Power-Quality Improvement in PFC Bridgeless SEPIC-Fed BLDC Motor Drive

BLDC motor specifications

Table 5 shows the specifications of BLDC motor used in the design of bridgeless SEPIC-fed BLDC motor drive.

Modeling of BLDC motor drive

A dynamic model of BLDC motor drive is developed by derg the mathematical equations consisting of time derivatives of phase current (di/dt), speed (dω/dt) and the rotor position (dθ/dt). These equations are modeled in MATLAB/Simulink to obtain the simulated performance of the BLDC motor drive. A generalized per phase voltage V_xn of the BLDC motor is given as [8, 18],

[19]

where x and n represent the phase and neutral terminal, R_s is the stator resistance, i_x is the per phase stator current, λ_x is the flux linkage and e_xn represents the back emf.

The flux linkage λ_x is represented as [8],

[20]

where L_s and M are the self and mutual inductance stator windings, respectively, and “x”, “y” and “z” represent the three-phases of BLDC motor.

Now for a three-phase star connected BLDC motor,

[21]

Hence, substituting eq. [21] in eq. [20] one gets

[22]

Now substituting eq. [22] in eq. [19], the current derivative is obtained as,

[23]

The speed derivative is obtained by arranging torque balance equation as [8],

[24]

where T_e and T_l represent the electromagnetic and load torque, respectively, J represents the moment of inertia and B is the frictional constant of the BLDC motor.

And finally, the position derivative of BLDC motor is expressed as [8],

[25]

Eqs. [23]–[25] represent the current, speed and position derivative, respectively, and hence the dynamic model of BLDC motor.

Moreover, the neutral voltage V_no with respect to mid-point “o” of the DC link as shown in Figure 4 is given as [18],

[26]

where V_xo and e_xn is the phase voltage with respect to terminal “o” and phase back emf with respect to terminal “n”, respectively.

Eq. [26] is used to obtain the per phase voltage V_xn as,

[27]

Eq. [26] is used with eq. [23] to obtain the dynamic model of the BLDC motor.

Finally, the generalized expression for the phase voltage V_xo is given as,

[28]

where S_U and S_L represent the switching states of upper and lower devices of a single leg of VSI which is to be replaced with “1” and “0” for “on” and “off” position of the switch, respectively.

Closed-loop stability of the proposed BLDC motor drive

A bridgeless SEPIC consists of two SEPIC operating for positive and negative half cycle. Hence the stability of SEPIC for the selected values of PI controller will determine the closed-loop stability of the overall system. The open-loop transfer function of the SEPIC is given as [19],

[29]

The small signal model parameters g_i, g_f and go for determining the parameters a₁, a₂, a₃, a₄ and b₂ are given as,

[30]

[31]

[32]

[33]

The parameters a₁, a₂, a₃, a₄ and b₂ are calculated as,

[34]

[35]

[36]

[37]

[38]

Moreover, the transfer function of the PI controller is given as,

[39]

where the values of K_p and K_i are selected as 0.3 and 3, respectively.

Hence, the closed-loop transfer function is given as,

[40]

After substituting the values of different parameters in the eqs. [29], [39] and [40], the open-loop transfer function and controller transfer function are obtained as,

[41]

[42]

Finally, the Bode plot for open loop and closed loop is obtained as shown in Figure 9. A positive and a high value of gain margin and phase margin are obtained, which determines the closed-loop stability of the system.

Figure 9

Bode plot of open-loop and closed-loop transfer functions showing closed-loop stability with positive gain and phase margin.