1 Introduction

Nowadays brushless motors are utilized additional often than brushed motors. The reason is that brushless motors are very good performing at the low sound noise and power efficiency improvements. Usually brushless motors use one or more sensors. With this function, the sensor is wired and the cost of operating it is high. Also, sensors cannot be used in rotor existing applications in closed housing. In applications where the motor is submerged in a fluid such as a compressor, or some pumps, must keep the number of electrical inputs to a minimum. So in terms of technology and cost reason, Sensorless BLDC Motor is considered as a major requirement. This Sensorless BLDC Motor gives very high performance, at very low cost. As a result of high performance, excessive torque to inertia ratio, excessive power density, low preservation need and extensive variety of speed manipulate; brushless DC (BLDC) motors are extensively favoured in lots of minimal and medium energy exeercises. It's far used in many house equipments of Gadget like fans, air conditioners, water pumps, Refrigerators, washing machines etc.It also finds applications in lots of commercial gear, medical equipments, Heating, air flow and air con, robotics and Particular movement control structures [1–3].

In the last decade, bridgeless configurations gained more importance due to reduced switching losses and improved PFC at AC mains. This is achieved by eliminating the DBR partially [4]. Conventional bridgeless configuration includes boost converter configuration which reduces the common mode noise. In paper [1], BL-BBC has been used. It is utilized to improve the level of energy, and in which Hall Effect sensors have been utilized. In paper [2], BL-CSCC has been utilized to progress the PF with usage of least number of components and conducting devices. This configuration exhibits the minimum conduction losses due to reduced component conduction in both the cycles. In paper [3], BL-CC is utilized to boost or raise the status of the power with a very simple voltage follower approach. This paper is mainly utilized in air conditioning applications and with applications of reduced sensors.

In paper [5], the BL-LC is utilized to raise the energy factor, and in which a one only sensor has been utilized to improved the PF. Moreover, the switching losses of the VSI is minimum with wide range of speed control. Also the switching stress is reduced comparatively with other bridgeless configurations. In paper [6], the LUO converter is utilized to improve the PFC which is a low cost solution for all low power applications. Also, LUO converter is widely used in many voltage lifting applications. In paper [4], the BL-SEPIC Converter is utilized to promote the PFC and speed control of brushless drive. The performance of this configuration is satisfactory for speed control and supply fluctuations with reasonable switching losses. In paper [7], the BL-ZC is used to attain a power factor close to unity at supply mains; It includes a single voltage sensor for speed control and PFC. In paper [8], the hysteresis comparator has been used to operate the BLDC motor without a sensor. Usage of this converter provides proper commutation pulses to the inverter and the presence of LPFs compensates the phase lag of back EMF which produces significant pulsating torques which in turn causes load disturbances.

Normally hall sensors will be used to get the alignment of rotor position for commutation purpose. Here in the poposed design hall sensors are removed and a sensorless control technique is proposed [9]. Although, position sensors are used to achieve noiseless torque, due to the immunity level and reduced consistency the position sensors are removed by implementing a sensorless control design. Usually, back emf estimation design will be used which is also termed as teminal voltage estimation technique provides the position of rotor with low amplitude [8]. To avercome this align and go techniques is used. Other SBLDC techniques like third harmonic terminal voltage technique and PLL are developed but leading to noise and interference problems which makes the commutation more difficult [9]. Also zero crossing point estimation techniqes has been suggested by researchers by using V and I sensors. To avoid the above said blemishes a hysteresis comparator technique is used with applicable high starting torque. Therefore, this paper presents a power quality improvement scheme using SBLDC motor with hysteresis comparator technique [8]. So in this proposed methodology, five types of converters with a voltage follower approach is used and fed to SBLDC motor with hysteresis comparator technique and then a comparison is done with the output parameters. Finally, a better converter configuration is identified for achieving better power factor and efficiency.

2 Proposed Methodology

In this proposed method, the AC to DC converters are utilized to wield the BLDC motor to improve PF in the supply mains, AC Supply is fed through LC Filter and to the AC-DC converter. The AC to DC converters which converts the AC to the required level of DC. It is then provided to VSI having six-stage switches. This paper uses the hysteresis comparator for sensorless control. This comparator incorporates the LPF to suppress high switching frequency ripples. Hysteresis comparator is utilized to create gating signals to the VSI. The gating signal generator is utilized to generate six PWM signals. The voltage across dc link capacitor is taken to the voltage controller and compared with the reference voltage. The voltage controller then turns them into a constant voltage and gives it to PWM. This is then compared with sawtooth generator and the input PWM is given to the AC to DC converter. Usage of hybrid controller improves the robustness of the system and suppresses the chattering of the load. Furthermore, design of hybrid controller can provide desirable performance which is not possible with linear control technique. [9–15] (Fig. 1).

2.1 TVS

Transients are temporary changes in frequencies. TVS device is a component that can protect and isolate circuits. It is utilized to filter and control an unstable and high voltage. This makes it possible to keep the VSI fed SBLDC circuit very secure. In the hardware part, this TVS device shall provide excellent surge protection to the 6-pack VSI Fed SBLDC. This, in turn, distorts or reverses the voltage spike from the circuits of the SBLDC motor. This means that if an instant enlarge in voltage is greater than three nanoseconds, the voltage fluctuation will occur. This, in turn, will attack the circuitry of the SBLDC motors. If the spike is sudden crossing over, then the PN junction is back to normal. Then, when comes to the next spike, the spike will hold tight. In normal function, the TVS are invisible to the round to be protected. Here may need to install a high voltage surge or a device that absorbs unnecessary heat to TVS. Generally, the peak power flowing through the TVS is handled in the kilowatt range.

In Fig. 2, on the y-axis, the voltage exceeds the 20 V upper limit. Then the TVS accept that high voltage range and responds immediately to that. TVS diodes protect the circuits from Electrostatic Discharge (ESD). Here TVS secures a signal chain in one direction. Thus, it allows the signal chain to only flow at the top. This means that the TVS defend the input power of the circuit [16–20] (Fig. 3).

Fig. 1
figure 1

Flow of this proposed method

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Fig. 2
figure 2

Diagram of clamping voltage

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Fig. 3
figure 3

TVS circuit diagram

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Typically the VMW is below 10–15% the VB. The voltage that TVS devices go into avalanche is called VB. Temperature affects VB size. Thus, the VMW is at least 10% lower than the VB. This is because when the temperature drops, the flow of VB is less. TVS should not have a breakdown voltage equal to the working peak voltage. The clamping voltage is the highest voltage in the TVS. The VC is 60% greater than the VMW and the 35–40% higher than the VB.PPP dispersion is one of the factors to safely suppress various upheavals or ratings. Therefore,

$$P_{{{\text{PP}}}} = \, V_{{\text{C}}} \times \, I_{{{\text{wcs}}}}$$

where VB = breakdown voltage, VMW = maximum working voltage, VC = clamping voltage, PPP = peak pulse power, Iwcs = worst-case surge current.

2.2 AC to DC Converter

Five types of AC to DC converters are utilized in this present method. Then, which of these 5 converters are found to be the best. The 5 types of schemes of AC–DC converters are given below:

  1. 1.

    Bridgeless landsman converter (BL-LC)

  2. 2.

    Bridgeless cuk converter (BL-CC)

  3. 3.

    Bridgeless buck-boost converter (BL-BBC)

  4. 4.

    Bridgeless zeta converter (BL-ZC)

  5. 5.

    Bridgeless canonical switching cell converter (BL-CSCC)

2.3 BL-LC

In Fig. 4 in which the converter balance on both Discontinuous Inductor Current Mode (DICM) and Continuous Inductor Current Mode (CICM).The converter manipulates in the Positive Half Cycle (PHC) and Negative Half Cycle (NHC) of the AC distribution fewer than three distinct systems. Here the functionality of the converter is described in each mode:

  • Mode 1 When the switch Q9 is attached by a gate signal, the energy from the mains is sent to the capacitor C4 input inductance L6 along with the stored charge. The inductor starts charging, the output inductor begins to settle. The output capacitor C6 begins to charge due to the ejection of the capacitor C4. Consequently the voltage Vdc over the output capacitor begins to increase.

  • Mode 2 After switch Q9 switch is off, output inductor L7 and capacitor C4 are supplied with energy from the supply mains. So C4 and L7 start charging, begin to discharge the inductor L6, then the energy is delivered from the capacitor C4 to the motor.

  • Mode 3 In this practice the converter works in DICM. In this method the input inductor L6 is completely eliminated and then the energy is zero in the inductor. The charge from the output inductor L7 is caring to the DC Link capacitor C6. Thus, when the converter is running at the DICM, a series of supply for the motor is also maintained.

Fig. 4
figure 4

Circuit diagram of BL-LC

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In DICM, the BL-LC is designed to function. In standard, the DC bus voltage is essential in the ink for speed control from 12 V/Vdcmn to 24 V/Vdcmx. This is set as Vsc in and below equation:

$$V_{{{\text{sc}}}} = \, V_{{{\text{pk}}}} {\text{Sin}} \, (2\pi f_{{{\text{li}}}} t)$$
(1)

The median rectified i/p voltage Vi is modeled as given in Eq. (2).

$$V_{i} = \frac{{2\sqrt 2 V_{{{\text{sc}}}} }}{\pi }$$
(2)

The BL-LC duty rate DR is expressed in Eq. (3).

$$D_{{\text{R}}} = \frac{{V_{{{\text{dc}}}} }}{{\left| {V_{{\text{p}}} {\text{Sin}} \left( {\omega t} \right)} \right| + V_{{{\text{dc}}}} }}$$
(3)

where Vdc and Vpk are the peak input voltage, voltage across the output capacitor and angular frequency, respectively. The output for output inductors with allowable ripple current \((\Delta i)\) is given in Eq. (4),

$${\text{L}}7, \, 8 \, = \frac{1}{{\Delta i\;f_{{\text{a}}} }}\left( {\frac{{V_{{{\text{sc}}}}^{2} }}{{P_{{\text{i}}} }}} \right)\left( {\frac{{V_{{{\text{dc}}}} }}{{V_{{\text{i}}} + V_{{{\text{dc}}}} }}} \right)$$
(4)

Using Eq. (5), the critical value of the i/p inductors Lci is derived,

$$L_{{{\text{ci}}1, \, 2}} = \frac{{V_{{{\text{sc}}}}^{2} }}{{P_{{\text{i}}} }}\frac{{V_{{{\text{dc}}}} }}{{2 V_{{\text{i}}} f_{{\text{a}}} }}\left( {\frac{{V_{{{\text{dc}}}} }}{{V_{{\text{i}}} + V_{{{\text{dc}}}} }}} \right)$$
(5)

To manage in DICM, the values of the input inductors L5, 6 are smaller than the critical value Lci1,2. Equation 6 is utilized to frame the values of the intermediate capacity.

$$C4, \, 5 = \frac{{V_{{{\text{dc}}}} }}{{K \left( {V_{{{\text{dc}}}} + V_{{\text{i}}} } \right)f_{{{\text{a}} }} \left( {\frac{{V_{{{\text{dc}}}}^{2} }}{{P_{{\text{i}}} }}} \right)}}\left( {\frac{{V_{{{\text{dc}}}} }}{{V_{{\text{i}}} + V_{{{\text{dc}}}} }}} \right)$$
(6)

Here the DC connector, the ripple inclusions of the voltage across the capacitor is introduced to as K. The value of the DC connector capacitor is designed to be Eq. (7),

$$C_{{{\text{dc}}}} = \frac{{P_{{\text{i}}} }}{{2\omega \Delta V_{{{\text{dc}}}}^{2} }}$$
(7)

In Eq. (8), the limit for maximum filter capacity Cfmx is given. Is and Vs reveal the peak value of V and I. The phase variation betwixt the IS and Vsc is indicated by theta, and it is selected as \(1^\circ\).

$$C_{{{\text{fm}}}} = \frac{{\left( {\frac{{\sqrt 2 P_{{\text{m}}} }}{{V_{{{\text{sc}}}} }}} \right)}}{{\omega_{{\text{L }}} V_{{{\text{sc}}}} }} \tan (\theta )$$
(8)

Capacitance in the filter has a selective value, rather than that of Cfm. From Eq. (9), the filter inductor Lf is estimated. LPF between the fl < fco < fsw is designed to have a cut-off frequency fco.fco has been chosen as 2000 Hz. The reason why this value is so high is to accommodate a minor amount of stimulation. By Eq. (9), the value required for inductor in the filter is calculated.

$$L_{{\text{f}}} = \, L_{{\text{r}}} + \, 0.04\left( {\frac{1}{{\omega_{{\text{L}}} }}} \right)\left( {\frac{{V_{{{\text{sc}}}}^{2} }}{{P_{{\text{o}}} }}} \right)$$
(9)

2.4 Bridgeless Cuk Converter

The converter here is designed to operate in DICM as shown in Fig. 5. In this event, when the current of the output inductor L11 and L12 is steady, the voltage across the transitional capacitors Vc13 and Vc8 and the current in the input inductor L17 and L9 continue to reach a PFC in the mains. The AC distribution has both PHC and NHC. The switch Q18 is transfer and via L17 and D36 to the PHC of the supply voltage. The energy is relocating via the energy transfer capacitor C13, L11 and D34. Likewise for the NHC of the supply voltage, the switch Q17 handles L9 and D35. A regular DC connector is utilized for the NHC and PHC of the capacitor C9 justification. DC connector capacitors C9 are utilized to attain the pace of the BLDC motor. The various modes of operation are explained below:

  • Mode 1 During the switch Q18 is turned on, the energy is gathered in the i/p inductor L17 via the diode D16. Inductor current iL17 improves. Also the power stored in the intermediate condenser C13 is dispensed to the output inductor L11 and DC link capacitor C9. So the DC link voltage Vdc and current iL11 are improved, throughout the voltage of the intermediate capacitor Vc13, this function mode decreases.

  • Mode 2 When switching off the switch Q18, the inductor discharges through the intermediate capacitor C13 exits through the diode D34 and D36. Inductor L11 then converts its stored energy to the DC-link capacitor C9, So in this function routine, the current of the inductors L17 and L11 persistent to lessen. At the similar time, the voltage of the intermediate condenser C9 and the DC coupling capacitor C13 is increased.

  • Mode 3 In this mode there is no energy in the inductor L11 of the output, that is, iL11 = 0. Input inductor iL17 raises the voltage of the intermediate capacitor C13. At this time, the DC connection provides the energy required for the capacitor C9. So the Vdc is reduced. This operation continues until the switch Q18 is switched on again.

Fig. 5
figure 5

Circuit diagram of BL-CC

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The input average voltage is given in equation below:

$$V_{{{\text{iavg}}}} = \frac{{2\sqrt 2 V_{{{\text{sc}}}} }}{\pi }$$
(10)

The BL-CC DC connector is designed from Vdcmn to Vdcmx for voltage control. Below is the Duty Rate (DR) for the BL-LC:

$${\text{DR}} = \frac{{V_{{{\text{dc}}}} }}{{V_{{{\text{dc}}}} + V_{{{\text{iavg}}}} }}$$
(11)

Hence the DR is for designed (dd), maximum (dmx) and minimum (dmn) corresponding to Vdcd, Vdcmx and Vdcmn are calculated. Now the nominal DR (dn) is taken less than dd for an efficient control in DICM, equation of both inductors L17 and L9,

$${\text{L}}17 \, = {\text{L}}9 \, = \frac{{V_{{\text{p}}} d_{{\text{n}}} T_{{{\text{sw}}}} }}{{\Delta i_{{{\text{Li}}}} }}$$

where Vp = peak of supply voltage, Tsw = switching period, fsw = switching frequency.

The important conduction parameter Kic equation,

$$K_{{{\text{ic}}}} = \frac{1}{{2\left\{ {\left( {\frac{{V_{{{\text{dcd}}}} }}{{V_{{\text{p}}} }}} \right) + n} \right\}^{2} }}$$
(13)

The conduction parameter Kc for the function in DICM,

$$K_{{\text{c}}} < \, K_{{{\text{ic}}}}$$
(14)

Equivalent inductive Le calculation,

$$L_{{\text{e}}} = \frac{{R_{{{\text{el}} }} T_{{{\text{sw}} }} K_{{\text{c}}} }}{{2}} = \frac{{\left( {\frac{{V_{{{\text{dcd}}}}^{2} }}{P}} \right)\left[ {\frac{1}{{f_{{{\text{sw}}}} }}} \right]K_{{\text{c}}} }}{2}$$
(15)

Here, Rel = equivalent load resistance. The equation for the value of the o/p side inductor,

$${\text{L}}11 \, = {\text{L}}12 \, = \frac{{L_{{{\text{in}}}} L_{{\text{e}}} }}{{L_{{{\text{in}}}} - L_{{\text{e}}} }}$$
(16)

The estimation for the capacity of energy transfer capacitors is,

$${\text{C}}13 = {\text{C}}8 \, = \frac{1}{{\omega_{{\text{re }}}^{2} \left[ {L_{{{\text{in}}}} + L_{{{\text{ou}}}} } \right]}}$$
(17)

where ωre = 2πfre, fre = the resonant frequency and fsw > fre > fli where fli = the line frequency. The equation of the value of the DC connecting condenser is as follows,

$$C_{{{\text{dc}}}} = \frac{{I_{{{\text{dc}}}} }}{{2\omega_{{{\text{li}} }} \Delta V_{{{\text{dcc}}}} }}$$
(18)

where Idc = DC couple current, ωli = line frequency, ΔVdcc = permitted ripple voltage in DC pairing condenser.

The sum of the maximum value of the filter is,

$$C_{{{\text{fmx}}}} = \frac{{I_{{\text{p}}} }}{{\omega_{{{\text{li}}}} V_{{\text{p}}} }}\tan (\theta )$$
(19)

2.5 BL-BBC

The behavior of the BL-BBC is partitioned into 2 types. This comprises the activity of the PHC and NHC of the supply voltage and the thoroughgoing switching cycle, Switches Q33 and Q48 in this BL-BBC handle in the PHC and NHC. For the PHC, 3 styles of workable during the proper transition cycle are discussed. The workable of those three methods is detailed below (Fig. 6).

  • Mode 1 This practice is utilized Q33 to charge L24. In this process the inductor current iL24 is increased. The diode D74 consummates the input side circuits. Then the DC connector is discharged by the capacitor C7.

  • Mode 2 In this form of performance, switch Q33 is switches off, the energy is collected in the inductor L24 is relocated to the DC-link capacitor C7 until the trigger is absolutely discharged. The current in the inductor L24 dwindles and then reaches zero.

  • Mode 3 In this mode, the inductor L24 enters into non-stop conduction. That is, there is no charge in the inductor. Hence the current iL24 becomes zero for the remaining transition period. The DC-coupling Capacitor C7 delivers energy. So the DC connection reduces the voltage Vdc across the capacitor. After a proper switching cycle, the operation is redo when the switch Q33 is turned on.

The equation for computing the median current is in Eq. (2). Equation of voltage conversion rate is in Eq. (11). The inductor Lci1 values equation to act as the critical conduction manner in the BBC converter,

$$L_{{{\text{ci}}1}} = \frac{{R_{{{\text{el}} }} 1 - \left( {{\text{DR}}} \right)^{2} }}{{2f_{{{\text{sw}}}} }}$$
(20)

Now, Lci1’s value is calculated at the worst duty rate in dmn. The equation corresponding to Vdcmn the value of the inductor Lcimn is given below,

$$L_{{{\text{cimn}}}} = \frac{{V_{{{\text{dcmn}}}}^{2} }}{{P_{{{\text{mn}}}} }}\frac{{1 - d_{{{\text{mn}}}}^{2} }}{{2f_{{{\text{sw}}}} }}$$
(21)

For the PFC function, the supply current Isu is in phase. Calculation of input power Pi,

$$\begin{aligned} P_{{\text{i}}} & = \sqrt 2 V_{{{\text{su}}}} \sin \omega t .\sqrt 2 I_{{{\text{su}}}} \sin \omega t \\ & = V_{{{\text{su}}}} I_{{{\text{su}}}} (1 - \, \cos 2\omega t) \\ \end{aligned}$$
(22)

The second line corresponds to harmonics; this is mirrored in the DC Link capacitor,

$$i_{{\text{c}}} \left( t \right) = - \frac{{V_{{{\text{su}}}} I_{{{\text{su}}}} }}{{V_{{{\text{dc}}}} }}\cos 2\omega t$$
(23)

Under is the DC pair voltage ripple associated with this Capacitor Current,

$$\Delta V_{{{\text{dc}}}} = \frac{1}{{C_{{{\text{dc}}}} }}\int i_{{\text{c}}} \left( t \right){\text{d}}t \, = \, - \frac{{I_{{{\text{dc}}}} }}{{2\omega C_{{{\text{dc}}}} }}\sin 2\omega t$$
(24)

In DC-incorporating condenser, the voltage to the maximum value, sin (\({\omega t}\)) is taken 1. So its sum is rewritten under,

$$C_{{{\text{dc}}}} = \frac{{I_{{{\text{dc}}}} }}{{2\omega \Delta V_{{{\text{dc}}}} }}$$
(25)

Now the DC Link capacitor, planned value, in Vdcd DC connection voltage, computed with permitted ripple. Equation of dc link condenser is,

$$C_{{{\text{dc}}}} = \frac{{\frac{{P_{{{\text{ou}}}} }}{{V_{{{\text{dcd}}}} }}}}{{2\omega \Delta V_{{{\text{dc}}}} }}$$
(26)
Fig. 6
figure 6

Circuit diagram of BL-BBC

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2.6 BL-ZC

Similarly for the NHC of the Vsc, the current does not flow through the switch and diode. Here the energy is converted by the high frequency transformer (HFT). Its proportion is given as F1: F1: F2, planned to perform as magnetization, in DCM. This is to reach an intrinsic PFC; broad gamut of DC connection middle conduction is reached for voltage control.

There are 3 modes of operations for this converter. One of those operations is, for the PHC of the Vsc function during the consummate switching cycle. When switch Q49 is running, the energy is saved in the inductor L27, the HFT and the intermediate capacitor C16. While the DC link Capacitor, The C15 delivers enough power for the load. When the switch is turned off, inductor and diode HFT eject give the power necessary for the DC coupling capacitor. In DCM process manner, HFT is totally eradicated. Whereas, following the inductor L27 the DC connection provides the energy required for the capacitor (Fig. 7).

Fig. 7
figure 7

Circuit diagram of BL-ZC

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The equation of the input voltage Vsc, given in an Eq. (1), the input average voltage Via is considering in the equation below,

$$V_{{{\text{ia}}}} = \frac{{2 V_{{\text{p}}} }}{\pi }$$
(27)

Output voltage, isolation of the isolated ZC converter is provided by Vdc. Equation is,

$$V_{{{\text{dc}}}} = \left( {\frac{F2}{{F1}}} \right)\frac{{{\text{DR}}}}{{\left( {1 - {\text{DR}}} \right)}}V_{{\text{i}}}$$
(28)

The equation of DR is calculated as,

$${\text{DR }} = \frac{{V_{{{\text{dc}}}} }}{{V_{{{\text{dc}}}} + \left( {\frac{F2}{{F1}}} \right)V_{{\text{i}}} }}$$
(29)

The value of the equivalent load resistance Rel is computed by the next equation:

$$R_{{{\text{el}}}} = \frac{{V_{{{\text{dc}}}}^{2} }}{{P_{{{\text{ou}}}} }}$$
(30)

To control on the border of CCM and DCM, HFT's magnetization inductor Lmc equation of critical value,

$$L_{{{\text{mc}}}} = \frac{{\left( {1 - {\text{DR}}} \right)^{2} R_{{{\text{el}}}} }}{{\left( {\frac{F2}{{F1}}} \right)^{2} 2Df_{{{\text{sw}}}} }}$$
(31)

The value of the magnetization inductor Lmag is picking as given below,

$$L_{{{\text{mag }} < < }} L_{{{\text{mc}}}}$$
(32)

The value of the o/p inductor L27,

$${\text{L}}27 \, = \frac{{V_{{{\text{ou}}}} \left( {1 - {\text{DR}}} \right)}}{{f_{{{\text{sw}}}} \Delta i_{{{\text{L}}27}} }}$$
(33)

The value of in-between capacitor C16,

$${\text{C}}16 = \frac{{V_{{{\text{dc}}}} {\text{DR}}}}{{\Delta V_{{{\text{ci}}}} R_{{{\text{el}}}} f_{{{\text{sw}}}} }} = \frac{{V_{{{\text{dc}}}} {\text{DR}}}}{{V_{{\text{p}}} R_{{{\text{el}}}} f_{{{\text{sw}}}} }}$$
(34)

The value of the DC coupling capacitor is given below,

$$C_{{{\text{dc}}}} = \frac{{I_{{{\text{dc}}}} }}{{2\omega_{{{\text{li}}}} \Delta V_{{{\text{dc}}}} }}$$
(35)

2.7 BL-CSCC

Here the BL-CSC converter is sketched to operate in DICM. That is, the inductors are L1 and L2, the switching time is constant. Here, using different operational methods, for the NHC and PHC of the supply voltage, displays the complete transition period. The three modes are as follows:

  • Mode 1 While the switch is turned on input inductor L1 via the diode D8 starts to charge, and the current iL1 expansions. The intermediate capacitor C1 initiates to discharge along the switch Q1. Therefore, the voltage minimizes in the intermediate capacitor Vc1. At the identical time, the DC-link voltage must be added to the Vdc.

  • Mode 2 When switch Q1 is turn off, the power saved in the inductor L1 is the DC connector through the diode D4 is discharged to the capacitor C2. Now the current iL1 is lessening. At the uniform time, in this way of manner, the voltage of the DC connection continues to increase. Now the intermediate condenser begins to charge the C1. Then the voltage Vc1 increases.

  • Mode 3 Since the current at the input inductor L1 becomes zero, its function is called the DCM. The intermediate condenser C1, is continuously holding the power, and keeps its charge. Alike behavior of the converter, the other − ve of the Vsc is felt for the half cycle (Fig. 8).

Fig. 8
figure 8

Circuit diagram of BL-CSCC

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The input voltage is offer in the usual Eq. (1). The equation for the value of the voltage now appearing in the inductor and switch amalgamation is given in the equation under,

$$V_{{{\text{i}}({\text{t}})}} = \left| {V_{{\text{p}}} \sin \left( {\omega t} \right)} \right|$$
(36)

The output voltage Vdc of the BL-CSC converter is,

$$V_{{{\text{dc}}}} = \frac{{{\text{DR}}}}{{\left( {1 - {\text{DR}}} \right)}}V_{{\text{i}}}$$
(37)

The duty rate DR (t) is depends on the required DC connection voltage and i/p voltage Vi (t).The equation of the instant value of the duty rate is,

$$D_{{\text{R}}} \left( t \right) \, = \frac{{V_{{{\text{dc}}}} }}{{V_{{\text{i}}} \left( t \right) + V_{{{\text{dc}}}} }}$$
(38)
$$D_{{\text{R}}} \left( t \right) = \frac{{V_{{{\text{dc}}}} }}{{\left| {V_{{\text{p}}} \sin \left( {\omega t} \right)} \right| + V_{{{\text{dc}}}} }}$$
(39)

By differentiating the VSI's DC connection voltage, the pace of BLDC's motor is controlled. So in the DC connection voltage Vdc, Instantaneous power Pins is taken as a task of the linear of Vdc.

$$P_{{{\text{ins}}}} = \left( {\frac{{P_{{{\text{mx}}}} }}{{V_{{{\text{dcmx}}}} }}} \right)V_{{{\text{dc}}}}$$
(40)

The critical value of the i/p inductive Lci is computed as follows:

$$L_{{{\text{ci}}}} = \frac{{V_{{\text{i}}} \left( t \right)D_{{\text{R}}} \left( t \right)}}{{2i_{{\text{i}}} \left( t \right)f_{{{\text{sw}}}} }} = \frac{{R_{{\text{i}}} D_{{\text{R}}} \left( t \right)}}{{2f_{{{\text{sw}}}} }}$$
(41)
$$L_{{{\text{ci}}}} = \left( {\frac{{V_{{{\text{sc}}}}^{2} }}{{P_{{{\text{ins}}}} }}} \right)\frac{{D_{{\text{R}}} \left( t \right)}}{{2f_{{{\text{sw}}}} }}$$
(42)

Estimation of the minimum critical value of the i/p inductor,

$$L_{{{\text{cimn}}}} = \left( {\frac{{V_{{{\text{scmn}}}}^{2} }}{{P_{{{\text{mx}}}} }}} \right)\frac{{D_{{\text{R}}} \left( t \right)}}{{2f_{{{\text{sw}}}} }}$$
(43)

The equation for intermediate capacitance C1 and C2,

$${\text{C}}1 \, = {\text{ C}}2 \, = \frac{{V_{{{\text{dc}}}} D_{{\text{R}}} \left( t \right)}}{{\Delta V_{{{\text{ic}}}} \left( t \right)f_{{{\text{sw}}}} R_{{{\text{le}}}} }}$$
(44)
$${\text{C}}1 = {\text{C}}2 = \frac{{V_{{{\text{dc}}}} D_{{\text{R}}} \left( t \right)}}{{\eta f_{{{\text{sw}}}} R_{{{\text{le}}}} \left[ {V_{{\text{i}}} \left( t \right) + V_{{{\text{dc}}}} } \right]}}$$
(45)

where \(\eta\) = permitted ripple voltage, \(R_{{{\text{le}}}}\) = emulated load resistance and \(V_{{{\text{ic}}}} \left( t \right)\) = intermediate capacitor’s voltage.

The value of the intermediate condenser ripple is computed at the topmost value. The equation is given below,

$${\text{C}}1 = {\text{C}}2 \, = \frac{{V_{{{\text{dcmx}}}} D_{{\text{R}}} \left( t \right)}}{{\eta f_{{{\text{sw}}}} R_{{{\text{le}}}} \left[ {\sqrt 2 V_{{{\text{scmx}}}} \left( t \right) + V_{{{\text{dc}}}} } \right]}}$$
(46)

The equation of the value of the DC coupling capacitor,

$$C_{{{\text{dc}}}} = \left( {\frac{{P_{{{\text{ins}}}} }}{{V_{{{\text{dc}}}} }}} \right)\frac{1}{{2\omega \kappa V_{{{\text{dc}}}} }}$$
(47)

2.8 Different Types of Driver System Control

2.8.1 Reference Voltage Generator (RVG)

A reference DC voltage that definition of Vdc is generated by a RVG; this is equivalent to the specific reference speed of the BLDC motor, To create the voltage error signal to be supplied to the speed controller, this voltage is differentiated to the perceived DC connection voltage. The reference voltage is produced by multiplying the voltage constant KV of the BLDC motor with the reference speed.

2.8.2 Speed Controller (SC)

Then the voltage error signal is furnished to the SC. This is for creating a controlled output for the PWM generation level, proportional integral controller. Equation for controller output signal VCO (k) and voltage error signal VER (k),

$$V_{{{\text{ER}}}} \left( k \right) \, = \, V^{\prime }_{{{\text{dc}}}} (k) - \, V_{{{\text{dc}}}} \left( k \right)$$
(48)
$$V_{{{\text{CO}}}} \left( k \right){\text{ }} = {\text{ }}V_{{{\text{CO}}}} \left( {k - 1} \right){\text{ }} + {\text{ }}K_{{{\text{pg}}}} \left[ {V_{{{\text{ER}}}} \left( k \right) + V_{{{\text{ER}}}} \left( k \right)} \right] + {\text{ }}K_{{{\text{ig}}}} V_{{{\text{ER}}}} \left( k \right)$$
(49)

where Kpg = proportional gain constants, Kig = integral gain constants.

2.8.3 PWM Generator

A constant frequency differential duty rate PWM the controlled release of the speed controller by a PWM generator, is created by comparing with a high-frequency saw-tooth generator.

If md (t) < VCO (k), Then S1 = S2 = 1, else S1 = S2 = 0. Where, S1, S2 = switch.

2.9 BLDC Motor

The dynamic modeling of the BLDC motor is rule by the equations given below. A phase voltage is given below; Vk refers to V1, V2, and V3.

$$V_{{\text{k}}} = \, R_{{\text{p}}} . \, i_{{\text{p}}} + \, T_{{{\text{dp}}}} .\lambda_{{\text{f}}} + \, e_{{\text{k}}}$$
(50)
$$V_{{\text{k}}} = \, V_{{{\text{pm}}}} - \, V_{{{\text{nm}}}}$$
(51)

where, Tdp = time differential operator, Rp = resistance per phase, ip = phase current, ek = back emf, \(\lambda_{{\text{f}}}\) = flux linkages, Vpm = phase at the mid point, Vnm = neutral at the mid point.

Flux connections are denoted by the equation below,

$$\lambda_{{\text{f}}} = \, L_{{{\text{Self}}}} * \, i_{{\text{p}}} - \, L_{{\text{M}}} \left( {i_{{\text{q}}} + \, i_{{\text{r}}} } \right)$$
(52)

where LSelf = self-inductance, LM = mutual inductance, If ‘p’ represents phase ‘1’, then ‘q’ and ‘r’ represent the phases ‘2’ and ‘3’, respectively, and vice versa (Fig. 9).

Fig. 9
figure 9

VSI circuit diagram

Full size image

The equation for the stator star-coupled three-phase torque at BLDC Motor,

$$\sum i_{{\text{p}}} = 0$$
(53)

Here, substitute Eq. (53) in Eq. (52), so the equation of flux inductance is,

$$\lambda_{{\text{f}}} = \left( {L_{{{\text{Self}}}} + \, L_{{\text{M}}} } \right) \, i_{{\text{p}}}$$
(54)

The phase current calculate by using (50) and (54) are derived as,

$$T_{{{\text{dp}}}} i_{{\text{p}}} = \frac{{V_{1} - i_{{\text{p}}} R_{{\text{p}}} - e_{1} }}{{\left( {L_{{{\text{Self}}}} + L_{{\text{M}}} } \right)}}$$
(55)

The sum of the expanded electromagnetic field of the BLDC motor,

$$T_{{{\text{em}}}} = \sum \frac{{e_{1} i_{{\text{p}}} }}{{\omega_{{{\text{rs}}}} }}$$
(56)

where Tem = electromagnetic Torque, \(\omega_{{{\text{rs}}}}\) = rotor speed electrical.

Since the induced EMFs are null, this disclosure of torque faces computational difficulty at zero speeds. So by exposing the back EMF as an operation of radar status angle, it is reorganized, so it can be noted as:

$$e_{1} = k_{{{\text{be}}}} f_{{\text{r}}} \left( \theta \right)\omega_{{{\text{rs}}}}$$
(57)

where kbe = back EMF constant, fr(θ) = functions of rotor position.

Substituting (57) into (56),

$$T_{{{\text{em}}}} = k_{{{\text{be}}}} \sum f_{{\text{r}}} \left( \theta \right)i_{{\text{p}}}$$
(58)

Equation of torque,

$$T_{{{\text{em}}}} = T_{{{\text{Load}}}} + C_{{\text{f}}} \omega_{{{\text{rs}}}} + M_{{\text{i}}} \left( {\frac{2}{{P_{{\text{n}}} }}} \right)T_{{{\text{dp}}}} \omega_{{{\text{rs}}}}$$
(59)

where TLoad = load torque, \(C_{{\text{f}}}\) = friction coefficient, \(M_{{\text{i}}}\) = moment of inertia, Pn = number of poles.

The Eq. (60) is used with Eq. (59) to find the torque time derivative. So the equation is,

$$T_{{{\text{dp}}}} \omega_{{{\text{rs}}}} = \frac{{T_{{{\text{em}}}} - T_{{{\text{Load}}}} - C_{{\text{f}}} \omega_{{{\text{rs}}}} }}{{M_{{\text{i}}} \left( {\frac{2}{{P_{{\text{n}}} }}} \right)}}$$
(60)

To avoid imbalance in the voltage utilized, the potential of the neutral terminal with zero energy must be considered. Equation (52) must be substitute in Eq. (51), the equation for as sum of the three phases,

$$\sum V_{{{\text{pm}}}} = R\sum i_{{\text{p}}} + \, \left( {L_{{{\text{Self}}}} + \, L_{{\text{M}}} } \right) \, T_{{{\text{dp}}}} \sum i_{{\text{p}}} + \sum e_{1}$$
(61)

Substituting Eq. (54) in (62) obtains,

$$\sum V_{pm} - 3V_{nm} = \sum e_{1}$$
(62)
$$V_{{{\text{nm}}}} = \frac{{\sum V_{{{\text{pm}}}} - \sum e_{1} }}{3}$$
(63)

The equation of the rotor spot derivative of the BLDC motor,

$$P_{{\text{r}}} (\theta ) = \omega_{{{\text{rs}}}}$$
(64)

where Eqs. (56), (61) and (65) regarded the equation current, speed and rotor position.

2.10 Voltage Source Inverter

Under is the sum for the release of the VSI for phase '1’,

$${\text{For}}\quad {\text{S}}1 = 1 \to {\text{V}}1_{{\text{O}}} = \left( {\frac{{V_{{{\text{dc}}}} }}{2}} \right)$$
(65)
$${\text{For}}\quad {\text{S}}2 = 1 \to {\text{V}}1_{{\text{O}}} = - \left( {\frac{{V_{{{\text{dc}}}} }}{2}} \right)$$
(66)
$${\text{For}}\quad {\text{S}}2 = 0 \to {\text{V}}1_{{\text{O}}} = 0$$
(67)

The ON and OFF conditions for S2 and S1 are, respectively, 1 and 0.

2.11 Sensorless Control Utilizing Terminal Voltage Sensing System

2.11.1 Terminal Voltage Sensing System(TVSS)

The hysteresis comparator with zero cross-detection technique achieves TVSS. In this it has the LPF of controlling the frequency ripples that are subject to high variations. At high speeds, there are comparators to compensate for the phase straggle of the Terminal Voltage (TV). In this condition; the motor neutral point voltage information is not used. Then perceive the 3 phase TV, each of the three phase TV essential a LPF to subdue high switching frequency noise or ripple. Since only 2 phases of the BLDC motor are running at any given time, during the open phase, back-EMF can be simplified from its TV.

During the two-phase abduction, the only variation betwixt the back EMF and its TV is, stator impedance is the voltage drop, and this may be less, differentiate to the DC voltage. Therefore the waveform of the TV is nearly the similar as that of the back EMF. TV can be utilized to discover the change points of the BLDC motor substitute of back EMF (Fig. 10).

Fig. 10
figure 10

Hysteresis comparator circuit diagram

Full size image

2.11.2 LPF

To repress immoderate switching noise or ripples, each of the three phase terminal voltages is sustain to a LPF. Therefore, to eliminate excessive harmonics in phase terminal voltages caused by inverter switching, three LPF are used here.

2.11.3 Hysteresis Comparator and Zero Cross Detection

To determine the correct transmission line of the inverter according to the radar position, and to compensate for the backlash of back EMF due to LPF, the hysteresis comparator is used. At terminal voltages, with these, the output changes caused by high frequency distortion can be prevented. Three hysteresis comparators are used here. The output of each terminal voltage emitted from the LPF is provided to the comparator.

As the rotor pace improves, the percentage contribution becomes phase lag for the whole duration. This setback would disarrange the back EMF arrangement. And at high speeds, transmission can cause serious problems. The phase lag of the transmission, in such a movement significant pulse torques may develop. The release of the hysteresis comparator is given to the zero crossover detector.

From three-stage hysteresis comparators, outputs become three transmission signals, then there are the six step PWM signals, this means that six gating signals are generated by the PWM method. Inverter switches control the boom and compassion of the signals along the margin of the transmission. Gating signaling is derived from hysteresis comparators and from each exchange event. By selecting Sensing and PWM correctly, without using the motor's unprejudiced point voltage data, back EMF signals can be obtained directly from the motor TV.

3 Results and Discussion

In this section, the comparative analysis of the 5 bridgeless converters reported in the top section is shown. In that comparison, using the five types of parameters are compared. They are Speed, THD, DPF, PF and Is.Below you will find how these five parameters are calculated.

Here speed values are taken from 450 to 2350 rpm and the input voltage values are taken from 90 and 290 V.

3.1 THCD (total harmonic current distortion)

THCD is the measure of existing compliant distortion. It is clarify as the energy of the foundational frequency current of the total of the energies of all the harmonic current elements.

$${\text{THCD }} = \frac{{\sqrt {I_{{{\text{D}}2}}^{2} + I_{{{\text{D}}3}}^{2} + I_{{{\text{D}}4}}^{2} \cdots + I_{{{\text{Dn}}}}^{2} } }}{{I_{{{\text{D}}1}} }} \times 100\%$$
(68)
$${\text{Crest}}\;{\text{factor}}\;\left( {{\text{CF}}} \right) = \frac{{\left| {I_{{\text{P}}} } \right|}}{{I_{{{\text{rms}}}} }}$$
(69)
$$I_{{{\text{rms}}}} = \sqrt {I_{{{\text{D}}1}}^{2} + I_{{{\text{D}}2}}^{2} + I_{{{\text{D}}3}}^{2} \cdots + I_{{{\text{Dn}}}}^{2} }$$
(70)

where IDn = individual HCD values, ID1 = Fundamental HCD value, ID2 = Second HCD values.

3.2 DPF (Displacement Power Factor)

At the base-line frequency, the DPF is established as the PF due to the phase change in V and I.

$${\text{DPF }} = \, \cos \, (\theta )$$
(71)

Here, \(\theta\) is the phase angle betwixt the base current and the voltage.

3.3 PF (Power Factor)

The proportional betwixt apparent power and true power. So the calculation of PF is,

$${\text{PF}} = \frac{{{\text{True}}\;{\text{power}}}}{{{\text{Apparent}}\;{\text{power}}}}$$
(7)

The multiply of the rms I and the rms V is called apparent power.

3.4 I S (Supply Current)

The IS is the load currents supplied to the loads by the constant current, switching current and outputs.

The THCD tells how much distortion of the current (Id) is there. If the Id is elevated, the wave of the current is not understandable. Thus, it is hugely tough to perfectly discover the value of the current wave. Therefore, in this contrast, the lowest THCD value is there only for the BL-CC. This is shown in Tables 1, 2.

Table 1 The value of THCD and DPF of bridgeless converters
Full size table
Table 2 The value of PF and IS of bridgeless converters
Full size table

This DPF expand the lifetime of the equipment. Hence, BL-CC converter has the best DPF value.

This PF reduces the heat dissipation of the apparatus and improves the life of the device. The converter with such a better PF is BL-CC. By varying the values of these parameters, BL-CC has a very high efficiency, so this BL-CC is the better of these five converters.

4 Conclusion

Using the proposed BLDC Drive method, generating results obtained for sensorless speed control, the isolated AC to DC converter has manifested the improve of power quality at AC mains. The hysteresis comparator technique has exceptional performance and sensing system. Moreover, the wider motor speed limits instantly, that means making it stable. Here is there a very important advantage of separating the inverter transmission from the speed control area. This enables the smooth and clean operation of the movement. The switch pattern required for the inverter is obtained using the terminal emf using hysteresis comparator. The increase in cost due to rotor position sensors is overcome by using this method and the noise undulation in the back emf can be reduced using this comparator technique. Also usage of sensorless techniques is highly recommended in rugged environments with wide range of operations and applications. Harmonics is been controlled by the proposed method, and therefore, various international standards of power quality improvement are achieved.