Per-unit system pu

What it is (precise)

A per-unit value is actual value divided by base value; percent is the same number times 100, so a 7% transformer impedance and 0.07 pu are one figure in two costumes. Only two bases are chosen freely — an apparent-power base S(base) and a voltage base V(base) — and the rest follow from circuit law: current base I(base) = S(base) / (√3 × V(base)) for a three-phase system, impedance base Z(base) = V(base)² / S(base).

Take the canonical BESS block: a 4.4 MVA PCS at 690 V has a current base of about 3,680 A, and that is what 1.0 pu current means on that unit's datasheet — the amperes its conductors, contactors and protection are actually sized against.

The voltage base is not one number but one number per voltage level, and the levels are tied together through the transformer turns ratios. Choose them that way — 690 V on the inverter bus, 34.5 kV on the collection bus, the POI voltage above that — and the turns ratio drops out of the mathematics entirely: a transformer in a per-unit model collapses to its series impedance, and the √3 that haunts every three-phase hand calculation is absorbed into the bases.

That is the practical reason a plant-wide fault or load-flow model is workable at all; without per-unit, every equation would carry ratio and √3 bookkeeping across three or four voltage transformations from battery block to grid.

One definitional distinction comes up daily: 1.0 pu voltage is the base — normally the nominal system voltage at that bus — not whatever the bus happens to be doing. A healthy grid rides above and below nominal through the day, so an operating point of 1.03 pu is unremarkable, and equipment ratings are stated against the base, not against the day's weather. Which nominal, at which bus, is exactly the kind of detail a study data sheet exists to pin down.

Why studies, OEM curves and grid codes speak per-unit

Grid codes write their requirements once, in per-unit, and the numbers then apply at any nominal voltage in any market. Continuous-operation bands sit around 0.9 to 1.1 pu; a low-voltage ride-through envelope demands surviving roughly 0 to 0.05 pu retained voltage for about 150 ms with recovery toward 0.9 pu; high-voltage ride-through tolerance sits near 1.2 pu briefly.

Those envelopes — the ride-through entry owns their anatomy — would be unwritable in volts: the same requirement would need a different curve for every POI voltage on the continent. In per-unit the compliance question at the meter is one division: measured voltage over nominal.

OEM curves normalize for the same reason. A PCS vendor publishes one P-Q capability chart with axes in pu of rated MVA, and it serves every frame size in the family — the p-q-capability and MVA entries cover the curve itself and what erodes it. The reading discipline per-unit imposes is the question pu of what, defined where: 1.0 pu on that chart is the nameplate MVA at reference voltage and temperature, so a hot site shrinks the real envelope while the axes stay put.

Fault behaviour is quoted the same way but on yet another base — an inverter-based resource contributes roughly 1.1 to 1.2 pu of its own rated current into a fault, versus about 5 to 7 pu from a synchronous machine — and that pu is of converter rated current, not of any system study base. Two per-unit numbers can share a sentence and different bases.

Choosing bases — and one worked conversion

A study picks one round system MVA base — 100 MVA is the classic choice — and nominal voltages as the voltage bases, level by level. Everything then re-bases onto that common footing before any arithmetic. The conversion rule is short: Z(pu,new) = Z(pu,old) × (S(base,new) / S(base,old)) × (V(base,old) / V(base,new))². The voltage term is squared because impedance base goes as V²/S; when the nameplate voltage matches the chosen base voltage it equals one, and only the MVA ratio remains.

Worked through on BESS hardware: a 5 MVA medium-voltage skid transformer carries 7% impedance on its own base — inside the 5.5 to 8% band typical for these units. On the 100 MVA study base that is 0.07 × (100 / 5) = 1.40 pu.

Same transformer, same physics, twenty times the number — and the factor of twenty is precisely what goes wrong if the nameplate percent is dropped into the model unconverted: a 0.07 pu entry on the system base makes the transformer look twenty times stiffer than it is, and the fault current computed through it inflates by the same ratio. Protection settings, switchgear interrupting duties and arc-flash results all inherit the error.

How it shows up in specs, studies and contracts

On a transformer nameplate the impedance is a percent figure bound to a stated MVA and a stated pair of windings — and large oil-filled units can carry several MVA ratings on one plate for different cooling stages (a 75/100/125 MVA style nameplate), so the first question is which rating the percent refers to. On a PCS datasheet, establish what 1.0 pu anchors to: the continuous MVA at which AC voltage, which ambient, which altitude. The apparent-power entry's advice to read the rating as a matrix applies doubly here, because a pu curve hides the matrix behind a clean unit circle.

In the interconnection process, per-unit is the transaction currency. The utility's data request wants impedances on stated bases; the study deliverable comes back in pu on the system base; and the numbers that leave the study — relay pickup settings, breaker duties, tap positions — must be translated back into amperes and volts at each level before anyone commissions against them.

Contractually, a capability commitment written in pu is only as firm as its base clause: guaranteeing reactive support to 1.0 pu MVA means nothing until the document states the MVA, the reference conditions, and the bus where it is measured. A one-page base sheet — S base, V base per level, and which nameplate each device's pu values came from — is cheap insurance across every study revision.

Common pitfalls

Every recurring per-unit error is a base error wearing a different hat. A pu number quoted without its base carries no information. A nameplate percent used on the system base without re-basing is the factor-of-twenty mistake from the worked example.

A fault-current figure in pu of converter rated current read as pu of system base current mixes two currencies at very different exchange rates — on a 100 MVA base at 34.5 kV the base current is about 1,674 A, while a single 4.4 MVA PCS's rated current is 3,680 A at 690 V and a far smaller number referred upward. And percent versus pu itself still catches people: a stray factor of 100 in either direction survives review surprisingly well because both forms look plausible in context.

The subtler trap is treating 1.0 pu voltage as the operating point. Ratings and curves are anchored to base voltage, but the grid delivers something else hour by hour, and for a current-limited converter the difference is capability: at 0.90 pu grid voltage the same rated current delivers about 10% less MVA — at exactly the moment a depressed grid wants maximum reactive injection. Checking a capability curve at 1.0 pu voltage only, when the grid code obliges performance across the 0.9 to 1.1 pu band, is how a plant passes its datasheet review and fails its study.