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This section describes various practical use diagrams of a salient pole machine that is operating under steady‐state conditions [2].

Most generators in operation are in the mode of supplying real power and either supplying or absorbing reactive power. A machine is said to have a lagging power factor when supplying reactive power and a machine is said to have a leading power factor when absorbing reactive power. It is also common to have the machine supply just real power and the machine is said to be at unity power factor. Figure 1.7-3 shows a diagram of a generator suppling power to the system with a lagging power factor and Figure 1.7-4 shows a diagram of the same generator with a leading power factor. When looking at these diagrams a few assumptions need to be kept in mind. First, the machine is in steady‐state operation, second, the machine is connected to an “infinite bus,” and lastly, magnetic saturation is neglected. The following explanation does not discuss how to develop these curves in detail and is left to the reader by referencing [2].

Figure 1.7-3 Vector diagram of generator with a lagging power factor.

Referring to Figure 1.7-3, the line OA represents the terminal voltage E_t, OG represents the internal generated voltage E_o, and I is the armature current lagging behind the terminal voltage by the angle φ which is the power factor angle. The armature current I can be represented by the direct and quadrature currents I_d and I_q, respectively. The vectors I_dX_d (parallel to E_o) and represented by AH and I_qX_q (perpendicular to E_o) and represented by HG are also mutually perpendicular. The angle (δ) is the torque or power angle. The diagram demonstrates the internal generated voltage is higher than the terminal voltage during lagging power factor operation. This makes sense as the generator must push out the reactive power and requires the higher internal potential voltage of E_o in order to accomplish this.

Figure 1.7-4 Vector diagram of generator with a leading power factor.

Referring to Figure 1.7-4, there are some key differences worth noting while operating at a leading power factor. The armature current I is now leading the terminal voltage E_t by the angle φ. The quadrature axis components I_q and I_qX_q are now larger in magnitude than when the machine was lagging. The takeaway from this diagram is that the terminal voltage is higher than the internal generated voltage. This also makes sense as the generator is now absorbing reactive power so the terminal voltage must be higher to push the power back into the machine.

It is important to recognize that as soon as the internal generated voltage is higher or lower than the terminal voltage, even by the smallest amount, reactive power will be supplied or absorbed by the machine accordingly.