One transformer, two wildly different ohm values depending which side you measure from — and exactly one per-unit value that works on both.
Power system studies almost never quote impedance in ohms. Instead everything — voltage, current, impedance, power — gets expressed as a fraction of a chosen base value: the per-unit (pu) system. It looks like an extra layer of abstraction bolted on top of Ohm's law, but it exists to solve a specific, concrete headache: comparing and combining equipment of wildly different physical sizes and voltage levels without a mess of turns-ratio conversions at every step.
You pick two numbers — a base power S_base (usually in MVA) and a base voltage V_base (in kV, chosen per voltage level) — and everything else is derived from them: base current I_base = S_base ÷ (√3 · V_base) for three-phase systems, and base impedance Z_base = V_base² ÷ S_base. Any actual quantity divided by its matching base becomes a per-unit value — a dimensionless number that says "this much, relative to the base I chose," with no units attached at all.
Referring impedance across a transformer in ohms means multiplying or dividing by the turns ratio squared (a²) — a 10:1 transformer changes the number by 100×. Do that at every transformer in a network and the bookkeeping becomes the whole job. Per-unit sidesteps it: when the base voltages on each side of a transformer are chosen to match its own turns ratio, its per-unit impedance comes out the same number viewed from either side. On top of that, per-unit keeps typical component impedances in a predictable, human-readable range — roughly 0.05 to 0.20 pu for most generators, transformers, and lines — regardless of whether the equipment is rated 500 kVA or 500 MVA, which makes a wildly wrong input (a decimal point error, a bad unit conversion) obvious at a glance in a way that raw ohms never would be.
That part is true — a per-unit value is always relative to a base, the same way a percentage is relative to 100. The part people miss is what happens next: a per-unit value is only meaningful, and only combinable with other per-unit values, when everyone involved has converted to the same base MVA and base voltage. 1.05 pu on a 100 MVA, 13.8 kV base is not the same physical quantity as 1.05 pu on a 10 MVA, 13.2 kV base— and adding, subtracting, or comparing per-unit values computed on different bases without first converting them (via the standard S_base and V_base ratio formulas) is one of the most common real errors in short-circuit and load-flow studies, especially when combining equipment data sheets that each quote impedance on the manufacturer's own nameplate rating instead of the study's system base.
Explains why power engineers express voltage, current, impedance, and power as per-unit (pu) fractions of a chosen base rather than in raw ohms and volts — using a side-by-side comparison of a transformer's wildly different primary vs. secondary ohmic impedance against its single, unchanging per-unit value.
Per-unit is often introduced as an arbitrary normalization step, disconnected from any physical motivation — just "divide by the base." That framing hides the real reason it exists: without it, every calculation spanning more than one voltage level (which is nearly every real power system study) would require repeatedly rescaling impedances by the square of a turns ratio at each transformer, a tedious and error-prone step that per-unit eliminates almost entirely.
Choose a base apparent power S_base and a base voltage V_base for a given part of the system. From those, base current is I_base = S_base ÷ (√3 · V_base) for a three-phase system, and base impedance is Z_base = V_base² ÷ S_base. Any actual value is converted to per-unit by dividing by its matching base: V_pu = V_actual ÷ V_base, I_pu = I_actual ÷ I_base, Z_pu = Z_actual ÷ Z_base. When base voltages on either side of a transformer are chosen in the same ratio as the transformer's own turns ratio, the transformer's per-unit impedance comes out numerically the same whether computed from the primary or secondary side — unlike its ohmic impedance, which differs by the turns ratio squared.
Per-unit is the standard language of load-flow studies, short-circuit studies, and protective relay coordination precisely because it lets a generator, a transformer, and a transmission line — each rated at a completely different voltage and MVA — sit on the same normalized scale and be combined by simple series/parallel arithmetic. It also acts as a built-in sanity check: because well-designed equipment consistently lands in a narrow pu range (roughly 0.05-0.20 pu impedance for most generators, transformers, and lines), a wildly out-of-range per-unit result is an immediate signal that something upstream — often a base mismatch — is wrong.
Ohmic impedance changes by the square of the turns ratio every time you cross a transformer, so a network spanning several voltage levels would need constant rescaling. Per-unit, chosen with matching base voltages across transformers, keeps a transformer's impedance numerically the same on either side, and lets components rated at very different physical sizes be compared and combined without any unit conversion.
Z_base = V_base² ÷ S_base, where V_base is the base voltage for that part of the system and S_base is the base apparent power (usually a single system-wide MVA value). It is the "yardstick" ohmic value against which an actual impedance is measured to produce a per-unit number.
Not without converting first. Nameplate impedance is almost always given on the equipment's own rated MVA and voltage, which rarely matches the system study's chosen base. It must be converted to the system base — using Z_pu,new = Z_pu,old × (S_base,new ÷ S_base,old) × (V_base,old ÷ V_base,new)² — before it can be added to or compared against other per-unit values in the same study.
Yes — the same base-value technique is used for DC systems, single-phase equipment, and even non-electrical engineering domains (fluid systems, structural loads) wherever comparing quantities across very different physical scales on a common normalized footing is useful. In power engineering it is simply most prominent because of how often multiple voltage levels appear in a single study.
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