Performance and High Robustness DPC for PWM Rectifier under Unstable VDC Bus

International Journal of Power Electronics and Drive System (IJPEDS)
Vol. 7, No. 1, March 2016, pp. 66~74
ISSN: 2088-8694  66
Journal homepage: http://iaesjournal.com/online/index.php/IJPEDS
Performance and High Robustness DPC for PWM Rectifier
under Unstable VDC Bus
M.S. Djebbar*, H. Benalla**
* Faculty of Engineering Sciences, on Electrical Laboratory, University of Tebessa, Ageria
** Faculty of Engineering Sciences, on Electrical Laboratory, University Constantine1, Ageria
Article Info ABSTRACT
Article history:
Received Sep 28, 2015
Revised Dec 5, 2015
Accepted Jan 3, 2016
This paper proposes a strategy de controlling a static AC / DC converter
based on direct power control (DPC). The instantaneous active and reactive
power is controlled in such a way to ensure the PWM rectifier with a
sinusoidal current absorption. This control has proven effective in terms of
reduction of total harmonic distortion (THD) of current absorbed. Offers a
good control of active and reactive power with an operation at unitary power
factor. The test of robustness carried out and the results have proven DPC
good performance with strong possibility of de integrate it into the field of
high voltage and high power as electric traction.
Keyword:
Direct power control
Power quality
Pulse width modulation
Pwm rectifier
Total harmonic distortion Copyright © 2016 Institute of Advanced Engineering and Science.
All rights reserved.
Corresponding Author:
Mohamed Salah Djebbar,
Faculty of Engineering Sciences, on Electrical Laboratory,
University of Tebessa, Algeria,
Constantine Road, Tebessa12002, Algeria.
Email: djebbarcn@yahoo.fr
1. INTRODUCTION
The principle of direct control was proposed by [1] and was later developed for many applications.
The objective was to eliminate the block of modulation and inner loops by replacing a switching table with
inputs errors of active and reactive power.
The first application developed was the control of an electrical machine, the control structure was
known under the name Control Direct Torque (Direct Torque Control, DTC). In this case, the control stator
flux and the electromagnetic torque of the machine without any modulation block [2].
Then, a similar technique called Direct Power Control (Direct Power Control, DPC) was proposed
by [4] and developed later by [5] for a PWM rectifier control application in order to improve the quality of
the energy electrical network. In this case, the controlled variables are the instantaneous active and reactive
power.
Thus, there are two different types of power direct control structures proposed in the literature. On
the one hand, references [4], [5] present a non linear control variable switching frequency, better known
under the name DPC classic, on the other hand in [6], the author proposes to associate the principle DPC with
a pulse width of vector modulation (SVM) in order to obtain a constant switching frequency without the use
of a switching table.
Two techniques for performing the calculation of instantaneous power without sensors have been
proposed.
The first technique proposed in this paper will be the subject of our work [4], [7], [8] estimates the
mains voltages from the values of the voltage of the converter and the RL filter (V-DPC) and establish
configurations DPC based on the position of the voltage vector in the stationary α-β reference.

 ISSN: 2088-8694
IJPEDS Vol. 7, No. 1, March 2016 : 66 – 74
67
The second technique, developed in [5], [6], [9], [10], the authors propose the estimation of virtual
flux as a method for estimating network voltages from the voltages of the converter and the RL filter, (VF-
DPC).
This control strategy assures decouples control of active and reactive power, while absorbing
sinusoidal currents, ensuring operation of the PWM Rectifier as a clean energy quality with very low THD
and power factor equal to unity [11].
We note at the end, that the essential aim of this work is highlighted the importance of this strategy
in terms of quality of electric power and in terms of robustness proven by the high performance developed.
2. PRINCIPLE FUNCTIONING OF THE DPC
The (DPC) is based on the direct control of active and reactive power in a PWM rectifier. The
errors between the reference values of the instantaneous active and reactive power and their measures are
introduced in two hysteresis comparators, which determine, using a switchboard and the value of the sector
where the mains voltage are located, the switching status of the semiconductor. The voltage's loop of the DC
bus is adjusted with a PI corrector, in order to control the error between the sensed voltage (continuous) and
its reference.
The reference reactive power is directly imposed zero for a current's sinusoidal absorption on a
source voltage supposed to be sinusoidal, in order ensure the running of the rectifier with a unitary power
factor.Figure (1) shows the overall configuration of the direct control of power applied to the rectifier. It is
analogous to that of the direct torque control (DTC) of induction machines [12], [13].
Figure 1. PWM rectifier control block on the network (classical DPC)
The tension and the source currents are measured and transformed by the Concordia matrix, in order to move
from a three-phase reference to a fixed two-phase refrence. (α, β).






























c
b
a
v
v
v
v
v
2
3
2
1
2
3
2
1
0
1
3
2
































c
b
a
i
i
i
i
i
2
3
2
1
2
3
2
1
0
1
3
2

 (1)
The network voltage is estimated by the expression (2)
dt
di
LSVe
cba
cbadccba
,,
,,,, . 

(2)
The calculation of the powers, instantaneous active and reactive, is given by the following equations:

IJPEDS ISSN: 2088-8694 
Performance and High Robustness DPC for PWM Rectifier under Unstable VDC Bus(M.S. Djebbar)
68
 
        














a
c
c
a
bacacbcbadc
c
c
b
b
a
a
ccbbaadc
i
dt
di
i
dt
di
LiiSiiSiiSUq
i
dt
di
i
dt
di
i
dt
di
LiSiSiSVp
..3
3
1
)...(...
(3)
The knowledge of the estimated voltage sector is required to determine the optimal switching statuses. For
this, the work plan (α, β) is divided into 12 sectors. These latter canbede termined by the following
relationship: [6]
6
)1(
6
)2(



 nn n
(4)
Where: n= 1…12,
n is the number of the sector instantaneously determined by the the voltage vector's position which is given
by:
)(



v
v
Arctg (5)
Figure 2. Plan (α, β) divided into 12 sectors
3. CONTROL OF DIRECT VOLTAGE (VDC)
Comparing the instantaneous active power at a reference power, this latter is obtained by the DC
voltage control block at the capacitor terminals, where we use a PI controller (Proportional, integrator) to
control the error between the sensed voltage (continuous) and reference.
Whilst to achieve a unity power factor, reactive power reference is directly imposed zero.
Figure 3. Determination of powers errors (Δp, Δq) Figure 4. Direct Voltage regulation with PI corrector
Figure 4 shows the regulation of the DC voltage by a PI controller. To control the closed loop system, it is
necessary to choose the coefficients kp and ki, in this case we use the imposition method of the poles [6],
[14].

 ISSN: 2088-8694
69
2
2
ni
np
Ck
Ck




(6)
4. HYSTERESIS CONTROL AND SWITCHING TABLE
The hysteresis control is to keep active and reactive instantaneous power in a desired band. This
control is based on two comparators that use as input the error signal between the reference values and
estimated values of active and reactive power. If the error is growing and reached the top level, the hysteresis
control changes its output to '1', on the contrary if the error signal reaches the lower band, then the output will
be switched to '0'.




0
1
0
1
Sq
Sq
Sp
Sp
hqqq
hqqq
hppp
hppp
ref
ref
ref
ref




(7)
The dynamics of active and reactive power can be given as follows :







)..(
1
)..(
1
)(
1 22


ee
ee
ueue
Ldt
dq
ueue
L
ee
Ldt
dp
(8)
The synthesis of the switching table is based on the signs of derivatives of active and reactive power
in each sector. For each sector, the change of the reactive power is positive for three vectors, negative for three
vectors, and zero for V0, V7. The sign of change in the active power is positive for four vectors, negative for two
or three vectors. For example, for the first sector, the vectors that influence the sign of change of active and
reactive power are summarized in the following table [15]:
Table 1. First sector of change of active and réactive power
0

p 0

p 0

q 0

q 0

p
V3, V4, V5, V0 V1, V6 V1, V2, V3 V4, V5, V6 V0, V7
The switching table proposed for all sectors is presented in the table below
Table 2. All sectors switching table
5. SIMULATION AND INTERPRETATION
The simulation was performed to confirm the theoretical study of the rectifier in static mode and
check the dynamic performance of the control of powers. Parameters used in simulation are as follows:
pS qS 1 2 3 4 5 6 7 8 9 10 11 12
1 0 V5 V5 V6 V6 V1 V1 V2 V2 V3 V3 V4 V4
1 1 V3 V3 V4 V4 V5 V5 V6 V6 V1 V1 V2 V2
0 0 V6 V1 V1 V2 V2 V3 V3 V4 V4 V5 V5 V6
0 1 V1 V2 V2 V3 V3 V4 V4 V5 V5 V6 V6 V1

70
 Power source:
RMS Voltage V = 230 V Frequency f =50 Hz
Internal resistor Rs = 1 mΩ, Internal inductor Ls = 0.1 mH
 Filter RL :
Lf =14 mH, Rf = 1.5 Ω
 Rectifier :
Three-phase bridge rectifier (PD3) to IGBT
 Load:
Storage capacity C=2mF
Voltage Reference VDC-ref = 600 V
Ohmic load (R= 100 Ω), Inductive load (R=45, L = 50mH), Capacitive load (R=100 Ω, C=200 μF).
 PI controller parameters and hysteresis regulators:
Sampling frequency Controller PI: fe = 100 kHz
Band width of hysteresis regulators: hp= 1 μW, hq= 1 μVAR
PI controller parameters: ki= 25, kp= 1
5.1. Performance of the DPC During the Variation of the DC Bus
All the figures which follows, shows the response of the rectifier controlled by the DPC when a
change of the reference of the DC bus voltage from 600 V to 800 V by a fixed step of 100 V in the moments:
0.4seconds and 0.7seconds.
The value of the reference then descends 550 V at time t = 1seconds and then it goes up to the value
of 850 V starting from t = 1.6 seconds (figure 5). The load at the output of the rectifier is of the inductive
type (R = 45Ω; L = 50 mH), remains constant during the variation of VDC.
Figure 5. VDC and Reference Voltage during an
adjusted variation 600V to 850V
Figure 6. Voltage and line current in the interval Time
0.3s - 0.8s
This variation during the simulation time does not affect the quality of the signals of the electrical
quantities.It is noted that the DPC provides a persistent control during disturbances of the DC bus voltage,
despite these disturbances, the figures (6 and 7) show that the source current has a sinusoidal shape that
changes in amplitude in accordance with the reference changes, harmonic distortion of the current (Figure 8),
have very low value (1.53%), which provides a clean power source for electric power quality and unity
power factor (Figure 9).
0 0.5 1 1.5 2
0
100
200
300
400
500
600
700
800
900
1000
T i m e ( s )
DirectVoltage(V)
V dc ref
V dc
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8
-500
-400
-300
-200
-100
0
100
200
300
400
T i m e ( s )
L i ne V o lt a g e ( V )
L i ne C ur r e nt ( A )

 ISSN: 2088-8694
71
Figure 7. Zoom Current line and Voltage in the
interval of time 0.75s - 0.9s
Figure 8. Total Harmonic Distortion of the line
current
The instantaneous active and reactive power follow their imposed references with minimal error
(Figures 10, 11 and 12), while the reactive power is always zero. By analyzing the results, it is determined
that the DPC provides a good dynamic of the system and keeps its robustness despite the imposed disuptions
on the reference of the DC bus.
Figure 9. Power Factor Figure 10. Active and Reactive power depending on
the variation of the reference VDC
Figure 11. Instantaneous Active Power P (W) and
Reference (Pref) during the variation VDC
Figure 12. Instantaneous Reactive Power q (VAR)
and Reference (qref) during the variation VDC
0.75 0.8 0.85 0.9
-500
-400
-300
-200
-100
0
100
200
300
400
T i m e ( s )
L i ne V o l t a g e ( V )
L i ne C ur r e n t ( A )
0 5 10 15 20 25
0
10
20
30
40
50
60
70
80
90
100
R a n k H a r m o n i c s
THD I = 1.53 %
0 0.5 1 1.5 2 2.5
0
0.2
0.4
0.6
0.8
1
1.2
T i m e ( s )
0 0.5 1 1.5 2
-5000
0
5000
10000
15000
20000
T i m e ( s )
A c t i v e p o w e r P ( W )
R e a c t i v e p o w e r Q ( VAR )
0 0.5 1 1.5 2
-4
-2
0
2
4
6
8
10
12
x 10
4
T i m e ( s )
I n s t a n t a n e o u s A c t i v e P o w e r p ( W )
p - ref ( W )
p ( W )
0 0.5 1 1.5 2
-0.5
0
0.5
1
1.5
2
2.5
3
3.5
x 10
4
T i m e ( s )
I n s t a n t a n e o us R e a c t i v e P o w e r q
q- ref ( VAR )
q ( VAR )

72
5.2. Performances of the DPC During a Load Variation
Figure 1.3 Vdc voltage and Vdc_ref during an load
Change At time t = 0.25 s and t = 0.75s for VDC =
600 V
Figure 14. Voltages and line current
For a DC voltage VDC = 600 V maintained constant. At first time, the rectifier feeds an inductive load with a
value R = 45 Ω; L = 50mH, we add in parallel in the second time t = 0.25seconds, a capacitive load value
(R = 100 Ω, C = 200μF), the we add at the time t = 0.75s a resistive load of R = 100 Ω.
It can be seen from Figures (13, 14, 15) that despite the variation of the load the DC voltage is constant, the
current and the voltage source have a sinusoidal shape and have a zero phase shift. The active power evolves
in amplitude with the change of the load, while the reactive power is always zero.
Figure 15. Active and Reactive power during the
change load at time t = 0.25 s and t = 0.75s for VDC
= 600 V
Figure 16. Change the load at time t = 0.25 s for
Vdc = 600 V and at time t = 0.75s for VDC = 700V
5.3. Performances of the DPC During an Variation of the DC Bus and the Load
It is noted from Figures (16, 17, 18) that the passage of the continuous voltage of 600 V to 700V at
time t = 0.5s and the change of the load to the instant t = 0.25s (R = 100 Ω, C = 200μF) and t = 0.75s (R =
100 Ω), does not affect the performance of the DPC since the reactive power is always zero, the current
maintains its shapesinusoidal and evolves with changing load and Vdc, the current phase shift / source
voltage is zero, and a unitary power factor .
The active power amplitude naturally reacts with the load current draw and increased VDC.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
100
200
300
400
500
600
700
T i m e ( s )
V dc ref ( V )
V dc ( V )
0.65 0.7 0.75 0.8 0.85
-400
-300
-200
-100
0
100
200
300
400
500
T i m e ( s )
L i n e V o lt a g e ( V )
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-1000
0
1000
2000
3000
4000
5000
6000
7000
T i m e ( s )
A c t i v e p o we r ( W )
R e a c t i v e p o we r ( V A R )
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
100
200
300
400
500
600
700
800
T i m e ( s )
V d c ref ( V )
V d c ( V )

 ISSN: 2088-8694
73
Figure 17. Voltage and line current during the
variation of the load and VDC
Figure 18. Active and Reactive power depending on
theVariation load at time t = 0.25 s and t = 0.75s for
a VDC = 600 V and 700 V
5.4. Comment
It remains to point out at the end that this subject was addressed in a way to confirm what has been
achieved by the authors [4], [5], [8] by adding a contribution from us which is to implement technical of
control (DPC) high performance, characterized by its robustness, efficiency and stability. These
performances were achieved and confirmed through the various disturbances created around the energy
system, by changing the load and the bus voltage VDC. It remains to be said that this work is characterized by
a continuous bus unstable reference during the various tested proposed in this work, which is different from
the developed research work and developed by the authors mentioned above.
6. CONCLUSION
The DPC can control the energy exchange between the rectifier and the electrical network with a
power factor equal to unity without using a voltage / current sensor.This technique relies on control loops of
the instantaneous power and not those currents.Simulation results obtained in this work showed that the
direct power control of guarantee reliable control, stable and robust with high dynamic performance, despite
the disruptions that has suffered the PWM rectifier.Spectral analysis of the line current obtained by this
control strategy shows that all harmonics are attenuated, resulting in a very low THD value of 1.53%, well
below the values imposed by international norms (5%).
The DPC provides a quick calculation of instantaneous power that allows obtaining a very high
dynamics of the system. It is also characterized by simplicity, not using nested loops (not transformations of
coordinated, not modulator).
The results obtained are very promising and high performance, which enables this technique to
(DPC), occupied a place of very advanced Among the techniques used to improve power quality and clean up
the electrical network
The Performance developed by the DPC during the various tests of robustness, has given to this
technique an important place in the field of high voltages and large power such as electric traction. We signal
at the end the major disadvantage of the (DPC) is that the converter switching frequency is not constant.
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0.2 0.3 0.4 0.5 0.6 0.7 0.8
-400
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0
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T i m e ( s )
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