Paper 33-FPGA Triggered Space Vector Modulated Voltage

FPGA Triggered Space Vector
Modulated Voltage
Source Inverter Using
MATLAB/System Generator®
P.Geeth Prajwal Reddy
SSN College of Engineering
International Conference on Advances in Power Electronics and Instrumentation Engineering 1

2
Voltage Source Inverter (VSI)
VSI is a power electronics topology of switches that
facilitates the conversion of Direct Current (DC) to
Alternating Current (AC)
While the VSI has six switches, it is mandatory that only
one switch in each leg can be turned on at any instant,
thus 8 different switching states are possible, i.e. the
combination in which the switches are turned ON.
However the use of the VSI in the conventional manner or
normal Pulse Width Modulation (PWM) gives rise to an AC
of a Sine wave with large harmonics
Objective of Space Vector Modulation(SVM)
International Conference on Advances in Power Electronics and Instrumentation Engineering
Ib Vb
VDC+
S1
Ia Va
VDC
VDC-
S3S2
S4 S5 S6
Ic Vc

3International Conference on Advances in Power Electronics and Instrumentation Engineering
Switching States of VSI
At any instant, it is mandatory that only one switch in each leg of the VSI can be ON, to
prevent short circuit of the source. Each switching state is represented by ON-OFF status
(1-0) of the upper arm switches of the VSI, while the status of the lower arm switches
would be their complement. The possible switching states of the VSI are listed
VSI Switching State Vectors
Type Vector
𝑆1 𝑆2 𝑆3
𝑆4 𝑆5 𝑆6
Va Vb Vc 𝑉𝑂𝑈𝑇 ∠𝑉𝑂𝑈𝑇
Active
V1 [100]
1 0 0
0 1 1
2
3
𝑉𝐷𝐶 −
1
3
𝑉𝐷𝐶 −
1
3
𝑉𝐷𝐶
2
3
𝑉𝐷𝐶 0
V2 [110]
1 1 0
0 0 1
1
3
𝑉𝐷𝐶
1
3
𝑉𝐷𝐶 −
2
3
𝑉𝐷𝐶
2
3
𝑉𝐷𝐶
𝜋
3
V3 [010]
0 1 0
1 0 1
−
1
3
𝑉𝐷𝐶
2
3
𝑉𝐷𝐶 −
1
3
𝑉𝐷𝐶
2
3
𝑉𝐷𝐶
2𝜋
3
V4 [011]
0 1 1
1 0 0
−
2
3
𝑉𝐷𝐶
1
3
𝑉𝐷𝐶
1
3
𝑉𝐷𝐶
2
3
𝑉𝐷𝐶 𝜋
V5 [001]
0 0 1
1 1 0
−
1
3
𝑉𝐷𝐶 −
1
3
𝑉𝐷𝐶
2
3
𝑉𝐷𝐶
2
3
𝑉𝐷𝐶
4𝜋
3
V6 [101]
1 0 1
0 1 0
1
3
𝑉𝐷𝐶 −
2
3
𝑉𝐷𝐶
1
3
𝑉𝐷𝐶
2
3
𝑉𝐷𝐶
5𝜋
3
Zero
V0 [000]
V7 [111]
0 0 0
1 1 1
1 1 1
0 0 0
0 -
Active Vectors alter the
Phase angle of the output
AC
Zero vectors are used to
make the magnitude
variation of the output AC
sinusoidal

4
Space Vector Modulation (SVM)
Using Clark Transform, the resultant Three Phase AC is modeled as a single Phase AC
𝑉𝛼
𝑉𝛽
=
2
3
.
1
−1
2
−1
2
0
3
2
− 3
2
𝑉𝑎
𝑉𝑏
𝑉𝑐
Where,
Vα is the Magnitude
Vβ is the Phase Angle of the 1φ AC
Plotting Vα and Vβ we get a rotating vector, this is called the Space Vector, as shown
below
1
2
3
5
64
Va
Vb
Vc
V1(100)
V2(110)V3(010)
V4(011)
V5(001) V6(101)
Output AC waveform on application of switching states of VSI
V1(100)
V2(110)
V3(010)
V4(011)
V5(001)
V6(101)
V0(000)

5
Space Vector Modulation (SVM)
Modeling of 3 Phase Alternating Current as a Space Vector

6
Ideology of Space Vector Modulation
Thus in order to obtain a sinusoidal AC with minimal Harmonics, SVM utilizes the
“Equal Area Theorem”
A reference vector is taken to rotate around
the Switching State Hexagon at a frequency
of the required value.
Based on the position of the Reference
Vector, the Switching states are applied for
a specified time period
𝛿1 = 𝑚 𝑣. sin
𝜋
3
− 𝜃𝑟
𝛿2 = 𝑚 𝑣. sin 𝜃𝑟
𝛿0 = 1 − 𝛿1 + 𝛿2
Vx
Vy
δ2Vy
VREF
δ1Vx
θr
SVM Inductor

7
Timing Diagram of Switching Vectors
δ1
δ1+δ2
T1
2
T0
TS
Vx
Vy
V0
Triangular Wave (Carrier)
Zero Vector
Active Vectors
Time
Duty
Cycle
T2
2
T2
2
T1
2
SVM in Symmetric switching

8
Digital Implementation of SVM- Block Diagram
Reference
Vector Angle
Triggering
Pulses
Duty Cycle
Calculation
Time Period
Calculation
Internal
Theta
Gating
Pattern
Switching
State Vectors
Sector
Number
v
3 Phase AC
Voltage
DC Voltage
Source
Voltage
Source
Inverter
v

9
Stages of Implementation
1
3
2
Reference Vector has magnitude constant but angle alone changes, thus a counter is used to
generate the change in angle from 0 to 360 degrees
Sector Number or the sector in which the Ref. Vector is currently in, is identified by comparing
the value of the counter with the angles of the sectors and passed on to the next block
1
2
3
5
64
Va
Vb
Vc
V1(100)
V2(110)V3(010)
V4(011)
V5(001) V6(101)
Vx
Vy
δ2Vy
VREF
δ1Vx
θr
The vector pair enclosing that sector are then identified, i.e. the Switching
state vectors that govern the output AC in that sector

10
4
Based on the Switching state Vector , the corresponding Gating Pattern, or the
indication of which switches of the Inverter are to be turned ON are generated.
Consider a switching state vector V1(100) whose sequence (100011) is treated as a
binary number, 1000112 and is represented by its equivalent decimal value, 3510
Switching
Vectors
Decimal
Equivalent
V1 35
V2 49
V3 21
V4 28
V5 14
V6 42

11
6
In order to calculate the duty cycles, Internal ϴ , i.e. the angle the reference
vector makes within a sector, this is done as follows
The Carrier Wave, for modulation, is a triangular wave of high frequency
5

12
7
With all the required parameters available, the duty cycles for each switching
vector are calculated.
Sin ϴ Calculation using CORDIC Sin-cos block
Duty Cycle Calculation

13
8
Finally the appropriate Gating pattern is generated and using ‘Bit slice’ option, individual bits of
the gating pattern are obtained and applied to the switches of the Voltage Source Inverter
Important Parameter
Explicit Period : The time period of the operations of the digital circuits are determined by the value
of the explicit period, which is given by :
𝑅𝑒𝑞𝑢𝑖𝑟𝑒𝑑 𝑇𝑖𝑚𝑒 𝑃𝑒𝑟𝑖𝑜𝑑 =
𝑀𝑎𝑥 𝐶𝑜𝑢𝑛𝑡 𝑣𝑎𝑙𝑢𝑒
𝑅𝑒𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛
× 𝐸𝑥𝑝𝑙𝑖𝑐𝑖𝑡 𝑇𝑖𝑚𝑒 𝑃𝑒𝑟𝑖𝑜𝑑
Where ‘x’ bits give the maximum digital value that can be accounted in the circuit and ‘y’ binary point
bits provide the necessary resolution for the transition of digital values
Thus for a given required digital value, resolution and time period of operation, the explicit period is
calculated and entered in the parameters of the appropriate block of the Xilinx Blockset.

14
Digital Implementation of SVM using Xilinx Blockset
Shown above is the working layout that is used to implement the SVM algorithm in Matlab using
the Xilinx Blockset of Simulink

Simulation Results
The simulation results not only proved the success of Space Vector Modulation (SVM) in producing
sinusoidal AC with minimal harmonic distortion but also confirmed the proper functioning of the
digital implementation of the SVM

16
Real Time Implementation of SVM
Field Programmable Gate Array (FPGA), one of the most recent additions to the family of
Logic Devices, is highly user reconfigurable and possess very high processing speeds. Thus
apt for implementation of SVM algorithm.
Since the FPGA is capable of generating digital output
pulses, it is used to generate the triggering pulses to
ON/OFF the switches of the Inverter as per the SVM
algorithm.
FPGA uses Very high-speed integrated circuits
Hardware Descriptive Language (VHDL) coding
System Generator/ Xilinx Blockset
These are two utilities present in Matlab, similar to the Powergui and
SimPower blockset. With the help of the Xilinx Blockset, digital circuits can be
simulated and the System Generator Converts that circuit into its equivalent
VHDL code

Using the System Generator (SG) utility, the digital logic simulated using the Xilinx Blockset of Matlab
Simulink is converted into the VHDL code. This code is compiled in Xilinx ISE Design Suite to generate
the ‘bit file’ which is loaded into the FPGA using the software Adept. Thus the FPGA now is capable
of generating the triggering pulses for the switches of the VSI to generate sinusoidal AC from DC.
Current and Voltage waveform as observed on the
Agilent DSO on real time implementation of SVM
using FPGA
Real Time Implementation of SVM

On application of the 3- Φ output voltage of the inverter to the induction motor load,
rated at 1HP, 1.8A, 50Hz, 1430 RPM, the following results were tabulated.
Comparison of Results
Comparison of Results
Matlab Simulation Practical
Implementation
Line-to-Line
Voltage (Peak)
415 V 400V
Line Current (rms) 1.1 A 0.8A
Frequency 50 Hz 50.0 Hz

Advantages of Using FPGA
• Economically, FPGAs are lot more cheaper than DSP processors
• Easily reconfigurable
• Comparatively more user friendly in terms of programming and implementation, which
is further more simplified with the help of Xilinx Blockset and System Generator of
Matlab Simulink
• FPGAs are very high processing power to size ratio, i.e. even small FPGA boards are
capable of high Processing capabilities.
Advantages of Space Vector Modulation
• Very low Value of harmonic distortion (THD) can be achieved in the output waveform
• Robust Dynamic response
• SVM enables more efficient use of the DC Voltage
Space Vector Modulation provides excellent output performance, optimized efficiency,
and high reliability compared to similar inverters with conventional Pulse Width
Modulation.

References
• Dorin O. Neacsu, "Space Vector Modulation-An Introduction", Proc.IEEE/IECON, 2001,
pp 1583-1592.
• Application Guidelines- Integrating Xilinx System Generator and Simulink HDL Coder.
• B.K.Bose, 1986, Power Electronics and AC Drives, Prentice-Hall.
• Jin-Woo-Jung, (2005), "Space Vector PWM Inverter", DECE, The Ohio State University.
• System Generator for DSP Getting Started Guide.
• www.mathworks.com
• Harrison, C.G.; Jones, P.L.;, "Xilinx FPGA design in a group environment using VHDL and
synthesis tools," Digital System Design Using Synthesis Techniques (Digest No: 1996-
029), IEE Colloquium On , vol., no., pp.5/1-5/4, 15 Feb 1996.

Thank you and a pleasant evening to all
“True knowledge exists in knowing that we know nothing.”
- Socrates
“Learning will be my life, my tombstone will be my diploma”
- Eartha Heart

Paper 33-FPGA Triggered Space Vector Modulated Voltage

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