V curves
Curves of armature current vs. field current (or excitation voltage to a different scale) are called V curves, and are shown in Fig. 58 for typical values of synchronous motor loads. The curves are related to the phasor diagram in Fig. 57, and illustrate the effect of the variation of field excitation on armature current and power factor for typical shaft loads. It can be easily noted from these curves that an increase in shaft loads require an increase in field excitation in order to maintain the power factor at unity. The locus of the left most point of the V curves in Fig. 58 represents the stability limit (_δ = −90◦). Any reduction in excitation below the stability limit for a particular load will cause the rotor to pullout of synchronism.
The V curves shown in Fig. 58 can be determined experimentally in the laboratory by varying If at a constant shaft load and noting Ia as If is varied. Alternatively the V curves shown in Fig. 58 can be determined graphically by plotting |Ia|vs.|Ef | from a family of phasor diagrams as shown in Fig. 57, or from the following mathematical expression for the V curves
Eqn. 74 is based on the phasor diagram and the assumption that Ra is negligible. It is to be noted that instability will occur, if the developed torque is less than the shaft load plus friction and windage losses, and the expression under the square root sign will be negative. The family of V curves shown in Fig. 58 represent computer plots of Eqn. 74, by tak- ing the data pertaining to a three-phase 10 hp synchronous motor i.e Vph = 230V and Xs = 1.2/phase.
Curves of armature current vs. field current (or excitation voltage to a different scale) are called V curves, and are shown in Fig. 58 for typical values of synchronous motor loads. The curves are related to the phasor diagram in Fig. 57, and illustrate the effect of the variation of field excitation on armature current and power factor for typical shaft loads. It can be easily noted from these curves that an increase in shaft loads require an increase in field excitation in order to maintain the power factor at unity. The locus of the left most point of the V curves in Fig. 58 represents the stability limit (_δ = −90◦). Any reduction in excitation below the stability limit for a particular load will cause the rotor to pullout of synchronism.
The V curves shown in Fig. 58 can be determined experimentally in the laboratory by varying If at a constant shaft load and noting Ia as If is varied. Alternatively the V curves shown in Fig. 58 can be determined graphically by plotting |Ia|vs.|Ef | from a family of phasor diagrams as shown in Fig. 57, or from the following mathematical expression for the V curves
Eqn. 74 is based on the phasor diagram and the assumption that Ra is negligible. It is to be noted that instability will occur, if the developed torque is less than the shaft load plus friction and windage losses, and the expression under the square root sign will be negative. The family of V curves shown in Fig. 58 represent computer plots of Eqn. 74, by tak- ing the data pertaining to a three-phase 10 hp synchronous motor i.e Vph = 230V and Xs = 1.2/phase.
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