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International Journal of Enhanced Research Publications, ISSN: XXXX-XXXX
Vol. 2 Issue 4, April-2013, pp: (1-4), Available online at: www.erpublications.com
Control of Three Phase PWM Rectifier Using
Virtual Flux Based Predictive Direct Power Control
and SVM under Harmonic Conditions
Vahid Eskandari-Torbati3
Hamid Eskandari-Torbati1,
Davood Arab Khaburi2
3
Fiber Optic Project Manager
Moniran Consultant Co., Mashhad, Iran
3
1,2
department of electrical engineering
Iran University of Science and Technology,
Tehran, Iran
1,2
Abstract: – In this paper a new predictive direct power control algorithm to control the PWM rectifier based on
Virtual Flux is presented. In this algorithm supply voltage and the line inductance are assumed as an induction
machine and so Virtual Flux space vectors are assumed corresponding to the space vectors of the voltages.
Instantaneous active and reactive powers and finally convertor average voltage in both stationary and reference
frames are calculated by the Virtual Flux space vector components. Main advantages of the proposed method is
low Total Harmonic Distortion (THD) of the input current and low ripple in the instantaneous active and reactive
powers and DC-bus voltage under harmonic distorted condition of the supply voltage in comparison with Voltage
based predictive direct power control. Proposed VF- predictive direct power control with SVM switching strategy
was tested in simulations and compared with the voltage based predictive direct power control.
Keywords: PWM rectifier, direct power control, space vector modulation (SVM), dead beat control, predictive
control
Introduction
Most of industrial process and domestic applications that need to rectify the electrical energy drawn from AC network, use
full bridge diode rectifiers. The most important advantages of these rectifiers are: simple configuration and low cost and
furthermore they don’t need any kind of control unit. Against these benefits, diode rectifiers have some disadvantages that
most important of them are: large amount of passive elements such as capacitive filter in DC side, high THD in the AC side
Currents, consumption of reactive power and so low power factor at the terminal of the network and high value in the DC
side voltage ripple [1]. These problems of the diode rectifiers and the attempts of researchers to eliminate them resulted in
presentation of PWM rectifiers. Main advantages of PWM rectifiers are: low THD in the input AC currents, low DC side
voltage ripple, unity power factor at the terminal of the network and no need to reactive power, but in return some cost
should be paid such as more complex control algorithms and more switching loss [1].
Idea of PWM rectifier firstly was proposed in [1], [2]. Development of power electronic switches such as IGBT and their
capability to operate under higher switching frequencies, made it possible for researchers to use more complex control
algorithms for these rectifiers in order to improve their performance. A better control algorithms results a lower value for
DC side capacitor, a lower THD in the input currents and lower ripple in the DC side voltage.
In the past years different control algorithms have been proposed in literatures to control and improve PWM rectifier
performance. According to the condition of the network voltage, these control methods can be classified in two groups; first
are those which consider the network voltage ideally and without any harmonic distortion or unbalance conditions and the
second are those which try to control and improve the rectifier performance under non-ideal condition of supply network.
The literatures in the second groups mostly investigate the effect of the unbalanced supply network on the rectifier and
propose methods to improve it [3]–[5].
On the other hand, various control algorithms presented in the literatures can be classified in two groups according to their
use of current control loop or active/reactive power control loop [6]. A well-known algorithm among indirect power control
that uses current controller is the method that called Voltage Oriented Control (VOC) which is the duality of Field Oriented
Control in the control of electrical machines by DC/AC inverters. The main idea of this method is to control space vector of
input AC current according to the position of space vector of the network voltage. Also to satisfy unity power factor (UPF)
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Vol. 2 Issue 4, April-2013, pp: (1-4), Available online at: www.erpublications.com
at the terminal of the network, reference value of the current on the quadrature axis is set to zero while reference of the
current on the direct axis comes from a PI controller which the input is the tracking error of DC side voltage [7]–[9]. Over
past decade a new method has been emerged which is based on direct control of active and reactive powers of the rectifier
and is called Direct Power Control (DPC). It is duality of a well-known method called Direct Torque Control (DTC) in
driving machines by DC/AC inverters. This method calculates instantaneous active and reactive power of the rectifier drawn
from the terminal of the network and compares them with their references to produce the tracking errors. These errors are
entered into two fixed band hysteresis controllers separately. At last, status of the switches will be indicated according to
the digital output of the controllers and the position of the space vector of input voltage by a predefined switching table.
Unity power factor (UPF) operation will be satisfied when the reference value of the reactive power is set to zero. On the
other hand the reference of the active power is generated by multiplying the DC side voltage and output signal of a PI
controller which its input is tracking error of DC voltage [10]–[12]. This algorithm needs to high sampling frequency which
is the main drawback [18].
VOC and DPC algorithms which are based on the position of the space vector of voltage have not good performance under
distorted condition of the network. So Malinowski et al. proposed an algorithm that uses Virtual Flux (VF) instead of Voltage
as base space vector [12]–[16]. This idea significantly improves the performance of rectifier just under harmonic distorted
supply voltage, but the requirement of high sampling frequency remains still with it. So after that, Malinowski et al. used
Space Vector Modulation (SVM) switching strategy with Virtual Flux based Direct Power Control in order to eliminate this
drawback (VF-DPC SVM) [17]. In this method hysteresis controllers are replaced by PI controller and the outputs of them
are transferred to stationary reference frame. After that, switching states will be indicated by using a SVM algorithm instead
of switching table. This method has the advantages of VOC and DPC simultaneously but the disadvantage is the tuning of
the PI controller. In [16] some ways for tuning the PI controllers is proposed. P. Antoniewicz and also the authors used
predictive algorithms based on Model Predictive Control (MPC) in order to control PWM rectifiers [17-19]. A. Bouafia et
al. proposed a new Predictive Direct Power Control in the sense of Dead Beat Control that uses SVM switching algorithm
to control PWM rectifier [20]. D. A. Khaburi et al. used VF-DPC algorithm and hysteresis controllers to design and control
a PWM rectifier which is connected to a micro turbine generator and hence it can work under high frequency supply voltage
[21]. Furthermore, some of the works have focused on the multilevel PWM rectifiers and some other has incorporated
different control theories, such as Fuzzy Logic, with conventional control methods in the PWM rectifiers in order to improve
them.
Presented method in [18] is based on the space vector of the network voltage and therefore has not good performance under
harmonic conditions of the supply voltage. This paper uses Virtual Flux instead of Voltage space vector in order to estimate
the value of active and reactive power of the system at the beginning of the next switching step and after that indicates the
space vector of the convertor voltage in beginning of the present switching step. By using this method the performance of
the system will be improved under harmonic conditions of the supply voltage. Theoretical discussion of the method in both
stationary (α-β) and rotating (d-q) reference frame has been presented and simulation studies have been performed in
MATLAB/SIMULINK. Finally simulation results of the method based on the both space vectors (Voltage and Virtual Flux)
have been presented and compared with each other’s.
Principles of Virtual Flux Based Predictive Direct Power Control (VF-PDPC)
In Virtual Flux based Direct Power Control using SVM that has been presented in [15], the rectifier average voltage vector
vαβ, comes from PI controllers of active and reactive powers errors after a coordinate transformation. Fig. 1 shows the block
diagram of VF-DPC with SVM switching strategy. As can be seen in Fig. 1, inputs of the PI controllers are instantaneous
errors of the active and reactive powers of the rectifier. Thus the switching states at each switching period are generated so
that the tracking errors could be canceled at the end of that switching period. While in the proposed method, the rectifier
average voltage vector at the start of the switching period is computed so that to cancel the instantaneous tracking errors of
active and reactive powers at the end of the switching period as shown in Fig. 2. Therefore the reference value of the active
and reactive powers at the end of each switching period should be estimated. In other word, this method needs a predictive
model of the instantaneous power behavior, which is described in the following steps.
A. Stationary Reference Frame
In the stationary reference frame (α-β) by considering the supply voltage as a balanced three phase network, the instantaneous
active and reactive powers of the rectifier based on the Virtual Flux are defined as follows [13]:
−𝜓𝑙𝛽
𝑃
[ ] = 𝜔[
𝑞
𝜓𝑙𝛼
𝜓𝑙𝛼 𝑖𝛼
] [ ]
𝜓𝑙𝛽 𝑖𝛽
where 𝜓𝑙𝛼𝛽 = [𝜓𝑙𝛼 𝜓𝑙𝛽 ]𝑇 is the Virtual Flux vector corresponding to the network voltage vector and 𝑖𝛼𝛽 = [𝑖𝛼
the input current vector of the rectifier and 𝜔 is the angular frequency of the network.

𝑖𝛽 ]𝑇 is
As it is shown in Fig. 3 the Virtual Flux vector components can be derived from the integration of the network voltage vector
components. In this Figure the feedback loop has been adopted in order to cancel the error that could be caused by assigning
a wrong value for the initial condition of the integral process.
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International Journal of Enhanced Research Publications, ISSN: XXXX-XXXX
Vol. 2 Issue 4, April-2013, pp: (1-4), Available online at: www.erpublications.com
Figure 1. VF based instantaneous DPC configuration of three phase PWM Rectifier
If switching period Ts is small enough so that the value of the Virtual Flux vector components could be considered constant
during a switching period (𝜓𝑙𝛼𝛽 (𝑘 + 1) = 𝜓𝑙𝛼𝛽 (𝑘)), the difference between amount of the instantaneous active and reactive
powers from the beginning of the switching period to the end can be written as (2):
[
−𝜓𝑙𝛽 (𝑘)
𝑃(𝑘 + 1) − 𝑃(𝑘)
] = 𝜔[
𝜓𝑙𝛼 (𝑘)
𝑞(𝑘 + 1) − 𝑞(𝑘)
𝜓𝑙𝛼 (𝑘) 𝑖𝛼 (𝑘 + 1) − 𝑖𝛼 (𝑘)
][
]
𝜓𝑙𝛽 (𝑘) 𝑖𝛽 (𝑘 + 1) − 𝑖𝛽 (𝑘)

In the above equation, P(𝑘), 𝑞(𝑘), 𝜓𝑙𝛼𝛽 (𝑘) and 𝑖𝛼𝛽 (𝑘) are determined at each sampling instant by measuring, and 𝜔 is
obtained from the available data of the supply network. In this step we suppose that the values of P(k+1) and q(k+1) are
determined too and we will correct the assumption later. Now as a result of the assumption, the values of 𝑖𝛼𝛽 (𝑘 + 1) could
be computed as:
[
−𝜓𝑙𝛽 (𝑘)
𝑖𝛼 (𝑘 + 1)
1
]=
2[
𝑖𝛽 (𝑘 + 1)
𝜓𝑙𝛼 (𝑘)
𝜔‖𝜓𝑙𝛼𝛽‖
𝜓𝑙𝛼 (𝑘) 𝑃(𝑘 + 1) − 𝑃(𝑘)
𝑖𝛼 (𝑘)
][
]+[
]
𝑖𝛽 (𝑘)
𝜓𝑙𝛽 (𝑘) 𝑞(𝑘 + 1) − 𝑞(𝑘)

Differential equation of a PWM rectifier in α-β frame can be expressed as (4):
[
𝑑 𝑖𝛼 (𝑡)
𝑒𝛼 (𝑡)
𝑣𝛼 (𝑡)
𝑖𝛼 (𝑡)
]=[
]+𝐿 [
]+𝑅[
]
(𝑡)
𝑒𝛽 (𝑡)
𝑣𝛽 (𝑡)
𝑖
𝑖𝛽 (𝑡)
𝑑𝑡 𝛽
(4)
Figure 3. Block diagram of Virtual Flux calculator
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Vol. 2 Issue 4, April-2013, pp: (1-4), Available online at: www.erpublications.com
Figure 2. VF based Predictive DPC-SVM configuration for three phase PWM
rectifier
By neglecting the effect of the resistance R in the presence of inductance L and taking integral of (4), the relationship between
Virtual Flux vector components of the PWM rectifier and input current vector components is obtained as below:
𝜓𝑙𝛼 (𝑡)
𝜓𝑠𝛼 (𝑡)
𝑖𝛼 (𝑡)
[
]=[
]+𝐿[
]
𝜓𝑙𝛽 (𝑡)
𝜓𝑠𝛽 (𝑡)
𝑖𝛽 (𝑡)
(5)
Therefore the values of the Virtual Flux components that corresponds to the converter side voltage at the end of switching
period could be computed as:
[
𝜓𝑠𝛼 (𝑘 + 1)
𝜓𝑙𝛼 (𝑘 + 1)
𝑖𝛼 (𝑘 + 1)
𝜓𝑙𝛼 (𝑘)
𝑖𝛼 (𝑘 + 1)
]=[
]−𝐿[
]=[
]−𝐿[
]
𝜓𝑠𝛽 (𝑘 + 1)
𝜓𝑙𝛽 (𝑘 + 1)
𝑖𝛽 (𝑘 + 1)
𝜓𝑙𝛽 (𝑘)
𝑖𝛽 (𝑘 + 1)

Hence substituting (3) in (6) results:
[
−𝜓𝑙𝛽 (𝑘)
𝜓𝑠𝛼 (𝑘 + 1)
𝜓𝑙𝛼 (𝑘)
𝐿
]=[
]−
2[
𝜓𝑠𝛽 (𝑘 + 1)
𝜓𝑙𝛽 (𝑘)
𝜓𝑙𝛼 (𝑘)
𝜔‖𝜓𝑙𝛼𝛽‖
𝜓𝑙𝛼 (𝑘) 𝑃(𝑘 + 1) − 𝑃(𝑘)
𝑖𝛼 (𝑘)
][
]−𝐿[
]
𝑖𝛽 (𝑘)
𝜓𝑙𝛽 (𝑘) 𝑞(𝑘 + 1) − 𝑞(𝑘)

And also it could be obtained from (5):
[
𝜓𝑠𝛼 (𝑘)
𝜓𝑙𝛼 (𝑘)
𝑖𝛼 (𝑘)
]=[
]−𝐿[
]
𝜓𝑠𝛽 (𝑘)
𝜓𝑙𝛽 (𝑘)
𝑖𝛽 (𝑘)

On the other hand we know that the convertor side voltage (𝑣𝛼𝛽 ) is the derivative of the corresponding Virtual Flux (𝜓𝑠𝛼𝛽 )
as (9).
𝑣𝛼𝛽 =
𝑑
𝑑𝑡
𝜓𝑠𝛼𝛽 

By using a discrete first order approximation of (9), the value of the components of the convertor voltage at the beginning of
the switching period can be obtained as (10):
𝑣𝛼 (𝑘) =
{
𝑣𝛽 (𝑘) =
𝜓𝑠𝛼 (𝑘+1)−𝜓𝑠𝛼 (𝑘)
𝑇𝑠

𝜓𝑠𝛽 (𝑘+1)−𝜓𝑠𝛽 (𝑘)

𝑇𝑠
Now we discuss about the values of the P(K+1) and q(K+1). The desired conditions are achieved when the active and reactive
powers of the PWM rectifier reach to their reference values. Thus the average of the convertor voltage vector should be
adopted so that to cancel the power errors as below:
[
𝑃𝑟𝑒𝑓 (𝑘 + 1)
𝑃(𝑘 + 1)
]=[
]
𝑞(𝑘 + 1)
𝑞𝑟𝑒𝑓 (𝑘 + 1)

Approximately in all DPC schemes, the reference value of the active power is derived from the output of a PI controller for
DC-bus voltage that is multiplied by the DC bus voltage. If the tracking error of DC side voltage is assumed constant during
switching period from start to end, the instantaneous active power command at the beginning of the next switching period
P(k+1) can be estimated using a linear extrapolation as shown in Fig. 4. While the reference value of the reactive power is
given directly from the outside of the control unit and usually is equal to zero for unity power factor operation. Therefore the
equation (12) can be expressed:
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International Journal of Enhanced Research Publications, ISSN: XXXX-XXXX
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[
𝑃𝑟𝑒𝑓 (𝑘 + 1)
2𝑃𝑟𝑒𝑓 (𝑘) − 𝑃𝑟𝑒𝑓 (𝑘 − 1)
]=[
]
𝑞𝑟𝑒𝑓 (𝑘 + 1)
𝑞𝑟𝑒𝑓 (𝑘)

Finally the equation (7) can be rewritten as below:
Figure 4. Estimation of the predictive value for active power command
[
−𝜓𝑙𝛽 (𝑘)
𝜓𝑠𝛼 (𝑘 + 1)
𝜓𝑙𝛼 (𝑘)
𝐿
]=[
]−
2[
𝜓𝑠𝛽 (𝑘 + 1)
𝜓𝑙𝛽 (𝑘)
𝜓𝑙𝛼 (𝑘)
𝜔‖𝜓𝑙𝛼𝛽‖
𝜓𝑙𝛼 (𝑘) Δ𝑃𝑟𝑒𝑓 (𝑘) + 𝜀𝑃 (𝑘)
𝑖𝛼 (𝑘)
][
]−𝐿[
]
𝑖𝛽 (𝑘)
𝜓𝑙𝛽 (𝑘)
𝜀𝑞 (𝑘)

Where 𝜀𝑃 (𝑘) and 𝜀𝑞 (𝑘) are the actual active and reactive powers tracking errors, respectively and Δ𝑃𝑟𝑒𝑓 (𝑘) is the actual
variation of active power command, defined as Δ𝑃𝑟𝑒𝑓 (𝑘) = 𝑃𝑟𝑒𝑓 (𝑘) − 𝑃𝑟𝑒𝑓 (𝑘 − 1).
B. Rotating Reference Frame
Virtual Flux based predictive control, represented in the stationary reference frame, can be expressed in the rotating reference
frame d-q using the following equations:
𝑖𝑞
𝑃
[ ] = 𝜔𝜓𝑙𝑑 [ ]
𝑞
𝑖𝑑

Under purely sinusoidal and balanced condition of the supply network, the amount of the 𝜓𝑙𝑑 is exactly constant in the steady
state condition and can be expressed as 𝜓𝑙𝑑 (𝑘 + 1) = 𝜓𝑙𝑑 (𝑘) = 𝜓𝑙𝑑 (𝑚𝑎𝑥). As a result, the difference between active and
reactive powers during a switching period can be expressed as
[
𝑖𝑞 (𝑘 + 1) − 𝑖𝑞 (𝑘)
𝑃(𝑘 + 1) − 𝑃(𝑘)
] = 𝜔𝜓𝑙𝑑 [
]
𝑞(𝑘 + 1) − 𝑞(𝑘)
𝑖𝑑 (𝑘 + 1) − 𝑖𝑑 (𝑘)

What mentioned in the stationary reference frame about the left side of the equation (2), remains true in the rotating reference
frame i.e. in (15). Hence the amount of the 𝑖𝑞 and 𝑖𝑑 at the start of the next switching period can be computed using (15).
On the other hand the differential equations of a PWM rectifier in d-q frame can be expressed as
[
𝑒𝑞 (𝑡)
𝑣𝑞 (𝑡)
𝑖𝑞 (𝑡)
𝜔𝐿(𝑡)
𝑑 𝑖𝑞 (𝑡)
]=[
]+𝐿 [
]+𝑅[
]+[
]
𝑑𝑡
−𝜔𝐿𝑖
(𝑡)
(𝑡)
(𝑡)
(𝑡)
𝑒𝑑
𝑣𝑑
𝑖𝑑
𝑖𝑑
𝑑 (𝑡)

In order to decouple the previous differential equation, it could be assumed that 𝑢𝑞𝑑 (𝑡) = 𝑣𝑞𝑑 (𝑡) ± 𝜔𝐿𝑖𝑞𝑑 (𝑡) and by
neglecting the influence of the resistance R and taking an integral from the obtained equation the result will be as follows:
[
𝜓𝑙𝑞 (𝑡)
𝜓𝑢𝑞 (𝑡)
𝑖𝑞 (𝑡)
]=[
]+𝐿[
]
𝜓𝑙𝑑 (𝑡)
𝜓𝑢𝑑 (𝑡)
𝑖𝑑 (𝑡)

By referring to the equations expressed in the α-β frame, following equations can be written in the d-q frame:
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𝜓𝑢𝑞 (𝑘)
𝜓𝑙𝑞 (𝑘)
𝑖𝑞 (𝑘)
]=[
]−𝐿[
]
𝜓𝑢𝑑 (𝑘)
𝜓𝑙𝑑 (𝑘)
𝑖𝑑 (𝑘)

𝜓𝑢𝑞 (𝑘 + 1)
𝜓𝑙𝑞 (𝑘 + 1)
𝑖𝑞 (𝑘 + 1)
]=[
]−𝐿[
]
𝜓𝑢𝑑 (𝑘 + 1)
𝜓𝑙𝑑 (𝑘 + 1)
𝑖𝑑 (𝑘 + 1)

[
[
And so
{
𝑢𝑞 (𝑘) =
𝑢𝑑 (𝑘) =
𝜓𝑢𝑞 (𝑘+1)−𝜓𝑢𝑞 (𝑘)
𝑇𝑠

𝜓𝑢𝑑 (𝑘+1)−𝜓𝑢𝑑 (𝑘)

𝑇𝑠
And finally the rectifier average voltage vector in the d-q reference frame is given by the following expression:
[
𝑣𝑞 (𝑘)
𝑢𝑞 (𝑘)
𝜔𝐿𝑖𝑞 (𝑘)
]=[
]+[
]
𝑣𝑑 (𝑘)
𝑢𝑑 (𝑘)
−𝜔𝐿𝑖𝑑 (𝑘)

To use SVM switching strategy, it is needed to transform 𝑣𝑞𝑑 to 𝑣𝛼𝛽 i.e. from rotating coordinates in to stationary one. It can
be done by using the following transformation matrix:
[
𝑣𝛼 (𝑘)
−sin⁡(𝜃)
]=[
𝑣𝛽 (𝑘)
cos⁡(𝜃)
cos⁡(𝜃) 𝑣𝑞 (𝑘)
][
]
sin⁡(𝜃) 𝑣𝑑 (𝑘)

Simulation Results
To study the performance of the VF based Predictive DPC (VF-PDPC) system under different supply voltage conditions, the
PWM rectifier with proposed control scheme in both stationary and rotating reference frames has been simulated using
MATLAB/Simulink tool. The main electrical parameters and control data of the system are given in Table. I Furthermore, V
based predictive DPC (V-PDPC) control scheme has been simulated on the same electrical system in order to compare the
operation of it with one of the VF-PDPC under distorted supply voltage conditions.
Table 1: Electrical parameters of power circuit
Item
Value
Switching period Ts
65 µS
Resistance of reactor R
0.56 [Ω]
Inductance of reactor L
19.5 [mH]
DC-bus capacitor C
1100 µF
Load resistance RL
68.6 [Ω]
Line to line AC voltage E
85 V rms
Source voltage frequency f
50 Hz
DC-bus voltage vdc
180 V
Simulation results in steady state and under ideal supply voltage condition obtained with Voltage based P-DPC in α-β
reference frame is shown in Fig. 5. Also simulation results with the proposed VF-PDPC in both α-β and d-q reference frames
are shown in Fig. 6 and Fig. 7 respectively. In these Figures (vα,vβ) is the components of the convertor average voltage vector
which are calculated by the corresponding algorithms.
As it can be seen from these results, the proposed Virtual Flux based P-DPC is as good as Voltage based P-DPC under ideal
voltage conditions. Furthermore the THD of the input currents is improved just by 0.01% which is very impalpable.
Fig. 9 to Fig. 20 show simulation results of the PWM rectifier under harmonic distorted supply voltage (%5 of fifth harmonic
have been added to the ideal supply voltage). Simulation results are obtained by both Voltage and Virtual Flux based P-DPC
in the stationary and rotating reference frames.
Moreover Fig. 8 presents dynamic response and transient behavior of the PWM rectifier in the startup conditions. This result
is obtained with proposed VF-PDPC in the rotating frame. As can be seen in this figure, the DC bus voltage reaches and stays
in its reference value in less than 120ms. There is some oscillations in the initial times (before t=120ms) of the response
which there is not in the response obtained by V-PDPC; this is because of the estimation process of the Virtual Flux.
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a)
b)
c)
d)
Figure 5. Simulation results of PWM rectifier in steady state for Voltage based P-DPC in stationary (α-β) reference frame. (a): Active/Reactive Powers,
qref=0, (b): three phase Currents, THD= 0.65%, (c): DC bus Voltage, Vdcref=180 v, (d): Convertor Average Voltage in α-β frame.
a)
b)
c)
d)
Figure 6. Simulation results of PWM rectifier in steady state for Virtual Flux based P-DPC in stationary (α-β) reference frame. (a): Active/Reactive
Powers, qref=0, (b): three phase Currents, THD= 0.64%, (c): DC bus Voltage, Vdcref=180 v, (d): Convertor Average Voltage in α-β frame.
a)
b)
c)
d)
Figure 7. Simulation results of PWM rectifier in steady state for Virtual Flux based P-DPC in rotating (d-q) reference frame. (a): Active/Reactive Powers,
qref=0, (b): three phase Currents, THD= 0.64%, (c): DC bus Voltage, Vdcref=180 v, (d): Convertor Average Voltage components in d-q frame
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Figure 8. Dynamic response of DC bus Voltage using proposed VF-PDPC method in d-q frame
Figure 9. Instantaneous Active and Reactive Powers in steady state
conditions under V-PDPC algorithm in α-β frame
Figure 10. Instantaneous Active and Reactive Powers in steady state
conditions under VF-PDPC algorithm in α-β frame
Figure 11. Instantaneous Active and Reactive Powers in steady state
conditions under V-PDPC algorithm in d-q frame
Figure 12. Instantaneous Active and Reactive Powers in steady state
conditions under VF-PDPC algorithm in d-q frame
Figure 13. DC bus Voltage in steady state under harmonic conditions
that is controlled by V-PDPC algorithm in α-β frame
Figure 14. DC bus Voltage in steady state under harmonic conditions
that is controlled by VF-PDPC algorithm in α-β frame
Fig. 9 to Fig. 12 present the steady state condition of the active and reactive powers (Fig. 9 and Fig. 11 are obtained by VPDPC in stationary and rotating frames respectively and Fig. 10 and Fig. 12 are obtained by VF-PDPC in stationary and
rotating frames respectively). Also Fig. 13 to Fig. 16 present DC-bus voltage in steady state (Fig. 13 and Fig. 15 are obtained
by V-PDPC in stationary and rotating frames and Fig. 14 and Fig. 16 are obtained by VF-PDPC in stationary and rotating
frames respectively).
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Figure 15. DC bus Voltage in steady state under harmonic conditions
that is controlled by V-PDPC algorithm in d-q frame
Figure 16. DC bus Voltage in steady state under harmonic conditions
that is controlled by V-PDPC algorithm in d-q frame
Figure 17. Three phase Currents of the rectifier under harmonic
conditions that is controlled by V-PDPC algorithm in α-β frame (THD
of phase A is 5.32% and THD of phases B,C is 5.77%)
Figure 18. Three phase Currents of the rectifier under harmonic
conditions that is controlled by VF-PDPC algorithm in α-β frame (THD
of phases A, B and C is 1.29%)
Figure 19. Three phase Currents of the rectifier under harmonic
conditions that is controlled by V-PDPC algorithm in d-q frame (THD of
phase A is 5.27% and THD of phases B,C is 5.74%)
Figure 20. Three phase Currents of the rectifier under harmonic
conditions that is controlled by VF-PDPC algorithm in d-q frame (THD
of phases A, B and C is 1.23%)
It is obvious in these results that the ripples of the active and reactive powers and also DC-bus voltage in the proposed Virtual
Flux based P-DPC are less than in Voltage based P-DPC method. Since the ripples of the mentioned wave forms are negligible
in both methods, it cannot be a good reason to use VF-PDPC algorithm instead of V-PDPC. But the main feature of the
proposed method reveals itself in the wave form of the input currents. This feature is discussed in the next paragraph and the
figures are presented after that.
Fig. 17 to Fig. 20 present three phase AC currents of the PWM rectifier in steady state conditions (Fig. 17 and Fig. 19 are
obtained by V-PDPC in stationary and rotating frames and Fig. 18 and Fig. 20 are obtained by VF-PDPC in stationary and
rotating frames respectively). As can be seen in these results, the main advantage of the proposed method is that the THD of
the input currents in the proposed algorithm is about 5 times less than in Voltage based P-DPC (for VF-PDPC: THD in α-β
is 1.29% and in d-q is 1.23% and for V-PDPC: THD in α-β is 5.34% and in d-q is 5.27%). This feature is because of the low
pass filter nature of the integrator element which exists in the estimation process of the Virtual Flux.
There is a negligible problem in the proposed algorithm that reactive power of the PWM rectifier has a small offset in both
α-β and d-q reference frame. This offset is caused by the effect of the low pass filter in the Virtual Flux estimator because the
estimated Virtual Flux is not exactly lagged by 90 degrees from the corresponding voltage and there is about 3 to 4 degrees
error in it.
In 2011, a paper has presented a novel Virtual Flux observer that tries to eliminate this problem from the Virtual Flux
estimation [22], but it has not been considered in this work.
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Conclusion
This paper presents a new Predictive Direct Power Control (P-DPC) for three phase PWM rectifier which is based on Virtual
Flux (VF) space vector instead of Voltage space vector of the network. The proposed algorithm uses space vector modulation
(SVM) switching strategy that works with constant switching frequency. The VF P-DPC scheme has been discussed
theoretically in both stationary (α-β) and rotating (d-q) reference frames. In both frames the instantaneous active and reactive
powers tracking errors are cancelled at the end of each switching period by applying the required rectifier average voltage
vector during the switching period based on the principles of dead beat control. Simulation results have proved that under
ideal condition of the supply voltage, dynamic and steady state operation of the VF P-DPC is as good as Voltage based PDPC in both stationary and rotating coordinates. On the other hand, when supply voltage is harmonic distorted, performance
of the PWM rectifier from point of view of the ripple of the active and reactive powers and DC-bus voltage and especially
THD of the input currents using VF-PDPC is significantly better than V-PDPC so that THD of input currents decreases more
than 4 times.
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