Synchronous Machine Armature Windings - 3 | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE) PDF Download

Behaviour of a loaded synchronous generator 

The simple working of the synchronous machine can be summed up as follows: A synchronous machine driven as a generator produces e.m.f.’s in its armature windings at a frequency f = np. These e.m.f.’s when applied to normal circuits produce currents of the same frequency. Depending on the p.f of the load, field distortion is produced, generating a mechanical torque and demanding an input of mechanical energy to satisfy the electrical output. As the stator currents change direction in the same time as they come from one magnetic polarity to the next, the torque is unidirectional. The torque of individual phases is pulsating just like in a single-phase induction machine - but the torque of a three-phase machine is constant for balanced loads.

For the cylindrical rotor machine the fundamental armature reaction can be more

Figure 22: Synchronous generator supplying a lagging pf load

convincingly divided into cross-magnetizing and direct-magnetizing components, since the uniform air-gap permits sinusoidal m.m.f s to produce more or less sinusoidal fluxes. Fig. 22 shows a machine with two poles and the currents in the three-phase armature winding produce a reaction field having a sinusoidally-distributed fundamental component and an axis coincident, for the instant considered, with that of one phase such as A − A′ . The rotor windings, energized by direct current, give also an approximately sinusoidal rotor m.m.f. distribution. The machine is shown in operation as a generator supplying a lagging current.

The relation of the armature reaction m.m.f. F_a to the field m.m.f. F_t is shown in Fig. 23.

The F_a sine wave is resolved into the components F_aq corresponding to the cross-component and F_ad corresponding to the direct-component, which in this case demagnetizes in accordance with Fig. 20. F_ad acts in direct opposition to F_t and reduces the effective m.m.f. acting round the normal magnetic circuit. F_aq shifts the axis of the resultant m.m.f. (and flux) backward against the direction of rotation of the field system.

Figure 23: Sinusoidal distribution of the components of armature reaction in a synchronous generator

Figure 24: Elementary synchronous motor action - Attraction of the unlike poles keep the rotor locked to the rotating field produced in the stator

Behaviour of a loaded synchronous motor Likewise when a synchronous machine operates as a motor with a mechanical load on its shaft, it draws an alternating current which interacts with the main flux to produce a driving torque. The torque remains unidirectional only if the rotor moves one pole-pitch per half-cycle; i.e. it can run only at the synchronous speed. In a balanced three-phase machine, the armature reaction due to the fundamental component of the current is a steady mmf revolving synchronously with the rotor - its constant cross-component producing a constant torque by interaction with the main flux, while its direct-component affects the amount of the main flux. A very simple way of regarding a synchronous motor is illustrated in Fig. 24. The stator, like that of the induction motor produces a magnetic field rotating at synchronous speed. The poles on the rotor (salient-pole is shown in Fig. 24 only for clarity), excited by direct current in their field windings, undergo magnetic attraction by the stator poles, and are dragged round to align themselves and locked up with with the stator poles (of opposite polarity- obviously). On no load the axes of the stator and rotor poles are practically coincident. When a retarding torque is applied to the shaft, the rotor tends to fall behind. In doing so the attraction of the stator on the rotor becomes tangential to an extent sufficient to develop a counter torque - however the rotor continues to rotate only at synchronous speed.
The angular shift between the stator and rotor magnetic axes represents the torque (or load) angle (as shown later, in the phasor diagram). This angle naturally increases with the mechanical load on the shaft. The maximum possible load is that which retards the rotor so that the tangential attraction is a maximum. (It will be shown later that the maximum possible value for the torque angle is 90 electrical degrees - corresponding to a retardation of the rotor pole by one half of a pole pitch). If the load be increased above this amount, the rotor poles come under the influence of a like pole and the attraction between the stator and rotor poles ceases and the rotor comes to a stop. At this point we say that the synchronous motor pulled out of step. This situation arises much above the rated loads in any practical machine.

It is to be noted that the magnetic field shown in Fig. 24 is only diagrammatic and for better understanding of the action of the synchronous machine - the flux lines may be considered as elastic bands which will be stretched by application of the mechanical load on the shaft. Actually the flux lines will enter or leave the stator and rotor surfaces nearly normally, on account of the high permeability of these members. In a salient-pole machine the torque is developed chiefly on the sides of the poles and on the sides of the teeth in a non-salient-pole machine.

Concept of Synchronous Reactance

The operation of the synchronous machine can be reduced to comparatively simple expression by the convenient concept of synchronous reactance. The resultant linkage of flux with any phase of the armature of a synchronous machine is due, as has been seen, to the combined action of the field and armature currents. For a simple treatment it is convenient to separate the resultant flux into components: (a) the field flux due to the field current alone; and (b) the armature flux due to the armature current alone. This separation does not affect qualitative matters, but its quantitative validity rests on the assumption that the magnetic circuit has a constant permeability. In brief the simplifying assumptions are: 1. The permeability of all parts of the magnetic circuit of the synchronous machine is constant - in other words the field and armature fluxes can be treated separately as proportional to their respective currents so that their effects can be superposed. 2. The air gap is uniform, so that the armature flux is not affected by its position relative to the poles - in other words we assume the rotor to be cylindrical 3. The distribution of the field flux in the air gap is sinusoidal. 4. The armature winding is uniformly distributed and carries balanced sinusoidal currents.

In other words, the harmonics are neglected so that the armature flux is directly proportional to the fundamental component of the armature reaction mmf implying that the armature reaction mmf is distributed sinusoidally and rotates at synchronous speed with constant magnitude.
Assumption (1) is roughly fulfilled when the machine works at low saturation; (2) and (3) are obviously inaccurate with salient-pole machines and assumption (4) is commonly made and introduces negligible error in most cases. The behaviour of an “ideal” synchronous machine can be indicated qualitatively when the above assumptions (1) to (4) are made.

The phasor diagrams Fig. 25 for the several conditions contain the phasors of two emfs viz. E_o and E . The latter is the e.m.f actually existing, while the former is that which would be induced under no-load conditions, i.e. with no armature current (or armature reaction).

Thus E_o is the e.m.f. corresponding to the flux produced by the field winding only, while E is that actually produced by the resultant flux due to the combined effect of stator and rotor ampere-turns. The actual e.m.f. E can be considered as E_o plus a fictitious e.m.f. proportional to the armature current.

Fig. 25 is drawn in this manner with E_r such that the following phasor relationship is satisfied:

E = E_o + E_r             (19)

It can be seen from Fig. 25, that E_r , is always in phase-quadrature with armature current and proportional to it (as per the four assumptions (1) to (4) above). The emf E_r is thus similar to an emf induced in an inductive reactance, so that the effect of armature reaction is exactly the same as if the armature windings had a reactance x_a = E_r /I_a . This fictitious reactance x_a can added to the armature leakage reactance x_l and the combined reactance ( x_a + x_l ) is known as the synchronous reactance x_s. The armature winding apart from these reactance effects, presents a resistive behaviour also. Synchronous impedance is a tern used to denote the net impedance presented by each phase of the alternator winding, consisting of both resistive and reactive components. The behavior of a synchronous machine can be easily predicted from the equivalent circuit developed using this synchronous reactance x_s, as explained in the following section.

Approximation of the Saturated Synchronous Reactance

Economical size requires the magnetic circuit to be somewhat saturated under normal operating conditions. However, the machine is unsaturated in the short-circuit test, and the synchronous reactance based on short-circuits and open-circuit test data is only an approximation at best. Nevertheless, there are many studies in which a value based on rated open-circuit voltage and the short circuit current suffices. Hence, in Fig. 29, if oc is rated voltage, ob is the required no-load field current, which also produces the armature current o′e on short circuit. The synchronous impedance assuming the armature winding is star-connected is, accordingly,

           20)

Except in very small machines, the synchronous reactance is much greater than the resistance (r_a ) of the armature and the saturated value as well as the unsaturated value of the synchronous reactance and therefore is considered equal to the magnitude of the synchronous impedance

       (21)

   
                                                                               (b)Motor unity power factor

(c) Generator                              (d)Generator zero power factor

Figure 25: Phasor diagrams for different operating conditions

The line of in Fig. 29 is more nearly representative of the saturated machine than is the air-gap line. On the basis of this line, an estimate of the field current can be obtained for a given terminal voltage, load current, and power factor. This is done by calculating E_af and making use of the saturated synchronous reactance as follows.

E_af = V + Z_sI                        (22)

The field current is that required to produce E_af on the line of.

Open-circuit and Short-circuit Tests 

The effect of saturation on the performance of synchronous machines is taken into account by means of the magnetization curve and other data obtained by tests on an existing machine. Only some basic test methods are considered. The unsaturated synchronous impedance and approximate value of the saturated synchronous impedance can be obtained form the open-circuit and short-circuit tests.

In the case of a constant voltage source having constant impedance, the impedance can be found by dividing the open-circuit terminal voltage by the short circuit current.
However, when the impedance is a function of the open-circuit voltage, as it is when the machine is saturated, the open-circuit characteristic or magnetization curve in addition to the short-circuit characteristic is required.

Figure 26: Synchronous generator(a) Open circuit (b) Short circuit

The unsaturated synchronous reactance is constant because the reluctance of the unsaturated iron is negligible. The equivalent circuit of one phase of a polyphase synchronous machine is shown in Fig. 26 for the open-circuit condition and for the short circuit condition. Now E_af is the same in both cases when the impedance Z_s. Where E_af is the open-circuit volts per phase and I_sc is the short-circuit current per phase.

Open-circuit Characteristic

Figure 27: (a) Open circuit characteristic and (b) Short-circuit characteristic

To obtain the open-circuit characteristic the machine is driven at its rated speed without load. Readings of line-to-line voltage are taken for various values of field current. The voltage except in very low-voltage machines is stepped down by means of instrument potential transformers. Fig. 27 shows the open-circuit characteristic or no-load saturation curve. Two sets of scales are shown; one, line to-line volts versus field current in amperes and the other per-unit open-circuit voltage versus per-unit field current. If it were not for the magnetic saturation of the iron, the open-circuit characteristic would be linear as represented by the air-gap line in Fig. 27. It is important to note that 1.0 per unit field current corresponds to the value of the field current that would produce rated voltage if there were no saturation. On the basis of this convention, the per-unit representation is such as to make the air-gap lines of all synchronous machines identical.

Short circuit Test

Figure 28: Connections for short-circuit test

The three terminals of the armature are short -circuited each through a currentmeasuring circuit, which except for small machines is an instrument current transformer with an ammeter in its secondary. A diagram of connections in which the current transformers are omitted is shown in Fig. 28.

The machine is driven at approximately synchronous (rated) speed and measurements of armature short-circuit current are made for various values of field current, usually up to and somewhat above rated armature current. The short-circuit characteristic (i.e. armature short circuit current versus field current) is shown in Fig. 27. In conventional synchronous machines the short-circuit characteristic is practically linear because the iron is unsaturated up to rated armature current and somewhat beyond, because the magnetic axes of the armature and the field practically coincide (if the armature had zero resistance the magnetic axes would be in exact alignment), and the field and armature mmfs oppose each other.

Unsaturated Synchronous Impedance 

The open circuit and short-circuit characteristics are represented on the same graph in Fig. 29. The field current oa produces a line-to line voltage oc on the air- gap line, which

Figure 29: Open-circuit and short circuit characteristic

would be the open-circuit voltage if there were no saturation. The same value of field current produces the armature current o’d and the unsaturated synchronous reactance is given by:

 phase, for a star connected armature                  (23)

When the open-circuit characteristic, air-gap line, and the short-circuit characteristic are plotted in per-unit, then the per unit value of unsaturated synchronous reactance equals the per-unit voltage on the air-gap line which results from the same value of field current as that which produces rated short-circuit (one-per unit) armature current. In Fig. 29 this would be the per-unit value on the air gap line corresponding to the field current og.