Page 1 of 7
2015-IACC-0418
An Optimized Algorithm for SVPWM Based on Three-Phase Stationary Frame
Weiyi Zheng
Zhiyong Zeng
Huan Yang
Zhejiang University
Hangzhou, 310027, China
weiyizheng@zju.edu.cn
Zhejiang University
Hangzhou, 310027, China
zhyzeng@zju.edu.cn
Zhejiang University
Hangzhou, 310027, China
yanghuan@zju.edu.cn
Chong Zhu
Qingwei Yuan
Rongxiang Zhao
Zhejiang University
Hangzhou, 310027, China
zhuchong@zju.edu.cn
Zhejiang University
Hangzhou, 310027, China
yuanqingwei@zju.edu.cn
Zhejiang University
Hangzhou, 310027, China
rongxiang@zju.edu.cn
Abstract--The conventional space vector pulse width modulation (SVPWM), including coordinate transformation, sector
identification, and active time calculations of voltage vectors,
needs lots of complex irrational number operations such as trigonometric function calculations, which introduces challenges for
real-time digital control chips. Considering the shortcomings of
traditional algorithm, this paper presents an optimized algorithm based on three-phase stationary frame. In the proposed
algorithm, the reference voltage vector is projected onto the
three-phase stationary frame firstly, then a unified formula is
obtained by utilizing the principle of symmetric, where only
normal mathematical operations of modulation wave is required.
With the unified formula, the duty ratios of three bridge-arms
will be calculated directly. Comparing with conventional algorithm, the proposed algorithm is more suitable for digital system owing to the characteristic of easier programming, faster
operating speed, and higher real-time ability. The simulation
and experimental results show the validity and feasibility of the
proposed algorithm.
Index Terms--real-time, space vector pulse width modulation
(SVPWM), symmetric, three-phase stationary frame, unified
formula.
I.
INTRODUCTION
Due to the high real-time control capability and flexible
control algorithm, digital control chips have been widely
used in the control systems of power converters [1], [2].
Compared to conventional sinusoidal pulse width modulation
(SPWM), space vector pulse width modulation (SVPWM)
possesses a better characteristic, such as higher DC voltage
utilization ratio, smaller switching losses, lower harmonics,
and easier digital implementation [3]-[5]. Thus, the SVPWM
strategy is becoming the mainstream of various PWM technologies in the digital control systems.
Usually, the switching frequency is required as high as
possible to ensure the locus of the voltage space vector closer
to a circle, reducing the harmonic of PWM signals. But, due
to the restrictions of manufacturing processes and material
This work was supported by the National Key Basic Research Program
of China (973 Program) under Grant 2013CB035600.
properties, the switching frequency for high voltage and
power semiconductor is generally between a few kHz to tens
kHz, which requires a system with high real-time performance. However, during the realization process of conventional SVPWM modulation, a lot of irrational number operations, such as trigonometric function and square root, are
applied to coordinate transformation, sector identification,
along with the active time operations of voltage vectors. The
complex and redundant calculation process of conventional
SVPWM algorithm, not only takes a large number of CPU
resources, but also increases the control time delay, which
seriously affect the dynamic performance of the system with
high switching frequency [6]-[8]. Therefore, how to simplify
the conventional algorithm is becoming more and more important. Reference [9] proposed a novel SVPWM algorithm
based on non-orthogonal coordinate system to avoid the traditional sector identification process. Although the algorithm
was simplified, a large number of trigonometric functions
still existed, reducing the system operation precision. In [10],
the proposed simplified algorithm utilized line-to-line voltage
to express the active time equation of voltage vectors. Reference [11] given the expressions for duty ratios of three
bridge-arms directly by calculating the components of reference voltage vector in a special coordinate system which reduced the six sectors in the traditional SVPWM modulation
to three. In [12], the switching time of three bridge-arms was
obtained directly by the components of reference voltage
vector in two-phase stationary coordinate system. Due to the
absence of the complicated trigonometric function and square
root operations, this kind of methods streamlined the procedure code. However, the look-up table and the sector identification are still required, reducing the real-time performance
of the system accordingly. In addition to the selection of reference frame, the synthesis method of voltage space vector
will also affect the simplification degree of algorithm. The
distinction between all kinds of synthesis methods is mainly
reflected by the selection and distribution of zero-voltage
vector. The seven-segment switching sequence and fivesegment switching sequence are the most commonly used
methods. Considering the advantages and disadvantages of
978-1-4799-8374-0/15/$31.00 © 2015 IEEE
Authorized licensed use limited to: WESTERN DIGITAL. Downloaded on June 20,2023 at 02:02:46 UTC from IEEE Xplore. Restrictions apply.
2015-IACC-0418
both methods, the seven-segment switching sequence and the
up-down-count mode are used to generate the symmetrical
PWM signals, decreasing the harmonica and switching losses
[13], [14].
This paper proposes an optimized algorithm for SVPWM
based on three-phase stationary frame. According to the geometric relationship reflected in the space vector hexagon,
the duty ratios of adjacent voltage space vectors for each sector are calculated respectively by the components of reference voltage vector in three-phase stationary frame. Then, the
synthesis method of seven-segment switching sequence is
utilized to derive the duty ratios of three bridge-arms for each
sector. Finally, a unified formula based on the three-phase
stationary frame is presented for SVPWM modulation. The
optimized algorithm skips over the procedure of the coordinate transformation, the sector identification, and the active
time calculations of voltage vectors existing in conventional
SVPWM algorithm. The proposed method calculates the duty
ratios of three bridge-arms directly by the simple addition
and subtraction operations, as well as a small amount of multiplications. Additionally, the complex irrational number operations are absented, improving the real-time ability. Finally,
the simulation and experimental results show the effectiveness of the proposed algorithm.
Page 2 of 7
2 sa − sb − sc
­
Vdc
°uan =
3
°
2 sb − sa − sc
°
Vdc
®ubn =
3
°
°
2 sc − sa − sb
Vdc
° ucn =
3
¯
Substituting eight combinations of switching states into
(1), and then mapping the obtained phase voltage of AC side
into a complex plane, a voltage space vector distribution diagram is shown in Fig. 2. With all possible combination of the
switch states, eight basic vectors, including two zero vectors
(V0 and V7) and six non-zero vectors (V1 to V6), are derived
and show in Fig. 2, where the eight basic vectors are located
in the vector plane symmetrically.
ȕ
V3(010)
V2(110)
II
ur
III
I
V0(000)
V4(011)
ș
TV1
V7(111)
IV
II.
VECTOR PLANE AND SYNTHESIS PRINCIPLE OF SVPWM
The topological structure of the digitally controlled threephase PWM rectifier is shown in Fig. 1. In the process of
building its mathematical model, utilizing sa, sb, sc to represent the switching state of three bridge-arms respectively.
When s=1, the switching device in upper arm is turned on
and that in lower arm is turned off, when s=0, the upper arm
switching device is turned on and the lower arm switching
device is turned off.
(1)
TV2
V1(100)
Į
VI
V
V5(001)
V6(101)
Fig. 2. Structure of the digitally controlled three-phase PWM rectifier
The amplitude of all the six non-zero vectors shown in
Fig. 2 is 2Vdc/3. And, a regular hexagon is built by connecting the six vertexes, and the regular hexagon denotes the
achievable modulation range of SVPWM strategy. The inscribed circle in the hexagon is the limitation for the linear
modulation. Usually, the hexagonal region is divided into six
sectors by the six non-zero vectors, where the vector V1 is
assigned to sector I, vectors V2 and V3 are assigned to sector
II, vector V4 is assigned to sector III, vectors V5 and V6 are
assigned to sector V. For the reference voltage ur, it can always be synthetized by the two adjacent basic space vectors.
When ur lies on the position shown in Fig. 2, it is synthetized
by vectors V1 and V2. According to the volt-second balance
principle, the following expression is obtained:
ur Ts = V1TV 1 + V2TV 2
(2)
where, Ts is the PWM switching cycle, TV1 and TV2 are the
active time in a switching cycle Ts for vectors V1 and V2 respectively.
Fig. 1. Structure of the digitally controlled three-phase PWM rectifier
According to the structure shown in Fig. 1, the expression
of three-phase voltage of AC side can be obtained as (1).
In addition, (2) can be rewritten as (3) in the form of duty
ratio.
ur = dV 1V1 + dV 2V2
978-1-4799-8374-0/15/$31.00 © 2015 IEEE
Authorized licensed use limited to: WESTERN DIGITAL. Downloaded on June 20,2023 at 02:02:46 UTC from IEEE Xplore. Restrictions apply.
(3)
Page 3 of 7
2015-IACC-0418
where, dV1 and dV2 are the duty ratios for vectors V1 and V2,
respectively.
III. DUTY RATIOS OF ACTIVE VECTORS BASED ON THREEPHRASE STATIONARY FRAME
In accordance with the sector division manner shown in
Fig. 2, the reference voltage is decomposed into uĮ and uȕ in
the Į-ȕ coordinate system, then, a novel section identification
approach based on three-phase stationary frame is developed.
The purpose of the procedure is not to identify which sector
that the ur lies on, it is to estimate roughly that whether the
expressions for the duty ratios of active vectors are correct or
not, and also provides the inductive basis for the derivation
of the unified formula for the duty ratios of three bridge-arms.
According to the geometric relationship, it can be found
that the conventional judgment condition can be replaced by
judging the component uȕ whether it is positive or negative
and also the value range of cot ș. Assuming:
­ x = uβ
°
® y = uα
°
uβ
¯
(4)
Therefore, the traditional sector division basis based on
variables x and y can be displayed as Table I.
Sector
TABLE I
SECTOR DIVISION BASIS
x
[ 0, + ∞ )
2
( 0, +∞ )
ª
3
3º
,
«−
»
3
3
¬
¼
3
[ 0, + ∞ )
§
3·
¨¨ − ∞ , − 3 ¸¸
©
¹
4
(−∞ , 0 )
§ 3
·
, +∞ ¸¸
¨¨
3
©
¹
5
(−∞ , 0 )
ª
3
3º
,
«−
»
3
3
¬
¼
6
(−∞ , 0 )
§
3·
¨¨ − ∞ , −
¸
3 ¸¹
©
­OB = dV 1V1
®
¯ BA = dV 2V2
1
­
°OB = uα − 3 uβ
°
®
° BA = 2 u
β
°̄
3
uan > ubn ≥ ucn
ubn ≥ uan ≥ ucn
ubn ≥ ucn > uan
ucn > ubn > uan
ucn ≥ uan ≥ ubn
uan > ucn > ubn
(6)
According to the geometric relationship shown in Fig. 3,
the expression about OB, BA and uĮ, uȕ can be obtained easily as (7).
Substituting the Clark transformation formula to Table I,
the criterion of sector division based on three-phase stationary frame can be expressed as (5).
­ Sector 1:
° Sector 2 :
°
°° Sector 3 :
®
° Sector 4 :
° Sector 5 :
°
°̄ Sector 6 :
Fig. 3. The synthesis principle of voltage space vector
The physical meanings of segments OB and BA displayed
in Fig. 3 are the active time of vectors V1 and V2 respectively.
Definition:
y
§ 3
·
, +∞ ¸¸
¨¨
© 3
¹
1
Equation (5) provides a more convenient method for sector identification of the conventional SVPWM algorithm,
which can be realized just by comparing the values of expected three-phase voltage without the traditional coordinate
transformation process. However, in this paper, it is only to
estimate roughly the correctness of the expressions for the
duty ratios of active vectors, and also provide the inductive
basis to the derivation of the unified formula for SVPWM.
After determining the sector where the given voltage
space vector ur locates with the method described above, the
duty ratios of active vectors based on three-phase stationary
frame can be derived from (3). Taking sector I for example,
the synthesis principle of voltage space vector are shown in
Fig. 3.
(5)
(7)
Substituting the Clark transformation formula to the simultaneous equations (6) and (7), the expression for duty ratios
of active vectors based on three-phase stationary frame can
be received as (8).
1 ∗
­
∗
°° dV 1 = 2 ( uan − ubn )
®
°d = 1 ( u ∗ − u ∗ )
°̄ V 2 2 bn cn
(8)
where, u*an, u*bn, and u*cn are the per-unit values for expected
three-phase voltage, and the reference value is Vdc/2.
The positive values of dV1 and dV2 denote the condition
978-1-4799-8374-0/15/$31.00 © 2015 IEEE
Authorized licensed use limited to: WESTERN DIGITAL. Downloaded on June 20,2023 at 02:02:46 UTC from IEEE Xplore. Restrictions apply.
2015-IACC-0418
u*an>u*bn>u*cn. In addition, the positive value of the dV1 and
the zero value of dV2 indicate the situation of u*an>u*bn=u*cn.
Summarizing the conclusions above, the relationship between
u*an, u*bn, and u*cn can be achieved as u*an>u*bn•u*cn, and it is
consistent with the identification of sector I. By parity of reasoning, the duty ratio expressions based on three-phase stationary frame for other sectors are shown in Table II, and
they all accord with the criterion of sector division.
TABLE II
DUTY RATIOS OF ACTIVE VECTORS FOR EACH SECTOR
Duty1
Duty2
Sector
1(V1,V2)
2(V2,V3)
3(V3,V4)
4(V4,V5)
5(V5,V6)
6(V6,V1)
1 ∗
( uan − ubn∗ )
2
1 ∗
( uan − ucn∗ )
2
1 ∗
( ubn − ucn∗ )
2
1 ∗
( ubn − uan∗ )
2
1 ∗
( ucn − uan∗ )
2
1 ∗
( ucn − ubn∗ )
2
TV 2 TV 1 TV 0
2 2
2
(11)
Then, combining with (5), (11) can be rewritten to a unified format as follow:
According to the duty ratio expressions of active vectors
deduced in the previous section, the duty ratios of three
bridge-arms based on three-phase stationary frame can be
derived as follow. Taking sector I for example, when the ur
locates in linear modulation region, the constraint shown as
(9) must be satisfied.
(9)
Where, the remaining time of a switching cycle Ts is
complemented by zero vectors V0 and V7. Considering the
harmonic, switching losses and other factors, the symmetric
characteristic is applied to generate the pulse sequences,
where the zero vector V0 is activated in both the initial state
and end state, and the zero vector V7 is also inserted into the
midpoint of the given voltage space vector. The calculations
for the active time of vectors V0 and V7 are obtained and
shown as:
1
(1 − dV 1 − dV 2 ) Ts
2
TV 7
1 1 ∗
­
∗
°d a = 2 + 4 ( uan − ucn )
°
1 1 ∗
°
∗
∗
® d b = − ( uan − 2ubn + ucn )
2
4
°
1 1 ∗
°
∗
° d c = 2 − 4 ( uan − ucn )
¯
IV. UNIFIED FORMULA FOR SVPWM STRATEGY BASED ON
SYMMETRIC PULSES
TV 0 = TV 7 =
TV 0 TV 1 TV 2
2 2 2
Fig. 4. The seven-segment switching sequence for sector I
1 ∗
( ubn − ucn∗ )
2
1 ∗
( ubn − uan∗ )
2
1 ∗
( ucn − uan∗ )
2
1 ∗
( ucn − ubn∗ )
2
1 ∗
( uan − ubn∗ )
2
1 ∗
( uan − ucn∗ )
2
TV 1 + TV 2 ≤ Ts
Page 4 of 7
(10)
where, TV0 and TV7 are the active time in a PWM switching
cycle Ts for vectors V0 and V7 respectively.
Therefore, the seven-segment switching sequence can be
achieved as shown in Fig. 4.
From Fig. 4 and equations (8) and (10), the expressions
for duty ratios of three bridge-arms based on three-phase
stationary frame can be easily obtained as (11).
1 1 ∗
1 ∗
­
∗
°d max = 2 − 4 ( umax + umin ) + 2 umax
°
1 1 ∗
1 ∗
°
∗
® d mid = − ( umax + umin ) + umid
2 4
2
°
1 1 ∗
1 ∗
°
∗
° d min = 2 − 4 ( umax + umin ) + 2 umin
¯
(12)
Analogizing the above derivation of sector I, it is easily to
find that the duty ratios of three bridge-arms for all the other
sectors can be expressed in the same form of (12). Consequently, the unified formula for SVPWM strategy based on
three-phase stationary frame is obtained as (13).
1 1 ∗
+ u x + M , ( x = a, b, c )
2 2
1 ∗
∗
M = − ( umax
+ umin
)
4
dx =
(13)
In accordance with (13), it can be observed that the duty
ratios of all the three bridge-arms include a common component M. It just needs to perform simple addition and subtraction operations, as well as a small amount of multiplications
on the maximum and minimum values of three-phase voltage,
eliminating the complex and redundant irrational number
operations. Hence, the optimized algorithm based on threephase stationary frame is more suitable for the high-precision
real-time control system, accounting of the easier programming and the faster operating speed.
The PWM pulse sequences corresponding to the duty ratios calculated from (13), are generated on the basis of Fig. 5,
which is utilizing the intersection of triangular carrier wave
and modulation wave as the switching time to toggle the sta-
978-1-4799-8374-0/15/$31.00 © 2015 IEEE
Authorized licensed use limited to: WESTERN DIGITAL. Downloaded on June 20,2023 at 02:02:46 UTC from IEEE Xplore. Restrictions apply.
Page 5 of 7
2015-IACC-0418
tus of PWM signals. Wherein, the period of the unipolar
isosceles triangular carrier wave is Ts, and the amplitude is
Ts/2. The modulation waves Taon, Tbon and Tcon are the switching time during a PWM switching cycle of the upper arms
switching devices, which can be calculated by (14) and updated at the initial time of each PWM switching cycle.
Txon
T
= s (1 − d x ) , ( x = a, b, c )
2
the SVPWM strategy can be equivalently implemented by the
typical SPWM strategy. Nonetheless, the SVPWM strategy
not only achieves a boost of DC voltage utilization ratio, and
also avoids the phase synchronization problem of zerosequence component in the improved SPWM strategy.
VI. SIMULATION AND EXPERIMENT VERIFICATION
(14)
Simulation Verification in MATLAB/Simulink
To verify correctness of the optimized algorithm proposed in this paper, a 5-kVA three-phase PWM rectifier simulation model is built in MATLAB/Simulink platform, and
the system parameters are given in Table III.
A.
Rs
0.1ȍ
Ua/Ub/Uc
110V
Fig. 5. The Schematic diagram of generating the PWM pulse sequences
In digital system, the interrupt function of the ePWM
module and also the up-down-count mode are applied into
the generation of the symmetric PWM pulse sequences. Writing the switching time of each switching device to the countcompare register, when the value in the time-base counter is
equal to the active count-compare register, toggling the
ePWM output (low output signal will be forced high, and a
high signal will be forced low). Through this process, the
required PWM pulse signals can be generated to trigger the
full-controlled switching devices.
V.
THE ESSENTIAL RELATIONSHIP BETWEEN SVPWM AND
SPWM
In order to explore further the relation and difference between SVPWM strategy and SPWM strategy, rewriting the
united formula for SVPWM strategy to the form of SPWM
strategy, that is to calculate the equivalent modulation function corresponding to triangular carrier wave for SVPWM
strategy. According to the regular sampling method, the relationship between the duty ratio of each bridge-arm and the
expected voltage of the same arm is shown as (15).
u x∗ = 2d xspwm − 1, ( x = a, b, c )
TABLE III
THE SYSTEM PARAMETERS
L
3mH
C
2000ȝF
Vdc
400V
Ts
10kHz
The simulation results are shown in Figs. 6, 7 and 8. Fig.
6 displays the comparison between the modulation waveform
and the filtered voltage waveform of AC side in case of
phase-A. It can be observed that the two waveforms match
with each other. Furthermore, analyzing the fundamental
component of phase-A real voltage through the FFT window,
it can be found that the valid value is 109.4V, and it also has
a phase angle of -7.6°, which means lagging the phase-A grid
voltage 7.6°. The data observed from FFT window is consistent with the estimated value calculated by the system parameters given in Table III. And, the duty ratios waveform of
three bridge-arms shown in Fig. 7 is consistent with the
standard saddle waveform obtained from the conventional
SVPWM algorithm. Fig. 8 shows the initial status and the
stable status of the three-phase current and the DC voltage,
which indicates that the simulation model achieves the rectification function with an excellent dynamic and low harmonics. Therefore, according to the above analysis and comparison of the simulation results, the correctness of the optimized
algorithm is verified.
(15)
So, the latent modulation function corresponding to triangular carrier wave for SVPWM strategy is given as (16).
u x∗svpwm =u x∗ + 2M , ( x = a, b, c )
(16)
From (16), it can be found that comparing with the modulation function for SPWM strategy, there is one more zerosequence component 2M in SVPWM strategy, it is equivalent
to inject zero-sequence component to the three-phase sinusoidal modulation wave of SPWM strategy. In other words,
Fig. 6. The expected voltage and the real voltage of phase-A
978-1-4799-8374-0/15/$31.00 © 2015 IEEE
Authorized licensed use limited to: WESTERN DIGITAL. Downloaded on June 20,2023 at 02:02:46 UTC from IEEE Xplore. Restrictions apply.
2015-IACC-0418
Page 6 of 7
1.0
0.8
0.6
0.4
0.2
0.0
0.03
Fig. 7. The duty ratios of three bridge-arms
0.04
Time (s)
0.06
0.05
Fig. 9. The duty ratios of three bridge-arms
30
20
10
0
-10
-20
-30
-0.02
(a) Three-phase input current
0.00
0.02
Time (s)
0.04
0.06
0.04
0.06
(a) Three-phase input current
420
400
380
360
340
-0.02
0.00
0.02
Time (s)
(b) DC voltage
(b) DC voltage
Fig. 8. Simulation results
Fig. 10. Experimental results
Experiment Verification
In order to further verify the feasibility, the optimized algorithm is applied to a 5-kVA three-phase PWM rectifier
experimental platform, which is implemented on a 16-bit
DSP TMS320F2808 development board, and the system parameters are given in Table III.
Fig. 9 shows the three-phase duty ratios waveform, the
standard saddle characteristic is consistent with the simulation result. And the initial status and the stable status of the
three-phase current and the DC voltage shown in Fig. 10 indicate that the experimental platform achieves the rectification function with an excellent dynamic and low harmonics.
The experimental results shown in Figs. 9 and 10 satisfy the
B.
978-1-4799-8374-0/15/$31.00 © 2015 IEEE
Authorized licensed use limited to: WESTERN DIGITAL. Downloaded on June 20,2023 at 02:02:46 UTC from IEEE Xplore. Restrictions apply.
Page 7 of 7
2015-IACC-0418
required operating characteristic of the three-phase PWM
rectifier, which verify the feasibility of the optimized algorithm for SVPWM strategy.
VII.
[14] D. A. Grant, M. Stevens, and J. A. Houldsworth, "The effect of word
length on the harmonic content of microprocessor-based PWM
waveform generators," IEEE Trans. Industry Applications, vol. 21, no.
1, pp. 218-225, Jan. 1985.
CONCLUSION
In this paper, an optimized algorithm of SVPWM strategy
based on three-phase stationary frame is proposed for the
digital control system with high-precision and real-time characteristic. The proposed algorithm skips over the procedure
of coordinate transformation, sector identification, and active
time calculations of voltage vectors existing in conventional
SVPWM algorithm, and calculates the duty ratios of three
bridge-arms in three-phase stationary frame directly without
the complex irrational number operations like trigonometric
function and square root operations. It streamlines the algorithm, accelerates the operating speed, and improves the realtime ability, making it easier for the implementation of digital
systems. Finally, the correctness and the feasibility of the
proposed algorithm have been verified through the simulation
analyses and experimental tests.
REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
C. Buccella, C. Cecati, and H. Latafat, "Digital control of power
converters - a survey," IEEE Trans. Industrial Informatics, vol. 8, no. 3,
pp. 437-447, Aug. 2012.
S. B. Leeb, "Foreword special issue on digital control in power
electronics," IEEE Trans. Power Electronics, vol. 18, no. 1, pp. 293,
Jan. 2003.
J. Holtz, "Pulsewidth modulation - a survey," IEEE Trans. Industrial
Electronics, vol. 39, no. 5, pp. 410-420, Oct. 1992.
V. Vlatkovic and D. Borojevic, "Digital-signal-processor-based control
of three-phase space vector modulated converters," IEEE Trans.
Industrial Electronics, vol. 41, no. 3, pp. 326-332, Jun. 1994.
J. Bhavani, J. Amarnath, and D. S. Rayudu, "Generalized PWM
algorithm for VSI fed induction motor drives using the only sampled
reference phase voltages," in 2012 IEEE 5th India International Conf.
Power Electronics, pp. 1-5.
D. W. Chung, J. S. Kim, and S. K. Sul, "Unified voltage modulation
technique for real-time three-phase power conversion," IEEE Trans.
Industry Applications, vol. 34, no. 2, pp. 374-380, Mar./Apr. 1998.
Y. Wang, M. Guan, and S. H. Shen, "Study on the control strategy of
novel voltage space-vector for three-phase bipolar mode rectifier," in
2007 2nd IEEE Conf. Industrial Electronics and Applications, pp.
1740-1745.
C. L. Chen, C. M. Lee, R. J. Tu, and G. K. Horng, "A novel simplified
space-vector-modulated control scheme for three-phase switch-mode
rectifier," IEEE Trans. Industrial Electronics, vol. 46, no. 3, pp. 512516, Jun. 1999.
S. C. Fang, B. Zhou, D. Li, and F. S. Cheng, "A novel space-vector
PWM algorithm for PMSM drive systems," in 2009 IEEE International
Conf. Industrial Technology, pp. 1-5.
H. Liu, X. N. Xiao, and Y. H. Xu, "Study on the simplified algorithm of
space vector PWM," in 2003 The Fifth International Conf. Power
Electronics and Drive Systems, pp. 877-881.
T. W. Yu, R. X. Ni, X. D. Wang, and B. Zhang, "A simplified SVPWM
algorithm and its application simulation on motor control," in 2010
International Forum on Strategic Technology, pp. 156-160.
C. J. Zhan, Y. D. Han, and M. C. Wong, "The 3 phase PWM voltage
source reversible rectifier based on a novel space vector control
method," in Proc. 1998 International Conf. Power System Technology,
pp. 668-671.
A. V. Peterchev and S. R. Sanders, "Quantization resolution and limit
cycling in digitally controlled PWM converters," IEEE Trans. Power
Electronics, vol. 18, no. 1, pp. 301-308, Jan. 2003.
978-1-4799-8374-0/15/$31.00 © 2015 IEEE
Authorized licensed use limited to: WESTERN DIGITAL. Downloaded on June 20,2023 at 02:02:46 UTC from IEEE Xplore. Restrictions apply.