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1 A Vector Modulated Three-Phase Four-Quadrant Rectifier – Application to a Dc Motor Drive Matti Jussila, Mika Salo, Lauri Kähkönen, and Heikki Tuusa Abstract–This paper introduces a theory for a space freewheeling diode drive can operate only in the first vector modulation of a three-phase four-quadrant PWM quadrant as presented in [3]. In [3] the two-quadrant rectifier (FQR). The presented vector modulation operation is achieved with four-quadrant dc-dc converter in method is simple to realize with a microcontroller and it field excitation circuit, which increases the complexity of replaces the conventional modulation methods based on the control system and also delays the control. the analog technology. The FQR may be used to supply With the FQR the four-quadrant operation of the dc drive directly a dc load, e.g. a dc machine. The vector is achieved using the vector modulation with a constant field modulated FQR is tested in simulations supplying a 4.5 excitation. Thus, the FQR is superior in dynamic response kW dc motor. The simulations show the benefits of the when compared to systems of thyristor bridges using field vector modulated FQR against thyristor converters: the excitation or mechanical switches to achieve reverse supply currents are sinusoidal and the displacement rotational speed. power factor of the supply can be controlled. The FQR is also a more supply friendly solution than a Furthermore the load current is smooth. conventional combination of two antiparallel connected six- Index Terms–PWM rectifier, dc motor drive, space pulse converters and simpler than a four-quadrant dc-dc vector modulation chopper needing a separate rectifier, both of which are presented in [10]. Furthermore, with the IGBTs with reverse I. INTRODUCTION voltage blocking capability presented in [11] the number of I N recent years research on current source PWM rectifiers conducting semiconductor switches in series in the FQR is (CSR), presented in Fig. 1, has become popular [1], [2], reduced to one. [3]. The polarity of the output voltage of the CSR can be reversed but the direction of the output current cannot. Thus, idc p it cannot act in all four quadrants when it is supplying a dc load without an additional converter bridge or mechanical systems. A four-quadrant operation can be achieved with a three-phase four-quadrant PWM rectifier (FQR) presented a in Fig. 2. It is also possible to use the FQR as a line bridge vdc b M of an indirect matrix converter (IMC) studied in [4], [5], [6], [7], [8]. Instead of using the FQR as a PWM rectifier the c same topology may be also used as a three-to-single-phase matrix converter, when the dc motor in Fig. 2 can be replaced with a single-phase system as in [9]. n Most research on FQR has been done using it as a rectifier stage of the IMC with triangular wave voltage Fig. 1. Current source PWM rectifier. command modulation [4], [5], which is suitable for analog technology but is complex when digital technology is used. idc p With modern digital technology space vector modulation is a less complex and more effective method. In this paper, the space vector modulation method for the FQR is introduced. iia The possible application to the vector modulated FQR is a a dc machine drive. When compared to the conventional iib solutions better efficiency, supply currents and controllable b vdc M displacement power factor are achieved as presented in [3], iic where the CSR has been used. However, the CSR can c produce only positive armature current. Thus it can operate with constant field excitation only in the first and the fourth quadrants if a freewheeling diode is not included. With n The authors are with the Institute of Power Electronics, Department of Fig. 2. Four-quadrant PWM rectifier. Electrical Engineering, Tampere University of Technology, P.O. Box 692, FIN-33101 Tampere FINLAND, Tel: +358-3-3115-4257, Fax: +358-3- 3115-2088, e-mail: matti.jussila@tut.fi 2 The theory for the space vector modulation of the FQR is i2(0,1,-1) i5(0,-1,1) presented in Section II, which is derived from the space iδ vector modulation of the IMC, presented in [8], [12], and i3(-1,1,0) i1(1,0,-1) i6(1,-1,0) i4(-1,0,1) dδ iδ the space vector modulation of the CSR, presented in [1], III II III II ii,ref [2]. The control system of a FQR supplied separately IV 0 I IV 0 I θi excited dc motor is presented in Section III and its V VI V VI dγ iγ simulation model and results in Section IV. Finally, i4(-1,0,1) i6(1,-1,0) i1(1,0,-1) i3(-1,1,0) iγ conclusions are drawn in Section V. i5(0,-1,1) i2(0,1,-1) ix(swa,swb,swc) (a) (b) (c) II. SPACE VECTOR MODULATION OF FOUR-QUADRANT PWM RECTIFIER Fig. 3. Input phase current sectors and current vectors of switching states of the vector modulation of the FQR (a) when idc > 0, and (b) when idc < 0; Space vector modulation of the FQR can be derived from (c) forming a reference vector of input current. the modulation of the CSR [1], [2] or the modulation of the line bridge of the IMC [8], [12]. the switching vectors are The space vector of the input current of the FQR ii may be ⎛π ⎞ (8a) defined [10]: Tγ = mi sin⎜ − θi ⎟Ts ⎝ 3 ⎠ ( i i = (2 3) iia + aiib + a 2iic ) (1) and where a = e j2π/3. Tδ = mi sin(θi )Ts , (8b) When each common-emitter connected IGBT pair in Fig. 2 is treated as a single bidirectional switch, the values of where the modulation index mi = |ii,ref | / |idc|. Then the phase switching functions (swa, swb, swc) can be defined to duration of a zero vector is be 1, 0 or –1, denoting the on-state of the upper switch, the T0 = Ts – Tγ – Tδ. (8c) off-state of both switches and the on-state of the lower switch in one phase leg respectively. Because only one input Equations (8) are identical to those presented in [2], but phase may be connected to each bar at a time, it is possible the difference is that now the link current is allowed to be to write: positive or negative. The ratio between the output dc voltage and the input ac swa + swb + swc = 0 (2) voltage of the FQR may be derived as follows: If the power Phase currents in (1) can be presented with the help of losses in the converter are neglected it can be assumed the switching functions and dc current: ac and dc powers of the converter are equal [10]: ( ) i i = (2 3) swa idc + aswb idc + a 2 swc idc = sw i idc (3) p = (3 2 ) Re{v i i * } = vdc idc , i (9) where swi is the space vector of switching functions of input where vi is the space vector of the input phase voltages and current: the superscript (*) denotes a complex conjugate. Substituting ( sw i = (2 3) swa + asw b + a 2 swc . ) (4) first (3) to (9) and then dividing by idc the dc voltage is Substituting permissible value combinations of swa, swb, found to be and swc into swi it is possible to derive the input current v dc = (3 2 ) Re{v i sw * }. i (10) vectors, which are presented in Fig. 3(a) when idc > 0 and in When the angle of vi is ω t the angle of ii is ω t – ϕ if, Fig. 3(b) when idc < 0. The ix(swa,swb,swc) denotes current which is the same as the angle of swi. Thus, by (10) the vectors produced by permissible switching states. E.g. for instant link voltage vdc in polar coordinates is found to be current vector i1 swa = 1, swb = 0, and swc = –1, when ia = idc, ib = 0, and ic = –idc, i.e. phase a is connected to the p-bar and { vdc = (3 2) Re | v i | e j(ωt −ϕ if ) | swi | e− jωt } phase c to the n-bar. { = (3 2 ) | v i | ⋅ | sw i | ⋅ Re e j( ωt − ωt −ϕ if ) . } (11) As presented in Fig. 3(c) it is possible to produce an input current reference vector ii,ref in one switching period as a According to (3) |swi| = |ii,ref|/|idc| = mi and (11) can be sum of two weighted current vectors [12]: written as ii,ref = dγiγ + dδiδ (5) vdc = mi (3 2) | v i | cos(ϕ if ) . (12) From (12) it is possible to solve the voltage ratio of the where e.g. iγ = i6 and iδ = i1 when ii,ref lies in sector I and idc FQR: > 0. In (5) the weighting coefficients dγ and dδ are the vdc relative durations of current vectors: = mi (3 2 ) cos(ϕif ) (13) | vi | | i i,ref | ⎛π ⎞ dγ = sin ⎜ − θ i ⎟ , (6) The maximum current ratio mi in (13) is unity in linear idc ⎝3 ⎠ modulation. Thus, the maxima of the ratio vdc/ |vi| are ±3/2, and which are achieved when ϕ if = 0 and ϕif = π. Thus, | i i,ref | dδ = sin (θ i ) . (7) |vdc|/ |vi,line-to-line| ≤ 3 / 2 and the FQR is a buck converter, idc which can produce average voltage up to ±487 V when the If the switching period is marked with Ts the durations of rms value of the line-to-line supply voltage is 400 V. 3 III. CONTROL SYSTEM OF DC MACHINE DRIVE antiparallel diodes of the IGBTs. In steady state operation it means overlapping in switchings may be used in the same As presented in Fig. 2 the FQR may supply the dc way as in the CSR. When the dc current reference value is machine directly. The block diagram of the control system reversed and the dc current is reaching a zero value, the of the FQR supplied dc motor drive is presented in Fig. 4. modulation is stopped. After a short dead time period the Its outer control loop is speed control and its inner loop is modulation of the IGBTs conducting to the reverse direction armature current control. The feedback signals for the when compared to the previous steady state is started and controllers are the angular rotor speed ω r and the armature the switchings are performed again using overlapping. The current iAr. result of this method is equal to the two-step commutation The speed control of the motor is based on [10]. It used in matrix converters [13]. produces the reference value of the armature current iAr,ref and it is executed every 800 µs. IV. SIMULATIONS The current control of the FQR is based on [2]. The current control and modulator are executed every 100 µs in The simulations were performed with Matlab Simulink® software. A selected dc machine in simulations is a 4.5 kW a 200 µs switching period, i.e. the switching frequency is 5 separately excited dc motor, whose parameters are presented kHz. Both the current and the speed controllers are discrete in Table I. The model of the separately excited dc motor is time anti-windup PI controllers. based on the equations: The current controller produces the reference value of the dc voltage of the FQR vdc,ref from which the value of the real diAr v Ar = RAr iAr + LAr + cψω r , (18) component of the input current iix,ref in a supply voltage dt oriented reference frame is generated using (9) when vi = vix t = cψ iAr, (19) + jviy and ii* = iix – jiiy: and { p = (3 2 ) Re (vix + jviy ) (iix − jiiy ) . } (14) t = t load + J dω r (20) dt In the supply voltage based reference frame the real axis is tied to the supply voltage vector, thus viy = 0 [2]: where cψ is a constant when excitation current iexcitation and excitation inductance are constants. p = (3 2 ) vix iix = vdcidc , (15) In simulations the control system of the drive was based from which we get for reference values: on the block diagram presented in Fig. 4. The modulation of 2 the FQR was performed as presented in Section II with ideal iix, ref = v dc,ref idc = kvdc,ref idc . (16) switches, i.e. the commutation method presented in Section 3vix III is not needed. The supply voltage (400 V, 50 Hz) The imaginary component iiy,ref of the input current in the waveform in simulations was purely sinusoidal and the LC input-voltage-oriented reference frame may be generated filter type supply filter consisted of 2.3 mH inductors and Y- from the definition of the reactive power as presented in [2]: connected 10 µF capacitors, so the resonance frequency of the filter was 1049 Hz. { } q = (3 2) Im v i i * = −(3 2) vix iiy , i (17) The simulation results at nominal speed with load torque i.e. iiy,ref may be used to control the reactive power of the step from nominal value to negative nominal value and back input. In this study it is set at zero, i.e. ϕ if = 0, and by (13) are presented in Fig. 5, i.e. the working of the motor drive in the maximum dc voltage vdc may be achieved. the first and the second quadrants is proved. The dc current The modulation of the FQR may be performed as sign is reversed very fast, which leads to 180° phase change presented in Section II. In practice switchings of the FQR of input currents. It produces together with current reference should be performed such that a dc current path is not cut oscillation small non-sinusoidal periods to the load steps. and the supply is not shorted. This can be done when the The oscillation of the dc current reference is caused by FQR is considered to consist of two CSRs connected speed controller, which is tuned concerning mainly on antiparallel, which series diodes are at the same time the transients situation of speed reference. idc= iAr TABLE I va LC- DC MOTOR PARAMETERS vb FQR vdc = vAr M vc filter ωr - Nominal shaft power, Pn 4.5 kW iAr + ωr,ref Nominal rotational speed, nn 1000 rpm θi Modulator Speed Nominal torque, Tn 42.6 Nm controller iiD,ref iiQ,ref Nominal armature voltage, VAr,n 440 V x,y -> Nominal armature current, IAr,n 13.7 A D,Q iAr,ref Nominal excitation current Iexcitation,n 1.33 A Dc current - k vdc,ref controller + iiy,ref iix,ref Armature inductance, LAr 121 mH Armature resistance, RAr 9.5 Ω Fig. 4. Separately excited dc motor drive supplied by vector modulated four-quadrant rectifier. 4 The speed reversal with constant load torque is presented Steady state waveforms of the supply and load currents in Fig. 6, thus the working of the FQR drive in the fourth and voltages with the supply current spectrum are presented quadrant is also proved. As can be seen from the presented in Fig. 7. The total harmonic distortion (THD) of the supply waveforms the FQR drive can operate both with positive current includes harmonics up to 2 kHz. As can be seen and negative dc current and voltage producing sinusoidal from the presented waveforms the FQR produces sinusoidal input current during the transients as well. supply currents and a smooth armature current. (a) (a) (b) (b) (c) (c) (d) (d) (e) (e) Fig. 5. Simulation results of load torque steps when nn = 1000 rpm: (a) Fig. 6. Simulation results of speed steps when T = 42 Nm: (a) mechanical mechanical speed n; (b) electrical torque T; (c) armature current iAr (black) speed n; (b) electrical torque T; (c) armature current iAr (black) and its and its reference (red) ; (d) armature voltage vAr; (e) supply current ia. reference (red) ; (d) armature voltage vAr; (e) supply current ia. 5 V. CONCLUSION In this paper the novel modulation method for the direct four-quadrant PWM rectifier (FQR) has been introduced. The vector modulated FQR supplying a dc motor was tested in simulations. The simulation results show that the vector modulated FQR can supply a dc machine. The FQR produces sinusoidal supply currents with low distortion and offer an opportunity to control input power (a) factor. In addition the load current of the FQR is smooth. Thus, the FQR may be used when dc drive with sinusoidal supply currents is required. Especially the FQR is a suitable solution when an integration of a converter on a dc machine is desired. REFERENCES [1] B.H. Kwon, and B. Min, “A fully software-controlled PWM rectifier with current link.” IEEE Trans. Ind. Electron., vol. 40, pp. 355–363, (b) June 1993. [2] M. Salo, and H. Tuusa, ”A vector controlled current-source PWM rectifier with a novel current damping-method,” IEEE Trans. Pow. Electron., vol. 15, pp. 464–470, May 2000. [3] H.F. Bilgin, K.N. Köse, G. Zenginobuz, M. Ermis, E. Nalcaci, I. Cadirci, and H. Köse, ”A unity-power-factor buck-type PWM rectifier for medium/high-power DC motor drive applications.,” IEEE Trans. Ind. Applic., vol. 38, pp. 1412–1425, Sep./Oct. 2002. [4] Y. Minari, K. Shinohara, & R. Ueda, “PWM-rectifier/voltage-source inverter without dc –link components for induction motor drive,” IEE (c) Proceedings-B – Electric power applications, vol. 140, pp. 363–368, Nov 1993. [5] M. Muroya, K. Shinohara, K. Iimori, and H. 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Lindemann, “A new IGBT with reverse blocking capability,” Proc. Conf. Rec. EPE, 2001, CD-ROM, 7 p. [12] L. Huber, and D. Borojević, “Space vector modulated three-phase to three-phase matrix converter with input power factor correction,” IEEE Trans. Ind. Applic., vol. 31, pp. 1234–1246, Nov./Dec. 1995. [13] P.W. Wheeler, J. Rodríguez, J.C. Clare, L. Empringham, and A. Weinstein, “Matrix converters: a technology review,” IEEE Trans. Ind. Electron., vol. 49, pp. 276–288, April 2002. (f) Fig. 7. Simulation results of the FQR drive in steady state, when T = 42 Nm, nr,n = 1000 rpm: (a) supply voltage va; (b) supply current ia; (c) armature current iAr; (d) armature voltage vAr; (e) more detailed iAr; (f) spectrum of supply current (f1=50 Hz).