AC machine equations derivation

[CasualKilla]

Hi

 

Looking to get some understanding of machine sizing, but I cannot seem to find a source for the derivation of these output equations for the IM/SynM.

 

 

Could anyone help with this derivation or point me in the direction of a source?

 

CK

[Enthalpy]

1 HP is 0.746 kW.

 

eta is the efficiency, it relates mechanical (kilo)watts to electric active power in (kilo)watts

 

cos(phi) results from the phase lag between the voltage and the current. The product of rms V and I is in VA, only after multiplication by cos(phi) do you get active power in W.

Note carefully that this applies to sine current only. When a semiconductor rectifier or a neon lamp consumes a bizarre waveform current, a phase doesn't suffice to caracterize it.

 

The upper formulas could relate the rotor dimensions and angular speed, the induction and the current with the power, but it depends on what each letter means exactly. Only must be very careful about winding factors, peak, rms, mean, per-phase, per-turn, per-bar values in electric machines.

 

A good book in English is

chapman, "electric machinery fundamentals"

nice drawings and pictures, it helps.