TRANSMISSION LINE DISTANCE

Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I Power System Protection for Engineers Transmission Line Distance Protection Part 1 Copyright © SEL 2005 Technical papers supporting this section: 6022.pdf, Z = V/I Does Not Make a Distance Relay by J. Roberts; A. Guzman; E.O. Schweitzer, III General books of Power System Protection. Transmission Line Distance Prot 1_r12 1 Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I Transmission Line Distance Protection (Part 1) Objectives z z z z Describe distance relay operation, design principles, and connections Discuss infeed effect in distance relays Describe the effect of fault resistance on the impedance measured by distance relays Discuss impedances measured by distance elements for different fault types, and the resulting need for fault type selection Transmission Line Distance Prot 1_r12 2 Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I Transmission Line Protection Principles z Overcurrent (50, 51, 50N, 51N) z Directional Overcurrent (67, 67N) z Distance (21, 21N) z Differential (87) This section is an introduction to the topic of transmission line protection using distance relays. Further sections and courses will complete the wide and interesting topic of distance protection. Transmission Line Distance Prot 1_r12 3 Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I Three-Phase Fault on a Radial Line L d Radial Line Three-Phase Bolted Fault For a perfect three-phase fault, only the positive-sequence impedance is involved in the calculations. With the usual convention, the phase “a” voltage and current are equal to the positive-sequence voltage and current. Transmission Line Distance Prot 1_r12 4 Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I Impedance Diagram ( d / L ) Z L1 Z S1 + V1 = Va + E - I1 = I a - I 1 = I a = I FAULT = z z Bolted Fault E Z S 1 + ( d / L ) Z L1 Zs1 is System’s Thevenin Equivalent Impedance. It Depends on Whole System State (Topology, Load, etc.) The positive-sequence impedance diagram for a three-phase fault is as shown in the figure. For this radial system, disregarding the influence of load, the fault current in each phase is balanced and is equal to the phase current measured by the relays at the substation. This current depends on the following parameters: • System voltage • Line impedance • Distance to the fault • Thevenin impedance equivalent to the system “behind” the substation bus The Thevenin impedance depends on the conditions of the system, such as the topology and system loading. Transmission Line Distance Prot 1_r12 5 Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I Overcurrent Relay Setting and Reach z Phase Instantaneous Element (50) Commonly Set to Reach Faults up to 80% of Total Line Length L 0.8L Radial Line Three-Phase Bolted Fault z Relay Setting Calculated for a Given Value of ZS1 I SETTING ≈ E Z S 1 + ( 0 . 8 ) Z L1 A phase instantaneous overcurrent element is set to detect fault currents up to 80 percent of the line length. This gives enough security margin (20 percent) to avoid non-selective operation for faults beyond the remote bus. The relay setting is calculated for a given value of the equivalent ZS1. Transmission Line Distance Prot 1_r12 6 Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I Overcurrent Relay Problem I SETTING ≈ z z E Z S 1 + ( 0 . 8) Z L1 Relay Operates When the Following Condition Holds: I FAULT = I a > I SETTING As Zs1 Changes, the Relay’s “Reach” Will Change, Since Setting is Fixed I FAULT ( LIMIT ) = E Z S′1 + ( 0 .8) Z L1 As the system topology behind the substation bus changes, ZS1 changes. As a result, the relay “reach” will change. The only way to avoid non-selective operations for faults beyond the remote bus is to calculate the instantaneous setting for the worst case value of ZS1, which results in a shorter reach of the instantaneous element for all other system configurations. It is highly probable that the system presents the worst case value for relatively short periods of time, meaning that the relay reach will be permanently sacrificed for a situation that occurs for short periods. This is a disadvantage of instantaneous overcurrent relays. Transmission Line Distance Prot 1_r12 7 Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I Distance Relay Principle L d Ia, Ib, Ic Va, Vb, Vc 21 Three-Phase Solid Fault Radial Line Suppose Relay is Designed to Operate When: | Va |≤ (0 .8) | Z L1 || I a | Suppose that it is possible to design a relay that operates not when the current is larger than a given threshold, but when the phase voltage is less than the current times a constant, as shown in the figure. This relay requires voltage and current information. Transmission Line Distance Prot 1_r12 8 Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I Distance Relay Principle For a Perfectly Balanced Three-Phase Fault at Distance d: V a = ( d / L ) Z L1 I a Therefore, the Relay will Operate when: | ( d / L ) Z L1 I a |≤ (0 .8) | Z L1 || I a | ⇒ d ≤ 0 .8 L This Result Does Not Depend on the Thevenin Impedance The inequality originally stated in terms of voltage and current implicitly states that the relay will operate when the distance to the fault is less than a given limit distance, called the distance relay reach. Ideally, the reach of such a relay does not depend on the source impedance. Transmission Line Distance Prot 1_r12 9 Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I Impedance Relay If Relay Operates for: | Va |≤ (0 .8) | Z L1 || I a |, Then Equivalent is: | Va | ≤ ( 0 .8) | Z L1 | | Ia | The Quantity | Va | | Ia | …is an impedance This relay is called impedance or “under-impedance” relay because the relay design is such that the relay operates for an impedance condition. The relay measures or “sees” a given impedance, equal to the ratio of the applied sinusoidal voltage and the applied sinusoidal current. Transmission Line Distance Prot 1_r12 10 Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I Apparent Impedance Define the Apparent Impedance for this Relay as: Z = R + jX = Z ∠ θ = Va Ia Relay Operating Condition Becomes: | Z |< (0 .8) | Z L1 | Which is Equivalent to: R 2 + X 2 ≤ ( 0 .8) | Z L1 | ⇒ R 2 + X 2 ≤ (( 0.8) | Z L1 |) 2 The apparent impedance is a concept used to describe the impedance “measured’ or “seen” by a distance relay. It is defined as the ratio between the voltage and current phasors applied to the relay. For the particular case that has been described, these quantities are Va and Ia. Transmission Line Distance Prot 1_r12 11 Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I Relay Setting Define the Relay Setting as: Z r 1 = ( 0 .8) | Z L1 | The Relay Operating Condition Becomes: Z ≤ Z r1 Or…. R 2 + X 2 ≤ Z r21 The maximum reach of the distance relay, in terms of impedance, is normally an adjustable value of the relay. Therefore, the same relay can be used for different lines. Transmission Line Distance Prot 1_r12 12 Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I Under-Impedance Relay Implementation V I Z r1 Z r1 I Operates When: Magnitude Comparator TRIP | V |≤| Z r 1 I | ⇒ Z ≤ Z r1 The figure shows the simplest design for an under-impedance relay. The current is passed through a single amplifier. The magnitude of the resulting quantity is compared to the magnitude of the voltage by a two-input magnitude comparator. The gain of the amplifier Zr1 is the relay setting. In the past, these devices were implemented through use of an electromechanical balance unit. Today, in computer-based relays, the relay equation is directly implemented in the relay routines. Transmission Line Distance Prot 1_r12 13 Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I Impedance Calculation Example Ia, Ib, Ic Va, Vb, Vc 69 kV Line zL1=0.24+j0.80 Ohms/mile L = 15 miles 21 Z L1 = (0.24 + j 0.8) ⋅15 = = 3.6 + j12 Ohms Relay setting: Z r1 = (0.8) | 3.6 + j12 |=10.02 Ohms Relay will operate for: R 2 + X 2 ≤ 10.02 2 = 100.4 Ohms This example shows the calculations involved in the determination of a simple impedance relay setting. Transmission Line Distance Prot 1_r12 14 Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I Primary and Secondary Ohms z Relay is Receiving Secondary Volts and Secondary Amps Vsec = V prim VTR ; I sec = I prim CTR VTR Define : ZTR = CTR V prim V prim I prim Z prim V Z sec = sec = VTR = VTR = I prim I sec ZTR CTR CTR The setting calculated in the former slide is in primary ohms. Because the relay is connected to CTs and VTs, the ratios of the instrument transformer must be considered. It is usual to find an impedance ratio ZTR = VTR/CTR to determine the secondary impedance measured by the relay. This ZTR is also used to determine the actual relay setting, in secondary ohms. Transmission Line Distance Prot 1_r12 15 Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I Impedance Calculation Example Ia, Ib, Ic Va, Vb, Vc 69 kV Line zL1 = 0.24+j0.80 Ohms/mile L = 15 miles 21 Z L1 = (0.24 + j 0.8) ⋅15 = = 3.6 + j12 Ohms VTR = 40000 / 120 CTR = 600 / 5 ⇒ ZTR = VTR / CTR = 2.77 Relay setting at 80% of Line Z: Z r1 = 10.02 / 2.77 = 3.62 Secondary Ohms This is the same example as before, but now the relay setting is calculated in secondary ohms. Transmission Line Distance Prot 1_r12 16 Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I The Complex Impedance Plane z The Apparent Impedance Z Can Be Represented in a Complex Plane Z = R + jX = Z ∠ θ X Z θ R The complex plane is commonly used to represent the apparent impedance measured by distance relays. Transmission Line Distance Prot 1_r12 17 Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I The Impedance Relay Characteristic R 2 + X 2 ≤ Z r21 X Plain Impedance Relay Z ≤ Z r1 Operation Zone Zr1 Radius Zr1 R A plain impedance relay will operate for any apparent impedance whose magnitude is less than, or equal to, the relay setting. In the complex plane, this is represented by the region within a circle with radius equal to the relay setting. The border of the circle represents the operation threshold of the relay. Transmission Line Distance Prot 1_r12 18 Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I Unit Distance Definition L d Ia, Ib, Ic Va, Vb, Vc 21 Radial Line Three-Phase Bolted Fault m= d L The unit distance is the distance to the fault in per unit of the total line’s length. This parameter is commonly used in protective relaying. Transmission Line Distance Prot 1_r12 19 Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I The Bolted Fault Locus L d Ia, Ib, Ic Va, Vb, Vc 21 Radial Line Three-Phase Bolted Fault V a = ( d / L ) Z L1 I a The Apparent Impedance is: Z = Va = ( d / L ) Z L 1 = m Z L1 Ia If the apparent impedance of a distance relay is calculated for three-phase bolted faults along the line, for distances varying from 0 miles to L miles, the resulting set of complex numbers can be plotted in the complex impedance plane. Transmission Line Distance Prot 1_r12 20 Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I The Bolted Fault Locus Apparent Impedance: Z = m Z L1 = mZ L1∠ θ L1 = mR L1 + jmX L1 ; For 0 ≤ m ≤1 X ZL1 XL1 θL1 RL1 This line segment is the locus of the apparent impedance for solid faults over the line. R This set of points is a line segment as shown in the figure. The segment has the same length and angle as the total line impedance and is called the bolted fault locus. Transmission Line Distance Prot 1_r12 21 Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I Line Protection With Impedance Relay Solid Fault Locus X Z = m Z L1 ; Z ≤ Z r1 Operation zone Zr1 0 ≤ m ≤1 R If the fault locus is superimposed with the relay operating characteristic in the same complex plane, the resulting plot indicates the degree of protection of the relay. The case shown in the figure represents a case in which the relay has been set to reach faults up to ~80 percent of the line. Transmission Line Distance Prot 1_r12 22 Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I Distance Protection Load vs. Fault Apparent Impedance V I Fault Relay Bolted Fault Locus X Fault Load V Z= I Operation Zone R During normal load conditions, the impedance “seen” by a distance relay has a magnitude much larger than the length of the bolted fault locus (line). When a fault occurs, the impedance moves instantly to a point in the complex plane located on, or very near, the bolted fault locus. The accuracy of this statement for non-bolted faults will be shown later. Transmission Line Distance Prot 1_r12 23 Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I Need for Directionality F1 F2 1 2 3 4 RELAY 3 Operation Zone 5 6 X F1 R F2 Non-Selective Relay Operation Transmission Line Distance Prot 1_r12 24 Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I Directionality Improvement F1 F2 1 2 3 RELAY 3 Operation Zone 4 6 X F1 Directional Impedance Relay Characteristic R F2 The Relay Will Not Operate for This Fault Transmission Line Distance Prot 1_r12 5 25 Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I Mho Element Characteristic (Directional Impedance Relay) Operates when: X V ≤ I Z M cos(ϕ − ϕ MT ) Z ≤ Z M cos(ϕ − ϕ MT ) ZM ϕMT ϕ Z R There are three traditional distance elements: impedance-type, reactance-type, and Mhotype distance elements. The figure shows the operation equation and operating characteristic of a Mho distance element. The characteristic is the locus of all apparent impedance values for which the relay element is on the verge of operation. The operation zone is located inside the circle, and the resraint zone is the region outside the circle. The Mho characteristic is a circle passing through the origin of the impedance plane. The Mho element operates for impedances inside the circle. The characteristic is oriented towards the first quadrant, which is where forward faults are located. For reverse faults, the apparent impedance lies in the third quadrant and represents a restraint condition. The fact that the circle passes through the origin is an indication of the inherent directionality of the Mho elements. However, close-in bolted faults result in a very small voltage at the relay that may result in a loss of the voltage polarizing signal. This needs to be taken into consideration when selecting the appropriate Mho element polarizing quantity. There are typically two settings in a Mho element: the characteristic diameter, ZM, and the angle of this diameter with respect to the R axis, ϕMT. The angle is equivalent to the maximum torque angle of a directional element. The Mho element presents its longest reach (greatest sensitivity) when the apparent impedance angle ϕ coincides with ϕMT. Normally, ϕMT is set close to the protected line impedance angle to ensure maximum relay sensitivity for faults and minimum sensitivity for load conditions. Transmission Line Distance Prot 1_r12 26 Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I How to Implement a Mho Relay Signal V S1 Phase Forming Comparison I Trip S2 Signal Forming S1 = −V + I Z r ; S2 = V Operation Condition: Operating Quantity − λ1 ≤ arg(S1 S 2 ) ≤ λ2 Polarizing Quantity The early electromechanical relays with a Mho characteristic used a product unit (induction cylinder element) to achieve the torque equation: V2 – V I cos(θ-θMT) > 0. Analog static relays used a two-input phase comparator to create the Mho characteristic. The inputs to the comparator are properly mixed from the original voltage and current to obtain the desired behavior. Transmission Line Distance Prot 1_r12 27 Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I How to Implement a Mho Relay S1 = −V + I Z r ; S 2 = V − 90o ≤ arg(S1 S 2 ) ≤ 90 o − 90o ≤ arg((−V + I Z r ) V ) ≤ 90o ⎛ −V / I + Zr ⎞ ⎟⎟ ≤ 90o − 90 o ≤ arg⎜⎜ ⎠ ⎝ V /I ⎛Z −Z ⎞ ⎟⎟ ≤ 90 o − 90o ≤ arg⎜⎜ r ⎝ Z ⎠ These simple algebraic manipulations show how the voltage-current equations become impedance equations. Transmission Line Distance Prot 1_r12 28 Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I How to Implement a Mho Relay Mho Circle Threshold: ( ) arg ( Z r − Z ) Z = ± 90 X B Zr Zr-Z 90o Z A R The operation condition is the region within the Mho circle. Zr and the angle, defining the circle diameter, are the relay settings. The shape and position of the circle can be changed by changing the inputs to the phase comparator. Currently, with computer-based relays, it is much easier to implement a Mho relay. Transmission Line Distance Prot 1_r12 29 Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I Distance Relay Timing and Coordination Operation Time Zone 3 Zone 2 Zone 1 1 A 3 2 4 B 5 6 C Zone 1 is Instantaneous So far, a directional distance relay, which operates instantaneously and is set to reach less than 100 percent of the protected line, has been described. Two important principles of protection have been missing: 1. What happens for a fault on the protected line that is beyond the reach of the relay? 2. If the relay operates instantaneously, it cannot be used as a remote back-up for a relay protecting a line adjacent to the remote substation. These two problems are overcome by adding time-delay distance relays. This is accomplished by using the distance relay to start a definite time timer. The output of the timer can then be used as a tripping signal. The figure shows how a second zone (or step) is added to each of the directional impedance relays. A third zone, with a larger delay, can also be added. The operation time of the second zone is usually around 0.3 seconds, and the third zone around 0.6 seconds. However, the required time depends on the particular application. The ohmic reach of each zone also depends on the particular power system. The figure and the next slide show a typical reach scheme for three zones. What about Circuit Breakers 2, 4 and 5? Transmission Line Distance Prot 1_r12 30 Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I The Reach of Mho Elements Relay Settings X Zone 3 C B Relays at A (CB 1) Zone 2 A R Zone 1 The slide shows how the instantaneous Zone 1, and the delayed Zones 2 and 3 look in a complex impedance plane if Mho units are used for all three zones. Note the reference to buses A, B, and C of the previous slide, which indicate that the distance elements correspond to the relays associate with Circuit Breaker 1, located at Substation A. Transmission Line Distance Prot 1_r12 31 Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I Three-Zone Distance Protection Time Zone 3 Zone 2 Zone 1 1 2 3 4 5 6 Time What about Circuit Breakers 2, 4, and 5? The figure shows the operating time as a function of the electrical distance for six distance relays. Here, the relays “looking” in both directions are shown. We show the characteristics for Relays 1, 3, and 5 above the system one-line diagram. We represent the characteristics for Relays 2, 4, and 5 below the one-line diagram. Zone 1 must underreach the remote line end to make sure that it will not operate for faults in the adjacent lines. Zone 2 is intended to cover the end of the protected line, so it must overreach the protected line. Zone 3 is intended to provide remote backup protection to adjacent lines, so it must overreach the longest adjacent line. We typically leave a coordination interval (including breaker tripping time) between Zones 1 and 2 and between Zones 2 and 3 of adjacent distance relays. This means that the end of Zone 2 of a backup relay should not overlap with the begininning of Zone 2 of the primary relay. The same is true for adjacent third zones. This is not always possible, however. In the figure, we can see that faults located in the central section of a given line are cleared by simultaneous and instantaneous operation of the first zones at both line ends. Should a first zone fail to operate, the remote backup relay operates in second or third zone. On the other hand, faults close to one line end will be cleared sequentially: the nearest line end will operate in first zone, and the remote end will operate in second zone. This sequential fault clearing is a limitation of distance protection, because it could jeopardize system stability. An advantage of distance protection over directional overcurrent protection is that the distance first zone reach depends less on system operating conditions than the reach of the instantaneous overcurrent element. In other words, distance protection provides better instantaneous line coverage. Transmission Line Distance Prot 1_r12 32 Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I Line Protection with Mho Elements X C B A R D E The figure is an impedance-plane representation of a line protection scheme using Mho distance relays (both directions). A longitudinal system is formed by transmission lines AB, BC, AD, and DE. The line impedances are plotted on the complex plane, using substation A as the origin of coordinates for convenience. The Mho circles represent the three zones of the distance schemes at both ends of line AB. Transmission Line Distance Prot 1_r12 33 Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I Circular Distance Relay Characteristics X PLAIN IMPEDANCE X OFFSET MHO (2) R R X X LENS (RESTRICTED MHO 1) MHO R X R X TOMATO (RESTRICTED MHO 2) OFFSET MHO (1) R R The figure shows several commonly used circular distance relay characteristics. For analog relays, these characteristics can be obtained with phase and/or magnitude comparators. In microprocessor-based relays, they are implemented through the use of mathematical algorithms. Transmission Line Distance Prot 1_r12 34 Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I Semi-Plane Type Characteristics X X DIRECTIONAL RESTRICTED DIRECTIONAL R R X X RESTRICTED REACTANCE REACTANCE R R X X OHM QUADRILATERAL R R Here is another group of traditional distance relay characteristics. The use of one characteristic or another depends on several factors associated with the power system. These factors will be studied during this course. Transmission Line Distance Prot 1_r12 35 Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I Quadrilateral Element Characteristic X C B A R Solid-state and digital relays permit creation of highly sophisticated distance characteristics. An example is the quadrilateral characteristic, shown here. You can shape the characteristic to meet different line protection requirements. The price for this flexibility is setting complexity: there are four settings in a quadrilateral characteristic. Transmission Line Distance Prot 1_r12 36 Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I Distance Relay Connections Transmission Line Distance Prot 1_r12 37 Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I Line Faults – Simplified Analysis POWER SYSTEM L d p q Ia, Ib, Ic Fault Va, Vb, Vc 21 So far, the design, operation, and setting of distance relays for three-phase bolted faults has been studied. In this part of the course, it will be shown that the voltage and current applied to the relay for it to correctly measure the “distance to the fault” depends on the type of fault. Different types of bolted short circuits on a transmission line will be studied to determine the phase currents and voltages (Ia, Ib, Ic, Va, Vb, Vc) at the distance relay location. Transmission Line Distance Prot 1_r12 38 Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I Line Equations During a 3-Phase Fault Ia a Ib b Ic c Va Vb V c Three-Phase Fault Va = m( Z S I a + Z m I b + Z m I c ) + 0 = m( Z S − Z m ) I a Vb = m( Z m I a + Z S I b + Z m I c ) + 0 = m( Z S − Z m ) I b Vc = m( Z m I a + Z m I b + Z S I c ) + 0c = m( Z S − Z m ) I c The three-phase, short-circuit case is repeated here to introduce the procedure to be used. The line equations correspond to a symmetrical, or transposed, line. The three phases are set to zero voltage at the fault location. The unit distance, m, is used as the distance to the fault point. Transmission Line Distance Prot 1_r12 39 Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I Review of Self and Mutual Impedances Z L1 = Z S − Z m ; Z L 0 = Z S + 2Z m ⇒ Z S = ( Z L 0 + 2 Z L1 ) / 3; Z m = ( Z L 0 − Z L1 ) / 3 Recall the relationships between the self and mutual impedances with the positivesequence and zero-sequence impedances. Transmission Line Distance Prot 1_r12 40 Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I Relay Connection for a 3-Phase Fault Va = m( Z S − Z m ) I a = mZ L1 I a Vb = m( Z S − Z m ) I b = mZ L1 I b Vc = m( Z S − Z m ) I c = mZ L1 I c ⇒ Va V V = mZ L1 ; b = mZ L1 ; c = mZ L1 ; Ib Ic Ia z z A single distance element could be enough to detect balanced three-phase faults. The element should be connected to any phase voltage and current. The algebraic development shows that a single distance element is enough to detect balanced three-phase faults. The element should be connected to any phase voltage and current to properly measure the positive-sequence impedance existing between the relay location and the fault. This impedance is directly proportional to the distance. Transmission Line Distance Prot 1_r12 41 Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I Line Equations for a “B-C” Fault a Ib b Ic c Va Vb Vc B-C Fault Va = m( Z S I a + Z m I b + Z m I c ) + V fa Vb = m( Z m I a + Z S I b + Z m I c ) + V fb Vc = m( Z m I a + Z m I b + Z S I c ) + V fb For a b-c fault, the relevant border condition is that the voltages of phase b and c are equal at the fault point. Transmission Line Distance Prot 1_r12 42 Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I Relay Connection for a B-C Fault Vb − Vc = m( Z S − Z m )( I b − I c ) Vb − Vc = mZ L1 ( I b − I c ) ⇒ Vb − Vc = mZ L1 Ib − Ic z A single distance element for Vb-Vc and Ib-Ic will measure the fraction of positive-sequence line impedance between the relay location and the fault The algebraic manipulation leads to the conclusion shown in the slide. A similar development can be done for a-b and c-a faults. Transmission Line Distance Prot 1_r12 43 Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I Phase Distance Element Connections Relay Element ab bc ca Voltage Va − Vb Vb − Vc Vc − Va Current Ia − Ib Ib − Ic Ic − Ia Measured Impedance (Solid Fault): m Z L1 The table summarizes phase distance element connections. Line-to-line voltages and the difference of the currents of these lines are used as relay input signals. The result is that the relay element, corresponding to the fault loop, measures the positive-sequence impedance of the faulted line section. Transmission Line Distance Prot 1_r12 44 Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I Phase A-to-Ground Fault Line Equations a Ib b Ic c Va Vb Vc A-to-Ground Fault Va = m( Z S I a + Z m I b + Z m I c ) + 0 Vb = m( Z m I a + Z S I b + Z m I c ) + V fb Vc = m( Z m I a + Z m I b + Z S I c ) + V fc The case of a Phase A-to-ground fault is studied by making the Phase A voltage equal to zero at the fault point. The equation for Phase A is then algebraically manipulated as shown in the next slide. Transmission Line Distance Prot 1_r12 45 Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I Phase A-to-Ground Fault Relay Connection Va = m( Z S I a − Z m I a + Z m I a + Z m I b + Z m I c ) = = m(( Z S − Z m ) I a + Z m ( I a + I b + I c )) = ⎡ ⎤ ⎡ ⎤ Z − Z L1 Z − Z L1 = m ⎢ Z L1 I a + L 0 ( I res )⎥ = mZ L1 ⎢ I a + L 0 I res ⎥ = 3 3Z L1 ⎣ ⎦ ⎣ ⎦ = mZ L1 I a + k0 I res ; where k0 = ( Z L 0 − Z L1 ) /(3Z L1 ) [ ] Va = mZ L1 I a + k0 I res The result of the manipulation is that, for the relay to properly measure the positive sequence impedance between the relay location and the fault, the relay must receive: • The phase “a” voltage • The phase “a” current plus a residual current compensation factor. The compensation factor, ko, is called the residual compensation factor, or the zero sequence compensation factor because the residual current is three times the zero-sequence current. A similar result is obtained for b-to-ground and c-to-ground faults. Transmission Line Distance Prot 1_r12 46 Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I Ground Distance Relay Connections Relay Element Voltage AG Va BG Vb CG Vc k0 = Z L 0 − Z L1 Current r I a + k0 I res r I b + k0 I res r I c + k 0 I res Compensation factor 3Z L1 Measured Impedance (Bolted Fault): m Z L1 The table summarizes ground distance element connections. Phase voltages and compensated line currents are used as relay input signals. The current signal is compensated by adding a factor derived from the zero-sequence current. The multiplying factor k0 is, in general, a complex number that depends on the line zero-sequence and positive-sequence impedances. There are two basic sources of error in this connection. One of these is line asymmetry. By using a symmetrical component scope, it is assumed that the line is ideally transposed. Untransposed lines, however, are becoming common. Line asymmetry could produce errors on the order of 5 percent in distance estimation. This error must be accomodated by pulling back the relay first zone reach. Another source of error is the typical assumption that angles ZL1 and ZL0 are equal. Under this assumption, k0 is a real number. In analog relays, it is much easier to create a real number than a complex multiplying factor. There are other connections for ground distance elements. One of these uses the phase voltage and a compensated line current as input signals. The connection uses the currents of the other two lines (instead of the zero-sequence current) for compensation. Asymmetrical lines are not a source of error for this connection. A drawback is complexity: you must set two multiplying factors (instead of only k0). Transmission Line Distance Prot 1_r12 47 Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I Self-Polarizing Scheme Connections RELAYS V I A-B Va-Vb Ia-Ib PHASE B-C Vb-Vc Ib-Ic RELAYS C-A Vc-Va Ic-Ib A Va Ia + k0 Ires B Vb Ib + k0 Ires C Vc Ic + k0 Ires GROUND RELAYS The table summarizes the results obtained in the former development. There are other ways of connecting (polarizing) the distance relays. This particular way is called the self-polarizing scheme. In the past, six relays (or measuring units) were required for each distance relay zone to implement a non-switching scheme like this. Today, this protection can be implemented in a single microprocessor-based relay. Transmission Line Distance Prot 1_r12 48 Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I Distance Protection Summary z z z z Current and Voltage Information Phase Elements: More Sensitive Than 67 Elements Ground Elements: Less Sensitive Than 67N Elements Application: Looped and Parallel Lines In summary, distance protection uses current and voltage information to make a direct, or indirect, estimate of the distance to the fault. Phase distance elements (21) are more sensitive than phase directional overcurrent elements (67). On the other hand, ground distance elements (21N) are less sensitive than ground directional overcurrent elements (67N). A widely used combination for transmission line protection uses 21 elements for phase fault protection and 67N elements for ground fault protection. Transmission Line Distance Prot 1_r12 49 Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I Distance Protection Problems z Infeed z Fault Resistance z Unequal Measured Impedances During Faults z Evolving Faults z Load Encroachment Transmission line protection is complex. Problems such as infeed, fault resistance, unequal measured impedances during faults, load encroachment, and mutual coupling affect the apparent impedance of distance relays. Fault resistance and mutual coupling also affect ground directional overcurrent relays. These problems may be complicated by the evolving character of many faults. Transmission Line Distance Prot 1_r12 50 Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I Distance Protection Problems z Mutual Coupling z Simultaneous Faults z Cross-Country Faults z Power Swings z Series-Compensated Lines All these problems may affect distance and directional overcurrent relays. Cross-country faults, simultaneous faults, and CT saturation may also present a problem for differential schemes. Series-compensated lines are extremely difficult to protect. All protection principles may have problems, because of the possibility of voltage and current inversions. If the series compensation capacitors are carefully selected, the possibility of current inversions can be eliminated. In this case, a differential protection scheme may be the best option. Transmission Line Distance Prot 1_r12 51 Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I Distance Protection Problems z Three-Terminal Lines z Short Lines z CT Saturation z CCVT Transients Three-terminal lines and short lines also have special protection requirements. The ringdown at subharmonic frequency resulting from compensation reactors may also create protection problems. Transmission Line Distance Prot 1_r12 52 Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I Infeed Effect V I ZL' ZL I' Fault 21 V = I ZL + I ' ZL' Z = V I = ZL + I' I ZL' > ZL + ZL' Infeed Produces Relay Underreach A generation source connected between the relay location and the fault point affects the value of the impedance a distance relay estimates. This is called the infeed effect. The intermediate generation source causes the relay to see an impedance that is equal to the adjacent line multiplied by a factor. This factor is the ratio of the current in the adjacent line to the relay current. The infeed-effect factor is, in general, a complex number with a magnitude greater than unity. The infeed effect results in the relay estimating an impedance value greater than the real impedance between the relay and the fault, ZL + Z’L. This inaccurate impedance value estimation produces distance relay underreach. Transmission Line Distance Prot 1_r12 53 Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I Example: Third Zone Setting A B ZAB IAB C ZBC IBC Fault 21 Z = ZAB + ZBC Without Infeed: With Infeed: Z = Z AB + IBC IAB ZBC Set Third Zone Considering Infeed The infeed effect needs to be taken into account when distance relay settings are calculated. For example, the third zone at A (see figure) will measure ZAB + ZBC for a fault at C without infeed. When the intermediate source is present, the impedance estimate is greater because of the IBC/IAB factor. The third zone needs to completely cover the adjacent line BC for all system operating conditions. Thus, the third zone reach needs to be set considering the possible infeed. As a result, the third zone may reach far beyond substation C when the intermediate source is out of service. This factor needs to be considered when checking adjacent third zones for possible overlap. Infeed effect does not affect first zones, except in three-terminal lines. In this case, the first zone needs to be set without infeed to make sure that the zone will not overreach the remote line end. Setting a first zone in this manner results in the presence of the intermediate source reducing the first zone reach, thus limiting the high-speed coverage of the protected line. The infeed effect also needs to be considered for second zone reach settings. In threeterminal lines, the second zone should be set with maximum infeed at the third terminal to ensure full coverage of the protected line. On the other hand, in two-terminal lines, the second zone should be set for minimum infeed at the remote-end substation to avoid overlapping with the beginning of the adjacent second zone. Transmission Line Distance Prot 1_r12 54 Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I Outfeed ZL Z L' I I' 21 ZL Z L' I' 21 Z = ZL + I' I ZL < ZL + ZL ' ' Outfeed Produces Relay Overreach Outfeed is the result of having two paths of current flow after the relay has monitored the current. An outfeed condition may exist when two or more adjacent lines are connected in parallel. In three-terminal lines, outfeed may exist if there is a strong external tie between two line terminals. The magnitude of the outfeed effect factor, I’ / I, is smaller than unity, which produces a reduced impedance estimate. The result is relay overreach. The outfeed effect also needs consideration when calculating settings for a distance relay. Transmission Line Distance Prot 1_r12 55 Power System Protection for Engineers – PROT 401 Section 13 - Transmission Line Distance Protection - Part I Any Questions? z Line Distance Protection is Continued in the Next Section Transmission Line Distance Prot 1_r12 56