Let us consider the phasor diagram for alternator as shown in the Fig. 1.

Fig. 1 |

Let E = E.M.F. induced in each phase

V = Terminal voltage

Φ = Phase angle between voltage and current

**δ**= Power angle

R

_{a }= Resistance of armature
X

_{s }= Synchronous reatance of alternator.**.**tanθ = X

^{.}._{s}/R

_{a }

**.**θ

^{.}.**= tan**

^{-1}(X

_{s}/R

_{a})

**α**= Φ +

**δ**

Power output per phase = V . I cos (V

**^**I)
= VI cos

Power input, P

_{i }= EI cos (E**^**I)
= E I cos (Φ +

**δ**) = E I cos**α**= I (E cos**α**)
= I (V cos Φ + I R

_{a})
= VI cosΦ + I

^{2}R_{a }
The voltage equation of alternator is given by,

P

_{i }is the power converted internally into electrical power from mechanical power which is given by,
P

_{i }= E^{o}. I
Note : With increase in

**δ**power increases and with decrease in**δ**power decreases. Power in case of synchronous machines depends on the angle**δ**. This angle**δ**is called power angle.
In case of large synchronous machines, X

_{s }>>> R**.**θ

^{.}.**= tan**

^{-1}(X

_{s}/R)= 90

^{o}(if resistance is neglected)

**θ = 90**

^{o}

Substituting this value in above expression for power

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