**Operating Characteristics of Synchronous Machine:**

The Operating Characteristics of Synchronous Machine are examined here under conditions of variable load and variable excitation. One of these quantities will be assumed to be held constant at a time while the other will be allowed to vary over a wide range. Further, here too the armature resistance will be assumed negligible. This does not significantly change the operating characteristic of the machine but leads to easier understanding of the machine operation. The more general case of the machine with armature resistance accounted for will be discussed in Sec. 8.9. By virtue of negligible resistance assumption, the electrical power at the machine terminals and the mechanical power at its shaft are simply related as follows:

**Generating Machine**

**Motoring Machine**

**Power-angle Characteristic **

Figure 8.29 shows the circuit diagrams and phasor diagrams of a synchronous machine in generating mode (Figs 8.29(a) and (c)) and motoring mode (Figs 8.29 (b) and (d)). The machine is assumed to be connected to infinite bus-bars of voltage V_{t}. It is easily observed from the phasor diagrams that in generating mode, the excitation emf E_{f} leads V_{t} by angle δ, while it lags V_{t} in the motoring mode. It follows from the phasor triangle OMP (Figs 8.29(c) and (d)) that

Multiplying both sides of Eq. (8.41) by V_{t}

where P_{e} = V_{t} l_{a} cos Φ = electrical power (per phase) exchanged with the bus-bars δ = Angle between E_{f} and V_{t} and is called the power angle of the machine (δ has opposite sign for generating/motoring modes).

The relationship of Eq. (8.42) is known as the power-angle characteristic of the machine and is plotted in Fig. 8.30 for given V_{t} and E_{f}. The maximum power

occurs at δ = 90° beyond which the machine falls out of step (loses synchronism). The machine can be taken up to P_{e,max} only by gradually increasing the load. This is known as the steady-state stability limit of the machine. The machine is normally operated at δ much less than 90°. The phasor diagram of a generating machine under condition of P_{e,max} is drawn in Fig. 8.31. Obviously /_{a} will be several timesmax larger than the rated machine current in this condition.

**Operation at Constant Load with Variable Excitation**

At constant load, from Eq. (8.42)

It is therefore, observed that at constant load, as the excitation emf E_{f}, is varied (by varying field current I_{f}), the power angle δ varies such that E_{f} sin δ remains constant. The machine behaviour is depicted by the phasor diagrams of Figs (8.32(a) and (b)). As E_{f} varies, the tip of phasor E̅_{f} moves on a line parallel to V̅_{t} and at distance E_{f}sinδ=P_{e}X_{s}/V_{t} from it. Since I_{a}cosΦ = constant, the projection of the current phasor on V_{t} must remain constant, i.e. the tip of the current phasor traces a line perpendicular to V_{t} at distance I_{a}cosΦ = P_{e}/V_{t} from the origin. The current phasor I̅_{a} is always located at 90° to phasor I̅_{a}X_{s} (phasor joining tips to E̅_{f} and V̅_{t} in the direction of E̅_{f}). The excitation (E_{f}) corresponding to unity power factor is known as normal excitation, while the excitation larger than this is called over-excitation and less than this is called under-excitation. The following conclusions* are drawn from the phasor diagrams of Figs 8.32(a)

**Generating Machine**

- The machine supplies a lagging power factor current when over-excited.
- The machine supplies a leading power factor current when under-excited.

**Motoring Machine**

- The machine draws a leading power factor current when over-excited.
- The machine draws a lagging power factor current when under-excited.

It is also easily observed from these phasor diagrams that the magnitude of the armature current exhibits a minimum when its excitation is continuously increased from an under-excited state. The nature of l_{a} versus excitation (I_{f}) plot for various values of load (real power) is shown in Fig. 8.33. These are known as V-curves of synchronous machine by virtue of their shape. Though only one figure is drawn for generating/motoring operation, the actual shape of V-curves for the two cases will not be identical. A little reflection will show that PF versus I_{f} plots will be inverted V-curves.

**Minimum Excitation**

From Figs. 8.32(a) and (b) it is seen that as excitation is reduced, the angle 5 continuously increases. The minimum permissible excitation, E_{f} (min), corresponds to the stability limit, i.e. δ = 90°. Obviously

Minimum field current and corresponding armature current for a given pu load at the limit of stability is indicated by the dotted curve in Fig. 8.33.

**Observation **

In a synchronous machine the real electrical power exchanged with the bus-bars is controlled by the mechanical shaft power irrespective of excitation. The excitation, on the other hand, governs only the power factor of the machine without affecting the real power flow. For example, in a generator if it is desired to feed more real power into the bus-bars the throttle must be opened admitting more steam into the turbine (coupled to generator) thereby feeding more mechanical power into shaft. As a consequence the power angle δ increases and so does the electrical power output (Eq. 8.42)). However, if it is desired to adjust the machine power factor, its excitation should be varied (well within the limit imposed by Eq. (8.46)).

**Compounding Curve **

The dotted curves of Figure 8.33 pertain to constant terminal voltage, constant power factor operation of a synchronous machine. For a generating machine operation these curves are called compounding curves. These are presented once again in Fig. 8.34 as the field current needed for a given armature current or kVA loading at a particular power factor for constant terminal voltage. These are useful guide for generator operation in a power house.

**Synchronous Condenser **

It has been seen above that a synchronous motor under over-excited condition operates at a leading power factor. Synchronous motors are therefore employed in large power

installations for improving the overall power factor of the installation.

At no-load with losses assumed negligible, a synchronous motor operates at

which means that E_{f} and V_{t} are in phase. It is seen from the phasor diagram of Fig. 8.35, that the machine (motor) draws zero power factor leading current

and draws zero power factor lagging current

Thus a synchronous motor at no-load behaves as a variable condenser or inductor by simply varying its excitation. The machine operated under such a condition (motor on no-load or light load) is known as a synchronous condenser and finds application in large integrated power systems for improving the power factor under heavy-load conditions and for deproving the power factor under light-load conditions, thereby controlling the voltage profile of the power system within reasonable limits.

**Dual-purpose Synchronous Motor **

Synchronous motor is used in an industry/factory for serving two purposes. It drives a constant speed mechanical load such as a large pump, a dc generator, etc. and at the same time it also corrects an otherwise low lagging pf of the electrical load such as induction motors and fluorescent tubes. Such a synchronous motor serving dual-purpose is called dual-purpose synchronous motor.