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15th International Power Electronics and Motion Control Conference, EPE-PEMC 2012 ECCE Europe, Novi Sad, Serbia Design and Control of a Bidirectional DC/DC Converter for an Electric Vehicle L. Albiol-Tendillo, E. Vidal-Idiarte, J. Maixé-Altés, J.M. Bosque-Moncusí, H. Valderrama-Blaví; University Rovira i Virgili, Tarragona, Spain laura.albiol@urv.cat, enric.vidal@urv.cat, xavier.maixe@urv.cat, josepm.bosque@urv.cat, hugo.valderrama@urv.cat Abstract — The recent emergence of plug-in electric vehicles in a global market can offer big challenges and opportunities for both basic and applied research. Although the electrical architecture of a Electric Vehicle (EV) or an Hybrid Electric Vehicle (HEV) can be considered standardized, the development of its different building blocks is an open problem whose solution could contribute to improve significantly the global performance of the vehicle. This paper details the design and control of a bidirectional DC/DC converter for an electric vehicle. The particularity of the chosen topology is the DC/DC converter control by means of a sliding mode control, using only one surface. The designed converter has been modelled and simulated together with an inverter, a motor and a load, which form the electric vehicle traction system. Keywords — Electric vehicles, power electronics, electric drives I. INTRODUCTION The growing concern on a post-petrol scenario, environment protection, energy conservation and global warming has prompted governments, companies and individuals to bet for an emerging market in which renewable energies appear in the horizon as one of its more solid foundations. A paradigmatic example is the electric vehicle (EV), becoming a subject of social interest and a coveted topic for researchers [1]. However, electric vehicles do not constitute a mature technology and important contributions can be expected, among others, in control of the electrical architecture. Fig. 1. Parts of an electric vehicle modeled in this article. Fig. 2. Topology of the bidirectional boost converter. 978-1-4673-1972-0/12/$31.00 ©2012 IEEE This paper details the design and control of an electric vehicle traction system. The traction system of a plug-in electric vehicle consists of an energy storage system –a battery, in this case–, a DC/DC bidirectional converter –because DC bus voltage is higher than battery voltage–, an inverter and a motor [2]. In this paper, the traction system is designed, modelled and simulated with the aforementioned parts, plus a mechanical load, as depicted in Fig. 1. The load forces the motor to operate the machine either as a motor or as a generator. The described topology has been chosen considering that the power of the drive for an EV would be comprised between 60 and 100 kW. We have simulated a 2.2 kW plant, because it will be power level of our test bed. In section II, the bidirectional DC/DC converter is analysed. Section III is devoted to the design of a traction system test bed. In III.A the value of its passive components is determined. Section III.B details the choice of the inverter topology and its control. In III.C, the motivation for using a Permanent Magnet Synchronous Machine (PMSM) is explained, and the modelled motor characteristics are detailed, for simulation reproducibility. The results and conclusion are presented in sections IV and V, respectively. II. BIDIRECTIONAL DC/DC CONVERTER The bidirectional operation of the DC/DC converter (alongside a bidirectional inverter) allows the PMSM to work either as a motor or as a generator. During motoring, the current will flow from the battery to the PMSM, and so the converter will act as a boost converter. During regenerative braking, the current will flow from the PMSM to the battery, and then the converter will act as a buck converter. A. Boost Converter Analysis The proposed converter is a bidirectional boost converter with output filter [3], since the output filter reduces the size of the bulky capacitors of both the inverter and the converter itself. The schematic is shown in Fig. 2. Considering continuous conduction mode, the converter is represented in the state-space during Ton by X ( t ) = A X ( t ) + B (1) ON ON where ⎡ iL1 ⎤ ⎢ ⎥ X ( t ) = ⎢ iL 2 ⎥ ; v ⎢ vC1 ⎥ ⎣ C0 ⎦ LS4d.2-1 ⎡ iL1 ⎤ ⎢i ⎥ X (t ) = ⎢ L2 ⎥ vC1 ⎢⎣ vC 0 ⎥⎦ (2) AON ⎡0 0 0 1 ⎢ ⎢0 0 L 2 ⎢ = ⎢0 −1 0 ⎢ C1 ⎢ 1 0 ⎢0 ⎣ C0 0 ⎤ −1 ⎥ ⎡ vg ⎤ ⎢ ⎥ L2 ⎥ ⎥ ⎢ L1 ⎥ 0 ⎥ ; BON = ⎢ 0 ⎥ ⎥ ⎢0⎥ −1 ⎥ ⎣0⎦ ⎥ R0C0 ⎦ matrix obtained is the jacobian matrix (J) of the system. ⎡ 1 ⎢0 L2 ⎡ eiLo 2 ⎤ ⎢ ⎢ −1 ⎢ o ⎥ ⎢ evC1 ⎥ = ⎢ C 0 o ⎥ ⎢ 1 ⎢evC ⎣ 0⎦ ⎢ 1 0 ⎢ ⎣⎢ C0 (3) During Toff, the converter is represented by X ( t ) = AOFF X ( t ) + BOFF (4) where AOFF −1 ⎡ ⎤ 0 ⎥ ⎢0 0 L 1 ⎢ ⎡ vg ⎤ 1 −1 ⎥ ⎢0 0 ⎥ ⎢L ⎥ L2 L2 ⎥ ⎢ ⎢ 1⎥ ; B = = OFF ⎢ 1 −1 ⎥ ⎢0⎥ 0 0 ⎥ ⎢ ⎢0⎥ ⎢ C1 C1 ⎥ ⎣0⎦ −1 ⎥ ⎢0 1 0 ⎢⎣ C0 R0C0 ⎥⎦ s3 s2 s and the matrices values are the following A = AOFF ; B = AON − AOFF δ = BOFF ; γ = BON − BOFF (7) Sliding mode control has been used for its robustness and fast response [4]. Besides, it enables the use of one control law for both the motoring and the regenerative braking of the drive. The chosen sliding surface is S ( X ) = iL1 − k (8) where k is a constant. We can verify that the transversality condition is accomplished, since ∇S , BX + γ = 1 vC1 ≠ 0 L1 (9) The equivalent control can be calculated as ueq = ∇S , AX + δ ∇S , BX + γ = vC1 − vg vC1 (10) 1 s0 1 R0C0 1 L2C0 1 C1 L2 R0C0 (13) 0 1 0 C1 L2 R0 C0 Note that L2, C1 y C0 are positive, so the first column terms are positive whenever R0 is positive. It means that the system under the sliding model control law defined in (8) will be stable when the machine operates as a motor (R0 negative values would mean that the machine is operating as a generator). The stability of the converter operating in buck mode is evaluated in the next section. B. Buck Converter Analysis After proving that the DC/DC converter operation in boost mode is stable with the sliding surface (8), it is necessary to perform the same analysis for the converter operating in buck mode. The inverter has been modelled as a voltage source and a series resistance, vi and Ri, respectively. The topology is represented in Fig. 3. The buck converter can be represented during TON by (1), and during TOFF by (4), where AON 1 ⎡ ⎤ 0 ⎥ ⎢0 0 L ⎡ − vg ⎤ 1 ⎢ −1 1 ⎥ ⎢ L ⎥ ⎢0 0 ⎥ ⎢ 1 ⎥ L2 L2 ⎥ ⎢ = ; BON = ⎢ 0 ⎥ ⎢ −1 1 ⎥ ⎢ 0 ⎥ 0 0 ⎥ ⎢C C ⎢ vi ⎥ 1 ⎢ 1 ⎥ ⎢⎣ Ri C0 ⎥⎦ −1 ⎥ ⎢ 0 −1 0 C0 Ri C0 ⎦⎥ ⎣⎢ (14) AOFF 0 ⎤ ⎡0 0 0 ⎡ −vg ⎤ −1 1 ⎥ ⎢ 0 0 ⎢ L ⎥ ⎢ L2 L2 ⎥ ⎢ 1 ⎥ ⎢ ⎥ ⎢ 0 ⎥ B ; = ⎢0 1 0 = OFF 0 ⎥ ⎢ 0 ⎥ ⎢ C1 ⎥ ⎢ vi ⎥ ⎢ −1 −1 ⎥ ⎢⎣ Ri C0 ⎥⎦ 0 ⎢0 ⎥ Ri C0 ⎦ ⎣ C0 (15) The expression of the equivalent control leads us to the following steady-state values of the state-space variables, represented as a transposed vector ⎛ ⎞ v k T ⎡⎣ X * ( t ) ⎤⎦ = ⎜ k , g , R0 vg k , R0 vg k ⎟ ⎜ ⎟ R0 ⎝ ⎠ C1 + C0 C1 L2C0 1 (5) (6) (12) From the jacobian, we obtain the characteristic polynomial of the system. In order to determine the stability of the system, we have applied the RouthHurwitz criterion to the characteristic polynomial, obtaining The bilineal state-space equation is: X ( t ) = [ AX + δ] + [ BX + γ ]U −1 ⎤ ⎥ L2 ⎥ ⎡e ⎤ ⎥ ⎢ iL 2 ⎥ 0 ⎥ ⎢ evC1 ⎥ ⎥ ⎢e ⎥ ⎣ vC 0 ⎦ −1 ⎥ ⎥ R0C0 ⎦⎥ (11) In sliding regime, the order of the system ideal dynamics is reduced. Then, we can represent the system dynamics with the error between the steady state value and the real value of the state-space variables. The 3 × 3 Fig. 3. Topology of the bidirectional buck converter. LS4d.2-2 The state-space variables of the converter during buck operation can be expressed by the bilinear equation in (6). The matrices A, B, δ and γ have to be recalculated according to (7). The sliding surface is (8), the same that during the boost operation. As we can see, in buck mode the transversality condition is also accomplished. ∇S , BX + γ = 1 vC1 ≠ 0 L1 (16) In this case, the equivalent control is ueq = ∇S , AX + δ ∇S , BX + γ = vg (17) vC1 and the value of the state-space variables at steady state is ⎛ ⎜ ⎜ ⎜ vi + * ⎡⎣ X ( t ) ⎤⎦ = ⎜ 1 ⎜ vi + ⎜ 12 ⎜ vi + ⎝2 ( ( ⎞ ⎟ ⎟ vi 2 − 4 Ri vg k ⎟ ⎟ vi 2 − 4 Ri vg k ⎟ ⎟ vi 2 − 4 Ri vg k ⎟ ⎠ k 2v g k ) ) (18) A. Converter Parameters The converter inductors L1 and L2, and capacitors C1 and C0 have to be sized according to the desired output voltage and ripple of the waveforms. Both the current in inductor L1 and voltage in capacitor C1 have triangular waveforms. In this case, we can use the small-ripple approximation to express the component value as a function of its state variable ripple [6]. So the value of the inductor L1 is L1 = 1 vg TON 2 ΔiL1 (22) and the value of the capacitor C1 is In sliding regime, the dynamics of the error around the equilibrium point is represented by ⎡ −1 1 ⎤ ⎢0 ⎥ L2 L2 ⎥ o ⎢ ⎡ eiL 2 ⎤ ⎡e ⎤ ⎥ ⎢ iL 2 ⎥ ⎢ o ⎥ ⎢1 0 ⎥ ⎢ evC1 ⎥ ⎢ evC1 ⎥ = ⎢ C 0 o ⎥ ⎢ 1 ⎥ ⎢e ⎥ ⎢evC ⎣ vC 0 ⎦ ⎣ 0 ⎦ ⎢ −1 −1 ⎥ 0 ⎢ ⎥ Ri C0 ⎥⎦ ⎢⎣ C0 III. DESIGN OF AN EV TRACTION TEST BED In order to test the DC/DC converter and its control, we have designed a test bed of an EV traction system. The voltage specifications will be the same that in an EV. However, since the final objective of the test bed is a physical implementation, the power rating has been reduced. The test bed has to meet the characteristics specified in Table I. (19) Calculating the characteristic polynomial and applying the Routh-Hurwitz criterion, we obtain C1 = 1 iL 2 TON 2 ΔvC1 (23) To design C0 the current iL2 is taken into account. Its DC component flows only through the output resistance R0, while the AC flows through C0 and R0. It is desirable that most of the AC component flows through C0 instead of R0. Considering this, the current and voltage waveforms in the output capacitor are represented in Fig. 4.(a). The shadowed area is the charge of C0. It can be calculated as the integral of iL2 during the interval in which it is positive 1 ( d +1)Ts 2 1 C0 dTs 2 qC 0 = ∫ i ( t ) dt = 1 ΔiL 2Ts 4 (24) C1 + C0 C1 L2 C0 but it can be also calculated as 1 Ri C0 1 C1 L2 Ri C0 Matching (24) and (25), the value of C0 is expressed depending on the ripple of iL2 and vC0. s 1 L2 C0 0 s0 1 C1 Ri C0 L2 0 s3 1 s 2 1 qC 0 = 2ΔVC 0C0 (20) C0 = Dual to boost stability analysis, the converter operation in buck mode is stable as long as Ri is positive. That is, the DC/DC converter operation will be stable whenever the machine acts as a generator. This means that the sliding surface (8) can be used regardless of the direction of the power flow. C. Voltage Control Loop We have added a second control loop, slower than the current loop. Its aim is to regulate the converter output voltage[5]. The sliding surface after including the voltage loop is S ( X ) = iL1 − k1 ( vref − vC 0 ) − k2 ∫ ( vref − vC 0 ) (25) 1 Ts ΔiL 2 8 ΔvC 0 (26) In a similar manner, L2 value is selected to ensure that most of the AC component of vC1 falls across its terminals. This means that the output voltage vC0 is nearly the DC component of vC1. The current and voltage waveforms in the inductor L2 are represented in Fig. 4.(b). The flux linkage of L2 can be calculated with two different expressions λL 2 = 2ΔiL 2 L2 1 λL 2 = ∫12 2 ( d +1)Ts dTs (27) vL 2 ( t ) dt = 1 ΔvC1Ts 4 (28) Matching (27) and (28), the value of L2 is obtained in function of vC1 and iL2 ripples (21) LS4d.2-3 electric vehicles, due to its suitability for regenerative operation and its smaller footprint [7]. Choosing a threelevel topology is a trade-off between achieving higher DC link voltages and less stress in devices, and keeping losses and cost of the circuit reasonably low. We use vector control because it enables the use of synchronous motor drives for high-performance applications [8, 9], like traction in the electric vehicle. In particular, the speed is controlled by a PI controller, and has an inner current loop. This current is decomposed into a magnetic field-generating part and a torquegenerating part, in the same way that in [10]. TABLE I DESIGN CRITERIA FOR DC/DC CONVERTER battery voltage 300 V DC bus voltage 550 V iL1 ripple 10 % iL2 ripple 10 % vC1 ripple 2.5 % vC0 ripple 0,5 % switching period (Ts) 50 μs TABLE II VALUE OF COMPONENTS L1 2.045 mH L2 94.53 μH C1 7.5 μF C0 2.1 μF C. (a) (b) Fig. 4. Current and voltage waveforms of (a) the output capacitor C0, and (b) the filter inductor L2. L2 = 1 Ts ΔvC1 8 ΔiL 2 (29) To calculate the values of the passive components, the relative ripple is set according to Table I. From (22), (23) (26), (29) and the ripple criteria, the values of the designed components are calculated, and annotated in Table II. B. Three-Level Inverter The aim of the demonstrative platform for electric vehicle’s traction study is to offer a hardware basis on which test and develop new control strategies, and also to allow topology modifications. Considering that this topology has been chosen for a 60-100 kW EV, it is convenient to use a multilevel inverter. The advantages of using a multilevel inverter at this power are reducing the stress of the components (compared with the H-bridge), improving the system efficiency and achieving higher voltages, extending the constant power region of the motor. Among the large list of topologies, we have chosen the voltage source inverter NPC (Neutral Point Clamped). It is an adequate starting point for traction Motor For vehicle traction, the most important parameter to select the electric motor is torque density, and permanentmagnet synchronous machines (PMSM) have the best torque density, apart from a good efficiency. The higher the torque density, the lower the weight and volume of the motor [11]. The main drawback of PMSM is their short constant power range. However, it can be extended by an adequate control. After considering the PMSM advantages and inconveniences, we have chosen this machine as our traction motor for the electric vehicle. In order to test the complete traction system as depicted in Fig. 1, a scale platform instead of the full-power system will be used for feasibility. The characteristics of the motor chosen for the scale platform are summarized in Table III. IV. SIMULATION RESULTS The objective of the simulations is to validate the chosen model with the low-power test bed. The simulation of the inverter control is performed with Simulink. The battery, the DC/DC converter, the sliding mode control, the inverter and the motor are modelled in PSIM, and included in the Simulink model. The values of the constants from the sliding surface have been adjusted experimentally. TABLE III PMSM CHARACTERISTICS voltage rating (Vrms) 380 V current rating (Irms) 4.1 A power rating (Pr) 2.2 kW speed rating (nr) 1750 rpm stator resistance (Rs) 3.3 Ω d-axis inductance (Ld) 0.04159 H q-axis inductance (Lq) .04159 H voltage constant (Ke) 261 V/krpm number of poles (p) 6 moment of inertia (J) 0.01007 kg·m2 mechanical time constant (tm) 4.9266 s Fig. 5. Motor starting at nominal load. LS4d.2-4 Fig. 7. Load torque transition. Fig. 6. Regenerative braking. The result of starting the motor at nominal load is shown in Fig. 5. The DC bus voltage is 550 V, but the voltage ripple depends on the current consumption. More current consumption causes more ripple. The sliding motion can be appreciated in the battery current waveform. Fig. 6 shows the performance of the motor decelerating from the nominal speed, at 50% of the nominal voltage. The DC bus voltage remains stable at 550 V. It is clearly shown that when reference speed is reduced, there is regenerative braking, and current flows from the motor to the battery (current reaches negative values). In the third test, the motor is started at nominal load, and after 0.8 s the load is reduced a 70%. The results of this torque transition are reproduced in Fig. 7. The current consumption drops when the load torque is reduced. The DC bus voltage regulation is performed despite the load perturbation. V. CONCLUSION This paper has presented the design and control of a bidirectional DC/DC converter for an electric vehicle. The particularity is the use of only one sliding mode control law to control the bidirectional DC/DC converter. Once designed and controlled, the converter has been modelled and simulated along with the rest of the traction system for an electric vehicle –inverter, motor and load. Results summarized in the previous section validate the operation of the bidirectional DC/DC converter and the inverter. 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