Total harmonic distortion THD

What it is (precise)

Take any periodic voltage or current, decompose it into a fundamental plus harmonics, and THD is the square root of the sum of the squares of the harmonic RMS magnitudes, divided by the RMS of the fundamental: THD = √(Σ X_h²) / X₁, quoted in percent, per phase. Under IEEE 519 the sum runs over harmonic orders 2 through 50.

The definition is built entirely on root mean square, which is what lets components at different frequencies combine by squares — their cross-products average to zero over a cycle — and it is a pure ratio: THD says how distorted the waveform is relative to its own fundamental, not how many harmonic volts or amperes are present. The spectrum being summarized — which orders a PCS actually emits, why the 5th, 7th, 11th and 13th dominate, where the switching sidebands sit — belongs to the harmonics entry; this page is about what the summary number means and where it misleads.

Voltage THD and current THD are separate quantities with separate limits, and they live on different scales. Delivered voltage on a healthy network is distorted by at most a few percent, so THD-V limits are single digits. Current distortion is a property of one load or source, and as a percentage it can legitimately reach tens of percent without any hardware fault — the denominator, not the numerator, does most of the moving. A THD figure with no subscript, no measurement location and no load condition attached is close to meaningless, and PCS marketing material produces exactly such figures.

One more property matters for equipment: THD is blind to where in the spectrum the energy sits. Five percent concentrated at the 5th harmonic stresses a tuned filter and a transformer differently than five percent spread thinly across forty orders, and interharmonics do not appear in the number at all. That is why standards never cap THD alone — IEEE 519 pairs the aggregate cap with individual per-order limits, and why a harmonic study needs the plant's per-order current spectrum, not the one-line summary.

Voltage THD vs current THD — the whole game at a POI

The division of labour at an interconnection is precise. The quantity everybody ultimately cares about is voltage distortion, because harmonic voltage at the point of common coupling is shared by every customer on the bus. But a battery plant does not emit voltage distortion directly — it injects harmonic current, and the network's frequency-dependent impedance converts those amperes into the harmonic volts the neighbours see.

So the utility caps THD-V as the outcome it protects — 5% in the 1-69 kV band where most utility-scale BESS connect, with 3% on any single order — and polices your plant on the current side, because current is what your equipment controls.

That split explains a result that surprises projects regularly: the same PCS fleet with the same emission spectrum can pass comfortably at a stiff POI and fail at a weak one. Nothing about the plant changed — the grid's source impedance did, and a weak connection turns the same harmonic current into much more voltage distortion.

It is also why the harmonic study in the interconnection process models the plant's per-order injection against the utility's network impedance across contingencies, rather than checking a datasheet number against a limit. Resonance between collector cables, filters and capacitor banks can amplify specific orders well beyond what the PCS alone produces; the mechanics are covered under harmonics.

Contractually, both quantities appear in the interconnection agreement with the POI as their reference plane, and commissioning must demonstrate both by field measurement. The clause worth negotiating early is allocation of background distortion: THD-V at the POI includes whatever pollution the network carried before your plant existed, and without a pre-energization baseline survey the commissioning measurement cannot separate your contribution from the grid's.

TDD — the denominator IEEE 519 actually uses

On the current side, IEEE 519 does not limit THD-I at all. It limits total demand distortion: the same RMS-of-harmonics numerator, referenced not to the fundamental current of the moment but to the maximum demand load current at the point of common coupling — for a new plant, in practice, its rated current.

At full output the two metrics coincide. At light output they diverge without bound, because THD-I's denominator collapses while TDD's stands still. The limits themselves scale with grid strength: below 69 kV, a weak connection with a short-circuit-to-demand ratio under 20 is allowed 5% TDD, loosening in steps to 20% above 1000.

The committee's reasoning is exactly the storage operator's problem. An inverter at 10% load can show 10%+ THD-I while its harmonic amperes are small and harmless — percentage distortion of a lightly loaded machine looks alarming precisely when it matters least. A BESS lives in that regime more than any other inverter-based plant: a unit holding frequency-regulation headroom hovers near zero megawatts for hours, and an arbitrage plant idles between the morning and evening spreads.

Judged on THD-I, a compliant storage plant would look like a power-quality incident every quiet afternoon; judged on TDD, the same operation is unremarkable. For BESS the THD-versus-TDD distinction is not a footnote, it is the difference between a metric that works for the asset class and one that does not.

The practical trap follows directly: comparing a datasheet 'THD < 3%' line against the 5% TDD in the interconnection agreement and concluding there is margin. Different numerators' conditions, different denominators, different measurement locations. The defensible move is to ignore aggregate numbers in vendor comparison and request the harmonic current spectrum per order at several load points — the harmonic study cannot run without it, and the aggregate can be recomputed from it under either definition.

Measurement point and window

Where you measure decides what you measure. Compliance quantities are defined at the point of common coupling — for a transmission- or distribution-connected plant, the POI — not at the inverter terminals.

A terminal measurement on a distorted network is contaminated in both directions: the plant absorbs harmonic current driven by background voltage distortion already on the grid, and a naive reading blames the BESS for amperes it did not originate. Directional, per-order analysis plus a baseline survey taken before energization are what keep the plant from paying for the network's pre-existing pollution.

How you measure is standardized too, and the interconnection agreement usually names the method: harmonic analysis per IEC 61000-4-7 on instruments meeting IEC 61000-4-30 Class A. The base measurement is a window of about 200 ms — ten cycles at 50 Hz, twelve at 60 Hz — and those windows are aggregated into longer statistical values.

IEEE 519 then judges compliance statistically over a measurement week: the 95th percentile of the aggregated values is held to the base limits, with short-duration values allowed defined extra headroom. A single clean snapshot proves nothing, and a single ugly transient condemns nothing.

For commissioning, the statistics have a practical corollary: the survey must capture the plant's real operating states — light load, standby, both power directions — not one full-load test window, because percentage distortion peaks exactly in the states a full-load test skips. Ride-through events and unbalanced faults temporarily raise distortion, but standards assess harmonics under normal operation; keep fault-window waveforms out of the steady-state compliance file.

What moves the number across the load range

A PCS's harmonic current does not scale down in proportion to its output. The residual distortion from PWM switching, dead-time effects in the phase legs and control-loop imperfections stays roughly constant in amperes as the fundamental shrinks, so the THD-I percentage climbs as load falls.

Utility-scale units typically sit below about 3% current THD at rated power, with distortion rising steeply below roughly 20-30% output — the same machine can post 10%+ THD-I at 10% load with nothing wrong. Any datasheet THD figure therefore needs three qualifiers before it is usable: the load level, the assumed grid impedance, and whether the quantity is THD-I or TDD.

Two external factors move the measured numbers without touching the plant. Grid stiffness sets how much THD-V a given injection produces, so the voltage-side reading at a weak POI drifts with network reconfiguration the operator does not announce. And background distortion raises the terminal-side readings whenever nearby loads change.

When a monthly power-quality report shows THD trending upward, the disciplined response is to check output level, per-order amperes and network state before suspecting the hardware — most THD 'events' at a storage plant are the denominator falling, not the numerator rising.