Journal of Engineering Sciences, Assiut University, Vol. 39, No. 4, pp.871-884, July 2011.
IMPLEMENTATION OF SPACE VECTOR-PWM FOR
DRIVING TWO LEVEL VOLTAGE SOURCE INVERTERS
Mahmoud Gaballah, Mohammed El-Bardini, Soliman
Sharaf and Mohammed Mabrouk
Dept. of industrial electronics & control engineering
Faculty of Electronic Engineering, Minufiya University, 32852, Egypt
(Received June 11, 2011 Accepted June 25, 2011)
This paper presents an implementation of space vector pulse width
modulation signal generation for driving three phase voltage source
inverter. The SVPWM technique gets the PWM switching times for
the inverter legs directly from the sampled amplitudes of the
reference phase voltages. The SVPWM switching strategy is based on
the right aligned sequence. This method is much simpler and more
executable than conventional means without look-up tables or
complex
logical
judgments.
The
SVPWM
scheme is
modeled/simulated using MATLAB SIMULINK software package,
and experimentally implemented / verified on the low cost microchip
8 bit microcontroller PIC16F747 platform. The experimental results
are presented for three phase two-level inverter followed by three
phase output LC filter.
I. INTRODUCTION
Voltage source inverter is nowadays commonly used to synthesize AC output
voltage and frequency from a constant DC voltage via Pulse width modulation
control technique. Nowadays many industries are based on voltage source
inverters such as motor drives, Uninterruptible power supplies (UPS’s),
Frequency converters, AC-AC PWM mode static voltage stabilizer, and active
filters [1- 2]. Pulse-width modulation (PWM) techniques have been studied
extensively during the last few decades. A large variety of methods different in
concept and performance have been developed to achieve the following aims:
wide linear modulation range, less switching losses, less harmonic distortion
(THD), easy implementation, and less computation time [3- 4].
Several modulation strategies differing in concept and performance have
been developed. Space vector modulation techniques have been increasingly used
in last decade to generate the inverter output voltage(s) because they allow
reducing commutation losses and/or the harmonic content of output voltage, and
to obtain higher amplitude modulation indexes if compared with conventional
Sinusoidal PWM techniques. Moreover, space vector modulation techniques can
be easily implemented in digital processors. In SVPWM scheme the reference
voltage space phasor is realized by switching between the nearest three inverter
voltage space phasors which form the sector in which the reference vector
resides. Each of the combined inverter voltage space phasor is realized by
switching a combination of the individual inverter voltage space vectors [5].
871
872
Mahmoud Gaballah, Mohammed El-Bardini, Soliman Sharaf ,.
A large variety of methods have been developed to implement the
SVPWM for voltage source inverters. In general the SVPWM implementation
involves the following steps: (a) sector identification in which the instantaneous
reference space vector lies (b) mapping this sector to an appropriate sector in the
inner hexagon through coordinate transformations (c) determination of the
inverter vector switching times (d) selecting appropriate individual vectors using
switching sequence tables [6-7]. The sector identification can be done by
coordinate transformation [8- 9- 10] or by repeated comparison of the three phase
reference voltages [6- 11]. The lookup tables can be used for determining the
switching vectors in optimum switching sequence [12]. The calculation of the
duration of the switching vectors can be simplified by mapping the sector of the
multilevel inverter to a corresponding sector of the two-level inverter [13- 14].
Another SVPWM method using the principle of equivalence with SPWM can
generate the SVPWM signals directly from the instantaneous reference phase
voltages for multilevel inverters without using lookup tables [15- 16]. The
inverter leg switching times are directly obtained from the instantaneous sampled
reference phase voltages and the inverter switching vectors are automatically
generated.
This paper aims to presents a low cost implementation of space vectorPWM signal generation technique in which the PWM switching times for the
inverter legs are directly derived from the sampled amplitudes of the reference
phase voltages. The SVPWM switching strategy is based on the right aligned
sequence .The switching vectors for the inverter is derived using a simple digital
logic which does not involve any complex computations and hence the
implementation time is reduced. The space vector PWM scheme is modeled /
simulated using MATLAB SIMULINK software package, and experimentally
implemented / verified on the low cost microchip PIC microcontroller
PIC16F747 platform. The experimental results are presented for three phase twolevel inverter followed by three phase LC filter.
II. THREE-PHASE INVERTER
Voltage source inverter (VSI) is the most widely utilized device with power
ratings ranging from fractions of a kilowatt to megawatt level and basically used
within motor drives, Uninterruptable power supplies and active filters. The VSI
consists of six power semiconductor switches with anti-parallel feedback diodes.
It converts a DC voltage to three phase AC voltages with controllable frequency
and magnitude. In the widely utilized Pulse Width Modulation (PWM) methods,
the inverter output voltage approximates the reference value through high
frequency switching for the six power semiconductor switches. The circuit model
of a typical two-level inverter is shown in Fig.1.
S1 to S6 are the six power switches that shape the output, which are
controlled by the variables a, à, b, b̀ , c, and c̀ . It is assumed that S1 and S2, S3,
and S4 as well as S5, and S6 are switched in a complementary way. Thus, there
are only eight possible switching vectors. Therefore, the ON and OFF states of
upper switches S1, S3, and S5 can be used to determine the output voltage. There
are only eight possible switching vectors. Six out of these eight vectors produce a
IMPLEMENTATION OF SPACE VECTOR-PWM FOR …
873
non-zero output voltage and are known as non-zero switching states, and the
remaining two vectors produce zero output voltage and are known as zero
switching states. Table.1 lists all the possible switching vectors and the respective
line to line / line to neutral voltages.
Fig.1. Two-level voltage source inverter
Table1. Possible switching vectors, phase voltage, and output line to line voltage
Switching
Pole voltage
Line Voltage
vectors
a b c
0 0 0
0
0
0
0
0
0
1 0 0
2/3
-1/3 -1/3
1
0
-1
1 1 0
1/3
1/3
-2/3
1
0
-1
0 1 0 -1/3
2/3
-1/3
-1
1
0
0 1 1 -2/3
1/3
1/3
-1
0
1
0 0 1 -1/3 -1/3
2/3
0
-1
1
1 0 1
1/3
-2/3
1/3
1
-1
0
1 1 1
0
0
0
0
0
0
All the respective voltage should be multiplied by VDC
Voltage
vectors
V0
V1
V2
V3
V4
V5
V6
V7
The output voltages of the inverter are composed by these eight switch
states. The six active vectors divide the space vector plane into six equal sized
sectors of 60° with equal magnitudes of
as shown in Fig.2.
In order to get a sinusoidal waveform from the voltage source inverter a
voltage reference
is provided in terms of a revolving space vector. The
magnitude and the frequency of the fundamental component are specified by the
magnitude and frequency respectively of the reference vector. The reference
vector is sampled once in every sub-cycle. The inverter is maintained in different
states for appropriate durations such that an average voltage vector equal to the
sampled reference vector is generated over the given sub-cycle.
874
Mahmoud Gaballah, Mohammed El-Bardini, Soliman Sharaf ,.
Fig.2. Output voltage space of the two-level inverter in dq coordinates.
III. BASIC THEORY OF SPACE VECTOR-PWM
Space vector PWM scheme became more and more popular due to its merits of
high utilization of the DC link voltage, possible optimized output distortion and
switching losses, and compatibility with a digital controller. It has been widely
used for high performance three-phase drive systems. In space vector approach
the voltage reference
is provided in terms of a revolving space vector. The
magnitude and the frequency of the fundamental component are specified by the
magnitude and frequency respectively of the reference vector. The reference
vector is sampled once in every sub-cycle. The inverter is maintained in different
states for appropriate durations such that an average voltage vector equal to the
sampled reference vector is generated over the given sub-cycle. The inverter
states used are the two zero states, and the two active states, whose voltage
vectors are the closest to the commanded voltage vector. For a commanded
vector in sector I, the states 0, 1, 2 and 7 can be used. To generate this vector in
an average sense, the durations for which the active state 1 (T1), the active state 2
(T2), and the two zero states together (TZ) must be applied. The relation between
voltage reference and the durations (T1, T2, and TZ) is obtained from the
following equations:
(1)
(2)
(3)
The division of the duration TZ between the two zero states 0 and 7 is a
degree of freedom in the space vector approach. This division of TZ in a subcycle is equivalent to adding a common-mode component to the 3-phase average
pole voltages.
To implement the SVM algorithm, the following switching rules should
be implemented: (a) The trajectory of Vref should be a circle, (b) only one
switching per state transition, (c) not more than three switching in one TS , (d)
IMPLEMENTATION OF SPACE VECTOR-PWM FOR …
875
The final state of one sample must be the initial state of the next sample. These
rules help in limiting the number of switching actions and hence, there is a
reduction in the switching losses. Also, they maintain symmetry in switching
waveforms at the VSI output to achieve the lower THD. The SVM algorithm
implementation using these switching rules is called Conventional SVM.
In general the Conventional SVPWM implementation involves the
following four steps: (a) sector identification in which the instantaneous
reference space vector lies, (b) mapping this sector to an appropriate sector in the
inner hexagon through coordinate transformations, (c) determination of the
inverter vector switching times, (d) selecting appropriate individual vectors using
switching sequence tables [6-7].
The main advantage of the SVM algorithm when compared to the Sine
PWM algorithm is that it is possible to get line to line voltage amplitude as high
as VDC using the SVM algorithm in the linear operating range for this reason the
Sine PWM generates sinusoidal phase voltages waveforms with 120° phase shift
between them, the resultant line to line voltage is approximately 86.6% of VDC
But, the SVM generates phase voltages have a third harmonic component
superimposed on the fundamental component “ the addition of this harmonic
component is due to the effective usage of inactive states which is not possible in
the Sine PWM ” with 120° phase shift between them, the third harmonic
component is cancelled out in the resultant line to line voltage in such a way that
the resultant line to line voltage is boosted to VDC (100%). Thus, SVM generates
line to line voltage with higher amplitude.
IV. SVPWM SIGNAL GENERATION USING ONLY THE
INSTANTANEOUS REFERENCE PHASE AMPLITUDES
In the sinusoidal PWM scheme for two-level inverter each reference phase
amplitudes. In the sinusoidal PWM scheme for two-level inverter each reference
phase voltage is compared with the triangular carrier and the individual pole
voltages are generated independent of each other [3]. To obtain the maximum
possible peak amplitude of the fundamental phase voltage in linear modulation a
is added to the reference phase voltages [17, 18],
common mode voltage
where the magnitude of
is given by the following equation:
(4)
In equation (4) Vmax is the maximum magnitude of the three sampled
reference phase voltages, while
is the minimum magnitude of the three
sampled reference phase voltages. In a sampling interval the addition of the
common mode voltage Voffset1 results in the active inverter switching vectors
being centered in a sampling interval, making the SPWM technique equivalent to
the SVPWM technique [3]. Equation (4) is based on the fact that in a sampling
interval the reference phase which has lowest magnitude (termed the min-phase)
crosses the triangular carrier first and causes the first transition in the inverter
switching state. While the reference phase which has the maximum magnitude
(termed the max-phase) crosses the carrier last and causes the last switching
876
Mahmoud Gaballah, Mohammed El-Bardini, Soliman Sharaf ,.
transition in the inverter switching states in a two-level SVPWM scheme [17,18].
Thus the switching periods of the active vectors can be determined from the
(max-phase and min-phase) sampled reference phase voltage amplitudes in a
two-level inverter scheme [19]. The SVPWM technique using only the
instantaneous reference phase amplitudes presents a simple way to determine the
time instants at which the three reference phases cross the triangular carriers
using only the instantaneous reference phase amplitudes. These time instants are
sorted to find the offset voltage to be added to the reference phase voltages for
SVPWM generation for the entire linear modulation range, so that the middle
inverter switching vectors are centered (during a sampling interval), as in the
case of the conventional two-level SPWM scheme [20]. The implementation of
the Space Vector Pulse Width Modulation (SVPWM) using only the
instantaneous reference phase amplitudes for the two-level inverter scheme
involves the following steps:
A: Read the sampled amplitudes of VAN, VBN, and VCN for the present sampling
interval and then calculate the time equivalents of phase voltages, i.e. ,
as:
and
(5)
(6)
(7)
Where
B: Find
is the sampling time period.
as:
(8)
Where
,
respectively.
C: Find
,
are the maximum and minimum of
and
,
and
as:
(9)
(10)
(11)
Where
and
are the gating signals during which the top switches in a
leg is turned on.
Equations (5) to (11) show that in this method the centering of the
middle inverter switching vectors of the SVPWM is achieved by the addition of
an offset time signal to the inverter gating signals derived from the sampled
amplitudes of the reference phase voltages. This SVPWM scheme covers the
entire modulation range including the over modulation region, also it does not
need any sector identification as is required in conventional SVPWM schemes.
Complicated calculations for inverter switching vector times and look-up tables
for selecting the inverter switching vectors are also avoided in this scheme. This
reduces the computation time required to determine the switching times for
inverter legs, making the algorithm suitable for real-time implementation.
IMPLEMENTATION OF SPACE VECTOR-PWM FOR …
877
V. SIMULATION RESULTS
The algorithm in section IV is modeled / simulated using MATLAB SIMULINK
software package. The MATLAB SIMULINK model is shown in Fig.4. The
simulation is performed under the following conditions: input voltage = 220
VAC, VDC = 620 V, Output voltage fundamental harmonic f = 50Hz, Switching
frequency fsw = 20 KHZ, and variable modulation index “0.1, 0.85 and 1.15”,
also the output of the system is connected to 1.5 KVA load with Power factor =
0.7 Inductive. The Simulation results are presented in Fig.5 to Fig.7.
Fig.4. MATLAB SIMULINK model for the system
A
B
Fig.5 shows the simulation results at modulation index = 0.1. A: Output pole
Voltage waveforms, B: Line voltage / current waveforms across load terminals
878
Mahmoud Gaballah, Mohammed El-Bardini, Soliman Sharaf ,.
A
B
Fig.6 shows the simulation results at modulation index = 0.85. A: Output pole
Voltage waveforms, B: Line voltage / current waveforms across load terminals
A
B
Fig.7 shows the simulation results at modulation index = 1.15. A: Output pole
Voltage waveforms, B: Line voltage / current waveform s across load terminals
From these simulation results we can say that the SV-PWM signal
generation using algorithm in section IV can work in the under-modulation
region with some small harmonics in pole and line voltages as shown in Fig.5,
also it can work in the over-modulation region with some small distortions in the
output line voltage at the largest modulation index of SV-PWM as shown in
Fig.7
VI. EXPERIMENTAL RESULTS
The algorithm in section IV is implemented on microchip PIC16F747
microcontroller platform and the experimental results are presented for two-level
inverter with output LC filter as shown in Fig.1. The overall block diagram of the
experiment is shown in Fig.8, The single phase AC input 220v is rectified to
±320 VDC, then synthesized to three phase programmable amplitude and
IMPLEMENTATION OF SPACE VECTOR-PWM FOR …
879
frequency AC waveform through two-level inverter followed by three phase LC
filter. All algorisms are implemented on microchip PIC16F747 microcontroller
platform in assembly language using MPLAB compiler. An image for the overall
view of experiment is shown in Fig.9.
Fig.8. Overall block diagram of the experiment.
Rectifier/Power
supply section
3 phase LC
filter section
Controller and
user interface
section
3 phase
VSI section
Fig.9. Real Image for the experiment.
880
Mahmoud Gaballah, Mohammed El-Bardini, Soliman Sharaf ,.
The modulation index is varied from a low modulation index to the over
modulation region. The experiment is done under the following conditions: DC
link = 400V is used for the inverter, Output voltage fundamental harmonic f =
50Hz, Switching frequency
, and three phase 1.5 KVA /0.7 power
factor load. The experimental results are presented in Figs. 10–14. Figure 10
shows the generated SV-PWM signal used to drive the inverter switches a, b and
c respectively. The SVPWM strategy is based on the right aligned sequence.
Figure 11-14 shows pole voltage / line voltage / line current waveforms at
modulation index 0.1, 0.85, 1.00, and 1.15 respectively.
Fig.10. shows the experimental SV-PWM gating signals. CH1= , CH2=
and the CH3= , X axis 400usec/div, Y axis 5volt/div
A
B
Fig.11. Experimental results for Modulation index = 0.1, (A) Pole
voltage
waveforms, (B) Line voltage
line Current
waveforms
,
,
IMPLEMENTATION OF SPACE VECTOR-PWM FOR …
A
881
B
Fig.12. Experimental results for Modulation index = 0.85, (A) Pole voltage
waveforms, (B) Line voltage
, line
Current
wave forms
A
B
Fig.13. Experimental results for Modulation index = 1.00, (A) Pole voltage
waveforms, (B) Line voltage
, line
Current
waveforms
A
B
Fig.14. Experimental results for Modulation index = 1.15, (A) Pole voltage
waveforms, (B) Line voltage
, line
Current
waveforms
882
Mahmoud Gaballah, Mohammed El-Bardini, Soliman Sharaf ,.
The experimental results for the under modulation region with a
modulation index 0.1 is shown in Fig.11.(A) Shows the pole voltage of three
phases,(B) shows the line voltage and line current for phase A. it may be noted
that the harmonics appear in voltage waveforms is due to low modulation index.
The experimental results for the modulation region with a modulation index 0.85,
and 1.00 is shown in Fig.12-13. The line voltage and line current signals seem to
be good with low harmonic and no distortion. Finally The experimental results
for the over modulation region with a modulation index 1.15 is shown in Fig.14.
(A)Shows the pole voltage of three phases it may be noted that this waveforms
tends to be square wave due to over-modulation. Fig.14 (B) shows the line
voltage and line current for phase A. the small distortion within line voltage is
due to large modulation index.
The simulation and experimental waveforms are exactly identical. It
demonstrates that the simplified implementation of SVPWM is feasible and
effectual in driving three phase two level inverter, and it is much simpler and
more executable than conventional means without look-up tables or complex
logical judgments.
VI. CONCLUSIONS
A simple and low cost implementation of space vector pulse width modulation
technique was presented. The presented SVPWM technique driving the inverter
gating signals from the sampled amplitudes of the reference phase voltages The
SVPWM strategy is based on the right aligned sequence. The switching vectors
for the inverter are derived using a simple digital logic which does not involve
any complex computations and hence reduces the implementation time. This
scheme can be used for any multilevel inverter configuration and can also work
in the over-modulation region. A MATLAB SIMULINK model, and simulation
results for different modulation indexes were presented .The space vector PWM
scheme is implemented on microchip PIC microcontroller 16F747 platform, and
the experimental results were presented for two-level inverter with output LC
filter.
REFERENCES
1
2
3
4
5
P.Channegowda, V.john“Filter optimization for grid interactive voltage
source inverter”, IEEE Trans.Ind.Electr. v. 157, pp. 4106-4114, Dec. 2010.
S.Yang, Q.Lei, F.Z.Peng and Z.Qian “Robust control scheme for grid
interactive voltage source inverter”, IEEE Trans. Ind.Electr. v. 158, pp.
202-212, Jan. 2011.
J. Holtz “Pulse-width-modulation–Asurvey”, IEEETrans. Ind. Electr.,v.
39,pp.410-419,Dec.1992.
S.R.Bowesand, Y.S.Lai, “The relationship between space-vector modulation
and
regular-sampled
PWM”,IEEE.Trans.Ind.Electr.,v.
44,pp.670679,Oct.1997.
H. W Van Der Broeck, H- C skudenly, and G.V Stanke “Analysis and
realization of a pulse width modulator based on voltage space vector”
IMPLEMENTATION OF SPACE VECTOR-PWM FOR …
6
7
8
9
10
11
12
13
14
15
16
17
18
883
IEEETrans. Ind. Electr.,v. 24,pp.142-150,Jan.1988.
N. Celanovic and D. Boroyevich, “A fast space-vector modulation
algorithm for multilevel three-phase converters,” IEEE Trans. Ind.Appl.,
vol. 37, no. 2, pp. 637–641, Mar./Apr. 2001.
N. Tekwani, S. Kanchan, and K. Gopakumar, “A dual five-level induction
motor drive with common-mode voltage elimination and DC-link capacitor
voltage balancing using only the switching-state redundancy—Part I,” IEEE
Trans. Ind. Electron., vol. 54, no. 5, pp. 2600–2608, Oct. 2007.
P. F. Seixas, M. A. Severo Mendes, P. Donoso Garcia, and A. M. N. Lima,
“A space-vector PWM method for three-level voltage source inverters,” in
Proc. IEEE APEC, 2000, vol. 1, pp. 549–555.
W. Yao, H. Hu, and Z. Lu, “Comparisons of space-vector modulation and
carrier-based modulation of multilevel inverter,” IEEE Transpower
Electron., vol. 23, no. 1, pp. 45–51, Jan. 2008.
V. T. Somasekhar, K. Gopakumar, M. R. Baiju, K. K. Mohapatra, and L.
Umanand, “A multilevel inverter system for an induction motor with openend windings,” IEEE Trans. Ind. Electron., vol. 52, no. 3, pp. 824–836, Jun.
2005.
E. G. Shivakumar, K. Gopakumar, S. K. Sinha, A. Pittet, and V. T.
Ranganathan, “Space-vector PWM control of dual inverter fed open-endwinding induction motor drive,” in Proc. IEEE APEC, 2001, pp. 399–405.
V. T. Somasekhar, S. Srinivas, and K. K. Kumar, “Effect of zero-vector
placement in a dual-inverter fed open-end-winding induction motor drive
with a decoupled space-vector PWM strategy,” IEEE Trans. Ind. Electron.,
vol. 55, no. 6, pp. 2497–2505, Jun. 2008.
E. G. Shivakumar, K. Gopakumar, S. K. Sinha, A. Pittet, and V. T.
Ranganathan, “Space-vector PWM control of dual inverter fed open-endwinding induction motor drive,” in Proc. IEEE APEC, 2001, pp. 399–405.
A. Gopinath, A. Mohamed A. S., and M. R. Baiju, “Fractal based space
vector PWM for multilevel inverters—A novel approach,” IEEE Trans. Ind.
Electron., vol. 56, no. 4, pp. 1230–1237, Apr. 2009.
M. R. Baiju, K. Gopakumar, V. T. Somasekhar, K. K. Mohapatra, and L.
Umanand, “A space-vector-based PWM method using only the
instantaneous amplitudes of reference phase voltages for three-level
inverters,” EPE J., vol. 13, no. 2, pp. 35–45, 2003.
R. S. Kanchan, M. R. Baiju, K. K. Mohapatra, P. P. Ouseph, and K.
Gopakumar, “Space-vector PWM signal generation for multilevel inverters
using only the sampled amplitudes of reference phase voltages,” Proc. Inst.
Elect. Eng.—Elect. Power Appl., vol. 152, no. 2, pp. 297–309, Mar. 2005.
Holmes, D.G.: ‘The general relationship between regular sampled pulse
width modulation and space vector modulation for hard switched
converters’. Conf. Rec. IEEE Industry Applications Society (IAS) Annual
Meeting, 1992, pp. 1002–1009
Baiju, M.R., Mohapatra, K.K., Somasekhar, V.T., Gopakumar, K., and
Umanand, L.: ‘A five-level inverter voltage space phasor generation for an
open-end winding induction motor drives’, IEE Proc. Electr. Power Appl.,
2003, 150, (5), pp. 531–538
‫‪Mahmoud Gaballah, Mohammed El-Bardini, Soliman Sharaf ,.‬‬
‫‪Kim, J., and Sul, S.: ‘A novel voltage modulation technique of the Space‬‬
‫‪Vector PWM’. Proc. Int. Power Electronics Conf., Yokohama, Japan, 1995,‬‬
‫‪pp. 742–747‬‬
‫‪Zhou, K., and Wang, D.: ‘Relationship between space-vector modulation‬‬
‫‪and three-phase carrier-based PWM: A comprehensive analysis’, IEEE‬‬
‫‪Trans. Ind. Electron., 2002, 49, (1), pp. 186–196‬‬
‫‪884‬‬
‫‪19‬‬
‫‪20‬‬
‫ﺘطﺒﻴق طرﻴﻘﺔ اﻝﺘﺤﻜم ﺒﺎﺴﺘﺨدام ﺘﻌدﻴل اﻝﻤﺘﺠﻪ اﻝﻔراﻏﻰ ﻝﻌرض اﻝﻨﺒﻀﺔ‬
‫ﻝﺘﺸﻐﻴل ﻋﺎﻜس ﻤﺼدر ﺠﻬد ﺜﻨﺎﺌﻰ اﻝﻤﺴﺘوى‬
‫ﻓﻰ ﻫذا اﻝﺒﺤث ﺘم ﺘﻨﻔﻴذ طرﻴﻘﺔ ﻝﺘوﻝﻴد اﻝﻨﺒﻀﺎت اﻝﻼزﻤﺔ ﻝﺘﺸﻐﻴل ﻋﺎﻜس ﻤﺼدر ﺠﻬد " ﺘﻴﺎر ﻤﺴﺘﻤر‪ -‬ﺘﻴﺎر‬
‫ﻤﺘردد " ﺜﻼﺜﻰ اﻷوﺠﻪ ﺜﻨﺎﺌﻰ اﻝﻤﺴﺘوى ﺒﺎﺴﺘﺨدام طرﻴﻘﺔ ﺠدﻴدة ﻝﺘﻌدﻴل اﻝﻤﺘﺠﻪ اﻝﻔراﻏﻰ ﻝﻌرض اﻝﻨﺒﻀﺔ ‪.‬‬
‫”‪ “Space vector-PWM‬اﻝطرﻴﻘﺔ اﻝﻤﺴﺘﺨدﻤﺔ ﻓﻰ اﻝﺒﺤث ﻴﻤﻜﻨﻬﺎ ﺘوﻝﻴد اﻝﻨﺒﻀﺎت اﻝﻼزﻤﺔ ﻝﺘﺸﻐﻴل اﻝﻌﺎﻜس‬
‫ﻤﺒﺎﺸرة ﻤن اﻝﻘﻴم اﻝﻠﺤظﻴﺔ ﻝﻠﻌﻴﻨﺎت اﻝﻤﺄﺨوذة ﻤن اﻝﻤوﺠﺔ اﻻﺴﺎﺴﻴﺔ وﺘﻌﺘﺒر ﻫذﻩ اﻝطرﻴﻘﺔ أﻓﻀل وأﻗل ﺘﻌﻘﻴدا ﻤن‬
‫اﻝطرق اﻝﺘﻘﻠﻴدﻴﺔ ﻝﺘﻌدﻴل اﻝﻤﺘﺠﻪ اﻝﻔراﻏﻰ ﻝﻌرض اﻝﻨﺒﻀﺔ وذﻝك ﻻﻨﻬﺎ ﻻ ﺘﺴﺘﺨدم أﻨظﻤﺔ اﻝﺠدوﻝﺔ ﻝﻠﺤﺼول‬
‫ﻋﻠﻰ ﻗﻴم ﺘﻌدﻴل ﻋرض اﻝﻨﺒﻀﺔ وﻻ ﺘﺤﺘﺎج اﻝﻰ ﻋﻤﻠﻴﺎت ﻤﻨطﻘﻴﺔ ﻤﻌﻘدة‪.‬‬
‫وﻗد ﺘم ﻋﻤل ﻨﻤوذج رﻴﺎﻀﻰ ﻝﻠﻨظﺎم ﻜﻜل وﻤﺤﺎﻜﺎﺘﺔ ﻤن ﺨﻼل ﺒرﻨﺎﻤﺞ اﻝﻤﺎﺘﻼب ﻋﻨد ﻨﺴب ﺘﻌدﻴل ﻤﺨﺘﻠﻔﺔ‬
‫وﺒﺄﺤﻤﺎل ﻤﺨﺘﻠﻔﺔ وﻋﻠﻴﻪ ﻓﻘد اﺜﺒﺘت اﻝﻨﺘﺎﺌﺞ اﻝﻨظرﻴﺔ أن ﻫذﻩ اﻝطرﻴﻘﺔ ﺼﺎﻝﺤﺔ ﻝﺘﺸﻐﻴل ﻋﺎﻜس ﻤﺼدر اﻝﺠﻬد‬
‫ﺜﻼﺜﻰ اﻷوﺠﻪ‪.‬‬
‫وﻗد ﺘم ﺒﻨﺎء اﻝﻨظﺎم اﻝﺴﺎﺒق ﻤﺤﺎﻜﺎﺘﻪ ﻋﻤﻠﻴﺎ وﺘم ﺘطﺒﻴق اﻝطرﻴﻘﺔ اﻝﻤﺴﺘﺨدﻤﺔ ﻓﻰ اﻝﺒﺤث ﻋﻠﻰ ﻤﺘﺤﻜم دﻗﻴق‬
‫ﻤﻴﻜروﻜﻨﺘروﻝر رﺨﻴص اﻝﺜﻤن ﻤن اﻝﻨوع "‪ "PIC16f747‬وﻗدﻤت اﻝﻨﺘﺎﺌﺞ اﻝﻌﻤﻠﻴﺔ ﻋﻠﻰ ﻋﺎﻜس ﺠﻬد "ﺘﻴﺎر‬
‫ﻤﺴﺘﻤر‪ -‬ﺘﻴﺎر ﻤﺘردد" ﺜﻨﺎﺌﻰ اﻝﻤﺴﺘوى ﺜﻼﺜﻰ اﻷوﺠﻪ ﻴﺘﺒﻌﻪ ﻤرﺸﺢ ﺜﻼﺜﻰ اﻷوﺠﻪ ﻤن اﻝﻨوع "‪ "LC‬وﻗد وﺠد‬
‫ﺘطﺎﺒق اﻝﻨﺘﺎﺌﺞ اﻝﻌﻤﻠﻴﺔ ﻤﻊ اﻝﻨﺘﺎﺌﺞ اﻝﻤﺤﺎﻜﺎﺘﻴﺔ ﻤﻤﺎ ﻴﺜﺒت ﺼﻼﺤﻴﺔ ﻫذﻩ اﻝطرﻴﻘﺔ ﻝﺘﺸﻐﻴل ﻋﺎﻜس ﻤﺼدر اﻝﺠﻬد ﺒطرﻴﻘﺔ‬
‫ﻤﺒﺴطﻪ وﺴﻬﻠﺔ اﻝﺘﻨﻔﻴذ‪.‬‬