The stator, also called the armature, carries the three-phase AC winding. The rotor, also called the field, carries the DC excitation or field winding. The field winding therefore rotates at the shaft speed and sets up the main magnetic flux in the machine.
The fundamental magnetic action between the stator and rotor is one of tangential pulling. In a generator, the rotor pole pulls the corresponding stator pole flux around with it. In a motor, the stator pole pulls the rotor pole flux around with it. The action is analogous to stretching a spring, the greater the power developed, the greater the pull and greater the corresponding distance that is created between the rotor and stator flux axes.
When a machine is not connected to the three-phase supply but is running at rated speed and with rated terminal voltage at the stator, there exists rated flux in the iron circuit and across the air gap. This flux cuts the stator winding and induces rated emf in winding and hence rated voltage at the main terminals. Consider what happens in a generator. Let the generator be connected to a load, or the live switchboard bus bars. Stator current is caused to flow. The current in the stator winding causes a stator flux to be created which tends to counteract the air-gap flux that is produced by the excitation. This reduction of air-gap flux causes the terminal voltage to fall. The terminal voltage can be restored by increasing the rotor excitation current and hence the flux. So the demagnetizing effect of the stator current can be compensated by increasing the field excitation current. This demagnetizing effect of the stator current is called ‘armature reaction’ and gives rise to what is known as the synchronous reactance, which is also called a ‘derived’ reactance.
Steady State Armature Reaction
A similar situation occurs when the rotor pole axis is at right angles to the axis of the stator coils. Here the magnetic reluctance is at its maximum value due to the widest part of the air gap facing the stator coils. The complete reactance in this position is called the quadrature axis synchronous reactance Xsq . Deducting Xa results in the quadrature axis reactance Xq .
Transient State Armature Reaction
The fundamental magnetic action between the stator and rotor is one of tangential pulling. In a generator, the rotor pole pulls the corresponding stator pole flux around with it. In a motor, the stator pole pulls the rotor pole flux around with it. The action is analogous to stretching a spring, the greater the power developed, the greater the pull and greater the corresponding distance that is created between the rotor and stator flux axes.
When a machine is not connected to the three-phase supply but is running at rated speed and with rated terminal voltage at the stator, there exists rated flux in the iron circuit and across the air gap. This flux cuts the stator winding and induces rated emf in winding and hence rated voltage at the main terminals. Consider what happens in a generator. Let the generator be connected to a load, or the live switchboard bus bars. Stator current is caused to flow. The current in the stator winding causes a stator flux to be created which tends to counteract the air-gap flux that is produced by the excitation. This reduction of air-gap flux causes the terminal voltage to fall. The terminal voltage can be restored by increasing the rotor excitation current and hence the flux. So the demagnetizing effect of the stator current can be compensated by increasing the field excitation current. This demagnetizing effect of the stator current is called ‘armature reaction’ and gives rise to what is known as the synchronous reactance, which is also called a ‘derived’ reactance.
The rotating field in the air gap of a synchronous machine is generally considered to be free of space harmonics, when the basic operation of the machine is being considered. In an actual machine there are space harmonics present in the air gap, more in salient pole machines than a cylindrical rotor machine. It is acceptable to ignore the effects of space harmonics when considering armature reaction and the associated reactance. Therefore the flux wave produced by the rotating field winding can be assumed to be distributed sinusoidally in space around the poles of the rotor and across the air gap.
If the stator winding, which consists of many coils that are basically connected as a series circuit, is not connected to a load then the resulting emf from all the coils is the open circuit emf of the phase winding. Closing the circuit on to a load causes a steady state current to flow in the stator coils. Each coil creates a flux and their total flux opposes the field flux from the rotor. The resulting flux in the air gap is reduced. The emf corresponding to the air-gap flux drives the stator current through the leakage reactance and conductor resistance of the stator coils. The voltage dropped across this winding impedance is small in relation to the air-gap voltage. Deducting this voltage drop from the air-gap voltage gives the terminal voltage of the loaded generator. In the circumstance described thus far the reduction in air-gap flux is called armature reaction and the resulting flux is much smaller than its value when the stator is open circuit. Restoring air gap and terminal voltage requires the field current to be increased, which is the necessary function of the automatic voltage regulator and the exciter.
When the rotor pole axis coincides with the axis of the stator coils the magnetic circuit seen by the stator has minimum reluctance. The reactance corresponding to the armature reaction in this rotor position is called the direct axis synchronous reactance Xsd . If the stator winding leakage reactance, Xa, is deducted from Xsd the resulting reactance is called the direct axis reactance Xd .
If the stator winding, which consists of many coils that are basically connected as a series circuit, is not connected to a load then the resulting emf from all the coils is the open circuit emf of the phase winding. Closing the circuit on to a load causes a steady state current to flow in the stator coils. Each coil creates a flux and their total flux opposes the field flux from the rotor. The resulting flux in the air gap is reduced. The emf corresponding to the air-gap flux drives the stator current through the leakage reactance and conductor resistance of the stator coils. The voltage dropped across this winding impedance is small in relation to the air-gap voltage. Deducting this voltage drop from the air-gap voltage gives the terminal voltage of the loaded generator. In the circumstance described thus far the reduction in air-gap flux is called armature reaction and the resulting flux is much smaller than its value when the stator is open circuit. Restoring air gap and terminal voltage requires the field current to be increased, which is the necessary function of the automatic voltage regulator and the exciter.
When the rotor pole axis coincides with the axis of the stator coils the magnetic circuit seen by the stator has minimum reluctance. The reactance corresponding to the armature reaction in this rotor position is called the direct axis synchronous reactance Xsd . If the stator winding leakage reactance, Xa, is deducted from Xsd the resulting reactance is called the direct axis reactance Xd .
Assume the generator is loaded and operating in a steady state. If the peak-to-peak or rms value of the stator current changes in magnitude then its corresponding change in magneto-motive force (mmf) will try to change the air-gap flux by armature reaction. Relatively slow changes will allow the change in flux to penetrate into the rotor. When this occurs an emf is induced in the field winding. This emf drives a transient current around a circuit consisting of the field winding itself and the exciter that is supplying the winding. The induction of current is by transformer action. An increase in stator current will be matched by an increase in field current during the transient state. A voltage drop will occur in the machine due to the armature reaction and the reduction in air-gap flux. Reactance is associated with this type of armature reaction.
When the rotor poles are coincident with the stator coils axis the armature reaction is a maximum and the reactance is called the direct axis transient reactance X’d .
When the rotor poles are coincident with the stator coils axis the armature reaction is a maximum and the reactance is called the direct axis transient reactance X’d .
The situation is different when the rotor poles are at right angles to the stator coils. There is no induction in the field circuit and the reluctance is high, being almost the same as for the steady state condition. In this situation the corresponding quadrature axis transient reactance X’q approximately equals the reactance Xq . Cylindrical rotors of two-pole high speed generators have a nearly uniform rotor diameter and almost constant air gap all around the periphery. Hence the reactance X’q is almost equal to X’d .
Sub-Transient State Armature Reaction
Sub-Transient State Armature Reaction
Again assume that the generator is loaded and operating in a steady state. In this situation the magnitude of the stator current is allowed to change rapidly, as in the case of a short circuit in the stator circuit. The additional flux produced by the stator winding will try to penetrate the surface of the rotor poles. Most oil industry generators are provided with damper bars to reduce the excursions in rotor speed during major disturbances. The bars are made of copper or copper alloy and placed longitudinally in the face of the rotor poles. They function in a manner similar to a squirrel cage induction motor when there is a transient change in rotor speed relative to the synchronous speed. As soon as the additional flux passes through the pole faces it will induce currents in the damper bars and the solid pole tips, by the process of transformer induction. These induced currents will set up flux in opposition in order to maintain constant flux linkages with the stator.
During this transient condition, or more appropriately called a sub-transient condition, the additional flux is forced to occupy a region consisting of air and the surface of the rotor poles. This is a high reluctance condition which gives rise to reactances of low values.
Some generators have the damper bars connected to a ring at either end of the pole structure, which provides some damping action from the quadrature axis. This provides a set of short-circuited coils in the quadrature axis, which are air cored and able to repel the flux that is attempting to enter their region.
By the same reasoning as for the ‘transient’ reactances so the sub-transient reactances are derived, and are called the direct axis sub-transient reactance X’’d and the quadrature axis subtransient reactance X’’q.
During this transient condition, or more appropriately called a sub-transient condition, the additional flux is forced to occupy a region consisting of air and the surface of the rotor poles. This is a high reluctance condition which gives rise to reactances of low values.
Some generators have the damper bars connected to a ring at either end of the pole structure, which provides some damping action from the quadrature axis. This provides a set of short-circuited coils in the quadrature axis, which are air cored and able to repel the flux that is attempting to enter their region.
By the same reasoning as for the ‘transient’ reactances so the sub-transient reactances are derived, and are called the direct axis sub-transient reactance X’’d and the quadrature axis subtransient reactance X’’q.
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