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10.2 Overcurrent Protection (50/51), Time-Current Curves (TCC) & Relay Coordination

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1 Chapter 1: Exam Overview & Power Engineering Fundamentals

1.1 PE Power Exam Structure, Official Specification & NCEES Reference Strategy 1.2 Units, Conversions, Engineering Constants & Fundamental Power Equations 1.3 Measurement & Metering Principles (Power, Energy, Power Factor) 1.4 Instrument Testing & Diagnostics (Insulation Megger & Ground Resistance)

2 Chapter 2: Circuit Analysis Fundamentals

2.1 DC Circuit Laws, Network Theorems (Thevenin, Norton, Superposition) & Transients 2.2 Single-Phase AC Steady-State Analysis, Phasors & Impedance 2.3 AC Power Relationships (Real, Reactive, Apparent Power & Power Factor Correction) 2.4 Resonance, Frequency Response & Harmonic Distortion

3 Chapter 3: Three-Phase Systems & Symmetrical Components

3.1 Three-Phase Circuit Analysis (Wye and Delta Configurations & Transformations) 3.2 Balanced Three-Phase Power Calculations & Phasor Relationships 3.3 The Per-Unit (pu) System: Bases, Conversions & System Modeling 3.4 Symmetrical Components (Fortescue Transformation, Sequence Networks & Unbalance)

4 Chapter 4: Electric Power Transformers

4.1 Transformer Theory, Equivalent Circuits & Open/Short-Circuit Testing 4.2 Transformer Voltage Regulation, Efficiency & Loss Calculations 4.3 Three-Phase Transformer Connections, Phase Shifts & Paralleling 4.4 Autotransformers, Instrument Transformers (CTs & VTs) & Special Transformers

5 Chapter 5: Rotating Machines: Induction & Synchronous

5.1 Three-Phase Induction Motors: Principles, Equivalent Circuits & Slip-Torque Characteristics 5.2 Induction Motor Starting, Speed Control & Braking Methods 5.3 Synchronous Generators: Operation, Excitation, Power-Angle Equations & V-Curves 5.4 Synchronous Motors & Condensers for Power Factor Correction

6 Chapter 6: DC Machines & Power Devices

6.1 DC Generators & Motors: Types (Shunt, Series, Compound), Characteristics & Speed Control 6.2 Power Capacitors, Shunt Reactors & Harmonic Filter Design 6.3 Battery Energy Storage Systems (BESS) & Ultra-Capacitors 6.4 Renewable Generation Integration: Solar Photovoltaics (PV) & Wind Power Systems

7 Chapter 7: Power Electronics & Industrial Controls

7.1 Power Semiconductor Switching Devices (Diodes, Thyristors, MOSFETs, IGBTs) 7.2 AC-to-DC Converters (Uncontrolled & Controlled Rectifiers) 7.3 DC-to-DC Switch-Mode Converters (Buck, Boost, Buck-Boost) & DC-AC Inverters 7.4 Variable Frequency Drives (VFDs), Motor Starters & Ladder Logic / PLC Controls

8 Chapter 8: Transmission & Distribution Systems

8.1 Transmission Line Parameters (Resistance, Inductance, Capacitance & GMD/GMR) 8.2 Line Models (Short, Medium Nominal-π, Long Lines) & ABCD Two-Port Parameters 8.3 Surge Impedance, Surge Impedance Loading (SIL) & Voltage Regulation 8.4 Distribution System Architectures, Voltage Drops & Feeder Loading 8.5 Power Flow Studies: Bus Classification, Y-Bus & Newton-Raphson Solutions 8.6 Power System Stability: Swing Equation, Equal-Area Criterion & Critical Clearing Time

9 Chapter 9: Power System Fault Analysis

9.1 Fault Analysis Fundamentals & Subtransient/Transient Machine Reactances 9.2 Three-Phase Symmetrical Fault Calculations 9.3 Single Line-to-Ground (SLG) & Line-to-Line (LL) Fault Analysis 9.4 Double Line-to-Ground (DLG) Faults & Bus Impedance Matrix (Zbus) Methods

10 Chapter 10: Power System Protection & Coordination

10.1 Protective Relaying Principles, IEEE Device Designations & Instrument Transformers 10.2 Overcurrent Protection (50/51), Time-Current Curves (TCC) & Relay Coordination 10.3 Differential Protection (87) for Transformers, Busbars & Generators 10.4 Distance / Impedance Protection (21) for Transmission Lines & Directional Relays (67)

11 Chapter 11: National Electrical Code (NEC) & Installation Design

11.1 NEC Fundamentals, Branch Circuit & Feeder Conductor Sizing (Ampacity & Derating) 11.2 Overcurrent Protection Sizing, Raceway Fill & Box Fill Calculations 11.3 Motor Branch Circuits, Controllers & Feeder Protection (NEC Article 430) 11.4 Grounding and Bonding Systems per NEC Article 250

12 Chapter 12: Electrical Safety, Standards & Facility Applications

12.1 Hazardous (Classified) Locations: Classes, Divisions, Zones, T-Codes & Sealing (NEC Articles 500-506) 12.2 Electrical Safety in the Workplace: NFPA 70E & Arc Flash Hazard Calculations 12.3 National Electrical Safety Code (NESC) Clearance & Utility Safety Requirements 12.4 Facility Applications: Illumination Design, Demand/Connected Loads & Lightning/Surge Protection 12.5 Special Occupancies & Systems: Health Care, Fire Pumps, Pools, Emergency & Standby (NEC Chapters 5-7)

10.2 Overcurrent Protection (50/51), Time-Current Curves (TCC) & Relay Coordination

Key Takeaways Explain This Topic AI

Instantaneous Overcurrent (Device 50) trips with zero intentional time delay (<2 cycles) and is set above the maximum downstream through-fault for selectivity, while Time-Overcurrent (Device 51) follows the IEEE C37.112 / IEC 60255 inverse characteristic t(I) = TDS * [A / ((I/I_pickup)^p - 1) + B], whose slope constants A, B, and exponent p define the Moderately Inverse, Very Inverse, and Extremely Inverse curve families.

Coordination Time Interval (CTI) is the required time margin between upstream and downstream protective devices (0.20 to 0.25 s for modern digital relays; 0.35 to 0.40 s for electromechanical disks) accounting for breaker interrupting time (3-5 cycles), relay overtravel, CT errors, and safety margin.

Fuses are characterized by Minimum Melting Time (MMT) and Total Clearing Time (TCT); selective fuse-to-fuse coordination requires the downstream fuse TCT curve to lie entirely below 75% of the upstream fuse MMT curve across all fault levels.

Transformer protection requires relay TCC curves to be positioned strictly ABOVE the transformer magnetizing inrush point (typically 8-12x FLA for 0.1 s) to avoid nuisance trips on energization, and strictly BELOW the ANSI/IEEE C57.109 thermal and mechanical damage withstand curve to guarantee asset protection.

Roughly 70% to 80% of overhead distribution faults are temporary, which is why reclosers trip and reclose automatically on fast-then-delayed curves; sectionalizers have no interrupting rating and open only during the recloser dead time after a preset count.

Last updated: August 2026

10.2 Overcurrent Protection (50/51), Time-Current Curves (TCC) & Relay Coordination

Overcurrent protection is the most universally applied form of power system protection. It operates on the fundamental premise that short circuits and severe overloads produce current magnitudes substantially higher than normal full-load operating levels. Achieving selective coordination ensures that the protective device closest to the fault opens first, isolating only the faulted branch while leaving the remainder of the electrical distribution system energized and operational.

On the NCEES PE Electrical and Computer: Power examination , overcurrent coordination problems require precise mathematical evaluation of IEEE/IEC inverse curve equations, determination of Time Dial Settings ( T D S TDS T D S ), calculation of Coordination Time Intervals ( C T I CTI CT I ), and validation against transformer damage curves (ANSI/IEEE C57.109) and inrush constraints.

1. Overcurrent Relaying Mechanics: 50 vs. 51

Modern microprocessor overcurrent relays integrate both instantaneous and time-delayed overcurrent elements: +---------------------------------------------------------------------------------------------------+

  • | INSTANTANEOUS (50) vs. TIME-OVERCURRENT (51) |
  • +---------------------------------------------------------------------------------------------------+
  • | Characteristic | Instantaneous Element (Device 50) | Time-Overcurrent Element (Device 51) |
  • | :--- | :--- | :--- |

| **Operating Time** | No intentional delay ($<1-2\text{ cycles}$) | Inverse time-delayed ($0.05-10.0\text{ s}$) |

  • | **Pickup Parameter** | $I_{pickup,50}$ (Amperes primary/sec) | $I_{pickup,51}$ (Amperes primary/sec)|
  • | **Setting Basis** | Set above maximum through-fault at | Set at $1.25\times$ to $1.50\times$ full-load|
  • | | downstream bus ($>1.25\times I_{f,max}$)| continuous rating ($FLA$). |
  • | **Primary Function** | Severe close-in short-circuit clearing | Overload protection & coordinated |
  • | | with minimum arc flash hazard. | backup fault clearing. |
  • | **Coordination Method**| Coordinate by current magnitude | Coordinate by time-current curves |
  • | | (definite current separation). | (CTI time separation). |

+---------------------------------------------------------------------------------------------------+ IDEALIZED TIME-CURRENT CURVE (TCC) PROFILE

  • Operating Time (Seconds)
  • ^
  • | \ (51 Inverse Time-Overcurrent Characteristic)
  • | \
  • 10.0 | \ <-- Long trip time at low overload (e.g., 1.5x FLA)
  • | \
  • | \
  • 1.0 | \
  • | \
  • | \ (50 Instantaneous Element Pickup)
  • 0.1 |------------+ - - - - - - - - - - *---------------------
  • | | <-- High-speed trip (<0.03 s)
  • 0.01 | | for faults > I_pickup,50
  • +----+-------+---------------------+---------------------> Current (Amperes)
  • FLA I_pickup,51 I_pickup,50
  • 2. Standard IEEE / IEC Inverse Time Curve Equations

Electromechanical overcurrent relays utilize an induction disk whose rotational torque is proportional to I 2 I^2 I 2 . Modern digital relays mathematically emulate or exceed these curves using standard parameterized equations defined by IEEE C37.112 and IEC 60255 .

IEEE C37.112 Standard Equation t ( I ) = T D S × [ A ( I I p i c k u p ) p − 1 + B ] [ seconds ] t(I) = TDS \times \left[ \frac{A}{\left(\frac{I}{I_{pickup}}\right)^p - 1} + B \right] \quad [\text{seconds}] t ( I ) = T D S × ​ ( I p i c k u p ​ I ​ ) p − 1 A ​ + B ​ [ seconds ]

Where:

t ( I ) t(I) t ( I ) = Relay operating time in seconds.

T D S TDS T D S = Time Dial Setting (typically adjustable from 0.5 0.5 0.5 to 15.0 15.0 15.0 ).

I I I = Measured primary or secondary fault current magnitude [ A ] [\text{A}] [ A ] .

I p i c k u p I_{pickup} I p i c k u p ​ = Relay current pickup setting [ A ] [\text{A}] [ A ] .

M = I I p i c k u p M = \frac{I}{I_{pickup}} M = I p i c k u p ​ I ​ = Plug Setting Multiplier (PSM) / Multiple of Pickup.

A , B , p A, B, p A , B , p = Dimensionless curve constants defining the degree of inverseness.

IEC 60255 Standard Equation t ( I ) = T M S × [ A ( I I p i c k u p ) p − 1 ] [ seconds ] t(I) = TMS \times \left[ \frac{A}{\left(\frac{I}{I_{pickup}}\right)^p - 1} \right] \quad [\text{seconds}] t ( I ) = TMS × ​ ( I p i c k u p ​ I ​ ) p − 1 A ​ ​ [ seconds ]

Where T M S TMS TMS is the Time Multiplier Setting (analogous to T D S TDS T D S ). Note that standard IEC equations do not include the additive constant B B B . +---------------------------------------------------------------------------------------------------+

  • | STANDARD IEEE & IEC INVERSE CURVE CONSTANTS |
  • +---------------------------------------------------------------------------------------------------+
  • | Curve Family | Standard Code | Constant A | Constant B | Exponent p | Typical Use |
  • | :--- | :--- | :--- | :--- | :--- | :--- |
  • | **IEEE Moderately Inverse** | IEEE MI | $0.0515$ | $0.1140$ | $0.02$ | Utility feeds|
  • | **IEEE Very Inverse** | IEEE VI | $19.61$ | $0.4910$ | $2.00$ | Long lines |
  • | **IEEE Extremely Inverse** | IEEE EI | $28.20$ | $0.1217$ | $2.00$ | Fuse coord. |
  • | **IEEE Short-Time Inverse** | IEEE STI | $0.00342$ | $0.00262$ | $0.02$ | Motor locked |
  • | **IEC Standard Inverse** | IEC Class A | $0.1400$ | $0.0000$ | $0.02$ | European grid|
  • | **IEC Very Inverse** | IEC Class B | $13.500$ | $0.0000$ | $1.00$ | Feeder lines |
  • | **IEC Extremely Inverse** | IEC Class C | $80.000$ | $0.0000$ | $2.00$ | XFMR & Fuses |
  • +---------------------------------------------------------------------------------------------------+

Tip

Curve Selection Rule:

Use Extremely Inverse (EI) curves when coordinating with downstream power fuses or protecting transformers, because the I 2 t I^2 t I 2 t shape ( p = 2.0 p = 2.0 p = 2.0 ) closely matches the thermal melting profile of fuses and the thermal damage envelope of transformers.

Use Moderately Inverse (MI) curves when fault current variations between minimum and maximum generation scenarios are large, ensuring consistent operating times.

3. Fuse Protection Characteristics: MMT vs. TCT

Power fuses are non-adjustable, direct-acting thermal interrupting devices. Their performance is defined by two standardized published time-current curves:

Minimum Melting Time (MMT) Curve: The lowest boundary of the time-current band. Represents the minimum time required for the fusible element to melt at a given current without arcing. Damage occurs if current flows beyond this time.

Total Clearing Time (TCT) Curve: The upper boundary of the band. Represents the maximum total time required for the fusible element to melt, establish an arc, and fully extinguish the arc at current zero ( T C T = M M T + t a r c TCT = MMT + t_{arc} TCT = MMT + t a rc ​ ). FUSE TIME-CURRENT CHARACTERISTIC BAND

  • Time (s)
  • ^
  • | Total Clearing Time (TCT): Maximum fault clearing time
  • | .-----------------------
  • | / /
  • | / Arcing Region /
  • | / (Melting + Arcing) /
  • | / /
  • | / /

| .-----------------------.

| Minimum Melting Time (MMT): Threshold of irreversible thermal damage

+----------------------------------------------> Current (A) +---------------------------------------------------------------------------------------------------+

  • | FUSE COORDINATION CRITERIA & RULES |
  • +---------------------------------------------------------------------------------------------------+
  • | Rule 1: Fuse-to-Fuse Coordination: |
  • | --> Downstream Fuse Total Clearing Time (TCT) MUST be ≤ 75% of Upstream Fuse Minimum Melting |
  • | Time (MMT) across the entire fault range: |
  • | |
  • | TCT_downstream(I_f) ≤ 0.75 * MMT_upstream(I_f) |
  • | |
  • | --> The 25% safety margin prevents pre-damaging or annealing the upstream fuse link during a |
  • | downstream through-fault. |
  • | |
  • | Rule 2: Relay-to-Fuse Coordination: |
  • | --> Upstream Relay Curve must clear above downstream Fuse TCT by at least 0.15 to 0.20 seconds. |
  • | --> Downstream Relay Curve must clear below upstream Fuse MMT by at least 0.20 seconds. |
  • +---------------------------------------------------------------------------------------------------+
  • 4. Time-Current Coordination & Coordination Time Interval (CTI)

The Coordination Time Interval ( C T I CTI CT I ) is the intentional vertical time buffer between the operating curves of two series-connected protective devices plotted on a common TCC. It guarantees that the downstream interrupting device completely isolates the fault before the upstream device's timing circuit reaches its trip threshold. COORDINATION TIME INTERVAL (CTI) STACK

  • Time (s)
  • ^
  • | [ Upstream Relay Curve (51) ] t_upstream
  • | ^
  • | | <-- Safety Margin (~0.05 s)
  • | | <-- CT / Relay Tolerance (~0.05 - 0.10 s)
  • | CTI | <-- Relay Overtravel / Coasting (0.00 s digital / 0.10 s disk)
  • | | <-- Downstream Breaker Clearing Time (3-5 cycles = 0.05-0.08 s)
  • | v
  • | [ Downstream Relay / Breaker Curve ] t_downstream
  • +-------------------------------------------------------------> Current (A)

Mathematical Breakdown of CTI Components C T I = t b r e a k e r + t o v e r t r a v e l + t t o l e r a n c e + t m a r g i n CTI = t_{breaker} + t_{overtravel} + t_{tolerance} + t_{margin} CT I = t b re ak er ​ + t o v er t r a v e l ​ + t t o l er an ce ​ + t ma r g in ​ +---------------------------------------------------------------------------------------------------+

  • | STANDARD COORDINATION TIME INTERVALS (CTI) |
  • +---------------------------------------------------------------------------------------------------+
  • | Coordinating Device Pair | Recommended CTI Range | Key Factor Driving Setting |
  • | :--- | :--- | :--- |
  • | **Digital Relay to Digital Relay** | **0.20 to 0.25 s** | Zero disk overtravel; |
  • | | ($12-15\text{ cycles}$)| high microprocessor accuracy.|
  • | **Digital Relay to Electromechanical Relay**| **0.25 to 0.30 s** | Disc overtravel on upstream. |
  • | **Electromechanical to Electromechanical** | **0.35 to 0.40 s** | Induction disk inertia coasting|
  • | | ($21-24\text{ cycles}$)| and mechanical calibration. |
  • | **Digital Relay to Downstream Low-Volt CB** | **0.15 to 0.20 s** | Direct-acting trip clearing. |
  • +---------------------------------------------------------------------------------------------------+
  • 5. Transformer Damage Curves (ANSI/IEEE C57.109) & Inrush Constraints

Properly coordinating primary overcurrent protection for a liquid-immersed or dry-type power transformer requires plotting two critical boundary points alongside the relay TCC:

The ANSI/IEEE C57.109 Transformer Damage Curve (Upper thermal/mechanical withstand bound).

The Transformer Magnetizing Inrush Point (Lower operating limit to avoid nuisance tripping). TRANSFORMER PROTECTION COORDINATION WINDOW

  • Time (s)
  • ^
  • 10.0 | [ ANSI/IEEE C57.109 Damage Curve ] (Upper Bound)
  • | \ /
  • 1.0 | \ [Relay] /
  • | \ [TCC] /
  • 0.1 |---[ Inrush Point ]-----\------/ (Lower Bound)
  • | (8-12x FLA @ 0.1s) \
  • 0.01 | \
  • +----+----------------------+---------------------------------> Current (A)
  • FLA I_fault,max
  • ANSI/IEEE C57.109 Transformer Categories

Transformers are categorized by three-phase kVA ratings to establish their thermal and mechanical through-fault withstand limits:

  • Category I: 15 to 500 kVA 15\text{ to }500\text{ kVA} 15 to 500 kVA (3-phase)
  • Category II: 501 to 5 , 000 kVA 501\text{ to }5,000\text{ kVA} 501 to 5 , 000 kVA (3-phase)
  • Category III: 5 , 001 to 30 , 000 kVA 5,001\text{ to }30,000\text{ kVA} 5 , 001 to 30 , 000 kVA (3-phase)
  • Category IV: > 30 , 000 kVA >30,000\text{ kVA} > 30 , 000 kVA (3-phase)
  • Frequent vs. Infrequent Fault Withstand Curves

Infrequent Fault Withstand Curve: Applies where faults occur rarely (e.g., secondary feeds encapsulated in metal-enclosed bus duct). Follows a pure I 2 t = K I^2 t = K I 2 t = K thermal limit line: t = 1250 I p u 2 ( for Category II transformers , 501 − 5000 kVA ) t = \frac{1250}{I_{pu}^2} \quad (\text{for Category II transformers}, 501-5000\text{ kVA}) t = I p u 2 ​ 1250 ​ ( for Category II transformers , 501 − 5000 kVA )

Frequent Fault Withstand Curve: Applies where transformers feed overhead distribution circuits subject to recurring lightning, tree contacts, and recloser operations. The curve transitions from thermal I 2 t I^2 t I 2 t slope to a horizontal mechanical withstand limit to prevent cumulative mechanical winding deformation.

Transformer Magnetizing Inrush Point

When a transformer is energized, core flux saturation produces a transient inrush current surge that flows only into the primary winding:

Standard Rule-of-Thumb Inrush Point: 8 × 8\times 8 × to 12 × 12\times 12 × Full Load Amps ( F L A FLA F L A ) for 0.10 seconds 0.10\text{ seconds} 0.10 seconds ( 6 cycles 6\text{ cycles} 6 cycles ) .

First Half-Cycle Crest Inrush: Up to 25 × F L A 25\times FLA 25 × F L A for 0.01 s 0.01\text{ s} 0.01 s . Primary Protection Criterion: t r e l a y ( 12 × F L A ) > 0.10 s \text{Primary Protection Criterion: } t_{relay}(12 \times FLA) > 0.10\text{ s} Primary Protection Criterion: t re l a y ​ ( 12 × F L A ) > 0.10 s ANSI Protection Criterion: t r e l a y ( I f a u l t ) < t A N S I _ D a m a g e ( I f a u l t ) \text{ANSI Protection Criterion: } t_{relay}(I_{fault}) < t_{ANSI\_Damage}(I_{fault}) ANSI Protection Criterion: t re l a y ​ ( I f a u lt ​ ) < t A NS I _ D ama g e ​ ( I f a u lt ​ )

  • 5a. Overhead Distribution Devices: Reclosers, Sectionalizers & Fuse Coordination
  • The NCEES specification lists protective devices (e.g., fuses, breakers, reclosers) as its
  • own sub-topic. Reclosers deserve separate treatment because they coordinate on a fundamentally

different principle from the relay/breaker pairs above.

  • Why reclosers exist. Roughly 70% to 80% of overhead distribution faults are temporary —
  • a branch contact, an animal, a lightning flashover. The arc self-extinguishes once current is
  • interrupted, so the circuit can be safely re-energized. A recloser (IEEE device 79) is a
  • self-contained interrupter with its own control that trips, waits a dead time, and recloses

automatically, typically up to four trips before lockout .

  • Parameter Typical setting
  • Operating sequence 2 fast + 2 delayed, or 1 fast + 3 delayed, to lockout
  • Fast (instantaneous) curve Clears in 2 to 6 cycles
  • Delayed (time-delay) curve Adds seconds of clearing time to let downstream fuses melt
  • Dead time (reclose interval) 0.5 s to 5 s; the first interval is often instantaneous
  • Fuse Saving vs. Fuse Clearing
  • This trade-off is the classic recloser exam item, and both schemes are defensible engineering —

which one is correct depends on what the question says the utility is optimizing.

Scheme Coordination Behaviour on a temporary lateral fault Cost

Fuse saving (fast trip) Recloser fast curve is set below the fuse minimum melting time Recloser clears before the fuse melts; the arc de-ionizes and the recloser restores service with no fuse blown and no truck roll Every customer on the whole feeder sees a momentary interruption, which disrupts sensitive electronic and industrial loads

Fuse clearing (fuse blowing) The fast curve is disabled ; the recloser uses only delayed curves above the fuse total clearing time The lateral fuse blows for any lateral fault, temporary or not Only the faulted lateral loses power, but every temporary lateral fault becomes a sustained outage requiring a crew

Modern practice on feeders serving power-quality-sensitive customers has shifted toward fuse

clearing, precisely because momentary interruptions carry a real economic cost.

The two fuse-coordination inequalities you must satisfy, using NEC- and IEEE-recognized

factors from the fuse manufacturer's time-current curves:

To save the fuse: t r e c l o s e r , f a s t × k < M M T f u s e t_{recloser,\,fast} \times k \; < \; MMT_{fuse} t rec l oser , f a s t ​ × k < MM T f u se ​ , where k k k (about 1.2 to

  • 1.35) accounts for cumulative fuse heating across successive fast operations — the fuse
  • does not fully cool between trips, so the second fast operation sees a partially damaged

fuse element.

To ensure selectivity on permanent faults: T C T f u s e < t r e c l o s e r , d e l a y e d TCT_{fuse} < t_{recloser,\,delayed} TC T f u se ​ < t rec l oser , d e l a ye d ​ at the

maximum available fault current on the lateral.

  • Sectionalizers
  • A sectionalizer is not a fault interrupter — it has no interrupting rating and cannot
  • break fault current. It counts the number of times an upstream recloser has interrupted fault
  • current and opens during the dead time , while the line is de-energized, after a preset count
  • (typically 2 or 3). Because it does not need a time-current curve, it can be applied where two
  • devices in series would otherwise be impossible to coordinate on time alone. Applying a
  • sectionalizer as though it were a fuse or recloser — expecting it to clear a fault — is a

frequent distractor.

6. Step-by-Step Selective Coordination Methodology (Load to Utility) +---------------------------------------------------------------------------------------------------+

  • | RADIAL SYSTEM SELECTIVE COORDINATION WORKFLOW |
  • +---------------------------------------------------------------------------------------------------+
  • | Step 1: Base Data Gathering: |
  • | - Obtain continuous full-load currents (FLA) for all loads and transformers. |
  • | - Compute maximum and minimum available short-circuit currents (3Φ and SLG) at every bus. |
  • | Step 2: Establish Common Voltage Base: |
  • | - Select a reference voltage base (typically the primary service voltage) and reflect all |
  • | downstream currents across transformer turns ratios: I_pri = I_sec * (V_sec / V_pri). |
  • | Step 3: Set Downstream Load/Branch Devices First: |
  • | - Select branch circuit breakers or fuses based on NEC 240 / 430 load and motor rules. |
  • | Step 4: Set Upstream Phase Overcurrent Relay Pickup (51P): |
  • | - Set pickup I_pickup = 1.25 to 1.50 * FLA (above maximum anticipated continuous load). |
  • | - Ensure pickup is sensitive enough to detect minimum end-of-line fault: I_pickup < 0.5 * I_f,min.|
  • | Step 5: Coordinate Time Dial Setting (TDS): |
  • | - Identify the Maximum Coordination Current (I_coord): The highest through-fault current seen |
  • | simultaneously by both devices (typically the maximum bolted fault on the downstream bus). |
  • | - Determine downstream clearing time t_downstream at I_coord. |
  • | - Target upstream operating time: t_upstream = t_downstream + CTI. |
  • | - Solve IEEE/IEC curve equation for required TDS. |
  • | Step 6: Set Instantaneous Element (50P): |
  • | - Set I_pickup,50 ≥ 1.25 to 1.30 * I_fault,downstream_bus to prevent misoperation during |
  • | downstream faults (or disable 50 element if selective reach cannot be achieved). |
  • | Step 7: Validate Asset Protection & Inrush Security: |
  • | - Verify relay curve clears BELOW transformer ANSI damage curve and ABOVE the 12x FLA @ 0.1s inrush.|
  • +---------------------------------------------------------------------------------------------------+
  • 7. Step-by-Step Worked Mathematical Example
  • Problem Statement

A 2500 kVA 2500\text{ kVA} 2500 kVA , 3-phase, 60 Hz 60\text{ Hz} 60 Hz step-down transformer rated at 13.8 kV 13.8\text{ kV} 13.8 kV (Delta) to 480 V 480\text{ V} 480 V (Grounded Wye) has a nameplate impedance of Z = 5.75 % Z = 5.75\% Z = 5.75% ( X / R = 8.0 X/R = 8.0 X / R = 8.0 ). The transformer feeds a 480 V 480\text{ V} 480 V main switchboard equipped with a secondary low-voltage power circuit breaker ( R 2 R_2 R 2 ​ ).

The primary side is protected at 13.8 kV 13.8\text{ kV} 13.8 kV by a microprocessor time-overcurrent relay ( R 1 R_1 R 1 ​ ) utilizing an IEEE Very Inverse (IEEE VI) curve ( A = 19.61 , B = 0.491 , p = 2.0 A = 19.61, B = 0.491, p = 2.0 A = 19.61 , B = 0.491 , p = 2.0 ) connected to 200 : 5 A 200:5\text{ A} 200 : 5 A CTs ( C T R = 40 CTR = 40 CTR = 40 ).

System data:

Primary Full-Load Amps: I F L A , p r i = 2500 kVA 3 × 13.8 kV = 104.59 A I_{FLA,pri} = \frac{2500\text{ kVA}}{\sqrt{3} \times 13.8\text{ kV}} = 104.59\text{ A} I F L A , p r i ​ = 3 ​ × 13.8 kV 2500 kVA ​ = 104.59 A

Secondary Full-Load Amps: I F L A , s e c = 2500 kVA 3 × 0.480 kV = 3007.03 A I_{FLA,sec} = \frac{2500\text{ kVA}}{\sqrt{3} \times 0.480\text{ kV}} = 3007.03\text{ A} I F L A , sec ​ = 3 ​ × 0.480 kV 2500 kVA ​ = 3007.03 A

Available short-circuit duty on the 480 V 480\text{ V} 480 V bus (bolted 3-phase fault): I f , s e c = 48.0 kA I_{f,sec} = 48.0\text{ kA} I f , sec ​ = 48.0 kA at 480 V 480\text{ V} 480 V

Downstream breaker R 2 R_2 R 2 ​ total clearing time at 48.0 kA 48.0\text{ kA} 48.0 kA : t d o w n s t r e a m = 0.060 s t_{downstream} = 0.060\text{ s} t d o w n s t re am ​ = 0.060 s ( 3.6 cycles 3.6\text{ cycles} 3.6 cycles )

Required Coordination Time Interval: C T I = 0.25 s CTI = 0.25\text{ s} CT I = 0.25 s

Primary relay pickup is set at 150 A 150\text{ A} 150 A primary ( I p i c k u p = 150 A I_{pickup} = 150\text{ A} I p i c k u p ​ = 150 A , which is 1.43 × F L A p r i 1.43\times FLA_{pri} 1.43 × F L A p r i ​ )

Calculate:

The maximum 480 V 480\text{ V} 480 V fault current reflected to the primary 13.8 kV 13.8\text{ kV} 13.8 kV voltage base.

The required operating time for upstream relay R 1 R_1 R 1 ​ at the maximum coordination fault current.

The exact Time Dial Setting ( T D S TDS T D S ) for relay R 1 R_1 R 1 ​ .

Verify that relay R 1 R_1 R 1 ​ will not nuisance-trip on transformer magnetizing inrush ( 12 × F L A p r i 12\times FLA_{pri} 12 × F L A p r i ​ for 0.10 s 0.10\text{ s} 0.10 s ). =========================================================================================

CALCULATION WORKFLOW & DETAILED STEP-BY-STEP SOLUTION:

=========================================================================================

  • Step 1: Reflect Secondary Fault Current to 13.8 kV Primary Base
  • Turns Ratio: a = V_pri / V_sec = 13,800 V / 480 V = 28.75

Primary Reflected Fault Current (I_coord):

  • I_coord = I_f,sec / a = 48,000 A / 28.75
  • = 1,669.57 A ≈ 1,670 A on 13.8 kV base
  • Step 2: Determine Required Upstream Relay Operating Time (t_upstream)
  • t_upstream = t_downstream + CTI
  • = 0.060 s + 0.250 s
  • = 0.310 seconds at I_coord = 1,669.57 A

Step 3: Calculate Plug Setting Multiplier (M) and Solve for TDS

Plug Setting Multiplier at fault current:

M = I_coord / I_pickup = 1,669.57 A / 150.0 A = 11.1305

Evaluate the IEEE Very Inverse bracket term with A = 19.61, B = 0.491, p = 2.0:

  • Bracket = [ A / (M^p - 1) ] + B
  • = [ 19.61 / ((11.1305)^2 - 1) ] + 0.491
  • = [ 19.61 / (123.887 - 1) ] + 0.491
  • = [ 19.61 / 122.887 ] + 0.491
  • = 0.15958 + 0.49100
  • = 0.65058

Solve for TDS:

  • t(I) = TDS * 0.65058 = 0.310 s
  • TDS = 0.310 / 0.65058 = 0.4765

Select next highest standard setting: TDS = 0.50

Recompute actual operating time at TDS = 0.50:

  • t_actual = 0.50 * 0.65058 = 0.3253 seconds
  • Actual CTI = 0.3253 - 0.060 = 0.2653 s ≥ 0.25 s (COORDINATION ACHIEVED!)
  • Step 4: Verify Security Against Transformer Magnetizing Inrush
  • Inrush Current Magnitude: I_inrush = 12 * FLA_pri = 12 * 104.59 A = 1,255.08 A
  • Inrush Duration: t_inrush = 0.100 seconds

Multiplier at Inrush:

M_inrush = I_inrush / I_pickup = 1,255.08 A / 150.0 A = 8.3672

Relay Trip Time at Inrush Current (with TDS = 0.50):

  • Bracket_inrush = [ 19.61 / ((8.3672)^2 - 1) ] + 0.491
  • = [ 19.61 / (70.010 - 1) ] + 0.491
  • = [ 19.61 / 69.010 ] + 0.491
  • = 0.28416 + 0.491 = 0.77516

t_trip(I_inrush) = 0.50 * 0.77516 = 0.3876 seconds

Security Verification:

Since t_trip (0.3876 s) > t_inrush (0.100 s), the relay will NOT nuisance-trip

during transformer energization. The scheme is robustly secure.

  • =========================================================================================
  • 8. Common PE Exam Traps & Tactical Pitfalls

Omitting Voltage Ratio Scaling in TCC Coordination: Coordinating an upstream 13.8 kV 13.8\text{ kV} 13.8 kV relay directly against a secondary 480 V 480\text{ V} 480 V breaker's physical amperes without dividing by the turns ratio ( a = 28.75 a = 28.75 a = 28.75 ). All device characteristics plotted on a single TCC sheet must be scaled to a single common reference voltage base .

Confusing IEEE and IEC Formula Structures: Omitting constant B B B when computing IEEE curve operating times, or erroneously adding constant B B B to IEC formulations. IEEE curves approach a horizontal asymptotic floor of T D S × B TDS \times B T D S × B as I → ∞ I \to \infty I → ∞ , whereas IEC curves decay to zero.

Setting TDS Based on Normal Load Current: Solving for T D S TDS T D S at nominal full-load amps ( F L A FLA F L A ) instead of the maximum through-fault coordination current ( I c o o r d I_{coord} I coor d ​ ). T D S TDS T D S is determined exclusively by the required C T I CTI CT I at the point of maximum through-fault current.

Neglecting the 75% Fuse Pre-Damage Rule: Aligning downstream fuse clearing time equal to upstream fuse melting time ( T C T d o w n = M M T u p TCT_{down} = MMT_{up} TC T d o w n ​ = MM T u p ​ ). Because the upstream fuse accumulates irreversible thermal heat during the downstream fault, the downstream fuse T C T TCT TCT must never exceed 75 % 75\% 75% of upstream M M T MMT MMT ( 0.75 × M M T u p 0.75 \times MMT_{up} 0.75 × MM T u p ​ ).

Loading diagram... TCC Coordination Architecture and Time-Current Stacking Flowchart