Ferroresonance occurs when an unloaded 3-phase system consisting of an inductive and a capacitive component is interrupted by single phase means. In practice this is typical of a high voltage electrical distribution network of transformers (inductive component) and power cables (capacitive component). If such a network has no load and the applied voltage is then interrupted on a single phase, a ferroresonance may be observed. If the remaining phases are not interrupted and the phenomenon continues, overvoltage can lead to the breakdown of insulation in connected components resulting in failure.
The phenomenon can be avoided by maintaining a minimal load on the circuit or by interrupting the applied voltage by a 3-phase interrupting device such as a ganged (3 pole) circuit breaker.
Ferroresonance is a mysterious phenomenon that seems to occur capriciously, causing much concern among utility operating personnel. It generally occurs during a system imbalance, usually during switching, that places capacitance in series with transformer magnetizing impedance. This can result in high overvoltages that can cause failures in transformers, cables, and arresters. Any system capacitance can be involved in ferroresonance, but the major concern is about underground cable capacitance.
As utilities moved cable systems into a 25-kV or 35-kV class, they found ferroresonance to be much more common than at lower voltage levels. They found they had to be more careful about how they switched the cable and how they arranged switch points to minimize the amount of cable isolated with lightly loaded transformers during switching. Ferroresonance is a greater problem at the higher voltage levels because the relative ratios of losses, magnetizing impedance and cable capacitance fall into a range more likely to produce ferroresonance. Ungrounded transformer primary connections go into ferroresonance quite easily. Therefore, many utilities no longer employ these connections and have switched to grounded-wye/grounded-wye connections for their three-phase loads fed from underground cable systems.
Grounded-wye transformers comprised of three separate units are virtually immune to the common varieties of ferroresonance. Grounded-wye/grounded-wye three-phase pads with 4-or 5-leg cores are less susceptible to ferroresonance than delta or ungrounded-wye connections, but they are not immune. They simply require more cable length and some different transformer characteristics. The common core configuration for the three-phase padmounts provides the necessary coupling between phases to produce ferroresonance.
There are several different modes of ferroresonance possible with grounded-wye 5-leg core transformers with sustained overvoltages reaching 2,0 to 2,5 per unit for some modes. Of course, if allowed to persist, these overvoltages might cause transformer failure, cable failure, and customer appliance failure. Frequent symptoms often reported are failed arresters, customer complaints of fluctuating voltage, and bubbled or charred paint on the transformer tank when the flux gets into the tank.
The evaluation of ferroresonance ties in closely with the decision of applying arresters on the cable system. If surge arresters are not installed on the cable system, it has no protection against overvoltages. This could contribute to premature cable failure or transformer failure if allowed to persist. On the other hand, if arresters are applied, arrester duty during phase-by-phase switching operations is a concern, and there is the possibility that arresters might fail violently.
The most dangerous time is when phase-by-phase cable switching occurs during construction of a subdivision or commercial area. The transformer involved might have no load and there will be more times that the transformer is exposed to the condition with one or two open phases.
However, ferroresonance can also occur accidentally due to such things as a faulty connector or splice opening, or an overhead line feeding the cable opening due to such things as an automobile collision with a pole. The no-load condition also occurs when customers install automatic relaying to disconnect from the utility at the first sign of trouble.
Ferroresonance is a general term applied to a wide variety of interactions between capacitors and iron-core inductors that result in unusual voltages and/or currents. In linear circuits, resonance occurs when the capacitive reactance equals the inductive reactance at the frequency at which the circuit is driven. Iron-core inductors have a nonlinear characteristic and have a range of inductance values. Therefore, there might not be a case where the inductive reactance is equal to the capacitive reactance, but yet very high and damaging overvoltages occur.
Because the phenomenon is nonlinear, it is difficult to visualize all the possible behaviours. The usual way of explaining ferroresonance is to consider the graphical steady-state solution to the simple series L-C circuit shown in the figure. This approximates the conditions in the power system that most frequently lead to ferroresonance. Keep in mind, however, that this simple example describes the steady-state solution. In reality, transient events might dominate and this graphical solution is inadequate to describe all that goes on.
If L is linear, the graphical steady-state solution to this circuit is shown in the figure. The intersection of the inductive reactance, X, line with the capacitive reactance, X, line yields the current in the circuit and the voltage across the inductor. These two lines represent the solution to the equation :
VL = (jωL)I =(jXL)I = V - (-jXC)I
At resonance, these two lines become parallel, yielding solutions of infinite voltage and current. Of course, this assumes lossless elements. Losses in the circuit can be represented graphically by converting the capacitance line into an ellipse.
Consider the case of the nonlinear, saturable inductor. The graphical solution is shown in the figure. It is apparent that there can be as many as three intersections of the capacitor line with the inductor curve. Intersection 2 is an unstable operating point, and the solution will not remain there in the steady state. However, it might pass through this point during a transient. Intersections 1 and 3 are stable and will exist in the steady state. Clearly, if the intersection 3 solution occurs, there will be both high voltages and high currents.
For small capacitances, the XC line is very steep, usually resulting in only one intersection in the third quadrant. The capacitive reactance is larger than the inductive reactance, resulting in a leading current and higher than normal voltages across the capacitor. The voltage across the capacitor is the length of the line from the system voltage intersection to the intersection with the inductor curve. As the capacitance increases, multiple intersections can develop as shown. The natural tendency then is to achieve a solution at intersection 1, which is an inductive solution with lagging current and little voltage across the capacitor. Note that the voltage across the capacitor will be the line-to-ground voltage on the cable in the typical ferroresonance case.
For a slight increase in the voltage, the capacitor line would shift upward, eliminating the solution at intersection 1. The solution would then try to jump to the third quadrant. Of course, the resulting current might be so great that the voltage then drops again and we get the solution point jumping between 1 and 3. Indeed, phenomena like this are observed during instances of ferroresonance. The voltage and current appear to vary randomly and unpredictably.
In the usual power system case, ferroresonance occurs when a transformer becomes isolated on a cable section in such a manner that the cable capacitance appears to be in series with the magnetizing characteristic of the transformer. For short lengths of cable, the capacitance is very small and there is one solution in the third quadrant at relatively low voltage levels. As the capacitance increases the solution point creeps up the saturation curve in the third quadrant until the voltage across the capacitor is well above normal. These operating points can be relatively stable, depending on the nature of the transient events that precipitated the ferroresonance.
Many utilities have operated 12kV systems for many years without experiencing any known ferroresonance. When some utilities switched to 25 and 35-kV levels in the 1960s and 1970s, they were caught by surprise at how easily ferroresonance developed and they suffered adverse consequences. This situation has led to the belief in some circles that ferroresonance is a problem unique to 25-kV and 35-kV levels. The fact is ferroresonance can occur at any voltage level. It is just a matter of having the right circuit parameters present at the right time. The reason that ferroresonance is unlikely to occur at 12kV is not completely known, but it is probably safe to speculate that the required combination of cable capacitance, magnetizing impedance, and low losses is less likely to occur.
The figure compares the graphical solution of the series LC circuit used to illustrate ferroresonance concepts for 12kV and 25kV transformers. For the same size transformer with the same percent magnetizing impedance, the actual ohmic value of the magnetizing impedance is 4 times greater at 24kV. The capacitance of the 25 kV cable will be similar to that of the same-sized 15-kV cable. Therefore, the capacitance line on the figure is drawn at the same slope in both cases.
For the 12kV transformer, the capacitor line intersects the saturation curve at a point where the voltage is lower than normal. In contrast, the same capacitance slope intersects the 25-kV saturation curve well above the knee of the curve, which will typically result in voltages of at least 130 +. As the capacitance increases (cable length increases), the capacitance line will pivot clockwise. It will intersect the saturation curve of the 25 kV transformer in the first quadrant at a much shorter length than for the 12kV transformer. This results in the development of other ferroresonant modes.
Another factor might be related to the age of the systems. Typical 12 kV systems contain many older transformers. Economic pressures in recent years have resulted in distribution transformers with lower losses and steeper magnetizing curves. This combination increases the range of capacitance for which ferroresonance can occur.
There are two main circuit configurations that cause ferroresonance:
There are two additional conditions that must be met:
These conditions can be met at a variety of times. The low resistive load requirement is often met on new construction when there might be no load on the transformer or only a few small loads. When the load on the transformer increases after a period of time, ferroresonance becomes less likely. Some common circumstances leading to ferroresonance include:
Normally, one might expect to be able to do load-break switching on older circuits during an emergency without threat of ferroresonance because of the presence of load. However, many industrial loads will shut down during storms when power interruptions are occurring. This leaves the transformer lightly loaded and more susceptible to ferroresonance than one might normally expect.
There are several modes of ferroresonance with varying physical and electrical displays. Some have very high voltages and currents while others have voltages close to normal.
There might or might not be failures or other evidence of ferroresonance in the electrical components. Therefore, it might be difficult to tell if ferroresonance has occurred in many cases unless there are witnesses or power quality recording instruments.
One thing common to all types of ferroresonance is that the steel core is driven into saturation, often deeply and randomly (otherwise, it is conventional resonance and not considered ferroresonance). As the core goes into a high flux density, it will make an audible noise due to the magnetostriction of the steel and to the actual movement of the laminations. In ferroresonance, this noise is often likened to shaking a bucket of bolts or to a chorus of a thousand hammers pounding on the transformer from within. In any case, the sound is distinctively different and louder than the normal hum of a transformer. It is difficult to describe accurately, but if one has the opportunity to be standing near a transformer that goes into ferroresonance, as one experienced person put it, "it will incite the 'fight-or-flight' reflex to want to flee".
Another common symptom of the high magnetic field is due to stray flux heating in parts of the transformer where magnetic flux is not expected. Since the core is saturated repeatedly, the magnetic flux will find its way into the tank wall and other metallic parts.
One possible side effect is the charring or bubbling of paint on the top of the tank. This is not necessarily an indication that the unit is damaged, but damage can occur in this situation if the ferroresonance has persisted sufficiently long to cause overheating of some of the larger internal connections. This can in turn damage insulation structures beyond repair.
If high overvoltages accompany the ferroresonance, there could be electrical damage to both the primary and secondary circuits. Surge arresters are common victims. They are designed to intercept brief overvoltages and clamp them to an acceptable level. While they might be able to take several overvoltage events, there is a definite limit to how much energy they can absorb. Ferroresonant modes with much available energy and high voltages would be expected to fail arresters quickly. However, even modes with little energy available can cause arrester failure if the ferroresonance is allowed to persist for many seconds and minutes.
With surge protectors common in computers and other consumer appliances, office equipment, and factory machines, these are probably the most common casualties of ferroresonance. In one case that was investigated, an auto struck a power pole causing one phase to become open circuited. This caused ferroresonance in a three-phase transformer feeding a shopping mall through a run of several hundred metres of cable. When utility personnel arrived on the scene, they found a circular spot of charred paint on top of the mall's service transformer. In addition, many point-of-sale cash registers in the mall were damaged by the sustained overvoltages, mostly, it is believed, due to the failure of MOV surge protectors in the power circuits. A number of primary arresters on the overhead line had also failed and blown their isolators.
Customers are frequently subjected to a wavering voltage magnitude. Light bulbs will flicker between very bright and dim. Some electronic appliances are reportedly very susceptible to the voltages that result from some types of ferroresonance. The failure mode is not known. Perhaps, it is simply MOV failure in the front end. These frequently fail catastrophically, going into thermal runaway and then burning open with considerable arcing display. This might do nothing more than pop a breaker, but surge protection is lost for any subsequent surge that might damage the appliance.
The transformers themselves can usually withstand the overvoltages without failing. Of course, they would not be expected to endure this stress repeatedly because the forces often shake things loose inside and abrade insulation structures. The cable is also not greatly in danger unless its insulation stress had been reduced by aging or physical damage. It might be difficult to clear arcs when pulling cable elbows if ferroresonance is in progress. The currents might be much higher than expected and the peak voltages might be high enough to cause re-ignition of the arc.
Some utilities will not perform cable switching involving three-phase padmount transformers without first verifying that there is substantial load on the transformers. Some have reported carrying a "light board" in the line truck for such purposes. This is a dummy resistive load consisting of several light bulbs that can be clipped onto the secondary bushings of the transformer of the smaller 3-phase pads until switching is complete.
One of the common solutions to ferroresonance during cable switching is to always pull the elbows and energize the unit right at the primary terminals. This will normally work because there is no external cable capacitance to cause ferroresonance. There is a little internal capacitance, but the losses of the transformers are usually sufficient to prevent resonance with this small capacitance.
Unfortunately, modern transformers are changing the old rules of thumb. Reports have circulated claiming that some of the newer low-loss transformers, particularly, those with amorphous metal cores, will go into ferroresonance by themselves. The combination of lower losses and steeper saturation curves seems to be the reason.
A network with insulated neutral potential can randomly switch from symmetrical operation to ferroresonance condition and vice-versa as a consequence of transient in the circuit (a fault, a switching operation, etc.). When ferroresonance occurs, a permanent voltage between neutral and earth exists and phase voltages of the circuit become asymmetrical. Under these conditions, grounded-neutral, wye-connected potential transformers are subjected to a permanent over-excitation flux and might be damaged, or potential transformer fuses, when adopted to protect the devices, might operate.
If potential transformers have a broken delta-connected secondary to detect ground faults, sometimes ferroresonance can give false indications of faults because it produces an abnormal voltage across the broken delta-connected winding.
The extent of ferroresonance for insulated neutral potential network with grounded neutral, wye-connected potential transformers depends on:
Experimentally it has been found that for “standard” PTs and for circuits with low zero-sequence losses, ferroresonance can take place if the ratio Xc/Xµ (equivalent reactance of system capacitance/equivalent magnetizing reactance of PTs) is between 0,01 and about 3.
For PTs adopted to detect ground-faults, it is customary to select a transformer rated at line-to-line system voltage and operate it a lower voltage (knee point at 3 of operating voltage). In this case, ferroresonance is less likely to occur, because the ratio Xc/Xµ should be between 0,01 and about 0,5.