A special LCC-S compensated WPT system with inherent CC-CV transition for electric bicycles charging

Generally, to ensure the high efficiency and safety of charging, the typical charging algorithm of electric bicycle onboard battery packs is first constant current (CC) and then constant voltage (CV). In order to design a WPT system that complies with the above-mentioned charging algorithm, three traditional closed-loop control methods of phase shift control^[1−3], frequency conversion control^[4−6], and DC–DC assistive control^[7−9] are adopted. However, the above three control methods all increase the complexity of the system controller design.

The hybrid topology switching method, is extensively studied for its simplicity of control. Various authors^[10−15] propose multiple types of hybrid topologies to realize CC and CV charging characteristics. However, additional passive components, AC switches, and corresponding driving circuits are unavoidable in hybrid topologies, which increases the complexity of the circuit structure.

Nowadays, as an alternative, the dual-frequency switching method is gaining popularity. Previous researchers^[16−21] present various types of dual-frequency switching methods to achieve CC and CV charging characteristics. However, since some standard frequency recommendations such as from 79 to 90 kHz in the SAEJ2954 standard from the Society of Automotive Engineers, it is difficult to tune circuit parameters to meet actual application requirements.

In addition, the three methods mentioned above have to rely on additional detection circuits and communication links to determine the timing of CC-CV transition. To prevent the risk of accidental load open-circuit in CC mode, it is essential to add open-circuit protection circuits in the above-mentioned methods. Committed to the further optimization of CC and CV WPT systems, this manuscript proposes an LCC-S compensated WPT system to realize inherent CC and CV characteristics and automatic CC-CV transition function. Complicated control, cumbersome circuit structure, difficult-to-adjust parameters, and expensive detection circuits, communication links, open-circuit protection circuits can be avoided, so the proposed system is robust, simple, and low-cost. The proposed system is preferentially recommended for low and medium-power charging applications such as electric bicycles.

The overall circuit structure of the proposed WPT system is depicted in Fig. 1. This structure can be seen as a cascade of a clamp circuit composed of diodes D₁, D₂, and a special LCC-S compensation WPT system. E is the DC input voltage. For the convenience of analysis, the components in the topology are recorded as L_R, L_S, L_P, C_R, C_P, and C_S respectively. The mutual inductance of L_S and L_P is denoted as M. U_AO and U_BO are the AC output voltages from the clamp circuit and the half-bridge inverter, respectively. The equivalent AC resistance of the part surrounded by the blue dotted line is expressed as R_E and satisfies the relation R_E = 2R_B/π². There are three operating modes for the clamp circuit: the turned-off mode, the partly activated mode, and the fully active mode, and these three modes correspond to CC mode, CC-CV transition process, and CV mode respectively. The analysis of the different modes is given as follows:

Figure 1. 

Overall circuit structure of the proposed WPT system and circuit structure of the WPT system working in CV mode.

Analysis of CC mode

At the initial stage of charging, since $ \sqrt 2 \left| {{{U}_{AO}}} \right| \leqslant E $, the clamp circuit is in the turned-off mode and the branch where LR is located is disconnected. The proposed system operates in an SS tank to perform CC charging, as shown in Fig. 2. C_R and C_P can be equivalent to C_PR, and the equivalent relationship is 1/C_PR = 1/C_P + 1/C_R. According to Kirchhoff's voltage law (KVL), Eqn (1) can be obtained as:

Figure 2. 

Circuit structure and equivalent circuit of the WPT system working in CC mode. (a) Circuit structure diagram. (b) Equivalent circuit diagram.

For simplicity of analysis, it is assumed that all compensation capacitors are fully compensated at a fixed angular frequency ω. The compensation relationships are as follows:

Combining Eqns (1) & (2), R_E = 2R_B/π² and $ {I_B} = (\sqrt 2 /{\text π}){I_3} $, Eqn (3) can be derived as:

It can be known from Eqn (3), the input impedance Z_in is purely resistive and the charging current I_B is independent of load resistance.

Analysis of CC-CV transition process

When $ E\leqslant\sqrt{2}\left|{U}_{\text{AO}}\right|\leqslant(4/{\text π} )E $, the clamp circuit is in the partly activated mode so that the branch where L_R is located is gradually turned on. When $ \sqrt 2 \left| {{U_{AO}}} \right| $ just exceeds E, the current I₁ is very weak and can be ignored. At this time, the system circuit structure is basically consistent with that in CC mode. When $ \sqrt 2 \left| {{U_{AO}}} \right| $ is close to (4/π)E, the current I₁ is gradually approaching stability and the system circuit structure is basically consistent with that in CV mode.

Analysis of CV mode

With the continuous increase of $ \sqrt 2 \left| {{U_{AO}}} \right| $, when $ (4/{\text π})E\leqslant\sqrt{2}\left|{U}_{AO}\right| $, the clamp circuit is fully activated. The proposed system operates in LCC-S topology to perform CV charging, as shown in Fig. 1.

For the clamp circuit composed of D₁ and D₂, the relationship between the RMS value of the output voltage U_AO and the input voltage E is $ {U_{AO}} = (\sqrt 2 /{\text π})E $, while for the half-bridge inverter composed of Q₁ and Q₂, the relationship between the RMS value of the output voltage U_BO and the input voltage E is $ {U_{BO}} = (\sqrt 2 /{\text π})E $. Therefore, U_AO = U_BO. From the above analysis, it can be concluded that the full conductive clamp circuit in CV mode is connected in parallel with the half-bridge inverter.

The equivalent circuit in CV mode is displayed in Fig. 3. According to KVL, Eqn (4) can be obtained.

Figure 3. 

Equivalent circuit of the WPT system working in CV mode.

Similar to the CC analysis process, Eqn (2) and jωL_R + 1/jωC_R = 0 need to be satisfied. Substituting Eqn (2), U_AO = U_BO and jωL_R + 1/jωC_R = 0 into Eqn (4), Eqn (5) can be deduced as:

where, U_O is the equivalent AC input voltage of the rectifier.

According to $ {U_O} = (\sqrt 2 /{\text π}){U_B} $, ${U_{AO}} = (\sqrt 2 /{\text π})E $, the expression of the charging voltage U_B is as follows:

Equations (5) & (6) prove that the system can achieve load-independent CV output and ZPA operation.

Given an electric bicycle battery pack with a nominal voltage of 60 V and a capacity of 10 Ah, an experimental prototype with 2 A/66 V charging outputs was fabricated, as shown in Fig. 4. The operating frequency f was set as 85 kHz and the input DC voltage E as 100 V. According to Eqns 1/C_PR = 1/C_P + 1/C_R, (2), (3), (6) and jωL_R + 1/jωC_R = 0, the parameters of each compensation component can be calculated, as listed in Table 1.

Figure 4. 

Experimental prototype.

Experimental results

Experimental waveforms for CC mode, CC-CV transition, and CV mode were captured, as shown in Fig. 5. Figure 5a & b show the experimental waveforms in CC mode at R_B = 10 and 15 Ω, respectively. I_B maintains at a constant value of 2 A and I₁ is null. Figure 5c & d display that the clamp circuit is partially activated, and the branch where L₂ is located generates discontinuous I₁ during the CC-CV transition process. In CV mode, the clamp circuit is fully activated, the current I₁ is continuous, U_B maintains at a constant value of 66 V and the relevant waveforms are shown in Fig. 5e & f. Furthermore, the phases of the input voltage U_BO and the input current I₂ are consistent in the three modes, the proposed system can achieve ZPA operation throughout the charging process.

Figure 5. 

Experimental waveforms. (a) R_B = 5 Ω. (b) R_B = 10 Ω. (c) R_B = 30 Ω. (d) R_B = 40 Ω. (e) R_B = 100 Ω. (f) R_B = 150 Ω.

Figure 6 shows the trends of I_B (represented in red), U_B (represented in blue), and charging efficiency (represented in purple) during the charging process. It can be obtained that when $ \sqrt{2}\left|{U}_{AO}\right|\leqslant E $, the system can achieve an approximate CC output of 2 A, while $ (4/{\text π})E\leqslant \sqrt{2}\left|{U}_{AO}\right| $, the system can achieve an approximate CV output of 66 V. Although the transition from CC to CV mode is not instantaneous, the transition occurs over a fairly short load variation range. Further observation of Fig. 6 shows that the maximum efficiency of the system is 93.3%.

Figure 6. 

Measured I_B, U_B, and efficiency curve vs R_B.

The current study proposes a special LCC-S compensated WPT system with inherent CC and CV output characteristics and automatic transition from CC to CV charging mode. In the initial stage of the charging, the CC mode can be realized through the SS structure. As charging proceeds, when the voltage peak on the clamp circuit satisfies $ (4/{\text π})E\leqslant\sqrt{2}\left|{U}_{AO}\right| $, the system automatically converts to the LCC-S structure to perform CV mode. The proposed system not only avoids complex controller design but also eliminates complex and expensive circuits such as wireless communication links, state-of-charge detection circuits, and open circuit protection circuits. Therefore, the system features easy control, a simple structure, and low cost. The proposed system is a potential and competitive candidate in low and medium-power applications.