A supply system with a large number of synchronous machines connected in parallel is referred to as infinite bus-bars. Any additional machine, whether to operate as a generator or as a motor is connected in parallel with the bus-bars.
Infinite bus-bars represent a system of large capacity whose frequency and the phase and magnitude of voltage are not affected even if there is a variation of excitation or power of a synchronous machine connected to it.
Here we will investigate the effect of varying the excitation and torque of the prime mover of a synchronous machine connected to infinite bus-bars.
Effect of Varying the Excitation of a Synchronous Machine Connected to Infinite Bus-Bars:
Consider an alternator, which has been just paralleled to infinite bus-bars and supplying no load (the torque supplied to its shaft being sufficient to meet with internal losses only). At this instant the open-circuit voltage of the incoming machine, E is equal and opposite of bus-bar voltage V, as shown in Fig. 13.12(a) and there is no current through the alternator circuit.
Let the excitation of the incoming machine be increased resulting increase in open-circuit voltage of the machine. The phasor sum of V and E is no longer zero and their phasor sum ER will cause a synchronising current Isy to flow in the alternator circuit making it to act as a generator supplying power to the bus-bars. This can be seen from the projections of Isy on the phasors E and V of Fig. 13.12 (b). But the torque supplied to the shaft of the incoming machine were such that it was supplying the friction, windage and iron losses of the machine only, and the condition of Fig. 13.12 (b) shows an electrical output of VIsy cos θ.
This indicates that at this particular instant, the prime mover is not supplying enough energy to make up the internal losses and electrical output, and therefore, the incoming generator will tend to slow down. Actually it will not slow down but will get retarded momentarily to change the time phase of E to the position shown in Fig. 13.12 (c). The delay in the time phase of E will cause a shift in ER in a clockwise direction and likewise a clockwise shift of Isy.
Due to shifting of Isy from the position of Fig. 13.12 (b) to that of 13.12 (c) the alternator synchronising current Isy shifts the direction of its power component and it will now receive energy from the bus-bars (VIsy cos θ1,) sufficient to meet the copper losses of the alternator. The amount of power transferred as a result of this change in excitation is determined by the change in the copper losses only.
The magnitude of the synchronising current Isy for this condition of operation is:
If there were no armature resistance, the synchronising current Isy would always be at 90° with respect to E and V. Thus variation in excitation will cause a large change in the reactive current supplied by the alternator, and because of armature resistance, there will be a slight change in the power that it receives or delivers to the bus. For all practical purposes it is assumed that variation in excitation causes change in power factor.
Figure 13.12 (c) shows stable operation of the machine on the bus-bars. A tendency of E to advance in time would tend to make it supply power to the bus-bars and thereby experiencing a retarding torque. A tendency for E to delay in time would tend to convert it into a synchronous motor, and it would be driven by energy drawn from the bus-bars.
It may be noted that when the alternator is overexcited, it operates at lagging power factor and when under-excited it operates at leading power factor.
When the excitation of an alternator connected to infinite bus-bars and supplying load at lagging of is increased, the alternator falls back (i.e., load angle decreases), power factor further drops and armature current increases due to reduced power factor; active component being constant.
Effect of Varying the Torque of the Prime Mover:
ADVERTISEMENTS:
When the torque of the prime mover of the alternator connected to the infinite bus-bars is increased (by increasing steam supply in the case of steam drive) the alternator connected to it will swing ahead in phase with respect to other alternator or alternators connected to the common bus-bars. It will cause a phase difference between V and E, the magnitude of E remaining unchanged. The resultant of these two voltages, ER will cause a synchronising current Isy. Thus the power delivered by the alternator, whose input power has been increased will increase by an amount equal to EIsy cos θ1.
Hence by increasing the torque of the prime mover of one alternator, it is further loaded and an equivalent load is removed from the other unit or units with which the machine is paralleled. If the output of the alternator, whose prime mover torque has been increased, become more than the total load being supplied, then the other machine or machines will operate as synchronous motor(s).
Thus active and reactive power loading of an alternator operating on infinite bus is controlled by controlling the input power to it and excitation respectively.
Power Output:
ADVERTISEMENTS:
Let us consider a 3-phase synchronous generator having effective resistance Re ohms per phase and synchronous reactance Xs ohms per phase. Let it be connected to the bus-bars having phase voltage of V volts and supply current I amperes at power factor cos ɸ. Let the phase angle between induced emf E and bus-bar voltage V be δ.
The phasor diagram is drawn with voltage phasor as reference phasor (Fig. 13.14).
Since effective resistance Re is generally negligible, therefore, synchronous impedance Zs can be taken equal to synchronous reactance Xs and internal angle θ = 90° and the expression for power output is reduced to the following expression:
Equation (13.13) is for electrical output in terms of constant bus-bar voltage V, induced emf E, (or excitation as the induced emf depends upon the excitation), synchronous impedance Zs, internal angle θ being equal to tan-1 Xs/Re and load angle δ.
Condition for maximum power output can be determined by differentiating the Eq. (13.13) with respect to δ and equating it to zero.
i.e., Power output for constant bus-bar voltage V and fixed excitation will be maximum when δ = θ and the expression for maximum power output per phase will become-
