10.4 Distance / Impedance Protection (21) for Transmission Lines & Directional Relays (67)

10.4 Distance / Impedance Protection (21) for Transmission Lines & Directional Relays (67)

Transmission lines form the interconnected grid network connecting power generation stations to regional distribution load centers. Because transmission circuits are exposed to atmospheric disturbances, lightning, tree contacts, and severe weather across hundreds of miles, they experience more faults than any other power system apparatus.

While overcurrent relays (51) struggle on transmission networks due to wide variations in fault current caused by changing generation dispatch, Distance Protection (IEEE Device 21) measures the ratio of voltage to current ($Z = V/I$). Because transmission line impedance is strictly proportional to physical line length ($Z_{line} = z \times L$), distance relay reach is fixed and independent of source impedance variations.

On the NCEES PE Electrical and Computer: Power examination, distance protection questions test your mastery of stepped zone reach settings (Zones 1, 2, 3), R-X diagram interpretation (Mho vs. Quadrilateral vs. Reactance characteristics), secondary impedance scaling ($CTR/PTR$), current infeed effects, pilot communication schemes (PUTT, POTT, DCB, 87L), and directional overcurrent polarization (67/67N).

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1. Operating Principle of Distance Relaying (Device 21)

A distance relay continuously samples local secondary phase voltages and line currents from substation VTs and CTs to compute the apparent impedance ($Z_{seen}$) seen looking into the transmission line:

$Z_{seen} = \frac{V_{relay}}{I_{relay}} = \frac{V_{pri} / PTR}{I_{pri} / CTR} = \left( \frac{V_{pri}}{I_{pri}} \right) \times \left( \frac{CTR}{PTR} \right) = Z_{pri} \times \left( \frac{CTR}{PTR} \right) \quad [\Omega_{\text{secondary}}]$

$\text{Secondary Impedance Conversion Factor: } K_Z = \frac{CTR}{PTR}$

$Z_{secondary} = Z_{primary} \times \left( \frac{CTR}{PTR} \right) \quad [\Omega]$

Where:

• $CTR = \frac{I_{pri,rated}}{I_{sec,rated}}$ = Current Transformer Ratio (e.g., $1200:5 \implies CTR = 240$).
• $PTR = \frac{V_{pri,rated}}{V_{sec,rated}}$ = Potential/Voltage Transformer Ratio (e.g., $230\text{ kV} : 115\text{ V} \implies PTR = 2000$).

                  DISTANCE RELAY IMPEDANCE MEASUREMENT SCHEMATIC

          Substation Bus A                                          Substation Bus B
        -------+-------------------- Transmission Line AB --------------------+-------
               |  Line Impedance: Z_AB = (r + jx) * Length                    |
              (●) CT (Ratio = CTR)                                            |
               |                                                              |
              [VT] (Ratio = PTR)                     Fault Point (F)          |
               |                                            |                 |
               +---> V_sec                                  v                 |
               |           +----------------+               |                 |
               +---------->| Distance Relay |<--------------+                 |
                     I_sec |   (Device 21)  | Z_seen = V_sec / I_sec = z * d  |
                           +----------------+                                 |
                                 | Trip (if Z_seen < Z_set)                   |
                                 v                                            |
                           [ Breaker 52 ]                                     |

Why Distance Relaying Outperforms Overcurrent on Transmission Grids:

1. Fixed Operating Zone: The reach of a distance relay depends on the physical series impedance of the line conductor ($z\ \Omega/\text{mile}$), remaining constant whether system generation is at peak or off-peak minimum.
2. High Selectivity: Discriminating between faults inside the protected zone and remote external faults is straightforward because impedance drops linearly as the fault approaches the relay terminal.

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2. Relay Characteristics on the R-X Complex Impedance Diagram

The operating boundaries of distance relays are plotted on the R-X Complex Impedance Plane, where the horizontal axis represents resistance ($R$) and the vertical axis represents inductive reactance ($X$).

                      R-X COMPLEX IMPEDANCE DIAGRAM CHARACTERISTICS

         Reactance (X)
              ^
              |                      Reactance Characteristic: X = X_set (Horizontal Line)
              |                     .-----------------------------------------------------
              |                    / 
              |                   /    Mho Circle Characteristic: Passes through Origin (0,0)
              |                  /    +----------------+
              |                 /   /         * (Reach)| \
              |                /  /         . '        |   \
              |     Line Angle/  |      . '            |    |
              |       (θ)    /  /   . ' Line Vector    |     \
              |             /  |  * Z_line             |      |
              |            /   |                       |      |
              |           /     \                     /      /
              |          /        \                 /      /
              |         /           +--------------+      /
              |        /                  Origin         /
   -----------+-------+---------------------*-----------+-----------------------> Resistance (R)
              |                                        /
              |        Quadrilateral Characteristic:  /
              |        [Independent X_reach & R_reach]

+---------------------------------------------------------------------------------------------------+
|                     COMPARISON OF R-X IMPEDANCE CHARACTERISTICS                                   |
+---------------------------------------------------------------------------------------------------+
| Characteristic Type | Geometric Boundary on R-X Plane       | Advantages & Application            |
| :---                | :---                                  | :---                                |
| **Mho (Admittance)**| Circle passing through origin $(0,0)$;| Inherently directional; self-       |
|                     | diameter aligned with line angle      | polarizing; standard for medium     |
|                     | $\theta_{line} = \arctan(X/R) \approx 75-85^\circ$.| and long transmission lines.        |
| **Quadrilateral**   | 4 independent boundary lines:         | Highly adjustable resistive reach;  |
| **(Quad)**          | Top (Reactance $X$), Right (Fault $R$),| ideal for short lines where arc and  |
|                     | Left ($R_{left}$), Bottom (Directional).| tower-footing resistance are high.  |
| **Reactance**       | Horizontal straight line ($X = X_{set}$).| Immune to fault arc resistance      |
|                     |                                       | ($R_{arc}$); requires directional sup.|
| **Impedance**       | Circle centered at origin $(0,0)$.    | Non-directional; highly vulnerable   |
| **(Plain Circle)**  |                                       | to load encroachment and power swings.|
+---------------------------------------------------------------------------------------------------+

Load Encroachment and Blinders

Under heavy line loading conditions, high power transfer ($P + jQ$) at nominal voltage produces a low apparent impedance ($Z_{load} = \frac{V_{LL}^2}{S^*}$) with a power factor angle close to the positive real axis ($\theta_{load} \approx 0^\circ$ to $25^\circ$). If the apparent load impedance enters the distance relay operating circle, a false trip occurs (a primary cause of historical cascading blackouts). Modern relays use Load Encroachment Blinders to carve out load sectors on the R-X plane, preserving trip security.

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3. Stepped Distance Protection Schemes (Zones 1, 2, and 3)

Because instrument transformer measurement errors, line parameter modeling inaccuracies, and DC offset transient overreach exist, a single distance element cannot protect $100%$ of a transmission line instantaneously without risking false tripping for faults on the adjacent line. Power systems utilize Stepped Distance Protection comprising three distinct, coordinated zones:

                   STEPPED DISTANCE PROTECTION REACH & TIME PROFILE

    Relay at Substation A                     Substation B                  Substation C
    [ 21A ] =======================================[ 52B ]=======================[ 52C ]===>
            |<------- Line AB (Z_AB) ------------->|<------- Line BC (Z_BC) ------>|

    Time (s)
        ^
    1.2 |                                          +----------------------------------- (Zone 3: 0.8-1.2s)
        |                                          | (Covers 100% AB + 120-150% Line BC)
    0.4 |                    +---------------------+ (Zone 2: 0.3-0.5s)
        |                    | (Covers 100% AB + 20-50% shortest adjacent line)
    0.0 |--------------------+ (Zone 1: Instantaneous, 0 s)
        | (80-85% of Line AB)
        +--------------------+---------------------+-----------------------------------> Distance
        0                  85%                   100%                            220%

+---------------------------------------------------------------------------------------------------+
|                     STEPPED DISTANCE ZONE SETTING CRITERIA                                        |
+---------------------------------------------------------------------------------------------------+
| Protection Zone | Reach Setting Formula                 | Intentional Delay | Operational Purpose |
| :---            | :---                                  | :---              | :---                |
| **Zone 1**      | $Z_{set,Z1} = 0.80 \text{ to } 0.85 Z_{AB}$| Instantaneous     | High-speed clearing |
|                 |                                       | ($0\text{ s}$, $1-2\text{ cyc}$)| for 80-85% of line; |
|                 |                                       |                   | never overreaches B.|
| **Zone 2**      | $Z_{set,Z2} = 1.0 Z_{AB} + 0.20-0.50 Z_{BC,min}$| $0.30 \text{ to } 0.50\text{ s}$| 100% coverage of AB |
|                 | (Typically $120\%$ to $150\%$ of $Z_{AB}$) | ($18-30\text{ cycles}$)| & local Bus B backup|
| **Zone 3**      | $Z_{set,Z3} = 1.0 Z_{AB} + 1.20-1.50 Z_{BC,max}$| $0.80 \text{ to } 1.20\text{ s}$| Remote backup for   |
|                 | (Covers line + longest adjacent line) | ($48-72\text{ cycles}$)| adjacent lines & bus.|
+---------------------------------------------------------------------------------------------------+

The Intermediate Current Infeed Effect

When evaluating Zone 2 or Zone 3 reach into an adjacent line (Line BC), additional generation connected to the intermediate Substation Bus B injects fault current ($I_{infeed} = I_B$) into the fault:

                         INTERMEDIATE CURRENT INFEED TOPOLOGY

             Substation A          Substation B               Fault Point (F)
        [ 21A ] -----[ Z_AB ]-----+---------[ d * Z_BC ]-------------*
          I_A                     |                                  |
                                 (~) Infeed Source (I_B)             |
                                  |                                  |

$V_{relay,A} = I_A Z_{AB} + (I_A + I_B) \cdot d Z_{BC}$

$Z_{seen,A} = \frac{V_{relay,A}}{I_A} = Z_{AB} + d Z_{BC} \times \left( \frac{I_A + I_B}{I_A} \right) = Z_{AB} + d Z_{BC} \times K_{infeed}$

$\text{Infeed Factor: } K_{infeed} = 1 + \frac{I_B}{I_A} > 1.0$

[!CAUTION] Critical Infeed Underreach Rule: Because $K_{infeed} > 1.0$, the apparent impedance measured by Relay A is greater than the actual physical line impedance ($Z_{seen} > Z_{actual}$). Current infeed causes the distance relay to UNDERREACH. To ensure Zone 2 covers $100%$ of Line AB under all system operating configurations, the infeed factor must be accounted for in the reach setting calculation.

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4. Pilot Protection & Teleprotection Communication Schemes

Stepped distance schemes have an intrinsic limitation: faults occurring in the final $15%$ to $20%$ of the line near the remote terminal are cleared instantaneously by the near-end breaker (Zone 1) but take $0.30$ to $0.50\text{ seconds}$ to clear from the far-end breaker (Zone 2). To achieve simultaneous, high-speed clearing ($<2\text{ cycles}$) for $100%$ of the line length, substations exchange digital logic signals over a teleprotection communication channel (optical fiber, microwave, or power line carrier):

+---------------------------------------------------------------------------------------------------+
|                         TELEPROTECTION PILOT SCHEMES MASTER TABLE                                 |
+---------------------------------------------------------------------------------------------------+
| Scheme Name          | Overreaching/Underreaching | Channel Signal Type | Principle of Operation  |
| :---                 | :---                       | :---                | :---                    |
| **PUTT** (Permissive | Underreaching (Zone 1)     | Permissive Signal   | Fast Zone 1 sends per-  |
| Underreach Transfer) | at both ends               | (Keyed on Zone 1)   | missive; remote trips   |
|                      |                            |                     | if Zone 2 sees fault.   |
| **POTT** (Permissive | Overreaching (Zone 2)      | Permissive Signal   | Both ends see forward   |
| Overreach Transfer)  | at both ends ($120\%$)     | (Keyed on Zone 2)   | fault in Zone 2, ex-    |
|                      |                            |                     | change signal & trip.   |
| **DCB** (Directional | Overreaching (Zone 2)      | Blocking Signal     | Tripping is blocked if  |
| Comparison Blocking) | with Reverse Zone 3 Block  | (Keyed on Rev Z3)   | remote reverse element  |
|                      |                            |                     | senses external fault.  |
| **Line Current Diff**| Unit Protection            | Digital Current     | Direct phase-by-phase   |
| **(Device 87L)**     | (Kirchhoff Current Law)    | Vectors (Fiber)     | current sample vector   |
|                      |                            |                     | comparison via GPS sync.|
+---------------------------------------------------------------------------------------------------+

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5. Directional Overcurrent Relaying (Device 67 / 67N)

In looped transmission/distribution systems or parallel feeder circuits, fault current can flow in either direction through a substation breaker. Standard non-directional overcurrent relays (51) cannot be selectively coordinated in loops. Directional Overcurrent Relays (67 Phase / 67N Ground) solve this by measuring the phase angle between the fault operating current and a fixed polarizing reference quantity:

                  DIRECTIONAL OVERCURRENT (67) OPERATING REGION

                      Polarizing Reference Vector (V_pol or I_pol)
                                           ^
                                           |
                            TRIP REGION    |    (MTA: Maximum Torque Angle)
                           (Forward Fault) |   /
                                           |  /
                                           | /  Operating Current Vector (I_fault)
                                           |/ ̲ ̲ ̲ ̲ ̲ ̲ ̲
   ----------------------------------------+--------------------------------------->
                                           |
                                           |   BLOCK / RESTRAIN REGION
                                           |   (Reverse Fault)
                                           |

Polarizing Methods for Directional Relays:

1. Phase Directional Relays (67P): Voltage Polarized using line-to-line or positive-sequence voltages ($V_{pol} = V_{bc}$ for phase A element). The Maximum Torque Angle (MTA) is set between $30^\circ$ and $60^\circ$ to match the inductive system impedance angle.
2. Ground Directional Relays (67N):
   • Zero-Sequence Voltage Polarization ($V_0$): Senses $3V_0$ derived from a broken-delta VT secondary winding.
   • Zero-Sequence Current Polarization ($I_0$): Senses $3I_0$ derived from the neutral grounding CT of a local step-up or grounding transformer.

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6. Step-by-Step Worked Mathematical Example

Problem Statement

A $230\text{ kV}$, $60\text{ Hz}$ transmission network consists of three substations (Substation A, Substation B, Substation C) connected in series:

• Line AB (Protected Line): Length $= 45\text{ miles}$, positive-sequence impedance $z = 0.12 + j0.88\ \Omega/\text{mile}$ $Z_{AB} = 45 \times (0.12 + j0.88) = 5.40 + j39.60\ \Omega = 39.967\angle 82.23^\circ\ \Omega$
• Line BC (Adjacent Line): Length $= 30\text{ miles}$, positive-sequence impedance $z = 0.12 + j0.88\ \Omega/\text{mile}$ $Z_{BC} = 30 \times (0.12 + j0.88) = 3.60 + j26.40\ \Omega = 26.645\angle 82.23^\circ\ \Omega$

Substation A Instrument Transformer Data:

• CT Ratio: $1200:5\text{ A}$ ($CTR = 240$)
• VT Ratio: $230\text{ kV} : 115\text{ V}$ ($PTR = 2000$)

At Substation B, connected generation contributes infeed current such that during a fault on Line BC, the infeed current from Bus B is equal to $60%$ of the current supplied from Substation A ($I_B = 0.60 I_A \implies K_{infeed} = 1.60$).

Calculate:

1. The secondary impedance conversion factor ($K_Z$).
2. The Zone 1 primary and secondary reach settings (set at $85%$ of Line AB) and operating time.
3. The Zone 2 primary and secondary reach settings required to cover $100%$ of Line AB plus $40%$ of adjacent Line BC considering the intermediate infeed factor ($K_{infeed} = 1.60$) and operating time.
4. If an engineer incorrectly sets Zone 2 without considering infeed, calculate the apparent impedance seen by Relay A for a bolted fault at $40%$ of Line BC and determine if the relay will trip.

=========================================================================================
CALCULATION WORKFLOW & DETAILED STEP-BY-STEP SOLUTION:
=========================================================================================

Step 1: Calculate Secondary Impedance Conversion Factor (K_Z)
    CTR = 1200 / 5 = 240
    PTR = 230,000 V / 115 V = 2000
    
    K_Z = CTR / PTR = 240 / 2000 = 0.1200

Step 2: Calculate Zone 1 Reach Settings
  Zone 1 covers 85% of Line AB with zero intentional time delay (t_Z1 = 0 s):
    Z_1,pri = 0.85 * Z_AB
            = 0.85 * 39.967 Ω
            = 33.972 Ω primary (4.59 + j33.66 Ω)

  Zone 1 Secondary Setting:
    Z_1,sec = Z_1,pri * K_Z
            = 33.972 Ω * 0.1200
            = 4.0766 Ω secondary

Step 3: Calculate Zone 2 Reach Settings with Infeed (K_infeed = 1.60)
  Target Coverage: 100% of Line AB + 40% of Line BC with infeed:
    Z_2,pri = Z_AB + (0.40 * Z_BC) * K_infeed
            = 39.967 Ω + (0.40 * 26.645 Ω) * 1.60
            = 39.967 Ω + (10.658 Ω) * 1.60
            = 39.967 Ω + 17.053 Ω
            = 57.020 Ω primary (7.70 + j56.49 Ω)

  Zone 2 Secondary Setting:
    Z_2,sec = Z_2,pri * K_Z
            = 57.020 Ω * 0.1200
            = 6.8424 Ω secondary

  Zone 2 Operating Time:
    t_Z2 = 0.35 seconds (21 cycles)

Step 4: Underreach Evaluation Without Infeed Compensation
  If Zone 2 is incorrectly set without infeed:
    Z_2,no_infeed = Z_AB + 0.40 * Z_BC = 39.967 + 10.658 = 50.625 Ω primary

  Now, evaluate apparent impedance seen by Relay A during a fault at 40% of Line BC with actual infeed:
    Z_seen,actual = Z_AB + 0.40 * Z_BC * (1 + 0.60)
                  = 39.967 + 10.658 * 1.60
                  = 57.020 Ω primary

  Comparison:
    Since Z_seen,actual (57.020 Ω) > Z_2,no_infeed (50.625 Ω),
    the fault impedance falls OUTSIDE the uncompensated Zone 2 reach!
    Relay A fails to trip in Zone 2, proving that intermediate infeed causes severe
    relay underreach and must be accounted for in the reach calculation.
=========================================================================================

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7. Common PE Exam Traps & Tactical Pitfalls

• Inverting the Secondary Impedance Conversion Factor: Using $Z_{sec} = Z_{pri} \times \frac{PTR}{CTR}$ instead of $Z_{sec} = Z_{pri} \times \frac{CTR}{PTR}$. Because $PTR \gg CTR$, inverting the ratio produces an answer off by thousands of percent. Always verify: $Z_{sec}$ in ohms is always smaller than $Z_{pri}$ on high-voltage transmission lines.
• Overreaching Zone 1 Beyond 85%: Setting Zone 1 reach to $100%$ of the line length. A $100%$ setting guarantees that transient overreach (caused by DC offset) and CT/VT errors will cause Zone 1 to trip instantaneously for faults on the adjacent line, causing a severe loss of selectivity.
• Ignoring Loss of Potential (LOP / VT Fuse Failure): When a VT secondary fuse blows, measured voltage drops to zero while line load current continues to flow. The distance relay calculates $Z = 0 / I = 0$, interpreting the blown fuse as a bolted close-in short circuit and false tripping. Relays incorporate Loss of Potential (Device 60FL) logic to block 21 tripping upon sensing zero voltage without corresponding negative/zero-sequence current.
• Power Swing False Tripping: Large electromechanical power oscillations between interconnected generator groups cause apparent impedance to slowly drift across the R-X plane into distance tripping zones. Relays use Power Swing Blocking (Device 68) elements (measuring the rate of change of impedance $dZ/dt$) to block 21 tripping during stable power swings.