Bidirectional Quadratic Converter-Based PMBLDC Motor Drive for LEV Application

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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 [1][2][3][4][5]. e problem with these BDCs is that they have a large number of component requirements and high voltage stress on the switches. e 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].
e leakage inductance of the transformer causes high voltage stress on switches. Another isolated converter of fullbridge 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. e converter becomes more complex and difficult to control. Recently, a different type of nonisolated double boost-flyback converter has been proposed in [10,11]. e 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. e various nonisolated bidirectional DC-to-DC converters have been compared based on their performance [12,13]. e 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. e study on the bidirectional power flow using the VSI was done in [16][17][18]. e 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. erefore, the converter's size, weight, and cost are reduced as presented in [20,21]. e quadratic converters have high voltage gain, thereby having more efficiency than conventional ones [22][23][24]. 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 selfinductance of the PMBLDC motor by controlling the switches of VSI described in [25,26]. e back EMF boost is controlled by switches using a hall sensor. e signal from the hall sensor will give the information for the switches to be ON or OFF.
e electrical system of a powertrain configuration for an EV is shown in Figure 1. e magnitude and direction of the power are controlled by the BDQC. Controlled electrical power flows between the battery and the PMBLDC motor. e 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. e 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. e topology of the BDQ buck-boost converter is shown in Figure 2. Four switches with antiparallel diodes have been implemented in this BDC. e number of components can be reduced by using the back diodes of the MOSFETs [27]. A battery with a voltage of V i is connected on the low voltage side, and the DC link, or the motor side voltage, is V o . e inductor in series with the battery is L 1 , and the inductor in the middle is L 2 . e capacitor in the center is C 1 , while the DC link capacitor is C 2 .
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) e developed system's designing, simulation, and hardware validation are performed is study describes the BDQC operation in motoring and regenerative braking modes. e motoring mode of operation is discussed in Section 2, and the regenerative braking mode of operation is given in Section 3. e 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. e conclusion is made in Section 7.

Motoring Mode of Operation
e converter is designed to operate in the continuous inductor current mode (CICM) in steady-state as well as in low load conditions. e capacitors C 1 and C 2 are sufficient to maintain a steady voltage during one period of switching (T s ). In motoring mode operation, the switches S 1 and S 4 are OFF, switch S 3 is always turned ON to avoid switching losses, and switching of switch S 2 is controlled with PWM to execute the boosting operation. e following two modes can explain the converter's motoring (boost) mode operation.

Mode 1 (0, T on ).
e switches S 2 and S 3 are ON for time intervals 0 to DT S , and S 1 and S 4 are OFF. In this mode, the energy stored in the capacitor C 1 is transferred to the inductor L 2 , and the battery voltage V i charges the inductor L 1 , as shown in Figure 3.

Mode 2 (T on , T s ).
In this mode, S 3 is ON, and the rest three switches are OFF for time interval (1-D)T s . During this mode, the inductor L 2 transfers its stored energy to the DC link capacitor C 2 , and capacitor C 1 is being charged by inductor L 1 , as shown in Figure 4. e 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 L 1 and L 2 with C 1 at voltage V c1 yields the following equations: By eliminating V c1 from (1) and (2), the voltage gain in boost mode is obtained as where D � T on /T s is the duty ratio, and the quadratic nature of the converter can be inferred from (3).

Regenerative Braking Mode of Operation
e 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 S 1 and S 4 are controlled with PWM simultaneously. e switches S 2 and S 3 are OFF throughout this mode of operation. e braking (buck) mode can be described in two stages of operation. ese operations have been explained briefly in subsequent subsections.
Converter in 3 1 inductor, 1 transformer, 3 capacitors, 6 power switches Converter in 5 2 inductors, 1 transformer, 2 capacitors, 9 power switches Converter in 15 is feeding the regenerated energy to capacitor C 2 , as shown in Figure 7. e waveforms of inductor currents and voltages are shown in Figure 8. For these two modes of operation, the voltage across the capacitor C 1 is assumed as V c1 . e volt-sec balance principle across the inductors L 1 and L 2 gives the following equations: By eliminating V c1 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.

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.
e self-inductances of the PMBLDC motor are charged by shorting all the three phases together. e stored energy in these inductances is transferred to the converter's output capacitor (C 2 ) 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. e equivalent circuit of the two active phases of the VSI during regenerative braking is shown in Figure 10. e back EMF, armature current of the PMBLDC motor, and switching signal of VSI are shown in Figure 11

Converter Design
e converter design is done as per the boost and buck operations, as shown in Figure 5 and Figure 8. e designed converter is thus operated in the CICM, and the output  capacitor value is selected for minimum output voltage ripple. e converter is designed as per the designated parameters given in Table 2. e lithium nickel manganese cobalt (Li-NMC) battery is used for the experiment, whose parameters are given in Table 3. e inductor values are calculated to keep the converter in CICM operation even at low load conditions. e duty ratio (D) is calculated as 30% for an output voltage of 98 V with an input battery voltage of 48 V. e switching frequency (f s ) of the converter is 15 kHz. e minimal load for the PMBLDC motor constitutes the switching losses in VSI, copper, iron, and windage losses.
us, a minimal burden of 40 W is considered for calculations.

Journal of Electrical and Computer Engineering
From (11), the value of input inductor L 1 is calculated as 0.6 mH.
us, for CICM operation, a higher value of inductance, i.e., 1 mH, is selected in this work. e calculation for L 2 is done as follows: e calculated value of I L2 at minimum load is 0.56 A. us, the current ripple at boundary condition is 1.12 A.    Journal of Electrical and Computer Engineering e value of inductor L 2 is calculated using (15) as 1.2 mH. us, for CICM operation, a higher value of inductance, i.e., 1.5 mH, is selected in this work. e calculation for C 1 is as follows: Taking ∆V C1 � 10% of V C1 , the value of capacitor C 1 is calculated as 43 μF. e readily available capacitor of 47 μF is selected in this work.
For ∆V co � 2% of V co and f s � 15 kHz, the value of C 2 is calculated as 102 μF. e commercially available capacitor with a higher value of 220 μF is selected for this work. e calculated values of passive components in buck mode of operation are lower than that of boost mode operation. us, for the CICM operation of the converter, the boost mode values of passive components are selected for converter design. e voltage stresses on switches S 1 , S 2 , and S 4 are calculated as e 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 V i , V o , and I o , all parameters, i.e., L 1 , L 2 , C 1 , and C 2 can be calculated. e calculated parameters of the converter are given in Table 4.

Simulation Results
e bidirectional quadratic converter and VSI for the PMBLDC motor are simulated using the MATLAB/Simulink software package. e vehicular load is simulated by an inertial load of 0.1 kg·m 2 . e inertial load is connected to a PMBLDC motor having parameters, as given in Table 5. e system is simulated for 7 s with 0-5 s in motoring mode and 5-7 s in regenerative mode. e intended regenerative action is observed as per the simulation results shown in this manuscript. e 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 i L1 is 3.3 A, and current i L2 is 2.35 A, as shown in Figure 12. Figure 13 shows the steady-state output voltage (V o ), voltage (V c1 ) of capacitor C 1 , and battery voltage (V i ) in boost (motoring) mode operation. In boost mode, the steady-state output voltage V o is 98 V, and capacitor (C 1 ) voltage V c1 is 68.5 V with battery voltage V i � 48 V at 30% duty ratio, as shown in Figure 13. e battery voltage (V i ) 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 I L1 � −5 A and I L2 � −4 A, respectively. e 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 S 1 and S 2 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    Journal of Electrical and Computer Engineering braking mode and reaches 650 rpm in 7 s. e 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. e plot between the percentage energy recovery and inertia is shown in Figure 18.

Validation through Developed Prototype
An experimental setup is developed to test the proposed system and the converter prototype. e system employs a 1.1 HP PMBLDC motor coupled with an inertia of the flywheel (J � 0.1 kg m 2 ). e 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 V c1 , and output voltage in a steady state during boost mode operation of the converter at a 30% duty ratio. e steadystate inductor currents I L1 , I L2 , and switching PWM are shown in Figure 21 for boost mode operation. e 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.
e voltage stress on switches S 1 and S 2 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.   Journal of Electrical and Computer Engineering e negative currents are indicative of the regenerative mode operation. During RB, the steady-state inductor currents I L1 , I L2 , 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. e value of inductor currents during RB is matched with the simulation result. e 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. e efficiency curve during boost mode is shown in Figure 25.

Conclusion
is study designs, develops, and tests a BDQC for RB application in LEV. e power flow direction is controlled successfully by changing the working mode of the VSI and the BDQC. e 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. e bidirectional DC-DC quadratic converter operates at a maximum efficiency of 95.4% at a 30% duty ratio during boost mode operation. e 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
e data used to support the findings of this study are available from the author Mukesh Kumar upon request (email: mukeshk.rs.eee16@iitbhu.ac.in).

Conflicts of Interest
e authors declare that they have no conflicts of interest.