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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.

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 = 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,

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

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