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 = 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_{ph}Kw

= 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^{-3}kW

PΦ = BavπDL, and 3Iph Zph/ πD = q

Output to motor = 1.11 x B_{av}πDL
x πD_{q} x n_{s} Kw η cos Φ x 10^{-3} kW

Q = (1.11 π^{2} B_{av}
q Kw η cos Φ x 10^{-3}) D^{2}L ns kW

Q = (11 B_{av} q Kw η cos Φ
x 10^{-3}) D^{2}L ns kW

Therefore Output Q = Co D^{2}L
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

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Design of Electrical Machines : Induction Motors : Output equation of Induction motor |

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