Transformer turns ratio

What it is (precise)

A transformer works because one alternating flux in the core links every turn of both windings, so the induced volts per turn is a single number shared across the machine and winding voltage divides in exact proportion to turns: V1/V2 = N1/N2 = n.

Magnetomotive-force balance forces the currents the other way, I1/I2 = 1/n, which is why apparent power passes through unchanged apart from losses — a transformer converts voltage, never MVA. That identity is per winding pair; at the terminals of a three-phase unit the rated line-voltage quotient equals the winding turns ratio only when both windings share a connection.

The working number on a BESS unit transformer is the rated-voltage ratio: 34.5 kV over 690 V is 50 — a Dyn unit's actual per-winding turns ratio is that 50 multiplied by √3 (≈ 86.6), and a YNd unit's is that 50 divided by √3 (≈ 28.9), because whichever winding is the delta sees line voltage while the wye winding sees line-to-neutral.

A 3,450 kVA PCS block pushing about 2,887 A at the LV terminals puts roughly 58 A onto the collection feeder. That inverse current scaling is the entire reason the step-up exists — conductor loss scales with current squared, so moving a block's output at one-fiftieth of the current is what makes a multi-hectare collection system affordable.

Impedance is the scaling people get wrong, because it goes with the square. An impedance on the LV side looks n² times larger viewed from the MV terminals, with n here the rated-voltage ratio of 50 — volts up by n and amps down by n move their quotient by n × n. For the 50:1 example unit at a typical 6% short-circuit impedance on its own 3,450 kVA base, that is about 8.3 milliohms seen from the 690 V winding and about 20.7 ohms from the 34.5 kV winding: the same physical machine, a factor of 2,500 apart in ohms.

The per-unit system exists largely to make that factor vanish — on the unit's own base the impedance is 6% from either side, which is why every fault and load-flow study runs in per-unit and why an ohmic impedance quoted without its reference side is a study error waiting to be found.

Rated-voltage ratio vs the actual turns

The nameplate does not state turns. It declares rated voltages winding by winding — 34 500/690 V — and their quotient is the rated-voltage ratio, defined at no load on the principal tapping.

The wound turns are integers chosen so that, through each winding's connection — wye or delta — the terminals produce that quotient at the designed volts per turn, and the distinction matters because the ratio is a property of the windings, not of the busbars: the moment load current flows, the terminal-voltage ratio departs from the rated-voltage ratio by the drop across the transformer's own impedance, in whichever direction the power is flowing.

A BESS makes that departure two-sided — the drop reverses between discharge and charge — so no loaded measurement of bus voltages will reproduce the nameplate quotient exactly.

What taps change is the turns themselves. An off-circuit tap is a set of connection points brought out along the winding; repositioning the link adds or removes turns and shifts the ratio in steps. The standard arrangement on a BESS unit transformer is plus/minus 2 taps of 2.5 percent — five positions spanning ±5%, which on the 50:1 example is anything from 47.5:1 to 52.5:1.

The purpose is not regulation but centering: the load-flow study finds the standing collection-bus voltage at the site, and the tap is chosen so the PCS terminals sit in the middle of their working range at that standing voltage rather than near an edge.

Off-circuit taps vs on-load tap changers

The two tap technologies answer different questions. An on-load tap changer (OLTC) is a motor-driven mechanical switch that steps the ratio under load, many times a day, with a diverter mechanism, arcing contacts and a maintenance schedule — it exists to chase a moving voltage. An off-circuit (de-energized) tap changer is a link repositioned only with the transformer switched out, expected to move a handful of times in the asset's life.

BESS unit transformers almost always carry the second kind, and the reason is architectural: the machine on their LV side is already a continuously acting voltage regulator. The PCS adjusts its output within each cycle and the plant controller dispatches reactive power across the fleet to manage the collection bus, so a mechanical regulator on every pad-mount would duplicate — more slowly, and with moving parts — a function the power electronics perform natively.

An OLTC is worth its complexity one level up: a main power transformer at the project substation regulating the whole collection system against the transmission grid, where the connection's standing voltage profile calls for it. Down at the unit transformers the ratio question collapses to one commissioning decision per unit — which of five taps — and the record-keeping around it.

The transformer entry's pitfall list is blunt about the failure mode: taps left at the factory setting rather than the value the load-flow study assumed shift the collection-bus arithmetic for every block at once, and the plant inherits the error until someone de-energizes and moves the links.

How it shows up in specs, studies and commissioning

On a datasheet the ratio appears as the rated-voltage pair, and it is really the quotient of two decisions made in different rooms. The MV figure follows the market's collection practice — commonly 34.5 kV in the US, 33 kV in the UK, 20 kV in continental Europe — while the LV figure matches the PCS variant, with 690 V the common grid-scale class in a 0.4 to 0.8 kV span.

Dual-secondary units, common where one MV transformer serves two inverter blocks, carry one MV winding against two galvanically separated LV windings and state the ratio for each pair. Check the tap range and step against what the load-flow study assumed, and check which winding carries the taps — on a step-up unit they normally sit on the MV winding, so a tap that adds MV turns raises n and lowers the LV voltage the PCS sees.

Studies see the ratio twice. In per-unit it disappears — which is precisely the warning, because a grid excursion at the point of interconnection lands on the inverter terminals scaled straight through: a collection bus 10% high is PCS terminals 10% high, and ride-through performance is verified with the transformer in the model for that reason.

And because a PCS is a current-limited machine, its apparent power scales with the AC terminal voltage the tap has positioned — the voltage entry's modular-PCS example gains about 43% kVA moving 480 V → 690 V at one current limit. Tap selection is therefore capability arithmetic, not voltage cosmetics: a setting that leaves the LV bus 2.5% low leaves every block's deliverable kVA about 2.5% short at the same current ceiling.

Commissioning owns the quantity by name. The transformer turns-ratio (TTR) test measures the actual ratio phase by phase, at every tap position, at the factory acceptance test and again at site, and compares it against nameplate.

A reading outside the acceptance band flags shorted turns, a wrong tap connection or windings connected against the wrong vector-group configuration — cheap findings on the pad, expensive ones after backfeed energization. The as-left tap position on every unit belongs in the commissioning record alongside the test sheets, because it is the one number tying the fleet's electrical reality to the studies the interconnection was approved on.

Common pitfalls

The recurring errors are all scalings. Referring an impedance across the transformer with n instead of n² corrupts a short-circuit result by a factor of fifty on this example unit; quoting a per-unit impedance without naming its MVA base leaves the next engineer guessing; and reading the nameplate quotient as a statement about loaded bus voltages ignores regulation entirely.

A subtler one is treating the tap range as an operating control — an off-circuit tap is a commissioning-time centering device, and a procedure that assumes the ratio can chase seasonal voltage drift is writing outages into the plan.

Keep the neighbours distinct, too. The turns ratio says how much the voltage changes between windings; the vector group says at what angle and with which winding connections — two separate nameplate facts, and conflating them hides exactly the grounding-system and protection consequences the transformer-vector-group entry covers. The ratio's apparent simplicity also invites copy-paste between projects: the same PCS block behind a 33 kV collection system needs a different transformer than behind 34.5 kV, with the tap study redone rather than transplanted.