6.5 Differential Protection (87T, 87B, 87G) and Impedance/Distance Protection (21)

Differential Protection (87T, 87B, 87G) and Impedance/Distance Protection (21)

Quick Summary: Differential Protection (ANSI 87) and Distance/Impedance Protection (ANSI 21) represent the pinnacle of high-speed power system protection. Differential schemes provide absolute selectivity for transformers, buses, and generators by comparing currents entering and leaving the apparatus. Distance schemes protect transmission and sub-transmission lines by measuring apparent line impedance (Z = V / I) across stepped geographical reach zones.

Commissioning and testing these sophisticated protection elements requires an in-depth understanding of percentage restraint slope curves, harmonic blocking algorithms, vector phase angle compensation, and R-X impedance plane plotting per IEEE C37.91, IEEE C37.113, and NETA ATS Section 7.9.

1. Principles of Differential Protection (ANSI 87)

Differential protection is a unit protection scheme based directly on Kirchhoff's Current Law (KCL): the algebraic vector sum of all currents entering and leaving a healthy electrical node or piece of equipment must equal zero.

$\sum I_{entering} - \sum I_{leaving} = 0$

+-----------------------------------------------------------------------------------------+
|                        DIFFERENTIAL PROTECTION OPERATING PRINCIPLE                      |
|                                                                                         |
|   EXTERNAL THROUGH-FAULT (Out-of-Zone):                                                 |
|   Primary:  ----( 1000 A -> )---- [ PROTECTED APPARATUS ] ----( 1000 A -> )---- [FAULT] |
|   CTs:           [ CT1 ]                                           [ CT2 ]              |
|   Secondary:      5.0 A ------>                        ------>      5.0 A               |
|                              |                                |                         |
|                              +-----------> [ 87 ] <-----------+                         |
|                                       Operating Current                                 |
|                                       I_op = |5.0 - 5.0| = 0 A  (RESTRAIN / NO TRIP)    |
|                                                                                         |
|   INTERNAL FAULT (In-Zone):                                                             |
|   Primary:  ----( 1000 A -> )---- [ * FAULT * ] <----( 800 A <--- )------------------- |
|   CTs:           [ CT1 ]                                   [ CT2 ]                      |
|   Secondary:      5.0 A ------>                        <------ 4.0 A                    |
|                              |                                |                         |
|                              +-----------> [ 87 ] <-----------+                         |
|                                       Operating Current                                 |
|                                       I_op = |5.0 - (-4.0)| = 9.0 A (HIGH-SPEED TRIP)   |
+-----------------------------------------------------------------------------------------+

The Percentage Differential Restraint Characteristic:

Under heavy external through-fault conditions, unequal CT saturation, CT ratio tolerances, and transformer tap changer positions create false spill current (differential current) in the operating winding. To prevent false tripping, percentage differential relays introduce a Restraint Quantity (I_rest):

$\text{Operating Current } (I_{op}) = |I_1 - I_2|$

$\text{Restraint Current } (I_{rest}) = (|I_1| + |I_2|) / 2 \quad \text{or} \quad \max(|I_1|, |I_2|)$

$\text{Tripping Criterion:} \quad I_{op} \ge \text{Slope} \times I_{rest} + I_{pickup\_min}$

Operating
Current (I_op)
    ^
    |                                      / Dual-Slope (Slope 2: 50% - 80%)
    |                                     /  (Heavy Through-Fault CT Saturation)
    |                         Breakpoint / 
    |                         ----------+
    |                                  / Slope 1: 20% - 35%
    |                                 /  (Normal Load & Small Tap Mismatch)
    |                       +--------+
    |       TRIP REGION     | I_min_pickup
    |                       +----------------------------------------
    |                                 RESTRAIN (BLOCK) REGION
    +-----------------------------------------------------------------> Restraint Current (I_rest)

2. Transformer Differential Protection (87T) Specifics

Protecting power transformers introduces complex physical phenomena that must be compensated within the differential algorithm:

1. Vector Group Phase Shift Compensation:

A Delta-Wye transformer (e.g., Dyn1 or Dyn11) introduces a 30° phase angle displacement between primary and secondary line currents.

• Legacy Electromechanical Method: Compensated via physical CT wiring connections (CTs on the Wye winding were wired in Delta; CTs on the Delta winding were wired in Wye).
• Modern Digital Relay Method: CTs on all windings are wired in standard Wye (Star). The relay software performs internal mathematical matrix phase rotation (e.g., rotating current vectors by ±30°).

2. Zero-Sequence Current Filtering:

An external ground fault on the grounded-Wye side of a Delta-Wye transformer produces zero-sequence current (I0) that circulates in the Wye winding and returns through the neutral, but cannot pass through the Delta winding. Without zero-sequence filtering, this through-fault current appears as false differential current, causing an improper trip. Modern relays subtract zero-sequence current (IA - I0, IB - I0, IC - I0) mathematically.

3. Magnetizing Inrush and Harmonic Restraint:

When a transformer is energized, core magnetization drives the iron into deep unipolar saturation, drawing magnetizing inrush current reaching 8x to 12x full load current on one side only. Because inrush flows into the transformer without exiting, it appears as an internal fault.

• 2nd Harmonic Restraint / Blocking: Magnetizing inrush current is rich in 2nd harmonic current (120 Hz). When the ratio of 2nd harmonic to fundamental current (I_2nd / I_fund) exceeds a preset threshold (typically 15% to 20%), the relay automatically blocks differential tripping.
• 5th Harmonic Restraint / Blocking: Transformer core overexcitation (excessive Volts/Hertz caused by system overvoltage or underfrequency) produces severe 5th harmonic current (300 Hz). Relays employ 5th harmonic blocking (typically set at 35% to 40%) to prevent tripping during temporary system voltage surges, allowing V/Hz relays (ANSI 24) to handle sustained overexcitation.

3. Bus Differential (87B) and Generator Differential (87G)

Bus Differential Protection (ANSI 87B):

Substation buses connect multiple circuits with massive available short-circuit currents. An external fault on a single feeder can drive that feeder's CT into severe saturation while all other incoming CTs remain linear, creating enormous false spill current.

High-Impedance Stabilizing Resistor Formula:

$V_{stabilizing} = I_{fault\_max\_sec} \times (R_{CT\_internal} + R_{lead\_one\_way})$

$R_{stabilizing} = (V_{stabilizing} / I_{relay\_pickup}) - R_{relay\_internal}$

Generator Differential Protection (ANSI 87G):

Protects generator stator windings against phase-to-phase and phase-to-ground faults. Because generators do not experience inrush or phase shifts, 87G elements operate as sensitive, high-speed percentage differential relays with very low pickup settings (typically 0.10 to 0.20 per-unit) and a single slope (typically 10% to 15%).

4. Transmission Line Distance / Impedance Protection (ANSI 21)

Distance protection calculates the electrical impedance of the transmission line by comparing measured secondary voltage (V) to secondary current (I):

$Z_{measured} = \frac{V_{secondary}}{I_{secondary}} = \frac{V_{primary} / \text{PTR}}{I_{primary} / \text{CTR}} = Z_{primary} \times \left(\frac{\text{CTR}}{\text{PTR}}\right)$

Because line impedance (Z = R + jX) is directly proportional to physical line length, the calculated impedance reflects the physical distance from the relay to the fault.

+-----------------------------------------------------------------------------------------+
|                        STEPPED DISTANCE PROTECTION ZONES                                |
|                                                                                         |
|   LOCAL SUBSTATION [A]                     REMOTE SUBSTATION [B]        SUBSTATION [C]  |
|   ====== [ 52A ] =============================== [ 52B ] =============== [ 52C ] ===== |
|          |                                          |                                   |
|          |<------------ ZONE 1 (80% - 85%) -------->|                                   |
|          |  [ 0 Cycles / Instantaneous Trip ]       |                                   |
|          |                                          |                                   |
|          |<---------------- ZONE 2 (120% - 130%) -------------->|                       |
|          |  [ 15 - 30 Cycles Time Delay (0.25 - 0.50 s) ]       |                       |
|          |                                                      |                       |
|          |<----------------------- ZONE 3 (150% - 200%) -------------------------->|    |
|          |  [ 45 - 90 Cycles Remote Backup Time Delay (0.75 - 1.50 s) ]             |    |
+-----------------------------------------------------------------------------------------+

Stepped Distance Zone Philosophy:

1. Zone 1 (Instantaneous Unit):

   • Set to reach 80% to 85% of the protected transmission line positive-sequence impedance (Z_1L).
   • Operates with zero intentional time delay (0 cycles).
   • Why not 100%? Prevents "overreaching" the remote substation bus due to CT/VT measurement errors, line impedance parameter inaccuracies, and DC offset transients.

2. Zone 2 (Overreaching Unit):

   • Set to reach 120% to 130% of the protected line impedance (covering the remaining 15-20% of the line plus 20-30% into the adjacent shortest line).
   • Operates with an intentional time delay of 15 to 30 cycles (0.25 to 0.50 seconds) to coordinate with Zone 1 relays at the remote terminal.

3. Zone 3 (Remote Backup / Reverse Unit):

   • Set to reach 150% to 200% of the protected line plus adjacent longest line impedance (or reverse reach behind the local bus).
   • Operates with a time delay of 45 to 90 cycles (0.75 to 1.50 seconds) to provide remote backup for bus or breaker failures at the remote station.

R-X Impedance Plane Characteristics:

+-----------------------------------------------------------------------------------------+
|                           R-X DIAGRAM CHARACTERISTICS                                   |
|                                                                                         |
|            +X (Reactance)                           +X (Reactance)                      |
|                  ^                                        ^                             |
|                  |       / Line Angle (75°-85°)           |       / Line Angle          |
|                  |   +--+--+                              |   +-------+ X_reach         |
|                  |  /   |   \                             |   |       |                 |
|                  | |    |    | MHO CIRCLE                 |   |       | QUADRILATERAL   |
|                  |  \   |   /  (Self-Polarized)           |   |       |                 |
|                  |   +--+--+                              |   +-------+                 |
|   ---------------+------+---------> +R     ---------------+-------+---------> +R        |
|                  | (Origin) (Resistance)                  | (Origin) R_reach (Fault Arc)|
|                  |                                        |                             |
+-----------------------------------------------------------------------------------------+

• Mho Characteristic: A circular operating boundary passing through the origin on the R-X diagram. Inherently directional; trips when measured impedance falls inside the circle.
• Quadrilateral Characteristic: A 4-sided polygonal boundary with independently adjustable reach in resistance (R_reach) and reactance (X_reach). Superior for detecting high-resistance ground faults and arc resistance on short lines.

5. Secondary Injection Testing of 87 and 21 Elements

Testing Transformer Differential (87T) Elements:

1. Minimum Pickup Test: Inject single-phase current into primary winding channel (I1) with secondary channel (I2) at zero. Incrementally increase current until relay asserts 87T. Verify pickup matches I_min_pickup ± 3%.
2. Percentage Restraint Slope Verification:
   • Set up dual current injection (I1 and I2) out-of-phase by 180° to simulate through-current.
   • Establish fixed restraint levels (I_rest = 2 A, 5 A, 10 A).
   • Increase differential current until trip occurs; calculate measured slope: Slope = (I_op / I_rest) × 100%.
   • Verify Slope 1, Slope 2, and Breakpoint knee.
3. Harmonic Restraint Testing:
   • Inject fundamental 60 Hz current above pickup simultaneously with a variable 120 Hz (2nd harmonic) component.
   • Gradually increase 2nd harmonic content; record the percentage threshold where the 87T trip contact is blocked (verify setting: 15% ± 2%).
   • Repeat with 300 Hz (5th harmonic) component (verify setting: 35% ± 3%).

Testing Distance / Impedance (21) Elements:

1. MTA (Maximum Torque Angle / Line Characteristic Angle) Verification:
   • Inject test voltage (V) and current (I) at varying phase angles (e.g., from 0° to 90°).
   • Identify the angle of maximum sensitivity (typically 75° to 85° for transmission lines).
2. Reach Verification (Z_reach):
   • At the Maximum Torque Angle, hold current constant (e.g., 5.0 A) and slowly reduce voltage until the relay trips.
   • Calculate secondary reach: Z_reach = V_trip / I_test.
   • Verify Zone 1 reach (Z1), Zone 2 reach (Z2), and Zone 3 reach (Z3) against setting sheet tolerances (±3% to ±5% per NETA ATS Table 100.10).
3. Zone Timer Verification:
   • Apply a dynamic step-change in impedance from healthy nominal load (150% reach) to fault impedance (50% Zone 1 reach, 110% Zone 2 reach). Record instantaneous Zone 1 trip time (< 25 ms) and Zone 2 timer delay (0.30 s ± 15 ms).