Novel Sensorless Direct Power and Torque Control ofSpace Vector. Modulated AC/DC/AC Converter. M. Jasinski, Student. IEEE, D. Swierczynski, Student. IEEE ...
Novel Sensorless Direct Power and Torque Control of Space Vector Modulated AC/DC/AC Converter M. Jasinski, Student. IEEE, D. Swierczynski, Student. IEEE, M. P. Kazmierkowski, Fellow, IEEE Warsaw University of Technology7. Institute of Control & Industrial Electronics, ul. Koszykowa 75, 00-662 Warszawa, Poland, tel. (48) 22 628 06 65. fax (48) 625 66 33, e-mail: mja,7a ,isep.pw.edu.pl, swierczd(a'isep.pw.edu.pl, mpk(aisep.pw.edu.pl.
Abstract- A novel control strateD,- for PWM rectifierinverter system is proposed. Fast controls strategies such as line voltage Sensorless Virtual Flux (VF) based Direct Power Control with Space Vector Modulator (DPC-SVM) for rectifier and Direct Torque Control with Space Vector Modulator (DTC-SVM) for inverter side are used. These strategies lead to good dynamic and static behaviour of the proposed control system- Direct Power and Torque Control- Space Vector Modulated (DPT-SVM). The results obtained in simulations and experiment show good performance of the proposed system. Additional power loop from motor to PWM rectifier side improved dynamic behaviors of the power flom control. As result, better input-output energy matching allows decreasing the size of the dc-link capacitor.
Index^ Terms- AC/DC/AC converter, direct power control, direct torque control, adjustable speed drives with PWM rectifier. L. INTRODUCTION
The adjustable speed drives (ASD) with diode rectifier nowadays is most popular on the marked. An large electrolytic capacitor is used as an energy storing device to decouple rectifier and the inverter. That capacitors have some drawback from reliability,. size, weight and cost. Hence, reliability, of the dc-link capacitor is the major factor limiting the lifetime of the ASD systems [1]. Development of control methods for Pulse Widtli Modulated (PWM) boost rectifier (active rectifier) was possible tlanks to advances in power semiiconductors devices and Digital Signal Processors (DSP), which allow fast operation and cost reduction. Therefore, the Insulated Gate Bipolar Transistors (IGBT) AC/DC/AC converter fully controlled by PWM is used in motor drive sv stems (Fig. 1). Thanks to active rectifier the dc-link capacitor can be reduced [2]. Farther reduction of the capacitor can be achieved b, power feedforward loop from motor side to the control of the rectifier. Therefore. a lot of work are inclined to reduce the dc-link capacitor. However, a small capacitance leads to a hligh dc-voltage fluctuations. To avoid this drawback various dc-voltage control schemes have been proposed. Some of them take into account the inverter dynamics to improve the PWM rectifier current control by feedback linearizing [3] and master-slave [1] manner. Another control methodology proposed a fast dc-link voltage controller which works with dc- voltage and motor variables as an inputs [4]. Moreover various method of the output power estimation have been discussed in [5].
0-7803-8304-4/04/$20.00 G2004 IEEE
In mentioned methods active and reactive powers of the PWM rectifier are indirectly controlled via current control loops. Besides, the torque and flux of the motor are controlled by stator current controllers too. In this paper a line voltage sensorless Virtual Flux (VF) based Direct Power Control with Space Vector Modulator (DPC-SVM) is applied to control of the PWM rectifier. The inverter with induction motor are controlled via Direct Torque Control with Space Vector Modulator (DTC-SVM). Contrary to the scheme proposed in [6] our solution includes not stator flux controller but space vector modulator. Hence, an AC/DC/AC converter Fig. 1, is controlled by Sensorless Direct Power and Torque Control- Space Vector Modulated (DPT-SVM). In comparison to methods which control an active and reactive power, torque and flux in indirect manner the coordinates transformation and decoupling are not required. Moreover, the current control loops are avoided. In respect of dynamic, of dc-voltage control the power balance between line and motor is very important. Therefore, to improve instantaneous input/output power matching the additional feedforward power control loop is introduced. Tlanks to better control of the power flow the fluctuation of the dc-link voltages will be decrease. So the size of the dc-link capacitor can be reduced. II. SENSORLESS DIRECT POWER AND DIRECT TORQUE CONTROL SPACE VECTOR MODULATED (DPT-SVM) SCHEME
Direct Power Control (DPC) for PWM rectifier is based on instantaneous control of active p and reactive q power flow from/to the line and to/from active load. In classical approach [7]. [8] of DPC there are two power control loops with hysteresis comparators and switching table. Therefore, tlhe kev point of the DPC inmplementation is sufficientlyT precise and fast estimation of the line powers. Hence, the most significant drawbacks of the DPC are variable switching and high sampling frequency. Above nmentioned problems can be eliminated by introducing a Space Vector Modulator (SVM) in control strategy [9. 10]. Moreover, the line voltage sensors can be replaced by Virtual Flux (VF) estimator, which introduces technical and economical advantages to the system (simplification, reliability, galvanic isolation, cost reduction). Such control syTstem is called in literature: Virtual Flux Based Direct Power Control Space Vector Modulated (DPC-SVM) [11]. In this method hysteresis comparators and switching table are replaced by linear PI controllers with Space Vector
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related as quantities of virtual AC motor and the integration of the line voltage gives flux linkage of the virtual AC motor the VF estimator with low pass filter is used.
a)
Ur
V-f L
=
f (ii-S
+
I
(3)
dt I III ) -.VL TC
The measured line currents and flux linkage obtained from (3) can be used in power calculations [11]: P
Line (Virtual Motor)
,
PWNI Rectifier
v
e
4
PWM Inverter
Motor
Fig. 1. Representation of three-phase PWM rectifier- inverter system, vector diagram and coordinate system for: a) PWM rectifier side b) inverter side
ear PI controllers with Space Vector Modulator. Similarly to DPC in classical Direct Torque Control (DTC) [12]. the command stator flux Vs, and torque A,ec values are compared with the actual Es and Af1, values in hyJsteresis flux and torque controllers. respectively. Therefore, the well-known disadvantages of DTC are: variable switching frequency. ± 1 switching over dc-link voltage Ud,. current and torque distortion caused by sector clhanges as well as high sampling frequency requirement for digital implementation of the hysteresis controllers. All above difficulties can be eliminated when. instead of the switcliing table, a SVM is used. Hence, the DTC-SVM strategy [13] for control of the inverter/motor part is proposed. Simplify matlhematical model of the system in stationanr oat coordinates is slhown in Fig.2a - PWM rectifier and in Fig.2b-inverter/motor side. 1. DPC-STj I with J `irtual Flux (F,.)
A line current iL is controlled bv voltage drop on the input inductance L which placed between two voltage sources (line on the one side and the converter on the otlher). From Kirhoffs law the input equations can be wrote: ULL
=UI
+/S,
(1)
where:
_I
=
'-L
LLL8 j d
- voltage drop on the inductance
dt a
Lae
dt I 1iL/)
+
COML,jLr (4L)iL,
dt a i)dt lL4U+)(oPiaC+L/3) For assumptions that line voltages is sinusoidal and balanced the derivatives of the flux equals to 0. so the Eq. (4) simplify to:
LELaiL i V'Lf8'L ) q = Cf(f7LaszLa + LqiLA )
P=
-
Both estimated powers are compared with references values Pc? q, respectively, were q, is set to zero for fulfilling unity power factor conditions. The reference of Active power pc is provided from outer PI dc-link voltage controller. Obtained errors are dc quantities. These signals are delivered to PI controllers that eliminate steadir state error. The PI controllers generate dc-values voltage commllands up., Uqc. After simple transformation to u,. u& signals are used for switching signals generation by SVM block in Fig.3 . 2.
DTC-ST WI
DTC-SVM is based on closed electromagnetic torque and stator flux control loops. The demanded torque is calculated from measured motor current and estimated stator flux. Proposed method works in cascade manner (Fig. 3). In this scheme the torque controller generates the command value of the torque angle increment A85,, which is added to the stator flux position Ys in the stator reference frame a,,/ to calculate the command stator flux vector _V Then the V, is compared with the estimated one § and the error is used for calculation of the commanded stator voltage vector according to (11). Hence, proposed solution allows simple limit of the motor torque and current (with constant stator flux magnitude). Therefore. accuracy of the flux calculation is indispensable. That goal can be obtained with a voltage model based estimator. with low pass filter.
(2)
where -
Ks
-
rs is )Y
(6)
f' s]di
where:
Voltage on the input of the converter can be calculate form measured dc-link voltage Udc and an duty cycles from modulator DA, DB? DC (2). Therefore, proposed DPC-SVM is sensorless line voltage control strategy. Based on assumption that line voltage e with input inductances can be
+DC2)) Us')
The electromagnetic torque can be calculated from:
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(7)
a) Rectifier
b) Inverter/motor
D
f __
X
U-
T
|
Taking into considleration the overall power supplied to iA telectric | motor stator and rotor windings from (12) can be write: =9 Resi]
19 D P.-,
I
j
i'
PbIm isL
Iw
Pb
(Msais8
From assumption that onhx active power is derived from the dc-link to an electric motor and reactive power is derived from the inverter only electromagnetic power can be taken into consideration. In a general way Pe is equal to electromagnetic torque -M-e developed by an electric motor multiplied bv mechanical angular rotor speed Q:
fsAs) 6(9)
Another expression of electromagnetic torque can be written [13]: A;Ie
-
m
in
?
VSC cos(yS +ZA)- V cos(y5)
sc sm (7s ++Ag) Lsf6c _ s(TS
Tt
Pe Al, D
-
+Rs
=ecHec nmc nc PeFc =A
6 (16)
Such calculated power can be simply added to the referenced active power of the PWM rectifier. To fulfill the stability conditions of the svstem the T1, delay should be taken into consideration:
Pe =- I 1 T.
I ec'
lp
~~~~~~~~(17)
Thanks to predictive abilities of feedforward loop better dclink voltage stabilization can be obtained. The fluctuation of dc-v-oltages expect to be reduced. Therefore farther reduction of the dc-link capacitor is possible.
Vs sin(7s)R-ss)( + S/
where T, - sampling time. 3.
(15)
Hence. active power feedforwNard can be realized based on Eq. 15. The electromagnetic power is the part of the power supplied to the electrical teniinals of a motor which is neither stored nor lost. It corresponds to the voltages induced in rotor windings and to the currents flowing into them [11]. For prediction of the power state of the motor (motoring, regenerating. loaded or unloaded) in computing can be taken the referenced values of the electromagnetic torque and mechanical speed.
(10)
From Eq. (10) can be seen that realized motor torque is proportional to stator, rotor flux amplitudes and sine of angle between them (Fig. lb). With assumption that stator flux dynamics is much higher then rotor one torque can be controlled by stator flux. Hence, through changing of the torque angle 8iT value (wliich can be set bv stator flux position) the electromagnetic torque can be controlled. Assuming that stator flux is equals to integrated voltage vector applied to a terminal of the stator (the voltage drop on stator resistance is neglected). Therefore, Me can be controlled by the value of stator voltage vector. In DTC-SVM from the reference of the stator flux and its position the appropriate voltage vector can be calculated, which is realized bv SVM block in Fig.3. LiT Lsa2c =
(14)
wlhere Pnha,' is the power stored in the magnetic fields, Peis the electromagnetic power.
(8)
-
p7f)mrag +Pe I
wlhere m,- number of phase=3. pb- nmnber of pole pairs=2. What gives in (c?, 3) coordinates: lIfe
(13)
Ipower is:
PkNV1RECI1FER STATM \INVERETRI Block 2. Fig. diagram of AC/DC/AC converter in a, , coordinates Ale =
ReLj
The losses in resistanices can be neglected. tlhus the internal
El ~~
I
(12)
] a2 P= nirsRekS2isI t dc
T(;TdJ
Pmax
Cd2UdCA- 4dcmax
(18)
Fig. 3. Block scheme of DPT-SVM control method for ACIDC AC converter with PWM rectifier
where AP,,,- maximum expected variation of the output power. Moreover. the general capacitor life equation is: L =LB X f(TAl
-TC) X fi(V )
I
(19)
where L is the life estimate in hours, LB is the base life elevated maximum temperature TA!, TC is the actual core temperature and T - is the applied dc-voltage. The voltage multiplierfi at higher stress level may. reduce the life of the capacitor [14]. Therefore, stability of the dc-voltage at required level is important. III. SIMULATION AND EXPERIMENTAL RESULTS
Proposed approach has been tested using Saber simulations packed softiware. The main data and parameters of the model are shown in Tab. 1. Experimental investigations was conducted on a laboratorNy setup (Fig. 4). The setup consists of: input inductance, two PWM converter (VLT5005. serially produced bv Danfoss with replaced control interfaces) controlled by dSPACE DS 1103 and induction motor set. The computer is used for software development and process visualization. Converters, motor and ilnput inductance parameters are shown in Tab.2. In below figures are shown different states of working of the DPT-SVM. In Fig.5a the svstem works in motoring mode, with power factor near to unity (tlhe current is in phase with the line voltage) and almost sinusoidal in shape (low Total Harmonic Distortion-THD factor) line current. In Fig.5b AC/DC/AC converter works in regenerating mode (as a transmitter of the energy from the motor to the line). The current is shifted by 180 degree in respect to the
Fig.4. Laboratory setup
line voltage, while in Fig.6. transients in power flow direction with different values of the dc-link capacitor are shown. In Fig.7. an experimental wavefonns of transients to a) commanded active power and b) electromagnetic torque are presented. More detail experimental results will be shown in the future.
1150
1685H
Mutual ind ucrsitance: w
C1.0~~~~~~~~~~~*
2 Number of pole airs: Moment of inertia: 0.01l9kgm' Phase voltage: 220 V(rms) 6. 9A(rmns) Phase current I: 2ONm Nomiinal torque MN: Base speed (Db 1415rpm lqput iniductanice Resistance of reactors R: 100mIQ lOmiH Iniductanice of reactors L: J 71T5005 Converters Sampling and switching frequencyN: 5kHz 235u]F DC-link capacitor: Nomiinal power PN: 5.5 kVA Mfeasuremnent conditions Phase voltage V: 100 RMS 50 Hz Source voltage frequency: DC-link voltage: 150V
--!
-------------------------------10 C, O.C. -?,,
I'~~~~~~~~~~~~~~~~~~~~~~~~d
a)
lIb)~
r-
700
]
,,.AL
~
69c) 0
jaa;]
.............
-------------
~
~
~
L
a!
---
-----------
.............
Me----------
mode-----
--------mode.h)-regenerating
Fig. 6.Transient in power flowx direction from the top:AMe electromagnetic torque. Uk wxithiout feedforward. Ud, with feedforwxard. IL-inme current. u1- line voltage-, a) C= 18OuF. b) C 235uF, c) C= 47OuF
leg 5
S e d
at es
Vita
e
cta e f o
er
Itop
are t
nd-usmager tq anttirq
e
Power lxBsdDirect
s.u
empnce nt
L
o
btained
ste
v
trol loop was implemented and tested. Proposed control system assures: *constant swvitching frequency-, * sinusoidal line current (low THJD) for ideal and distorted line voltage. * noise resistant power estimation algorithm. * low motor current and torque ripple. *high dynamiics of power and torque control, *good stabilization of the dc-v,,oltage. Power feedforward loop from the motor side to the PWM rectif'ier improved control dyTnam-ics of the dc-link voltage. It allows to fulfill power matchiing conditions under transient for PWM rectifier and inverter/motor system.
o
Sotaensor
Control-wt Space
(DPt-SVM)e Mecoreover,laddtiona powerVMfeafrearpidcon
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[2] L. Malesanil, L. Rossetto. P. Tenti and P. Tomasin. "AC/DC/AC Power Converter with Reduced Energy Storage in the DC Link." IEEE Transaction on induistrial A4pplictions. vol. 31, NO. 2. March/April 1995. pp. 287-292. [3] J. Jung,, S. Lim, and K. Namn "A Feedback Linearizing Control
Scheme for a PWM Converter-Inverter Having a Very Small DC-link
Capacitor," IEEE Transaction on Industrial.Applictions. vol. 35., NO. 5. September/October 1999. pp. 1 124 113 1. [4] J. S. Kim and S. K. Sul, "'New control schieme for ac-dc-ac converter without dc link electrolytic
PE,SC'93, 1993. pp. 300 306.
capacitor.."
in Proc.
of the IEEE
[5] R. UThrin. F. Profumo "Performance Comparison of Output Power [6] 1-1-im" A
[7]
[8]
~4
[9] [10] [11]
[12] Fig. 7. Experimental results. Transients to refere-nce: a) pr-commanded active povwer from 0.1I to 0.5 PN. p- actual active power. q- reactive. power: b) AleC' commnanded torque from 0 to 1 MN, ~ actual electromagnetic torque
[13]
Estimators Used in AC'DC, AC Converters,"' IEEE, 1994. pp. 344348. A. Tripathi. A.M. Khambadk-one. S5K. Panda. "Space-vector based. conistanit frequency. direct torque control and dead beat stator flux conitrol of AC machines." Proc. of the IECON '0]. V ol.: 2 'pp. 1219 -1224 vol. 2. Noguichi T.. Tomnik-i H.. Kondo S.. Takahashi I.: "Direct Power Control of PWM1 coniverter withiout power-source voltage sensors." IEEE Trans. on Jnd. .4ppl. Vol.34. No.3. 1998. pp. 47-3-479. Ohnislil T.: "Thiree-phase PWM converter inverter- by means of in.stanitalieous active anid reactive power control," In Proc. of the 1EEE-IECQ\VCon/f. 1991. pp. 819-824. J. Holtz "Piulsewsidth Moduilationi for Electronics Power Conversion." Proceecdings of The IEEE. vol. 82. no. 8. Auigust 1994. pp. 1 19412 14. M. P. Kazmiierk-ow ski. R. Krishnian and F. Blaabjerg Contr-ol in Power Electr-onics. Academilc Press. :2002. pg. 579. M.Malinow ski. NI.P. Kazmierk~ow ski "Simple Direct Power Control of Three-Phiase PWNM Rectifier Using Space Vector Modulation- A Comparatix e Study."- in EPE .iurnal. vol. 13. NO. 2. May 2003. pp. 28-34. I. Takahashi. anid T. Noguchil. "A New Quick-Response and Highi Efficiency Control Strateg\- of ani Induiction Machine." IE-EE Transaction on IhiduLsti'icil .4pplictions~. v7ol. I.A-22. NO. 5. September/October 1986. pp. 820-827. D. Swierczyniski. M.P. KaznijeroW ~Nski "Direct Torque Control of Permanient Magnet Synlchronouis M-otor (PMSM) Using Space Vector Modulation (DTC-S\'M1)." Slimuliation and Experimental Results".
IECONV 2002. Sevilla. Spaini. oni-CD. [14] 5. G. Perler "Deriving Life Mlultipliers for Electrolytic Capacitors." IEE-E PES' ewsletter. First Quar-ter- 2004. pp. 11I- 12. [15] H. Tajima. and Y. Horn. "Speed Senisorless Field-Oriented Control of the Induction Machinie". IEEE Troi-inactuon on Induistrial .4pplictions
V. ACKNOW1LEDGEMENT
Authors would like to thank the Polish Research Commiittee (KBN) for the financial support of the work (thie grant no. 4 T1IOA 073)24).
.Vol. 29. NO. 1. 1993. pp. 175-180.
VI.REFERENCES [1] H. Hur J. Jung., K. Nani. "A Fast Dynamics DC-link- PowerBalancing Scheme for a PWM Converter-Inverter Svstem"'. IEEE Transaction on Industrial Electronics. vol. 48. NO. 4. August 200 1,
[16] T.G. Habatler "A space vector-ba.sed rectifier regulator for AC !DC/AC converters". IE-EE Tr-ansaction on Power Electronics. vol. 8.. February 1993. pp. 30 36. [17] J.Ch. Liao and S.N. Yen. "A Novel Instantaneous Power Control Stratego- and .Analiic M-odel for Integrated Rectifier'Inverter Systems"'. IEEE Transacition on Powter Electronics, vol. 15. NO. 6, November 2000., pp. 996 1006.
pp. 794-803.
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