A Novel Tri-Mode Bidirectional DC–DC Converter for Enhancing Regenerative Braking Efficiency and Speed Control in Electric Vehicles

Abstract

A bidirectional dc–dc converter is used to match the voltage levels between a low-voltage battery and a high-voltage traction machine in an electric vehicle. Using a conventional bidirectional converter with a standard voltage range, there is a limitation to the fine variation in the electric vehicle speed. During the regenerative braking process, when the speed decreases below a certain value, the generated voltage is insufficient to charge the battery, hence the regenerated energy cannot be stored. This paper proposes a novel bidirectional converter featuring three distinct operational modes: boost, buck and buck-boost. In the normal driving mode, it operates as a boost converter, providing double gain and accommodating a wide voltage range. During regenerative braking, the proposed converter switches to the buck or buck-boost mode based on the control algorithm. This adaptation is intended to either decrease the generated voltage to charge the battery effectively or to raise the voltage if it is insufficient for charging the battery. This configuration provides voltage stress of half the dc link voltage on the switches. This paper provides a comprehensive analysis of the proposed circuit, a detailed description of the control strategy with pulse generation logic for all switches and a mode transition algorithm. The simulation results of a circuit operating at a 1500 W power level are presented and compared with those of a standard bidirectional converter.

1. Introduction

The automobile industry is being revolutionized by electric vehicles (EVs), which are paving the way for a more sustainable future in light of recent technological developments and increased climate change awareness [1]. Over the course of their full lives, including production and use, EVs emit fewer emissions [2].

The popularity of EVs has accelerated technological development in the auto sector [3]. Subsidy plans based on the economic valuation of reduced greenhouse gas emissions have been suggested in order to encourage the purchase of BEVs [4]. Techniques for calculating a vehicle’s life cycle and its environmental effect have been demonstrated and are used to analyze whether an EV can compete in a particular market and to pinpoint the key factors that affect an EV’s viability [5]. The increasing use of EVs also makes it easier to incorporate renewable energy sources into the power grid. EVs can act as mobile energy storage units by being connected to the grid, facilitating energy transmission between the vehicle and the grid [6]. A more adaptable and sustainable energy system is facilitated by such integration, which also eases grid load [7].

In recent times, the EV range has been extended, and charging times have decreased due to more effective batteries and battery chargers [8,9]. The goal of continuing research in this field of EVs is to increase the capacity and longevity of energy storage systems. It also focuses on control strategies for battery management and wireless power transfer technologies [10,11]. Another research area in this field that holds great significance is efficient power conditioning systems. As EV technology advances, power electronics continue to evolve to improve efficiency, reliability and performance [12]. Research focuses on developing semiconductor materials with improved efficiency, advanced control algorithms and innovative power conversion topologies to enhance the overall efficiency and capabilities of electric vehicles [13,14,15,16,17,18]. Research and development are focused on determining and analyzing dependable and effective power converter topologies [19].

DC–DC converters effectively transfer power between various voltage levels inside the vehicle by stepping the voltage up or down as necessary [20]. Based on whether galvanic isolation is offered or not, dc–dc converters are mainly categorized into two types: isolated and non-isolated [21]. Unlike isolated converters, which incorporate transformers to provide isolation, non-isolated converters are without transformers and are commonly used in various applications which do not require isolation or can be achieved using other means. According to this perspective, non-isolated dc–dc power converters are used for EVs over their bulkier and more expensive isolated equivalents [22]. The most common configurations in the non-isolated category are buck, boost, buck-boost, CUK, SEPIC, ZETA, positive output super-lift Luo and ultra-lift Luo [23,24,25,26,27,28,29].

Electric motors in EVs are powered by batteries using voltage source inverters. Maintaining the battery rated voltage at a relatively low level is useful for optimizing vehicle performance because it uses fewer series-connected cells. A higher number of parallel connected cell strings increases the redundancy of the backup system. Furthermore, it also helps to address the issues brought on by charge imbalance [30]. A high-voltage DC bus is required since the rated voltage and the output power of the motor are interdependent. Most models of electric cars that have entered the market in recent years are 400 V based. For instance, the Tesla Model 3 is built for 350 V dc link voltage and the Audi e-tron for 396 V [31,32]. However, Porsche was the first carmaker to design an EV with an 800 V powertrain when it introduced Taycan [33].

Figure 1 shows the power flow and the charging of the EV. Since the voltage level of the battery, grid and dc-link are different, battery–grid compatibility and battery-motor compatibility ought to be maintained. This necessitates the use of directional dc–dc converters in the vehicle to manage bidirectional power flow between battery and grid and also between battery and motor. The bidirectional feature in DC–DC converters pertains to their ability to transfer power in both directions, enabling power flow and voltage conversion in either direction between the input and output.

Bidirectional converters play a vital role in managing power flow, voltage regulation and energy optimization. The battery, which has a lower voltage, provides power to the higher-voltage-rated motor/inverter/dc link during normal vehicle operation. Consequently, the dc–dc converter serves as a boost converter. The buck action of the converter comes into play during the regenerative braking of the vehicle. Here, the power flows from the traction motor, now behaving like a generator, to the battery [34]. Therefore, as seen in Figure 2, the bidirectional dc–dc converter will increase the voltage when power flows in one direction and decrease the voltage when power flows in the opposite direction. The arrows show the direction of power flow.

The contributions of this research work are given below.

Conventional bidirectional half-bridge dc–dc converters with buck and boost modes have their own limitations [35]. Firstly, the achieved voltage gain does not allow precise speed control of the vehicle during running. Secondly, in order for the regenerative energy to be stored in the battery during the low-speed regenerative braking phase, the voltage generated by the traction machine must be increased. The objectives of this research are as follows:

• To propose a novel tri-mode non-isolated bidirectional dc–dc converter with three modes of operation: buck, boost and buck-boost;
• To develop a novel control strategy with pulse generation logic for all the switches;
• To introduce a mode transition algorithm for smooth changeover between modes.

The proposed converter operates as a boost converter during normal vehicle operation mode and gives double gain with a wide voltage range as compared to conventional bidirectional converter. As a result, the driver can obtain precise speed variation with the accelerator pedal, providing improved speed control. During regenerative braking, depending on the magnitude of voltage generated by the traction machine, the converter either works in the buck mode or the buck-boost mode depending on the control algorithm. If the generated voltage is more than double the voltage required for charging the battery, it works as buck converter giving half the gain at a broad voltage range compared to conventional buck converter. Else, the proposed converter operates in the buck-boost mode initiating its buck action should the voltage produced by the traction machine is more than the voltage required for charging the battery. If the generated voltage is less than what is required for charging the battery, the mode initiates its boost action. This usually happens at lower braking speeds and the converter boosts the voltage sufficiently to feed the regenerative energy to the battery. So during regenerative braking, both the buck and buck-boost modes are applicable. As energy is extracted even during low-speed regenerative braking, the efficiency of regenerative braking is enhanced. This research makes a significant contribution to the field of electric vehicles by enhancing regenerative braking efficiency and speed control.

This paper is organized as follows: Section 2 gives a review of the related research works. Section 3 presents the circuit configuration of the proposed converter and its operation and analysis for all the operating modes. Section 4 provides the design and the control strategy adopted along with the pulse generation logic for all the modes. It also gives the mode transition algorithm. Results are presented in Section 5 and the conclusion is given in Section 6.

2. Related Research Works

The development of non-isolated bidirectional converter with high gain, improved efficiency, and high-power density is the current area of research emphasis. It is anticipated to be smaller and lighter. Meanwhile, gain and efficiency must be preserved over a broad working load range. R. J. Wai et al. [36] proposed a coupled inductor-based dc–dc bidirectional converter with three power switches to accomplish soft switching, voltage clamping, and a good voltage conversion ratio. Y P Hsieh et al. [37] designed a coupled inductor-based bidirectional dc–dc converter with a low component count in which two capacitors are charged in parallel and discharged in series with the linked inductor. A variable inductor in the bidirectional converter presented in [38] allows it to accommodate a variety of changes in load.

To produce high step up/down voltage gain, coupled inductors and voltage multiplier cells are occasionally combined [39]. Y. Zhang et al. introduced coupled inductor with adjustable turns ratio to give a wide voltage-gain range [40]. Recently, Malik et al. designed the bidirectional converter using coupled inductor to achieve all the mentioned features using lower number of components. The volume and cost of the said converter is significantly lower achieving a high efficiency [41].

Bidirectional dc–dc converters based on switching capacitors provide an effective means of moving energy back and forth between DC sources. Although they require careful consideration in both their design and control, they offer great response times and efficiency [42,43,44]. A switched-capacitor bidirectional dc–dc converter with a high step-up/step-down voltage gain is proposed for use in electric vehicles equipped with hybrid energy systems. The benefits of the converter include a common ground, a limited number of components, a simple circuit, and a wide voltage-gain range [45]. A bidirectional switched-capacitor/switched-quasi-Z-source hybrid dc–dc converter with a broad voltage gain range is presented by same researcher. The benefits of wide voltage gain range and lower voltage stress on the power switches are achieved [46]. Y Zhang et al. [47] introduced a novel bidirectional converter that employs a switched capacitor interleaved configuration, integrating the three-phase interleaved structure with switched capacitor cells. Sometimes, researchers have combined the switched inductor and switched capacitor techniques to achieve a broad voltage gain range along with reduced voltage stress on power switches [48].

To increase the voltage gain and efficiency, [49] introduced bidirectional converter that has two boost converters with four power switches a capacitor and two inductors. N Elsayad et al. [50] designed a new bidirectional switched-capacitor and quadratic-based dc–dc converter. A unique non isolated bidirectional dc–dc converter composed of a quadratic voltage cell, a switched-capacitor cell, and a zero-current ripple cell was developed [51]. T. Sojoudi et al. [52] proposed similar topology with fewer switches using Input–Output Feedback Linearization (IOFL) controller to obtain the same benefits as in [51]. Interleaved structures have the advantages of distribution of energy through multiple phases, enhancing overall performance, decrease in voltage stress across switches and current ripples [53,54]. V. Rathore et al. [55] proposed the topology structure which converts two split capacitor half-bridge circuits into series and parallel by symmetrically modulating a bidirectional two quadrant switch. In the same lines, R. R. De Melo et al. [56] provides an interleaved architecture which is a good option for high power, high current levels with minimum number of components and a higher efficiency over a broad load range.

A study carried out by Tine Konjedic et al. [57] examines a control strategy for synchronous rectification-based conventional non-isolated bidirectional dc–dc converters that uses the entire operating range to reliably achieve zero-voltage switching transitions. J Chen et al. [58] carried out research work and developed a multistage non-isolated bidirectional high-voltage conversion ratio converter. The converter uses just n+2 switches and is n times more efficient than a traditional buck/boost converter.

Switching losses in conventional DC–DC converters can be rather large, especially at high frequencies or high load currents. By guaranteeing that the switching transitions take place while the voltage or current across the switching devices is nearly zero, soft switching approaches work to lessen these losses and improve efficiency [59,60]. To decrease current ripple and switching loss and considerably improve converter efficiency and power density, a multiphase quasi-resonant zero-current switching (ZCS) switched capacitor bidirectional dc–dc converter construction is presented [61]. L Jiang et al. [62] presents the auxiliary circuit comprising of switches, diodes, coupled inductor and an independent inductor and applies it to half-bridge configuration. The proposed converter in [63] uses four switches alongside an inductor and capacitor and can turn on all switches with zero voltage and turn off some switches with zero current in continuous conduction mode in both forward and reverse modes. J.W. yang et al. [64] developed a high-efficiency bidirectional dc–dc converter that exhibits ZVS over the full range of loads and low circulating current. Once more, they introduced a converter that uses an active snubber made up of auxiliary switches, diodes, an inductor, and a capacitor to accomplish ZVS of main switches [65].

M Aamir et al. [66] proposed circuit with a voltage clamping network along with three active switches and a coupled inductor to obtain ZVS. In order to provide soft switching in all four switches in both buck and boost operation modes, S. Dusmez et al. [67] merged two identical zero-voltage transition (ZVT) cells with the traditional three level topology. This made it possible to operate with a higher switching frequency and achieve a better power density and improve efficiency. To provide ZVS, a reduced component bidirectional converter with an auxiliary resonant network is introduced [68]. N. Molavi et al. [69] introduced a bidirectional DC–DC converter with soft switching, high-voltage conversion ratio, and low-voltage stress across semiconductor devices. Additionally, zero-current switching performance totally resolves the body diode reverse recovery issue.

R.H. Ashique et al. [70] proposed converter with high gain in the continuous current mode by using energy storage element in between. Soft-switching conditions for both switches are also provided by maintaining a recycling current in the auxiliary circuit made up of a small inductor and two capacitors [71].

The literature review shows that bidirectional converter research is focused on improving efficiency, power density, and voltage conversion ratios. Various approaches, such as coupled inductors, switching capacitors and interleaved structures have been explored. These designs aim to reduce voltage stress across switches, minimize current ripple and achieve soft switching, ultimately improving efficiency and power density. Researchers have also combined multiple techniques, like coupled inductors and switching capacitors, to achieve a wide voltage gain range and efficient power transfer. Different control strategies, including synchronous rectification, have been employed to further enhance performance. The proposed novel converter configuration provides the wide voltage gain necessary and more recovery of regenerative braking energy.

3. Configuration and Operation

The circuit configuration of the proposed converter and its operation in all the three modes is described in this section.

3.1. Configuration of the Proposed Converter

The proposed non-isolated bidirectional converter, as shown in Figure 3, consists of six switches (S₁–S₆), an inductor (L), capacitances (C_H1 and C_H2) on the high-voltage side and capacitance (C_L) on the low-voltage side. As a modification of the conventional bidirectional buck and boost converter, it uses two sections of the same. Also two additional switches one in series and one in shunt are used. V_b is the battery voltage and V_d is the dc link voltage. V_b′ is the output voltage of the converter when it operates in the buck or buck-boost mode during regenerative braking. So this is the voltage available at the terminals of the battery for charging it during regenerative braking.

In normal vehicle operation (boost mode), switch S₁ is always ON and S₂ is OFF. Switches S₃ and S₄ are controlled using PWM techniques. During regenerative braking, when the converter operates in the buck mode, again switch S₁ is always ON and S₂ is OFF but switches S₅ and S₆ are controlled for their duty cycles. The buck-boost mode of regenerative braking utilizes switches S₂, S₅ and S₆ for PWM control. There are four operational intervals for all the modes of operation. The following assumptions are made for carrying out the analysis: (i) ON-state resistance of the MOSFETs and ESR of capacitors are not taken into account. (ii) The voltage across the capacitors C_H1, C_H2, and C_L is constant as they are sufficiently large capacitors C_H1, C_H2, and C_L are large enough, and the voltages across the capacitors can be treated as constant. (iii) The capacitors C_H1 and C_H2 have the same capacitance; hence, the voltage across each of them is V_d/2.

3.2. Operation and Analysis

This sub-section gives the detailed circuit operation for the boost, buck and buck-boost modes. Circuit analysis for every interval of the mode based on the theoretical waveforms with PWM switching is presented.

3.2.1. The Boost Mode

This mode corresponds to the normal running of the electric vehicle. i_d is the dc link current. V_L is the voltage across the inductor. The equivalent circuit is shown in Figure 4. V_s1 to V_s6 and i_s1 to i_s6 are the voltages and currents for the respective switches S₁ to S₆. R_d is the dc link resistance for boost equivalent circuit. i_CH1, i_CH2 andV_d1, V_d2 are the currents and voltages through the dc link capacitances C_H1 and C_H2. For this mode, switch S₁ is ON and S₂ is OFF. T_p is the switching time period and δ is the duty cycle factor for the MOSFETs. V_g1 to V_g6 are the gate pulses for the MOSFETs.

(a)

Interval-I (t₀–t₁): Switches S₅ and S₆ are OFF. Switches S₃ and S₄ are turned ON. As seen in Figure 5a, the current flows from the battery to the inductor L through switch S₁ and back to the battery through switches S₃ and S₄. L receives energy from the battery at voltage V_b and the current through it rises as seen in the theoretical waveforms depicted in Figure 6. C_H1 and C_H2 provide energy to the dc link to maintain voltage V_d.

Therefore, the voltage across L is given by Equation (1),

$${\mathrm{V}}_{\mathrm{L}}={\mathrm{V}}_{\mathrm{b}}$$

(1)

The current through L as shown by Equation (2) is,

$${\mathrm{i}}_{\mathrm{L}}\left(\mathrm{t}\right)={\mathrm{i}}_{\mathrm{L}}\left({\mathrm{t}}_0\right)+\frac{{\mathrm{V}}_{\mathrm{b}}}{\mathrm{L}}\left(\mathrm{t}-{\mathrm{t}}_0\right)$$

(2)

(b)

Interval-II (t₁–t₂): At t₁, Switch S₃ is turned OFF and S₅ turned ON. The current now flows from the battery and inductor to the dc link and capacitor C_H1 through the switches S₁, S₅ and S₄ as shown in Figure 5b.The inductor and battery provide energy to the dc link. C_H1 is also charged with this energy. Current flow through L decreases and its polarity is reversed as shown. C_H1 and C_H2 maintain the dc link voltage V_d. Switch S₅ is employed as synchronous rectifier.

Synchronous rectification is a technique in which the rectification diode of in the converter is replaced by active switch in order to improve efficiency. Diodes have inherent voltage drop and large reverse recovery loss leading to reduced efficiency. In synchronous rectification, the switches are turned on and off in synchronization with the input voltage, thereby actively directing the current flow in the circuit. This active control allows faster switching times and improves the dynamic performance of the converter [72]. The switch which performs the role of the diode is called the synchronous rectifier for that interval. Equations (3) and (4) represent the voltage and current equations for this interval.

$$\begin{gathered} {-\mathrm{V}}_{\mathrm{L}}=\frac{{\mathrm{V}}_{\mathrm{d}}}{2}-{\mathrm{V}}_{\mathrm{b}} \\ {\mathrm{V}}_{\mathrm{L}}={\mathrm{V}}_{\mathrm{b}}-\frac{{\mathrm{V}}_{\mathrm{d}}}{2} \end{gathered}$$

(3)

$${\mathrm{i}}_{\mathrm{L}}\left(\mathrm{t}\right)={\mathrm{i}}_{\mathrm{L}}\left({\mathrm{t}}_1\right)+\frac{1}{\mathrm{L}}\left({\mathrm{V}}_{\mathrm{b}}-\frac{{\mathrm{V}}_{\mathrm{d}}}{2}\right)\left(\mathrm{t}-{\mathrm{t}}_1\right)$$

(4)

(c)

Interval-III (t₂–t₃):Switch S₅ is turned OFF and S₃ is turned ON at instant t₂. Similar to interval I, this interval sees an increase in current flowing through L and the transfer of energy from the battery. Polarity across L changes once more. C_H1 and C_H2 discharge energy to the dc link as depicted in Figure 5a. So the inductor voltage and current are shown in Equations (5) and (6).

$${\mathrm{V}}_{\mathrm{L}}={\mathrm{V}}_{\mathrm{b}}$$

(5)

$${\mathrm{i}}_{\mathrm{L}}\left(\mathrm{t}\right)={\mathrm{i}}_{\mathrm{L}}\left({\mathrm{t}}_2\right)+\frac{{\mathrm{V}}_{\mathrm{b}}}{\mathrm{L}}\left(\mathrm{t}-{\mathrm{t}}_2\right)$$

(6)

(d)

Interval-IV (t₃–t₄): At instant t₃, the switch S₄ is turned OFF and S₆ is turned ON.As seen in Figure 5c, the current is now flowing from the battery and inductor to the dc link and capacitor C_H2 through the switches S₁, S₃, and S₆. The DC link is powered by the inductor and battery. This energy is also charged in C_H2. As shown, the polarity of L is inverted and its current flow decreases. DC link voltage V_d is maintained by C_H1 and C_H2. Switch S₆ performs the role of synchronous rectifier.

The voltage across L is given by Equation (7),

$${\mathrm{V}}_{\mathrm{L}}={\mathrm{V}}_{\mathrm{b}}-\frac{{\mathrm{V}}_{\mathrm{d}}}{2}$$

(7)

Also current through L as given by Equation (8) is,

$${\mathrm{i}}_{\mathrm{L}}\left(\mathrm{t}\right)={\mathrm{i}}_{\mathrm{L}}\left({\mathrm{t}}_3\right)+\frac{1}{\mathrm{L}}\left({\mathrm{V}}_{\mathrm{b}}-\frac{{\mathrm{V}}_{\mathrm{d}}}{2}\right)\left(\mathrm{t}-{\mathrm{t}}_3\right)$$

(8)

The average value of the voltage applied across an ideal inductor winding must be zero, according to the inductor volt-second balance principle [73].

Therefore, considering the four intervals Equation (9) is formulated,

$$\left[{\int }_0^{\mathsf{\delta }\frac{{\mathrm{T}}_{\mathrm{p}}}{2}}{\mathrm{V}}_{\mathrm{L}}\mathrm{d}\mathrm{t}\right]+\left[{\int }_0^{\left(1-\mathsf{\delta }\right)\frac{{\mathrm{T}}_{\mathrm{p}}}{2}}{\mathrm{V}}_{\mathrm{L}}\mathrm{d}\mathrm{t}\right]+\left[{\int }_0^{\mathsf{\delta }\frac{{\mathrm{T}}_{\mathrm{p}}}{2}}{\mathrm{V}}_{\mathrm{L}}\mathrm{d}\mathrm{t}\right]+\left[{\int }_0^{\left(1-\mathsf{\delta }\right)\frac{{\mathrm{T}}_{\mathrm{p}}}{2}}{\mathrm{V}}_{\mathrm{L}}\mathrm{d}\mathrm{t}\right]$$

(9)

Substituting Equations (1), (3), (5) and (7) in Equation (9),

Equation (10) gives the voltage gain of the proposed converter. As seen, it is double as compared to the conventional converter.

$$\frac{{\mathrm{V}}_{\mathrm{d}}}{{\mathrm{V}}_{\mathrm{b}}}=\frac{2}{1-\mathsf{\delta }}$$

(10)

3.2.2. The Buck Mode

This mode corresponds to the regenerative braking of the electric vehicle. The equivalent circuit and circuit operation for the buck mode are shown in Figure 7 and Figure 8, respectively. R_b is the output resistance as seen when the proposed converter operates in the buck mode. For this mode, switch S₁ is ON and S₂ is OFF. The theoretical waveforms with PWM switching for this mode are shown in Figure 9.

(a)

Interval-I (t₀–t₁):Both the switches S₃ and S₆ are OFF. S₄ and S₅ are switched ON at t₀. The current flows from the dc link capacitance C_H1 to the inductor L through switch S₅ and then to the output capacitance C_L/battery through switch S₁ and back to the dc link through switch S₄ as indicated in Figure 8a. L receives energy from the dc link and current through it rises. Also, C_L is charged by this energy. This energy comes from the regenerative braking of the vehicle.

Therefore, Equation (11) gives voltage across L,

$${\mathrm{V}}_{\mathrm{L}}=\frac{{\mathrm{V}}_{\mathrm{d}}}{2}-{\mathrm{V}}_{\mathrm{b}}^{\prime }$$

(11)

The current through L is given by Equation (12),

$${\mathrm{i}}_{\mathrm{L}}\left(\mathrm{t}\right)={\mathrm{i}}_{\mathrm{L}}\left({\mathrm{t}}_0\right)+\frac{1}{\mathrm{L}}\left(\frac{{\mathrm{V}}_{\mathrm{d}}}{2}-{\mathrm{V}}_{\mathrm{b}}^{\prime }\right)\left(\mathrm{t}-{\mathrm{t}}_0\right)$$

(12)

(b)

Interval-II (t₁–t₂): Now, switch S₅ is turned OFF and S₃ turned ON. Through switches S₁, S₄, and S₃, energy stored in the inductor L is transmitted to the battery. During this time, the current is allowed to freewheel through the synchronous rectifiers S₃ and S₄. As shown in Figure 8b, the polarity of L is reversed as the magnitude of current flow through it decreases. C_L also transfers its stored energy to the battery.

The voltage across L is given by Equation (13),

$$\begin{gathered} {-\mathrm{V}}_{\mathrm{L}}={\mathrm{V}}_{\mathrm{b}}^{\prime } \\ {\mathrm{V}}_{\mathrm{L}}=-{\mathrm{V}}_{\mathrm{b}}^{\prime } \end{gathered}$$

(13)

Equation (14) gives current through L,

$${\mathrm{i}}_{\mathrm{L}}\left(\mathrm{t}\right)={\mathrm{i}}_{\mathrm{L}}\left({\mathrm{t}}_1\right)-\frac{{\mathrm{V}}_{\mathrm{b}}^{\prime }}{\mathrm{L}}\left(\mathrm{t}-{\mathrm{t}}_1\right)$$

(14)

(c)

Interval-III (t₂–t₃):This interval starts with the turning OFF of switch S₄ and turning ON of switch S₆.As shown in Figure 8c, the current flows from the dc link capacitance C_H2 to the inductor L via switch S₃, to the output capacitance C_L/battery through switch S₁, and back to the dc link via switch S₆. The dc link provides energy to L, which causes a rise in current flow. This energy charges C_L as well. The vehicle’s regenerative braking is where this energy is generated. So the inductor voltage and current are as given by Equations (15) and (16).

$${\mathrm{V}}_{\mathrm{L}}=\frac{{\mathrm{V}}_{\mathrm{d}}}{2}-{\mathrm{V}}_{\mathrm{b}}^{\prime }$$

(15)

$${\mathrm{i}}_{\mathrm{L}}\left(\mathrm{t}\right)={\mathrm{i}}_{\mathrm{L}}\left({\mathrm{t}}_2\right)+\frac{1}{\mathrm{L}}\left(\frac{{\mathrm{V}}_{\mathrm{d}}}{2}-{\mathrm{V}}_{\mathrm{b}}^{\prime }\right)\left(\mathrm{t}-{\mathrm{t}}_2\right)$$

(16)

(d)

Interval-IV (t₃–t₄): Switch S₆ is turned OFF and S₄ turned ON. During this interval, the current freewheels through switches S₁, S₄, and S₃, to transfer the energy stored in the inductor to the battery. This is shown in Figure 8b. S₃ and S₄ operate as synchronous rectifiers. Current flow through L decreases and its polarity is inversed.

The inductor voltage is shown by Equation (17).

$${\mathrm{V}}_{\mathrm{L}}=-{\mathrm{V}}_{\mathrm{b}}^{\prime }$$

(17)

The current is given by Equation (18),

$${\mathrm{i}}_{\mathrm{L}}\left(\mathrm{t}\right)={\mathrm{i}}_{\mathrm{L}}\left({\mathrm{t}}_3\right)-\frac{{\mathrm{V}}_{\mathrm{b}}^{\prime }}{2}\left(\mathrm{t}-{\mathrm{t}}_3\right)$$

(18)

Applying the volt-second balance principle to the inductor taking into consideration the four intervals, Equation (19) is formulated [73].

$$\left[{\int }_0^{\mathsf{\delta }\frac{{\mathrm{T}}_{\mathrm{p}}}{2}}{\mathrm{V}}_{\mathrm{L}}\mathrm{d}\mathrm{t}\right]+\left[{\int }_0^{\left(1-\mathsf{\delta }\right)\frac{{\mathrm{T}}_{\mathrm{p}}}{2}}{\mathrm{V}}_{\mathrm{L}}\mathrm{d}\mathrm{t}\right]+\left[{\int }_0^{\mathsf{\delta }\frac{{\mathrm{T}}_{\mathrm{p}}}{2}}{\mathrm{V}}_{\mathrm{L}}\mathrm{d}\mathrm{t}\right]+\left[{\int }_0^{\left(1-\mathsf{\delta }\right)\frac{{\mathrm{T}}_{\mathrm{p}}}{2}}{\mathrm{V}}_{\mathrm{L}}\mathrm{d}\mathrm{t}\right]$$

(19)

Substituting Equations (11), (13), (15) and (17) in Equation (19),

Equation (20) gives the voltage gain of the proposed converter in the buck mode. It is half as compared to the conventional converter.

$$\frac{{\mathrm{V}}_{\mathrm{b}}^{\prime }}{{\mathrm{V}}_{\mathrm{d}}}=\frac{\mathsf{\delta }}{2}$$

(20)

3.2.3. The Buck-Boost Mode

This mode is used during the regenerative braking of the electric to buck or to boost the regenerated voltage. Figure 7 and Figure 10, respectively, depict the corresponding equivalent circuit and circuit operation for this mode. The theoretical waveforms are presented in Figure 11.

(a)

Interval-I (t₀–t₁):The switches S₁, S₃ and S₆ are OFF and S₂,S₄ and S₅ are turned ON. The current flows from the dc link capacitance C_H1 to the inductor L through switch S₅ and then back to the dc link through switch S₂ and S₄ as shown in Figure 10a. L is energized by the dc link, and the current via it increases. The inductor polarity is indicated as such. C_L releases the energy it has stored into the battery. The voltage across L is given by Equation (21).

$${\mathrm{V}}_{\mathrm{L}}=\frac{{\mathrm{V}}_{\mathrm{d}}}{2}$$

(21)

Current, as given by Equation (22) is

$${\mathrm{i}}_{\mathrm{L}}={\mathrm{i}}_{\mathrm{L}}\left({\mathrm{t}}_0\right)+\frac{1}{\mathrm{L}}\left(\frac{{\mathrm{V}}_{\mathrm{d}}}{2}\right)\left(\mathrm{t}-{\mathrm{t}}_0\right)$$

(22)

(b)

Interval-II (t₁–t₂):This interval starts with switches S₂ and S₅ being turned OFF. At the same time switches S₁ and S₃ are turned ON. The source that is the dc link is cut off by switch S₅ and the energy stored in the inductor during interval-I, charges the battery and the capacitor C_L. Inductor L experiences a drop in current and a polarity change. The current flow direction during this interval is shown in Figure 10b. S₃ and S₄performthe role of synchronous rectifiers.

The voltage across L is given by Equation (23),

$$\begin{gathered} {-\mathrm{V}}_{\mathrm{L}}={\mathrm{V}}_{\mathrm{b}}^{\prime } \\ {\mathrm{V}}_{\mathrm{L}}=-{\mathrm{V}}_{\mathrm{b}}^{\prime } \end{gathered}$$

(23)

Equation (24) gives current through L.

$${\mathrm{i}}_{\mathrm{L}}\left(\mathrm{t}\right)={\mathrm{i}}_{\mathrm{L}}\left({\mathrm{t}}_1\right)-\frac{{\mathrm{V}}_{\mathrm{b}}^{\prime }}{\mathrm{L}}\left(\mathrm{t}-{\mathrm{t}}_1\right)$$

(24)

(c)

Interval-III (t₂–t₃): Switches S₁ and S₄ are currently turned OFF. S₂ and S₆ switches are turned on. As depicted in Figure 10c, the current flows from the dc link capacitance C_H2 to the inductor L via switch S₃, and then it returns through switches S₂ and S₆ to the dc link. In the process, L stores energy from the dc link, as current through it increases. The inductor has the indicated polarity. The battery receives the energy that C_L held during the prior interval. So Equations (25) and (26) gives voltage and current through the inductor respectively.

$${\mathrm{V}}_{\mathrm{L}}=\frac{{\mathrm{V}}_{\mathrm{d}}}{2}$$

(25)

$${\mathrm{i}}_{\mathrm{L}}\left(\mathrm{t}\right)={\mathrm{i}}_{\mathrm{L}}\left({\mathrm{t}}_2\right)-\frac{{\mathrm{V}}_{\mathrm{d}}}{\mathrm{L}}\left(\mathrm{t}-{\mathrm{t}}_2\right)$$

(26)

(d)

Interval-IV (t₃–t₄):Switch S₂ and S₆ are turned OFF to start this interval. This is accompanied by the turn ON of switches S₁ and S₄. Figure 10b indicates this switching. This interval is similar to interval-II, and the battery and capacitor C_L are charged by the energy stored in the inductor.

The voltage across L is given by Equation (27) as,

$$\begin{gathered} {-\mathrm{V}}_{\mathrm{L}}={\mathrm{V}}_{\mathrm{b}}^{\prime } \\ {\mathrm{V}}_{\mathrm{L}}=-{\mathrm{V}}_{\mathrm{b}}^{\prime } \end{gathered}$$

(27)

The current through L is indicated by Equation (28),

$${\mathrm{i}}_{\mathrm{L}}\left(\mathrm{t}\right)={\mathrm{i}}_{\mathrm{L}}\left({\mathrm{t}}_3\right)-\frac{{\mathrm{V}}_{\mathrm{b}}^{\prime }}{\mathrm{L}}\left(\mathrm{t}-{\mathrm{t}}_3\right)$$

(28)

Utilizing the volt-second balancing concept to the inductor while taking the four intervals into account, Equation (29) is formulated [73],

$$\left[{\int }_0^{\mathsf{\delta }\frac{{\mathrm{T}}_{\mathrm{p}}}{2}}{\mathrm{V}}_{\mathrm{L}}\mathrm{d}\mathrm{t}\right]+\left[{\int }_0^{\left(1-\mathsf{\delta }\right)\frac{{\mathrm{T}}_{\mathrm{p}}}{2}}{\mathrm{V}}_{\mathrm{L}}\mathrm{d}\mathrm{t}\right]+\left[{\int }_0^{\mathsf{\delta }\frac{{\mathrm{T}}_{\mathrm{p}}}{2}}{\mathrm{V}}_{\mathrm{L}}\mathrm{d}\mathrm{t}\right]+\left[{\int }_0^{\left(1-\mathsf{\delta }\right)\frac{{\mathrm{T}}_{\mathrm{p}}}{2}}{\mathrm{V}}_{\mathrm{L}}\mathrm{d}\mathrm{t}\right]$$

(29)

Substituting Equations (21), (23), (25) and (27) in Equation (29),

Equation (30) gives the voltage gain of the proposed converter in the buck-boost mode. It is half as compared to the conventional buck-boost converter.

$$\frac{{\mathrm{V}}_{\mathrm{b}}^{\prime }}{{\mathrm{V}}_{\mathrm{d}}}=\frac{\mathsf{\delta }}{2(1-\mathsf{\delta })}$$

(30)

4. Design and Control Strategy

The circuit parameter design based on the specifications considered is provided in this section. Also the control strategy applied is explained. A mode transition algorithm to change the pulse pattern during mode switching is given.

4.1. Design of the Proposed Converter

The proposed converter is designed considering the specifications as listed in

Table 1. Design specifications for the proposed converter.

Design Specifications	Notation	Values
Power level	P	1500 W
DC link voltage (High side)	Vd	300 V
Battery voltage (Low side)	Vb	48 V (41–54.6 V)
Converter output voltage-buck and buck-boost mode (Low side)	Vb′	56 V (56–56.8 V)
Switching frequency	fs	100 kHz
Main inductor	L	110 µH
Low-side capacitor	CL	100 µF
High-side capacitors	CH1 and CH2	100 µF

. The power level corresponds to the power rating of the traction machine. The dc link voltage is the motor voltage if it is DC or it is the inverter input voltage if the motor is AC. This is the high-voltage side of the converter. The lithium-ion battery is rated for 48 V, with the voltage range mentioned in the bracket corresponding to the battery charge condition from discharged to fully charged condition. The voltage range 56–56.8 V is the voltage required for charging the battery. This should be the converter output voltage in the buck and buck-boost modes which corresponds to the regenerative braking.

The switching frequency is set to 100 kHz and the inductor and capacitor values are calculated for the given specifications [74]. The inductor value is selected optimally to take care of all the three modes.

Critical value of inductance is given by Equation (31),

$${\mathrm{L}}_{\mathrm{C}}=\frac{{\mathrm{V}}_{\mathrm{b}}({\mathrm{V}}_{\mathrm{d}}-{\mathrm{V}}_{\mathrm{b}})}{{∆\mathrm{I}}_{\mathrm{b}}·{\mathrm{f}}_{\mathrm{s}}·{\mathrm{V}}_{\mathrm{d}}}$$

(31)

ΔI_b is the ripple current of inductor and is considered to be 15% of the input current.

The calculated value of critical inductance is 86 µH. Since continuous conduction mode is considered, the selected value of inductance is higher than the critical value.

Similarly, critical value of capacitance as given by Equation (32) is,

$${\mathrm{C}}_{\mathrm{C}}=\frac{{∆\mathrm{I}}_{\mathrm{b}}}{8·{\mathrm{f}}_{\mathrm{s}}·{∆\mathrm{V}}_{\mathrm{o}}}$$

(32)

ΔV_o is the ripple value of output voltage and is assumed to be 0.1% of the output voltage. The critical value of capacitance is calculated as 26 µF. The selected value is higher than the critical value. The selected values are tabulated in Table 1.

4.2. Control Strategy

The closed loop controller and the pulse generation logic for all the three operating modes of the proposed converter are presented in this section.

4.2.1. Closed Loop Controller

The control strategy for the proposed bidirectional converter is shown in Figure 12. Depending on the current working mode, the converter’s input and output voltages are V_b or V_d and V_d or V_b′, respectively. The single accelerator/brake pedal decides the normal drive operation or the braking operation depending on whether the pedal is engaged or released.

During normal vehicle driving operation (boost mode), the reference voltage V_dref is varied depending upon the motor speed expected. V_dref is calculated by the reference voltage calculation block from speed command N_c based on the accelerator/brake pedal and the proportionality constant K. The output voltage V_d is sensed, conditioned and then compared with the reference voltage. Accordingly, the duty cycle is estimated by the PWM block and pulses are generated for the corresponding MOSFETs to attain the intended output voltage in order to attain the required speed. The motor energy control unit controls these actions.

Regenerative braking corresponds to the buck and buck-boost modes of the converter. The voltage generated by the traction machine during regenerative braking varies depending upon the speed of the machine at that instant. The generated voltage (dc link voltage) is now the input to the converter. If the generated voltage is greater than V_b′, the converter needs to lower the voltage to V_b′. As mentioned earlier, V_b′ is the voltage required to charge the battery. But if the generated voltage is less than V_b′, it has to boost it to give the required voltage V_b′ to charge the battery. From Equations (20) and (30), it is clear that the proposed converter has to work in the buck mode only if the generated voltage V_d is greater than 2V_b′ to reduce the voltage. Else it has to operate in the buck-boost mode to increase the voltage. V_b′_ref is kept constant.

The transfer functions derived from the converter modeling and motor modeling equations are used to design the proportional–integral (PI) controller. The Ziegler Nichols technique is used to tune the controller, and the values for Kp and Ki (proportional and integral constants) are determined as 58.55 × 10⁻³ and 0.718, respectively [75]. Due to the fact that the duty cycle is half that of a conventional converter, the gain block with 0.5 gain is introduced. The major switches (S₃ and S₄) executing the boost action must run for an additional amount of time during the boost mode that is equal to half the switching time period T_p/2 above the duty time. As a result, the constant block with T_p/2 is merely added to the pulse width modulation (PWM) block input only for the boost mode. It is shown with dotted block in Figure 12.

4.2.2. Pulse Generation Logic

After the PWM generator generates the duty cycle for the main switch S₄ in the boost mode the gate pulses for the other switches are based on the logic as shown in Figure 13a, in tune with the waveforms for the boost mode. The switch S₆ operates complementary to switch S₄. So the pulse to it is through a NOT gate from S₄. Pulse to S₃ is after a time delay of T_p/2 from S₄. Switch S₅ receives a pulse complementary to S₃.

Similarly for the buck mode, the logic for the gate pulses is shown in Figure 13b.The switch S₃ operates complementary to switch S₅. So the pulse to it is through a NOT gate from S₅. Pulse to S₆ is after a time delay of T_p/2 from S₅. Switch S₄ receives a pulse complementary to S₆. The logic for the buck-boost mode is shown in Figure 13c. The switch S₃ operates complementary to main switch S₅. As shown NOT gate is used. Switch S₆ and S₄ pulse logic is same as that for the buck mode. Switch S₂receivesa pulse only when either S₅ or S₆ is ON, hence it is through the OR gate. Switch S₁ receives a pulse complementary to S₂.

4.2.3. Mode Transition

When an EV is on a road, it is either driving or braking. The proposed converter has six modes transitions when switching from one operation to another.

Table 2. Converter mode transitions during EV operation.

Vehicle Operation	Outgoing Mode	Incoming Mode
Driving to regenerative braking	Boost	Buck
	Boost	Buck-boost
Regenerative braking to driving	Buck	Boost
	Buck-boost	Boost
Regenerative braking	Buck	Buck-boost
	Buck-boost	Buck

lists the mode transitions as per the control logic in Figure 12. The gate pulse pattern for the switches will alter in accordance with the incoming mode when the converter transitions between modes. This is referred as mode transition. In Figure 14, the mode transition algorithm is displayed.

The signal for mode transition is taken from the motor energy control unit based on the accelerator/brake pedal operation and control algorithm. Once the signal is received, the gate pulses to all the switches are blocked. The inductor current drops. After the inductor current reaches zero, the gate pulse pattern corresponding to the incoming mode comes into action. If the incoming mode is buck mode, then switch S₁ is activated first followed by switch S₅. All the other switches except switch S₂, will receive the pulses as per the logic shown in Figure 13b. Also for the boost mode, S₁ is operated first, followed by S₄. Switches S₃, S₅ and S₆ will receive pulses as per the logic shown in Figure 13a. Switch S₅ will be turned ON initially for the buck-boost mode. As per the logic in Figure 13c, all other switches will receivethe pulses.

The converter may enter the buck or buck-boost mode during regenerative braking, according to the voltage supplied by the traction machine. If the road is flat, the speed will drop as the braking advances, and the machine’s voltage output will decrease. Therefore, if the converter had selected the buck mode at the start of braking, there is a chance that it could now switch to the buck-boost mode. This turns into the transition from the buck to the buck-boost mode in regenerative braking. Another instance is when the vehicle is moving downwards when the converter was initially in the buck-boost mode at the beginning of regenerative braking. The voltage may rise as the vehicle accelerates at a faster rate, causing the converter to switch to buck mode. The buck-boost to buck mode transition is seen in this case.

5. Results and Discussion

MATLAB/Simulink software (MATLAB 22a, MathWorks, Natick, MA, USA) is used to simulate both the proposed bidirectional dc–dc converter and the conventional half-bridge configuration based bidirectional dc–dc converter [31]. The simulations are carried out to verify the proposed converter’s performance during the normal drive operation of the vehicle corresponding to the boost mode of operation of the converter. The regenerative braking of the vehicle which corresponds to the buck and buck-boost modes of operation of the converter is simulated. The converter model for simulation is built as per the specifications given in Table 1 in Section 4.1. The simulations are run for 5 s. The purpose of the simulations is to compare and analyze the performance of the proposed converter.

5.1. Boost Mode Output

The input to the converter in this mode is the battery voltage. The battery rated voltage is 48 V, but depending upon the State of charge (SOC) it will range from 41 V to 54.6 V for the lithium-ion battery which is considered for the simulation. The output of the converter is the dc link voltage, which is 300 V for full speed of the vehicle. The same is the voltage for the inverter/traction motor.

Figure 15a shows the input and output voltage waveforms. The input voltage, V_b is 48 V and the reference voltage, and V_dref in the closed loop is set for 300 V. So the output voltage V_d obtained is 300 V. The next simulation is carried out with V_dref set to 250 V and then after 2 s changed to 280 V. As can be seen in Figure 15b, the boost mode gave the required output of 250 V initially and 280 V after 2 s. The gate pulses for the switches S₃, S₄, S₅, and S₆ are shown in Figure 15c corresponding to the output voltage of 300 V. S₃ and S₄ being the main switches for the boost action, their gate pulses are directly based on the duty cycle factor, δ = 0.68; and as explained in Section 3.2.1 and shown in Figure 12, half the time period T_p/2 is added to it.

5.2. Buck Mode Output

The input to the converter in this mode is the dc link voltage. This is the voltage generated by the traction machine during regenerative braking. It will depend on the speed of the machine while regenerating. But for the battery to charge, it needs 56 to 56.8 V at its terminals. Considering 56 V as the output voltage of the buck mode V_b′, the reference voltage, V_b′_ref is set to 56 V.

For this mode, first the simulations are performed with the input voltage, V_d as 300 V and the reference voltage, V_b′_ref in the closed loop set to 56 V. So the output voltage V_b′ obtained is 56 V. This is seen in the waveforms in Figure 16a. Further simulation is carried out with input V_d kept at 120 V and after 2 s varied to 90 V from 2 s to 5 s. Consequently, the buck mode produced the necessary output of 56 V, as shown in Figure 16b. The gate pulses for the switches S₃, S₄, S₅, S₆ are shown in Figure 16c corresponding to the output voltage of 56 V with input voltage of 300 V. Since S₅ and S₆ are the primary switches for the buck action, the duty cycle factor, δ = 0.3734 directly determines the gate pulses for these switches.

5.3. Buck-Boost Mode Output

Similar to the buck mode, this mode also comes into action during regenerative braking. The dc link voltage/generated voltage is the input to the converter for this mode. This mode comes into action when the regenerated voltage V_d is less than or equal to twice the voltage required to charge the battery V_b′.

The first simulation is performed with input voltage of 90 V and after 2 s the voltage dropping from 90 V to 30 V within the next 3 s. As seen in Figure 17a, the buck-boost mode gave the required output of 56 V throughout. The buck action is seen till the input voltage varied from 90 V to 56 V and the boost action is noticed when the input voltage dropped below 56 V. The action changeover is seen at 3.7 s time in Figure 17a. The next simulation is with input voltage of 30 V rising to 90 V after 2 s within the next 3 s. The results are shown in Figure 17b and it is clear that the output voltage remains consistently 56 V.

The buck action comes into effect since the input voltage is above 56 V. Figure 17c displays the gate pulses for the switches S₁, S₂, S₃, S₄, S₅, S₆. These pulses correspond to an output voltage of 56 V and an input voltage of 90 V. Since S₅ and S₆ are the main switches for the buck-boost action, the gate pulses for these switches are directly determined by the duty cycle factor, δ = 0.5544.

Further the simulations are carried out in the similar way with the input voltage of 50 V slowly dropping to 30 V after 2 s as depicted in Figure 18a. Also the input voltage of 30 V slowly rises to 50 V, as seen in Figure 18b. In both these simulations, the boost action of this buck-boost mode comes into action to maintain the required voltage of 56 V at the output. The boost action is noticed in the beginning till 3.3 s after which the buck action comes into effect since the input voltage is above 56 V. For the switches S₁, S₂, S₃, S₄, S₅, and S₆, the gate pulses are displayed in Figure 18c, which corresponds to an output voltage of 56 V with an input voltage of 30 V. The duty cycle factor, δ = 0.7887, directly defines the gate pulses for S₅ and S₆, which are the main switches for the buck-boost action.

5.4. Mode Transition Output

Simulation for mode transition carried out considering that the vehicle is in propulsion with the converter in the boost mode giving dc link voltage of 300 V. At 2.5 s, regenerative braking is applied and the converter power flow reverses. The converter which is now operating in the buck mode gives an output voltage of 56 V to charge the battery. This is depicted in Figure 19a. The inductor current during mode transition is highlighted in Figure 19b. During the transition from the boost mode to the buck mode, the inductor current direction reverses. The buck mode is initiated only after the inductor current reaches zero.

Figure 20a brings out the comparison of voltage gain against duty cycle between the proposed converter and the conventional converter. The voltage gain of the proposed converter is double as compared with the conventional converter for the same duty cycle factor. 300 V output for the boost mode was obtained with δ = 0.68 for proposed converter. But conventional converter requires δ = 0.84 to obtain the same output voltage. Also for the buck mode, as seen in Figure 20b, to obtain an output voltage of 56 V from 300 V input, the duty cycle factor required is δ = 0.3734 for proposed converter as against δ = 0.1867 for the conventional converter. This confirms that the voltage gain is half for the proposed converter compared to the conventional one.

The voltage gain against duty cycle for the buck and buck-boost modes for the proposed converter is shown in Figure 21. With the condition for the selection of the buck or buck-boost mode for regenerative braking, the buck mode will provide the required voltage of 56 V at output for input voltage above 112 V. With the input voltage nearing 112 V, δ reaches close to 1 as against 0.5 for the conventional converter. Voltages equal to and below 112 V are handled by the buck-boost mode. When the input voltage is in the range above 56 V to 112 V, the buck action of the buck-boost mode comes into effect. Input voltages below 56 V are handled by the boost action of the buck-boost mode. This is tabulated in

Table 3. Regenerative braking voltage and corresponding operating mode.

Generated Voltage	Operating Mode
Above 2Vb′ up to Vd (max)	Buck mode
Above Vb′ up to 2Vb′	Buck-boost mode	Buck action
Vb′ and below		Boost action

.

Table 4. Comparison of proposed bidirectional converter with conventional half-bridge bidirectional configuration for EV.

Feature/Parameter	Half-Bridge Converter	Proposed Converter
Modes of operation	Buck, boost	Buck, boost and Buck-boost
Voltage gain in boost mode	Normal	Double
Voltage range	Normal	Wide
Voltage stress on switches	High-side voltage	Half the high-side voltage
Cost	Low cost	Additional cost

is a comparative table that illustrates the superiority of the novel proposed converter over the half-bridge based converter. The comparison is based on several factors including the number of modes of operation, voltage gain in the boost mode, voltage range, and voltage stress on the switches and cost. The first four factors reveal the benefits of the proposed converter. The cost of the proposed converter is comparatively more than the half-bridge based converter due to the utilization of four additional switches and implementation of the control logic. Comparison of proposed converter with the available converters in the literature is shown in

Table 5. Comparison of proposed bidirectional converter with all other bidirectional configuration in the literature for EV application.

Feature	Other Converter Configurations in Literature	Proposed Converter
Potential to use regenerative energy at low braking speeds when the voltage generated is less than that needed to charge the battery.	No	Yes

. The comparison is specific for the EV application. Due to the use of both the buck and buck-boost modes during regenerative braking, this novel configuration makes it possible for power to flow from the traction machine to the battery even if the regenerated voltage is lower than the voltage required for charging the battery. This unique feature makes it a favorable topology for EV application.

6. Conclusions

This research paper introduces atri-mode dc–dc non-isolated bidirectional converter designed to address the limitations associated with a wide voltage range for precise speed control and the recovery of regenerative braking energy at low speeds in electric vehicles. This novel converter is based on the modified version of the conventional bidirectional buck and boost converter and incorporates additional switches. It operates in three modes: buck, boost and buck-boost. An in-depth analysis of the converter operation for all the three modes with theoretical waveforms incorporating PWM switching is provided. A novel closed loop control strategy with pulse generation logic for all the switches is presented. An algorithm for mode transition is developed in order to influence the pulse pattern when changing over between modes.

Results show that the proposed novel converter provides double the voltage gain with a broad voltage range in the boost mode during running. During regenerative braking, the converter switches between the buck and buck-boost modes based on the voltage generated by the traction machine and a control algorithm. It acts as a buck converter when the generated voltage exceeds double the battery charging requirement and switches to the buck-boost mode when the voltage falls short. This mode-switching feature helps to maintain the required voltage for battery charging for all braking speeds. The configuration also reduces the voltage stress on the switches to half the dc link voltage.

The results confirm the converter’s functionality. Thus, for electric vehicles with bidirectional buck and a boost converter between battery and the traction motor/inverter, the proposed tri-mode converter can be a promising topology for enhancing regenerative braking efficiency and fine speed control of the vehicle during running.