Harmonics and transformer derating

Load loss in a transformer is not one number. It is the sum of three components: the resistive loss in the windings, which depends only on the square of the RMS current; the eddy-current loss in the windings, which rises with the square of frequency; and the stray loss in structural parts such as core clamps, tank walls and busbars, which rises with frequency raised to a power between about 0.8 and 2 depending on the path the flux takes. Only the first component is frequency-independent. A current containing 5th, 7th, 11th and 13th harmonics, plus components near the switching frequency, therefore produces more heat than a sinusoidal current of the same RMS value.

The heat also lands in the worst place. Winding eddy currents are generated inside the conductor, where the cooling path is longest. That is why the winding hot-spot rises faster than the average winding temperature as distortion increases, and why two transformers with the same rated load loss can behave differently under the same harmonic current.

IEEE Std C57.110 is the recommended practice for establishing transformer capability when supplying nonsinusoidal load currents. It does not produce a single derating percentage: it takes the declared loss split and the load spectrum, and returns the maximum RMS current the unit can carry.

The calculation runs in four steps. First, the spectrum is expressed as per-unit harmonic currents relative to the fundamental, and the total RMS current in per-unit is found. Second, the harmonic loss factor for winding eddy currents is the weighted sum of the squared per-unit harmonic currents multiplied by the square of the harmonic order, normalised to the squared total RMS current; a second factor does the same for other stray loss with an exponent of 0.8 rather than 2. Third, the rated winding eddy-current loss ratio gives the maximum permissible harmonic loss factor for that design. Fourth, the two limits are compared, and whichever binds governs the available capacity.

The standard also discusses the K-factor designation used in North America for dry-type units serving harmonic-rich loads. A K rating is a declared classification, not a computed result, and it does not replace the loss-based calculation. Where a specification quotes a K rating, the underlying loss split should still be requested.

Two inputs are needed from the manufacturer and are frequently missing from a quotation: the ratio of winding eddy-current loss to total load loss at rated current, and the ratio of other stray loss to total load loss. Without them, no third party can reproduce the derating.

Inverter duty transformer harmonics depend on the front-end topology, and the two common families behave differently. Line-commutated and six-pulse rectifier front ends produce characteristic harmonics at 6k plus or minus 1 — the 5th, 7th, 11th, 13th and so on — with magnitudes falling roughly in proportion to the harmonic order. Voltage-source PWM inverters with a switching frequency of a few kilohertz have low current distortion at rated output, but they concentrate energy in sidebands around the switching frequency and its multiples.

That second family is the one that catches people out. Because the eddy-loss weighting goes with the square of the harmonic order, a modest component at 3 kHz weighs far more heavily than the 5th harmonic at 50 Hz.

Distortion is also worst at part load. Harmonic currents do not fall in proportion to the fundamental, so the distortion index of a PCS at 25 percent output is typically higher than at 100 percent. Ask for the harmonic spectrum at 25, 50, 75 and 100 percent of output, and separately for reactive-only operation, rather than accepting a single THD value.

Energy storage transformer harmonic derating is not the same problem as solar. A PCS both rectifies and inverts, so the transformer carries a distorted current in both directions, and the spectrum in charging mode differs from the spectrum in discharging mode. A unit sized on the discharge spectrum alone can be wrong half the time.

Storage duty adds two further cases that a continuous rating does not describe. During reactive support the transformer carries current with little or no active power: losses are generated, no energy is sold. During standby the PCS may still inject a small distorted current while the transformer's no-load loss runs continuously. Over a year of daily cycling, both effects accumulate in the winding hot-spot.

IEEE 519-2022 is a system-level standard. It sets harmonic current and voltage distortion limits at the point of common coupling; it does not rate transformers. Compliance is the plant's obligation, and the transformer's role is to survive the current that a compliant plant still produces. The limits scale with the ratio of maximum short-circuit current to maximum demand load current at that point, so a strong grid connection permits more harmonic current than a weak one. Some utilities add their own planning values: Saudi Electricity Company, for example, applies a planning total harmonic distortion of 6.5 percent at the medium-voltage connection point for large-scale solar.

What the transformer specification should carry is narrower: the harmonic current spectrum at the transformer terminals at defined load points; the calculation standard and its edition; the declared loss split; the maximum permissible hot-spot temperature under that spectrum; and the evidence that will be provided. A specification that says only compliant with IEEE 519 leaves the transformer's actual duty undefined.

Derating exists to hold the hot-spot temperature inside its limit, not to hold current inside a limit. IEC 60076-2 sets the temperature-rise reference for oil-immersed units, including a 65 K average winding rise at rated current under its reference ambient conditions. IEC 60076-7 and IEEE C57.91 then model insulation ageing as an exponential function of hot-spot temperature: for thermally upgraded kraft paper the reference hot-spot is 110 degrees Celsius, and the ageing rate roughly doubles for each 6 K above it.

Two consequences follow. First, the difference between a design that meets the limit and one that does not is small in temperature terms and large in life terms. Second, because harmonic losses concentrate in the winding, the hot-spot penalty for a given distortion is set by the eddy-loss fraction. This is why the loss split, rather than the headline efficiency, is the number that decides whether a unit is still inside its thermal limits in year 15.