Output equation of Induction motor

 output equation is the mathematical expression which gives the relation between the various physical and electrical parameters of the electrical machine. In an induction motor the output equation can be obtained as follows Consider an ‘m’ phase machine, with usual notations Out put Q in kW = Input x efficiency

 Input to motor = mV_ph I_ph cos Φ x 10^-3 kW For a 3 Φ machine m = 3

 Input to motor = 3V_ph I_ph cos Φ x 10^-3 kW Assuming

 V_ph = E_ph, V_ph = E_ph = 4.44 f Φ T_phKw  = 2.22 f ΦZphKw

 f = PN_S/120 = Pn_s/2,

 Output = 3 x 2.22 x Pn_s/2 x ΦZphKw I_ph η cos Φ x 10^-3 kW

Output = 1.11 x PΦ x 3I_ph Zph x ns Kw η cos Φ x 10^-3kW

PΦ = BavπDL, and 3Iph Zph/ πD = q

 Output to motor = 1.11 x B_avπDL x πD_q x n_s Kw η cos Φ x 10^-3 kW

 Q = (1.11 π² B_av q Kw η cos Φ x 10^-3) D²L ns kW

Q = (11 B_av q Kw η cos Φ x 10^-3) D²L ns kW

Therefore Output Q = Co D²L n_s kW

where

Co = (11 B_av q Kw η cos Φ x 10^-3)

V_ph = phase voltage ;

I_ph = phase current

Z_ph = no of conductors/phase

 T_ph = no of turns/phase

 Ns = Synchronous speed in rpm

ns = synchronous speed in rps

p = no of poles,

 q = Specific electric loading

 Φ = air gap flux/pole;

 B_av = Average flux density

kw = winding factor

η = efficiency cosΦ= power factor

D = Diameter of the stator,

 L = Gross core length

 Co = Output coefficient