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# Main Dimensions and Output equations - Design of Synchronous Machines

Internal diameter and gross length of the stator forms the main dimensions of the machine.

## Main Dimensions:

Internal diameter and gross length of the stator forms the main dimensions of the machine. In order to obtain the main dimensions it is required to develop the relation between the output and the main dimensions of the machine. This relation is known as the output equation.

## Output equations

Output of the 3 phase synchronous generator is given by

Output of the machine Q = 3Vph Iph x 10-3 kVA

Assuming Induced emf Eph = Vph

Output of the machine Q = 3Eph Iph x 10-3 kVA

Induced emf Eph = 4.44 f TphKw

= 2.22 f ZphKw

Frequency of generated emf f = PNS/120 = Pns/2,

Air gap flux per pole = Bav DL/p, and Specific electric loading q = 3Iph Zph/ D Output of the machine Q = 3 x (2.22 x Pns/2 x Bav DL/p x Zphx Kw) Iph x 10-3 kVA Output Q = (1.11 x Bav DL x ns x Kw ) (3 x IphZph ) x 10-3 kVA

Substituting the expressions for Specific electric loadings Output Q = (1.11 x Bav DL x ns x Kw ) ( D q ) x 10-3 kVA Q = (1.11 2 D2L Bav q Kw ns x 10-3) kVA

Q = (11 Bav q Kw x 10-3) D2L ns kVA

Therefore Output Q = Co D2Lns kVA or D2L = Q/ Cons m3

where Co = (11 Bav q Kw x 10-3)

Vph = phase voltage ; Iph = phase current Eph = induced EMF per phase Zph = no of conductors/phase in stator

Tph = no of turns/phase

Ns = synchronous speed in rpm

ns = synchronous speed in rps

= air gap flux/pole; Bav = Average flux density

kw = winding factor

From the output equation of the machine it can be seen that the volume of the machine is directly proportional to the output of the machine and inversely proportional to the speed of the machine. The machines having higher speed will have reduced size and cost. Larger values of specific loadings smaller will be the size of the machine.

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