
vector equivalent with the rotating voltage vector, and that all is SVPWM.
The figure2-4 show the SVPWM transform course, a f = 50Hz single phase voltage
transform into DC voltage, then transform into a f=100Hz 3-phase voltage.
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AN706-00036-1v0-E
DC
AC
AC
Figure 2-4
2.2
SVPWM Actualize
3-phase AC voltage rotating speed :
ω
2πf , rotating a cycle need time T=1/f, if carrier
wave frequency is fs , the frequency ratio R =fs/f, it’s means voltage rotating plane plot out R
unit increment , so the voltage vector increment
angle is
r
2π
R
2πf
fs
2πTs /T
For example, need compose a voltage vector Uref , it’s station at I at sector first increment,
then will use two non-zero vector(U4,U6) and two zero vector(U0,U7), shown the Figure 2-4.
Figure 2-5
In stationary system 2-phase (α-β), the Uref with U4 angle is θ, then
|Uref |
|T4 U4 /Tz |
|T6 U6 /Tz |
π
sin2π/3
sinθ
sin 3 θ
(13)
Because:
U4
U6
2
U
3 dc , the vector hold time is
10
AN706-00036-1v0-E
π
θ
3
mTs sin θ
mTs sin
4
6
(14)
√3|Uref |
Udc
Where m is SVPWM regulate ratio:
Then
zero vector hold time:
For reduce the switch waste, every time only changes one phase switch state, and the best
sequence is below the Table 2-2.
Table 2
Uref
I
switch sequence
sector (0°≤θ≤60°)
0-4-6-7-7-6-4-0
II
sector (60°≤θ≤120°)
0-2-6-7-7-6-2-0
III
sector (120°≤θ≤180°)
0-2-3-7-7-3-2-0
IV
sector (180°≤θ≤240°)
0-1-3-7-7-3-1-0
V
sector (240°≤θ≤300°)
0-1-5-7-7-5-1-0
VI sector (300°≤θ≤360°)
0-4-5-7-7-5-4-0
Then use the table 2-2 ,after voltage rotating a cycle, will have R unit compose vector, and
in I sector have 3-phase voltage wave shown in figure2-5.
Figure 2-6
11
AN706-00036-1v0-E
2.3 SVPWM Arithmetic in FM3 family
In FM3 family Inverter platform SVPWM compose sine wave need have 4 steps:
1. Make sure the Uref belong to which sector.
2. To calculate X,Y,Z which are used to determine open time of 2 adjacent basic vector.
3. To determine each conduction time for 2 adjacent basic vector.
4. To determine To write OCCP register value to CH1,CH3,CH5 which used to create
SVPWM waveform
2.3.1 Make sure the Uref belong to which sector
Function Application
Function: To calculate sector no. of SVPWM voltage vector.
Function Name: CalcSectorNo
C file name: SVPWM.C, SVPWM.H
Function interface:
INT8U CalcSectorNo(_stDataInFixAxis *pstDataInFixAxis //fixed 2-axis system)
typedef struct
{
Q15_VAL32 alpha_Q15;//
Q15_VAL32 beta_Q15;//
}_stDataInFixAxis;
Table 3
Item
Inputs
Outputs
Name
alpha
beta
SectorNo
Description
phase- alpha of fixed 2- phase
phase- beta of fixed 2- phase
Sector no. of SVPWM voltage vector
The following code is example for this module.
void example_ CalcSectorNo ()
{
CurrentInFixAxis. alpha_Q15= INa;//Input alpha
CurrentInFixAxis. beta_Q15= INb;//Input beta
CalcSectorNo (&pstDataInFixAxis);
OUTa= SectorNo;
}
12
Format
Q15_VAL32
Q15_VAL32
Q15_VAL32
AN706-00036-1v0-E
2.3.1
Determine open time of 2 adjacent basic vector
Function Application
Function: To calculate X,Y,Z which is used to determine open time of 2 adjacent basic vectors.
Function Name: CalcDutyTime
C file name: SVPWM.C, SVPWM.H
void CalcDutyTime(_stDataInFixAxis *pstDataInFixAxis, _stXYZ *pstXYZ,
INT8U WhichMFT, INT8U WhichFRTCh)
typedef struct
{
Q15_VAL32 alpha_Q15;
Q15_VAL32 beta_Q15;
}_stDataInFixAxis;
typedef struct
{
INT32S X;
INT32S Y;
INT32S Z;
}_stXYZ;
Table 4
Item
Name
Description
Format
alpha
phase- alpha of fixed 2- phase
Q15_VAL32
beta
phase- beta of fixed 2- phase
Q15_VAL32
Inputs
WhichMFT
Which MFT, valid value is MFT0, MFT1
INT8U
WhichFRTCh Which FRT channel to configure
INT8U
X
X is conduction time
INT32S
Outputs
Y
Y is conduction time
INT32S
Z
Z is conduction time
INT32S
The following code is example for this module.
void example_ CalcDutyTime ()
{
pstDataInFixAxis. alpha_Q15= INa;//Input alpha
pstDataInFixAxis. beta_Q15= INb;//Input beta
WhichMFT=0;
WhichFRTCh=0;
CalcDutyTime (&pstDataInFixAxis,& pstXYZ, WhichMFT, WhichFRTCh);
OUTa= pstXYZ->X;
OUTb= pstXYZ->Y;
OUTc= pstXYZ->Z;
}
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2.3.2
Calculate conduction time
Function Application
Function: To determine each conduction time for 2 adjacent basic vectors.
Function Name: CalcTon
C file name: SVPWM.C, SVPWM.H
void CalcTon(INT8U SectorNo, _stXYZ *pstXYZ, _stOnTimingOfUVW *pstOnTimingOfUVW,
INT8U WhichMFT, INT8U WhichFRTCh)
typedef struct
{
INT32S X;
INT32S Y;
INT32S Z;
}_stXYZ;
typedef struct
{
INT32S TU;
INT32S TV;
INT32S TW;
}_stOnTimingOfUVW;
Table 5
Item
Inputs
Name
X
Y
Z
SectorNo
WhichMFT
WhichFRTCh
TU
Outputs
TV
TW
Description
X is conduction time
Y is conduction time
Z is conduction time
Sector no. of SVPWM voltage vector
Which MFT, valid value is MFT0, MFT1
Which FRT channel to configure
Conduction time of A phase connecting to DC power
supply
Conduction time of B phase connecting to DC power
supply
Conduction time of C phase connecting to DC power
supply
The following code is example for this module.
void example_ CalcTon ()
{
pstXYZ .X= INa;
pstXYZ .Y = INb;
pstXYZ .Z=INc;
SectorNo=1;
WhichMFT=0;
WhichFRTCh=0;
CalcTon (SectorNo ,& pstXYZ,& pstOnTimingOfUVW, WhichMFT, WhichFRTCh);
OUTa= pstOnTimingOfUVW ->TU;
OUTb= pstOnTimingOfUVW ->TV;
OUTc= pstOnTimingOfUVW ->TW;
}
14
Format
INT32S
INT32S
INT32S
INT8U
INT8U
INT8U
INT32S
INT32S
INT32S
AN706-00036-1v0-E
2.3.3
Create SVPWM waveform
Function Application
Function: To determine To write OCCP register value to CH1,CH3,CH5 which used to create
SVPWM waveform
Function Name: WriteCmpValToReg
C file name: SVPWM.C, SVPWM.H
void WriteCmpValToReg(INT8U WhichMFT, _stOnTimingOfUVW *pstOnTimingOfUVW)
typedef struct
{
INT32S TU;
INT32S TV;
INT32S TW;
}_stOnTimingOfUVW;
Table 6
Item
Name
TU
Inputs
TV
TW
WhichMFT
Description
Conduction time of A, phase connecting to DC power
supply
Conduction time of B, phase connecting to DC power
supply
Conduction time of C phase connecting to DC power
supply
Which MFT, valid value is MFT0, MFT1
Format
INT32S
INT32S
INT32S
INT8U
The following code is example for this module.
void example_ WriteCmpValToReg ()
{
pstOnTimingOfUVW .TU=INa;
pstOnTimingOfUVW .TV=INb;
pstOnTimingOfUVW .TW=INc;
WhichMFT=0;
WriteCmpValToReg (WhichMFT,& pstOnTimingOfUVW);
}
- End of File -
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