Electrical Machines 101 · Synchronous Machines

Synchronous generator under load: isolated island vs. infinite bus

X_s = 0.60 pu · R_a = 0 · linear OCC

Terminal voltage V_t 1.017 pu · +1.7% vs nominal

Machine state Within ±5% δ = 19.4° · stable

Load angle δ 19.4° E_a leads V_t

Real power P 0.733 pu · 74% of P_max

Reactive power Q 0.354 pu · supplied

Voltage regulation 27.8% (E_a − V_t) / V_t

Load & excitation

Load current |I_a| 0.80

0 (no load)1.50 pu

Load power factor 0.899 lag

← leadinglagging →

θ = +26° · inductive load

Field current I_f 1.30

0.202.00 pu

|E_a| = 1.300 pu (E_a = K·I_f)

Phasor diagram — phase a

Power–angle characteristic

Operating point — numeric view

Every quantity in per unit unless marked. Phase angles are referred to V_t.

Quantity	Symbol	Magnitude	Angle	Note

Model. Round-rotor, balanced, steady state, per unit on the machine base. Ē_a = V̄_t + jX_s·Ī_a with X_s = 0.60 pu and R_a neglected. Excitation is taken on the linear (air-gap) part of the OCC, so |E_a| = I_f in pu — saturation is not modelled.