## Synchronous Reactance :

#### The armature reaction reactance and the leakage reactance present in a synchronous machine and acting at a same time. The two reactances are combined together and the sum is called the Synchronous reactance (Xs).

####
Z_{s} = √ (R_{a})^{2} + (X_{s})^{2}

####
E_{o} = No-Load emf

####
= √ ( V Cos φ + I*R_{a} )^{2} + ( V
Sin φ + I*X_{s} )^{2}

#### E = emf induced on load

####
It is vectorially less than E_{o} by I*X_{a}. Sometimes it is also written as E_{a}.

####
V = Terminal voltage. It is vectorially less than E_{o} by I*Z_{s}.

#### I = Armature current / phase

#### φ = Load p.f. angle

####
Z = √ (R_{a})^{2} + (X_{L})^{2}

####
Z_{s} = √ (R_{a})^{2} + (X_{L})^{2}

#### As the load on the alternator is increased, the terminal voltage changes ( for constant excitation ) due to the following reasons :

####

(i) voltage drop due to armature resistance, I*R_{a}.

####
(ii) voltage drop due to armature leakage reactance, I*X_{L}.

#### (iii) voltage drop due to armature reaction.

####
The voltage drop due to armature reaction may be accounted for by assuming the presence of a fictitious reactance X_{a} in the armature winding. The value of X_{a} is such that I*X_{a} of leakage reactance X_{L} and ( fictitious ) armature reactance X_{a} is known as synchronous reactance X_{s}.

#### i.e.,

####
X_{s} = X_{L} + X_{a}

_{s}= X

_{L}+ X

_{a}

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