You've outlined a good understanding of the challenges posed by harmonic currents and their impact on cable and transformer sizing. Here's a breakdown of your logic, with some refinements and additional considerations

Cables:
Your Assessment: CORRECT. You're absolutely right. For cable sizing, the primary concern is the Joule heating (I²R losses). This is directly proportional to the square of the RMS current. The peak current, by itself, doesn't determine the heat generated. While a higher peak might suggest a higher harmonic content and thus a higher RMS value overall, the RMS value itself is the key driver of heating. Skin Effect

You correctly mention the skin effect. At low frequencies (5th and 7th harmonics of 50/60Hz), the skin effect in larger cables might be noticeable, but usually not significant enough to drastically alter the cable's ampacity. However, it's always good to double-check, especially for larger conductors. You can use derating tables or formulas that account for skin effect if needed.

Derating for Harmonics

Codes (like the NEC) often have derating factors for cable ampacity when significant harmonic currents are present. This is because multiple conductors in a conduit, carrying harmonic currents, can cause increased heating. The derating is often based on the percentage of non-linear loads connected to the circuit. This effectively addresses the combined effect of increased RMS current due to harmonics and potential skin effect.

Insulation Temperature Rating

Ensure your chosen cable insulation temperature rating is appropriate for the environment and anticipated conductor operating temperature (which is determined by the RMS current).

Transformers



Your Assessment: GENERALLY CORRECT, but needs refinement. Your intuition about the transformer saturation is accurate, but the reasoning for the equivalent RMS calculation needs adjustment. Core Saturation and Peak Flux

Core saturation depends on the peak magnetic flux density (B) in the core. This, in turn, is related to the voltage waveform applied to the transformer and the number of turns. While current harmonics contribute to the issue, the primary driver is the voltage waveform and the transformer's design. A flattened voltage waveform can result in higher peak flux for a given RMS voltage.

VA Rating vs. kVA Rating

Transformers are generally rated in kVA (kilovolt-amperes). The kVA rating is based on the product of RMS voltage and RMS current. A transformer designed to deliver 100 kVA RMS at a certain voltage is designed to handle a specific amount of total power, including the power from harmonics.

K-Factor Transformers

This is the key point. To address harmonic-rich loads,

K-rated transformers are used. These are specifically designed to handle the additional heating caused by harmonic currents. They have: Heavier conductors to reduce I²R losses (copper losses). More robust core designs to handle the increased flux density and reduce core losses. Improved insulation to withstand higher temperatures. Why your "equivalent RMS" calculation is not quite right

Your calculation of 180A peak / sqrt(2) = 127A RMS might not be directly applicable. The transformer doesn't "see" an equivalent sine wave. It experiences the actual harmonic-distorted current waveform. The total RMS current, including all harmonics, is the relevant factor. A 100kVA transformer delivering 100Arms with significant harmonic content is already experiencing a higher total power dissipation than a 100kVA transformer delivering 100Arms of pure sine wave current.

Practical Approach


Calculate the total RMS current of your load, including all harmonics. You can use a power analyzer or harmonic analysis software to determine this.2. Determine the K-factor of your load. K-factor indicates the transformer's ability to handle harmonic currents. Loads with high harmonic content will have a higher K-factor. (e.g., a load with a K-4 factor generates 4 times the heat from harmonic currents compared to a linear load)3. Select a transformer with a K-factor equal to or greater than the K-factor of your load. If your load has a K-4 rating, you need a K-4 or K-higher transformer. If no K-rating is available, consult the transformer manufacturer.4. Ensure the transformer's kVA rating is sufficient to supply the total RMS current at the rated voltage, considering the harmonic content. If the transformer is not K-rated, you may need to upsize the transformer significantly to avoid overheating.

In summary



Cables

Size based on the total RMS current and consider derating factors for harmonic content and conduit fill. Skin effect is usually negligible at low harmonic frequencies but verify for larger conductors.

Transformers

The key is to use a

K-rated transformer designed to handle the specific harmonic load. Size the transformer based on the total RMS current and ensure the K-factor matches or exceeds that of your load. If you can't use a K-rated transformer, consult with the manufacturer to determine the appropriate derating or upsizing needed to handle the harmonic currents.

Example

Let's say your load is a rectifier drawing 100A RMS with a significant 5th and 7th harmonic.1.

Measure the Total RMS Current

You measure the total RMS current with a power analyzer and find it's 110A RMS due to the harmonics.2.

Determine the K-Factor

Based on the type of rectifier and its harmonic profile, you determine it has a K-4 rating.3.

Choose a Transformer: You would need a K-4 rated transformer with a kVA rating of at least (Voltage 110A RMS) / 1000. For example, at 480V, you'd need at least a (480V * 110A) / 1000 = 52.8 kVA transformer. You would likely select the next standard size up (e.g., 75 kVA K-4 rated).By following this approach, you can ensure that your cables and transformers are appropriately sized to handle the challenges posed by harmonic currents, preventing overheating, saturation, and premature failure. Always consult with relevant electrical codes and standards (like the NEC, IEC) for specific requirements in your region. Flag for review