Harmonics & Relay Coordination Toolkit

Understanding RMS Values in Protection

This toolkit demonstrates the difference between Fundamental RMS and True RMS current values, especially when harmonics are present in the electrical system. Understanding this difference is crucial for coordinating protective devices correctly.

Fundamental RMS

• Definition: The Root Mean Square (RMS) value calculated using only the fundamental frequency component (typically 50 Hz or 60 Hz) of the waveform. It ignores any harmonic distortion.
• Calculation: Digital relays often use algorithms like the Fast Fourier Transform (FFT) or Discrete Fourier Transform (DFT) to isolate the fundamental component's magnitude before calculating its RMS value (I_fund_rms = Amplitude_fund / sqrt(2)).
• Relevance: Many modern digital protective relays are designed to operate based on the fundamental RMS value for their primary overcurrent protection functions. This is often done intentionally to prevent nuisance tripping caused by harmonics that might not necessarily represent a dangerous overload or fault condition in terms of equipment heating or magnetic stress related to the fundamental frequency.

True RMS

• Definition: The Root Mean Square (RMS) value calculated considering the fundamental component plus all harmonic components present in the waveform.
• Calculation: It's calculated as the square root of the sum of the squares of the RMS values of the fundamental and each harmonic component:
  I_true_rms = sqrt( I_fund_rms² + I_h3_rms² + I_h5_rms² + I_h7_rms² + ... )
  where I_hn_rms is the RMS value of the nth harmonic.
• Relevance: True RMS represents the actual heating effect of the current flowing through a resistive element. The total power dissipated as heat (I²R) is proportional to the square of the True RMS current.

Protective Device Response

Different types of protective devices respond differently to harmonic content:

• Fuses & Thermal Overload Relays/Breakers: These devices operate based on the heating effect of the current. Therefore, their operating time is primarily determined by the True RMS value of the current. Higher True RMS (due to harmonics) will cause them to operate faster for the same fundamental current.
• Electromechanical Relays (Induction Disc/Plunger): Their response is more complex and depends on the specific design. They often respond to a value somewhere between the fundamental and True RMS, or sometimes closer to the peak value, but generally, they are significantly affected by the total energy, leaning towards True RMS behaviour compared to purely fundamental-based relays.
• Digital (Microprocessor-Based) Relays:
  • Overcurrent Elements (e.g., 50/51): Often use Fundamental RMS calculated via digital filtering (FFT/DFT). This makes them less sensitive to harmonic distortion for phase/ground fault detection, focusing on the fundamental power frequency component.
  • Thermal Overload Elements (e.g., 49): If included, these elements within a digital relay are typically designed to calculate or estimate the True RMS value to accurately model the heating effect on equipment like motors or transformers.
  • Other Functions: Some functions might use peak values or other derived quantities.

Coordination Challenge: As this toolkit demonstrates, if a digital relay operating on Fundamental RMS is protecting a circuit where a fuse or thermal breaker (operating on True RMS) is downstream, the presence of harmonics can cause miscoordination. The fuse/breaker might operate faster than expected (because it sees the higher True RMS current) before the relay (seeing only the lower Fundamental RMS current) has time to operate according to its settings. This requires careful consideration during protection coordination studies.