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 = mVph Iph cos Φ x 10-3 kW For a 3 Φ machine m = 3
Input to motor = 3Vph Iph cos Φ x 10-3 kW Assuming
Vph = Eph, Vph = Eph = 4.44 f Φ TphKw = 2.22 f ΦZphKw
f = PNS/120 = Pns/2,
Output = 3 x 2.22 x Pns/2 x ΦZphKw Iph η cos Φ x 10-3 kW
Output = 1.11 x PΦ x 3Iph Zph x ns Kw η cos Φ x 10-3kW
PΦ = BavπDL, and 3Iph Zph/ πD = q
Output to motor = 1.11 x BavπDL x πDq x ns Kw η cos Φ x 10-3 kW
Q = (1.11 π2 Bav q Kw η cos Φ x 10-3) D2L ns kW
Q = (11 Bav q Kw η cos Φ x 10-3) D2L ns kW
Therefore Output Q = Co D2L ns kW
where
Co = (11 Bav q Kw η cos Φ x 10-3)
Vph = phase voltage ;
Iph = phase current
Zph = no of conductors/phase
Tph = 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;
Bav = Average flux density
kw = winding factor
η = efficiency cosΦ= power factor
D = Diameter of the stator,
L = Gross core length
Co = Output coefficient
