Exposure to unbalanced currents…
As you know, generators and motors are supposed to operate with balanced three-phase loading, but exposure to unbalanced currents is inevitable. Unbalances could arise from many different sources like unbalanced loads, untransposed transmission line construction, faults and open phases, etc.
These unbalances appear as negative sequence current in the generator leads. By definition, negative-sequence quantities have a rotation opposite that of the power system. This reversed rotating stator current induces double frequency currents in rotor structures.
The resulting heating can damage the rotor very quickly.
Potentially damaging low-current conditions such as an open phase or restricted fault were undetectable.
With the advent of solid-state and microprocessor technology, relaying is now available to provide generator protection over a full range of unbalance conditions.
So what is negative sequence current?
The concept of negative-sequence current is rooted in symmetrical component methodology. The basic theory of symmetrical components is that phase currents and voltages in a three-phase power system can be represented by three single-phase components.
These are positive-, negative- and zero-sequence components. The positive sequence component of current or voltage has the same rotation as the power system. This component represents balanced load.
If the generator phase currents are equal and displaced by exactly 120°, only positive-sequence current will exist. A current or voltage unbalance between phases in magnitude or phase angle gives rise to negative and zero-sequence components.
The negative sequence component has a rotation opposite that of the power system. The zero-sequence component represents an unbalance that causes current flow in the neutral.
The negative sequence component is similar to the positive sequence system, except that the resulting reaction field rotates in the opposite direction to the d.c. field system. Hence, a flux is produced which cuts the rotor at twice the rotational velocity, thereby inducing double frequency currents in the field system and in the rotor body.
The resulting eddy currents are very large and cause severe heating of the rotor.
So severe is this effect that a single-phase load equal to the normal three-phase rated current can quickly heat the rotor slot wedges to the softening point.
They may then be extruded under centrifugal force until they stand above the rotor surface, when it is possible that they may strike the stator core.
A generator is assigned a continuous negative sequence rating.
For turbo-generators this rating is low – standard values of 10% and 15% of the generator continuous rating have been adopted. The lower rating applies when the more intensive cooling techniques are applied, for example hydrogen-cooling with gas ducts in the rotor to facilitate direct cooling of the winding.
Using this approximation it is possible to express the heating by the law:
I22t = K
- I2 = negative sequence component (per unit of maximum continuous rating)
- t = time (seconds)
- K = constant proportional to the thermal capacity of the generator rotor
For heating over a period of more than a few seconds, it is necessary to allow for the heat dissipated. From a combination of the continuous and short time ratings, the overall heating characteristic can be deduced to be:
where I2R is the negative phase sequence continuous rating in per unit of maximum continuous rating (MCR)
To illustrate the derivation of these components refer to the loading on the sample system generator shown in Figure 2.
The generator loading is unbalanced and therefore, negative- and/or zero-sequence current is present in addition to the positive-sequence current. The sequence currents can be resolved from the phase currents when magnitude and phase angle are known.
Mathematically, positive (I1), negative (I2) and zero (I0) sequence currents in a system with ABC rotation are defined as (Equation 1):
Substituting phase currents and angles from Figure 1 into Equation (1), the sequence currents are found to be:
The rated current for the sample system is 4370 A. The positive-sequence current is then 4108 A/4370 A = 0.94 pu and the negative-sequence current is 175 A/4370 A = 0.04 pu.
The sample system generator is connected to the delta winding of a Generator Step Up (GSU) transformer. With no neutral return path, zero-sequence current can not exist. The calculated zero-sequence current is a result of measurement errors and should be considered zero.
Effects of negative-sequence current
Magnetic field in the air gap that rotates at synchronous (rotor) speed in the same direction as the rotor. Because the rotor and the positive sequence induced rotor magnetic field move at the same velocity and direction, the field maintains a fixed position with respect to the rotor and no current is induced into the rotor.
Unbalanced current produces negative sequence current, which in turn produces a reverse rotating field in the air gap. This magnetic field rotates at synchronous speed, but in a reverse direction to the rotor.
Portions of the resulting induced current path present high electrical resistance to the induced current. The result is rapid heating.
Damage due to loss of mechanical integrity or insulation failure can occur in seconds.
Cylindrical Rotor Generators
A cylindrical rotor is constructed from a solid-steel forging with slots cut along its length. Each field coil requires two slots, one for each side of the coil winding. A slot may contain one or more coil windings.
The ridges between the slots are called teeth. Figure 3 illustrates the rotor configuration.
Groves are machined into the sides of each tooth to allow wedges to be forced in along the full length of the slot. The wedges hold the field windings in the slots. In some machines, conducting strips are installed in the slots between the wedge and the field coil.
These strips are connected at the retaining rings to provide a low-resistance path for the induced currents. The loops formed by these strips are known as amortisseur windings.
The slot configurations of the wedge, field coil and the optional amortisseur winding are shown in Figure 4.
At the ends of the rotor body, the retaining rings hold the ends of the field windings in place against centrifugal force. The retaining rings are usually shrink fit to the rotor body, but in older machines they can be free floating with random contact with the rotor body.
The induced 120 Hz currents flow in loops along the body of a cylindrical rotor, as shown in Figure 5. There are as many current loops in the rotor as there are stator poles.
When alternating current passes through a conductor, in this case the rotor body, current densities are not uniform.
The “skin effect” causes alternating current to migrate to the outer surface of the conductor. This tendency increases with frequency.
In a cylindrical rotor, the 120 Hz induced current occupies a cross-section extending from the surface to a depth no greater than 0.1 to 0.4 inches. This forces the induced current into the teeth and wedges at the rotor surface. The resulting high current density significantly increases rotor resistance for 120 Hz current over that for DC or 60 Hz current.
Higher resistance produces higher losses and more heat per amp for the 120 Hz current than for lower frequency current.
The negative sequence tolerance of a generator is dependent on good electrical contact being maintained between rotor structures. Low resistance minimizes heating and prevents arcing at contact points. Designers include many features to improve conductivity.
These include the addition of amortisseur windings in the rotor slots to form low-resistance paths across the rotor surface. The ends of the amortisseur windings are connected to the retaining rings to provide a low-resistance bridge from the slot to the ring.
Aluminum slot wedges can also be used to reduce resistance in this current path.
Silver-plated aluminum fingers can provide a low-resistance current path from the wedges to the retaining rings. The rotor surface at the location of the retaining ring’s shrink fit is often silver-coated to minimize resistance and heating at the junction.
Two types of rotor failures are associated with unbalanced current.
Overheating of the slot wedges will cause annealing and a shear failure against the force of material in the slots. The second failure would be the retaining ring. Excessive heating can cause a shrink fit retaining ring to lift free of the rotor body. This would pose two problems.
The retaining ring may not realign after it cools, reseating in a cocked position on the rotor body. Vibration would result.
Also, the loss of good electrical contact while floating would result in pitting and burning at points of intermittent or poor contact. Retaining rings that are designed to float will also experience arc damage at points of intermittent contact or poor conductivity.
The resulting localized high temperatures can embrittle areas of the ring and lead to cracking under the varied stress of repeated unit startup and shutdown.
The heating characteristics of various designs of generator are shown in Figure 6 below.
Salient Pole Generators
Salient pole generators normally have amortisseur winding in the form of conductive bars spaced across the face of each rotor pole. The ends are brazed to form a low-resistance path on the pole face.
There are two basic types of amortisseurs: Non-connected amortisseur windings are isolated on each pole face. Connected amortisseurs have conducting bars that bridge between poles to interconnect the ends of all the amortisseurs groups at each pole.
However, amortisseurs’ current tends to flow in the outer bars and the induced current can cause stress damaging due to unequal expansion of the bars.
If the amortisseurs are not connected between poles – A large portion of the current induced in these windings flows down the pole body into the dovetail that holds the pole to the rotor then back into the adjacent pole. The junction at the dovetail will afford resistance, thus producing heat that can damage insulation and the rotor structure.
If the amortisseurs are connected between poles – The dovetail current is sharply reduced, but high current will flow in the connection between poles.
Connecting the amortisseurs also has a current balancing effect on the pole face bars.
Salient-pole machines with connected amortisseurs will have a higher negative sequence current capability than those without. The limiting components on the connected machines are often the bars that bridge the poles.
The large induced current flowing in these bars can cause sufficient heat to anneal the bar, resulting in mechanical failure under centrifugal force.
The negative-sequence current produces a reverse rotating magnetic field in the air gap. This field produces a shaft torque pulsation at twice line frequency. The magnitude of the torque is proportional to the per unit negative-sequence current in the stator. The pulsations are transmitted to the stator.
If the stator is spring mounted, the pulsation will be absorbed. Without spring mountings, the pulsation will be transmitted to the stator foundation, where they can be a design factor.
In general, problems associated with torque pulsation are secondary to rotor heating concerns.
- Protective relaying for power generation systems by Donald Reimert
- Network protection and automation guide by Alstom