Field Oriented Control for an Induction Machine Based Electrical Variable Transmission

Transcription

1 Field Oriented Control for an Induction Machine Baed Electrical Variable Tranmiion Joachim Druant, Member, IEEE, Frederik De Belie, Member, IEEE, Peter Sergeant Member, IEEE, and Jan Melkebeek Member, IEEE Abtract An electrical variable tranmiion (EVT) i an electromagnetic device with dual mechanical and electrical port. In hybrid electric vehicle (HEV ) it i ued to plit the power to the wheel in a part coming from the combution engine and a part exchanged with the battery. The mot important feature i that the power plitting i done in an electromagnetic way. Thi ha the advantage over mechanical power plitting device of reduced maintenance, high efficiency and inherent overload protection. Thi paper give a conceptual framework on how the torque on both rotor of the EVT can be controlled imultaneouly by uing a field oriented control cheme. It decribe an induction machine baed EVT model in which no permanent magnet are required, baed on the claical machine theory. By the ue of a predictive current controller to track the calculated current reference value, a fat and accurate torque control can be achieved. By electing an appropriate value for the flux coupled with the quirrel-cage inter-rotor, the torque can be controlled in variou operating point of powerplit, generation and pure electric mode. The concluion are upported by imulation and tranient finite element calculation. Index Term Electrical variable tranmiion, modeling, field oriented control I. INTRODUCTION An electrical variable tranmiion (EVT) i an electromagnetic device with two mechanical (MP ) and two electrical (EP ) port a can be een in Fig. 1. The mechanical port conit of a primary (driven) haft, and a econdary (driving) haft. The electrical port are provided by two power electronic converter (PEC ) with a common DC-bu. The EVT erve a a power plit device between the electrical and mechanical power ource. In literature, the EVT i often found to be ued in hybrid electric vehicle (HEV ). While full electric car are limited by the unatifactory performance of battery technologie and the high cot of fuel cell [1], [], the HEV need only limited battery torage. Thee car are powered both by an internal combution engine and an electric motor. A power plit device Copyright (c) 15 IEEE. Peronal ue of thi material i permitted. However, permiion to ue thi material for any other purpoe mut be obtained from the IEEE by ending a requet to pub-permiion@ieee.org. J. Druant wa awarded a Ph.D. Fellowhip from the Reearch Foundation- Flander (FWO) in 1 ( Joachim.Druant@ugent.be). J. Druant, F. De Belie, P. Sergeant and J. Melkebeek are with the Electrical Energy Laboratory of the department of Electrical Energy, Sytem and Automation (EESA) of Ghent Univerity, B-9 Ghent, Belgium. Thi reearch ha alo been carried out in the frame of project G.3.13 of the Reearch Foundation-Flander (FWO), and in the frame of Flander Make. Fig. 1: Principle of a hybrid electric vehicle with electrical variable tranmiion (EVT). Alo the poible power flow are indicated by arrow. i required to plit the power to the wheel in a part directly coming from the combution engine and a part exchanged with the battery. Thi tak i nowaday performed through a mechanical planetary gear [3], [], for which two electric motor/generator are needed, each connected to a different haft of the gear. The remaining haft i connected to the combution engine. Alo other topologie can be found in literature. In [5] a puh-belt CVT i ued a power plit, while a flywheel i ued to tore ome of the energy. In [] a conventional automatic tranmiion replace the planetary gear. Finally [7] compare the automated tranmiion with the continuouly variable tranmiion. The power plit in all topologie make it poible to drive the engine in an energy-efficient region of the torque-peed map over a wide range of torque and peed delivered to the wheel. The fuel conumption, the noie level and the emiion of harmful gae from the vehicle can thu be reduced. Alo, while braking, ome of the braking energy can be recuperated and tored in the battery []. Although having a lot of advantage, thi hybrid concept with a mechanical power plit ha ome drawback inherent to mechanical gear. The mot important are mechanical friction, the need for lubrication and ealing and the abence of overload protection. In addition, two electrical motor/generator are needed in the concept. The electromagnetic equivalent of thi ytem combine the power plit and the two electrical motor into one electromagnetic device called an electrical variable tranmiion (EVT) a can be een in Fig. 1. There exit baically two type of EVT, depending on whether or not permanent magnet are ued. Within the permanent magnet verion, different topologie can be found in literature. In [9] and [1] the magnetic 1

2 PM Rotor M/G 1 Stator of M/G Segment ring Stator Double layer PM Interrotor Stator Single layer PM Interrotor Stator of M/G1 Rotor Rotor PM Rotor M/G M/G 1 MG M/G (a) EVT with magnetic gear (MG) inide [9], [1]. Fig. : Schematic of the permanent magnet EVT. (b) EVT with double layer of PM [11] (c) EVT with ingle layer of PM [1] equivalent of a planetary gear i ued within the EVT a can be een in Fig. a. Such a magnetic gear wa propoed in [13], and can have a comparable power denity a it mechanical counterpart according to [1]. Moreover, it ha the advantage of high efficiency, abence of mechanical friction and wear, lower maintenance and inherent overload protection [15]. The two motor/generator are added concentrically to the magnetic gear a can be een in the figure to form an EVT. The loe in a motor-integrated permanent-magnet gear are conidered in [9] and [1]. They mainly conit of iron loe. Among the advantage of thi kind of EVT are the high efficiency, high power denity and the abence of lip ring. The mechanical contruction i however complicated becaue of the three concentrically rotating element. Alo four layer of expenive permanent magnet are needed. In [11], [17] another type of PM-EVT i conidered avoiding the aforementioned drawback. However lip ring are needed to feed the wound inner rotor. The machine further conit of a wound tator, and an outer rotor (called interrotor in thi paper) with a double array of permanent magnet. The topology can be een in Fig. b. The yoke inbetween both layer of magnet i made thick o that the tator and rotor are magnetically decoupled. By controlling both the rotor and tator current the torque on both the rotor and the inter-rotor can be controlled. Becaue of the decoupling, the control i identical a for conventional PMSM machine. In [1] finally the inter-rotor i provided with a ingle array of PM a can be een in Fig. c. Now the tator and rotor are magnetically coupled, making the control more challenging. Depending on the peed of the rotor and interrotor, the electrical frequencie of tator and rotor need to be controlled in order to ynchronize the different magnetic field to one unique rotating field. Different operating point are conidered in [1]. On the other hand, in the induction machine baed EVT no permanent magnet are ued. Thi machine wa introduced in [19], []. In contrat to [1] here both rotor are electromagnetically coupled, ince the inter-rotor yoke i made thin to ave volume and weight. The machine can thu not be een a two concentric conventional induction motor, but a one electromagnetically coupled device. With repect to the permanent magnet verion it ha the advantage of lower cot ince no expenive (rare earth) magnet need to be provided. Alo the irreverible demagnetization rik of magnet i avoided []. Furthermore, the magnetic field can eaily be weakened at high peed in contrat to EVT with permanent magnet. The diadvantage of thi type of EVT i the higher joule lo due to on the one hand the inherent lip between the hort-circuited rotor and the field and on the other hand due to the magnetization current. In thi paper the concept of thi latter type of EVT i conidered. The topology of the machine can be een in Fig. 3, which conit of a tator, a hort circuited quirrel-cage interrotor and a wound rotor with lip ring a alo decribed in conference paper [3] where an equivalent cheme for thi machine type i derived for modeling of teady-tate operation. More pecifically it i invetigated in thi paper how field oriented control can be applied to control the torque on both rotor along with the flux. The goal i to have the control working in the mot energy-efficient way by electing appropriate current vector for tator and rotor. The current are applied uing voltage ource inverter (VSI ) and an appropriate current controller. Drive line of EVT are often equipped with an overall energy management ytem chooing the optimal torque and peed on each haft in order to fulfill the wihe of the driver while minimizing the energy conumption a preented in many recent article [] [7]. To do thi the machine need to be controlled both in teady-tate a well a in tranient operation, according to the demand of the energy management, which i the ubject of thi paper. Firt a machine model for an induction machine baed EVT i dicued, from which the torque

3 B. Electromagnetic Modeling PEC3 Battery PEC1 Wheel An analytical model for the EVT can be derived taking into account the following aumption: Combution Engine Rotor Shaft 3 Shaft Inter-rotor Stator EVT (a) Schematic of an EVT ued in a hybrid vehicle. (b) Cro ectional view. Fig. 3: Induction machine baed electrical variable tranmiion. on both rotor can be calculated. Further the propoed field oriented control cheme i explained, and the importance of chooing an appropriate inter-rotor flux i dicued. Finally, imulation reult upport the theoretical derivation. The aim i to give the reult of a general concept tudy howing ome poibilitie of thi kind of machine, and to encourage further invetigation into thi new technology. II. THE INDUCTION MACHINE BASED ELECTRICAL VARIABLE TRANSMISSION A. General Decription The electrical variable tranmiion (EVT) conidered in thi paper i an electromagnetic device with two mechanical port and two electrical port. It can be een a an induction machine with two concentric rotor. The tator i coupled through a power electronic converter (PEC) to the battery. The middle rotor i called the inter-rotor and i a quirrelcage rotor. The mot inner rotor finally i connected through lip ring and a power electronic converter to the battery. The tator and the two rotor are electromagnetically coupled. A chematic overview can be een in Fig. 3a. A three phae ymmetrical machine Sinuoidally ditributed winding No kin- or proximity effect No aturation No influence of the lot on the field When Faraday and Ohm law are conidered in a reference frame rotating along with the magnetic field (ynchronou qd-reference frame) equation (1) to (3) model the relation between the voltage applied to the terminal of the machine and the reulting current. Note that there i only one rotating magnetic field. In each equation the flux i multiplied with the peed with repect to the field i.e. ω, ω and 3 ω for the tator, inter-rotor and rotor repectively. The derivation i made uing tandard modeling technique a for conventional induction motor []. The ubcript 1 i ued for the tator quantitie, for the inter-rotor and 3 for the rotor. The ymbol R i ued for the reitance, Ψ for flux linkage, and p i the Laplace operator. Note that although the inter-rotor i a hort-circuited quirrel-cage rotor, an equivalent wound rotor i conidered. V 1q = R 1 I 1q + pψ 1q ωψ 1d V 1d = R 1 I 1d + pψ 1d + ωψ 1q (1) V q = = R I q + pψ q ωψ d V d = = R I d + pψ d + ωψ q () V 3q = R 3 I 3q + pψ 3q 3 ωψ 3d V 3d = R 3 I 3d + pψ 3d + 3 ωψ 3q (3) ω i the pulation of the magnetic field in a two-pole repreentation, wherea i the lip of the conidered rotor with repect to the field: = ω ω ω 3 = ω ω 3 ω with ω and ω 3 the inter-rotor and rotor pulation repectively. N p finally repreent the number of pole pair in the machine. The fluxe are defined a: Ψ 1 L 11 L 1 L 13 I 1 Ψ = L 1 L I () L 13 L 33 Ψ 3 which are the flux vector linked to the tator, inter-rotor and rotor repectively conidered in a reference frame rotating with pulation ω: I 3 () (5) 3

4 Ψ i = Ψ iq + jψ id I i = I iq + ji id (7) with i 1,, 3}. The real axi i thu along the q-axi, while the imaginary axi i the d-axi. The parameter L ij are determined uing finite element calculation. A current vector I i, i 1,, 3} of unity length i applied to the machine. The correponding fluxe are the i th column of the inductance matrix. Finally uing Lorentz law, the torque on both rotor can be expreed a T = 3 N p(i q Ψ d I d Ψ q ) T 3 = 3 N () p(i 3q Ψ 3d I 3d Ψ 3q ) In () it i given that the torque magnitude and direction not only depend on the magnitude of the magnetic flux and the current, but alo on their relative angle. Thu, the concept of vector control applie for thi kind of machine. III. TORQUE CONTROL ON A DOUBLE ROTOR INDUCTION MACHINE A with field oriented control (FOC) on a conventional induction machine, the EVT i conidered in a qd-reference frame rotating with the magnetic field. In thi intantaneouly ynchronou reference frame all current are DC-current. The relative phae of the frame can be choen freely. For implicity of the equation, the inter-rotor flux Ψ i choen to be oriented along the negative d-axi. The mathematical expreion for field orientation i thu: I Ψ q (9) Ψ Fig. : dq-reference frame oriented along inter-rotorflux. The flux Ψ induce a voltage E in the hort-circuited inter-rotor. A. The inter-rotor in a field oriented reference frame From (), the torque can be written a d E q T = 3 N pψ d I q (1) The fluxe in (3) can be plit up in their d-axi and the q-axi component. By combining (3) and (9), the following equation for the q-axi current in the inter-rotor i obtained: I q = 1 L (L 1 I 1q + I 3q ) (11) In order to control the torque, the flux thu ha to be known. From the inter-rotor equation () and uing definition (9): pψ d = R I d (1) meaning that the reitive voltage drop equal the induced voltage in the inter-rotor. The torque T i thu the multiplication of two orthogonal component Ψ d and I q. Thi i a reult of the fact that the inter-rotor i hort-circuited. Combining (1) with the definition of the inter-rotorflux (3) yield: Ψ d = L 1I 1d + I 3d 1 + p L R (13) Note that in teady tate, I d =. The denominator in (13) then become 1. It i concluded that by conidering the inter-rotor in thi pecific reference frame attached to the inter-rotor flux, the inter-rotor current from (11) and the inter-rotor flux from (13) can be written in term of tator quantitie, and o i the torque in (1). B. The rotor in a field oriented reference frame The torque on the rotor i given in () which i the cro product of Ψ 3 and I 3. The factor L 33 I 3 in Ψ 3 doe not contribute in thi cro product (a winding cannot exert torque on itelf) o: T 3 = 3 N p(i 3q (L 31 I 1d + L 3 I d ) I 3d (L 31 I 1q + L 3 I q )) (1) C. Field oriented control With the expreion above in a qd reference frame it poible to derive a control cheme that control the torque on both rotor. To thi end the controller need to elect at every update intant a et of current vector (I 1,I 3 ) atifying the torque equation (1) and (1) repectively. Since there are only two torque equation to be fulfilled and four unknown, two degree of freedom remain. To thi end alo the inter-rotor flux Ψ i controlled. There are everal reaon to control the flux along with the torque: From (13) it can be een that the flux cannot be changed intantaneouly, which i a fundamental law of electromagnetim. In order to have a fat torque repone without tranient, the flux need to be held at a certain value, a can be een from (1). The magnitude of the flux determine the degree of aturation. The inductance ued in the equation are contant parameter determined in a certain operating point. In order for the torque control to be correct, the magnetization tate of the machine cannot deviate too far from thi point. Controlling the flux limit the current for a certain torque. More flux mean that the torque-forming current component I q of the inter-rotor can be decreaed, but that on the other hand the flux forming component I d of

5 the inter-rotor increae. The current in the inter-rotor are directly related to the tator and rotor current. The magnitude of the flux determine the back-emf of the machine. The voltage applied to the terminal of the machine i limited by the DC-bu voltage. Summarized, the field oriented controller need to elect a et of current vector (I 1,I 3 ) atifying the following et of equation: τ = L 1 I 1q + I 3q Ψ d = L 1 I 1d + I 3d τ 3 = L 31 I 1d I 3q I 3d (L 31 I 1q + L 3 I q ) (15) with τ = L 3N pψ d T, Ψ d and τ 3 = 3N p T 3 known, and I q calculated in (11). Note that I d i zero and thu p = in (13) becaue the flux i held at a contant value. Combining the equation lead to an equivalent et of equation: I 3q = τ L1 I 1q I 3d = Ψ d L 3 L1 I 1d (1) I 1q a I 1d = a 1 with a 1 = L3τ3+L3Ψ di q L 31Ψ d a = L31τ+L1L3Iq L 31Ψ d (17) Equation (1) how that there i one degree of freedom left. Thi can be exploited to elect the olution with the minimal joule loe. Thi lead to the following problem: minimize known. To thi end an indirect field oriented control cheme can be ued where the o-called lip equation i ued to ynchronize the current with the field. Uing () the pulation of the field with repect to the inter-rotor (lippulation) can be calculated: ω = R I q Ψ d () with I q known from (11) and Ψ d from (13). IV. SIMULATION To upport the theoretical derivation, imulation were performed in a Matlab-Simulink environment. A chematic overview of the imulated etup can be een in Fig. 5. Starting from the etpoint value for flux and torque the etpoint current are calculated in a qd-reference frame attached to the inter-rotor flux. Uing indirect FOC the current are tranlated to the correponding phae current. Uing a predictive current controller the optimal gate ignal (G) for the inverter are elected. The power electronic converter (PEC ) are ideal voltage ource inverter, receiving their gate ignal from a controller. The controller ue poition feedback to locate the rotating magnetic field uing indirect field oriented control. The poition of the field i then ued to tranform the tator current from the dq reference frame to the tationary tator frame, and the rotor current to a reference frame rotating along with the rotor. Thoe current are controlled uing a predictive current controller. The motor parameter were identified uing finite element calculation. mea I 1,abc R 1 I 1q + R 1 I 1d + R 3 ( τ L 1 I 1q ) + R 3 ( Ψ d L 1 I 1d ) ubjected to the contraint (1) T Ψ T 3 PPPPFOC PPPcurrentP calculation I 1q I 1d I 3q I 3d InverePRotation InverePClarkeP Tranformation I 1,abc MBPC current control I 3,abc mea I 3,abc G G L-VSI L-VSI IMEVT I 1q a I 1d = a 1 (19) which can be olved uing Lagrange multiplier. The olution i: I 1q = 1 h 1 (λ + h ) I 1d = 1 h 1 ( a λ + h 3 ) I 3q = τ I 3d = Ψ d L1 I 1q L1 I 1d () with h 1 = R 1 + ( L1 ) R 3 h = L1 R L 3 τ 3 h 3 = Ψ dl 1 (1) R L 3 3 λ = a1h1 h+ah3 1+a In order to calculate the correponding phae current in the tator and rotor, the orientation of the qd-frame need to be SlipPequation 1 p θ θ 3 PoitionPFeedback Fig. 5: Field Oriented Control Scheme for induction machine baed EVT. The FOC current controller calculate the optimal et of current needed to achieve the et point torque and flux value. Uing the lip equation the calculated current are tranformed to the tator and rotor phae current. Finally the phae current are actually applied to the machine uing a voltage ource inverter and a dead beat current controller. A. The Machine The machine under conideration for imulation i baed on the tator yoke of a 9kW induction machine. A geometrical optimization ha been performed in order to elect the width of the inter-rotor to achieve optimal efficiency. Finite element calculation have been performed to calculate the electromagnetic machine parameter. The machine parameter can be een in table I. For the inter-rotor an equivalent wound rotor ha been conidered. Rated value are baed on rated heat diipation in a conventional induction machine of the ame 5

6 power. The rated peed i baed on the peed of the ICE and direct drive operation. The correponding rated current are given for the choen number of winding depending on the inverter ued. TABLE I: rated machine parameter tator inter-rotor rotor T rat [Nm] N rat [rpm] rat [] -.. I rat [A] 1 - number of lot N i 3 number of winding w i number of lot q i 3 3 per pole and per phae number of pole pair N p outer radiu [mm] inner radiu [mm] winding reitance [Ω] The inductance matrix from equation (3) i calculated a: L 11 L 1 L L 1 L = H L 13 L (3) The machine can be characterized by a map of torque veru peed. Thi machine however ha two rotor, o the torque - peed map i a four dimenional map. In order to have a two dimenional plot, the rotor peed i choen to be 15 rpm, which i a conventional ICE peed. The torque on the rotor (and the ICE) i choen a uch that the power to the wheel i entirely covered by the ICE power, o the battery i not ued: T 3 Ω 3 = T Ω + P j (T, T 3 ) () Thi leave only two variable: the torque T and peed Ω to the wheel. The reultant power and efficiency plot can be een in Fig. For the efficiency calculation both joule and iron loe are taken into account. The flux i held at it maximum value correponding to a flux denity of 1.T in the teeth. Only at high and low inter-rotor peed the flux ha been weakened. The reaon that the flux alo need to be weakened at low peed i becaue the rotor voltage depend on the peed difference between inter-rotor and rotor a will be hown. T [Nm] Ω [rpm] Efficiency ContantPPowerPLineP1 PkW MaximumPContinuouPTorque Fig. : Efficiency map. Ω 3 = 15 rpm, V dc = 3V The rated power of the machine i about 7kW, which i lower than the 9kW of an induction machine with the ame tator. The reaon for thi i that the rotor diameter need to be choen lower becaue of the inter-rotor. Thi limit the maximum flux through the machine. The rotor lot can be choen maller but thi increae the joule loe. Thi i an inherent diadvantage of thi type of machine. Moreover heat removal will be harder becaue of the two rotor. B. Choice of the inter-rotor flux A mentioned in paragraph III-C the inter-rotor flux trongly influence the back-emf of the machine, the loe and the dynamical behaviour. The magnitude of the voltage induced in the tator and rotor winding can in inuoidal teady-tate be written a: E 1 = ωψ 1 = ( ω + ω )Ψ 1 (5) E 3 = 3 ωψ 3 = ( ω + ω ω 3 )Ψ 3 () Every choice of inter-rotor flux Ψ yield a et of current vector (I 1,I 3 ), the olution of (). Every olution give rie to a unique lip pulation and et of fluxe and thu determine the induced voltage. Further E 1 depend linearly on the peed of the inter-rotor, while E 3 depend linearly on the difference in peed of inter-rotor and rotor a can be een in (5) and () repectively. At the terminal of the machine the reitive voltage drop over the winding i added to the induced voltage a can be een in equation (1) and (3). Thi reitive part i mainly of interet when the torque i high or the flux level of the machine i low ince then high current are demanded. However, in mot operating point the influence i negligible. Then the relation between voltage V 1 and peed ω or between V 3 and peed difference ω 3 ω i linear and i characterized by the voltage at zero peed and it lope. The voltage at zero peed i determined by the lip pulation ω which i a function of the inter-rotor torque uing equation (1) and ():

7 ω = R 3N p T Ψ d (7) The reaon for thi i that a current need to be induced in the inter-rotor in order to have an electromagnetic torque. To thi end an alternating magnetic field i required, thu a lip pulation. The lower the inter-rotor flux i choen, the more current need to be induced in the inter-rotor bar in order to have the ame torque. Thu the lower the inter-rotor flux, the higher the lip pulation, and thu the voltage at zero peed. With increaing peed or peed difference, the voltage increae almot linearly with lope Ψ 1 and Ψ 3 repectively a can be een in equation (5) and (). If the tator voltage i the limiting factor, equation (5) combined with equation (7) give the maximum inter-rotor peed. ω,max = V max Ψ 1 R T 3N p 1 Ψ () The ame can be done if the rotor voltage i the limiting factor by uing equation (): ω,max = V max R T 1 Ψ 3 3N p Ψ + ω 3 (9) with V max the maximum achievable voltage, which i equal to V dc 3 ince pace vector modulation i ued to yntheize the voltage vector. Fig. 7a how the relation between maximum peed and inter-rotor flux for a pecific operating point for both the tator and rotor voltage a limiting factor. Starting form maximum flux level and weakening the flux, the maximum achievable peed or peed difference increae a can be expected. However at a pecific flux level a maximum i reached and the achievable peed drop. Thi ha two main reaon. Firt the influence of leakage field on the tator and rotor play an important role at low inter-rotor flux level. The third curve in the plot repreent the peed relation for tator and rotor if no leakage were preent, o that Ψ 1 = Ψ = Ψ 3 in equation () and (9). The leakage field thu trongly decreae the maximum peed. The other important factor i that the influence of the lip pulation become dominant at low inter-rotor flux a explained before. If the ICE peed Ω 3 i aumed to be held contant at 15 rpm, and by taking the mot trict limitation of tator and rotor voltage, the peed-flux range of Fig. 7b reult. Alo the joule loe are given which decreae toward higher flux for thi operating point. For part load the minimum joule loe are poibly ituated at flux level lower that Ψ,max. Thi i however dynamically not alway achievable ince flux cannot be changed intantaneouly. The flux range lower than Ψ,min a given in Fig. 7b i not of interet for thi operating point ince the ame peed can be achieved at higher flux and thu lower loe. It i concluded that the flux reference for the inter-rotor i choen to be a high a poible, except when the peed i too high or low. Minimum and Maximum peed [rpm] range Ω range Ω Ω 3 no leakage Ψ [Wb] (a) Speedrange of inter-rotor Ω if the tator voltage i the limiting factor, and peed range of inter-rotor with repect to rotor Ω Ω 3 if the rotor voltage i limiting factor. MinimumPandPMaximumPpeedP[rpm] range Ω rangepnopleakage P j [W] Ψ,min Ψ [Wb] Ψ,max (b) Speed range of inter-rotor if ICE peed Ω 3 = 15rpm. Alo joule loe P j are given. Fig. 7: Choice of the inter-rotor flux, imulation reult. T = 5Nm, T 3 = -5Nm, V dc = 5V. C. Current control The control cheme derived above give the reference value for the tator and rotor current. Thoe current however cannot directly be applied to the terminal of the machine ince only the voltage can be teered. To thi end a current controller i needed in order to elect at every intant the optimal voltage vector that need to be applied to the machine in order to track the current reference a accurately a poible. Since an EVT form a MIMO ytem to be controlled, a predictive current controller i particularly attractive. Deadbeat Current Control i a pecific type of model baed predictive control (MBPC) that can be ued to control everal output. Suppoe the preent time t i equal to kt u, k Z with T u the controller update period. At thi moment an optimal witching equence S k i applied to the inverter. Thi witching equence wa calculated in the previou time interval. The goal i now to calculate the next witching equence to be applied at t = (k + 1)T u till t = (k+)t u. The calculation of thi witching tate happen in the interval from t = kt u to t = (k + 1)T u. The algorithm 7

8 can be divided into three main tep: 1) Etimation: The tate of the current at t = (k + 1)T u i fixed becaue of the witching equence S(k), but i not know at the current moment kt u. To thi end the current at t = (k +1)T u are etimated uing the model of the EVT. For the calculation to be carried out in a controller, the model i dicretized and a firt order Euler approximation i ued. The time derivative of the current at kt u are calculated uing a initial condition the meaurement of the current at t = kt u. Alo the flux i needed to pecify the tate of the machine at thi moment. Thi i done by etimating the flux uing equation (1) and (3). The voltage i known ince the witching tate i known. ) Prediction: Uing the invere dicretized model, the voltage needed to force the current on their reference current at t = (k + )T u are calculated. To thi end the etimated current and fluxe at t = (k +1)T u are ued. 3) Modulation: ince the voltage ource inverter are ued, only a et of dicrete voltage vector can be applied to the machine. In order to yntheize the deired voltage vector from the prediction tep, a pace vector modulation i ued. Uing thi modulation principle the voltage vector applied to the machine terminal are on average equal to the deired voltage vector over the controller time interval. D. Simulation The imulation reult aim to how how FOC can accurately control the inter-rotor flux and the torque on both rotor in different working condition. The imulation conit of five part a can be een in Fig. 9a. Firt both rotor are in noload condition. The inter-rotor peed Ω 3 i equal to the ICE peed and i aumed to be held contant at 15rpm. The energy withdrawn from the battery plotted in Fig. i ued to keep the machine magnetized at the predefined inter-rotor flux level, which i hown in Fig. 11a. To thi end a dc current i ent through the tator in Fig. 1a and an alternating current through the rotating rotor in Fig. 1b. The frequency of the current i equal to the rotational peed of the rotor in order to maintain a tationary magnetic field. Conequently no current are induced in the inter-rotor a can be een in Fig. 11b and the torque on the inter-rotor i zero. From t = 5m a torque reference i impoed on the inter-rotor, while the torque on the rotor remain zero. Thi correpond to EVmode of a hybrid vehicle, with the power entirely delivered by the battery. A q-axi current i induced in the inter-rotor ince the magnetic field i forced to have a certain lip with repect to the inter-rotor bar. The torque track the reference very accurately, and tep are tracked without overhoot with thi predictive current controller. The torque ripple i about 1% of the reference torque a can be een in the figure and i due to the current regulation. In the imulation the controller ha perfect knowledge of the machine parameter. In the third imulation tage from t = 1m the ICE i loaded with a negative torque in order to tranmit the ICE power and charge the battery. From t = 15m the torque to the wheel i tripled o that the battery need to ait the ICE. Finally from t = m a negative torque i impoed on the interrotor and regenerative braking i ued to charge the battery and low the inter-rotor down. A uch the different operation mode of the EVT are illutrated. Energy to the battery [J] time [] Fig. : Energy fed to the battery, correponding to the battery tate of charge. T [Nm] time [] T T 3 T,ref T 3,ref (a) Torque on the inter-rotor and rotor of an induction machine baed EVT. Mechanical peed [rpm] time () (b) Mechanical peed of inter-rotor and rotor. Fig. 9: Field Oriented Control, imulation reult. Stator current [A] time [] (a) Stator current applied via PEC1. Rotor current [A] time [] (b) Current through the rotor, applied via the lip ring and PEC3. Fig. 1: Current controlled by the current controller. Ω 3 Ω

9 Interrotorflux [Wb] time [] (a) inter-rotor flux Interrotorcurrent [A] time [] (b) Induced inter-rotor current. Fig. 11: inter-rotor quantitie in a ynchronou qd-reference frame. V. VALIDATION USING TRANSIENT FINITE ELEMENT A. Finite Element Analyi CALCULATIONS In order to validate the torque control technique, finite element calculation were performed. The analyi i performed in D and conit of a meh with 959 node, of with the denity i highet in the two air gap. The imulation i timetranient with.m time tep. The material i conidered linear, but the flux i choen a uch that the flux denity in the teeth never exceed 1.T. The firt two torque tep of Fig. 9a where applied a etpoint. A field oriented torque controller calculate the deired phae current, which are then directly applied to the winding of the machine (ideal current regulation). The peed of both rotor and inter-rotor are aumed to be held contant over the calculated time interval at 15rpm and 1rpm repectively. The torque i calculated uing the Maxwell tre harmonic filter method from [9]. According to Maxwell tre tenor the electromagnetic torque on a rotor can be written a T = 1 π r B r B θ dθ (3) µ where B r and B θ are calculated from the derivative of the magnetic vector potential A z to θ and r repectively. Conequently the induction waveform are an order le accurate than the vector potential that evolve linearly in the triangular meh element. To cope for thi iue the vector potential i written in term of a Fourier erie and i then analytically derivated. Thi way an analytical olution for (3) can be found a function of the Fourier coefficient of the vector potential along two circle in the air gap. B. Finite Element Reult The imulation i, depending on the torque etpoint, divided into three part. The firt m both torque etpoint are zero and the controller maintain the flux in the machine. Ψ q Ψ d I q I d The magnetic field rotate along with the inter-rotor ince the lip pulation i zero. In the tator a rotating current layer i applied rotating at the peed of the inter-rotor, o with frequency of 33.3Hz. Since the rotor rotate at 5 rpm with repect to the inter-rotor, current are applied with a frequency of 1.Hz and with revered phae order. The applied current can be een in Fig. 1a and Fig. 1b where the current denity i plotted. Alo the correponding current and flux waveform in pace are given. The inter-rotor current i converted to the number of winding of the tator. Every circular marker on the figure repreent one inter-rotor bar. The tator and rotor current are at every moment in phae with the inter-rotorflux. The fundamental harmonic of the induced inter-rotor current i zero o no net torque i impoed on the inter-rotor a can alo be een in Fig. 13. Higher pace harmonic current component of order 3, 5, 7 and 9 are preent, which are due to the tator and rotor mmf waveform. At t = m a torque tep of 3Nm i given to the inter-rotor. The applied current to tator and rotor induce a fundamental q-axi current in the inter-rotor. Thi can be een in Fig. 1c where the induced inter-rotor current i 9 hifted with repect to the field. Finally at t = m a torque on the rotor i impoed by hifting the rotor current with repect to the induced magnetic field a can be een in Fig. 1d. Fig. 1 how the induced interrotor current in a qd-reference frame. The ripple i due to the effect of lotting on the airgap field. Harmonic due to the tator and rotor lot can be oberved in the current induced in the inter-rotor bar t [] Fig. 13: Electromagnetic Torque, Tranient Finite Element Calculation t [] I q T 1 T T 3 I d etpoint Fig. 1: Induced inter-rotor current, Tranient Finite Element Calculation 9

10 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY A/m² e I1WfundamentalW[A] MagneticWVectorWPotentialWInterrotorW[mWb/m] IW[A] IWfundamentalW[A] I3WfundamentalW[A] -e electricalwanglew[rad] 1 1 controller in combination with a deadbeat current controller can accurately control the torque and flux of an EVT in different operating point. It i alo illutrated that thi kind of machine can be ued to tranmit power, to generate electrical energy and to work in full electric mode with the propoed controller. 1 R EFERENCES (a) t = m A/m² e I1WfundamentalW[A] MagneticWVectorWPotentialWInterrotorW[mWb/m] IW[A] IWfundamentalW[A] I3WfundamentalW[A] -e electricalwanglew[rad] (b) t = m A/m² e 15 I1PfundamentalP[A] MagneticPVectorPPotentialPInterrotorP[mWb/m] IP[A] IPfundamentalP[A] I3PfundamentalP[A] e 15 electricalpanglep[rad] (c) t = 5m A/m² e 15 I1 fundamental [A] Magnetic Vector Potential Interrotor [mwb/m] I [A] I fundamental [A] I3 fundamental [A] e 15 electrical angle [rad] (d) t = 7m Fig. 1: Tranient D finite element calculation reult howing the applied and induced current denitie (left) and the correponding pacial current and flux wave form (right). VI. C ONCLUSION In thi paper an induction machine baed EVT ha been conidered. Thi type of machine ha the advantage that no expenive magnet are needed. Alo the irreverible demagnetization rik of magnet i avoided and the magnetic field can eaily be weakened at high peed. The propoed field oriented controller calculate at every update intant a et of tator and rotor current in order to control the torque on both rotor along with the inter-rotor flux. The additional degree of freedom in the et of torque and flux equation i ued to minimize the joule loe. Alo the inter-rotor flux i choen o that the limited battery voltage i taken into account along with the joule loe. Finally, computer imulation and finite element calculation are performed for an EVT baed on a 9kW induction machine. It how that a field oriented [1] E. Hela, Electric propulion [hitory], Indutry Application Magazine, IEEE, vol. 15, no., pp. 1 13, July 9. [] F. Ju, J. Wang, J. Li, G. Xiao, and S. Biller, Virtual battery: A battery imulation framework for electric vehicle, Automation Science and Engineering, IEEE Tranaction on, vol. 1, no. 1, pp. 5 15, Jan 13. [3] Y. Cheng, R. 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11 [19] M. Hoeijmaker and J. Ferreira, The electric variable tranmiion, Indutry Application, IEEE Tranaction on, vol., no., pp , July. [] M. Hoeijmaker, Electromechanical converter, Jan. 1 7, us Patent 7,1,19. [Online]. Available: [1] C. Shumei, H. Wenxiang, C. Yuan, N. Kewang, and C. Chan, Deign and experimental reearch on induction machine baed electrical variable tranmiion, in Vehicle Power and Propulion Conference, 7. VPPC 7. IEEE, Sept 7, pp [] X. Sun and M. Cheng, Thermal analyi and cooling ytem deign of dual mechanical port machine for wind power application, Indutrial Electronic, IEEE Tranaction on, vol., no. 5, pp , May 13. [3] J. Druant, P. Sergeant, F. De Belie, and J. Melkebeek, Modeling and control of an induction machine baed electrical variable tranmiion, in IEEE International Conference on Electrical Machine, Sept 1, pp. 1. [] J. Kim, T. Kim, B. Min, S. Hwang, and H. Kim, Mode control trategy for a two-mode hybrid electric vehicle uing electrically variable tranmiion (evt) and fixed-gear mode, Vehicular Technology, IEEE Tranaction on, vol., no. 3, pp , March 11. [5] Y. Murphey, J. Park, L. Kiliari, M. Kuang, M. Marur, A. Phillip, and Q. Wang, Intelligent hybrid vehicle power control;part ii: Online intelligent energy management, Vehicular Technology, IEEE Tranaction on, vol., no. 1, pp. 9 79, Jan 13. [] M. Choi, J. Lee, and S. Seo, Real-time optimization for power management ytem of a battery/upercapacitor hybrid energy torage ytem in electric vehicle, Vehicular Technology, IEEE Tranaction on, vol. 3, no., pp , Oct 1. [7] Z. Chen, C. Mi, J. Xu, X. Gong, and C. You, Energy management for a power-plit plug-in hybrid electric vehicle baed on dynamic programming and neural network, Vehicular Technology, IEEE Tranaction on, vol. 3, no., pp , May 1. [] V. P., in Electrical Machine and Drive: A Space-Vector Theory Approach. Oford Univerity Pre, 199. [9] M. Popecu, Prediction of the electromagnetic torque in ynchronou machine through maxwell tre harmonic filter (hft) method, Electrical Engineering, vol. 9, no., pp ,. [Online]. Available: Peter Sergeant received the M.Sc. degree in electromechanical engineering in 1, and the Ph.D. degree in engineering cience in, both from Ghent Univerity, Ghent, Belgium. In 1, he became a reearcher at the Electrical Energy Laboratory of Ghent Univerity. He became a potdoctoral reearcher at Ghent Univerity in (potdoctoral fellow of the Reearch Foundation - Flander) and at Ghent Univerity College in. Since 1, he i aociate profeor at Ghent Univerity. Hi current reearch interet include numerical method in combination with optimization technique to deign nonlinear electromagnetic ytem, in particular, electrical machine for utainable energy application. Jan Melkebeek wa born in Gent, Belgium on February, 195. He received the Ingenieur degree in electrical and mechanical engineering from the Univerity of Gent, Belgium in 1975, and the degree of Doctor in Applied Science from the ame univerity in 19. In 19 he obtained the degree of Doctor Habilitu in Electrical and Electronical Power Technology. Since 197 he i Profeor in Electrical Engineering at the Engineering Faculty of the Univerity of Gent. He i the head of the Department of Electrical Power Engineering, Sytem and Automation and the director of the Electrical Energy Laboratory (EELAB). Prof. Melkebeek i a fellow of the IEE and a enior member of the IEEE. He erved a the preident of the IEEE Benelux IAS-PELS joint chapter from to 3 and i a long-time member of the IEEE-IAS Electric Machine Committee, the IEEE-IAS Electric Drive Committee and of the IEEE-PES Machine Theory Subcommittee. Joachim Druant wa born in Ieper, Belgium on February 19, 199. He received the M.Sc. degree in electromechanical engineering in 13 from Ghent Univerity, Ghent, Belgium. Since then, he ha been with the Electrical Energy Laboratory (EELAB), Department of Electrical Energy, Sytem and Automation (EESA) of Ghent Univerity and i currently working toward a Ph.D. degree. In 1, he wa awarded a Ph.D. Fellowhip from the Reearch Foundation-Flander (FWO). Hi preent reearch interet include digital control of converter-fed electrical machine, fault tolerant control, and modeling and control on electrical variable tranmiion. Frederik De Belie wa born in Belgium in He received the Mater degree in electromechanical engineering from Ghent Univerity, Ghent, Belgium, in, and the Ph.D. degree in March 1. He currently a pot-doctoral aitant in the Electrical Energy, Sytem and Automation Department of the Ghent Univerity. Hi preent reearch interet include modelling theory and control-ytem theory applied to electrical drive and, in particular, elfening control of ynchronou machine. 11