Chapter nine differential protection. Current differential relaying is applied to protect many elements of a power system. A simple example of a current differential relaying scheme is shown in this slide. The protected element might be a length of circuit conductor or a bus or a generator winding or a transformer. It can be seen that the current differential relaying is a basic balancing of current using the application of kerchief current law. The relay operates on the sum of currents flowing in the CP secondaries under normal conditions or for a fault outside the zone of protection And the zonal protection is divided is defined by the placement of the CTS I one is equal to i two in the primary of both CTS.
If the turns ratios of the CTS are the same, both currents in the CT secondaries will be the same. Therefore, by virtue of the CT connections I one and I to add to zero through the relay or I subscript diff, which stands for the differential current is equal to i one plus i two and I one is equal to an opposite I two, so, I one plus i two is equal to zero. The secondary currents plus appear to circulate only in the CT secondaries and nothing will be flowing through the differential coil of the relay. Under fault conditions inside the zonal protection, it reverses direction and in all likelihood will not equal I want in fact it is 180 degrees out of phase with I want the currents in the CT secondaries will be quite different than it will flow in the reverse direction. Therefore, by virtue of CT connections I want an eye to add to a value greater than zero through the relay.
Therefore, the differential current IDF is going to be equal to i one plus i two and is definitely not going to be equal to zero in fact, it's probably going to be a pretty high value. The secondary current status will no longer appear to circulate in the CPU side. secondaries only but will add to a substantial amount flowing through the relay coil. This is important and it's going to be worth repeating under normal conditions or for faults outside the zone of protection defined by the CTS I one will equal I two in the primary of both CTS. If the turns ratios of the CTS are the same, then the the currents in the secondaries will look like they're circulating only through the secondaries of the CT. And the current through the differential coil of the relay will add to zero hands the relay will not operate under fault conditions inside the zone of protection, it reverses Therefore, by virtue of the CT connections, I want an AI to add to a value greater than zero through the relay.
So that I, the differential current IDF will not be equal to zero, the secondary currents will add to a substantial amount flowing through the differential relay coil. Before looking further, at differential protection, we need to quickly review phenomena that occurs in magnetism called saturation. In order to understand this phenomenon of saturation, I want to in the next two slides just review some of the basics of electromagnetism. magnetic flux through a ferromagnetic material such as iron or steel, is analogous to current through a conductor it must be motivated by some force in order to occur in electric circuits. Current is motivated, motivated By EMF and emf is voltage in magnetic circuits, this motivating force is magnet motive force or mmf magnet motive force mmf or magnetic flux are related to each other by a property of magnetic materials known as rowlock reluctance. The latter quantity symbolized by this strange looking capital R in this equation, the mmf required to produce this changing magnetic flux must be supplied by a changing current through the coil.
Magnet motive force generated by an electrical coil is equal to the amount of current through that coil in amps multiplied by the number of turns of that coil around the core and the SI unit for mmf ampair turns or amp turns because the mathematical relationship between magnetic flux and mmf is directly proportional and because the mathematical relationship between mmf and current is also directly proportional, that current through the coil will be in phase with the magnetic flux wave. In this case, I've indicated the the wave shapes of the voltage and the current and the magnetic flux, you can see that the green and the magnetic flux wave is definitely in phase with the current even though the current maybe 90 degrees or is 90 degrees out of phase with the voltage that's applied to it. Now let's look at some current releases. Ships if we connect a load across the terminals of the secondary of this transformer which could be a CT the circuit on the secondary side of the transformer is complete and a current it or sorry current I too will start to flow through it.
The magnetic flux in coil one is the same as a magnetic flux in coil two Vmf in coil one is the same as the mmf in coil to the magnet motor force corresponding to the current in the windings is given by m m f is equal to n two times I two which is equal to n one times I one. This is also known as field intensity if we measure the flux density against the field intensity for an ideal transformer, it would look like this, it would be what we call linear a linear relationship. The more current that flows through the coil, the more magnetic flux would appear in the core in the core of the, of the material. However, in the real world material doesn't work like that, it looks like this. You can see I've plotted cast iron, cast steel and sheet steel and there's lots of other different materials that would have curves in in between those curves.
At some point, the magnetic flux density created by the primary current does not increase as fast as the primary current. At this point, we say the core is magnetically saturated, and definitely the output is not linear with the input This is the phenomena of saturation that we mentioned a few slides ago. Now, if we excite the core of a transformer with AC, such as happens in the case of a CT in a save busbar the actual result will look like this, where we have what is called the magnetic histories curve for the material that we're talking about. And this is what will give rise to a problem in differential equation which we'll look at in the next few slides. So, looking at a real transformer including a current transformer with iron or a steel When it starts to saturate and as in the case of large current flows in the primary there the result in current flows will look something like this.
And as you can see, even though the current in the primary given by the green line or the green current line there, even though it's out of phase by 90 degrees with the voltage applied, it is still sinusoidal. However, the secondary current because of this saturation phenomenon, it will not be sinusoidal. And this indeed presents a problem for differential type relay. Because of very low impedance, bus structures, fault currents generally associated with buses will be very high as well The downstream total summation CTS of a bus differential protection scheme will be quite regularly saturated during an external through fault, causing the protection to mal operate for external faults if not corrected. The downstream CTS will receive the total summation of all the currents of the incoming buses. That's it is a lot of current.
We're going to look at some correcting features of this saturation phenomenon in the next few slides. In the case of a large bus through fault, if the CC CTS are not matched, one could go into saturation before the other causing an imbalance in the secondary currents. Now I've shown the imbalance here and As length of the of the vector arrows, however, the saturation effect changes over the period or the cycle of the current. But suffice to say at any instant, the current of the ITU CT will definitely be different than the current in the eye one CT. Hence, the summation of the two currents or the differential current in the relay is not going to be equal to zero. This more realistically demonstrates how mismatch can occur when one or more CTS in a differential protection reaches saturation before the others in the differential circuit.
In this circuit, if a fault occurs outside the differential zone of protection, the current in the 87 a relay should be zero However, if the feeder CT reaches saturation, which could be likely the current node is no longer balanced. In this case the CTS carry sorry in this case, CT two carries all of the fault current flow, whereas CT three will carry only a portion of the fault current can see conceivably less than a half. CT two will reach saturation before any of the other CTS and the protection and the relay will operate even though it's through fault. A solution to these difficulties is the percent differential type relay. The differential current required to operate this relay is a variable quantity now owing to the effect of the restraining coils indicated by the capital letter are here. The difference Rancho current in the operating coil is proportional to the vector sum of i one I two and the equivalent current of the restraining coil is proportional to the magnitude of AI one plus the magnitude of AI.
Two. This is intended to improve the security and selectivity of this relay and the operating current must be greater than the sum or some percentage k of the restraining quantity which is derived from the sum of the magnitudes of the individual CT currents k times the magnitude of AI one plus a magnitude of AI to the operating characteristic of such a relay as shown here, except for the slight effect of the control spring at low currents or minimum pickup value, the ratio of the differential operating current to the Average restraining current is a fixed percentage, which explains the name of this relay. The advantage of this relay is, it is less likely to operate incorrectly than differently connected over current relay. When a short circuit occurs for an external fault fault in the protected zone, the operating characteristic of this percent restraint current differential relay with a slope of K one is shown.
The operating zone is indicated in green, the restraining zone is in red. Constant percent slope relay characters can look like this and can be selected depending on the relay itself and its capabilities. The traditional percentage restraint characteristic is commonly used in current differential relays and it may be modified by the use of a dual slope restraint as shown in this slide. The dual slope percentage restraint characteristic improves the security of the current differential Relay for faults external to the protected zone. This is a particular advantage because current transformers may not accurately reproduce the primary fault currents under transient fault conditions. The dual slope restraint characteristic is a form of adaptive restraint in which the magnitude of the restraint quantity is increased for high current conditions where CT accuracy is worse and CT saturation becomes probable.
The minimum pickup region is used between zero and approximately point five per unit regression Current, it provides security against CT remnants and accuracy errors. Slope one region is used between the minimum pickup region and slope to bring point slope one provides security against fault tripping false tripping due to CT inaccuracy and where there may be a significant DC current component present. slope to is normally set at 60 to 80%. The slope to region provides security against false tripping due during through faulty events where CTE saturation is likely. Another method of compensating for CTE mismatch problems is to use high impedance differential protection. The differential protection method implies that for normal load or through faults of vector, somebody Have all currents entering and leaving the protected zone must be equal.
Therefore, there will be no current flow in the protection Relay for load for load or external faults, but there will be a relay current proportional to fault current for internal faults. As I have already mentioned, a common problem exists for differential buss protection and that is CP saturation. During an external fault condition, the CTS in the faulted circuit can become saturated where it's parallel connection then becomes and looks like a low impedance short circuit. The saturated CT will not perform correctly in order to transform the the affected fault current. The other CTS that do not saturate will outputs secondary fault current accurately as a result the differential relay receives air current and could trip in incorrectly. In the case of high voltage buses and transformers, the system cannot tolerate this protection problem.
If we could increase the impedance of the relay path substantially above that of the saturated CT two, we could then prevent the relay from operating with an external resistance added in series with the relay coil. The current output of CT one will now be forced through the low impedance short short circuit of a CT two. Therefore, no or very little current will pass through the relay coil and the relay will not operate. If we now consider an internal fault Both CP one and CP two transform the fault currents correctly as the protection will operate fast enough to prevent any CT saturation. Both I won and I too will add and flow through the resistor a relay combination to correctly provide an instantaneous trip. With high voltage buses, the fault currents are normally very large with the addition of external resistance in the relay path.
The voltage developed across our relay and the CTE secondaries will therefore be very very high. The high voltage could in turn damage the secondary winding of the CT and or the overcurrent relay. If we install a nonlinear resistor in parallel with the external resistor relay combination, we can limit The voltage to a safe level. This type of nonlinear resistor used with a with the high impedance relay is called a metro cell. It will limit the voltage to approximately 300 volts for internal faults at low voltage the metro cell will have or it'll behave as an open circuit and for voltages greater than 300 volts it will begin to conduct and shunt some of the relay current. As a result, the differential junction voltage is limited to a safe value and still allows a relay to operate correctly.
This is what an installed microcell looks like. It will limit the voltage to approximately 300 volts for internal faults. Here are some CT requirements and Some other associated considerations for differential protection. The CTS forming the differential zone must be of identical turns ratio. A low secondary winding resistance of the CPE will permit the voltage setting to be set low making the protection more sensitive for internal faults, the ideal situation would be when the loop lead resistance is half the secondary winding resistance. In the formula for calculating relay stability voltage, the re resistance of the secondary winding is considered an a leakage reactance is ignored.
The CT therefore should be a low reactance type for leakage reactance to be low, the secondary windings need to be destroyed. Repeated around the core. This is accomplished physically in bushing CTS by distributing each section of the tap secondary winding completely around the circumference of the core. Preferably, all CTS should be operated on their full tap setting. sensitivity and the electrical stability of a differential scheme will be adversely affected if auxiliary CTS for ratio correction or any other devices placed in a secondary circuit that will add burden to that circuit. There you should then be avoided.
In order to ensure a high speed positive operation of the relay on internal faults into obtain an inherent stability for transient currents. The knee point of all CTS should preferably be at least twice The relay setting I subscript are as indicated in this diagram. CT saturation is sometimes caused by the transient DC component of primary fault current. The remnant flux may either aid or detract from the transient flux buildup depending on the relative direction of the remnant flux and the flux variation required by the DC component. The high impedance differential protection scheme ensures stability for external faults even under saturated CP conditions. For the scheme to be stable and sensitive the resistance of the CP secondary circuits must be kept low bushing CTS or CPS with trial While cores are best suited for high impedance buss protection schemes, the installed cost of bushing CTS is much less than the other types of say free standing current transformers.
The bushing CP is therefore widely used this end chapter nine