**Synchronous Machine Operation:**

The Synchronous Machine Operation 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 Synchronous Machine Operation but leads to easier understanding of the machine operation.

**Generating Machine:**

**Motoring Machine:**

**Power-angle Characteristics of Synchronous Machine Operation:**

Figure 8.29 shows the circuit diagrams and phasor diagrams of a Synchronous Machine Operation 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 Î´, 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 Î¦Â = electrical power (per phase) exchanged with the bus-bars - Î´ = Angle between E
_{f}and V_{t}Â and is called the**power angle**of the machine (Î´ has opposite sign for generating/motoring modes).

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

occurs at Î´Â = 90Â° beyond which the machine falls out of step (loses synchronism). The machine can be taken up to P_{e,max}Â only by gradually increasing the load. This is known as the **steady-state stability limit** of the machine. The machine is normally operated at Î´ much less than 90Â°. The phasor diagram of a generating machine under condition of P_{e,max} is drawn in Fig. 8.31. Obviously I_{a} will be several times max 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 Î´ varies such that E_{f} sin Î´ 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 EÌ…_{f}Â moves on a line parallel to VÌ…_{t} and at distance E_{f}sin Î´=P_{e}X_{s}/V_{t}Â from it. Since I_{a}cosÎ¦ = 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 }cos Î¦ = P_{e}/V_{t} from the origin. The current phasor IÌ…_{a} is always located at 90Â° to phasor IÌ…_{a}X_{s} (phasor joining tips to EÌ…_{f} and VÌ…_{t} in the direction of EÌ…_{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 PFÂ 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 Î´ continuously increases. The minimum permissible excitation, E_{f} (min), corresponds to the stability limit, i.e. Î´ = 90Â°. 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 Operation 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 Î´ 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 Synchronous Machine Operation. 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 Characteristics of Synchronous Machine Operation at

which means that E_{f} and V_{t}Â 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 currentÂ

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.