Negative Sequence Directional Element for a Relay Useful in Protecting Power Transmission Lines

This invention relates generally to directional elements used in protective relays for power transmission lines and more specifically concerns a negative sequence directional element.

In the identification of faults on a power transmission line by a protective relay which is located at a given point along the line, it is extremely important to be able to identify the direction of the fault on the transmission line relative to the location of the relay. The fault direction is either downstream of (in front of) the protective relay, which is referred to herein as a forward fault, or upstream of (in back of) the relay, which is referred to herein as a reverse fault. The ability of a protective relay to provide direction information for faults is referred to generally as its directional security. High directional security, meaning providing accurate directional information, is of great importance in the overall operational value of the relay.

Accurate directional information guarantees that the relay will never assert, i.e. provide a fault indication which results in the tripping of a circuit breaker, for faults in the reverse direction if the fault is located in the forward direction and vice versa. A relay which looks for faults in both directions will have either separate forward and reverse directional elements or a single element capable of providing information for both directions.

There are different types of directional elements, among the most popular being negative sequence polarized directional elements, and zero sequence polarized directional elements. Negative sequence directional elements are capable of declaring fault direction for all unbalanced faults. However, it is known that negative sequence elements, i.e. those elements using negative sequence quantities of voltage and current to make direction determinations, do have certain advantages over other approaches, including zero sequence elements. These advantages include insensitivity to zero sequence mutual coupling, and a generally nigher sensitivity to remote ground faults with high fault resistance.

In the conventional negative sequence element technique, the phase angle of the negative sequence voltage is compared against the phase angle of the negative sequence current. If the negative sequence current leads the negative sequence voltage, regardless of the amount of the angular difference, then the fault is in the forward direction; otherwise it is in the reverse direction.

However, there are certain disadvantages to conventional negative sequence directional elements when the negative sequence source upstream of the relay is strong, such that the impedance is low. In this situation, the negative sequence voltage at the relay will be quite low, which in turn reduces the sensitivity of the relay. It is desirable that such relays be sufficiently sensitive that they operate both for close-in faults and for remote faults, as well as operating very fast (less than one cycle) in response to the occurrence of a fault. With a strong source, the negative sequence directional element may not produce reliable results for close-in and remote faults.

In order to increase the sensitivity of the conventional negative sequence directional element in such situations, a compensating boost to the negative sequence voltage is sometimes provided, which in turn makes the phase angle measurement for close-in and remote faults easier and more reliable. However, this compensating boost in turn creates a disadvantage in certain situations, because a significant boost could result in a reverse fault looking like a forward fault to the forward directional element, a very undesirable result. In addition, it is often difficult and/or time consuming for the operator/engineer to make a proper selection of the boost.

It would be most desirable for a directional relay to have separate forward and reverse direction sensitivities, individually selectable; however, this has not been accomplished heretofore with negative sequence directional elements.

Hence, there remains a need for a directional element which is secure but also sensitive to faults on the transmission line.

Accordingly, the present invention is a directional element for use in a relay for protection of power transmission lines, comprising: means for obtaining negative sequence voltage and current quantities of the power signal which is present on the power transmission line; means for calculating from said negative sequence voltage and current quantities a directional quantity which is related to the negative sequence impedance of the transmission line; and means for comparing said directional quantity against at least one threshold quantity to identify at least one of a forward fault and a reverse fault on the transmission line relative to the relay.

FIG. 1 is a sequence network diagram for a ground fault on a Dower transmission line with sources of fault current at both ends of the line.

FIG. 2 is an impedance plane diagram showing the operation of the directional element of the present invention.

FIG. 3 is a diagram showing the directional element system of the present invention.

In conventional directional elements using negative sequence quantities, the torque (T) produced by forward faults is given by the following equation:

T=Re[V.sub.2 .multidot.(Z.sub.L2 .multidot.I.sub.2)*], where * denotes the complex conjugate. Only negative sequence quantities are used. Only the real portion of the entire expression is used. The mathematical operator on the Z.sub.L2 .multidot.I.sub.2 expression is a complex conjugate, as indicated above. V.sub.2 and I.sub.2 are negative sequence voltage and current quantities, respectively, both of which are measured, and Z.sub.L2 is the modeled negative sequence line impedance, which is known. In a compensated (boosted) negative sequence directional element, the boost provided to V.sub.2 for low impedance strong sources is .alpha..multidot.Z.sub.L2 .multidot.I.sub.2. The amount of compensation is determined by the value of the e constant selected. The compensated torque equation is thus T (Compensated)=Re [(V.sub.2 -.alpha..multidot.Z.sub.L2 .multidot.I.sub.2).multidot.(Z.sub.Ld .multidot.I.sub.2).multidot.]. Again, the quantity T is negative for forward faults and positive for reverse faults if the proper .alpha. constant is used. As indicated above, however, the compensated negative sequence torque T can in certain situations cause difficulties because an actual reverse fault can appear as a forward fault to the compensated directional element, i.e. when the expression .alpha..multidot.Z.sub.L2 .multidot.I.sub.2 has a greater magnitude than V.sub.2.

Referring now to FIG. 1, a sequence network for a single line to ground fault is shown involving a near source 12 and a remote source 14. The positive sequence, negative sequence and zero sequence portions 16, 17 and 18, respectively, form the sequence network. In the above arrangement, the negative sequence current seen by the relay for forward faults is I.sub.S2, and -I.sub.R2 for reverse faults. The negative sequence impedance for forward faults is thus ##EQU1## while for reverse faults, ##EQU2## The measured negative sequence impedance thus is different between forward faults and reverse faults, thus providing in effect a fault direction determination.

This is shown graphically in the impedance plane representation in FIG. 2, where line 22 is equal to Z.sub.L2 +Z.sub.R2, while line 24 is equal to Z.sub.S2. There is a significant gap 25 between them. Hence, a fault can be identified as forward of the relay if Z.sub.2 is less than a first threshold setting, designated Z.sub.2F herein, which is in the gap 25, and reverse if it is greater than a second threshold setting, designated Z.sub.2F herein, which is also in gap 25, but greater than the first threshold setting. The first threshold setting Z.sub.2F is set less than the second threshold setting Z.sub.2R to avoid any overlap condition where Z.sub.2 might satisfy both forward and reverse conditions, but not too far apart, which would result in a significant "no decision" area. Generally, the two thresholds are separated by at least 0.1 ohm.

FIG. 3 shows a system for implementing the directional element approach outlined theoretically above. As discussed above, the approach of the present invention, instead of using voltage and current quantities and the phase angle difference therebetween for direction determination, is to use voltage and current quantities to determine negative sequence impedances or quantities representative of those impedances in the form of a scalar number, which may then be conveniently compared with threshold numbers to determine fault direction.

The embodiment described herein provides a scalar quantity related to impedance, but it should be understood that actual impedance values could be used as well. Referring now to FIG. 3, V.sub.2 (negative sequence voltage) and the quantity Z.sub.L2 .multidot.(I.sub.2) are applied as inputs to a calculation block 30. The V.sub.2 and I.sub.2 quantities (I.sub.2 is the negative sequence current) are produced conventionally by measuring the analog voltage and current on the transmission line, low pass filtering the voltage and current, converting the resulting quantities to digital quantities, filtering the digital quantities, and then deriving the negative sequence components of those quantities. These are all common, well-known procedural steps. The Z.sub.L2 quantity is the negative sequence component of the modeled line impedance, which is known, of the transmission line. The quantities V.sub.2 and Z.sub.L2 .multidot.I.sub.2 are used to produce a scalar quantity Z.sub.2, which is related to the negative sequence impedance Z.sub.2.

The scalar quantity Z.sub.2 is derived as follows. As indicated above with respect to the conventional compensated negative sequence element, T (torque)=Re[(V.sub.2 -.alpha. Z.sub.L2 .multidot.I.sub.2).multidot.(Z.sub.L2 .multidot.I.sub.2)*]. A so-called balance condition, in which neither a forward nor reverse direction indication is produced, requires a zero torque, i.e. Re[(V.sub.2 -.alpha..multidot.Z.sub.L2 .multidot.I.sub.2).multidot.(Z.sub.L2 .multidot.I.sub.2)*]=0. If .alpha. is Z.sub.2 (scalar) and Z.sub.L2 is 1.angle..THETA., where .THETA. is the angle of Z.sub.L2, then for a zero torque (balanced) condition, Re[V.sub.2 -Z.sub.2 .angle..THETA..multidot.I.sub.2).multidot.(I.sub.2 .multidot.1.angle..THETA.)]=0, and ##EQU3## This is equivalent to the calculation shown in FIG. 3. Since the term (.alpha..multidot.Z.sub.L2 .multidot.I.sub.2) increases the amount of V.sub.2 for directional calculations, which is equivalent to increasing the magnitude of the negative sequence source behind the relay, increasing the forward Z.sub.2 to a threshold number has the same effect. Hence, if Z.sub.2 is less than the forward threshold, the fault is forward, while if Z.sub.2 is greater than the reverse threshold, the fault is reversed.

Referring again to FIG. 3, the scalar quantity Z.sub.2 from calculation block 30 is compared against threshold impedance settings Z.sub.2F and Z.sub.2R, as shown by blocks 32 and 34. If the output from block 30 is less than Z.sub.2F, then an output occurs on line 36 indicating a forward fault, while if the output from block 30 is greater than Z.sub.2R, an output occurs on line 38, indicating a reverse fault.

The system of FIG. 3 also includes several security features. First, the negative sequence current I.sub.2 is compared to the positive sequence current I.sub.1 (multiplied by a scalar quantity a.sub.2) by comparator 40. If I.sub.2 is quite low, such as might occur where the positive and negative sequence networks have significant coupling relative to three-phase faults, computation block 30 is not enabled for Z.sub.2 calculations. Thus, there is no output of block 30. Typically a.sub.2 is in the range of 0.02-0.5. The output of comparator 40 is applied to AND gate 46.

The other enable comparisons involve minimum values of 3I.sub.2. A 50QF element is a conventional fault detection element. It measures 3I.sub.2 and establishes a minimum value for current sensitivity in the forward direction. The preferred setting is above normal load unbalance and below the lowest expected negative sequence current for forward direction unbalanced (phase-phase, phase-phase-ground and single line to ground) faults. In the embodiment shown, 50QF has a setting range of 0.5 amps to 5 amps. The 50QF setting is compared against 3I.sub.2 in comparator 42 and the output applied to "OR" gate 44. The 50QR fault detector element measures 3I.sub.2 current and establishes a minimum value of current sensitivity in the reverse direction. The 50QR element preferably has a setting which is above normal load unbalance and below the lowest expected negative sequence current magnitude for reverse direction unbalanced faults, within the range of 0.5 amps to 5 amps. The 50QR setting is then compared with 3I.sub.2 by comparator 48 and the output applied to OR gate 44. If the output of either comparator 42 or 48 is high, the OR gate produces a high output to AND gate 46.

In summary, if the signal from comparator 40 is high and one of the signals from comparators 42 or 48 is high, calculating block 30 is enabled to produce the Z.sub.2 scalar quantity. The Z.sub.2 quantity is then, as indicated above, compared with the Z.sub.2F threshold in comparator 32, which establishes the minimum negative sequence source impedance behind the relay for a forward fault. Z.sub.2F typically will be 0, although where the local source is strong, Z.sub.2F is some positive number to assure a strong torque for remote single line to ground faults. However, Z.sub.2F must always be less than Z.sub.L2 +Z.sub.R2. If Z.sub.2 is less than Z.sub.2F, the output from comparator 32 goes high, indicating a forward fault.

The Z.sub.2 quantity is compared with the reverse threshold Z.sub.2R by comparator 34. Z.sub.2R sets the minimum negative sequence remote source plus line impedance for faults behind the relay. The minimum Z.sub.2R in the embodiment shown is Z.sub.2F plus 0.1 ohm. If the Z.sub.2 quantity is greater than Z.sub.2R, then the output of comparator 34 is is high.

The circuit of FIG. 3 includes two additional security aspects. The output of forward threshold comparator 32 is applied to an AND gate 68, along with a "not" output line from OR gate 70. The output from reverse threshold comparator 34 is applied to an AND gate 72, along with a not output line from 0R gate 74. The output of AND gate 72 is applied as an input to OR gate 70, along with a not line input from forward direction enable comparator 42, while the output of AND gate 68 is applied as one input to OR gate 74, along with a not line input from reverse direction comparator 48. Thus, when there is an output from AND gate 72, indicating a reverse fault, forward fault declarations are blocked; and where there is an output from AND gate 68, indicating a forward fault, reverse fault declarations are blocked. The outputs of AND gates 68 and 72 respectively, are referred to as 32QF and 32QR, the industry nomenclature for directional element outputs.

Hence, a directional element for protective relays has been disclosed which uses negative sequence quantities for calculation of a scalar quantity which is related to the negative sequence impedance. The scalar quantity is compared against two selected thresholds to determine whether it is a reverse or forward fault. The apparatus may be used to determine just forward or reverse faults, by using only one threshold/comparison, or may be used to distinguish between forward and reverse faults and identify both.

Although a preferred embodiment of the invention has been disclosed for illustration, it should be understood that various changes, modifications and substitutions may be incorporated in such embodiment without departing from the spirit of the invention which is defined by the claims which follow: