The magnetizing reactance of a cylindrical

machine with uniform Airgap and with three

phase winding is,

Xm = 𝐾𝑤2 7.54𝑓𝑇𝑝ℎ

2

𝑝2𝑙𝑔𝐾𝑔

Per unit magnetizing reactance Xm = Iphxm/Eph

To obtain the armature reactance in the

direct & Quadrature axis for salient pole

machines, the expression must be multiply

by flux distribution co-efficients

Per unit direct axis armature reaction reactance

Xad= Ad1Xm

Whrere Ad1= Flux distribution co-efficient for direct axis

Ad1 = ρd ⨯A1

ρd =ɑ+𝑠𝑖𝑛ɑ

4𝑠𝑖𝑛ɑ/2

And A1=Bm1/Bg

Per unit quadrature axis armature reaction reactance

Xad= Aq1Xm

Where Aq1 = Flux distribution co-efficient for

quadrature axis

= Flux distribution Co-efficient for

quadrature axis

= 4𝜓+1

5-𝑠𝑖𝑛𝜓𝜋

𝜋

Where 𝜓 = 𝑟𝑎𝑡𝑖𝑜 𝑜𝑓 𝑝𝑜𝑙𝑒 𝑎𝑟𝑐 𝑡𝑜 𝑝𝑜𝑙𝑒 𝑝𝑖𝑡𝑐ℎ

Per unit values of unsaturated synchronous

reactance for the two axis are:

Direct axis synch. Reactance Xd = Xl +Xad

Quadrature axis synch. Reactance Xq = Xl +Xaq

Where Xl is the per unit leakage rectance

The phasor diagram based upon two reaction

theory for the generator id given in following fig.

In above fig.

V=Terminal Voltage,

I= Armature current per phase

Cos𝜙= Power factor, Lagging in this case

Eg=Generated Voltage per phase,

E0= No load voltage per phase

𝛿= Power angle

𝜓 = 𝜙 + 𝛿 for lag. Power factor

Id= Direct axis current= Isin𝜓

Iq= Quadrature axis current= Icos𝜓

Phasor dia. For Cylindrical rotor machine is shown

in below fig.

In above fig,

Xs = Synchronous Reactance = Xd

The reduction Factor for direct axis armature

mmf for cylindrical rotor machines

ρd = 𝜋2𝜓

8sin(𝜓𝜋/2)

****************

A Course in electrical Machine Design- By

A.K. Sawhney

Query ???

Thank you !