Modular Battery Charger for Light Electric Vehicles

Abstract

Rapid developments in energy storage and conversion technologies have led to the proliferation of low- and medium-power electric vehicles. Their regular operation typically requires an on-board battery charger that features small dimensions, high efficiency and power quality. This paper analyses an interleaved step-down single-ended primary-inductor converter (SEPIC) operating in the discontinuous conduction mode (DCM) for charging of battery-powered light electric vehicles such as an electric wheelchair. The required characteristics are achieved thanks to favourable arrangement of the inductors in the circuit: the input inductor is used for power factor correction (PFC) without additional elements, while the other inductor is used to provide galvanic isolation and required voltage conversion ratio. A modular interleaved structure of the converter helps to implement low-profile converter design with standard components, distribute the power losses and improve the performance. An optimal number of converter cells was estimated. The converter uses a simple control algorithm for constant current and constant voltage charging modes. To reduce the energy losses, synchronous rectification along with a common regenerative snubber circuit was implemented. The proposed charger concept was verified with a developed 230 VAC to 29.4 VDC experimental prototype that has proved its effectiveness.

1. Introduction

Developments in electronic systems together with improvements in battery technology enable spread of light electric vehicles (LEVs) in a wide range of applications: from electric bicycles, scooters and autonomous package carriers to utility vehicles and electric wheelchairs for disabled or elderly people [1,2,3,4,5]. Such applications typically employ a low-voltage battery (24–48 V nominal) and are charged from the AC grid with power up to 1 kW [6,7,8,9,10]. The chargers generally include two-stage ac-dc converters with a power factor pre-regulator (PFP) that is followed by a dc-dc converter [11,12,13] Such systems generally include a DC-bus formed by high voltage (>350 V) electrolytic capacitors [14,15], which are among the most critical parts of power electronic converters in terms of reliability [16].

Different solutions based on a variety of single-stage systems without DC-link have been proposed: resonant LLC topology [17,18], boost full bridge converter [19], flyback [20,21], SEPIC (single-ended primary-inductor converter) [22], quasi-resonant bridgeless converter [23], matrix converter [24], and dual active bridge [25]. Furthermore, a range of hybrid topologies have been introduced for PFC applications, such as: SEPIC-flyback [26], boost-flyback [27,28], boost-forward [29,30], and forward-flyback [31].

As compared to other single-stage converters, the SEPIC operating in discontinuous conduction mode (DCM) features important advantages: the voltage follower mode allows the current control loop to be omitted, while galvanic isolation provides for several isolated outputs. Moreover, the primary transistor turns on with zero voltage switching (ZVS), and the output diode turns off with zero current switching (ZCS).

Modern design approaches allow easy integration of batteries into various parts of the EV to achieve better ergonomics. For example, two separate batteries can be integrated into armrests of the wheelchair for easier access and swapping [1]. Optimal charging of such systems would require a charger with multiple outputs and charge balancing functionality. In addition, the charger should be compact and fit special on-board compartment for easy deployment upon necessity.

Present study focus is on the further development of the interleaved SEPIC concept recently proposed as a candidate topology for the battery charger of power-assist wheelchairs [32]. According to the specification, the charger is stored in a compartment under one of the armrests. The dimensions available are limited to 125 × 149 × 40 mm, as shown in Figure 1. To realise such low-profile design, the modular approach is implemented. It allows the distribution of the power between the interleaved cells, avoiding bulky components. As a result, the charger with low profile can be realised with standard components in accordance with the design specifications. Such configuration can also bring benefits in other applications due to the possibility of charging several devices simultaneously.

Section 2 analyses the SEPIC and estimates the number of interleaved cells. Section 3 addresses the topology configuration and its control strategies for different charging modes. Section 4 is devoted to the description of the flyback regenerative snubber implemented to reduce voltage overshoots. The final converter prototype layout is presented in Section 5, followed by the experimental verification in Section 6. Finally, the conclusions are drawn in Section 7.

2. Analysis of the Modular SEPIC for PFC Application

The number of cells of a modular SEPIC has an impact on the input current quality parameters: power factor (PF) and total harmonic distortion (THD). Theoretical considerations addressed in this section will help to define the number of cells N for given values of quality parameters.

2.1. SEPIC Cell Model

The isolated version of the SEPIC topology in Figure 2a features a transformer instead of the second inductor to provide required voltage conversion ratio, along with galvanic isolation. Our assumptions in the analysis were as follows:

• All the elements of the SEPIC are lossless;
• Capacitors C_i and C_o are large enough to neglect the voltage ripple across them;
• PWM switching period T is significantly shorter than the fundamental input voltage period Θ (T << Θ); therefore, the input voltage u_in during the switching period has approximately constant value.

SEPICs operating in DCM can be represented by three equivalent circuits, as shown in Figure 2b–d. When the transistor S₁ is turned on during the first interval (Figure 2b), the cell input current i_cell rises from zero value to maximum value I_{cell_max} as follows:

$$i_{cell}(t)=\frac{U_{in}}{L_1}t,0<t\le \gamma T$$

(1)

where U_in is the input voltage value, L₁ is the inductance value of the input inductor (Figure 2).

During the second interval, the cell input current declines to zero (Figure 2c):

$$i_{cell}(t)=I_{cell\_\max }-\frac{U_b}{n\cdot L_1}(t-\gamma T),\gamma T<t\le T-t_0$$

(2)

where U_b is the output battery voltage, t₀ is the duration of the third interval (DCM).

During the third interval (Figure 2d), the cell input current is zero, i_cell = 0. In the practical circuits, this mode is typically accompanied with oscillations that occur due to the presence of parasitic circuit components.

Two SEPIC cells connected in parallel and operating with a 180° phase shift can provide continuous input current i_in, since in this case, it will be formed by the sum of currents in the two cells i_cell1 and i_cell2 (see Figure 3a). However, increased duration of DCM results in a more distorted input current [32]; therefore, it has to be minimised and the converter should preferably operate close to the boundary conduction mode (BCM).

According to Equation (2), during the second interval, the current declines with a constant slope, which is determined by the output voltage U_b. Therefore, the third interval with zero input current has a varying interval of t₀, which is inversely proportional to the input voltage U_in. Assuming the constant pulse width γ·T [32], the optimal operating mode can be achieved with BCM provided at the maximum input voltage U_{in_max} and DCM at lower U_in values, as depicted in Figure 3a.

For a sinusoidal grid voltage with a period Θ, u_in = U_{in_max} sin(2 πt/Θ), the grid current generated with one SEPIC cell operating with a switching period T may be represented based on piecewise linear functions, which are characterised by interval durations and current slopes (see Figure 3b).

The current slope k_r on the first interval when the current increases is

$$k_r=\frac{U_{in\_\max }\sin (2\pi t/\Theta )}{L_1}$$

(3)

The peak current I_m during the first interval is calculated according to Equation (1), where t = γ·T.

During the second interval, current decreases with the constant slope k_f, which is determined by the peak current value I_m. To obtain maximum PF, the value of k_f is chosen for providing BCM (t₀ = 0) at the points 2 πt/Θ = π/2 + πm, where m is an integer. However, in the practical converter, minimal zero current duration t_{0_min} should be defined to avoid entering continuous conduction mode (CCM).

The current at the point φ = 2 πt/Θ = π/2 of the grid current is

$$i_{cell}\left(\pi /2\right)={\left\{\begin{array}{l}{k}_r\cdot t^{\prime },0\le t^{\prime }<\gamma T;\\ \frac{I_m(T-t_{0\_\min })}{T-t_{0\_\min }-\gamma T}-k_f{t}^{\prime },\gamma T\le t^{\prime }<T-t_{0\_\min };\\ 0,T-t_{0\_\min }\le t^{\prime }<T,\end{array}\right.}_{}$$

(4)

where t^′ is relative time since the beginning of the switching period, I_m is the peak cell current during the first interval.

Hence, the current slope k_f on the second interval is k_f = I_m/(T − t_{0_min} − γT). For the other intervals, the input current slope results in a different t₀ duration:

$$t_0=T-\gamma T\mp (T-\gamma T-t_{0\_\min })\sin (2\pi t/\Theta ){,}_{}$$

(5)

where the sign “−” corresponds to a positive sine wave and “+” to the negative one.

According to (4) and (5), the cell current can be estimated for an arbitrary value of the input current phase φ:

$$i_{cell}\left(\phi \right)={\left\{\begin{array}{l}{k}_r{t}^{\prime },0\le t^{\prime }<\gamma T;\\ I_m\sin (2\pi t/\Theta )\mp \frac{I_m}{T-t_{0\_\min }-\gamma T}(t^{\prime }-\gamma T),\gamma T\le t^{\prime }<T-t_0;\\ 0,T-t_0\le t^{\prime }<T.\end{array}\right.}_{}$$

(6)

2.2. Estimation of the Number of SEPIC Cells Based on Current Quality Parameters

According to the analysis in the previous section, although sinusoidal input current can be achieved with two interleaved SEPIC cells, its quality can be compromised due to the presence of DCM intervals, particularly around zero crossings of the grid voltage. Increasing the number of interleaved cells can solve this issue, while keeping the constant pulse width γ·T. Another advantage lies in the reduction of current stresses of the individual cells, which enables distributed power dissipation and design using more compact components.

The total input current i_Σ(t) for a predefined number of cells N is estimated as:

$$i_{\Sigma }(t)={{\displaystyle \sum _{k=0}^{N-1}{i}_{cell}\left(t+\frac{kT}{N}\right)}}_{}$$

(7)

After defining the current of each cell with Equation (6) and substituting that in Equation (7), it is possible to calculate the RMS current value I_ΣRMS and the first harmonic value I_Σ(1) to estimate PF and THD values:

$$PF=\frac{I_{\Sigma (1)}}{I_{\Sigma RMS}}\cos ({\phi }_{(1)})$$

(8)

where φ₍₁₎ is the phase shift between the first harmonics of the grid voltage and current.

$$THD=\frac{\sqrt{I_{\Sigma RMS}{}^2-I_{\Sigma (1)}{}^2}}{I_{\Sigma RMS}}\times 100\%$$

(9)

As was mentioned, the maximum PF and minimum THD values are achieved when t₀ = 0; therefore, the modular converter mostly operates close to this mode. Figure 4 shows PF and THD for the BCM mode with t₀ = 0 with the given cell number N.

As was observed, PF and THD values improve with the increased duty cycle γ until a certain critical value γ_cr > 0.5, for instance, if N = 4, γ_cr ≈ 0.77. However, due to high voltage stress across the main transistor U_{T1_max}, the duty cycle range should be limited within γ ϵ [0, 0.5]. The steady state voltage stress across the main MOSFET is calculated as follows:

$$U_{VT\_\max }=\frac{U_{in\_\max }}{1-\gamma }$$

(10)

The duty cycle range γ ϵ (0.5, 1] marked with the red area in Figure 1 is avoided. Among the allowed duty cycle γ range, the subrange with PF > 0.99 is selected from the SEPIC regulating characteristics:

$$U_{out}=\frac{\gamma \cdot U_{in}}{1-\gamma }$$

(11)

The cell number N used for battery charging in the predefined voltage range U_b = 17.5–29.4 V can be determined according to

Table 1. Duty cycle range for battery charging in the predefined range U_b = 17.5–29.4 V.

Cell Number, N	Range of γ with PF > 0.99	Voltage Range, V
2	0.41–0.5	17.5–25.1
3	0.28–0.5	17.5–45.0
4	0.22–0.5	17.5–62.0

.

As follows, the charger may consist of only three cells, N = 3. However, in order to improve redundancy, ensure the possible range of regulation and counter various manufacturing tolerances that may impact the conversion factor, the number of cells chosen for the current design is 4. With the cell number N = 4, the charger PF exceeds 0.99 for the wider range of γ. It is possible to estimate the resulting average PF during the whole charging process after analysing the charging control strategies.

3. Charger Configuration and Control Strategies

3.1. Charger Configuration

The charger developed for the considered wheelchair application should provide separate galvanically isolated output for charging each of the two installed batteries. In the configuration presented in Figure 5, the SEPIC cells have two secondary windings. The batteries are connected to one of the secondary windings of each SEPIC cell, which allows natural charge balancing when the initial state of the charge (SOC) of batteries is different. The arrangement provides for modular design with standard low-cost components and low-profile converter design. Potentially, such a configuration can be extended to provide charge to individual cells within a battery.

3.2. Constant Current and Constant Voltage Charging Modes

In the current work, the battery is charged with the standard constant current/constant voltage method (CC/CV). To ensure operation close to the BCM (t_{0_min} → 0) for both CC and CV modes, a special modulation method for the SEPIC cells is required.

In the CC mode, the cell current has a constant average value I_cell = I_CC and voltage increases gradually from U_{b_min} = 17.5 V to U_{b_max} = 29.4 V. With the constant RMS value of the grid voltage (U_in=const), the CC mode is accompanied with gradually increasing (together with U_b) RMS value of the grid current I_in from the minimal value I_{in_min} to the maximal value I_{in_max}:

$$I_{in\_\min }=\frac{I_{CC}\cdot U_{b\_\min }}{U_{in}\cdot {\eta }_{cell}}$$

(12)

$$I_{in\_\max }=\frac{I_{CC}\cdot U_{b\_\max }}{U_{in}\cdot {\eta }_{cell}}$$

(13)

where η_cell is the SEPIC cell efficiency.

Increased input current results in an increased duration of the first and second intervals (Figure 3b) estimated according to Equations (1) and (2), respectively. At the same time, increased battery voltage leads to a decreased duration of the second interval. Therefore, different operating modes are required to implement the battery charging function.

Initially, for the (low) battery voltage U_b1, the converter cell operates in BCM with t₀ = 0, its operation period is T₁, the pulse duration is γ₁·T₁, and the input current is I_in1. After a certain time, the battery voltage is increased by the value ΔU_b. Then the input current I_in2 is changed by the value ΔI_in:

$$I_{in2}=I_{in1}+\Delta I_{in}=I_{in1}+\frac{\Delta U_b}{U_{b1}}\cdot I_{in1}$$

(14)

And the pulse duration γ₂·T₂ is estimated according to Equation (1):

$${\gamma }_2\cdot T_2={\gamma }_1\cdot T_1+\frac{\Delta I_{in}}{I_{in1}}\cdot T_1$$

(15)

The DCM duration (1 − γ₂) T₂, on the one hand, is increased together with the pulse duration γ₂·T₂; on the other hand, it is decreased with U_b. The equation for the estimation of DCM duration (1 − γ₂) T₂ is:

$$I_{in2}-\frac{U_{b2}}{L_1}(1-{\gamma }_2)\cdot T_2=0$$

(16)

After substitution of the current I_in2 and the voltage U_b2, we obtain

$$(1-{\gamma }_2)T_2=\frac{L_1{I}_{in1}}{U_{b1}}$$

(17)

which indicates the permanent duration of the DCM, i.e., (1 – γ₂)·T₂ = (1 – γ₁)·T₁. Therefore, for the CC mode, pulse frequency modulation (PFM) with constant off-time is provided, as depicted in Figure 6a.

In the CV mode, the battery voltage is constant, U_b = U_CV, and the current i_b is exponentially reduced:

$$i_b(t^{\prime })=I_{cc}{e}^{-\frac{t^{\prime }}{\tau }}$$

(18)

where t^′ is time from the beginning of the CV mode, and τ is the decay rate.

During the CV charging mode, the converter operates in BCM with PFM at the constant duty cycle, γ = const, as shown in Figure 6b. The PFM frequency is inversely proportional to the battery current i_b. The typical practice is to finish the charging process when the current in the CV mode reduces to 0.05 C [33]. For the nominal charging rate of 0.5 C, it is required to change the switching frequency in the range of 1:10 to keep the SEPIC in the BCM. Since this range is difficult to implement in the practical converter, in the designed system, it is limited by a predefined value of f_max. If the frequency f reaches the maximum value f_max, the cell starts to operate in DCM with PWM and constant frequency f_max, as depicted in Figure 6c.

In the PWM mode, the battery current i_b depends on the duty cycle γ as follows:

$$i_b=k_b\cdot {\gamma }^2$$

(19)

where k_b is a constant coefficient.

As it follows from Equation (19), the current regulation in the range 10%–100% of I_CC can be achieved with the duty cycle regulation of 1:3.1. Hence, during the whole charging process:

-

In the CC mode, the PFM modulation with battery current stabilisation and BCM detection is used;

-

In the CV mode with BCM, the PFM with battery voltage stabilisation is used;

-

In the CV mode with DCM, the PWM with battery voltage stabilisation is used.

3.3. Boundary Conduction Mode Control

The described control strategies require an effective and preferably simple method of the BCM detection. Figure 7 depicts generalised operating waveforms during one fundamental half-period of the rectified grid voltage u_in. The DCM duration t_0(k+2) should have its minimum value at the voltage maximum U_{in_max}. Therefore, the converter operating parameters should be chosen such that BCM is achieved at this point.

DCM may be easily detected using the transformer secondary voltage u_s (Figure 7). As compared with the battery voltage U_b, the rectangular voltage pulses can be obtained (see Figure 7c). The high-level comparator signal corresponds to the second interval when the output diode is conducting. The low-level corresponds to the sum of the first interval (when the input transistor is switched on) and the third interval (DCM). Since the duration of the first interval is known and equals to the constant value γ·T during the fundamental half period Θ/2 of rectified voltage, the DCM interval t₀ can be defined by subtracting γ·T from the duration of the low-level comparator voltage.

To minimise the converter dimensions and cost, the control of the BCM mode can be realised based on the signal from a synchronous rectifier driver DA₁ at the output of the SEPIC cell, as shown in Figure 8.

The synchronous transistor control signal generated by the driver DA₁ is used for DCM detection using “D” input of a trigger. Simultaneously, the trigger input “C” gets the signal from Ch 1 of the MCU PWM unit that is synchronised with Ch 2, which controls the input transistor S₁ according to the principle shown in Figure 9. Due to the configurable pulse width of Ch 1 PWM signal u_ch1, a predefined DCM duration Δγ·T can be achieved. Otherwise, a low-level interrupt signal is generated and MCU increases the period of PWM from T to T + ΔT value.

The described method shifts all the high frequency control to external ICs and allows the use of the MCU resources only for the control of the battery charging process. Thus, within one fundamental period, the charger control is provided with PWM, while throughout the whole charging process (Figure 6), a more sophisticated control is used. A generalised realisation principle of CC and CV modes during the charging process is presented in Figure 10. As shown, the parameter recalculation is performed at the points with maximum rectified voltage by generating signal u_INT. These parameters are then implemented at the beginning of the next grid half-period.

3.4. Calculation of Average Power Factor of the Battery Charger

During the battery charging, the duty cycle γ is increased from the minimal γ_min to the maximum γ_max value. At the same time, the PF is also changed accordingly. As shown before, the chosen duty cycle range γ ϵ [0.22, 0.5] allows regulation of the battery voltage in a much wider range (17.5–62.0 V) than necessary for the case study system (17.5–29.4 V). This enables estimation and choice of the duty cycle range γ ϵ [γ_min, γ_max], which provides the maximum average PF. A relation between γ_min and γ_max from the battery voltage range U_{b_min} = 17.5 V, U_{b_max} = 29.4 V can be defined as:

$$U_{b\_\min }=U_{in}\frac{{\gamma }_{\min }}{1-{\gamma }_{\min }};U_{b\_\max }=U_{in}\frac{{\gamma }_{\max }}{1-{\gamma }_{\max }}$$

(20)

Expressing γ_max from Equation (20), we obtain:

$${\gamma }_{\max }=\frac{{\gamma }_{\min }}{{\gamma }_{\min }+k_U(1-{\gamma }_{\min })}$$

(21)

where k_u = U_{b_min}/U_{b_max}.

According to Equation (20) for γ_min = 0.22, γ_max = 0.321, and for γ_max = 0.5, γ_min = 0.373. Therefore, γ_min can vary in the range of [0.22, 0.373] and γ_max in the range of [0.321, 0.5].

Average power factor, PF_av can be calculated as follows:

$${\mathrm{PF}}_{\mathrm{av}}=\frac{1}{T_{\mathrm{charge}}}\frac{{\displaystyle \underset{0}{\overset{T_{\mathrm{charge}}}{\int }}\mathrm{PF}(\gamma (t))\cdot p(t)dt}}{{\displaystyle \underset{0}{\overset{T_{\mathrm{charge}}}{\int }}p(t)dt}}$$

(22)

where T_charge is the charging time, and p(t) is the instantaneous power used as a weighting factor.

Equation (22) describing the charging modes may be rewritten as:

$$\begin{array}{c}{\mathrm{PF}}_{av}=\frac{1}{T_{charge}{\displaystyle \underset{}{\overset{T_{charge}}{\int }}p(t)dt}}\left({\displaystyle \underset{0}{\overset{T_{CC}}{\int }}\mathrm{PF}(\gamma (t))\cdot I_{CC}\cdot u_b(t)dt}+\right.\\ \left.+{\displaystyle \underset{0}{\overset{T_{CV\_BCM}}{\int }}\mathrm{PF}({\gamma }_{\max })\cdot U_{b\_\max }\cdot i_b(t)dt}+{\displaystyle \underset{0}{\overset{T_{CV\_DCM}}{\int }}\mathrm{PF}(\gamma (t))\cdot U_{b\_\max }\cdot i_b(t)dt}\right)\end{array}$$

(23)

where T_CC, T_{CV_BCM}, T_{CV_DCM} are charging time intervals in CC, CV with BCM and CV with DCM modes, respectively, u_b, i_b are instantaneous battery voltage and current.

In CC mode battery, voltage is linearly changed with time:

$$u_b(t)=U_{b\_\min }+\frac{(U_{b\_\max }-U_{b\_\min })t}{T_{CC}}.$$

(24)

The battery current in the CV mode can be calculated by Equation (18). For Li-ion batteries, the typical CC mode duration can be more than one hour, whereas the total charging time is around three hours [34,35]. Therefore, the CC mode duration can be assumed as one third of the total charge time, T_CC = T_charge/3. The interrelation between durations of the CV mode with BCM and the total duration of the CV mode depends on the frequencies of the relation maximum f_max and the minimum f_min, k_f = f_min/f_max and the relation between the nominal I_CC and the minimal charging current I_min, k_i = I_min/I_CC. It can be estimated as follows:

$$T_{CV\_BCM}={\log }_{k_i}\left(k_f\right)\left(T_{CV\_DCM}\right)$$

(25)

After substitution of all relations in Equation (23), the average PF is calculated depending on the γ_min, which varies in the range [0.22, 0.373] for k_f = 1/4. The dependence PF = f(γ) is shown in

Table 2. Average estimated PF for different γ ranges.

γmin	γmax	PFav
0.22	0.321	0.992
0.25	0.359	0.993
0.30	0.419	0.994
0.373	0.5	0.996

. As observed, it is preferable to operate with γ_min = 0.373 when the PF is at its maximum value of 0.996.

4. Flyback Regenerative Snubber

Since the SEPIC transformer operation and design is similar to a flyback transformer, it is typically necessary to apply a snubber to eliminate voltage spikes caused by the transformer leakage inductance [36]. The standard solution is to suppress the spikes by an RCD snubber that dissipates the leakage inductance energy in the snubber resistor. On the other hand, higher efficiency can be obtained if the leakage energy is redirected to the converter input or output by using passive regenerative snubbers [37,38] or active ZVS or ZCS snubbers [39,40]. However, for the given four-cell SEPIC configuration, such solutions can be redundant and sub-optimal. Therefore, the proposed approach for the regeneration of leakage inductance energy is to collect it from all the cells to a common capacitor and then transfer to the output using an auxiliary flyback converter. The auxiliary function of the stored energy is to supply the converter control system.

A simplified schematic of the proposed modular SEPIC configuration with the flyback regenerative system is shown in Figure 11. Each cell features a low-power high-voltage diode D_cl placed near the transformer that transfers the leakage energy released after turn-off of the main MOSFET to capacitors C₂ and C₃. These capacitors are used as an input source for the auxiliary flyback converter that transfers the energy to the load. Additional circuit with the diode D_c provides energy for the control system from the AC grid when the charger is not operating.

The control system power supply consumes approximately constant power (around 1 W), while the regenerative flyback operates only if the capacitor C₂ voltage U_C2 is greater than the minimal value U_{C2_min}, U_C2 > U_{C2_min}. Minimal voltage U_{C2_min} must exceed the maximum output voltage reflected to the transformer primary winding U_{C2_min} > U_b/n to avoid consumption of the SEPIC cell primary energy by the regenerative system. Since with chosen γ ϵ [0.37, 0.5], the reflected output voltage would not exceed maximum input voltage, the regenerative flyback has to operate only when:

$$U_{C2\_\min }>U_{in\_\max }$$

(26)

If the condition (26) is not satisfied, the regenerative flyback stops its operation.

The capacitor C₂ is calculated as a filter, taking into account the double grid frequency f_g and the regenerative system power P_r:

$$C_2=\frac{P_r}{2f_g{U}_{in\_\max }^{}\Delta U_{C2}}$$

(27)

where ΔU_C2 is capacitor voltage ripple.

Capacitor C₁ is charged together with the capacitor C₂, and the voltage overshoots from leakage inductance appear on the voltage U_{C1_max}:

$$U_{C1\_\max }=U_{in\_\max }+\Delta U_{C2}$$

(28)

The capacitor C₁ energy is used to supply the control system. The value of C₁ should be chosen such that it would not discharge to a voltage less than U_{in_max}:

$$C_1=\frac{P_{cs}}{2f_{reg}\left[{(U_{in\_\max }^{}+\Delta U_{C2})}^2-U_{in\_\max }^2\right]}$$

(29)

where P_cs is the power consumed by the control system, and f_reg is the converter operating frequency.

Capacitor C₃ is placed close to the SEPIC transformers to limit the voltage overshoots caused by the leakage inductance. Therefore, its capacitance is determined by the admissible voltage level at the converter transistor S₁. Assuming that the maximum voltage overshoot is ΔU_T1, the C₃ value is:

$$C_3=\frac{L_k{I}_{pr\_\max }^2}{\left[{(U_{b\_\max }/n+\Delta U_{VT})}^2-U_{out\_\max }^2/n^2\right]}$$

(30)

where L_k is the leakage inductance, U_{b_max} is the maximum battery voltage, I_{pr_max} is the transformer primary winding peak current, n is the transformer ratio, U_max is the maximum output voltage.

The other elements of the regenerative system are selected according to general rules. The implemented regenerative system shown in Figure 12a is based on a typical low-power flyback topology with an intelligent device TinySwitch-4 [41].

According to the design, the regenerative flyback has to operate only when the voltage level at the capacitor C₂ exceeds the value U_{C2_min}, which is defined with the resistor R₂ = 13 MΩ to set U_{C2_min} = 325 V [41].

The generalised operation principle of the regenerative flyback is illustrated in Figure 12b. As shown, the leakage inductance energy is mostly generated when the rectified input voltage is close to the maximum value. In this case, the capacitor C₂ voltage is increased, which activates the regenerative flyback and it starts to operate continuously with maximum power (mode 1). When the input voltage reaches an intermediate value, the regenerative system operates in a burst mode (mode 2). During the low input voltage, all the energy is consumed by the control system and the regenerative flyback operation is stopped (mode 3).

For the experimentally measured value of the transformer leakage inductance L_k = 20 μH, the regenerative power P_r of the flyback is calculated as follows:

$$P_r=N\frac{L_k\cdot I_{pr\_\max }^2}{2}{f}_{\min }=9(\mathrm{W})$$

(31)

where N = 4 is the SEPIC cell number, f_min = 30 kHz is the minimum operation frequency of the SEPIC cell, I_{pr_max} = 2.7 A is the maximum cell current.

The regenerative flyback component values chosen for the total power P_r = 9 W at the maximum output voltage U_max = 30 V are shown in

Table 3. Main components of the regenerative flyback snubber.

Component	Symbol	Value/Type
Capacitors	C1	400 nF, 750 V
	C2	7 μF, 750 V
	C3	3 nF, 750 V
	C5	100 nF, 25 V
	C6, C7	220 μF, 35 V
Voltage reg. resistor	R2	13 MOhm, 0.25 W
Current sense resistors	R3, R4	6.8 Ohm, 1 W
Output diodes	D6, D7	2 A, 100 V, SR2100
Flyback IC	DA2	TNY280
Optocouplers	PS1, PS2	PC817
Isolation transformer	TV	POL15020

.

5. Converter Design and Layout

The modular SEPIC charger was designed for f_min = 30 kHz, f_max = 120 kHz, and cell power P_cell = 100 W [32]. According to the design specifications, the dimensions of the battery charger printed circuit board (PCB) are limited to 230 × 145 mm. The maximum height of the elements is varied from 25 to 35 mm. The final placement of the elements in the given volume is depicted in Figure 13. The largest components (input inductors L₁, transformers TR, output capacitors C_O, regenerative flyback transformer TV) are placed in the middle or around the edges of the PCB. As a result, the 4-cell structure of the charger was implemented without exceeding the required application limits. The types and dimensions of the important components are listed in

Table 4. SEPIC cell component parameters.

Component	Symbol	Value	Dimensions, mm
DO5022P-154 MLD	L1	900 μH (6 in series)	6 × (15.2 × 18.5 × 0.28)
C3M0280090D	S1	900 V, 280 mΩ
CBB21	Ci	1 μF, 400 V	21.8 × 10.7 × 17
Isolation transformer	TR	520 μH, 1:10	35.2 × 35.2 × 25
IPP126N10N3	S2	100 V, 12.3 mΩ
Output capacitor	Co	6.8 mF, 35 V	D = 18, h = 40

.

6. Experimental Results

This section is devoted to the experimental verification of the developed modular SEPIC-based charger and its components. The following functions and operating characteristics are addressed in detail:

• BCM of input current provided by logic circuits and MCU interrupt generation;
• Operation of regenerative flyback snubber;
• Verification of voltage and current stresses on main components: primary MOSFETs, transformers and rectifier transistors;
• Validation of PF, THD and efficiency during battery charging in CC and CV modes.

6.1. Verification of Operation in BCM

For the case study charger, the BCM and DCM are the main operating modes, therefore, t₀ duration should be stable and easily configurable. As described in the previous section, the synchronous rectifier gating signal, except its direct function of reducing losses, is also used to control the DCM duration. As Figure 14 shows, the synchronous rectifier on-time increases together with the input voltage. The DCM detection is clearly demonstrated in Figure 15a,b, when the feedback is open and the microcontroller does not respond to the interrupt signal.

In the proposed control method, the interrupt signal u_INT appears when the duration of the zero-current interval t₀ is less than that predefined with the duty cycle value of u_ch1, see Figure 9 and Figure 15b. Since the DCM duration decreases as the input voltage u_in rises, the interrupt signal u_INT is symmetrically positioned relative to the amplitude value of the voltage, as shown in Figure 15a. The falling edge of the interrupt signal u_INT appears when the synchronous rectifier signal u_DRV is high at the rising edge of the PWM signal u_ch1 (see Figure 15b). When the interrupt is activated, the DCM duration is regulated only during one period of PWM, which prevents the converter from entering the CCM.

6.2. Verification of Regenerative Flyback Snubber

The operating waveforms of the implemented flyback snubber are presented in Figure 16. Since the filter capacitor C₂ was chosen taking into account the grid frequency, it allowed to minimise the input voltage and output current ripple of the flyback, as shown in Figure 16a. The current value is defined by the optocoupler forward voltage that is approximately U_F = 1 V.

6.3. General Switching Waveforms

The experimental waveforms presenting the formation of continuous grid current are presented in Figure 17a. As shown, despite DCM, the resulting input current ripple is significantly reduced thanks to interleaving of the four SEPIC cells. The effect of flyback snubber depicted in Figure 17b shows that the peak voltage overshoot across the main MOSFET was limited to approximately 600 V. The operational waveforms of the synchronous rectifier MOSFET and SEPIC transformer are demonstrated in Figure 18.

The voltage and charging current waveforms of equally charged batteries are depicted in Figure 19a, while the case with batteries at uneven charge is presented in Figure 19b. As shown, the battery with lower voltage (and SOC) is being supplied with larger current. In both cases, the double grid frequency ripple (100 Hz) can be clearly observed, which is the peculiarity of the SEPIC topology. This ripple can be reduced by applying larger output filter capacitors. Nevertheless, according to assumptions in previous studies, its negative impact on Li-ion batteries is incognisant [42].

6.4. Verification of PF, THD and Efficiency During the Charging Process

The batteries used in the current case study are based on LG 18650 MJ1 3500 mAh cells (7 series, 4 parallel). To estimate average weighted efficiency, THD and PF, it is necessary to analyse converter operation during different charging modes. Examples of the input current shapes during different operating modes are presented in Figure 20. The operating parameters estimated taking into account the charge profile of the case study batteries are shown in Figure 21.

According to the experiments, for γ ϵ [0.15; 0.5] that was used for charging, the grid current shape is very close to sinusoidal. The experimentally obtained THD and PF of the grid current for different γ are listed in

Table 5. Experimentally measured values of THD and PF.

γ	THD (ig)	PF	η, %	THD (Ug)
0.15	18.037	0.984	88.5	2.732
0.2	15.636	0.988	90.6	2.613
0.25	13.183	0.989	91.9	2.831
0.3	9.024	0.995	92.3	2.359
0.35	7.446	0.996	92.6	2.743
0.4	5.749	0.998	92.8	2.441
0.45	4.347	0.998	92.7	2.931
0.5	3.024	0.999	92.4	2.646

and the efficiency is shown in Figure 22.

7. Discussion and Conclusions

The paper has introduced a novel concept of a modular PFC charger based on the interleaved SEPIC topology. The converter has two isolated outputs for simultaneous charging of two batteries integrated into armrests of a power-assist wheelchair. Thanks to the interleaved structure, the prototype features a low-profile power stage design of only 35 mm in height that was realised with standard components. Moreover, the charger features galvanic isolation from input to output, as well as between the two outputs.

Design and operation aspects of the proposed charger and its subsystems are presented and verified experimentally. The features required for the application were realised with a simple control strategy that also achieved high input current quality with PF > 0.99 and THD < 3%. Thanks to the natural state of charge balancing and low height, the concept can be suitable for other applications that require simultaneous charging of different batteries or integration in a low-profile frame.