Full-Bridge, Series-Resonant Converter Supplying the SAE 5-1773 Electric Vehicle Inductive Charging Interface

John G. Hayes', John T. Hall DELCO Power Control Systems, 3050 West Lomita Boulevard, Torrance, CA 90505, USA

Abstract - In January, 1995 the Society of Automotive Engineers, Inc. (SAE) published a recommended practice for electric vehicle battery charging using Inductive Coupling (SAE 5-1773) for use in the United States of America. This paper considers the case of a series- resonant converter driving the coupling interface. The resultant topology, a four element series-parallel LLCC- type (SP-LLCC) resonant DC-DC converter with capacitive output filter, is analyzed and the time-based modal equations are solved in steady-state by using a state-variable transformation. The analytical results are validated experimentally.

1. INTRODUCTION

Inductive coupling is a method of transferring power magnetically rather than by direct electrical contact and the technology offers advantages of safety, power compatibility, connector robustness and durability to the users of electric vehicles. The technology is presently being researched and productized at levels varying from a few kilowatts to hundreds of kilowatts [2-51. In January, 1995 the Society of Automotive Engineers, Inc. (SAE) published a recommended practice for electric vehicle battery charging using inductive coupling (SAE J-1773) for use in the United States of America. The inductive coupling port, inlet and load can be simplified to an equivalent electrical circuit which consists of a parallel resonant tank and a capacitive output filter supplying the battery load. Different driving topologies and regulation methods can be employed to charge the batteries via the inductive coupling port. This paper considers the case of a full-bridge series resonant converter supplying the parallel resonant tank and the capacitively-filtered battery load.

Interest in resonant converters has recently shifted to higher-order topologies in which circuit parasitics are included or additional elements added to achieve desirable improved operating characteristics. Two-element and three-

Michael G. Egan, John M.D. Murphy Dept. Of Electrical Engineering and Microelectronics, University Colllege, Cork, Ireland

element resonant circuits, L,LC-type and LCC-type, have been comprehensively discussed and analyzed. Four-element and higher order topologies provide many variations with unique characteristics but have not been treated comprehensively in the literature due to their complexity and number. However, higher order models must be considered if, as in the case of this paper, the effect of magnetizing inductance of the output transformer, or inductive coupler, on the basic LCC-type converter with capacitive output filter is considered. Thus, the three element series-parallel LCC-type becomes a four- element series-parallel LLCC (SP-LLCC) converter if the magnetizing inductance is included in the analysis.

The four-element SP-LLCC converter has previously been analyzed with an inductive output filter [6]. The use of a capacitive output filter has been discussed in [7] for the simple LC parallel resonant circuit and in [SI for the three- element LCC circuit. The analysis of such converters is complex because the capacitive output filter stage is decoupled from the resonant stage for a significant period during the switching cycle. As a result, the number of active resonant elements changes during the switching cycle, giving so-called multi-resonant operation. The circuit is analyzed by using the state variable transformation, introduced in [6], which defines two pairs of decoupled variables and solves for the characteristics of the converter. This method of analysis generates the describing equations for the state variables in the various modes and the resultant equations are subsequently reduced and solved numerically.

The objectives of the paper are to present the induction coupling application as defined in SAE J-1773, to drive the port with a series resonant converter and to analyze the resulting SP-LLCC-type topology with a capacitive output filter in the time domain. Induction coupling is presented in Section 11. The basic converter topology is described in Section I11 and its modes of operation are discussed. The state-variable analysis is presented in Section IV. Experimental validation is presented in Section V.

Author is a Howard Hughes Corporate Doctoral Fellow studying at U.C. Cork.

0-7803-3500-7196/$5.00 0 1996 IEEE 1913

11. INDUCTIVE COUPLING

The basic principle underlying inductive coupling is that the two halves of the induction coupling interface are the primary and secondary sides of a take-apart transformer. When the charge coupler (i.e. primary) is inserted in the vehicle inlet (i.e. the secondary), power can be transferred magnetically with complete electrical isolation just like a standard transformer. The number of turns on the secondary is "matched" to the vehicle's battery pack voltage so that the same charger can charge any vehicle.

Figure 1 shows the simplified power flow and control diagram for inductive charging of electric vehicles. The charger converts the 60 Hz AC utility power to high frequency AC (HFAC) power. Operation at high frequencies is required to reduce the size and weight of the on-vehicle components. The HFAC is transformer-coupled at the vehicle inlet, rectified and supplied to the batteries. Battery charging information is fed back to the primary side using a radio- frequency communication link contained within the coupler and inlet.

I I

I/COUPLER!INLET

CHARGER

3111 4 I I I CONTROLLER

INDUCTIVE ' COUPLING

Figure 1. Power flow and control (Ref. SAE J- 1773)

Per SAE J-1773, the induction coupler can be represented by the equivalent transformer model shown in Fig. 2(a). For this analysis the model can be simplified further to include only the topologically significant components as shown in Fig. 2(b). These are the magnetizing inductance, Lp, and the parallel capacitor, C,. The leakage inductances, Lpli and L,,,, can be lumped together with the series resonant inductor for the purpose of this analysis.

Lpli Rpli Rsec kec p'3pq;; :;;%;; p*

(4 (b) Figure 2. Simplified electrical equivalent circuit of induction coupler

111. BASIC CONVERTER DESCRIPTION, OPERATION AND MODES

The full-bridge SP-LLCC resonant dc-dc power converter with simplified inductive coupler and capacitive output filter is shown in Fig. 3. The full bridge consists of the controlled switches, Q,, Q2, Q3 and Q,, their antiparallel diodes, D,, D,, D, and D,, and the snubber capacitors, C,, C,, C, and C , to implement zero-voltage-switching. The resonant network consists of two separate resonant tank circuits: the L,, - C,, series tank and the Lp - Cp parallel tank. As noted previously this circuit is multi-resonant. When the output rectifiers are not conducting, the input voltage is the only voltage source in the circuit and the resonant tank consists of the four passive elements. Alternately, when the output rectifiers are conducting, the parallel tank is clamped to the output voltage and the series tank is connected to both the input and the output voltage sources. In this mode, only the two series elements are resonating.

Several principal state plane trajectories exist, each of which consists a sequence of characteristic modes. For the purposes of this paper only one particular trajectory, designated Trajectory 1, is discussed. The voltage and current waveforms in the resonant tank for this trajectory are shown in Fig. 4 for operation above the resonant frequency where the switches can transition at zero voltage.

. PZ

Figure 3. Full bridge SP-LLCC dc-dc converter

The basic circuit operation, as shown in Fig. 4, can be understood as follows. Mode MI occurs from time to to t,. At time to, transistors Q2 and Q, are gated off and Q, and Q, can be gated on after a short deadtime but they do not conduct because their inverse diodes, D, and D,, are conducting. At time t , , current ir, equals current iLp and the output rectifiers commutate, thus decoupling the capacitively-filtered load

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from the resonant tank. During Mode M2, from time t, to t2, capacitor C, is charged from -Vo at t , to +Vo at t2. At instant ta during Mode M2, current irs changes polarity, commutating diodes D, and D3 without reverse recovery and transistors Q, and Q3 now begin to conduct. At t2, the output rectifiers become forward biased and the parallel tank is once more clamped to the output voltage. Mode M3, from t2 to t3, is the main power transfer mode. At t3, Q, and Q3 are gated off and Q2 and Q, can be gated on after a short deadtime, beginning the complementary half-cycle. These devices can be gated off at zero-voltage as current irs is sufficient to completely charge the parallel capacitances, C, and C3, and discharge C, and C, prior to gating on transistors Q, and Q,. Modes Ml', M2' and M3' are the complementary modes of M1, M2 and M3 respectively and occur during the time intervals, t3 -t, , t, -t5 and t5 -t6 respectively. Clearly in this trajectory, the switches tum on at zero voltage and zero current and tum off at zero voltage. The inverse diodes tum off without reverse recovery.

1

0 . 5

0

- 0 . 5

-1

MI M2 M3 Ml'M2' M3'

t

, . , . . . t3 i j t4 t5 ; t , ; t : :

0 ; i t 1 t 2 ; . . I . . . . . Figure 4. Typical normalized waveforms for Trajectory 1, vAB, yes, ih, vcp, iLp vs time

Clearly, two different types of mode can be distinguished in the operation of this trajectory. Type A modes are defined as modes in which the capacitively-filtered load is decoupled and the input source voltage supplies only the four passive elements as shown in Fig. 5.

iLs "CS -I +.-

I - - 0

Figure 5. Equivalent circuit for Type A modes

Type B modes are defined as modes in which the load is diode-coupled to the resonant tanks. The voltage across the parallel capacitor, Cp, is clamped to the output voltage. Consequently, only the two series elements are resonating since the current in the third element, iLp, varies linearly as it is in parallel with a fixed voltage source. Thus, the equivalent circuit for Type B modes can be reduced to the two simple decoupled circuits shown iri Fig. 6 (a) and (b).

'Ls "CS

+ +

L

(4 (b) Figure 6 . Simplified decoupled sub-circuits (a) and (b) for Type B modes

Trajectory 1 has a total of six modes as outlined in Table 1. Column 2 in Table 1 shows the polarity of the input voltage for the particular mode. Column 3 shows the polarity of the output voltage or if an open-circuit condition is present. Columns 4 and 5 define the equivalent voltage sources for the simplified equivalent circuits. Column 6 lists the modal type. Column 7 shows the time duration of each mode.

M3

Table 1. Different modes for the equivalent circuit

Iv. STATE-VARIABLE STEADY-STATE ANALYSIS

Initially the operation governing the two distinct generic resonant modes is examined and a general solution is proposed. The resultant equations are then assigned initial and final values for each mode in the trajectory and the solution set is reduced to two equations in two unknowns. These equations are in transcendental form and the final solution is obtained numerically. For this analysis the following assumptions are made: ( 1 ) The output voltage is ripple-free. (2) The switches are gatecl in a complementary fashion for

(3) All switches and components are ideal. (4) No resistive or dissipative elements are accounted for.

exactly 50% of the period.

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IV-1 Modal Type A General Solution Equations

For Type A modes the load is decoupled from the resonant tanks as in Fig. 5 . The following differential equation in matrix form gives the mathematical description of the circuit model :

where x(r) = [v,, vcp , ir, , iLp 1'1 is the vector representing the four coupled state variables vcs, vcp , ir, , iLp . AA is the characteristic matrix, BA is the input matrix and U, is a scalar representing the source voltage as defined in Appendix Eqn. Al .

The above equation represents a fourth order system which can be solved in a systematic way by using the state variable transformation matrix approach as described in [6 ] . This technique allows the replacement of the four coupled state variables, x(t), by the mutually decoupled state variable pairs (vl, iJ and (v,, i 2 ) defined by the transformation T:

or x ( t ) = Tx(t) (2)

L where K I , K2, K3 and K4 are real constants.

variables can be defined by combining Eqns. (1) and (2): A new differential equation in terms of the decoupled state

(3) -- h L (4 - TA,T-'x,(~) + TB,U, dt To achieve mutual decoupling of the selected state

variable pairs it can be shown that the parameters, K,, K,, K3 and K4, have the following values:

Additionally, there exist impedances, Z,,, and ZO2, and radial frequencies, mol and a,,,, corresponding to the resonant transitions of the decoupled pairs which are given by:

Using the above equations it can be shown that the general solution to Eqn. 3 for the state variables pairs can be shown to be:

where ti is the initial time instant of the mode. The complete form of Eqn. 4 is given in Eqn. A2.

Given the general solution in terms of the decoupled state variables, the corresponding solution using the actual component variable values can be found using the inverse of the transformation matrix, T:

x ( t ) = T-'xL (1) (5) The above general solution to Type A modes describes

four equations containing nine variables: the four initial conditions, the four final conditions and the time interval.

IV-2 Modal Type B General Solution Equations

Type B modes differ from Type A modes as only three passive elements have to be considered since vcp is clamped to the output voltage. The equivalent circuit, illustrated in Fig. 6, can be described in state variable format as shown in complete form in Eqn. A3.

The generic solution to these state variable equations can be shown to be of the form:

The complete solution form is shown is Eqn. A4. The above general solution to Type B modes involves three equations containing 7 variables (assuming a defined output voltage): the three initial conditions, the three final conditions and the time interval.

IV-3 Trajectory Solution

For the trajectory being considered, there are eleven

tp , and t,, assuming that the input and output voltages, the switching frequency, f; and the four component values of the series and parallel tanks are defined. Additionally there are 11 mode transition equations as follows: 4 Type A, 6 Type B and the frequency equation defined as:

unknowns as follOws vc,Slh ILSO, ILplh ' c S , > I h l , vc,S22 ILS27 ILp2, ty2

(7)

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Thus, there are 11 equations and 11 unknowns and a unique solution exists for given component values, input voltage, output voltage and switching frequency, f: The reduction of the equations to a single equation with one unknown variable has not yet been found but the equations have been reduced to two nonlinear equations in terms of two variables. The unique solution can easily be determined numerically and waveforms as shown in Fig. 4 can be generated. Once the mode durations and the critical voltages and currents as listed above are known, then all the converter characteristics can be derived. For example, the average dc output current can be shown to have the following solution:

I Var I Unit I Analysis] Exp’t IError(%ll

v. EXPERIMENTAL VALIDATION

Var Unit I O A

Vrcn V

A MOSFET-based prototype converter has been built and experimentally tested. Typical experimental results are presented in Fig. 7 for the following circuit values and conditions:

Cp = 0.039pF,p150kHz F‘y = 220V, Vo = I85V, Ls = 1 1 pH, Cs = 1 pF, L p = 45pH,

Analysis Exp’t Error(%) 16.3 14.7 11 -23 -2 1 10

Figure 7. Experimental waveforms for vAB, ir, and vcp

Io I A I Vrcn I V I

The following table compares the experimental data with the results of the theoretical analysis presented.

. I

16.3 14.7 11 -23 -2 1 10

I””

Ilk0 A Vcs, V -3 1 Z,d A -4.5 -5.2

t” US 1.89 1.87

Table 2. Comparison of experimental and analytical data

The comparison of experimental and analytical data in Table 2 shows good correlation between the two data sets. The approximate error of 11% in the output current can be easily accounted far by the converter inefficiency and the slewing of the input squarewave voltage, vAB.

VI. CONCLUSIONS

The application of a series resonant converter to the SAE J- 1773 inductive charger int’erface has been investigated. The resultant multi-element, multi-resonant topology was analyzed using a time-base’d modal approach utilizing a state variable transformation. Describing equations were generated and solved for the topological modes. The circuit was built and tested and excellent agreement was found between the analytical and experimental data.

ACKNOWLEDGMENTS

The authors wish to acknalwledge the contributions of Dick Bowman, Steve Hulsey, Dave Ouwerkerk, Ray Radys, Steve Schulz, Rudy Severns, Eddie Yeow, George Woody and Kwang Yi to this field of research and development.

REFERENCES

I . “SAE Electric ’Vehicle Inductive Coupling Recommended Practice, SAE J-1773”, Society of Automotive Engineers, Draft Feb. 1, 1995. 2. Anan et al., “A High Efficiency High Power EV Charging System with Inductive Connector”, IPEC- Yokohama, 1995, pp. 807-2112. 3. N. Kutkut, D.M. Divan and D. W. Novotny, “Inductive Charging Technologies for Electric Vehicles”, IPEC- Yokohama, 1995, pp. 119-1 24. 4. N. Kutkut, D.M. Divan, D. W. Novotny and R. Marion, “Design Considerations and Topology Selection for a

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120kW IGBT Converter for EV Charging”, IEEE Power Electronics Conf. Rec., 1995, pp. 238-244. 5. R. Severns, E. Yeow, G. Woody, J. Hall and J. Hayes, ”An Ultra-Compact Transformer for a 1OOW to 120kW Inductive Coupler for Electric Vehicle Battery Charging”, IEEE Applied Power Electronics Conf. Rec., 1996, pp. 32-38. 6. I. Batarseh and C.Q. Lee, “Steady-State Analysis of the Parallel Resonant Converter with LLCC Commutation Network”, IEEE Trans. Power Electronics, Vol. 6, No. 3,

1 ---sinwol(t - t i ) Z

01

1 - C 0 S W o 2 ( f - t i )

Trans. Industry Applications, Vol. 27, No. 3, MayIJune 199 1,

8. R.L. Steigenvald, “Analysis of a Resonant Transistor DC-DC Converter with Capacitive Output Filter”, IEEE Trans. Industrial Electronics, Vol. 1E-32, Nov. 1985, pp. 439- 444. 9. R.L. Steigenvald, “Practical Design Methodologies for Load Resonant Converters Operating above Resonance”, IEEE Applied Power Electronics Conf. Rec., 1992, pp. 172-

pp. 523-530.

V ’ El

~.

July 1991, pp. 525-538. 179. 7. A.K.S. Bhat, “Analysis and Design of a Series-Parallel Resonant Converter with Capacitive Output Filter”, IEEE

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