# A Bridgeless Cuk-BB-Converter-Based BLDCM Drive for MEV Applications

^{1}

^{2}

^{*}

## Abstract

**:**

_{2}during buckboost converter operation to enhance the power quality. The total component count reduction in the BL-Cuk-BB converter is also achieved by eliminating the usage of extra/external back-feeding diodes, which are generally used in bridgeless schemes. The present scheme uses the inbuilt anti-parallel diodes for the same purpose. The lesser components requirement in the BL-Cuk-BB-converter-based BLDCM drive implies lesser cost and volume, along with greater reliability, lower conduction losses, and lower weight of the BLDCM drive, which adds to the merits of the model. The paper includes a detailed mathematical model and stability analysis using pole-zero maps and bode plots of the BL-Cuk-BB converter for each half-supply AC voltage cycle. The BL-Cuk-BB-converter-based BLDCM drive for an EV application has been developed on the MATLAB/Simulink platform for a DICM operation, and the MATLAB simulation results have been presented for validation of the BL-Cuk-BB-converter-based BLDCM drive.

## 1. Introduction

_{IN}) for the presented BLDCM drive. The BL-Cuk-BB converter works differently for both half-cycles of supply AC voltages due to the presence of two different converters for different half-cycles. The asymmetrical BL-Cuk-BB converter operates as a Cuk converter and a buckboost converter for positive and negative half-cycles of supply AC voltage, respectively. The presence of an input inductor in the Cuk converter eliminates the filter requirement for the positive half-cycle. However, the second-order buckboost converter in the negative half-cycle needs to be fed with a filter due to the absence of an inductor at its input terminal. The input inductance of the Cuk converter also serves as a filtering element along with capacitor C

_{2}(not a part of the Cuk converter) to feed the negative half-cycle buckboost converter so the requirement of a separate filtering inductor has been eliminated. This led to a decrement in the component count. The BL configurations generally make use of two extra/external diodes for the back-feeding purpose to complete the circuit. In the present BL-Cuk-BB converter configuration, the inbuilt anti-parallel diode of the insulated gate bipolar transistor (IGBT) switch conducts to perform the back-feeding operation to complete the circuit. Therefore, there is no need for extra/external diodes in the present configuration. The second stage of Figure 1. consists of electronically commutated VSI-fed BLDCM. The rotor position of BLDCM is monitored or sensed by Hall-effect sensors. These sensed Hall signals generate the VSI gate pulse.

## 2. BL-Cuk-BB Converter Configuration

_{2}for the negative half-cycle buckboost converter. The presented scheme utilizes the inbuilt anti-parallel diodes of IGBT switches for the back-feeding purpose to complete the circuit during both half-cycles of the supply AC voltage cycle. However, BL schemes generally utilize two separate/extra diodes one for each half-cycle of input AC voltage for the same purpose of back-feeding to complete the circuit.

#### 2.1. BL-Cuk-BB AC-DC Converter Operation

_{P}conducts.

_{P}does not conduct.

_{P}and diode does not witness any current flow through them (DICM).

_{N}conducts.

_{N}does not conduct.

_{N}and inductor L

_{3}do not witness any current flow through them (DICM).

_{P}and the loops formed during this mode are V

_{IN}-L

_{1}-C

_{2}-V

_{IN}, and C

_{1}-S

_{P}-C

_{DC}||R-L

_{2}-C

_{1}. In this mode capacitor C

_{1}discharges through the load. The conduction loops for the present mode have been depicted in Figure 3a for better understanding. The following relation is used to find the current through an inductor:

_{P}during mode-I can be estimated by using the equation.

_{S}represents the time interval and d

_{1}denotes the duty cycle.

_{P}is switched off and the conduction paths for this mode are deployed in Figure 3b. Capacitor C

_{1}charges during this interval and this mode also witness the conduction of diode D

_{1}. V

_{IN}-L

_{1}-C

_{1}-D

_{1}-C

_{2}-V

_{IN}is one conduction loop during mode-II. The second loop consists of diode D

_{1}, inductor L

_{2,}and a load in parallel with the DC-link capacitor. Maximum diode current through diode D

_{1}can be calculated by using the equation

_{P}is calculated as

_{1}drops to zero and the currents flowing through the capacitor C

_{1}and inductor L

_{2}are equal. The switch S

_{P}is still off throughout this mode. The conduction loop during this mode is V

_{IN}-L

_{1}-C1-L

_{2}-R||C

_{DC}-C

_{2}-V

_{IN.}This mode is also known as the discontinuous inductor current mode (DICM) for a positive (+ve) half-cycle of AC supply voltage (output voltage of DEG). The conduction loop for this DICM is depicted in Figure 3c.

_{N}is supplied with a gate pulse. Additionally, the current flows through components following path V

_{IN}-C

_{2}-L

_{1}-V

_{IN}and C

_{2}-S

_{N}-L

_{3}-C

_{2}. In this mode, the antiparallel diode of the switch S

_{P}also conducts to complete the loop. The conduction loop during mode-IV is shown in Figure 3d. The maximum current through switch S

_{N}during this mode can be calculated using the relation:

_{N}

_{,}and the conduction loops for this mode are shown in Figure 3e. In this mode, the inductor L

_{3}discharges through load and diode D

_{2}. The current through the diode can be calculated by using the relation as follows;

_{IN}). The conduction loop during this loop is depicted in Figure 3f. This loop begins as soon as the energy stored in the inductor vanishes.

_{ON}= d

_{1}and d

_{OFF}= d

_{2}+ d

_{DICM}

#### 2.2. Distinctive Factors of BL-Cuk-BB Converter

_{2}and L

_{3}) to improve the load current profile during positive (+ve) and negative (−ve) half-cycles of supply AC voltages. Table 1 shown below compares distinct BL converter-based BLDCM drives and lists the number of inductors, capacitors, switches, and diodes used in the drive system along with total components counts in different topologies.

#### 2.3. Selection of BL-Cuk-BB Converter Components

_{1}current which is achieved, when the current across inductor L

_{2}changes its polarity and becomes equal to current across capacitor C

_{1}. However, the negative cycle DICM operation starts after the complete discharge of energy stored in inductor L

_{3}. For DICM, operation it is necessary to choose such values of inductors L

_{2}, and L

_{3}so that the inductor gets completely discharged before the completion of each half-cycle of diesel engine generator (DEG) voltage. However, the energy storage capacitor voltage V

_{C1}and V

_{C2}remain continuous throughout the complete cycle. A 426 W BLDCM (specification details of BLDCM is deployed in Appendix A) is being used in the ongoing article to validate the MEV drive performance at MATLAB/Simulink platform. So, for the BLDCM drive, an input-side PF-corrected converter with a 500 W maximum power rating is intended to design in this work. The nominal value of DC-link voltage is taken as 180 V to check the speed control operation of BLDCM over a wide range of DC-link voltage. The rated DC-link voltage and its lowest value are taken as 300 V and 80 V, respectively. The supply voltage, V

_{IN}(output voltage of DEG) can be written as

_{m}is peak input AC voltage and f

_{L}is line frequency in Hz equal to 50 Hz and ω

_{L}is line frequency in radian/second.

_{CDC_n}symbolizes the nominal voltage across the DC-link capacitor.

_{CDC_m}symbolizes the maximum voltage across the DC-link capacitor whereas, rated power is denoted by P

_{m}for the BL-Cuk-BB converter. The value of inductance L

_{1}and switching frequency do require proper selection for DICM operation. Switching frequency and inductance values are important parameters for deciding the switching losses and inductor size. As the switching frequency increases, the magnitude and size of the inductor reduce but the solid state device (switch) suffers greater switching losses and thus the requirement of a heat sink having a large surface area felt, moreover a lesser value of inductance has associated problem of increased current stress in DICM operation of BL-Cuk-BB converter; less switching frequency, however, results in much lower switching losses, but on the other hand the inductor cost, size, and magnitude increases. So, by considering above the things in mind, the switching frequency for the ongoing work is taken as 20 kHz. The critical value of input inductance, L

_{1}for the BL-Cuk-BB converter can be calculated by using the formula

_{1}chosen for the ongoing work is 5 mH. The value of output inductance can be calculated using the formula.

_{1}can be calculated by using the formula

_{1}, the value chosen must be greater than the calculated value. So, for this work, the value of C

_{1}is chosen to be 1.5 µF.

_{DC}) can be evaluated by rearranging the power equation

_{DC}value can be calculated using Equation (21)

## 3. BL-Cuk-BB Converter Fed BLDCM Drive Control

#### 3.1. BL-Cuk-BB Converter Control Scheme

_{1}ϕ). The resultant equation can be written as

_{DC}

^{*}is the output of RVG

_{DC}

^{*}and the actual DC-link voltage. The error signal, the output of the error generator can be expressed at the n

^{th}sample instant as under

_{DC}), the error signal is supplied to the voltage P-I controller. The controller output voltage, V

_{Con}can be expressed as

_{I}and K

_{P}are respective P-I controllers’ integral gain and proportional gain. Controlled voltage (V

_{Con}) when compared with high-frequency saw-tooth wave (U

_{ST}) produces gate signal for switches S

_{P}and S

_{N}when passed through the relational operator. The logic used in the relational operator is explained as under

_{IN}> 0

_{ST}≤ V

_{Con}implies IGBT S

_{P}conducts

_{ST}> V

_{Con}implies IGBT S

_{P}is “SWITCHED OFF”

_{ST}≤ V

_{Con}implies switch S

_{N}conducts

_{ST}> V

_{Con}implies IGBT S

_{N}is “SWITCHED OFF”.

#### 3.2. BLDCM Speed Control

_{1}and S

_{6}conducts. At this instant of time, DC-link voltage is applied across BLDCM, following the path as shown in Figure 5. So the direction of current and also its magnitude, both depend on DC-link voltage V

_{DC}, self-inductances of windings (A and C), mutual inductance (M

_{AC}), resistances of windings (A and C), and also the back-EMFs (E

_{AN}and E

_{CN}). Additionally, the switching states of all six switches of VSI based on the information provided by 3 Hall sensors (H

_{A}, H

_{B}, H

_{C}) feeding BLDCM have been shown in Table 2.

## 4. State-Space Model (SSM) and Small-Signal Analysis of BL-Cuk-BB Converter

_{1}, X

_{2}, X

_{3}for the input supply voltage’s positive cycle and Y

_{1}, Y

_{2}, Y

_{3}for the input supply voltage’s negative cycle. Utilizing the Bode diagram and pole-zero map, the stability study of both positive and negative cycle converters is performed in this work. Figure 2 depicts the BL-Cuk-BB converter model undergoing a stability test. A Bode plot is a graphical representation of the system’s frequency response. It is typically a mix of a Bode magnitude plot, which expresses the frequency response’s amplitude (in dB), and a Bode phase plot, which expresses the phase shift. The bode plots are used to see the system’s stability. The stability of any system depends on its gain and phase margin. The stability analysis of any system is necessary to certify the proper working of the system over a long period. The gain margin is the factor by which the system’s gain can be increased so that system can be pushed to the border between stability and instability and the phase margin is the additional lagging in the phase that can be given to the system to make the system unstable so, both these quantities are always positive for a stable system. Graphically gain margin is seen as the gain at phase cross-over frequency (phase angle graph touches −180°) and the phase margin can be seen as the phase at gain cross-over frequency (magnitude graph is unity).

#### 4.1. Stability Assessment of Converter operating in Supply AC voltage’s Positive Cycle

_{4}= L

_{1}− L

_{2}.

_{PR}and K

_{INT}are tuned proportional and tuned integral constants and tuned values of both K

_{INT}and K

_{PR}are chosen as 0.05 and 0.00186, respectively. Figure 6b depicts the bode-plot of the entire system (converter and control) utilizing the BL-Cuk-BB converter’s positive-cycle transfer function and TF

_{ct}(b). Large and non-negative values of phase (57.9°) and gain (89.3 dB) margins confirm good stability of the positive half-cycle converter.

#### 4.2. Stability Assessment of Converter Operating in Negative Cycle of Supply AC Voltage

## 5. Validation and Result

#### 5.1. BLDCM Drive Steady-State Performance

#### 5.2. Performance of BL-Cuk-BB Converter

_{1}and filter capacitor C

_{2}. The capacitor C

_{1}voltage maximum value is found 778 V whereas the maximum voltage across capacitor C

_{2}is found to be 586 V. Figure 11c–e show the current across the inductors L

_{1}, L

_{2,}and L

_{3}, respectively.

#### 5.3. BL-Cuk-BB Converter Fed BLDCM Drive Dynamic Performance

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A

^{−4}m/s

^{2}.

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**Figure 3.**BL-Cuk-BB converter operation during (

**a**) Mode-I, (

**b**) Mode-II, (

**c**) positive cycle DICM, (

**d**) Mode-IV, (

**e**) Mode-V, (

**f**) Negative cycle DICM.

**Figure 6.**Positive (+ve) cycle BL-Cuk-BB converter scrutiny using (

**a**) pole-zero (P-Z) plot, (

**b**) The Bode-diagram.

**Figure 7.**Negative (-ve) cycle BL-Cuk-BB converter scrutiny using (

**a**) pole-zero (P-Z) plot, (

**b**) The Bode- diagram.

**Figure 8.**BLDCM drive performance at 300 V DC-link voltage and a supply voltage of 220 V-(

**a**) Supply voltage, (

**b**) input AC, (

**c**) armature current of BLDCM, (

**d**) Back-EMF, (

**e**) DC-link voltage.

**Figure 9.**BLDCM drive performance at 80 V DC-link voltage and a supply voltage of 220 V-(

**a**) Supply voltage, (

**b**) input AC, (

**c**) armature current of BLDCM, (

**d**) Back-EMF, (

**e**) DC-link voltage.

**Figure 11.**BL-Cuk-BB converter under steady state (

**a**) capacitor C

_{1}voltage, (

**b**) filter capacitor C

_{2}voltage, (

**c**) current through inductor L

_{1}, (

**d**) output inductor L

_{2}current, (

**e**) output inductor L

_{3}current.

**Figure 12.**Current across BL-Cuk-BB converter’s—(

**a**) switch S

_{P}(

**b**) switch S

_{N}, (

**c**) diode current I

_{D1}, (

**d**) current through diode D

_{2}.

**Figure 13.**BLDCM drive dynamic performance with supply voltage step variation from 220 to 130 V at t = 0.5 s and 130 V to 220 V at 1.2 s (

**a**) Supply voltage (

**b**) Supply mains current, (

**c**) V

_{DC}(voltage across DC-link), (

**d**) BLDCM stator current, (

**e**) BEMF.

**Figure 14.**BLDCM drive dynamic performance with DC-link voltage step variation from 300 to 220 V at t = 0.5 s and 220 V to 300 V at 1.2 s (

**a**) Supply mains voltage (

**b**) Mains current, (

**c**) V

_{DC}(voltage across DC-link), (

**d**) BLDCM stator current, (

**e**) BEMF.

**Figure 15.**BLDCM drive dynamic performance with a sudden increase in load from 1.52 to 2 N m at t = 0.5 s and 2 to 1.52 N m at 1.2 s (

**a**) Supply mains voltage (

**b**) input mains current, (

**c**) V

_{DC}(voltage across DC-link), (

**d**) stator current of BLDCM, (

**e**) load torque (N-m), (

**f**) BEMF.

S. No. | Configurations | Components Count | ||||
---|---|---|---|---|---|---|

Switch | C | L | D | Total | ||

01 | BL-Buck-Boost [22] | 2 | 2 | 3 | 4 | 11 |

02 | BL-Cuk [23] | 2 | 5 | 6 | 4 | 17 |

03 | BL-SEPIC [24] | 2 | 3 | 4 | 4 | 13 |

04 | BL-zeta [25] | 2 | 2 | 3 | 3 | 10 |

05 | BL-Luo [26] | 2 | 3 | 4 | 4 | 13 |

06 | BL-CSC [28] | 2 | 3 | 2 | 4 | 11 |

07 | BL-Sheppard-Taylor [27] | 4 | 3 | 4 | 10 | 21 |

08 | BL-Landsman [29] | 2 | 3 | 4 | 4 | 13 |

09 | Proposed BL-Cuk-BB | 2 | 3 | 3 | 2 | 10 |

$\mathit{\theta}$ (Radians) | Hall Signals | Switching States of VSI | |||||||
---|---|---|---|---|---|---|---|---|---|

H_{A} | H_{B} | H_{C} | S1 | S2 | S3 | S4 | S5 | S6 | |

NA | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

0–(π/3) | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 |

(π/3)–(2π/3) | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 1 |

(2π/3)–π | 1 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 1 |

π–(4π/3) | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 |

(4π/3)–(5π/3) | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 0 |

(5π/3)–2π | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 |

NA | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

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## Share and Cite

**MDPI and ACS Style**

Shukla, T.; Nikolovski, S.
A Bridgeless Cuk-BB-Converter-Based BLDCM Drive for MEV Applications. *Energies* **2023**, *16*, 3747.
https://doi.org/10.3390/en16093747

**AMA Style**

Shukla T, Nikolovski S.
A Bridgeless Cuk-BB-Converter-Based BLDCM Drive for MEV Applications. *Energies*. 2023; 16(9):3747.
https://doi.org/10.3390/en16093747

**Chicago/Turabian Style**

Shukla, Tanmay, and Srete Nikolovski.
2023. "A Bridgeless Cuk-BB-Converter-Based BLDCM Drive for MEV Applications" *Energies* 16, no. 9: 3747.
https://doi.org/10.3390/en16093747