Fundamental Research of Power Conversion Circuit Control for Wireless In-Wheel Motor using Magnetic Resonance Coupling

Transcription

1 Fundamental Research of Power Conversion Circuit Control for Wireless In-Wheel Motor using Magnetic Resonance Coupling Daisuke Gunji The University of Tokyo / NSK Ltd. 5--5, Kashiwanoha, Kashiwa, Chiba, , Japan / -5-5, Kugenumashinmei, Fujisawa, Kanagawa, 5-85, Japan gunji@hflab.k.u-tokyo.ac.jp Takehiro Imura and Hiroshi Fujimoto The University of Tokyo 5--5, Kashiwanoha, Kashiwa, Chiba, , Japan Phone: imura@hori.k.u-tokyo.ac.jp fujimoto@k.u-tokyo.ac.jp Abstract The In-Wheel Motor (IWM) is the most preferable driving mechanism of electric vehicles for vehicle motion control, energy efficiency, and vehicle design flexibility. One technical issue of the IWM is the reliability of power and signal wires. Wireless power transfer technology is the best solution. In this paper, a bidirectional wireless power transfer circuit using a primary inverter and a secondary converter is proposed. We propose a control method of both the inverter and the converter to stabilize the secondary DC-link voltage. The proposed method is verified by simulation and experiments using simulated test equipment. I. INTRODUCTION Electric vehicles (EVs) have advantages of environmental performance and motion control performance over internal combustion engine vehicles due to the outstanding performance of electric motors []. Especially, the in-wheel motor (IWM) is the best solution because the motor is directly connected to a wheel. Many IWM have been developed in previous research such as [] [4]. All of them are powered using electrical wires. Reliability and safety issues of these wires are one of the shortcomings of IWM. Wireless power transfer (WPT) technology is the best solution for the above problem. We call this concept the Wireless In-Wheel Motor (W-IWM). W-IWM is also applicable to wireless power supply from power transmitting equipment which is installed under the road. Due to the motion of suspension links, the relative position will change between W-IWM and the vehicle chassis. Then, WPT using magnetic resonance coupling [5] [6] is suitable for W-IWM. However, it is known that load voltage or current change with mutual inductance variation and load variation [7]. In order to realize W-IWM, stabilization control of the load voltage is necessary. Much research on power conversion circuit control of WPT have been carried out [8] []. However, most focused on efficiency improvement and application for slow load variation such as battery charging of EVs. In the case of a W-IWM, the load is an electric motor and the load variation is very fast. As far as we know, there has been little research about a power conversion circuit control method of WPT. Inverter Battery Transmitting coil On-board Primary coil Power Fig.. In-wheel Secondary coil Converter Power source PWM inverter command (wireless) Concept of W-IWM. electric motor wheel Ground (Road) In this paper, we present a control method of the power conversion circuit for W-IWM. Motor drive experiments have been carried out to validate the effectiveness of the proposed control method, where the motor has been subjected to mutual inductance variation and rotation speed variation. A. Structure II. CONCEPT OF W-IWM The concept of the W-IWM is shown in Fig.. The W-IWM consists of a power source (battery), primary DC-AC inverter, primary coil, secondary coil, secondary AC-DC converter, inverter for driving the electric motor, and, an electric motor. Here, primary means on-board side, and secondary means inwheel side. The primary DC-AC inverter converts the DC supply voltage to a high frequency AC voltage. The primary coil is mounted on a vehicle chassis and the secondary coil is mounted on an IWM. Each coils are oppositely positioned and electrical power is transmitted via these coils. Received power is converted to DC by the secondary AC-DC converter. Then the electric motor is driven by the inverter. When the electric motor acts regeneratively, electric power flow is inverted, meaning the secondary converter acts as a DC-AC inverter and the primary inverter acts as an AC-DC converter. Signal communication between the on-board side and the in-wheel side is also wireless. B. Experimental vehicle and st prototype of W-IWM Fig. (a) shows the experimental EV FPEV4-Sawyer which was developed by our research group. The drive unit of that

2 Brushless geared motor Powder brake Primary coil Secondary coil Primary inverter Primary coil Secondary coil Secondary converter & electric motor (a) Experimental vehicle. Fig.. (b) st prototype W-IWM unit. Experimental vehicle and st prototype unit. Motor driver Linear actuator Power conversion circuits vehicle can be easily exchanged. We are now developing the st prototype of a W-IWM unit shown in Fig. (b). C. Simulated test equipment In this research, simulated test equipment, which is shown in Fig. 3, is used instead of the prototype unit. The structure of the equipment is same as the above W-IWM concept. The primary coil and the secondary coil are the same shape: flat rectangular spiral coils. The primary coil is fixed, and the secondary coil is mounted on the linear actuator. Then position misalignment of the two coils is controlled by the linear actuator. This mechanism simulates the suspension link motion on a vehicle. Specifications of the two coils are shown in TABLE I. The resonance frequency is diffenrent form international standard (85 khz) for production reasons. A three phase geared brushless motor is used on the equipment. Maximum power of the motor is 5 W. The motor is connected to a powder brake. The motor speed is controlled by the motor driver, and the powder brake provides load torque. III. CIRCUIT STRUCTURE AND MODELING A. Circuit structure The whole circuit structure of the W-IWM is shown in Fig. 4. The primary coil and the secondary coil are indicated by a T-type equivalent circuit []. Both the primary inverter and the secondary converter are H-bridge circuits. Both the primary resonance capacitor C and the secondary resonance capacitor C are connectied in series to each coil. Then the circuit structure is symmetrical and suitable for bidirectional power transfer. The electric motor is driven by the voltage type three phase PWM inverter. Then the secondary DC-link voltage has been controlled to fixed value. In order to realize this, some previous studies have proposed a secondary circuit structure which consists of a full-wave rectifying circuit and a DC- DC converter []. However, in the case of the W-IWM, the available space of the in-wheel side is limited and downsizing of the in-wheel side equipment is required. Then the proposed circuit structure also has an advantage of downsizing. B. Equivalent load resistance model We consider the condition when electrical power is transmitted from the primary side to the secondary side. A previous study [] has suggested that if fundamental harmonics power factor of the secondary converter equals to and electrical loss of the secondary converter can be ignored, the whole Fig. 3. Simulated test equipment. TABLE I SPECIFICATIONS OF COILS. primary coil secondary coil resistance R.97 Ω.35 Ω inductance L 7.85 µh 7.3 µh capacitance C 359 pf pf resonance frequency f 99.8 khz 99.5 khz Mutual inductance L m.43 µh (gap: 8 mm) secondary converter and load are equated to an equivalent pure electrical resistance. If the load is an electrical motor which is driven by an inverter, the relation between mechanical output P m and electrical power is expressed as P m = η m η inv I dc () where η m is the motor efficiency, η inv is the inverter efficiency, and I dc is the DC-link current. Then is calculated as = η m η inv P m. () If is controlled to a fixed value, depends on P m. Therefore, the electric motor is treated as pure electrical resistance. C. Dynamics of the power transfer circuit The transfer function from the primary voltage to the secondary current is expressed as P io (s) = where each coefficient are defined as b 3 s 3 s 4 + a 3 s 3 + a s + a s + a (3) a 3 = L (R + ) + R L L L L m, (4) a = R C C (R + ) + C L + C L C C (L L L, m ) (5) a = R C + C (R + ) C C (L L L m ), (6) a = C C (L L L m ), (7) b 3 = L m L L L. m (8) Every parameter corresponds to parameters shown in Fig. 4. The bode diagram of the transfer function is shown in Fig. 5 while specifications are shown in TABLE I. At the resonance

3 i Cin S S 3 S S 3 E i inv R C L -L m L -L m C R C s M S S 4 v inv L m v conv S S 4 PMSM primary inverter T-type equivalent circuit of coils and resonant capacitors secondary converter load equivalent load resistance Fig. 4. Circuit structure of W-IWM. gain [db] phase [deg] 4 6 =5 Ω =5 Ω frequency [Hz] =5 Ω =5 Ω frequency [Hz] Fig. 5. Bode diagram of T-type equivalent circuit. frequency, the secondary current phase advances 9 deg from the primary voltage. D. Dynamics of the smoothing capacitor The transfer function from the secondary smoothing capacitor input current i Cin to the DC-link voltage is expressed as the following equation. P Cs (s) = C s s + E. Duty ratio versus DC link voltage Fig. 6(a) and (b) show switching state of the primary inverter and the secondary converter, respectively. The duty ratio of the primary inverter d inv and the secondary converter d conv are defined as T p /.5T where T is periodic time, and T p is time of the pulse width. Therefore, d inv = means a square wave which has ±E voltage amplitude. According to Fig. 5, the transfer function P io (s) has bandpass characteristic. Then, we only focus on the fundamental harmonics of the primary inverter output voltage. The amplitude of the fundamental harmonics voltage V inv is calculated as V inv = 4E π sin πd inv. () Gate states of the secondary converter are shown in TABLE II and Fig. 7. There are three switching modes. In the case of modes and, the secondary current passes the secondary converter. By contrast, in the case of mode 3, the secondary coil is shorted and the secondary current does not flow into the load. This means load resistance is equated to zero. Then we define the pseudo load resistance as (9) p = sin πd conv. () +E -E.5T T p.5t.75t (a) PWM inverter. Fig. 6. T mode.5t mode 3 Definition of duty ratio. input current.75t.5t mode (b) PWM converter. TABLE II SWITCHING MODE OF THE SECONDARY CONVERTER. mode Gate state circuit behavior S, S 4 = ON operate as rectifier S, S 3 = ON operate as rectifier 3 S, S 4 = ON shorted From eq.(3), the amplitude of is I conv = P iop (jω in ) V inv () where ω in is the driving frequency of the primary inverter, and P iop (s) is the transfer function P io (s) with replaced by p. Assuming that the time constant of P Cs (s) is sufficiently slower than the driving frequency of the primary inverter, input value of P Cs (s) can be treated as an average passing current through the secondary converter. The average passing current I Cave is calculated as I Cave = π π + π dconv I conv sin θdθ π π dconv = π I conv sin πd conv. (3) Substituting eq.() and () in (3), I Cave is expressed as I Cave = 8E π P iop(jω in ) sin πd inv Therefore, the steady-state value of is t= = 8E π P iop (jω in ) sin πd inv sin πd conv. (4) sin πd conv. (5) The switching timing of the secondary converter has to synchronize with in order to make the fundamental harmonics power factor to. Then, we generate the PWM carrier of the secondary converter from zero-cross timing of as shown in Fig. 7. T

4 secondary converter i Cin d conv G G 3 G G 4 C s v conv.5t.5t P m eq.() or map + - d inv v inv eq.(6) PWM P iop (s) C FF (s) C PI (s) primary inverter + + I Cave eq.() d conv I Cave PWM PCs (s) secondary converter primary side (on-board) secondary side (in-wheel) zero cross saw PWM carrier Fig. 8. Block diagram of the proposed control method. Fig. 7. A. Control strategy Voltage and current of secondary converter. IV. DC LINK STABILIZATION CONTROL In this section, we propose a DC-link voltage stabilization control method. The circuit of the W-IWM has two control degrees-offreedom: the duty ratios of the primary inverter and the secondary converter. Signal communication between the primary side and the secondary side is wireless communication. Then, there are delay and speed limitations. In order to avoid these effects, the primary inverter is controlled by a feedforward controller and the secondary converter is controlled by a DClink voltage feedback controller. B. Primary inverter controller Assuming that the torque response of the electric motor is fast enough, the equivalent load resistance RL is determined by the DC-link voltage value Vdc, the angular speed of the electric motor, and the torque command of the electric motor. In fact, it is useful to refer to the prepared RL map which describes the relation of the angular speed and the torque of the electric motor to RL. We use the nominal value of the mutual inductance L m. Also, we introduce the nominal duty ratio of the secondary converter d conv in order to determine the control margin of the secondary converter. That means, if there are no model errors or disturbance, d conv becomes d conv by the secondary feedback controller. Then, the duty ratio command of the primary inverter d inv is derived from eq.(5) as ( ) d inv = π V π sin dc 8ERL P iop(jω in ) sin π d. (6) conv C. Secondary converter controller The secondary converter controller is a two-degree-offreedom controller, the control target plant of which is P Cs (s). We use a PI controller which is designed by the pole placement method. C P I (s) = K p + K i s (7) K p = pr L C s RL (8) K i = p C s (9) where p [rad/s] is a closed loop pole (multiple root). Also, the feedforward controller is expressed as ω c C F F (s) = P Cs (s) () s + ω c where ω c [rad/s] is the cutoff frequency of the low-pass filter. The manipulated variable of the controller is the average input current to the smoothing capacitor ICave. Then, the duty ratio command of the secondary converter d conv is calculated as ( ) d conv = π I π sin Cave. () 8E P iop (jω in ) sin πd inv The block diagram of the proposed DC-link stablization controllers are shown in Fig. 8. V. SIMULATION AND EXPERIMENT A. Duty ratio versus DC-link voltage Experiments have been carried out to verify eq.(5). We measured under the following two conditions. Condition : d inv is variable, d conv is fixed to.. Condition : d inv is fixed to., d conv is variable. The DC source voltage E was set to 5. V, the loads were 5 Ω and 5 Ω non-inductive electrical resistance, and C s was µf. Both switching signals of the primary inverter and the secondary converter were generated from the same triangular carrier signal. The carrier frequency was set to khz. The phase of the primary inverter gate signal was delayed by 9 deg by a delay circuit in order to synchronize the secondary voltage and current. Experimental results are shown in Fig. 9(a) to (c). The markers on the figure are measured values, and lines are calculated values of by eq.(5). Experimental results are in agreement with theoretical values. Fig. 9(c) shows the voltage and current waveforms of the primary inverter output and the secondary converter input where = 5Ω, d inv =.7, and d conv =.5. The measured waveforms are also in agreement with circuit simulation results. B. Acquisition of the equivalent load resistance map An electrical motor drive experiment was conducted in order to verify the effectiveness of the proposed DC-link voltage stabilization control. First, the equivalent load resistance map was obtained by experiment where d conv =.5, E = V, and Vdc = 4 V. The experimental process is as follows:

5 5 5 5Ω, calc. 5Ω, exp. 5Ω, calc. 5Ω, exp primary invertr duty ratio [ ] (a) d inv vs. ( d conv =. ) Ω, calc. 5Ω, exp. 5Ω, calc. 5Ω, exp Fig. 9. (b) d conv vs. ( d inv =. ). Duty ratio versus DC link voltage. v inv [V] i inv [A] v conv [V] [A] time [us] (c) Voltage and current waveforms. (solid: measured, dotted: simulation) load torque [Nm] motor rotation speed [rpm] Fig Equivalent load resistance map. Perform the proposed control. Change the motor speed every rpm, and the motor torque every. Nm. Adjust R L so that d conv equals to d conv on every driving condition. Values between measured points are calculated by linear interpolation. The obtained map is shown in Fig.. C. Mutual inductance variation while motor drive The effectiveness of the proposed control method to mutual inductance variation is verified by experiment. Position misalignment was applied to the secondary coil by the linear actuator as shown in Fig. (a). Then, mutual inductance variation occurred as shown in Fig. (b). The rotation speed of the motor was 5 rpm, and the load torque was.5 Nm. In this condition, RL was 4. Ω from the equivalent road resistance map. C s was assumed to be µf (it is inside the brushless motor driver and the correct capacitance value is unknown). Closed loop poles of the secondary converter controller was set to -5 rad/s. A low-pass filter with the cutoff frequency of rad/s was applied to the measured value in order to suppress measurement noise. Simulation results are shown in Fig. (a) and (b). The load resistance value is treated as fixed value in the simulation. Without the proposed control method (both duty ratios are fixed), varies with the variation of the L m. By contrast, using the proposed method, the duty ratio of the secondary converter is appropriately controlled. Then, variation of the is suppressed and is almost kept to the value. equivalent load resistance [Ω] position misalignment [mm] (a) misalignment. Fig.. mutual inductance [uh] (b) mutual inductance. Misalignment and variation of L m in experiment. Experimental results are shown in Fig. (c) and (d). Without the proposed control, varied greatly with the variation of L m. In the case of the experiment, the equivalent load resistance also varies with. Then, the variation of was bigger than the simulation result. By contrast, the proposed method suppressed variation of and the motor stably operated. D. Motor speed variation The effectiveness of the proposed method on the motor speed variation is also verified. The load torque was set to.5 Nm. The speed command of the motor was changed from 5 rpm to rpm and then again to 5 rpm as shown in Fig. 3(a). In this condition, RL was derived from the map shown in Fig. 3(e). The closed loop poles of the secondary converter controller were set to -5 rad/s. The cutoff frequency of the feedforward controller was set to rad/s. Simulation results are shown in Fig. 3(b) to (d). Without the proposed control, varies greatly with variation of the motor speed command. By contrast, using the proposed method, is kept almost to the value. The duty ratio of the secondary converter is almost unchanged because of the effectiveness of the primary feedforward controller. Experimental results are shown in Fig. 3(f) to (h). These results also fit in well with the simulation results. Without the proposed control, the primary inverter operation stopped due to the protective function of the circuit and the motor also stopped. By contrast, the proposed method suppressed variation of and the motor stably operated. Steady-state value of the secondary converter duty ratio was about.5. It was equal to the d conv, meaning the primary feedforward controller effectively worked.

6 (a) (simulation). Fig (b) d conv (simulation) (c) (experiment). Simulation and experimental results of variation in mutual inductance (d) d conv (experiment). rotation speed command [rpm] primary inverter duty ratio [ ] (a) Rotation speed command. (b) (simulation). (c) d inv (simulation). (d) d conv (simulation). equivalent load resistance [ Ω] primary inverter duty ratio [ ] (e) R L Fig. 3. (f) (experiment) (g) d inv (experiment). Simulation and experimental results of variation in motor load (h) d conv (experiment). VI. CONCLUSION In this paper, a control method of a power conversion circuit is proposed as a fundamental study of the W-IWM using magnetic resonance coupling. We derive an equation which express the relation between the secondary DC-link voltage and the duty ratio of the primary inverter and the secondary converter. A DC-link voltage stabilization control method was proposed, and the effectiveness of the proposed method is verified by simulation and experimentation. Further works are as follows: Establish a regenerative control method for the power conversion circuit. Current feedback on the primary side. Experiments using the prototype unit on the vehicle. REFERENCES [] Y. Hori: Future Vehicle Driven by Electricity and Control Research on Four Wheel Motored: UOT Electric March II, IEEE Trans. Ind. Electron., Vol. 5, No. 5, pp , 4 [] G. Freitag, M. Klopzig, K. Schleicher, M. Wilke, and M. Schramm: High-performance and highly efficient electric wheel hub drive in automotive design, Proc. 3 3rd International Electric Drives Production Conference, pp.-7, 3, Nuremberg [3] A. Kock, M.Groninger, and A. Mertens: Fault Tolerant Wheel Hub Drive with Integrated Converter for Electric Vehicle Applications, Proc. IEEE Vehicle Power and Propulsion Conference, pp.9-3,, Seoul [4] A.J. Rix, and M.J. Kamper: Radial-Flux Permanent-Magnet Hub Drives: A Comparison Based on Stator and Rotor Topologies, IEEE Trans. Ind. Electon., Vol.59, No.6, pp , [5] A.Kurs, A. Karalis, R. Moffatt, J.D. Jonnopoulos, P. Fisher, M.Soljacic, Wireless Power Transfer via Strongly Coupled Magnetic Resonances, Science Expression on 7 June 7, Vol.37, No.58, pp.83-86, 7 [6] T. Imura, H. Okabe, T. Uchida, and Y. Hori: Wireless Power Transfer during Displacement Using Electromagnetic Coupling in Resonance - Magnetic- versus Electric-Type Antennas-, Trans. IEE Japan Industrial Application, Vol.3, No., pp.76-83, (in Japanese) [7] M. Kato, T. Imura, and Y. Hori: New Characteristics Analysis Considering Transmission Distance and Load Variation in Wireless Power Transfer via Magnetic Resonant Coupling, Proc. IEEE th International Telecommunications Energy Conference,, Scottsdale [8] D.J. Thrimawihana, and U.K. Madawala: A Generalized Steady-State Model for Bidirectional IPT System, IEEE Trans. Power Electronics, Vol.8, No., 3 [9] T. Nayuki, K. Fukushima, N. Gibo, K. Nemoto, and T. Ikeya: Preliminary Demonstrations of a Bi-directional Inductive Power Transfer System, Electric power engineering research laboratory report, No.H7, (in Japanese) [] S. Nakadachi, S. Mochizuki, S. Sakaino, Y. Kaneko, S. Abe, and T. Yasuda: Bidirectional Contactless Power Transfer System Expandable from Unidirectional System, Proc. 3 IEEE Energy Conversion Congress and Exposition, pp.5-57, 3, Denver [] K. Takuzaki, and N. Hoshi: Consideration of Operating Condition of Secondary-side Converter of Inductive Power Transfer System for Obtaining High Resonant Circuit Efficiency, Trans. IEE Japan Industrial Application, Vol.3, No., pp , (in Japanese) [] T. Imura, and Y. Hori: Maximizing Air Gap and Efficiency of Magnetic Resonant Coupling for Wireless Power Transfer Using Equivalent Circuit and Neumann Formula, IEEE Trans. Ind. Electron., Vol.58, No., pp ,