Synchronous Machines - E-Courses

Electrical Machines II Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao
2.8.4 Unsaturated Synchronous Impedance
The open circuit and short-circuit characteristics are represented on the same graph
in Fig. 29. The field current 08 produces a line-to line voltage oc on the air- gap line, which
would be the open-circuit voltage if there were no saturation. The same value of field current
produces the armature current o’d and the unsaturated synchronous reactance is
Indian Institute of Technology Madras
Zdu = oc
√ 3o ′ d Ω phase,forastar connected armature (24)
When the open-circuit characteristic, air-gap line, and the short-circuit characteristic
are plotted in per-unit, then the per unit value of unsaturated synchronous reactance equals
the per-unit voltage on the air-gap line which results from the same value of field current
as that which produces rated short-circuit (one-per unit) armature current. In Fig. 29 this
would be the per-unit value on the air gap line corresponding to the field current og.
3 Synchronous Generator Operation
3.1 Cylindrical Rotor Machine
The synchronous generator, under the assumption of constant synchronous reactance,
may be considered as representable by an equivalent circuit comprising an ideal winding
in which an e.m.f. Et proportional to the field excitation is developed, the winding being
connected to the terminals of the machine through a resistance r and reactance (X+Xa) = Xs
all per phase. This is shown in fig. 30. the principal characteristics of the synchronous
generator will be obtained qualitatively from this circuit.
3.1.1 Generator Load Characteristics
Consider a synchronous generator driven at constant speed and with constant excitation.
On open circuit the terminal voltage V is the same as the open circuit e.m.f. Et
Suppose a unity-power-factor load be connected to the machine. The .flow of load current
produces a voltage drop Izs in the synchronous impedance, and terminal voltage V is reduced.fig.
31 shows the complexor diagram for three values of load. It will be seen that
the angle σ between Et and V increases with load, indicating a shift of he flux across the
pole faces due to cross- magnetization. The terminal voltage is obtained from the complex
summation
V + Iz, = EtorV = E − Iz8
(25)
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