FIGURE 9-6

Equivalent electrical circuit and phasor diagram of synchronous machine.

increased by increasing the power angle up to a certain limit, beyond which the rotor would no longer follow the stator field and will step out of the synchronous mode of operation. In the nonsynchronous mode, it cannot produce steady power.

9.3.2Excitation Methods

The synchronous machine excitation system must be designed to produce the required magnetic field which is controllable to control the voltage and the reactive power of the system. In modern high power machines, Xs can be around 1.5 units of the base impedance of the machine. With reactance of this order, the phasor diagram of Figure 9-6 can show that the rotor filed excitation required at rated load (100 percent load at 0.8 lagging power factor) is more than twice that at no load with the same terminal voltage. The excitation system has the corresponding current and voltage ratings, with capability of varying the voltage over a wide range of 1 to 3 or even more without undue saturation in the magnetic circuit. The excitation power, primarily to overcome the rotor winding I2R loss, ranges from 1⁄2 to 1 percent of the generator rating. Most excitation systems operate at 200 to 1,000 Vdc.

For large machines, three types of excitation systems — DC, AC and static — are possible. In the DC system, a suitably designed DC generator supplies the main field winding excitation through conventional slip rings and brushes. Due to low reliability and high maintenance requirement, the conventional DC machine is seldom used in the synchronous machine excitation system.

Most utility scale generators use the AC excitation system shown in Figure 9-7. The main exciter is excited by a pilot exciter. The AC output of a permanent magnet pilot exciter is converted into DC by a floor standing rectifier and supplied to the main exciter through slip rings. The main exciter’s AC output is converted into DC by means of phase controlled rectifiers, whose firing angle is changed in response to the terminal voltage variations. After filtering the ripples, this direct current is fed to the synchronous generator field winding.

An alternative scheme is the static excitation, as opposed to the dynamic excitation described in the preceding paragraph. In the static excitation

© 1999 by CRC Press LLC

FIGURE 9-7

AC excitation system for synchronous generator.

scheme, the controlled DC voltage is obtained from a suitable stationary AC source rectified and filtered. The DC voltage is then fed to the main field winding through slip rings. This excitation scheme has a fast dynamic response and is more reliable because it has no rotating exciters.

The excitation control system modeling for analytical studies must be carefully done as it forms a multiple feedback control system that can become unstable. The IEEE has developed industry standards for modeling the excitation systems. The model enters nonlinearly due to magnetic saturation present in all practical designs. The stability can be improved by supplementing the main control signal by auxiliary signals such as speed and power.

9.3.3Electrical Power Output

The electrical power output of the synchronous machine is as follows:

Using the phasor diagram of Figure 9-6, the current can be expressed as follows:

This part, when multiplied with the terminal voltage V gives the output power:

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FIGURE 9-8

Power versus power angle of round rotor and salient pole synchronous machine.

The output power versus the power angle is a sine curve shown by the solid line in Figure 9-8, having the maximum value at δ = 90°. The maximum power that can be generated by the machine is therefore:

max Xs

Some synchronous machine rotors have magnetic saliency in the pole structure. The saliency produces a small reluctance torque superimposed on the main torque, modifying the power angle curve as shown by the dotted line.

The electromechanical torque required at the shaft to produce this power is the power divided by the angular velocity of the rotor. That is as follows:

The torque also has the maximum limit corresponding to the maximum power limit, and is given as follows:

9.3.4Transient Stability Limit

The maximum power limit just described is called the steady state stability limit. Any loading beyond this value will cause the rotor to lose synchronism, and hence, the power generation capability. The steady state limit must not

© 1999 by CRC Press LLC