Direct Power Control for three-phase PWM rectifier
with active filtering function
ABSTRACT:
A novel Virtual Flux based Direct Power Control Space Vector Modulated
(DPC-SVM) for 3-phase PWM rectifier with compensation of higher harmonics function is
presented. The active and reactive power is used as a control variables for the PWM rectifier and
active filtering operation. As a result several coordinate transformations are eliminated.
Simulated and experimental steady state and dynamic performance for PWM rectifier and active
filtering operation are presented. Among the main advantages of DPC-SVM are: simple
algorithm, good dynamic and operation at constant switching frequency. Additionally a line
voltage sensors were replaced by the virtual flux estimator which also help to achieve sinusoidal
line current in case of distorted line voltage.
I. INTRODUCTION
Harmonics-related problems in utility are a result of usage equipments like a
diode or thyristor rectifiers, which takes non-sinusoidal currents from the grid. Several solutions
to eliminate pollution problems have been developed. They are an answer for more and more
restricted norms which intend to limit the harmonic current of power electronic converters.
Active power filters and PWM rectifiers are two typical examples of these methods. Both of
them have basically the same circuit configuration and can operate based on the same control
principle.
Active filters are able to compensate not only current harmonics, but also a reactive power and
unbalance of load.
Design and control have been investigated in many papers [9]- [12] where useful of active filters
were proofed.
PWM Rectifiers [1], [4] as a non-polluting equipment with sinusoidal input currents are going to
be more popular because of several advantages described as:
- Precise regulation of output DC voltage,
- Low harmonic distortion of line currents,
- Near sinusoidal current waveforms,
- Regulation of input power factor to unity,
- Bi-directional power flow.
This paper explores another task of PWM rectifier –
Active filtering function, which intend to connect advantages of active filters and PWM
rectifiers. So, the PWM rectifiers supply its load and at the same time compensate AC line
current (Fig. 1). This concept was previously introduced by some authors [6] - [8]. However, in
this paper a new approach for this problem is presented. The Virtual Flux based Direct Power
Control (DPC) [1] - [3] with Space Vector Modulator (SVM) [13] is applied to control of a
PWM rectifier. Thanks to DPC-SVM, AC line voltage sensor-less operation and sinusoidal line
current in case of distorted line voltage is obtained. Moreover, thanks to SVM algorithm, PWM
rectifier operates at constant switching frequency.
Block scheme of PWM Rectifier with active filtering function
II. BASIC PRINCIPLES OF VIRTUAL FLUX BASED ACTIVE AND
REACTIVE POWER ESTIMATION
It is economically motivated to replace the AC-line voltage sensors with a virtual
flux (VF) estimator The principle of VF is based on assumption that the voltages imposed by the
line power in combination with the AC side inductors can be quantities related to a virtual AC
motor (see Fig. 2). Where R and L represent the stator resistance and leakage inductance of the
virtual motor. Phase-to-phase line voltages: Uab, Ubc, Uca can be considered as induced by a
virtual flux. Hence the integration of the voltages leads to a virtual flux vector ΨL , in stationary
α-β coordinates as follows:
Figure 2. Three-phase PWM rectifier system with AC-side presented as virtual AC motor
Where
Operation of PWM rectifier is based on assumption, that input current ic is controlled
by the voltage drop across the inductor L interconnecting line and converter voltage sources. It
means that the inductance voltage uI equals the difference between the line voltage uL and the
converter voltage uS
And similarly a virtual flux equation can be presented as:
Figure 3. Reference coordinates and vectors: ΨL – virtual line flux vector, ΨS – virtual flux
vector of converter, ΨL – virtual flux vector of inductor, uS – converter voltage vector, uL -
line voltage vector, uI – inductance voltage vector, iL – line current vector
Based on the measured DC link voltage Udc and the duty cycles of SVM
modulator DA, DB, DC the virtual flux ΨL components are calculated in stationary coordinates
system as follows:
The measured input converter currents ica, icb and the estimated virtual flux
components ΨLα ,ΨLβ are used for the power estimation. The voltage equation (using (2)) can
be written as:
In practice, R can be neglected, giving
Using complex notation, the instantaneous power can be calculated as follows:
Where * denotes the conjugate line current vector. The line voltage can be expressed by the
virtual flux as:
Where denotes the space vector and its amplitude.
That gives
And
For sinusoidal and balanced line voltage the derivatives of the flux amplitudes are zero. The
instantaneous active and reactive powers can be computed as:
Fig. 4. Presents the block scheme of virtual flux and power estimators including active filtering
function
Figure 4. Block scheme of estimators
III. CONTROL ALGORITHM OF PWM RECTIFIER WITH ACTIVE
FILTERING FUNCTION
Control algorithm presented in Fig. 5. is divided into two parts: active rectifier and
active filtering operation described below.
A. PWM Rectifier operation
The commanded (delivered from the outer PI DC voltage controller) active power
pref and reactive power qref (set to zero for unity power factor) values are compared with the
estimated instantaneous p and q values, respectively. The errors are delivered to PI controllers,
where the variables are DC quantities and steady state error were eliminated. The output signals
from PI controllers after transformation described as:
Figure 5. Block scheme of control strategy
are used as a reference signals for Space Vector Modulator. Simulations and experimental results
for PWM rectifier under DPC-SVM control are presented on Fig. 6. and Fig. 7.
B. Active filtering operation
In 1983, Akagi has proposed the "The Generalized Theory of the
Instantaneous Reactive Power in Three-Phase Circuits", also known as instantaneous power
theory , or p-q theory. It was used to calculate the reference compensation currents in the α -β
coordinates [5], [9]. This paper presents modified algorithm based on virtual flux, which operates
directly on instantaneous active and reactive power components. The instantaneous active and
reactive powers are estimated using currents intended to compensate (diode rectifier input
currents see Fig. 1.) and virtual flux according to Eqs (11a and b) as:
The calculated active power (pA) and reactive power (qA) are delivered to the
high pass filter to obtain the variable value of the instantaneous active power ( p A) and reactive
power ( %q A) which finally are used as a compensating components. Enclosure of active
filtering function will cause suitable distortion of input PWM rectifier current. This will assure
almost sinusoidal line current. It permits to use non polluting equipment what is PWM rectifier
as a current harmonics eliminating device. Simulations and experimental results for active
filtering operation are presented in Fig. 8, 9 and 10
Fig. 8b. Presents the experimental results for PWM rectifier having active filtering
function. The notches visible on the line voltage waveform are generated by highly distorted
currents drawed by the diode rectifier and PWM rectifier. The active filtering operation startup
and the transient of the step change of the diode rectifier load are presented in Fig. 9. and Fig. 10
respectively. Those figures demonstrate stability of the system during dynamic conditions. It is
shown that line current during active filtering operation is almost sinusoidal
The main electrical parameters of the power circuit and control data are given in the Table I.
V. CONCLUSIONS
The line voltage sensor less Virtual Flux based Direct Power Control Space Vector Modulated
(DPC-SVM) for 3-phase PWM rectifier with active filtering function is presented. Based on
simulation study carried-out in SABER simulation package as well as experimental results
measured in the laboratory setup of Fig. 11. the main features and advantages of the system can
be summarized as:
1. No line voltage sensors are required,
2. Simple control algorithm without several coordinate transformation,
3. No current control loops, the system operates directly on instantaneous active and
reactive powers,
4. Good dynamics and no coupling between active and reactive power,
5. Sinusoidal line currents for ideal and distorted line voltage, thanks to the natural low-pass
filter behavior of the integrators used in flux estimator (Eqs. 4a and 4b),
6. Constant switching frequency thanks to SVM,
7. Proposed system can operate as a PWM rectifier, Shunt Active Filter or it can take the
role of PWM rectifier
8. Having active filtering function. This extends tasks of PWM rectifier on eliminating of
higher harmonics in line current. In this case PWM rectifier supply its load and at the
same time compensate for harmonics AC line current,
9. Thanks to active filtering function it is possible to use non polluting equipment what is
PWM rectifier as a current harmonics eliminating device, it is also possible to add this
function to currently working PWM rectifiers,
10. The system has been verified by the simulation and experimental study,
11. Compared to standard PWM rectifier, it have to be dimensioned for a bigger power ratio.
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