IEEE ISIE 2006, July 9-12, 2006, Montreal, Quebec, Canada
A
Simple
Switch Selection State Power Control
for
SVM
Direct
Jose Restrepo, Julio Viola, Jose Manuel Aller, Alexander Bueno Universidad Simon Bolivar Caracas, Venezuela Email:
[email protected]
TABLE I
Abstract- This work presents a simple scheme for vector selection in Direct Power Control (DPC) in a three-phase rectifier without the use of switch selection tables. The method is simulated using a C language description of the system and its results are later verified on an experimental test rig. Additional states are obtained using Space Vector Modulation (SVM) which reduce the hysteresis band of the active and reactive power controller.
RECTIFIER VOLTAGE SPACE VECTORS
I. INTRODUCTION The widespread use of solid state converters is a cause of concern due to its impact to the power system and more specifically to the general power quality, due to the injection of harmonics and phase displacement in the current of conven-
tional diode rectifiers. The strategies for dealing with this problem are, to compensate the effect of existing contaminating loads (active filters), or the use of new rectifier schemes with unity power factor or a combination of both, where the new rectifier system endeavors for an overall improvement of the power quality. Commonly these rectifier schemes use standard circuitry found in inverters. Most of the unity power factor rectifiers can be classified for its use of current loop controllers or active/reactive controllers. The control scheme employed defines the best method for driving the switching elements, for classical Direct Power Control [1], the state of the switching elements is established as on or off for the complete sample period, eliminating in this way the use of additional software or hardware. A direct consequence of this on-off control is an increase in the current ripple and in the high frequency noise injected to the power system, depending on the line inductance the effect of this commutation can be seen in the line voltage waveform. In this work a strategy for selecting the switching state without using predefined switching tables is proposed. An additional reduction of the current ripple is achieved by turning on the switches during part of the sampling period applying a SVM-PWM technique. II. THE PRINCIPLE OF DIRECT POWER CONTROL (DPC)
The use of a control strategy using switching tables similar to the one found in the control of ac machines are described in
[1] for V-DPC and in [2] for VF-DPC. A simple switch selection technique can be obtained by analyzing the instantaneous complex power s(t), defined as. s(t) =v *S (isysa * vsysa + isys Vsys) (1) +j(tsys a * Vsys tsys d sys a) 1-4244-0497-5/06/$20.00 © 2006 IEEE
Vrec
SA
SB
SC
Vrec a
Vrec8
0
0
0
0
0
0
1I
1
0
0
VDC
0
2
0
1
0
aD c
XDc
3
1
1
a VDC
XVc
4
0
0
5
1
0
6
0
1
VDC
IVDC
1
VD C
I
1
-=VDC
I
VD C 0
There are several ways of obtaining a measurement of the complex power; one that does not require line voltage sensors [1] is obtained using estimated values of this line voltage, by means of the rectifier switching state, DC-link voltage, and system current derivative as follows.
vsys (t)
=
Vrec (t) + R isys (t) + L
disy dt
(2)
Where R is the reactor resistance, L is the reactor inductance and vrec is the selected rectifier voltage. The rectifier voltage is defined as. Vrec '= d =
(SA + SBPi
3
+
Scj- 47) VDC
(3)
Vrec ag + j Vrec d
Where SA, SB, and SC indicates the switch state for each phase, and VDC is the DC bus link. The typical space vector representation for each basic switching state and its corresponding (a, Q) values are shown in Table I. III. ACTIVE AND REACTIVE POWER COMPENSATION
From (2) the instantaneous system current isys(t) can be controlled by selecting the proper rectifier voltage vrec. It can be seen from (2) that the change in line current depends on the actual system voltage, on the selected rectifier voltage, and in less measure on the actual line current. Hence, for correcting the active and reactive power there are six basic non
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zero rectifier voltages and two zero rectifier voltage vectors available. Rearranging (2) the line current change is provided by the following expression. dt
L
[vsys - R isys
-Vrecl
(4)
For a practical implementation a discrete first order approximation of these equations is used. The estimated system current for the next control period is given by
isys (k+I1)
=
isys (k) + disdt 5 (k) Ts = isys (k) +Aisys (k) (5)
Using this expression for the system current and from the complex power (1) the active power can be readily estimated for the next control cycle (k + 1) as.
Aqj(k) =Aqo(k) -[Vsys o (k)Vrec
vsys d (k)vrec a] LS
(16)
There are different ways of selecting the corresponding switching state that controls the evolution in active and reactive power [1], [2]. In this work the switching state that minimize a cost function (, the resulting error in active and reactive power in a square sense, is selected. In this way there is not need to be concerned with the choice of hysteresis bands for controlling the active and reactive power. The cost function ( is defined as.
-APk)2+kq (EQ Apk)2 Vk ={0 ...6} (17) p(k+l ) = vsys oe(k+l ) isys oe(k+l )+vsys d(k+l ) isys ,3(k+l) Where the constants kp and ki can be selected to control the (6) relative ripple of the active and reactive power, and Ep and EQ The estimated system voltage for the next control cycle is
vsys(k + 1) v5y5(k) + Av5s5(k) =
(7)
(8)
And for the reactive power
q(k+l)
=
v5y5a1 c-
ct
208 VRMS 60 Hz 600 V 10 ml 0.1 Q 10 A
0
0.1
0.2
0.3
0.4
0.5
Time (s) Fig. 12. Current and voltage from phase a when using 7 vectors.
ACKNOWLEDGMENT
1000 ,uF 10 kHz
The authors would like to thank the Dean of research and development at the Simon Bolivar University for the financial support to this work.
TABLE III POWER CIRCUIT EXPERIMENTAL PARAMETERS Per phase system voltage
-2
-10
REFERENCES
16 VRMS 60 Hz 64 V 10 ml 1.5 Q 1000 ,uF 10 kHz
vector. The increase in the amount of synthesized vectors allows for a reduction in the amount of ripple present in
[1] T. Noguchi, H. Tomiki, S. Kondo, and I. Takahashi, "Direct power control of pwm converter without power-source voltage sensors," IEEE Trans. Ind. Applicat., vol. 34, pp. 473-479, 1998. [2] M. Malinowski, M. P. Kazmierkowski, S. Hansen, F. Blaabjerg, and G. Marques, "Virtual flux based direct power control of three-phase pwm rectifiers,," IEEE Trans. On Ind. Applicat., vol. 37, pp. 1019-1027, 2001. [3] N. Mohan, Advanced Electronic Drives. Minneapolis, MN: MNPERE, 2001. [4] VisualDSP++ 4.0, C/C++ compiler and library, Manualfor ADSP-21xxx DSPs. Analog Devices Inc., 2005. [5] J. Restrepo, M. I. Gim6nez, V. Guzman, J. M. Aller, A. Bueno, and A. Millan, "PLATFORM III: A new version for the integrated test system for ac machine drives performance analysis," in Proceedings of the Fourth International Caracas Conference on Devices, Circuits and Systems, Apr. 2002, pp. 1036(1)-1036(6).
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