Precise analytical formula for starting time calculation of medium- and high-voltage induction motors under conventional starter methods

Abstract

Large medium- and high-voltage (MV and HV) squirrel-cage induction motors are widely used in most industrial processes. Their starting times are very much required for suitable setting of over-current-protective devices and assessing power quality of distribution power system. Mostly, the starting time can be precisely computed from time-domain numerical computation. This approach is rather tedious and time-consuming. Therefore, this paper presents precise analytical formula to evaluate the starting times of large MV and HV induction motors under conventional starting techniques. The motor simplified first-order dynamic model is employed to derive the formula. An accuracy of the newly proposed formula is evaluated by comparing the obtained starting times against those from laboratory measurement and numerical time-domain simulations under full fifth-order motor model. The studied results confirm that the starting times analytically calculated by the proposed compact formula closely agree with the measured and simulated time-domain results.

Appendices

Appendix A

List of coefficients of acceleration torque expression in (7):

$$\begin{aligned}&a_2 =R_\mathrm{th}^2 +(X_\mathrm{th} +X_\mathrm{lr} )^{2}\end{aligned}$$

(A1)

$$\begin{aligned}&a_1 =-2\left( {R_\mathrm{th}^2 +R_\mathrm{th} R_\mathrm{r} +(X_\mathrm{th} +X_\mathrm{lr} )^{2}} \right) n_\mathrm{s} \end{aligned}$$

(A2)

$$\begin{aligned}&a_0 =\left( {(R_\mathrm{th} +R_\mathrm{r} )^{2}+(X_\mathrm{th} +X_\mathrm{lr} )^{2}} \right) n_\mathrm{s}^2 \end{aligned}$$

(A3)

$$\begin{aligned}&b_4 ={-a_2 AT_\mathrm{m}^0 }/{n_\mathrm{s}^2} \end{aligned}$$

(A4)

$$\begin{aligned}&b_3 =-({a_1 A}/{n_\mathrm{s}^2 }+{a_2 B}/{n_\mathrm{s} })T_\mathrm{m}^0 \end{aligned}$$

(A5)

$$\begin{aligned}&b_2 =-({a_0 A}/{n_\mathrm{s}^2 }+{a_1 B}/{n_\mathrm{s} }+a_2 C)T_\mathrm{m}^0 \end{aligned}$$

(A6)

$$\begin{aligned}&b_1 =-\left( {{a_0 B}/{n_\mathrm{s} }+a_1 C} \right) T_\mathrm{m}^0 -{3U_\mathrm{th}^2 R_\mathrm{r} n_\mathrm{s} }/{\omega _\mathrm{sm}} \end{aligned}$$

(A7)

$$\begin{aligned}&b_0 ={3U_\mathrm{th}^2 R_\mathrm{r} n_\mathrm{s}^2 }/{\omega _\mathrm{sm}}-a_0 CT_\mathrm{m}^0 \end{aligned}$$

(A8)

Appendix B

Appendix B gives parameters (in ohm) of 4 kW and 350 HP motors.

Output	V	$R_\mathrm{s}$	$R_\mathrm{r}$	$X_\mathrm{ls}$	$X_\mathrm{lr}$	$X_\mathrm{m}$	$N_\mathrm{rated}$	f	J
4 kW	400 Y	2	1.14	2.7	2.7	60.7	1435	50	0.0463
350 HP	2400 $\Delta$	1.18	2.08	5.91	6.06	163.06	1730	60	10