http://ieeexplore.ieee.org/Xplore Compensation Topologies of High-Power Wireless Power Transfer Systems

Wei Zhang, Student Member, IEEE, Chunting Chris Mi, Fellow, IEEE

Abstract—Wireless power transfer (WPT) is an emerging technology results in a much lower magnetizing inductance and mutual that can realize electric power transmission over certain distances inductance. without physical contact, offering significant benefits to modern For coils of an WPT system operating at a frequency well below automation systems, medical applications, consumer electronics, etc. their self-resonant frequencies (SRF) [37], additional This paper provides a comprehensive review of existing compensation capacitors are needed to form the resonant tanks in compensation topologies for the loosely coupled transformer. Compensation topologies are reviewed and evaluated based on their both the primary and secondary sides. Single sided compensation basic and advanced functions. Individual passive resonant networks appears in some previous wireless circuit designs [19, 38]. It has used to achieve constant (load-independent) voltage or current been replaced by double sided compensation since single sided output are analyzed and summarized. Popular WPT compensation compensation has fewer adjustable resonant parameters, which topologies are given as application examples, which can be regarded cannot provide enough degrees of freedom to satisfy all WPT as the combination of multiple blocks of resonant networks. Analyses system design criteria. This paper reviews, compares, and of input zero phase angle (ZPA) and soft-switching are conducted as evaluates compensation topologies for WPT systems and its well. This paper also discusses the compensation requirements for applications. achieving the maximum efficiency according to different WPT application areas. Index Terms—Wireless power transfer system, compensation II. REQUIREMENT FOR COMPENSATION topology, load-independent voltage & current output, zero input 1) Minimized VA rating and maximized power transfer capability phase angle, soft switching, efficiency. The basic requirement for a compensation capacitor is to resonate with the primary and/or secondary inductance, in order to I. INTRODUCTION provide the reactive power required for the inductances to generate ENGINEERS have dreamt of delivering electrical power an adequate magnetic field [39]. Therefore, for the primary coil of wirelessly over the air for more than a century. Wireless or the loosely coupled transformer, the basic function of inductive power transfer was first suggested soon after the compensation is to minimize the input apparent power, or to proposition of Faraday's law of induction, which is the minimize the VA rating of the power supply [28, 40, 41]. In the underpinning of modern wireless power transfer (WPT), as well secondary side, the compensation cancels the inductance of the as electrical engineering. In the 1910s, Nikola Tesla, the pioneer secondary coil in order to maximize the transfer capability [29, 42, of WPT technology, put forward his aggressive ideas of using his 43]. Wardenclyffe Tower for wirelessly transmitting useful amounts of 2) Constant-voltage or current output electrical power around the world [1, 2]. Although his strategy for A WPT system has many parameters which may change during accomplishing this desire was impractical and ultimately operation. For instance, the air gap changes in real-time for a unsuccessful, his contribution to wireless energy transmission has transcutaneous energy transmission system (TETS) when the never faded [3, 4]. patient is breathing [44, 45]. The number of loads may change Nowadays, wireless power transfer has grown to a $1 billion during charging for a roadway vehicle inductive power transfer commercial industry around the world [5]. This technology has (IPT) system [5, 25, 29]. Therefore, good controllability is found applications to charging home appliances such as electric desirable for a WPT system in order to cope with parameter toothbrushes, wireless charging of mobile phones using a charging variation. Meanwhile, compensation topology can be selected to platform [6-13], and medical uses such as wireless power supply realize constant (or load-independent) current or constant-voltage to implantable devices [14-20]. Medium- to high-power output without a control circuit, which is advantageous for applications of this technology include continuous power transfer achieving good controllability. to people movers [21, 22] and contactless battery charging for 3) High efficiency moving actuator [23, 24], or electric vehicles (EVs) [25-36]. According to the study in [46, 47], the maximum achievable In order to transfer power without physical contact, a loosely efficiency of a WPT system is only decided by two parameters, coupled transformer that involves a large separation between the the coupling coefficient and the quality factors of the windings. primary and secondary windings is essential. Due to the large However, an adequate compensation is necessary to achieve this winding separation, it has a relatively large leakage inductance, as maximum efficiency. High efficiency is also guaranteed by soft- well as increased proximity-effect and winding resistances. switching. A half-bridge or full-bridge converter is commonly Furthermore, the magnetizing flux is significantly reduced, which used for the modulation of a DC voltage to drive the resonant circuit. If MOSFETs are used as the switching components, the Copyright (c) 2015 IEEE. Personal use of this material is permitted. However, converter can benefit from turn-on zero voltage switching (ZVS) permission to use this material for any other purposes must be obtained from the by operating at above resonance, where the resonant-tank current IEEE by sending a request to [email protected]. is lagging the voltage modulated by the active switches [48]. Since Digital Object Identifier 10.1109/TVT.2015.2454292 this input phase angle can be adjusted by the value of

0018-9545 © 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. 2 compensation capacitors, the compensation should also be IOUT selected with consideration for soft-switching. 4) Bifurcation resistant and others Passive resonant The bifurcation phenomenon in a WPT system refers to the UIN network RL UOUT situation in which the frequency to realize zero phase angle (ZPA) is not unique [40, 49]. The number of frequency points to realize ZPA is related to the loading condition, compensation topologies and capacitor values. This bifurcation phenomenon, which (a) accompanies with multiple loading and variable frequency IOUT control, should be avoided to guarantee system stability. Other features, such as insensitivity to parameter change and suitability I Passive resonant R U for bi-directional power flow, should also be considered for IN network L OUT special applications. Compensation topologies should be evaluated based on the aforementioned compensation purposes and by combining their applications and expected operations. The (b) following sections discuss some of the primary features mentioned Fig. 1. Resonant circuit with (a) voltage source input and (b) current source input. above, along with several typical compensation topologies. I I IN Z1 Z2 OUT III. CONSTANT-VOLTAGE OR CONSTANT-CURRENT OUTPUT PRINCIPLES A B This section investigates how to achieve constant-current or U R U IN Z L OUT constant-voltage output using resonant circuits. The constant- 3 current or constant-voltage output realized by a resonant network C C refers to the voltage or current magnitude (U or I ) on the OUT OUT loading resistance RL is irrelevant with the value of RL, so the (a) resonant network has an output of voltage or current source a characteristics. In WPT resonant circuit analysis, the frequency-domain equivalent circuit is always assumed and only the fundamental component is considered for simplicity [12, 28, 40, 50, 51]. The L1 fundamental component approximation is a simple analysis method that can usually achieve sufficient accuracy for a high C quality factor resonant circuit that works near resonance; however, the switching components of an H-bridge inverter and rectifier L2 will introduce some error. Then, if a more accurate study is c b conducted, such as investigating zero current switching (ZCS) (b) requirements (the accurate primary current when switching on), the higher order harmonics should be considered [49]. In this a paper, we use only the fundamental component to analyze the resonant network characteristics.

A. Constant-voltage output principle C1

1) Input voltage source C2 The model of a passive resonant network is depicted in Fig. 1. The power source can be a voltage source or a current source. In L order to make the output voltage amplitude irrelevant with the c b value of RL, the configuration of the passive resonant network must depend on the type of power source. If a voltage power (c) Fig. 2. Resonant network configuration with (a) T circuit model, (b) type A and source is used, the resonant network to have a constant-voltage (c) type B to have constant-voltage output from a voltage source. output should have a T-circuit configuration as Fig. 2 (a) shows. The T-circuit in Fig. 2(a) has equations ZZ ZZ ZZ / 12 23 13 (3) UIROUT OUT˜ L Z3

UIZIIIN IN˜13 IN  OUT ˜ Z (1) In (2), if Λ = 0, the output voltage UOUT is independent of RL, and its output has the characteristics of a voltage source. UIZIZUIN IN˜12 OUT ˜ OUT If circuit points A, B and C in Fig. 2(a) are connected with The relationship between the input voltage U and output voltage IN circuit points a, b and c in Fig. 2(b) respectively, then UOUT can be derived as 2 LL12Z LLC 12 §·Z1 / / (4) UUUIN ¨¸1 OUT  ˜ OUT (2) jLCZ ZR 2 ©¹3 L And Λ = 0 requires the operating frequency of the resonant where network at

3 TABLE I. SUMMARY OF CONSTANT-VOLTAGE OUTPUT FROM A VOLTAGE IIN L IOUT SOURCE Number Passive resonant network Resonant frequency

C RL UOUT L1 L2 11 V-V-1 Z  C LC12 LC Passive resonant network (a)

1 IIN I V-V-2 C1 C2 Z OUT L LC12 LC C L RL UOUT L 1 V-V-3 C2 Z LC LC C1 12 Passive resonant network (b) Fig. 3. Resonant circuits (a) type A and (b) type B to have constant-voltage output L 1 from a current source. V-V-4 C1 Z LC LC C2 12 TABLE II. SUMMARY OF CONSTANT-VOLTAGE OUTPUT FROM A CURRENT SOURCE L1 C 11 V-V-5 Z  Number Passive resonant network Resonant frequency L2 LC12 LC L 1 C-V-1 Z C LC L2 11 V-V-6 C Z  L1 LC12 LC C 1 C-V-2 L Z LC L C 1 V-V-7 Z LC Z =Ğ 3 operating frequency. While for V-V-8, if Z1=Z2=0, which is a Z1=0 Z2=0 V-V-8 short circuit, the output voltage is equal to input voltage regardless Z −− 3 of the value of Z . 3 2) Input current source 11 Z  (5) If the input is a current source as in Fig. 1 (b), the resonant LC12 LC networks needed to realize a constant-voltage output should have It has a constant-voltage output the topologies shown in Fig. 3. The output voltage U and input current I of type A topology U L OUT IN OUT 2 (6) in Fig. 3 (a) can be represented by the following ULL IN 12 11§· If the circuit in Fig. 2(b) is rotated 120 degrees, and connect circuit UijLiOUT IN¨¸Z OUT (9) jCZZ jC points A, B and C in Fig. 2 a) with circuit points c, b and a ©¹ respectively, the circuit can also achieve a constant-voltage output It is readily to see that the second term on the right side of (9) can of be eliminated if L and C resonate at the operating frequency, thus 1 UOUT L1 UIjLI=  Z (10) (7) OUTjCZ IN IN ULLIN 12 at the operating frequency of (5). The output voltage is load-independent, meaning it is determined We name the T-circuit topology in Fig. 2(b) which has two only by the input current and can be adjusted by the resonant resonant inductors and one capacitor as type A. Similarly, type B components. Type B topology has a similar analysis process, as configuration with two resonant capacitors and one inductor in Fig. well as similar results. 1 2(c) can also be used as the constant-voltage output. The operating UjLII Z =  (11) frequency is given without derivation, OUT INjCZ IN 1 Z (8) The configurations for achieving constant-voltage from a current LC12 LC source are listed in Table II. Several typical compensation topologies can be summarized B. Constant-current output principle based on Fig. 2 for constant-voltage output from a voltage source. In some charging applications, the voltage to current conversion The configurations with numbers are listed in Table I. and a load-independent current output are desirable. For instance, a constant-current output is preferred for driving a LED for stable luminance [52]. The constant-current output is discussed below Topology V-V-7 and V-V-8 operate as two special cases. For V- with different input sources. V-7, if Z3 = ∞, which is operating as an open circuit, the output voltage is equal to the input voltage when L and C resonate at the

4 TABLE III. SUMMARY OF CONSTANT-CURRENT OUTPUT FROM A VOLTAGE TABLE IV. SUMMARY OF CONSTANT-CURRENT OUTPUT FROM A CURRENT SOURCE SOURCE Number Passive resonant network Resonant frequency Number Passive resonant network Resonant frequency

L 1 11 V-C-1 Z C-C-1 C Z  L1 L2 C LC LC12 LC

C 1 L V-C-2 L Z 1 LC C-C-2 Z C1 C2 LC LC 12

1) Input voltage source 1 When the input is a voltage source and there is a constant- C-C-3 C1 Z L C2 LC LC current output, it is the reverse conversion of the topologies listed 12 in Fig. 3. Therefore, the resonant topology used to realize the conversion from a voltage source to a constant-current output 1 C-C-4 C2 Z should also have two types, as listed in Table III. The output C1 L LC LC currents are 12

1 V-C-1: IUjCU Z OUT IN IN L2 11 jLZ C-C-5 Z  (12) L1 C LC LC 1 12 V-C-2: IjCUU Z  OUT INjLZ IN L1 11 C-C-6 Z  2) Input current source C L2 LC12 LC If the input is a current source, the resonant method for achieving a constant-current output is a π-circuit configuration as Z =0 1 shown in Fig. 4. Since it is similar to a constant-voltage output, to C-C-7 1 Z achieve a constant-current output from a current source, several L C LC typical compensation topologies can be derived by changing the

connections of circuit points A, B and C in Fig. 4(a) with circuit

Z1 Ğ points a, b and c in Fig. 4(b) or Fig. 4(c). The derivation is omitted C-C-8 Ğ −− = = 2 3 Z for simplicity. The configurations are listed in Table IV. Z

IIN Z IOUT 1 n A B L RPeq LLP LS RSeq UIN RL UOUT LM Z2 Z3 C C ideal transformer Fig. 5. Loosely coupled transformer circuit model. (a) a IV. APPLICATIONS AND EXAMPLES In this section, several typical compensation topologies that can achieve either constant-voltage output, constant-current output, or both, are analyzed by using the passive resonant networks studied L1 C in section III. A WPT system has the same fundamental principle of magnetic induction as that of other widely used L 2 electromechanical devices with good coupling, such as b c transformers and induction motors; therefore, the circuit model of (b) a loosely coupled transformer is identical to that of a traditional a transformer as shown in Fig. 5. In the analysis, the turns-ratio n is selected as 1 for simplicity. LLP and LLS are the leakage inductances of the primary and secondary. LM is the magnetizing inductance. RPeq and RSeq are the resistances of the primary and

C1 C2 secondary of the transformer respectively, including the winding resistance and the equivalent resistance of the power loss in the L magnetic material. Since the values of RPeq and RSeq which are b c relatively small compared with the compensation components’ (c) impedances and have limited influence on the resonant Fig. 4. Resonant network configuration with (a) π circuit model, (b) type A and (c) type B to have constant-current output from a current source. characteristic, they are neglected in this section.

5

ķ ĸ one of these two scenarios can be achieved with one group of RL circuit parameters. Therefore, one operating frequency exists such that at ωH the resonant circuit operates as V-V-5 (when LLS CP LLP CS LM ZLP(ω) >0 and ZLS(ω) <0) or V-V-6 (when ZLP(ω) <0 and VIN ZLS(ω) >0) in Table I. In the meantime, with the same group of circuit parameters, another operating frequency can always (a) be found to have ZLP(ω) <0 and ZLS(ω) <0. Therefore, the

RL other operating frequency exists such that at ωL the resonant circuit operates as V-V-2 in Table I. L LLS CP LP CS These two frequencies can also be derived by using LM VIN mathematical equations. To make sure the derivation is applicable for a general loosely coupled transformers instead of the ones with (b) n=1, the turn ratio is introduced in the analysis below. While in the Fig. 6. Primary series and secondary series compensation circuit models to realize (a) constant-current and (b) constant-voltage output following figures, transformer with n=1 is maintained to have a clear explanation with the blocks of resonant circuits in Section III. The output voltage on RL is calculated as A. Series-series compensation UUGOUT IN v (15) 1) Constant-current output where Gv is the voltage transfer ratio, which can then be Primary series and secondary series (S/S) compensation, shown represented as U jnLRZ in Fig. 6, is one of the four basic compensation topologies [28, 40]. G OUT ML (16) C and C are external compensation capacitors in the primary and v 222 P S UIN ZZPS nZ L M secondary. Let where ZS is the impedance of the secondary resonant tank 1 ZjL ZZ  including load resistance RL. ZP is the impedance of the primary LP LP jCZ resonant tank, where L and L are the self-inductances P (13) P S 1 1 ZjL Z   R ZjLLS ZZ LS  SS L jCZ jCZ S S (17) Usually, the S/S compensation is designed to have a constant- 1 ZjL Z  current output [28], and the operating frequency is unique. This PP jCZ P can be explained by the resonant networks in Section III. From Fig. The voltage transfer characteristics can be obtained by further 6 (a), if ZLP(ω) < 0 and the resonant tank in the red block is manipulation of (16) equivalent with a capacitor, which can resonate with L , then the M 1 block ķ can be regarded as the resonant network V-C-2 in Table G (18) v Z G III, and a constant-current is achieved in the branch circuit parallel P  3 with LM. Therefore, the output current is constant regardless of the ZnLM Z nLMPSL C C R 422 value of LLS, CS and RL, since block ĸ can be regarded as the GZ LCLCPPSS k11 Z LC PP LC SS (19) resonant circuit C-C-8 in Table IV which has constant-current ௡௅ where݇ ൌ ಾ is the coupling coefficient of the loosely coupled output from the current source generated by block ķ. The unique ඥ௅ು௅ೄ resonant frequency to have constant-current output is transformer. Equation (19) shows that if δ = 0, then |Gv| is load- 11 independent, and the output voltage remains constant when RL ZZ P == (14) changes. Solving for roots of δ=0, the frequencies at which |Gv| is LLCLP M P LCPP independent of RL can be obtained where LP is the self-inductance of the primary coil. ZZ22' Z PS (20) 2) Constant-voltage output L 21  k 2 The S/S topology can also be compensated to have constant- voltage output, and the operating frequency for realizing constant- ZZ22' Z PS (21) voltage output is not unique. If we choose the compensation H 21  k 2 capacitors CP and CS randomly, two situations may exist a) An operating frequency ωH can be found to have ZLP(ω) = 222 222 ' ZZPS  41 k ZZ PS (22) ZLS(ω)=0. Operating at ωH, the S/S topology can be regarded as the resonant circuit V-V-8 in Table I. If ω exists, a ଵ H where ߱ௌ ൌ is the resonant frequencies of LS and CS. LS is ඥ௅ೄ஼ೄ frequency area should also exist, in which ZLP(ω)<0 and the self-inductance of the secondary coil. Thus, the existence of ZLP(ω)<0. The series connected resonant components in both primary and secondary are both equivalent with capacitors. A ωL and ωH is verified mathematically. Research [45] is conducted to compare self-inductance frequency ωL can be found in order to create the resonant compensation and leakage inductance compensation. The only circuit V-V-2 in Table I. Therefore, ωH and ωL are the two frequencies that realize constant-voltage output. difference between the two compensations is the capacitors’ values. Therefore, according to the analysis above, both types of b) An operating frequency cannot be found to have ZLP(ω)= compensation can achieve constant-voltage/current output but ZLS(ω)=0. In this situation, the operating frequency can be operating at different frequencies. adjusted within a certain range such that ZLP(ω) >0 and ZLS(ω) <0, or within a range such that ZLP(ω) <0 and ZLS(ω) >0. Only

6

ķ ĸ ķĸitrack Ĺ LM RL UIN RL

LR L L LP LS CP L C CP LLP CS CR LM LS S UIN

(a) (a)

ķĸitrack Ĺ RL UIN RL

LR L LLP LP LLS LLS C LM CS CP P CR LM CS UE

(b) (b) Fig. 7. Primary series and secondary parallel (S/P) compensation circuit models to ķĸ Ĺ ĺ have (a) constant-voltage and (b) constant-current output (Thévenin’s equivalent UIN circuit). LRP LLP LLS CS L C RS C P R RP LM CRS L B. Series-parallel compensation Primary series and secondary parallel (S/P) compensation is (c) usually designed to have constant-voltage output. From Fig. 7 (a), Fig. 8. Primary LCC series–parallel-compensation circuit models with (a) if ZLP(ω) <0, the S/P compensation topology can be regarded as secondary series compensation, (b) secondary parallel compensation and (c) the combination of the resonant network V-V-6 in block ķ and secondary LCC compensation

V-V-8 in block ĸA constant-voltage output can be achieved inductor placed in proximity to the track wires. Therefore, the only when operating at track current is always preferred to be constant in order to 1 Z (23) guarantee constant power delivery to each pick-up system [5, 29]. A series of primary LCC series–parallel-compensations, as §·LLMLS CLPLP¨¸ shown in Fig. 8, are widely used for the track WPT system design ©¹LLMLS [29, 49]. Itrack is the current through the track, and the design S/P compensation can also realize constant-current output. By purpose is to maintain Itrack constant during operation. And at the further manipulation using Thévenin’s equivalent circuit, S/P meantime, each load powered by the track should have constant- compensation topology can be reorganized as Fig. 7 (b), which voltage or constant-current output. illustrates the constant-current output. UE is the equivalent input All primary LCC series–parallel-compensations will have a voltage after Thévenin’s conversion. constant-current in the primary coil if LR and CR in block ķare jLZ UU M (24) selected to resonate at the operating frequency of the converter. EINZ P The primary LCC series–parallel-compensation topology block ķ If the operating frequency is selected to let the impedance in the shownin Fig. 8can be regarded as the resonant circuit V-C-1 in red dotted block performs as an equivalent inductor, which can Table III. Since the constant-current of the primary coil (track) can resonate with CS, it can be regarded as the resonant circuit V-C-1 be regarded as a current source, block ĸis the resonant circuit C- in Table III, and the output current is constant. The C-8. In the secondary of the transformer, if a constant voltage is transconductance ratio can be derived, achieved on the load, a compensation capacitor should be

IOUT 1 connected in series with the secondary coil as shown in Fig. 8 (a). Gi (25) U jLZZ In Fig. 8 (a), block Ĺis C-V-1 while CS resonates with LM+LLS. IN ZJnLSP R MLZnL Therefore, the constant-voltage output requires M 111 where Z=== (27) 2 LLCLS M S LCSS LC RR ZLCPSS 1Z JZ jnLC2  (26) If the compensation capacitor is connected in parallel with the MS ZnL M secondary coil as shown in Fig. 8 (b), resonant network C-C-1 is Similarly, operating at frequencies at which γ=0 guarantees that IO formed in block Ĺ, a constant-current can be achieved when is independent of RL. It has been found that ωL and ωH in (20) and satisfying (27). A double-sided LCC compensation topology (21) are also the two roots of γ=0 [47]. Therefore, ωL and ωH are shown in Fig. 8(c) is proposed in [53], which has a symmetrical the frequencies at which S/P compensation achieves load- compensation in the primary and secondary. By adding a capacitor independent current output. in block ĹC-C-1 and a block ĺC-C-8, a constant current output C. Primary LCC compensations is achieved. The primary LCC series–parallel-compensations are designed In battery charger applications, an additional converter is for a WPT system with multiple loadings, such as roadway usually placed on the secondary side to manage battery load powered vehicle IPT systems, which are composed of a primary profile (a first step at constant-current and a second one at track made up of an elongated loop as the primary of the loosely constant-voltage) [54]. By using appropriate compensations and coupled transformer. The primary track is required to provide operating frequency selection control, voltage or current power to a number of independent loads (electric vehicles) conversion can be achieved by a single stage of WPT converter. wirelessly, each of which couples to the track using a pickup

7

ķĸ IAC jX jXb IO UIN CSP

Zin jXa -jX RL CP LLP LM LLS CS RL UIN

Fig. 9. Primary series and secondary series-parallel (S/SP) compensation circuit load- V-V-8 V-C-1 C-C-8 model. Fig. 10. Two or more stages (including V-C-1) to have constant-current output as well as input ZPA.

V. ZERO PHASE ANGLE AND SOFT SWITCHING independent current output simultaneously. Fig. 10 shows the resonant network with V-C-1 and the other stage. The other stage The phase angle θin between the input voltage and current is an important parameter that decides the VA rating on the power can be added either before or after the V-C-1 stage. We add them supply, as well as on the switching components. It also relates to both for the analysis to include all possible circuit topologies. In the realization of soft switching of an H-bridge converter. The practice, jXa=∞ or jXb=0 can be selected to represent one stage. Since the inductor and capacitor in stage V-C-1 resonate with minimum VA rating requires that θin is equal to zero, while soft- each other, let switching of MOSFETs requires that θin is larger than zero. 1 Therefore, θin is usually selected such that it is slightly greater than XL Z (30) zero, so as to realize soft-switching, as well as a reasonable VA ZC rating. And The input phase angle is calculated as 22 2ªº 2 RXLa X jXX a¬¼ X X a X X b 180 1 Im Zin Zin (31) 2222 Tin tan (28) ªºXXXXabLa RX S Re Zin ¬¼

We study the situation of θin = 0. It can be achieved when Im(Zin) If Xa→∞, then C-C-8 has been added behind the V-C-1 stage, = 0. RX22 jX X X Z | Lb (32) According to the analysis of passive resonant networks in in X a of 2 RL Section III, due to the value change of loading resistance, which is To realize Im(Z )=0 and θ = 0, X should be equal to X. If X =0, connected in parallel with one of the resonant components, it is in in b b then V-V-8 has been added before the V-C-1 stage, and impossible to keep θin = 0 with only one stage of passive resonant 22 2ªº 2 network. Two special topologies, V-V-7 and C-C-7, are special RXLa X jXX a¬¼ X XX a Zin| X 0 (33) exceptions, though. Take the S/S compensation topology as an b 2222 ªºXXXRX example. From Fig. 6 (b), if the S/S compensation is designed to ¬¼aLa have a constant-voltage output, since it has only one stage of In order for θin to equal 0, Xa should be equal to -X. If the stages of resonant block, the value of θin is dependent on the value of both V-V-8 and C-C-8 are added, then according to (31), the loading resistances. θin can be positive or negative with variable impedances should satisfy 2 RL [55]. Therefore, S/S compensation topology can not realize XXXXab 0 (34) ZPA when it has the constant-voltage output. in order to make θin = 0 for all loading conditions. If load-independent voltage/current output and θin = 0 at the full For all the primary LCC series–parallel-compensations, since loading range are realized at the same time, two or more stages of they also utilize the V-C-1 or V-C-2 resonant networks in order to resonant circuit studied in Section III are needed. As shown in Fig. realize constant-current in the primary coil, the series connected 6 (a), when a S/S compensation has constant-current output, it is capacitor CP (see Fig. 8) can be regarded as one more stage C-C- the combination of two resonant networks V-C-2 and C-C-8. Stage 8. This stage has no contribution of constant-current, but is added C-C-8 does not contribute to creation of a constant-current, but it to adjust θ . According to (31), ZPA can be achieved when is capable of adjusting the value of θ . Therefore, S/S in in C compensation can have input ZPA and constant-current output at C R (35) P L the same time [47]. P 1 A primary series and secondary series-parallel compensated LR topology (S/SP) is proposed as an improvement for the S/S compensation topology to have ZPA and constant-voltage output VI. SYSTEM EFFICIENCY simultaneously [56]. In the S/SP circuit shown in Fig. 9, CP and To calculate system efficiency, the resistances RPeq and RSeq in CS are selected the same to form the resonant network in Fig. 6 (b), Fig. 5 should be considered. Then ZP and ZS are redefined as a secondary parallel connected capacitor C is added to realize SP 1 another stage of V-V-8. This stage has no contribution to the ZjL Z   R R SSjCZ SeqL constant-voltage output, but θin of this S/SP compensation is S (38) controlled and adjusted by CSP in order to realize soft-switching. 1 ZjLPP Z   R Peq 1 jCZ P CSP 22 (29) Z nLM The expression of power transfer efficiency can be obtained by Similarly, S/P compensation also has this problem. For the solely considering the active power [47, 54], and thus the resonant circuit V-C-1 in Fig. 7 (b), which is the single stage efficiency ηP of the primary loop and the efficiency ηS of the adapted to have constant-current output, another stage of secondary loop can be calculated separately as resonant network is needed to achieve ZPA for all loads and

8 Re Z 1 L ref secondary series compensation Q S KP (36) L RZ Re RCLS Peq ref (44)

Re ZRSSeq CS K (37) secondary parallel compensation QRLL S L Re ZS S where Zref is the reflected impedances from the secondary to the Therefore, considering the need to achieve maximum efficiency, primary. secondary series and parallel compensations have varying 222 applications. For instance, in EV battery wireless charging, Z nLM Zref (38) suppose the battery on board has a voltage of 400V and internal ZS resistance of 0.7 ohm. If the recharging power is 3.3kW for private The efficiency η is therefore given by cars, by simple derivation, the output voltage and current of the

K KKPS˜ (39) wireless converter should be 405.7V and 8.13A. Therefore, the From (36) to (39), the circuit efficiency is related to RPeq, RSeq, equivalent loading resistance RL is 49.9 ohm. Typically, the nLM and ZS. If the operating frequency is fixed or varies in a winding quality factors QP and QS can reach 200 by using proper narrow region, RPeq, RSeq is related with the selected electric wire litz wire, and we assume the coupling coefficient to be 0.2. and the magnetic material. nLM represent the mutual inductance According to (43), QL can be calculated to have a value of 5. From and is determined by the coupling coefficient of the transformer. (44), if secondary series compensation is selected, LS equals 468 These parameters can be regarded as fixed when the loosely μH when the converter operates at 85 kHz. If secondary parallel coupled transformer is built; they are not discussed in this paper. compensation is selected, LS should be designed as 18 μH. For the Therefore, ZS is the only parameter determines the circuit coil to install on the chassis of a vehicle and with k=0.2, 18 μH is efficiency. If the compensation capacitors have no equivalent not a reasonable value. Therefore, secondary series compensation series resistance (ESR), from (36) to (39), the efficiency does not is more suitable for this EV wireless charging example in order to depend on the primary compensation network. Compensation in achieve maximum efficiency. the primary only influences the reactive power of the circuit, the Generally, when considering the ESRs of compensation VA rating of the input power source, and the realization of soft- conductors and capacitors, the more compensation components switching. From (38), ZS is decided by 1) the impedance of the there are, the lower the circuit efficiency. S/S and S/P secondary resonant network and 2) the value of loading resistance. compensation circuits have the highest efficiencies due to only For a given transformer, the maximum circuit efficiency can be two compensation components being applied. The system with achieved by adjusting these two parameters deciding ZS. S/S and S/P compensations have almost the same maximum With regard to the impedance of the secondary resonant efficiency [47] and ηmax can be represented as network, the compensation capacitor should be well designed in c Kmax 2 order to achieve the maximum efficiency. According to the study 11c (45) in [47, 54], the maximum efficiency appears when 2 1 ckQQ PS secondary series compensation CS 2 Z L This ηmax can be achieved when both (40) and (43) are satisfied. It S (40) 1 relates only to the values of k and the winding quality factors. secondary parallel compensation CS 22 A loosely coupled transformer shown in Fig. 11 was built to Z LS * verify the circuit efficiency of a 3.3kW stationary EV wireless where charging prototype. The specifications of the transformer is listed 1 in Tab. V. Based on the built transformer, to calculate the system §·4 QP 2 efficiency, we select the quality factor of the transformer * ¨¸1+ k (41) ©¹QS QP=QS=200, which is a typical value for a loosely coupled and QP and QS are defined as the winding quality factors, which transformer operating around 85 kHz. The double-sided LCC can be expressed as compensation topology aforementioned in Fig. 8(c) is used for experiment. For the compensation inductor in the circuits, since it ZLP ZLS QP and QS (42) uses the same wire with the loosely coupled transformer, the R R Peq Seq quality factor of the resonant inductor is also selected as 200, and Therefore, to achieve the maximum efficiency, the capacitor in the the capacitor have a dissipation factor (DF) of 0.05% based on the secondary resonant network should be designed as in (40). With datasheet. The circuit efficiency is measured and calculated. The regard to the loading resistance, if RL is expressed by the circuit calculated system efficiency (DC-DC) is 93.6% while the quality factor QL, according to the study in [47, 54], to achieve the measured efficiency is 92.6%. The consistency of measurement maximum efficiency, QL should satisfy with calculation verifies that the QP, QS and the ESR values of the QS compensation components are accurate. QL (43) 2 1+kQQPS for both secondary series and parallel compensations. The circuit quality factor QL in (43) has different expression for secondary series and parallel compensations.

9 compensation is calculated under the condition of constant- Secondary pad voltage output since it is the original purpose [45]. The operating frequency having constant-voltage output is ωL or ωH in (19) and (20), instead of the secondary resonant frequency in (40) at which the maximum efficiency can be achieved. Therefore, S/S topology

Primary pad with leakage-inductance compensation to have constant-voltage output is lower in efficiency than self-inductance compensation to have constant-current output.

primary VII. CONCLUSION

secondary The constant-current/voltage output function of a passive resonant network is introduced based on individual resonant Coils size Experiment setup Fig. 11. Loosely coupled transformer prototype. blocks. These basic resonant blocks are used to explain some characteristics of popular compensation topologies nowadays, TABLE V. SPECIFICATIONS OF THE LOOSELY COUPLED TRANSFORMER such as constant-voltage or constant-current output and the PROTOTYPE Transformer & circuit realization of input zero phase angle, as well as soft-switching. By Specifications parameters correctly combining these resonant blocks, any type of compensation topology can be created, guaranteeing a WPT Coil topology Unipolar circuit that achieves constant output and a minimum input VA Circular, 600 mm dia., 32 turns, litz wire with rating simultaneously. In addition, system efficiency is analyzed primary 800 strands AWG38, two wires connected in with different resonant circuits. The compensation conditions to coil parallel as one turn, LP= 420 μH Circular, 300 mm dia., 16 turns, litz wire with achieve the maximum efficiency is reviewed. The WPT system secondary 800 strands AWG38, LS= 110 μH application area should be considered for a reasonable circuit 48 bars of PC40 with 8mm thickness, same primary design to achieve this maximum efficiency. Furthermore, primary- external diameter with the primary coil. core series and secondary-series topologies with leakage-inductance 48 bars of PC40 with 8mm thickness, same secondary external diameter with the secondary coil. compensation and self-inductance compensation are studied and 2 mm aluminum circular sheet, same size with compared. Shieldings the coil Air gap 150 mm REFERENCES 1. http://en.wikipedia.org/wiki/Wardenclyffe. 2014. Coupling coefficient 0.182 2. Tesla, N., Apparatus for transmitting electrical energy. 1914, US Patent 1119732. Output power 3.3 kW 3. Tesla, N., My Inventions: The Autobiography of Nikola Tesla. 2005: Wildside Press. Battery voltage 400 V 4. Lomas, R., The Man Who Invented the Twentieth Century.: Nikola Tesla, Forgotten Genius of Electricity. 2000: Headline Book Publishing. Input voltage 350 V 5. Covic, G.A. and J.T. Boys, Inductive Power Transfer. Proceedings of the IEEE, 2013. 101(6): p. 1276-1289. Operating frequency 85 kHz 6. Hui, S.Y.R. and W.W.C. Ho, A new generation of universal contactless Battery Charging platform for portable Consumer Electronic equipment. IEEE Transactions on Power Electronics, , 2005. 20(3): p. 620-627. Based on the same loosely coupled transformer and same 7. Hui, S.Y., Planar Wireless Charging Technology for Portable Electronic compensation components ESR values, the efficiency of various Products and Qi. Proceedings of the IEEE, 2013. 101(6): p. 1290-1301. compensations topologies are calculated and listed in Tab. VI. It 8. Xun, L. and S.Y.R. Hui, Equivalent Circuit Modeling of a Multilayer Planar Winding Array Structure for Use in a Universal Contactless Battery Charging is proved that S/S and S/P compensations have better efficiencies Platform. IEEE Transactions on Power Electronics, , 2007. 22(1): p. 21-29. than other topologies, as well as the accuracy of equation (45). 9. Xun, L. and S.Y.R. Hui, Optimal Design of a Hybrid Winding Structure for Planar Contactless Battery Charging Platform. IEEE Transactions on Power TABLE VI. MAXIMUM EFFICIENCIES OF DIFFERENT COMPENSATION TOPOLOGIES Electronics, , 2008. 23(1): p. 455-463. 10. Xun, L. and S.Y.R. Hui, Simulation Study and Experimental Verification of a Constant output Compensation topology Maximum efficiency Universal Contactless Battery Charging Platform With Localized Charging type Features. IEEE Transactions on Power Electronics, , 2007. 22(6): p. 2202- 2210. Series-series 94.6% current 11. Chang-Gyun, K., et al., Design of a contactless battery charger for cellular phone. IEEE Transactions on Industrial Electronics, , 2001. 48(6): p. 1238- Series-parallel 94.6% voltage 1247. 12. Waffenschmidt, E. and T. Staring. Limitation of inductive power transfer for Series-series with leakage consumer applications. in 13th European Conference on Power Electronics 93.3% voltage inductance compensation and Applications, 2009. . 2009. 13. Yungtaek, J. and M.M. Jovanovic, A contactless electrical energy LCC-series 94.2% voltage transmission system for portable-telephone battery chargers. IEEE Transactions on Industrial Electronics, , 2003. 50(3): p. 520-527. 14. Dissanayake, T.D., et al., Experimental Study of a TET System for LCC-parallel 94.3% current Implantable Biomedical Devices. IEEE Transactions on Biomedical Circuits and Systems, , 2009. 3(6): p. 370-378. LCC-LCC 93.5% current 15. Ho Yan, L., D.M. Budgett, and A.P. Hu, Minimizing Power Loss in Air-Cored Coils for TET Heart Pump Systems. IEEE Journal on Emerging and Selected Topics in Circuits and Systems,, 2011. 1(3): p. 412-419. The efficiency of S/S topology with leakage-inductance

10 16. Nishimura, T.-H., et al. A large air gap flat transformer for a transcutaneous 42. Keeling, N.A., G.A. Covic, and J.T. Boys, A Unity-Power-Factor IPT Pickup energy transmission system. in 25th Annual IEEE Power Electronics for High-Power Applications. IEEE Transactions on Industrial Electronics, , Specialists Conference, PESC '94. 1994. 2010. 57(2): p. 744-751. 17. Takura, T., et al., Basic evaluation of signal transmission coil in 43. Elliott, G.A.J., et al., A New Concept: Asymmetrical Pick-Ups for Inductively transcutaneous magnetic telemetry system for artificial hearts. IEEE Coupled Power Transfer Monorail Systems. IEEE Transactions on Transactions on Magnetics, , 2005. 41(10): p. 4173-4175. Magnetics,, 2006. 42(10): p. 3389-3391. 18. Miura, H., et al., Improvement of the Transcutaneous Energy Transmission 44. Gyu Bum, J. and B.H. Cho, An energy transmission system for an artificial System Utilizing Ferrite Cored Coils for Artificial Hearts. IEEE Transactions heart using leakage inductance compensation of transcutaneous transformer. on Magnetics,, 2006. 42(10): p. 3578-3580. Power Electronics, IEEE Transactions on, 1998. 13(6): p. 1013-1022. 19. Ghahary, A. and B.H. Cho, Design of transcutaneous energy transmission 45. Chen, Q., et al., Analysis, Design, and Control of a Transcutaneous Power system using a series resonant converter. IEEE Transactions on Power Regulator for Artificial Hearts. IEEE Transactions on Biomedical Circuits Electronics, , 1992. 7(2): p. 261-269. and Systems, , 2009. 3(1): p. 23-31. 20. Gyu Bum, J. and B.H. Cho, An energy transmission system for an artificial 46. Pinuela, M., et al., Maximizing DC-to-Load Efficiency for Inductive Power heart using leakage inductance compensation of transcutaneous transformer. Transfer. IEEE Transactions on Power Electronics, , 2013. 28(5): p. 2437- IEEE Transactions on Power Electronics, , 1998. 13(6): p. 1013-1022. 2447. 21. Kissin, M.L.G., H. Hao, and G.A. Covic. A practical multiphase IPT system 47. Zhang, W., et al., Analysis and Comparison of Secondary Series- and for AGV and roadway applications. in IEEE Energy Conversion Congress Parallel-Compensated Inductive Power Transfer Systems Operating for and Exposition (ECCE), 2010 2010. Optimal Efficiency and Load-Independent Voltage-Transfer Ratio. IEEE 22. Zaheer, A., et al. Magnetic design of a 300 W under-floor contactless Power Transactions on Power Electronics,, 2014. 29(6): p. 2979-2990. Transfer system. in 37th Annual Conference on IEEE Industrial Electronics 48. Steigerwald, R.L., A comparison of half-bridge resonant converter Society. 2011. topologies. IEEE Transactions on Power Electronics,, 1988. 3(2): p. 174-182. 23. Basset, P., et al., Complete System for Wireless Powering and Remote Control 49. Pantic, Z., B. Sanzhong, and S. Lukic, ZCS LCC-Compensated Resonant of Electrostatic Actuators by Inductive Coupling. IEEE/ASME Transactions Inverter for Inductive-Power-Transfer Application. IEEE Transactions on on Mechatronics, , 2007. 12(1): p. 23-31. Industrial Electronics, , 2011. 58(8): p. 3500-3510. 24. Jeroen de, B., E.A. Lomonova, and A.J.A. Vandenput, Optimization of 50. Covic, G.A., et al., A Three-Phase Inductive Power Transfer System for Contactless Planar Actuator With Manipulator. IEEE Transactions on Roadway-Powered Vehicles. IEEE Transactions on Industrial Electronics,, Magnetics, , 2008. 44(6): p. 1118-1121. 2007. 54(6): p. 3370-3378. 25. Zhang, W., et al., An Optimized Track Length in Roadway Inductive Power 51. Sallan, J., et al., Optimal Design of ICPT Systems Applied to Electric Vehicle Transfer Systems. IEEE Journal of Emerging and Selected Topics in Power Battery Charge. IEEE Transactions on Industrial Electronics, , 2009. 56(6): Electronics,, 2014. PP(99): p. 1-1. p. 2140-2149. 26. Villa, J.L., et al., Design of a high frequency Inductively Coupled Power 52. Qu, X., et al., Design of a Current-Source-Output Inductive Power Transfer Transfer system for electric vehicle battery charge. Applied Energy, 2009. LED Lighting System. IEEE Journal of Emerging and Selected Topics in 86(3): p. 355-363. Power Electronics,, 2014. PP(99): p. 1-1. 27. Musavi, F., M. Edington, and W. Eberle. Wireless power transfer: A survey 53. Li S., et al., A Double-Sided LCC Compensation Network and Its Tuning of EV battery charging technologies. in IEEE Energy Conversion Congress Method for Wireless Power Transfer. IEEE Transactions on Vehicular and Exposition (ECCE), 2012 2012. Technology, , vol. PP, pp. 1-1, 2014. 28. Chwei-Sen, W., O.H. Stielau, and G.A. Covic, Design considerations for a 54. Yilmaz, M. and P.T. Krein, Review of Battery Charger Topologies, Charging contactless electric vehicle battery charger. IEEE Transactions on Industrial Power Levels, and Infrastructure for Plug-In Electric and Hybrid Vehicles. Electronics, , 2005. 52(5): p. 1308-1314. IEEE Transactions on Power Electronics, , 2013. 28(5): p. 2151-2169. 29. Covic, G.A. and J.T. Boys, Modern Trends in Inductive Power Transfer for 55. Zhang, W., et al., Design for Efficiency Optimization and Voltage Transportation Applications. IEEE Journal of Emerging and Selected Topics Controllability of Series-Series Compensated Inductive Power Transfer in Power Electronics, , 2013. 1(1): p. 28-41. Systems. IEEE Transactions on Power Electronics, , 2014. 29(1): p. 191-200. 30. Huh, J., et al., Narrow-Width Inductive Power Transfer System for Online 56. Hou, J., et al., Precise Characteristics Analysis of Series/Series-Parallel Electrical Vehicles. IEEE Transactions on Power Electronics, , 2011. 26(12): Compensated Contactless Resonant Converter. IEEE Journal of Emerging p. 3666-3679. and Selected Topics in Power Electronics, , 2014. PP(99): p. 1-1. 31. Kissin, M.L.G., J.T. Boys, and G.A. Covic, Interphase Mutual Inductance in Polyphase Inductive Power Transfer Systems. IEEE Transactions on Industrial Electronics, , 2009. 56(7): p. 2393-2400. 32. Kissin, M.L.G., G.A. Covic, and J.T. Boys, Steady-State Flat-Pickup Loading Wei Zhang (S’11) received the B.Sc. degree from HeFei Effects in Polyphase Inductive Power Transfer Systems. IEEE Transactions University of Technology, Hefei, China in 2007, the on Industrial Electronics, , 2011. 58(6): p. 2274-2282. M.Sc, degree from Nanjing University of Aeronautics 33. Kutkut, N.H., et al., Design considerations and topology selection for a 120- and Astronautics, Nanjing, China in 2010 and the Ph.D. kW IGBT converter for EV fast charging. IEEE Transactions on Power degree from the Hong Kong Polytechnic University, Electronics, , 1998. 13(1): p. 169-178. Kowloon, Hong Kong in 2014, all in electrical 34. Sungwoo, L., et al. On-Line Electric Vehicle using inductive power transfer engineering. system. in IEEE Energy Conversion Congress and Exposition (ECCE), 2010. He is currently a Post-doctoral fellow with the 2010. University of Michigan, Dearborn, MI, USA. His current 35. Sungwoo, L., C. Bohwan, and C.T. Rim, Dynamics Characterization of the research interests include wireless power transfer system Inductive Power Transfer System for Online Electric Vehicles by Laplace and resonant converters. Phasor Transform. IEEE Transactions on Power Electronics,, 2013. 28(12): p. 5902-5909. 36. Sato, F., et al., Contactless energy transmission to mobile loads by CLPS-test Chunting Chris Mi (S’00–A’01–M’01–SM’03–F’12) driving of an EV with starter batteries. IEEE Transactions on Magnetics, , received the B.S.E.E. and M.S.E.E. degrees from 1997. 33(5): p. 4203-4205. Northwestern Polytechnical University, Xi’an, China, 37. Garnica, J., R.A. Chinga, and L. Jenshan, Wireless Power Transmission: and the Ph.D. degree from the University of Toronto, From Far Field to Near Field. Proceedings of the IEEE, 2013. 101(6): p. Toronto, ON, Canada, all in electrical engineering. 1321-1331. He was an Electrical Engineer with General Electric 38. Ghahary, A. and B.H. Cho. Design of a transcutaneous energy transmission Canada Inc., Toronto. He is a Professor and Chair of the system using a series resonant converter. in 21st Annual IEEE Power Department of Electrical and Computer Engineering at Electronics Specialists Conference, 1990. . 1990. San Diego State University, San Diego, CA. He was 39. Erickson, R.W. and D. Maksimovic, Fundamentals of Power Electronics. previously Professor and Director of the DOE funded 2001: Springer. GATE Center for Electric Drive Transportation at the 40. Chwei-Sen, W., G.A. Covic, and O.H. Stielau, Power transfer capability and University of Michigan, Dearborn, MI, USA. His current research interests include bifurcation phenomena of loosely coupled inductive power transfer systems. electric drives, power electronics, electric machines, renewable energy systems, IEEE Transactions on Industrial Electronics, , 2004. 51(1): p. 148-157. electrical and hybrid vehicles. He has conducted extensive research and authored 41. Chwei-Sen, W., G.A. Covic, and O.H. Stielau, Investigating an LCL load more than 100 articles. resonant inverter for inductive power transfer applications. IEEE Dr. Mi was the Chair from 2008 to 2009 and the Vice Chair from 2006 to 2007 Transactions on Power Electronics,, 2004. 19(4): p. 995-1002. of the IEEE Southeastern Michigan Section. He is an Area Editor of the IEEE

11 TRANSACTIONS ON VEHICULAR TECHNOLOGY and the IEEE TRANSACTIONS ON POWER ELECTRONICS, and an Associate Editor of the IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS. He was a recipient of the Distinguished Teaching Award and the Distinguished Research Award of the University of Michigan, the2007 IEEE Region 4 Outstanding Engineer Award, the IEEE Southeastern Michigan Section Outstanding Professional Award, and the SAE Environmental Excellence in Transportation Award.