II. SP COMPENSATED CPT SYSTEM

A) Contactless charging system

The circuit diagram of contactless charging system with SP compensation is depicted in Fig. 1. A DC voltage source V _dc is applied to the input of H-bridge inverter. For the experiment purpose, a variable DC source is used to keep the current and voltage constant during charging of the battery bank in CC and CV modes, respectively.

Fig. 1.

Schematic of contactless charging system with SP compensation.

The compensated primary coil is excited with high-frequency current, generated by the high-frequency H-bridge inverter. On the secondary side, a parallel compensated coil is connected with a diode bridge rectifier, which converts high-frequency AC voltage to DC voltage. In order to get pure DC voltage and current, LC filter is used. Diode D ensures charging of the battery bank only when the anode voltage is greater than the cathode voltage. The battery bank is represented as E-Load. The symbols R _P and R _S denote AC resistance of the primary and secondary coils, respectively.

The primary and secondary compensation capacitors C _P and C _S are calculated at resonance frequency ω _o , using (1) and (2), respectively [Reference Joy, Kushwaha, Rituraj and Kumar6, Reference Aditya and Williamson8, Reference Aditya and Williamson9, Reference Jiang, Wang, Chen, Wang and Wang13].

(1) $$C_P = \displaystyle{1 \over {\omega _o^2 (L_P - (M^2/L_S))}},$$

(2) $$C_S = \displaystyle{1 \over {\omega _o^2 L_S}},$$

where L _P and L _S represent the primary and secondary self-inductances, respectively.

B) Equivalent model of the charging system

An equivalent circuit model of the charging system is shown in Fig. 2 [Reference Kushwaha, Rituraj and Kumar18]. The relation between coupling coefficient k and mutual inductance M is given in (3).

(3) $$k = \displaystyle{M \over {\sqrt {L_PL_S}}}, $$

(4) $$Z_P = R_P + j\left( {h\omega L_P - \displaystyle{1 \over {h\omega C_P}}} \right),$$

(5) $$Z_r = \displaystyle{{{(h\omega M)}^2} \over {R_S + jh\omega L_S + \left( {R_{ac}/(1 + jh\omega C_SR_{ac})} \right)}},$$

(6) $$R_{ac} = \displaystyle{{\pi ^2} \over 8}R_L,$$

(7) $$\eqalign{Z_T & = R_P + j\left( {h\omega L_P - \displaystyle{1 \over {h\omega C_P}}} \right) \cr & \quad + \displaystyle{{{(h\omega M)}^2} \over {R_S + jh\omega L_S + \left( {(R_{ac}/1 + jh\omega C_SR_{ac})} \right)}}.}$$

Fig. 2.

Equivalent circuit model of the SP compensated CPT system.

For (4)–(7), Z _P , Z _r , Z _T represent the primary side, reflected, and total impedances of the CPT system for h ^th harmonic, respectively. R _ac is the effective load resistance, seen from the input side of the rectifier. R _L is the equivalent load resistance of the battery bank, which depends on charging status of battery voltage and current [Reference Zheng15].

The Fourier series expressions of the primary instantaneous voltage v _p (t) (inverter output) and current i _p (t) are given in (8) and (9), respectively.

(8) $$v_p(t) = \sum\limits_{h = 1,3,5..}^\infty \displaystyle{{4V_{dc}} \over {\pi h}}\sin h\omega t,$$

(9) $$i_p(t) = \sum\limits_{h = 1,3,5..}^\infty \displaystyle{{4V_{dc}} \over {\pi h \vert Z_T \vert}} \sin (h\omega t - \theta _{Z_T}),$$

where $\theta _{Z_T}$ is the load phase angle of total impedance Z _T , seen from the output of H-bridge inverter.

The compensated coil (transmission) efficiency η _cc of the SP compensated CPT system is calculated using AC equivalent circuit based on T-model of contactless coils, as shown in Fig. 3. Equivalent series resistance of C _P and C _S are not considered in the efficiency calculation due to its insignificant effect. Hence, the real power consumed in capacitor is zero, and the η _cc of the SP compensated CPT system is given as

(10) $$\eta _{cc} = \eta _P \cdot \eta _{mutual} \cdot \eta _S,$$

where η _P , η _mutual , and η _S are the efficiencies of the equivalent primary, mutual, and secondary of the system, respectively. Since the mutual has only a reactive component, the active power consumed is zero (η _mutual  = 1). From Fig. 3, $\eta _P = P_{P_{out}}/P_{P_{in}}$ and $\eta _S = P_{S_{load}}/P_{S_{in}}$ , where the input power $P_{P_{in}} = (P_{P_{out}} + {\rm loss}\;{\rm in}\;R_P)$ and $P_{S_{in}} = (P_{S_{load}} + {\rm loss}\;{\rm in}\;R_S)$ . Therefore, the expression (10) can be written as

(11) $$\eta _{cc} = \displaystyle{{\Re (Z_{P_{out}})} \over {\Re (Z_{P_{out}}) + R_P}} \cdot 1 \cdot \displaystyle{{\Re (Z_{S_{load}})} \over {\Re (Z_{S_{load}}) + R_S}},$$

where the symbol $\Re $ represents the real part of the respective impedances, $Z_{S_{load}} = R_{ac}/(1 + j\omega C_SR_{ac})$ , and $Z_{P_{out}} = j\omega MZ_{S_{in}}/(j\omega M + Z_{S_{in}})$ . By substituting $Z_{S_{load}}$ and $Z_{P_{out}}$ in (11), the final expression of η _cc is given as

(12) $$\eta _{cc} = \displaystyle{{M^2\omega ^2R_{ac}} \over {(C_S^2 R_{ac}^2 (L_S^2 R_P + M^2R_S)\omega ^4 + A\omega ^2 + R_P(R_S^2 + 2R_SR_{ac} + R_{ac}^2 )}},$$

where $A = (((C_S^2 R_S^2 - 2C_SL_S)R_{ac}^2 + L_S^2 )R_P + M^2(R_S + R_{ac}))$ and ω = 2πf.

Fig. 3.

AC equivalent circuit based on T-model of contactless coils for SP compensated CPT system.

From (12), the optimum operating frequency (f _optimum ), at which the maximum η _cc is achieved, can be obtained by (13) and is given in (14).

(13) $$\left. {\displaystyle{{\partial \eta _{cc}} \over {\partial f}}} \right \vert _{f_{optimum}} = 0,$$

(14) $$f_{optimum} = \displaystyle{1 \over {2\pi}} \displaystyle{{R_P^{1/4} \sqrt {R_S + R_{ac}}} \over {\sqrt {R_{ac}C_S} {(L_S^2 R_P + M^2R_S)}^{1/4}}}.$$

III. EXPERIMENTAL DISCUSSION

Figure 4 shows the laboratory view of real-time implementation for charging the battery bank using SP compensated CPT system. Six number of sealed maintenance-free lead acid batteries connected in series are used as a battery bank in the experiment. However, the other technologies of batteries like lithium, sodium, etc. can also be used. The details of power switches and the battery bank used in CPT system are provided in Table 1. The primary and secondary coils are made using Litz wire, having American wire gauge #32 copper wire. The vertical distance between primary and secondary coils can be adjusted up to 10 cm, while in the experiment it is kept at 2 cm. A resonance frequency of 197.60 kHz is selected for the SP compensated CPT system. To vary the output frequency of H-bridge inverter, a pulse width modulation controller IC SG3525A is used. The remaining specifications of the SP compensated CPT system are given in the Table 2.

Fig. 4.

Laboratory view of the experimental setup.

Table 1.

Specifications of power components and battery bank.

Table 2.

Specifications of the SP compensated CPT system.

The charging of lead acid battery bank is performed in open loop (by manually controlling the input DC voltage to maintain CC and CV modes) at the resonance frequency. The measured charging profile and the equivalent resistance profile of a lead acid battery bank are shown in Fig. 5. The initial voltage of the battery bank is 74.1 V, which is first charged in CC mode for about 4 h, then in CV mode for about 5 h, as shown in Fig. 5(a). The charging current in CC mode is set to a constant 700 mA. Whereas, in CV mode, the voltage across the battery is maintained at 81.6 V by decreasing the input DC voltage. This results in a decrease in the charging current. The equivalent resistance profile of battery bank, as shown in Fig. 5(b), is obtained from Fig. 5(a).

Fig. 5.

(a) Measured charging profile and (b) equivalent resistance profile of a lead acid battery bank at the resonance frequency.

In Fig. 6, the variation of compensated coil efficiency, calculated from (12), with respect to (w.r.t.) different operating frequencies (0–500 kHz) for R _ac  = 126 Ω and 717 Ω, is given. Two cases for the variation in compensated coil efficiency are presented in Fig. 6. One is for the CC mode (R _ac  = 126 Ω) and another is for the CV mode (R _ac  = 717 Ω). For both the cases in Fig. 6, the maximum compensated coil efficiency ( $\eta _{cc_{max}}$ ) is shown by zooming the dotted circle area. From the zoomed version, it can be seen that $\eta _{cc_{max}}$ lies on the left side of the resonance frequency (f ₀), marked as a f _optimum . Further investigation on $\eta _{cc_{max}}$ and ZVS at different operating frequencies in CC and CV modes with the experimental results has been done from the next paragraph.

Fig. 6.

Variation of calculated compensated coil efficiency w.r.t. different operating frequencies for R _ac  = 126 Ω and 717 Ω.

At the time of charging in CC and CV modes, the voltage and current waveforms of the inverter and battery bank are observed. In CC mode, the waveforms are recorded for inverter output and battery bank, as shown in Fig. 7. Since the current is constant in CC mode, an effective load resistance R _ac will change only due to the voltage rise, which is less significant, as shown in Fig. 5(b). In CC mode, at a particular instant of time, R _ac is experimentally measured as 126 Ω [marked in Fig. 5(b)]. Since the electrical characteristics of the battery bank will change over the time, the battery bank is replaced by an equivalent resistive load of 126 Ω to maintain same R _ac for further experiment.

Fig. 7.

Experimental waveforms in CC mode at the resonance frequency.

In Fig. 8(a), the variation of load phase angle obtained from (9) and measured from the experiment are shown for different operating frequencies when R _ac  = 126 Ω. It can be observed from Fig. 8(a) that both the curves are following the same nature. It can also be seen that to increase the load phase angle of the system, operating frequency should be decreased from its resonance frequency. The plot of η _cc versus load phase angle obtained from (9) and (12), and measured from the experiment, is given in Fig. 8(b). From Fig. 8(b), an almost constant nature of η _cc is seen with variation in the load phase angle. However, in zoomed version, a parabolic nature is seen with an increase in load phase angle. Hence, it has a maximum efficiency point, which is about 15^° from the calculation and 17^° from the measurement.

Fig. 8.

Experimental results at R _ac  = 126 Ω. (a) Load phase angle versus operating frequency and (b) compensated coil efficiency versus load phase angle.

At resonance frequency, the experimental waveforms of primary voltage (inverter output) and current are given in Fig. 9. In Fig. 9, undesirable notches (due to inappropriate ZVS), marked in the red circle are noticed in the primary voltage waveform, which can affect the system stability. An improved waveform (due to proper ZVS) of the primary voltage is recorded at 184.3 kHz frequency (measured f _optimum ), which is about 17^° of load phase angle, as shown in Fig. 10.

From Figs 8–10, it can be seen that to obtain a stable performance, load phase angle should be increased by decreasing the operating frequency to f _optimum . In this way, the system stability can be improved with a maximum efficiency for lower load resistance in CC mode.

Fig. 9.

Experimental waveforms of primary voltage and current (inverter output) at 197.6 kHz operating frequency (resonance frequency) and R _ac  = 126 Ω.

Fig. 10.

Experimental waveforms of primary voltage and current (inverter output) at 184.3 kHz operating frequency and R _ac  = 126 Ω.

In CV mode, the voltage and current waveforms of inverter output and battery bank are recorded at the end stage of CV mode for a charging current of 140 mA, as shown in Fig. 11. An effective load resistance R _ac is experimentally measured as 717 Ω [marked in Fig. 5(b)], which is higher than CC mode. To maintain R _ac (717 Ω), the battery bank is replaced with the resistive load for further experiment.

Fig. 11.

Experimental waveforms in CV mode at the resonance frequency.

At R _ac  = 717 Ω, again operating frequency is varied to maintain ZVS with maximum efficiency. The variation of load phase angle for different operating frequencies obtained from (9) and measured from the experiment when R _ac  = 717 Ω is plotted in Fig. 12(a), and the η _cc observed at each load phase angle calculated from (9) and (12) is given in Fig. 12(b). From Fig. 12(a), it can be examined that both the curves are following the same pattern. In CV mode, the waveform of inverter voltage is stable throughout the variation, even at the resonance frequency, as shown in Fig. 11. From Fig. 12(b), it is observed that the η _cc is maximum when load phase angle is about 40^° (obtained at f _optimum  = 186.5 kHz) from the calculation and about 45^° (obtained at f _optimum  = 184.4 kHz) from the measurement. In addition, a parabolic nature of the η _cc curve is noticed with an increase in the load phase angle.

Fig. 12.

Experimental results at R _ac  = 717 Ω. (a) Load phase angle versus operating frequency and (b) compensated coil efficiency versus load phase angle.

From the above discussion, it can be noticed that, by controlling the load phase angle in both CC and CV modes, a stable performance and maximum efficiency can be achieved.