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 Ci and Co 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 uin 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
icell rises from zero value to maximum value
Icell_max as follows:
where
Uin 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):
where
Ub 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,
icell = 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
iin, since in this case, it will be formed by the sum of currents in the two cells
icell1 and
icell2 (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
Ub. Therefore, the third interval with zero input current has a varying interval of
t0, which is inversely proportional to the input voltage
Uin. Assuming the constant pulse width
γ·
T [
32], the optimal operating mode can be achieved with BCM provided at the maximum input voltage
Uin_max and DCM at lower
Uin values, as depicted in
Figure 3a.
For a sinusoidal grid voltage with a period Θ,
uin =
Uin_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
kr on the first interval when the current increases is
The peak current Im during the first interval is calculated according to Equation (1), where t = γ·T.
During the second interval, current decreases with the constant slope kf, which is determined by the peak current value Im. To obtain maximum PF, the value of kf 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 t0_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
where
t′ is relative time since the beginning of the switching period,
Im is the peak cell current during the first interval.
Hence, the current slope
kf on the second interval is
kf =
Im/(
T −
t0_min −
γT). For the other intervals, the input current slope results in a different
t0 duration:
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:
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
iΣ(
t) for a predefined number of cells
N is estimated as:
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
IΣRMS and the first harmonic value
IΣ(1) to estimate PF and THD values:
where
φ(1) is the phase shift between the first harmonics of the grid voltage and current.
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
γcr > 0.5, for instance, if
N = 4,
γcr ≈ 0.77. However, due to high voltage stress across the main transistor
UT1_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:
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:
The cell number
N used for battery charging in the predefined voltage range
Ub = 17.5–29.4 V can be determined according to
Table 1.
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.
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
Dcl 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
Dc 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
UC2 is greater than the minimal value
UC2_min,
UC2 >
UC2_min. Minimal voltage
UC2_min must exceed the maximum output voltage reflected to the transformer primary winding
UC2_min >
Ub/
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:
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
fg and the regenerative system power
Pr:
where Δ
UC2 is capacitor voltage ripple.
Capacitor
C1 is charged together with the capacitor
C2, and the voltage overshoots from leakage inductance appear on the voltage
UC1_max:
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
Uin_max:
where
Pcs is the power consumed by the control system, and
freg 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 Δ
UT1, the
C3 value is:
where
Lk is the leakage inductance,
Ub_max is the maximum battery voltage,
Ipr_max is the transformer primary winding peak current,
n is the transformer ratio,
Umax 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 C
2 exceeds the value
UC2_min, which is defined with the resistor
R2 = 13 MΩ to set
UC2_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
Lk = 20 μH, the regenerative power
Pr of the flyback is calculated as follows:
where
N = 4 is the SEPIC cell number,
fmin = 30 kHz is the minimum operation frequency of the SEPIC cell,
Ipr_max = 2.7 A is the maximum cell current.
The regenerative flyback component values chosen for the total power
Pr = 9 W at the maximum output voltage
Umax = 30 V are shown in
Table 3.