Short-Circuit Calculation in Generators With and Without Exciters – IEEE, IEC

Short-circuit calculation in generators is critical for ensuring electrical system safety and reliability. It determines fault currents and helps design protective devices accurately.

This article explores short-circuit calculations for generators with and without exciters, referencing IEEE and IEC standards. It covers formulas, tables, and real-world examples.

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  • Calculate three-phase short-circuit current for a 10 MVA generator with exciter, 11 kV, Xd”=0.2 pu.
  • Determine subtransient reactance for a 5 MVA generator without exciter, 6.6 kV, using IEC standards.
  • Find initial symmetrical short-circuit current for a 15 MVA synchronous generator with exciter, 13.8 kV, Xd”=0.18 pu.
  • Evaluate short-circuit current decay for a 20 MVA generator without exciter, 11 kV, using IEEE recommended values.

Common Values for Short-Circuit Calculation in Generators With and Without Exciters – IEEE, IEC

ParameterTypical Range (pu)IEEE Std. 399-1997 ReferenceIEC 60909-0:2016 ReferenceNotes
Subtransient Reactance (Xd”)0.15 – 0.25Table 5, IEEE Std. 399Clause 7.3, IEC 60909Lower for generators with exciters; critical for initial fault current.
Transient Reactance (Xd’)0.3 – 0.4Table 5, IEEE Std. 399Clause 7.3, IEC 60909Relevant for fault current after initial transient period.
Synchronous Reactance (Xd)1.0 – 1.5Table 5, IEEE Std. 399Clause 7.3, IEC 60909Steady-state reactance, used for long-term fault current.
Zero-Sequence Reactance (X0)0.5 – 1.0IEEE Std. 399, Annex BIEC 60909-0, Clause 7.4Important for unbalanced fault calculations.
Time Constants (T’d”, T’d, T’d0)0.02 – 0.1 s (T’d”)IEEE Std. 399, Table 6IEC 60909-0, Annex CDefines decay rates of subtransient and transient currents.
Rated Voltage (U)3.3 kV – 24 kVGenerator nameplate dataGenerator nameplate dataVoltage level impacts fault current magnitude.
Rated Power (S)1 MVA – 1000 MVAGenerator nameplate dataGenerator nameplate dataBase for per-unit system calculations.

Fundamental Formulas for Short-Circuit Calculation in Generators With and Without Exciters

Short-circuit current calculations rely on per-unit system and reactance values. The following formulas are essential for accurate fault current estimation.

1. Base Current Calculation

The rated current of the generator is the base current, calculated as:

Ibase = Srated / (√3 × Urated)
  • Ibase: Base current in amperes (A)
  • Srated: Rated apparent power in volt-amperes (VA)
  • Urated: Rated line-to-line voltage in volts (V)

2. Initial Symmetrical Short-Circuit Current (Ik”)

This is the peak fault current immediately after the fault occurs, dominated by subtransient reactance:

Ik” = Ibase / Xd”
  • Ik”: Initial symmetrical short-circuit current (A)
  • Xd”: Subtransient reactance (pu)

3. Transient Short-Circuit Current (Ik’)

After the initial transient, the fault current decays to a lower value governed by transient reactance:

Ik’ = Ibase / Xd’
  • Ik’: Transient short-circuit current (A)
  • Xd’: Transient reactance (pu)

4. Steady-State Short-Circuit Current (Ik)

Long after the fault, the current stabilizes at a value determined by synchronous reactance:

Ik = Ibase / Xd
  • Ik: Steady-state short-circuit current (A)
  • Xd: Synchronous reactance (pu)

5. DC Offset and Peak Current Calculation

The instantaneous peak short-circuit current includes an AC component and a DC offset, calculated as:

Ipeak = √2 × Ik” × (1 + e−t/τ)
  • Ipeak: Peak instantaneous short-circuit current (A)
  • t: Time after fault initiation (seconds)
  • τ: DC time constant (seconds), typically 0.02 – 0.1 s

6. Zero-Sequence Current Calculation

For unbalanced faults, zero-sequence current is calculated using zero-sequence reactance:

I0 = Ibase / X0
  • I0: Zero-sequence current (A)
  • X0: Zero-sequence reactance (pu)

Impact of Exciters on Short-Circuit Calculations

Generators equipped with exciters exhibit different short-circuit characteristics compared to those without. Exciters provide field current during faults, influencing reactance values and fault current decay.

  • With Exciters: Subtransient reactance (Xd”) is typically lower, resulting in higher initial fault currents.
  • Without Exciters: The field current decays rapidly, increasing subtransient reactance and reducing initial fault current magnitude.
  • IEEE Std. 399 and IEC 60909 provide guidelines to adjust reactance values based on exciter presence.

Real-World Example 1: Short-Circuit Calculation for a Generator With Exciter (IEEE Method)

A 10 MVA, 11 kV synchronous generator with exciter has the following parameters:

  • Subtransient reactance, Xd” = 0.2 pu
  • Transient reactance, Xd’ = 0.3 pu
  • Synchronous reactance, Xd = 1.2 pu
  • DC time constant, τ = 0.05 s

Calculate the initial symmetrical short-circuit current and peak current immediately after a three-phase fault at the generator terminals.

Step 1: Calculate Base Current

Ibase = (10 × 106) / (√3 × 11 × 103) = 525.7 A

Step 2: Calculate Initial Symmetrical Short-Circuit Current

Ik” = 525.7 / 0.2 = 2628.5 A

Step 3: Calculate Peak Short-Circuit Current at t = 0

At fault initiation (t=0), e−t/τ = 1, so:

Ipeak = √2 × 2628.5 × (1 + 1) = 1.414 × 2628.5 × 2 = 7437.6 A

The peak instantaneous short-circuit current is approximately 7.44 kA.

Real-World Example 2: Short-Circuit Calculation for a Generator Without Exciter (IEC Method)

A 5 MVA, 6.6 kV synchronous generator without exciter has the following parameters:

  • Subtransient reactance, Xd” = 0.25 pu (adjusted for no exciter)
  • Transient reactance, Xd’ = 0.4 pu
  • Synchronous reactance, Xd = 1.3 pu
  • DC time constant, τ = 0.03 s

Calculate the initial symmetrical short-circuit current and peak current immediately after a three-phase fault at the generator terminals.

Step 1: Calculate Base Current

Ibase = (5 × 106) / (√3 × 6.6 × 103) = 437.0 A

Step 2: Calculate Initial Symmetrical Short-Circuit Current

Ik” = 437.0 / 0.25 = 1748.0 A

Step 3: Calculate Peak Short-Circuit Current at t = 0

At fault initiation (t=0), e−t/τ = 1, so:

Ipeak = √2 × 1748.0 × (1 + 1) = 1.414 × 1748.0 × 2 = 4946.0 A

The peak instantaneous short-circuit current is approximately 4.95 kA.

Additional Technical Considerations

  • Effect of Saturation: Generator reactances can vary with fault current magnitude due to magnetic saturation, affecting accuracy.
  • Temperature Dependence: Resistance and reactance values change with temperature; standards recommend adjustments for hot and cold conditions.
  • Exciter Type: Brushless exciters maintain field current longer during faults, reducing subtransient reactance.
  • System Impedance: Generator short-circuit current must be combined with network impedance for complete fault analysis.
  • Standards Compliance: IEEE Std. 399-1997 (“IEEE Recommended Practice for Industrial and Commercial Power Systems Analysis”) and IEC 60909-0:2016 (“Short-circuit currents in three-phase AC systems – Part 0: Calculation of currents”) provide authoritative methodologies.

Summary of Key Differences Between IEEE and IEC Approaches

AspectIEEE Std. 399IEC 60909-0
Reactance ValuesUses typical per-unit reactances from manufacturer data or tables.Defines standard values and correction factors for different generator types.
Exciter InfluenceExplicitly accounts for exciter presence in reactance adjustments.Includes correction factors but less detailed on exciter types.
Fault Current CalculationFocuses on symmetrical components and time-domain decay.Emphasizes steady-state and initial symmetrical currents with correction factors.
Zero-Sequence CurrentsDetailed zero-sequence reactance tables and methods.Standardized zero-sequence impedance values for unbalanced faults.
Application ScopePrimarily for industrial and commercial power systems.Widely used internationally for utility and industrial systems.

Practical Tips for Engineers Performing Short-Circuit Calculations

  • Always verify generator nameplate data and consult manufacturer’s short-circuit data sheets.
  • Use per-unit system consistently to simplify calculations and comparisons.
  • Consider the presence and type of exciter to select appropriate reactance values.
  • Apply time constants to model fault current decay accurately for protective device coordination.
  • Combine generator reactances with network impedances for system-wide fault current analysis.
  • Validate calculations with simulation software compliant with IEEE and IEC standards.

Short-circuit calculations for generators with and without exciters are fundamental for power system protection and design. Understanding the influence of exciter presence, reactance values, and time constants ensures accurate fault current estimation and system safety.

By adhering to IEEE Std. 399 and IEC 60909-0 guidelines, engineers can confidently perform these calculations, optimize protection schemes, and maintain system stability under fault conditions.