In this study, a bidirectional DC-to-DC quadratic converter (BDQC) is designed and developed for the motoring and regenerative braking (RB) of a permanent magnet brushless DC (PMBLDC) motor for a light electric vehicle (LEV) application. A PMBLDC motor is deemed more suitable for an electric vehicle (EV) due to its high efficiency and torque density. In the present work, a BDQC of 1 kW is designed to drive a 1.1 HP PMBLDC motor through a conventional voltage source inverter (VSI). An EV’s load cycle is emulated using a highly inertial load driven by a PMBLDC motor during the converter’s boost mode operation. RB is a crucial factor in extending the driving range of EVs by efficiently utilizing battery power. The converter operates in buck mode during RB, and simultaneously, the back electromotive force (EMF) of the PMBLDC machine is boosted by the self-inductance of the PMBLDC motor and the VSI. The braking technique used in this work eliminates the traditional drawback of RB in buck mode, as the power is extracted even when the motor’s back EMF is lower than the battery’s voltage. The control strategy has been implemented using the TMS320F28335 DSP controller for a developed converter prototype of the converter and driving the PMBLDC motor. The experimental results are compared to the simulation results, and a good alignment has been found.

1. Introduction

In recent years, electric vehicles (EVs) have drawn more attention as a substitute for conventional internal combustion engine (ICE) vehicles. With the advancement of batteries and motors, EVs have become an optimistic substitute for ICE vehicles. Due to its high efficiency and controllability, the PMBLDC motor is the most popular option in the drive train of low-to-medium power EVs. In the past decade, to improve the drivetrain’s efficiency, research on bidirectional DC-to-DC converters (BDCs) for EV applications has been extensively done [15]. The problem with these BDCs is that they have a large number of component requirements and high voltage stress on the switches. The leakage inductance of the transformer also causes high voltage stress on the switches. Different types of nonisolated and isolated bidirectional DC-DC converters have been introduced. A half-bridge type converter with more components, high voltage stress on switches, and a high-frequency transformer is used [6]. A full-bridge type converter with low voltage gain, a large number of power switches, and a transformer are required for isolation [7, 8]. The leakage inductance of the transformer causes high voltage stress on switches. Another isolated converter of full-bridge with flyback snubber has high voltage gain, but two transformers are used, which have leakage inductance. Leakage inductance causes high voltage stress on switches [9]. A clapping circuit is used to reduce the voltage and current stress. The converter becomes more complex and difficult to control. Recently, a different type of nonisolated double boost-flyback converter has been proposed in [10, 11]. The voltage gain is high in a double boost converter, but it requires two coupled inductors, and there is no common ground between input and output.

The various nonisolated bidirectional DC-to-DC converters have been compared based on their performance [12, 13]. The voltage gain of the converter is two times that of a conventional buck-boost converter. A modified nonisolated BDC for improved performance and efficiency is presented in [14, 15]. In this case, the efficiency is improved, but the voltage gain is the same as with the conventional buck-boost converter. The study on the bidirectional power flow using the VSI was done in [1618]. The converter requires a large number of power switches and imposes high voltage stress on the switches. A three-port DC-DC converter based on quadratic boost operation for stand-alone PV/battery systems is presented [19]. Recent research focuses on the modified converters because they are nonisolated (transformerless) topologies. Therefore, the converter’s size, weight, and cost are reduced as presented in [20, 21]. The quadratic converters have high voltage gain, thereby having more efficiency than conventional ones [2224]. Regenerative braking can be achieved by reversing power flow from the battery to the PMBLDC motor. It can be done even at low back EMF by boosting it using the self-inductance of the PMBLDC motor by controlling the switches of VSI described in [25, 26]. The back EMF boost is controlled by switches using a hall sensor. The signal from the hall sensor will give the information for the switches to be ON or OFF.

The electrical system of a powertrain configuration for an EV is shown in Figure 1. The magnitude and direction of the power are controlled by the BDQC. Controlled electrical power flows between the battery and the PMBLDC motor. The BDQC operates in two modes: motoring (boost) and regenerative braking (buck) mode. In the motoring mode, electrical power flows from the battery to the PMBLDC motor through VSI. Simultaneously, the kinetic energy of the PMBLDC motor is converted into electrical energy and fed back to the battery through the bidirectional VSI during regenerative braking. In turn, a converter with fewer components has lower losses and is needed to fulfill the requirements of high efficiency and significant voltage gain in EVs. A comparison of different bidirectional converters with different parameters is given in Table 1.

The presented nonisolated BDQC has a simple topology, control strategy, and a large voltage gain, which ensures wide voltage range operation when compared to conventional bidirectional buck or boost converters. The topology of the BDQ buck-boost converter is shown in Figure 2. Four switches with antiparallel diodes have been implemented in this BDC. The number of components can be reduced by using the back diodes of the MOSFETs [27]. A battery with a voltage of Vi is connected on the low voltage side, and the DC link, or the motor side voltage, is Vo. The inductor in series with the battery is L1, and the inductor in the middle is L2. The capacitor in the center is C1, while the DC link capacitor is C2.

In this work,(i)An efficient regenerative technique with the help of the self-inductance of the PMBLDC motor is presented(ii)An optimum switching technique is employed for operating the converter at reduced switching losses(iii)A back EMF boosting technique is used to extract power even at low motor speed(iv)The developed system’s designing, simulation, and hardware validation are performed

This study describes the BDQC operation in motoring and regenerative braking modes. The motoring mode of operation is discussed in Section 2, and the regenerative braking mode of operation is given in Section 3. The design parameters of the converter are presented in Section 4. Simulation results and validation results through a developed prototype are explained in Sections 5 and 6, respectively. The conclusion is made in Section 7.

2. Motoring Mode of Operation

The converter is designed to operate in the continuous inductor current mode (CICM) in steady-state as well as in low load conditions. The capacitors C1 and C2 are sufficient to maintain a steady voltage during one period of switching (Ts). In motoring mode operation, the switches S1 and S4 are OFF, switch S3 is always turned ON to avoid switching losses, and switching of switch S2 is controlled with PWM to execute the boosting operation. The following two modes can explain the converter’s motoring (boost) mode operation.

2.1. Mode 1 (0, Ton)

The switches S2 and S3 are ON for time intervals 0 to DTS, and S1 and S4 are OFF. In this mode, the energy stored in the capacitor C1 is transferred to the inductor L2, and the battery voltage Vi charges the inductor L1, as shown in Figure 3.

2.2. Mode 2 (Ton, Ts)

In this mode, S3 is ON, and the rest three switches are OFF for time interval (1-D)Ts. During this mode, the inductor L2 transfers its stored energy to the DC link capacitor C2, and capacitor C1 is being charged by inductor L1, as shown in Figure 4. The converter’s boost mode operating principle in steady-state is shown in Figure 5.

For these two modes of boost operation, the volt-sec balance principle across inductors L1 and L2 with C1 at voltage Vc1 yields the following equations:

By eliminating Vc1 from (1) and (2), the voltage gain in boost mode is obtained aswhere is the duty ratio, and the quadratic nature of the converter can be inferred from (3).

3. Regenerative Braking Mode of Operation

The converter’s braking (buck) mode is employed to perform RB, and this allows the mechanical energy stored in the inertial load and the rotor of the PMBLDC motor to be transferred back to the source. In the braking (buck) mode operation, the switches S1 and S4 are controlled with PWM simultaneously. The switches S2 and S3 are OFF throughout this mode of operation. The braking (buck) mode can be described in two stages of operation. These operations have been explained briefly in subsequent subsections.

3.1. Mode 1 (0, Ton)

S1 and S4 are ON for the time interval 0 to DTs in mode 1 of the buck operation. During this time interval, current in L1 and L2 increases, as inductors are being charged by capacitors C1 and C2, respectively, as shown in Figure 6.

3.2. Mode 2 (Ton, TS)

All the switches S1, S2, S3, and S4 are OFF for the time interval (1-D)Ts. The stored energy of inductor L1 is transferred to the battery at voltage Vi and energy of inductor L2 to capacitor C1. The load at voltage Vo is feeding the regenerated energy to capacitor C2, as shown in Figure 7.

The waveforms of inductor currents and voltages are shown in Figure 8. For these two modes of operation, the voltage across the capacitor C1 is assumed as Vc1.

The volt-sec balance principle across the inductors L1 and L2 gives the following equations:

By eliminating Vc1 from (4) and (5), the converter gain is obtained as a function of D as follows:

(6) shows that the converter buck mode voltage gain is quadratic in nature.

3.3. Working of VSI during Regenerative Braking

In the RB (buck) mode, energy flow from the PMBLDC motor to the battery is required. Only by controlling the converter, the mechanical energy cannot be transferred from the PMBLDC motor, and the motor needs to be operated in the second quadrant. Instead of direct rectification, a back EMF boosting technique is applied in this work during regenerative braking.

The self-inductances of the PMBLDC motor are charged by shorting all the three phases together. The stored energy in these inductances is transferred to the converter’s output capacitor (C2) by turning OFF all switches of VSI. A flow diagram showing the converter operation based on the driver’s on-road decision is shown in Figure 9. The equivalent circuit of the two active phases of the VSI during regenerative braking is shown in Figure 10. The back EMF, armature current of the PMBLDC motor, and switching signal of VSI are shown in Figure 11.

4. Converter Design

The converter design is done as per the boost and buck operations, as shown in Figure 5 and Figure 8. The designed converter is thus operated in the CICM, and the output capacitor value is selected for minimum output voltage ripple.

The converter is designed as per the designated parameters given in Table 2. The lithium nickel manganese cobalt (Li-NMC) battery is used for the experiment, whose parameters are given in Table 3. The inductor values are calculated to keep the converter in CICM operation even at low load conditions. The duty ratio (D) is calculated as 30% for an output voltage of 98 V with an input battery voltage of 48 V. The switching frequency (fs) of the converter is 15 kHz. The minimal load for the PMBLDC motor constitutes the switching losses in VSI, copper, iron, and windage losses. Thus, a minimal burden of 40 W is considered for calculations.

No-load power = 40 W.

From (11), the value of input inductor L1 is calculated as 0.6 mH. Thus, for CICM operation, a higher value of inductance, i.e., 1 mH, is selected in this work. The calculation for L2 is done as follows:

The calculated value of IL2 at minimum load is 0.56 A. Thus, the current ripple at boundary condition is 1.12 A.

The value of inductor L2 is calculated using (15) as 1.2 mH. Thus, for CICM operation, a higher value of inductance, i.e., 1.5 mH, is selected in this work. The calculation for C1 is as follows:

Taking ∆VC1 = 10% of VC1, the value of capacitor C1 is calculated as 43 μF. The readily available capacitor of 47 μF is selected in this work.

For ∆Vco = 2% of Vco and fs = 15 kHz, the value of C2 is calculated as 102 μF. The commercially available capacitor with a higher value of 220 μF is selected for this work. The calculated values of passive components in buck mode of operation are lower than that of boost mode operation. Thus, for the CICM operation of the converter, the boost mode values of passive components are selected for converter design.

The voltage stresses on switches S1, S2, and S4 are calculated as

The voltage stress on switches is low as compared to the converter in [1, 3].

With the help of equations (7)–(20) and the value of Vi, Vo, and Io, all parameters, i.e., L1, L2, C1, and C2 can be calculated. The calculated parameters of the converter are given in Table 4.

5. Simulation Results

The bidirectional quadratic converter and VSI for the PMBLDC motor are simulated using the MATLAB/Simulink software package. The vehicular load is simulated by an inertial load of 0.1 kg·m2. The inertial load is connected to a PMBLDC motor having parameters, as given in Table 5. The system is simulated for 7 s with 0–5 s in motoring mode and 5–7 s in regenerative mode. The intended regenerative action is observed as per the simulation results shown in this manuscript. The steady-state inductor currents with a gate driving signal in the converter’s boost mode operation are shown in Figure 12.

In boost mode, when the switch is ON, both inductor’s current increases, and when the switch is OFF, both inductor’s current decreases. In steady-state, the average value of current iL1 is 3.3 A, and current iL2 is 2.35 A, as shown in Figure 12. Figure 13 shows the steady-state output voltage (Vo), voltage (Vc1) of capacitor C1, and battery voltage (Vi) in boost (motoring) mode operation. In boost mode, the steady-state output voltage Vo is 98 V, and capacitor (C1) voltage Vc1 is 68.5 V with battery voltage Vi = 48 V at 30% duty ratio, as shown in Figure 13.

The battery voltage (Vi) and state of charge (SOC) are shown in Figure 14. It is depicted that during motoring (boost) mode, the battery SOC decreases, and a dip in battery voltage is observed during 0–5 s of simulation. At t = 5 s, regenerative braking is applied; then, the converter starts to operate in buck mode, and battery voltage and SOC increase. In buck (regenerative braking) mode, the steady-state inductor currents are IL1 = −5 A and IL2 = −4 A, respectively. The negative value of inductor currents means the current is flowing from load to source, as shown in Figure 15. Figure 16 shows the voltage stress on switches S1 and S2 during boost mode operation of the converter.

From time 0 s to time 5 s, the motor speed in boost mode reached 2000 rpm. At 5 s, regenerative braking is applied. As shown in Figure 17, the motor speed starts to decrease in braking mode and reaches 650 rpm in 7 s. The performance of the PMBLDC motor under different levels of inertia is simulated in MATLAB. Regenerative braking is applied at different inertial loads, and energy is fed back into the battery from the stored energy of the inertial load. The plot between the percentage energy recovery and inertia is shown in Figure 18.

6. Validation through Developed Prototype

An experimental setup is developed to test the proposed system and the converter prototype. The system employs a 1.1 HP PMBLDC motor coupled with an inertia of the flywheel (J = 0.1 kg m2). The TMS320F28335 DSP microcontroller controls the developed DC-DC converter and the VSI in both the motoring and regenerative modes. Figure 19 shows the setup for the experimental verification of the proposed system.

A PMBLDC motor coupled with a high inertia flywheel is used to emulate the vehicular load. To reduce the impulse torque condition and safety of the system, a pulley belt system is employed for mechanical coupling of the motor and inertial load. Figure 20 shows different voltages, battery voltage, capacitor voltage Vc1, and output voltage in a steady state during boost mode operation of the converter at a 30% duty ratio. The steady-state inductor currents IL1, IL2, and switching PWM are shown in Figure 21 for boost mode operation. The waveforms and the values are confirmative of those obtained, as shown in Figure 12. Both the inductors charge during the ON time of the switch and discharge during the OFF time. The voltage stress on switches S1 and S2 during the boost mode of the converter is shown in Figure 22. Figure 23 shows the transition of the system operation from motoring to the RB mode.

The negative currents are indicative of the regenerative mode operation. During RB, the steady-state inductor currents IL1, IL2, and switching PWM are presented, as shown in Figure 24, aligned with those obtained in the simulation. It indicates the converter operation in the buck mode and the successful energy transfer from the PMBLDC motor to the battery. The value of inductor currents during RB is matched with the simulation result.

The continuous charging of the output capacitor due to VSI performing the boosting operation keeps the DC link voltage almost constant during the initial period of the braking process. The efficiency curve during boost mode is shown in Figure 25.

7. Conclusion

This study designs, develops, and tests a BDQC for RB application in LEV. The power flow direction is controlled successfully by changing the working mode of the VSI and the BDQC. The inertial load’s mechanical energy is converted to electrical energy in the regenerative braking and fed back to the battery, as evident from the results. A control strategy is implemented to boost the back EMF of the PMBLDC motor by controlling the VSI and using the self-inductance of the motor. The bidirectional DC-DC quadratic converter operates at a maximum efficiency of 95.4% at a 30% duty ratio during boost mode operation. The implemented strategy and the system configuration proposed in this study have shown an economical and practical approach to eliminate the drawbacks of regenerative braking in the buck mode of BDC.

Data Availability

The data used to support the findings of this study are available from the author Mukesh Kumar upon request (email: [email protected]).

Conflicts of Interest

The authors declare that they have no conflicts of interest.


The authors thank the Electrical Machine and Drive Lab of the Department of Electrical Engineering at the Indian Institute of Technology (BHU), Varanasi, Uttar Pradesh, India, and the Department of Electrical and Computer Engineering, Hawassa University, Hawassa, Ethiopia.