Imported: 13 Feb '17 | Published: 18 Jan '11
USPTO - Utility Patents
A method and an adaptive distance protection relay for compensating for a remote line end infeed effect during determination of a distance to a resistive fault on a three-phase power transmission line. It is assumed that a fault current flows through the fault resistance. A fault loop impedance is first calculated by a known algorithm from phase voltages and phase currents. A shift of the fault loop impedance is determined from the fault loop impedance, the impedance of the transmission line for the positive current sequence and the phase angle of a complex fault current distribution factor, where the fault current distribution factor is the ratio of the fault loop current to the fault current. The distance to fault is calculated by subtracting the impedance shift from the fault loop impedance and dividing the result by the impedance of the transmission line for the positive current sequence.
This application claims priority to Swedish patent application 0600322-2 filed 10 Feb.2006 and is the national phase under 35 U.S.C. §371 of PCT/EP2006/070082 filed 21 Dec.2006.
This invention relates to a method and a device for an adaptive distance protection of power transmission lines and relates more particularly to a distance protection relay with improved operation under resistive faults, adapted to reduce under-reaching and overreaching of the relay, that is caused by a remote line end infeed effect.
Power transmission lines carry electric power from generating sources to users. The power transmission lines are typically high voltage lines and the electric voltage is typically transformed to a lower voltage at a power substation, before being distributed to individual electric power users such as homes, factories, business buildings etc. At many power substations, protective relays are installed.
The detection of a fault in the line involves measuring critical system parameters and, when a fault occurs, quickly making a rough estimate of the fault location and of certain characteristics of the fault so that the faulted line can be isolated from the power grid as quickly as possible. A fault occurs when a transmission line, typically due to external causes, diverts electrical current flow from its normal path along the transmission line.
The major types and causes of faults are insulation faults, caused by design defects, manufacturing defects, improper installation, and aging insulation; electrical faults, caused by lightning surges, switching surges, and dynamic overvoltages; mechanical faults, caused by wind, snow, ice, contamination, trees, and animals; and thermal faults, caused by overcurrent and overvoltage conditions.
Power systems have, over time, been more complicated in construction, larger in size and higher in voltage, and associated protection systems have also become very complicated in construction. In this regard, provided that such a protection system cannot show its appropriate protection ability with respect to a fault occurring at some part of an associated power system, the resulting accident ripple range and strength will be very great.
If a protection relay bearing a primary responsibility does not accurately detect a fault occurring at any one part of a power system, a power interruption zone will be wider according to the rules of protection coordination. All backup protection relays for transmission lines and most main protection relays therefore are directional distance relays that are generally degraded in detection performance upon occurrence of a resistance earth fault. Further, as a transmission system becomes more complicated in construction, the average length of a trans-mission zone through which heavy load current flows is shortened, thereby causing a distance relay to perform a mal-operation or non operation due to a reactance effect which is a mutual coupling effect of a fault resistance and load current.
A transmission line may include three-phase lines; however, a transmission line may also contain one phase, or some other number of phases.
The issue of locating faults on power transmission lines has been disclosed in different prior art.
In A. Wiszniewski, Accurate fault impedance locating algorithm, IEE Proceedings, Part C, Vol. 130, No. 6, 1983, pp. 311-315 an algorithm for locating faults on power transmission lines for the inspection-repair purpose, and thus not for protective relaying, has been presented. For all fault types the total fault current, i.e. the current flowing through a fault path resistance is estimated with use of the ‘pure line current’ at the fault locator installation point. This ‘pure line current’, or in other words the ‘incremental line current’, is determined as the difference of the post-fault line current and the load current. Moreover, this measured ‘incremental line current’ is considered for particular phases, depending on the type of a fault.
In M. M. Saha, Method and device for locating a fault point on a three-phase power transmission line, U.S. Pat. No. 4,559,491, Dec. 17, 1985, an algorithm for locating faults on a power transmission line for the inspection-repair purpose, and thus not for protective relaying, has been presented. The distance to fault is calculated with use of the quadratic equation, which is suitable for the off-line fault location purpose and rather difficult for on-line application to protective relaying.
In Zhang et. al, An adaptive approach in digital distance protection, IEEE Transactions on Power Delivery, Vol. 6, No. 1, January 1991, pp 135-142, an adaptive approach to distance protection of a transmission line has been disclosed. The approach deals only with single-phase-to-ground faults, while the invention deals with all fault types. For the single-phase-to-ground faults considered, the total fault current is estimated with use of the zero sequence current. The authors propose to use a pre-set value for the adaptive change of operating characteristics of the distance protection. This pre-set value corresponds to a fault at the end of the relay nominal reach which is determined under the simplifications. However, if the remote-end and local zero-sequence contributions are out of phase, an error in the dynamic response would occur.
In D. Novosel, Yi Hu, M. M. Saha, Adaptive Distance protection system, U.S. Pat. No. 5,956,220, Sep. 21, 1991, an adaptive distance protection system has been introduced. This adaptive system is designed to compensate correctly for mutual coupling effects. Thus, it deals with specific problems for parallel transmission lines under single-phase-to-ground faults and with taking into account different operation modes of the healthy parallel line, where the operation modes are being in operation or switched-off and grounded. These specific problems for parallel transmission lines have no relation to the presented invention.
In L. Yang, Adaptive Quadrilateral Characteristic Distance Relay, U.S. Pat. No. 5,796,258, Aug. 18, 1998, an adaptive quadrilateral characteristic distance relay has been presented. The tilt of the quadrilateral characteristic is determined using the negative sequence current for a single-phase-to-ground fault and the pure line currents from the respective phases at the relaying point, i.e. the incremental currents understood as the differences between the fault and the load currents, for inter-phase faults. The distance to fault and impedance parameters of the network are not present in the equations. This means that the method is simplified and does not consider compensation of the remote end infeed effect accurately.
In Yong Jin Ahn, Distance Relay for protection of transmission line having minimized reactance effect, U.S. Pat. No. 6,661,630, Dec. 9, 2003, a distance relay for protection of a transmission line having minimized reactance effect has been presented. It considers both the single and parallel line cases. The single-phase-to-ground as well as inter-phase faults are taken into account. The total fault current is estimated using the zero sequence current for single-phase-to-ground faults, and using the pure line currents from the respective phases at the relaying point for inter-phase faults. Incremental currents are understood as the difference between the fault and the load currents. This means that the procedure of estimation of the total fault current is entirely different than in the invention. Also the fault current distribution factors are utilized. Compensation for the remote end infeed effect is performed using iterative calculations with the starting point being determined under the assumption that the angle of the fault current distribution factor is equal to zero. It is worth to notice that performing iterative calculations for the on-line application of protection is rather difficult and in certain conditions the convergence of iterative calculations is not obtained.
In J. Izykowski, E. Rosolowski, M. M. Saha, Locating faults in parallel transmission lines under availability of complete measurements at one end, IEE Generation, Transmission and Distribution, Vol. 151, No. 2, March 2004, pp. 268-273, a fault location algorithm designed for application to parallel transmission lines under availability of complete measurements at one end has been delivered. Complete measurements are understood as three-phase voltages and three phase currents from both faulted and parallel healthy line. Similarly as in the invention the total fault current is estimated with avoiding the zero sequence quantities. Due to availability of complete measurements at one end, the final fault location algorithm is of very simple form. The invention is not related to the availability of measurements considered in the reference, since a rather standard availability of measurements is considered in the invention.
In J. Izykowski, E. Rosolowski, M. M. Saha, Adaptive digital distance algorithm for parallel transmission lines, 2003 IEEE Power Tech, Bolonia, Jun. 23-26, 2003, CD Rom, IEEE Catalogue Number 03EX719C, ISBN 0-7803-7968-3, paper 343, pp. 6, further investigation of the method from the above reference is performed. In particular, due to a very simple first order equation for a distance to fault, its application to adaptive distance protection is considered. As described above the availability of complete measurements at one end of parallel transmission lines is different from the situation assumed with respect to the present invention.
The object of the present invention is to solve the problems related to known methods and prior art and to create an improved, simple and reliable method and device for an adaptive distance protection of three-phase power transmission lines.
A further object is to improve the operation under resistive faults and by reducing underreaching and overreaching of the relay which is caused by a remote line end infeed effect.
The method is performed by the distance protection relay in case of a resistive fault on a three-phase transmission line, when a fault current I_{F }flows through the fault resistance R_{F}. The method starts with the step, known in the art, to calculate a fault loop impedance Z_{relay }by dividing a fault loop voltage V_{relay }by a fault loop current I_{relay }measured from one end A of the transmission line AB, which is the end where the distance protection relay is arranged. The fault loop voltage V_{relay }is composed of the respective phase voltages V_{ph1}, V_{ph2}, V_{ph3 }and the fault loop current I_{relay }is composed of the respective phase currents I_{ph1}, I_{ph2}, I_{ph3 }of those phases which are involved in the fault.
The method according to the invention comprises the step of determining a shift ΔZ of the fault loop impedance using the fault loop impedance Z_{relay}, the impedance Z_{1L }of the transmission line for the positive current sequence and the phase angle γ of a complex fault current distribution factor k_{F}, according to the equation
where Z_{relay}=R_{relay}+jX_{relay}, Z_{1L}=R_{1L}+jX_{1L }and where the fault current distribution factor k_{F }is the ratio of the fault loop current I_{relay }to the fault current I_{F}.
The next step of the method according to the invention is to determine a distance to fault d by subtracting the impedance shift ΔZ from the fault loop impedance Z_{relay }and dividing the result by the impedance Z_{1L }of the transmission line for the positive current sequence.
The determination of the fault loop impedance Z_{relay }only from phase voltages and currents measured at the relay side A is not a direct measure of the distance to fault d in case of a resistive fault. In that case, the fault current I_{F }flowing through the fault resistance R_{F }has to be considered, where the fault current can not be determined from the relay side A alone. The phase currents coming from the remote end B of the line have to be regarded as well, since they feed the fault from the remote end B. This effect is called remote line end infeed effect. If the influence of the fault current I_{F }is neglected in such a resistive fault case, a wrong distance to fault d is determined which might lead to overreaching or underreaching of the distance protection relay.
According to the invention, the fault loop impedance Z_{relay }is adapted by shifting it in the complex plane along the impedance shift ΔZ, which represents the influence of the fault current I_{F }by taking into account the phase angle γ of the fault current distribution factor k_{F}. Thereby, the method and the adaptive distance protection relay according to the invention compensate for the remote line end infeed effect and increase the accuracy of the determined distance to fault d.
For calculation of the phase angle γ, three different possibilities are proposed.
In the simplest case, the phase angle γ of the fault current distribution factor k_{F }is assumed to be zero, i.e. it is assumed that only a resistive shift of the fault loop impedance Z_{relay }needs to be performed:
In case that the distance protection relay on side A of the line is also able to receive synchronized current measurements from the remote side B, the phase angle γ is calculated from the fault loop current I_{relay }and the fault current I_{F}, where the fault current I_{F }is determined
In the case that only current measurements from the relay side A are to be used, the phase angle γ is calculated three times, each time from the fault loop current I_{relay}, the fault current I_{F }and one of three different, predetermined line distances d_{i}, where the fault current I_{F }is determined
The invention provides a new digital distance algorithm for both single and parallel power transmission lines. In case of parallel lines, the third solution can be applied which requires providing standard measurements from one end of the parallel lines. An approach which originates initially from fault location aimed at inspection-repair purposes was enhanced to be utilized here for assuring adaptability of a distance relay to the “reactance effect” which is relevant for resistive faults. An improved estimation of the voltage drop across the fault path resistance R_{F }is introduced into the algorithm. As a result of that, determination of the zero sequence currents is avoided and the incremental positive sequence component and the negative sequence component are utilized. In that the provided method differs from known algorithms. The method according to the invention has been tested with the fault data obtained from simulations performed using the known ATP-EMTP software.
According to the invention, the total fault current is estimated using the generalized fault model formulated for the sequence quantities. This approach based on sequence quantities is utilized in order to avoid an adverse influence of uncertainty with respect to the zero sequence line impedance parameter, which additionally causes that an estimation of the total fault current is identical for both the single and parallel lines, using the incremental positive sequence current for the majority of faults, i.e. single-phase to ground faults and phase-to-phase faults.
In comparison with the prior art of Yong Jin Ahn, the iterative calculations used there are avoided in the current invention by determining the total fault current from either two-end synchronized measurements of currents or alternatively by using three specific impedance shifts of the impedance characteristic, for example the MHO characteristic.
Remote End Infeed Influence on Distance Relay Operation
The following explanations relate to the relay A, arranged at the respective position A in the transmission line depicted in FIG. 1.
According to standard typical distance protection, a fault loop impedance Z_{relay }is determined from a fault loop voltage V_{relay }and a fault loop current I_{relay}, both composed, according to the current fault type, of measurements of phase voltages or currents, respectively, taken by relay A (see Table 1):
If there is a solid fault, i.e. a fault not involving a fault resistance so that R_{F}≈0 applies, then the determined fault loop impedance Z_{relay }according to equation (1) is a direct measure of the distance to fault d, where d is preferably given in p.u.:
Z_{relay}=d·Z_{1L }if: R_{F}≈0 (2),
where:
Z_{1L}=R_{1L}+jX_{1L }is the impedance of the line AB of FIG. 1 for the positive sequence.
In case of resistive faults, i.e. faults involving a fault resistance of not negligible value so that R_{F}≠0 applies, the determined fault loop impedance Z_{relay }according to equation (1) is no longer a direct measure of the distance to fault d. The equation (2) is not applicable here. Instead the fault loop is described as follows:
V_{relay}−d·Z_{1L}I_{relay}−R_{F}I_{F}=0 (3)
where:
I_{F }is the total fault current, also called fault path current, which results from the current I_{A}, flowing from the relaying point A, and also from the current I_{B}, feeding the fault from the remote end B, see FIG. 1.
Dividing both sides of equation (3) by the relaying current I_{relay }one obtains the following impedance equation:
or in the alternative form:
Z_{relay}−d·Z_{1L}−ΔZ=0 (5)
where:
ΔZ is the impedance shift resulting from the remote end infeed effect which is caused by the resistive fault.
Introducing the fault current distribution factor k_{F }as the following ratio:
the equation (4) can be written as:
Substitution of the fault current distribution factor k_{F }by its polar form into equation (7) results in:
where:
k_{F }is the magnitude of the fault current distribution factor,
k_{F}=|k_{F}|, and γ is the angle of the fault current distribution factor, γ=angle (k_{F}).
The alternative form of equation (8) is as follows:
Taking into account that the term
is a real number, which is so since both, fault resistance R_{F }and magnitude of the fault current distribution factor k_{F }are real numbers, the equation (9) can be resolved into the real and imaginary parts:
Equation (10) can then be multiplied by sin(γ) and equation (11) by cos(γ). The results are then added while cancelling the term
As a result of that a distance to fault d can be determined according to the following simple equation:
The obtained equation (12) is used for determining the compensation for the remote end infeed effect, which can cause under-reaching and/or over-reaching of distance relays under faults close to the border of the first protection zone and which can also slow down the tripping of the distance relays. In order to overcome these features of traditional distance relays it is proposed to compensate for the remote end infeed effect.
Method of Compensation for the Remote End Infeed Effect
In the proposed adaptive distance protection, an adaptation to the remote end infeed effect is introduced. The innovative idea is further presented in relation to the MHO impedance characteristic of the distance relay, where the MHO impedance characteristic as such is generally known and is represented by a circle in the R/X diagram whose circumference passes through the origin, as illustrated in FIG. 2. However, this method can also be used for other shapes of the impedance characteristic of the distance relay.
In the proposed adaptive distance relay the traditional way of computing the fault loop impedance Z_{relay }according to equation (1) is kept. The innovation lies in that the determined fault loop impedance Z_{relay }is compared with the impedance characteristic MHO_{adapt}, see FIG. 2, which is obtained by shifting the original characteristic MHO by the specific shift impedance, which according to equation (5) can be expressed as:
ΔZ=ΔR+jΔX=Z_{relay}−dZ_{1L} (13).
The equation (13) can also be rewritten in the form:
ΔZ=ΔR+jΔX=(R_{relay}−dR_{1L})+j(X_{relay}−dX_{1L}) (14).
Substituting equation (12) into equation (14) results in the shift of the characteristic for the resistance:
and for the reactance:
Taking into account equations (15) and (16), the required impedance shift of the original impedance characteristic MHO for obtaining the adaptive characteristic MHO_{adapt }equals:
This means that the required impedance shift (17) is determined by:
The value of tg(γ) is not known since it is determined by the equation (6) in which the total fault current I_{f }is involved and this total fault current I_{f }is not measurable using only local measurements.
The simplest way of compensating for the remote infeed effect can be performed by assuming zero for the angle γ of the fault current distribution factor k_{F}, which results in tg(γ)=0. In this case the required shift of the impedance characteristic equals:
This means that if the simplification tg(γ)=0 can be assumed, i.e. if the angle γ of the fault current distribution factor k_{F }is approximately zero, then the impedance characteristic MHO of the distance relay is to be shifted only for the resistance as determined in equation (18) in order to compensate for the remote infeed effect.
In general, i.e. without assuming the simplification tg(γ)=0, the value of tg(γ) has to be determined in order to substitute it into equation (17):
A total fault current I_{F }is composed of the currents flowing to the fault point F from both sides of the line (see FIG. 1):
I_{F}=I_{A}+I_{B} (20).
In case of providing the synchronized measurements at both sides of the line and high speed of communication between the line ends for transmitting the remote current to the distance relay, the total fault current according to equation (20) can be simply determined and then tg(γ) from equation (19) is calculated. This allows determination of the required impedance shift of the impedance characteristic (17), applied for compensation for the remote end infeed effect.
The equation (20) indicates that the total fault current I_{F }can be determined with use of currents measured synchronously at both ends of the transmission line. Such measurements are performed for use by a differential relay. Since both a differential relay and a distance relays are together in modern protection terminals for power transmission lines, these measurements, i.e. currents measured synchronously at both ends of the transmission line, can be easily utilized also for performing an adaptive distance protection. This is a subject of the present invention. However, the solution proposed here is not a direct application of the equation (20).
When considering the application of synchronized two-end measurements of currents for determining the total fault current I_{F}, it is worth noting that equation (20) is valid under neglecting shunt capacitances of the transmission line. In case of lines of length exceeding some threshold value, which can be for example 150 km, neglecting of shunt capacitances can be a cause of unacceptable errors in determining the total fault current according to equation (20). Therefore, in order to minimize an influence of shunt capacitances on determination of the total fault current I_{F}, i.e. the current flowing through the fault path resistance R_{F}, a specific determination of this current is proposed. Instead of direct use of the equation (20) in which the currents of faulted phases from both ends are summed, the total fault current I_{F }is determined after resolving three phase currents from both ends into their symmetrical components and then after using the advantageous ones. Advantageous are those which minimize the shunt capacitances effect.
Basics of the Determination of the Total Fault Current I_{F }
It is proposed to utilize the generalized fault model in the form of the following equation for determining the total fault current I_{F}:
I_{F}=a_{F1}I_{F1}+a_{F2}I_{F2}+a_{F0}I_{F0} (21)
where:
I_{1F}, I_{F2}, I_{F0 }are the symmetrical components of the total fault current and where the second subscript denotes the following: 1 the positive, 2 the negative and 0 the zero sequence, respectively;
a_{F1}, a_{F2}, a_{F0 }are the share coefficients, dependent on the fault type according to Tables 1, 2 and 3.
The particular sequence components of the total fault current I_{F }are determined by adding up the respective sequence components of currents from the line terminals. At the right-hand side of the equations below, the first subscript denotes the terminal A or B, while the second subscript denotes the sequence component, with 1 for the positive, 2 for the negative and 0 for the zero sequence component:
I_{F1}=I_{A1}+I_{B1} (22),
I_{F2}=I_{A2}+I_{B2} (23),
I_{F0}=I_{A0}+I_{B0} (24).
Alternatively, the positive sequence component I_{F1 }of the total fault current I_{F }can be determined using the superimposed incremental positive sequence currents ΔI_{A1 }and ΔI_{B1}, where the term incremental denotes the subtraction of the pre-fault values from the post-fault values:
I_{F1}=ΔI_{A1}+ΔI_{B1} (25).
It is known that the use of the positive sequence currents I_{A1 }and I_{B1 }from the line terminals, according to equation (22), for determining the total fault current I_{F }according to equation (21) is affected by the pre-fault load flow. Therefore, in the cases where the positive sequence currents I_{A1 }and I_{B1 }are used, the fault location accuracy is deteriorated, especially significantly if a high fault resistance is involved. In contrast, using the negative and the zero and the superimposed positive sequence components, according to equations (23) to (25), is advantageous for assuring high accuracy for determining the total fault current I_{F}. As a result of that, the following priority for usage of the particular sequence components of the measured currents is proposed:
The share coefficients a_{F1}, a_{F2 }and a_{F0 }from equation (21) can be determined by considering the boundary conditions of the faults considered in this section, which are phase-to-ground and phase-to-phase faults. However, there is a certain freedom in that. Among many possibilities, the share coefficients for the negative and zero sequence are chosen as a_{F2}=a_{F0}=0, see Table 2. This assures that only the superimposed positive sequence components ΔI_{A1 }and ΔI_{B1 }are used for determining the total fault current I_{F}:
I_{F}=a_{F1}I_{F1} (26)
where: a_{F1 }is set according to Table 2, I_{F1 }is determined according to equation (25).
In the case ph1-ph2-g fault, where ph1 and ph2 each denote one of the phases a, b or c, the total fault current I_{F }which flows in the considered inter-phase fault loop is equal to the difference of the phase fault currents I_{F}_{—}_{ph1 }and I_{F}_{—}_{ph2 }at the fault point F of the faulted phases ph1 and ph2:
I_{F}I_{F}_{—}_{ph1}−I_{F}_{—}_{ph2} (27).
Resolving equation (27) into symmetrical components and considering the recommended priority for usage of the particular sequence components, i.e. using superimposed positive sequence components and negative sequence components, one obtains:
I_{F}=a_{F1}I_{F1}+a_{F2}I_{F2}+a_{F0}I_{F0} (28),
where the share coefficients are:
a_{F1 }as in Table 3, a_{F2 }as in Table 2, a_{F0}=0, and where I_{F1 }is defined by equation (25) and I_{F2 }by equation (23).
In case of three-phase balanced faults, the respective phase-to-phase fault loop, which is usually the ‘a-b’ loop, is considered. In consequence of that, the share coefficient for the zero sequence a_{F0 }equals to zero, a_{F0}=0. For the negative sequence, a non-zero share coefficient a_{F2 }is obtained as given in Table 4. However, due to lack of negative sequence components, which is applicable for the three-phase balanced faults, the value of this coefficient is not important, i.e. it can be assumed as being equal to zero. So, finally the total fault current I_{F }for three-phase balanced faults is equal to:
I_{F}=a_{F1}I^{F1}a_{F2}+a_{F0}I_{F0} (29),
where the resultant coefficients are:
a_{F1}=1−a^{2}, a_{F2}=0, and a_{F0}=0
and where
I_{F1 }is defined by equation (25).
An alternative way of determining the value of tg(γ) from equation (19) is shown in the following.
An alternative way of determining the value of tg(γ) relies on considering the fault current distribution factor k_{F }and calculating tg(γ) as the ratio of the imaginary and the real parts of this factor:
The fault current distribution factor k_{F }can be expressed as follows:
where:
ΔI_{A1}, I_{A2 }are the incremental positive and the negative sequence component of the currents at the relay point A,
M_{1}=Z_{1SA}+Z_{1SB}+Z_{1L }with the local source impedances Z_{1SA }and Z_{1SB }at the respective relays,
K_{1}=−Z_{1L},
L_{1}=Z_{1SB}+Z_{1L }and
a_{F1}, a_{F2 }are share coefficients, dependent on fault type according to Table 5.
In equation (31) the fault current distribution factor k_{F }is derived for the single line case by avoiding zero sequence quantities. It is also taken into account that the positive and negative sequence impedances of the transmission network are identical.
The fault current distribution factor k_{F }according to equation (31) can be further written in the form:
where:
h_{1}=a_{F1}M_{1}=a_{F1}(Z_{1SA}+Z_{1SB}+Z_{1L}),
h_{2}=a_{F2}M_{1}=a_{F2}(Z_{1SB}+Z_{1SB}+Z_{1L}) and
q(d)=K_{1}d+L_{1}=−Z_{1L}d+Z_{1SB}+Z_{1L}.
In order to calculate the required adaptive shift ΔZ from equation (17) with taking into account equations (30) and (32), the impedance parameters of the network are required to be known. For this purpose the relay A measures the local source impedance Z_{1SA }while information on the remote source impedance Z_{1SB }is taken from the memory of relay A which is updated after each line fault by sending the actual measured remote source impedance value Z_{1SB }via the communication channel. The coefficient q(d) is dependent on the distance to fault d, which in fact is unknown, and therefore the three specific values of the distance corresponding to the beginning with d_{i}=0, the middle with d_{i}=0.425 p.u. and the end with d_{i}=0.85 p.u. of the first zone of the distance protection are substituted. Afterwards it is verified, which one of them is closest to the reality. As a result of that the fault current distribution factor is expressed as:
where:
d_{i}=0 or
d_{i}=0.425 p.u. or
d_{i}=0.85 p.u.
Therefore, there are three specific shifts of the impedance characteristic ΔZ_{i }which are considered and finally, after certain checking, one of them is utilized.
Use of the proposed method assures adaptation of the impedance characteristic of the distance relay to the actual fault conditions and as a result of that the relay operation improvement.