Compared to LC resonance, LCL resonance has distinct advantages such as a large resonant capability, low voltage and current stresses of the power device, constant voltage or current output characteristics, and fault-tolerance capability. Thus, LCL resonant compensation is employed for a movable Inductive Contactless Power Transfer (ICPT) system with a multi-load in this paper, which achieves constant current output characteristics. Peculiarly, the primary side adopts a much larger compensation inductor than the primary leakage inductor to lower the reactive power, reduce the input current ripple, generate a large current in the primary side, and realize soft-switching. Furthermore, this paper proposes an approximate resonant point for large inductor-ratio LCL resonant compensation through fundamental wave analysis. In addition, the PWM control strategy is used for this system to achieve constant current output characteristics. Finally, an experimental platform is built, whose secondary E-Type coils can ride and move on a primary rail. Simulations and experiments are conducted to verify the effectiveness and accuracy of both the theory and the design method. f : Input AC frequency L : Inductance value of resonant inductor L L_a : Inductance value of resonant inductor L_a C : Capacitance value of the resonant capacitor C R : Load resistance λ : ≡ L_a ⁄ L , ratio of inductors L_a and L Q : ≡ ω_oL ⁄ R , the Q -value of the resonant circuit Ω : ≡2 πf , the angular input frequency (in radians per second) ω_o : ≡1⁄( LC ) ^0.5 , the angular resonant frequency (in radians per second) ω_n : ≡ ω ⁄ ω_o , the normalized angular frequency Z_in : Input impedance in the LCL resonance model I_L : RMS value of the output current in the LCL resonance model U_o : RMS value of the output voltage in the LCL resonance model ω_op : Approximate angular resonant frequency L_pc : Inductance value of the primary compensation inductor L_pc L_p : Inductance value of the primary leakage inductor L_p C_p : Capacitance value of the primary compensation capacitor C ω_op : ≡1⁄( L_p C_p ) ^0.5 , the primary angular resonant frequency ω_np : ≡ ω ⁄ ω_op , the primary normalized angular frequency λ_p : ≡ L_pc ⁄ L_p , the ratio of inductors L_pc and L_p Q_p : ≡ ω_op L ⁄ R , the Q -value of the resonant circuit M_k : Mutual inductance ( k =1,2) L_sk : Inductance value of the secondary leakage inductor L_sk ( k =1,2) Lsck : Inductance value of the secondary LCL compensation inductor Lsck (k=1,2) Csk : Capacitance value of the secondary compensation capacitor Csk (k=1,2) Rk : Secondary load resistance (k=1,2) ωosk : ≡1⁄(LskCsk)0.5, the secondary angular resonant frequency (k=1,2) ωnsk : ≡ω⁄ωosk, the secondary normalized angular frequency (k=1,2) Qsk : ≡ωosk Lsk⁄Rk, the Q-value of the secondary side (k=1,2) λsk : ≡Lsck⁄Lsk, the ratio of inductors Lsck and Lsk (k=1,2) Zsk : Input impedance of the secondary side (k=1,2) Zpsk : Equivalent secondary impedance in the primary side (k=1,2) Req : Equivalent load in the primary side Css : Capacitance value of the secondary series compensation capacitor Css ωos : ≡1⁄(LskCss)0.5, the secondary angular resonant frequency of the series compensation Uos : RMS value of the secondary output voltage with series compensation Ip : RMS value of the primary rail current Iosk : RMS value of the secondary output current (k=1,2) Usk : RMS value of the secondary input voltage (k=1,2) Pos : Output power of the secondary side with series compensation PoLCLk : Output power of the secondary side with LCL compensation (k=1,2) D : Duty cycle Based on the electromagnetic induction principle, Inductive Contactless Power Transfer (ICPT) systems transform power from the primary side of the coupling coils to the secondary side by converting electrical energy into magnetic energy. ICPT systems have a number of advantages such as high security performance and low maintenance cost. For example, eliminating the friction and spark caused by naked conductors, ICPT systems can enhance security and prolong the service life of trolley cars. It also has been the preferred power-delivery approach in many special applications, e.g., underwater and explosive environments. In addition, multi-load ICPT systems can supply power to a product line containing several electronic actuators with only one primary rail, which avoids the use of cables and improves the security performance. This paper focuses on constant-current-output movable ICPT systems with multi-loads, which are a good fit for magnet power supplies, capacitor charging power supplies, laser diode drivers, etc. The basic block diagram of a movable ICPT system with a multi-load is shown in Fig. 1 . Through the rectifier and filter circuits, the power frequency source supply provides a constant dc voltage to the high-frequency inverter, which produces a high-frequency ac current in the primary coil and a high-frequency alternating magnetic field around the loosely coupled transformer. The secondary coils obtain energy from the magnetic field via an air gap and then induce alternating electromotive forces. At last, the alternating electromotive forces supply power for loads. It is important to note that one primary side coil can complete power transfer with multiple secondary coils at the same time. To reduce the reactive power and losses caused by the low coupling coefficient of the coupling coils, it is essential to compensate movable ICPT systems. Parallel and series compensations are common and widely used in such systems [1] - [6] . However, series compensation is unsuitable for the primary side of a movable ICPT system due to its difficulty in generating a large primary current. Meanwhile, parallel compensation cannot meet the requirements of the secondary sides in multi-load or variable-load ICPT systems since its resonant frequency is related to the load resistor. To analyze and solve these problems, the fundamental wave analysis method is adopted for LC resonance [5] , [6] , which is also valuable for other resonance analyses. Furthermore, the stability, load range, and output power of ICPT systems are analyzed in [7] . Recently, many composite resonances have been put forward to overcome such defects as the low resonant capacity and high power device stress of LC resonance [8] , [9] . However, among them only LCL resonant compensation with two similar-value inductors has been applied to movable ICPT systems [10] - [13] . Unlike the work in [14] , this paper puts forward a large inductor-ratio LCL resonance to compensate the primary side of a movable ICPT system with a multi-load and a two-equal-inductor LCL resonance for the secondary side. Against analyzing a large-ratio LCL resonance comprehensively, an approximate resonant point is given out. The primary LCL compensation can lower reactive power, generate a large current in the primary side, suppress harmonic current and realize soft-switching. The secondary LCL compensation can increase output power and achieve a constant current output. This paper is organized as follows. The analysis of LCL resonant compensation is first reviewed in Section II. Then, Section III presents the structure and model of a movable ICPT system with a multi-load as well as the design ideas and compensation requirements. Next, the design process of LCL resonant compensation is described in Section IV. Finally, the LCL compensation results and system characteristics are illustrated in Section V, and a summary is given in Section VI. This section analyzes the effects of the normalized angular frequency ω_n and the ratio of the inductors λ on the LCL resonance characteristics. Then, an approximate resonant point is derived to simplify the system design, which can make the input impedance nearly pure resistive. In this case, the power factor can be significantly improved. Fig. 2 shows a schematic diagram of an LCL circuit. Considering the fundamental wave only, the input impedance of the LCL circuit can be written as: Furthermore, the inductance L current, i.e., output current, can be easily derived: Similarly, the resistance R voltage, i.e., output voltage, can be expressed as: When ω_n is varying, the LCL circuit can present constant current (or voltage) output characteristics. Considering (2) can be written as: It can be seen that the output current is unrelated to the load resistor, which means that is possesses the constant current output characteristic. Similarly, (1) can be derived as: Substituting into (3) results in: This shows that there is no relationship between the output voltage and the load resistor, i.e., the constant voltage output characteristic. Similarly, (1) can be derived as: The ratio of the inductors λ influences the impedance characteristics and the equivalent circuit model of the LCL resonance circuit. 1) Input Impendence when λ=1: Considering substituting λ =1 into (1) and (2) leads to the following equivalent expressions: Obviously, when λ =1 and ω_n =1, the LCL circuit presents constant current output and pure resistive input impedance characteristics. However, the input impedance is inductive in the case of a constant voltage output, which can be seen from expression (7). 2) Equivalent Circuit Model when λ is large : With a large inductor L_a determined by λ ( λ >10), the voltage source and inductor L_a , in Fig. 2 , are equal to a current source, as shown in Fig. 3 . According to the equivalent circuit in Fig. 3 , the approximate resonant angular frequency of the LCL resonant circuit is given below. where the resonant condition is: When operating at this approximate resonant angular frequency, the LCL circuit still can show great resonant characteristics, such as a pure resistive impedance characteristic. This section introduces the structure of a movable multi-load ICPT system and establishes the equivalent circuit model of a system with two loads. As can be seen from Fig. 4 , this movable ICPT system with a multi-load consists of a primary side and secondary sides (more than one). The primary side contains a rail, a primary compensation circuit, an inverter circuit and a DC voltage source. The secondary side is formed by a pick-up coil, a secondary compensation circuit and a load, which can move on a primary guide rail. The secondary pick-up coil couples with the primary rail to form a loosely coupled transformer as the power transfer mechanism of the ICPT system, which can be regarded as a transformer with low coupling coefficient or two coupling inductors. An Ansoft 3-D model of the movable ICPT system is constructed in Fig. 5 . If one secondary E-Type coil moves along the rail in the Y direction, a mutual inductance between the primary side and the secondary side is almost constant since the magnetic field intensity is constant, which can be seen from Fig. 6 (a). If the secondary side has an X-direction or Y-direction deviation, the mutual inductance will decrease and eventually both the primary and secondary resonance compensation will detune and the transfer power will drop. From Fig. 6 (b), the central column of the E-Type coil has the strongest magnetic field. Therefore, it is assumed that the magnetic fields of the secondary sides will not influence each other and disturb the primary magnetic field. To simplify the modeling process, the fundamental wave analysis method is adopted to analyze and model this system. Firstly, the primary rail is considered as an inductor L_p . Secondly, the secondary pick-up coils are regarded as inductors L_{s 1} and L_{s 2} whose mutual inductances are M ₁ and M ₂ . Finally, the dc source and inverter are replaced by an ac voltage source u_in . An equivalent circuit model of a movable ICPT system with two loads is given in Fig. 7 (a). The secondary input impedance can be written as: The primary equivalent circuit model is redrawn with the secondary reflecting impedance in Fig. 7 (b), where Z_{ps 1} and Z_{ps 2} are defined as: Likewise, the secondary circuit model can be easily deduced as presented in Fig. 7 (c). The voltage u_sk ( k =1, 2) is induced by the primary current i_p , whose RMS value can be expressed as where I_p stands for the RMS value of the primary current i_p . The movable ICPT system with a multi-load has the following two characteristics: 1) increasing the amplitude and frequency of the primary current to improve the transfer power due to a low coupling coefficient between the primary side and the secondary sides; 2) guaranteeing each secondary side under stand-alone operation. 1) The Primary Side and Secondary Sides are Controlled Independently : As can be seen from expression (15), if the mutual inductance is constant, keeping ω and I_p constant will ensure the induced the voltage u_sk to be constant in the secondary coils. Then, each secondary side can operate independently. This method, controlling the primary side and the secondary sides separately, can make every secondary side work independently and remove the feedback loop between the secondary sides and the primary side. 2) The Secondary Reflected Impedances in Primary Side are Pure Resistive : If the reflected impedance in the primary side is inductive or capacitive, the primary resonant frequency will be forced to change and the reactive power will increase. Therefore, the secondary input impedance should be kept pure resistive when designing the secondary compensation. 3) The Primary Compensation Measure Aims at Reducing the Reactive Power : As shown in Fig. 7 (b), the large current in the primary side is generated by the resonance of C_p and L_pc . In order to decrease the current flowing from C_p to the source, the value of L_pc has to be improved. Although a larger L_pc decreases the transfer power, it can reduce the reactive power effectively and achieve soft-switching more easily. From equation (8), only when λ =1 and ω_n =1 is it possible for the LCL circuit to achieve a constant current output and a pure resistive input impedance. For this, the above conditions must be met during the design of the secondary LCL compensation. Then, the output current can be written as: The output power can be expressed by: The relationship between the secondary output power and the primary current RMS current is shown in Fig. 8 . When I_p =50A and R ₁ = R ₂ =40Ω, the total output power of the secondary sides is about 50W. Hence, the primary RMS current is selected as 50A. If LCR series circuit resonates, the input impedance is pure resistive and the output voltage is equal to the input voltage. The equivalent circuit of the series resonance compensation circuit in the secondary side is shown in Fig. 9 . While resonating, the RMS value of the output voltage is: The output power can be derived and written as: Comparing (18) to (20), the power ratio can be achieved by: As shown in (21), when the Q -value of the secondary side Q_sk >1, the output power of the series compensation is larger than that of the LCL compensation. However, the LCL compensation can achieve much more power when Q_sk <1. This is obvious in Fig. 10 . Taking the LCL compensating secondary side as an example, the secondary equivalent load in the primary side can be derived through (13) and (14): Consequently, the primary equivalent circuit in Fig. 7 (b) can be converted to a new model as shown in Fig. 11 (a). From the analysis in Chapter 3 Section C Point 3, the primary ratio of the inductors λ_p needs to be large enough ( λ_p >10). In this case, the primary equivalent circuit is transformed into the LCR parallel circuit according to Chapter 2 Point 2, as shown in Fig. 11 (b). Due to the very low coupling coefficient of this movable ICPT system, the values of M_k / L_sk and R_eq are very small. From expression (9), the primary approximate resonant angular frequency can be further simplified to: Combining the limitation of (10), the range of the primary load (i.e. secondary equivalent load) can be given by: which determines the maximum load that the secondary sides are able to carry. The secondary equivalent loads in the primary side must satisfy equation (24) during the design process. The primary input apparent power is discussed by the following expression: Obviously, the input active power is P =Re( S ), and the input reactive power is Q =Im( S ). By a Mathcad calculation, the relationships among the input power, the primary normalized angular frequency ω_np , and the ratio of the inductors λ_p is shown in Fig. 12 . P and Q present the input active power and the input reactive power, respectively; D is the duty cycle of the input voltage source; and R ₁ and R ₂ are the load resistors in the secondary sides. As can be seen from Fig. 12 , as λ_p increases, the maximum value of the input active power decreases. However, the maximum input active power point is close to the position where ω_np =1. This means that the operating frequency closest to the angular resonant frequency and the input impendence is nearly pure resistive, which will increase the input power factor. For this reason, the operating frequency is set at the point of ω_np =1, and λ_p =60 is chosen for the purpose of achieving a 50W transfer power. Considering that the primary normalization frequency ω_np is set at ω_np =1, the relationships among the primary RMS current I_p , the load resistance, the duty cycle D , and the ratio of the inductors λ_p is researched here. In Fig. 13 (a), the inductor ratio λ_p is kept constant while the two load resistances are 20Ω, 40Ω, and 60Ω and the duty cycle D varies from 0 to 1. In Fig. 13 (b), the load resistance is kept constant while the duty cycle D is 0.2, 0.5, and 0.8 and the ratio of the inductors λ_p changes from 40 to 80. From the curves in Fig.13 , the primary RMS current is 50A when R ₁ = R ₂ =40Ω, D =0.5, and λ_p =60, which corresponds with the previous analysis. According to former research, the design method of the LCL compensation in a constant-current movable ICPT system with a multi-load is summarized as follows: 1) The resonant angular frequency of each secondary side and the primary side are equal to the operating frequency. 2) The secondary ratio of the inductors λ _sk in the LCL compensation should be set at 1. 3) The primary RMS current I_p is determined by the secondary output power as shown in Fig. 7 . 4) The primary ratio of the inductors λ_p in the LCL compensation is conditioned by the primary RMS current I_p and the duty cycle D at the steady state, which can determine the value of the primary compensation inductor as shown in Fig. 10 . 5) According to the resonant angular frequency and the values of the inductors, the values of the primary and secondary compensation capacitors can be calculated by following equations: According to the schematic diagram in Fig. 14 , the platform is constructed with f =25kHz, λ_p =60, where the inverter topology is a phase-shifted full-bridge circuit. On this platform, the PWM control strategy has been adopted to realize the constant-current characteristic as shown in Fig. 15 . The primary side control and the secondary side control are independent of each other. In the primary side, the current control is used to make the primary RMS current constant; and in the secondary sides, the control strategy and the converter topology are chosen according to the load units which are replaced by resistors here. Generally, a load unit contains a power electronic converter, electric equipment and a control unit. The parameters of the simulation and experiment are listed in Table I . As shown in Fig. 16 (a), the primary rail is constructed with a copper sheet (18mm*0.4mm) by four layers parallel winding, which is packed and fixed by an insulating plate. The interval of the guide rail is set in accordance with the size of the secondary pick-ups. In Fig. 16 (b), the secondary pick-ups employ E-Type cores with 43 and 45 turns ( d =1mm) wound on their central columns. The pick-ups can ride on the primary rail and slide freely. To verify the effectiveness of the analyses of the LCL compensation, experiments were performed using the designed ICPT system, which contains a one-meter rail (as the primary side). Fig. 17 - Fig. 21 exhibit the experiment results. Fig. 17 shows the tendency of the output current affected by the load when the secondary side is compensated by the LCL circuit. Although R ₁ changes, the output current is approximately constant, i.e., the constant current output characteristic is obtained. The efficiency of the LCL compensating ICPT system varying with the output power is shown in Fig. 18 . Obviously, the efficiency improves with an increase of the output power, and reaches its maximum value of 72% at the 50W-point. The characteristic of the secondary series compensation is different from the secondary LCL compensation as shown in Fig. 19 . Obviously, in the case of an increasing load, the secondary LCL compensation is superior to the secondary series compensation. When R ₂ is suddenly added to the system, the voltage u_{o 1} of the load R ₁ and the primary current i_p will change as shown in Fig. 20 . In the instant of the load rising up, the amplitudes of u_{o 1} and i_p decline first. Then with the closed-loop PWM control, the duty cycle of the input voltage will increase and eventually both u_{o 1} and i_p return to their initial values. Fig. 21 shows the waveforms of the input voltage u_in , the input current i_in , and the primary compensation capacitor voltage u_cp when the load changes. From Fig. 21 , it can be seen that when the load resistance increases, the duty cycle of u_in increases and the phase deviation between u_cp and i_in decreases, which lead to an increase of the input active power. This paper draws a conclusion that keeping the frequency and amplitude of the primary current constant can make each load operate independently when the mutual inductance does not change. For a complex ICPT system with a large-inductor-ratio LCL compensation, this paper proposes a method to obtain an approximate resonant angular frequency. The system used in this paper is compensated by an LCL circuit in both the primary and secondary sides. The primary LCL compensation can lower the reactive power and generate a large current in the primary side. In addition, it can also suppress the harmonic current and realize soft switching. The secondary LCL circuit can increase the output power and achieve a constant current output. Simulation and experiments have been conducted to verify the effectiveness and accuracy of the theory and design method. It needs to be pointed out that due to an almost constant mutual inductance in this movable ICPT system, there is no consideration for variable mutual inductance situations, which is a deficiency of this paper. Jie Hua was born in China, in 1991. She received her B.S. degree from the Department of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, China, in 2013. She is presently working toward her M.S. degree in Automation Engineering from the Nanjing University of Aeronautics and Astronautics. Her current research interests include inductive contactless power transfer systems. Hui-Zhen Wang was born in China, in 1964. She received her B.S. degree from the Department of Electrical Engineering, Nanjing Aeronautical Institute, Nanjing, China, in 1983. She is presently a Professor in the College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, China. She is the holder of 13 Chinese invention patents. Her current research interests include power electronics and the control of electrical machines. Professor Wang was a recipient of a Second Prize of the State Technology Invention Award. Yao Zhao was born in China, in 1987. He received his B.S. degree in Automation from Anhui University, Hefei, China, in 2009, and his M.S. degree in Electrical Engineering from the Shanghai Maritime University, Shanghai, China, in 2011. He is presently working toward his Ph.D. degree in Automation Engineering at the Nanjing University of Aeronautics and Astronautics, Nanjing, China. His current research interests include doubly salient electrical machines for aircraft power and electric vehicles, and new energy generation systems. Ai-Long Zou was born in China, in 1988. He received his B.S. degree in Automation Engineering from Hohai University, Nanjing, China, in 2011, and his M.S. degree in Automation Engineering from the Nanjing University of Aeronautics and Astronautics (NUAA), Nanjing, China, in 2014. From 2011 to 2014, he studied wireless power transfer (WPT). Since 2014, he has been working on WPT and active power filters in the 724 research institute of the China Shipbuilding Industry Corporation, Beijing, China.