Electronics Guide

The Power Transformer in the Network

Roles

Transformers stand at every change of voltage level:

• Generator step-up transformers connect a generator, or the collector system of a wind or solar plant, to the transmission network.
• Interconnection transformers, many of them autotransformers, link transmission voltages such as 345 and 138 kV.
• Substation transformers step transmission or subtransmission voltage down to the primary voltage of distribution feeders, often with an on-load tap changer.
• Distribution transformers, on poles, on pads, or in vaults, supply service voltage.
• Special-purpose transformers include phase-shifting, grounding, converter, rectifier, and furnace transformers.

Construction

The core is a stack of grain-oriented silicon steel laminations. In core-form construction, concentric windings surround the limbs of the core; a three-phase core-form unit has three wound limbs and sometimes two unwound outer limbs, forming a five-limb core. In shell-form construction the core surrounds the windings. Larger units are usually liquid-immersed: mineral oil or an ester liquid insulates the windings and carries heat to radiators or coolers, and a conservator or sealed gas space absorbs the liquid's thermal expansion. Dry-type units, insulated by air or cast resin, serve indoor and fire-sensitive locations.

Ratings and the Nameplate

The nameplate gives rated power for each cooling stage, rated voltages and frequency, winding connections and phase displacement, impedance, tap range, insulation levels, and cooling class. Rated voltages are no-load voltages: IEC 60076-1 defines a winding's rated voltage as the voltage applied, or developed at no load, between its terminals.

The Equivalent Circuit

Magnetically Coupled Circuits derives the practical transformer model: an ideal transformer, resistance and leakage inductance in series with each winding, and a magnetizing inductance and core-loss resistance in shunt. Power engineers write it with reactances at rated frequency, usually in per unit, where the ideal transformer drops out.

The Approximate Circuit

The series impedance is a small fraction of base impedance, 8 percent in the example below, and the excitation current is a small fraction of rated current, so moving the shunt branch to the terminals changes almost nothing. The series branches then combine into one impedance, R_eq + jX_eq, referred to either winding, or r + jx in per unit. Load-flow and short-circuit studies usually omit the shunt branch; energization and no-load loss studies keep it.

What the Linear Model Leaves Out

The real core saturates, which dominates energization and overexcitation, and its excitation current is distorted even in normal service. Eddy and stray losses rise with frequency, so harmonic load currents raise load loss more than their RMS value suggests. Winding capacitances, absent from the model, govern the response to surges.

Open-Circuit and Short-Circuit Tests

Two tests supply the parameters. IEC 60076-1:2011, the IEC general standard for power transformers, lists the measurement of no-load loss and current and of short-circuit impedance and load loss among its tests, and IEEE C57.12.90-2021 is the North American test code. The same programs measure winding resistance, check the voltage ratio and phase displacement, and can measure zero-sequence impedance.

The Open-Circuit Test

One winding, usually the low-voltage winding, is energized at rated voltage and frequency with the other winding open. The excitation current I₀ is so small that its drop in the series impedance is negligible, so the shunt branch sees the rated voltage V and the measured power is core loss, P₀. For one phase,

G_c = P / V²; |Y₀| = I₀ / V; B_m = √(|Y₀|² − G_c²)

where, for a three-phase unit, V is the line-to-neutral voltage, I₀ the line current, and P one third of P₀. Then R_c = 1/G_c and X_m = 1/B_m, referred to the energized winding. In per unit on the rated power S_r, g = P₀/S_r, and the admittance magnitude equals the per-unit excitation current. Core loss depends largely on peak flux, which follows the average of the rectified voltage rather than its RMS value, so test codes correct readings taken with a distorted supply.

The Short-Circuit Test

With the low-voltage terminals short-circuited, a reduced voltage V_sc applied to the high-voltage winding is raised until rated current I flows. The core flux is then small, so the measured power is the load loss P_k: the I²R loss of the windings plus the stray losses that leakage flux induces in the windings, clamps, and tank. Per phase, referred to the energized winding, with V_sc taken line to neutral and P as one third of P_k,

R_eq = P / I²; |Z_eq| = V_sc / I; X_eq = √(|Z_eq|² − R_eq²)

and in per unit, with V_r the rated voltage,

z = V_sc / V_r; r = P_k / S_r; x = √(z² − r²)

The percent impedance is 100z. The test cannot split the leakage impedance between the two windings; a model that needs the split usually assumes equal per-unit halves.

Correcting Load Loss to a Reference Temperature

Winding resistance rises with temperature, so load loss measured in a cool test bay is corrected to a reference temperature, 85 °C for liquid-immersed transformers with a 65 °C rise under IEEE C57.12.00. The usual method scales the I²R loss P_R in proportion to resistance and the stray loss P_s inversely, because eddy currents weaken as resistivity rises:

P_k(T_r) = P_R(T_m) × (T_k + T_r) / (T_k + T_m) + P_s(T_m) × (T_k + T_m) / (T_k + T_r)

Here T_m is the winding temperature during the test, T_r the reference temperature, and T_k = 234.5 °C for copper, whose resistance extrapolates linearly to zero at −234.5 °C, or 225 °C for aluminum. A test at 30 °C that finds 62.0 kW of I²R loss and 18.0 kW of stray loss corrects to 74.9 kW and 14.9 kW at 85 °C, a total of 89.8 kW rather than 80.0 kW.

Worked Example: Parameters from Test Data

A 20 MVA, 60 Hz three-phase transformer has a 69 kV delta winding and a 13.8 kV grounded-wye winding; the test data are illustrative. Rated currents are 167.35 A at 69 kV and 836.74 A at 13.8 kV, and the base impedances are 238.05 Ω and 9.522 Ω.

1. Open-circuit data. Energized from the 13.8 kV side at rated voltage, the unit draws I₀ = 2.510 A, 0.30 percent of rated current, and P₀ = 14.0 kW.
2. Shunt branch. Per phase, V = 13,800/√3 = 7,967 V and P = 4,667 W, so G_c = 7.351 × 10⁻⁵ S, |Y₀| = 3.151 × 10⁻⁴ S, and B_m = 3.064 × 10⁻⁴ S. Referred to the 13.8 kV side, R_c = 13.6 kΩ and X_m = 3.26 kΩ. In per unit, g = 0.00070 and |y| = 0.00300, so b = 0.00292, r_c = 1,429, and x_m = 343.
3. Short-circuit data. Energized from the 69 kV side with the 13.8 kV terminals shorted, the unit draws rated current at V_sc = 5,520 V line to line, 8.0 percent of rated voltage. The load loss, corrected to 85 °C, is P_k = 100 kW.
4. Series branch. Per phase, |Z_eq| = (5,520/√3)/167.35 = 19.04 Ω, R_eq = 33,333/167.35² = 1.190 Ω, and X_eq = 19.01 Ω, all referred to the 69 kV side. In per unit, z = 0.0800, r = 100/20,000 = 0.0050, and x = 0.0798, an X/R ratio of 16.0.
5. Check the approximations. In the open-circuit test, the excitation current through half the leakage impedance drops 0.0030 × 0.04 = 0.00012 per unit of voltage; in the short-circuit test, the shunt branch at half the 0.08 per-unit test voltage draws about 0.00012 per unit of current. Neglecting either branch costs about 0.01 percent.

Percent Impedance

The 8.0 percent found above is the transformer's percent impedance: the voltage, as a percentage of rated voltage, that drives rated current through the unit with its other winding short-circuited. Divided by 100, it is the per-unit impedance on the transformer's rating, the same from either winding, and it governs both fault current and voltage drop.

Fault Current

Behind an infinitely strong source at rated voltage, a bolted three-phase fault at the secondary terminals draws 1/z per unit:

I_sc = I_r / z

For the example unit, that is 12.5 times rated current, about 10,460 A at 13.8 kV. A 69 kV source with 1,500 MVA of short-circuit power adds 20/1,500 = 0.0133 per unit on the transformer's base, which, added as a reactance, reduces the fault current to about 8,970 A. Forces on the windings rise with the square of the current, so the impedance also sets the mechanical duty that IEC 60076-5 addresses. Fault Analysis and Symmetrical Components extends the calculation to unbalanced faults.

Regulation and Reactive Power

At full load, the example unit absorbs x times its rating in reactive power, 0.0798 × 20 MVA = 1.60 Mvar, and its secondary voltage falls by several percent at lagging power factor. Specifying impedance is therefore a compromise: a higher impedance limits the fault duty of downstream breakers and buses, and a lower one improves regulation and reduces reactive losses. Rectifier transformers, for example, are given a high impedance deliberately to limit short-circuit current; Per-Unit System and One-Line Diagrams tabulates typical values.

On Which Base?

A multi-rated unit's impedance is often stated on its self-cooled rating, and the same ohms are a larger percentage of a larger rating: 8 percent on 60 MVA is 10.7 percent on 80 MVA. Impedance also varies with tap position, so paralleling and fault studies need it at the extreme taps as well as at the principal tap.

Voltage Regulation and Efficiency

Regulation

Regulation is the change in secondary voltage between no load and a stated load, with the primary voltage held at its rated value, expressed as a fraction of the no-load voltage. Take the secondary voltage V₂ as the reference phasor, and let the load current be n per unit at power factor angle φ, positive for a lagging load, so that I = n e^−jφ. Then

V₁ = V₂ + I(r + jx) = V₂ + a + jb

a = n(r cos φ + x sin φ); b = n(x cos φ − r sin φ)

Holding |V₁| at 1 per unit gives V₂ = −a + √(1 − b²), so

regulation = 1 − V₂ ≈ a + b²/2

The result neglects the magnetizing branch, and the dropped term, b⁴/8, is 0.0002 percent in the example. For the example unit at full load and 0.8 power factor lagging, a = 0.0519 and b = 0.0609, and the regulation is 5.38 percent. At unity power factor it is 0.82 percent, because the reactance acts almost entirely in quadrature. At 0.8 power factor leading it is −4.17 percent, because capacitive current through the leakage reactance raises the secondary voltage. At half load and 0.8 power factor lagging it is 2.64 percent. Some texts divide by the full-load voltage instead, so a quoted regulation needs its definition. Tap changers and the feeder regulators described in Transmission and Distribution Lines compensate for the drop.

Losses

No-load loss, P₀, is core loss from hysteresis and eddy currents; it depends on voltage and frequency, not on load, and accrues in every hour the unit is energized. Load loss, P_k at rated current, is I²R loss plus stray loss and varies with the square of the load current. Fans and pumps add auxiliary loss, which specifications and loss evaluations treat separately; the European peak efficiency index described below counts the cooling power drawn at no load.

Maximum Efficiency

At per-unit load n and power factor cos φ, with voltage and frequency at rated values, the efficiency is

η = n S_r cos φ / (n S_r cos φ + P₀ + n² P_k)

Efficiency is greatest where the loss per unit of load, (P₀ + n²P_k)/n, is least. Its derivative, −P₀/n² + P_k, vanishes where load loss equals no-load loss:

n_max = √(P₀ / P_k)

The result assumes a constant power factor, a constant winding temperature so that load loss scales exactly with n², and negligible auxiliary loss. For the example unit, n_max = √(14/100) = 0.374, or 7.48 MVA, where the losses total 28.0 kW and the efficiency at unity power factor is 99.63 percent. At full load and 0.8 power factor the losses are 114 kW and the efficiency is 99.29 percent; at half load and unity power factor the efficiency is 99.61 percent. The curve is flat near its peak, so a unit that spends most hours at partial load can be designed to peak well below its rating.

Energy and Loss Evaluation

Energy lost matters more than efficiency at any one load. If the example unit runs at unity power factor for 8 hours at 0.3 per unit, 10 hours at 0.7 per unit, and 6 hours at full load each day, it delivers 308 MWh, loses 336 kWh in its core and 1,162 kWh in its windings, and achieves an energy efficiency of 99.52 percent. Purchasers therefore compare bids by total owning cost:

total owning cost = price + A × P₀ + B × P_k

The factors A and B, in currency per kilowatt, give the present value of a kilowatt of no-load loss and of load loss over the unit's life. No-load loss accrues in every energized hour, while load loss scales with the square of a load that is often well below rating, so A normally exceeds B. IEEE C57.120, the IEEE guide for loss evaluation of distribution and power transformers and reactors, sets out how to derive them. With illustrative values of A = $8,000/kW and B = $2,500/kW, the example unit's losses are worth $112,000 and $250,000, which can justify a costlier, lower-loss design.

Three-Phase Connections and Vector Groups

Banks and Three-Phase Units

Three-phase power passes through either a bank of three single-phase transformers or one three-phase unit, which uses less core steel, has lower losses, and costs less; a bank can be shipped a phase at a time and backed up by one spare unit.

The Basic Connections

The IEC Connection Symbol

IEC 60076-1 writes a transformer's winding connections and phase displacements as a connection symbol of letters and clock-hour figures, often called the vector group:

• A capital letter, D, Y, or Z, gives the high-voltage winding's connection: delta, wye (star in IEC usage), or zigzag.
• Lowercase letters, d, y, or z, give the other windings in descending order of rated voltage.
• N or n after a wye or zigzag letter shows that the winding's neutral is brought out.
• The letter a denotes an auto-connected pair of windings, as in YNa0 for an autotransformer with its neutral brought out.
• A clock number after each lower-voltage winding gives its phase displacement from the high-voltage winding.

The displacement is defined with a positive-sequence voltage applied to the high-voltage terminals in their alphabetical or numerical order, with phasors rotating counterclockwise. With the high-voltage line-to-neutral phasor at 12 o'clock, the corresponding lower-voltage phasor points to the clock number, and each hour is 30° of lag. Dyn1 places the low-voltage side 30° behind the high-voltage side; Dyn11 places it 330° behind, which is 30° ahead. Yy, Dd, and Dz connections give even hours, such as 0 or 6; Dy, Yd, and Yz connections give odd hours, such as 1, 5, 7, or 11.

IEEE Practice in Clock Terms

IEEE C57.12.00 fixes the displacement of standard North American units. With standard terminal markings, delta–delta and wye–wye units have none, and for delta–wye and wye–delta units the line-to-neutral voltage at low-voltage terminal X1 lags that at high-voltage terminal H1 by 30° in positive sequence, whichever winding is the delta. In IEC terms, a standard delta–wye substation unit is Dyn1 and a standard step-up unit with a grounded-wye high-voltage winding is YNd1; a Dyn11 unit shifts the other way. The shift reverses in negative sequence, which is why Fault Analysis and Symmetrical Components rotates positive- and negative-sequence currents in opposite directions across such a unit. Three-Phase Circuits and Power explains the 30° shift and the clock-number notation.

Zero-Sequence Behavior and Grounding

Zero-sequence currents are in phase in all three lines, so they need a return through a neutral or ground. A wye winding passes them only if its neutral is grounded, and a delta winding lets them circulate inside it but not leave through its lines. Fault Analysis and Symmetrical Components tabulates the resulting equivalent circuits; here the same rules become choices of apparatus.

Ground Sources

A grounded-wye winding backed by a delta is a zero-sequence source: during a ground fault on the wye side, current returns through the neutral while the balancing current circulates in the delta. The transformer grounds the system on its wye side, and its zero-sequence impedance, with any neutral resistor or reactor, sets the ground-fault current and the voltage rise on the unfaulted phases. The delta also separates the two systems, so a ground fault on one side draws no zero-sequence current from the other. A delta–grounded-wye substation transformer thus gives a four-wire distribution system its own ground source, whatever the grounding of the system that feeds it.

Wye–Wye Units and Tertiary Windings

A grounded wye–grounded wye unit passes zero-sequence current straight through, so a ground fault on either side draws current from the other. With an isolated primary neutral, the zero-sequence part of an unbalanced line-to-neutral load on the secondary finds no balancing current in the primary, acts as magnetizing current, and shifts the neutral. Single-phase banks and five-limb or shell-form units give that zero-sequence flux an easy path through the core and suffer a large shift. A three-limb core-form unit resists it, because its zero-sequence flux must close through the air and the tank, which gives a low zero-sequence magnetizing impedance, although the stray flux heats the tank. A delta tertiary winding cures these problems: it carries the triplen components of the magnetizing current and the currents that balance unbalanced load, holds the neutral steady, and lowers the zero-sequence impedance. Such a stabilizing winding may have no external terminals at all.

Grounding Transformers

A grounding transformer, either a zigzag unit or a grounded wye–delta unit whose delta supplies no load, gives an ungrounded system a ground source. It presents a high impedance to positive- and negative-sequence voltages, so it draws only magnetizing current in balanced service, and a low impedance to zero sequence, so it supplies ground-fault current. It is sized for the fault current and its duration rather than for continuous load. A resistor in its neutral limits that current and appears at three times its value in the zero-sequence network.

Autotransformers and Tertiary Windings

The Rating Advantage

An autotransformer connects its windings in series, so part of the power passes by conduction rather than induction. With high-voltage terminal H and low-voltage terminal X, the series winding lies between H and X and carries the high-voltage line current I_H; the common winding lies between X and the neutral and carries the difference between the low-voltage line current I_X and I_H. Neglecting losses and magnetizing current, V_HI_H = V_XI_X = S, the throughput, and each winding's rating is

S_w = (V_H − V_X) I_H = V_X(I_X − I_H) = αS, where α = 1 − V_X/V_H

The co-ratio α is the fraction of the throughput that the windings must be built for. A 300 MVA, 345/138 kV autotransformer has α = 0.60, so its windings are rated 180 MVA. Its line currents are 502 A at 345 kV and 1,255 A at 138 kV, and its common winding carries only the 753 A difference. The advantage fades as the ratio grows: α is 0.50 for 230/115 kV but 0.90 for a 10:1 ratio.

Impedance, Losses, and Isolation

Seen from H with X short-circuited, an autotransformer presents the leakage impedance of its series and common windings acting as a two-winding transformer. On the throughput base rather than the winding base, that impedance shrinks by the co-ratio:

z_auto = α z_2w

where z_2w is the per-unit impedance of the two windings on their own rating, αS. A design with z_2w = 0.10 on 180 MVA presents 23.8 Ω at 345 kV, or 0.060 per unit on the 300 MVA throughput. Losses scale the same way: losses of 0.5 percent of the 180 MVA winding rating are 0.3 percent of the throughput. The price is higher fault current and no galvanic isolation, so a surge or fault on one system reaches the other directly, and the two systems share a neutral point, so their grounding cannot be chosen independently.

Tertiary Windings

Large autotransformers and grounded wye–wye units may carry a third, delta-connected winding. Besides stabilizing the unit, a tertiary brought out to terminals can supply station service or connect shunt reactors, capacitor banks, or a static var compensator, placing reactive equipment on the transformer rather than at transmission voltage. It must withstand the current that circulates in it during ground faults on either system. Per-Unit System and One-Line Diagrams models a three-winding transformer as a star of three impedances.

Tap Changers

A tap changer alters the turns ratio in steps, to hold the secondary voltage within limits as primary voltage and load change or to match a transformer to its site. Taps often sit in the high-voltage winding, where the current to be switched is smaller. IEC 60076-1 describes a tapped winding by its principal tapping, to which the rated quantities refer, and by the tapping factors of the other tappings; a plus tapping has a tapping factor above 1. The standard also distinguishes full-power tappings from reduced-power tappings.

De-Energized Tap Changers

A de-energized tap changer may be operated only with the transformer switched off, which suits rare adjustments such as matching a new unit to its site. IEEE C57.12.10-2010, for example, calls for four full-capacity taps in the high-voltage winding, at 2.5 and 5 percent above and below rated voltage. Contacts left in one position for years can form an oxide film, and a poor tap contact is among the sources of the overheating gases that dissolved-gas analysis detects.

On-Load Tap Changers

An on-load tap changer, also called a load tap changer, changes taps under load. It must never open the load circuit or short-circuit the turns between adjacent taps, so it switches make-before-break through a transition impedance that carries the load while two taps are connected and limits the current circulating between them. Two families are common:

• Resistor-type tap changers bridge the taps briefly through resistors, and a spring-operated mechanism completes each transition in a fraction of a second. Larger designs pair a tap selector, which moves to the next tap without breaking current, with a diverter switch, which transfers the load.
• Reactor-type tap changers bridge the taps through a center-tapped reactor, called a preventive autotransformer, that can carry load continuously, so the bridging position becomes a working position and doubles the number of steps.

The switching arc erodes contacts and decomposes oil, so diverter switches sit in their own oil compartment, and many modern designs interrupt the current in vacuum interrupters instead. A change-over selector that reverses a tapped winding or adds a coarse winding extends the range. When a load tap changer is specified, IEEE C57.12.10-2010 places it in the low-voltage winding, with about plus or minus 10 percent of regulation in 32 steps of 0.625 percent, the range that feeder step-voltage regulators usually provide.

Control and Coordination

A voltage-regulating relay commands a tap change when the regulated voltage stays outside a bandwidth around its set point for longer than a time delay, and line-drop compensation lets it regulate the estimated voltage at a load center, as Transmission and Distribution Lines explains for feeder regulators. Paralleled transformers with on-load tap changers must keep their taps coordinated, using master–follower control, which moves all units in step, or circulating-current and negative-reactance methods, which act on the reactive current flowing between units. IEC/IEEE 60214-2 is the joint application guide for tap-changers.

Parallel Operation

Paralleled transformers share both terminal voltages, so they operate well only if:

1. their phase displacements match, with like terminals connected to like phases;
2. their voltage ratios match, including tap positions;
3. their per-unit impedances, compared on a common basis, are close, preferably with similar X/R ratios; and
4. their ratings suit the load division that those impedances produce.

Load Sharing

Paralleled units carry the same voltage drop, so each carries a current inversely proportional to its impedance in ohms. With equal impedance angles and per-unit impedances z_A and z_B on their own ratings, the loadings as fractions of their ratings stand in the ratio

(S_A/S_rA) / (S_B/S_rB) = z_B / z_A

The unit with the lower per-unit impedance takes more than its share. A 20 MVA unit at 8.0 percent in parallel with a 15 MVA unit at 9.0 percent carries 21.0 MVA, 105 percent of its rating, when the pair supplies 35 MVA, while the smaller unit carries 14.0 MVA, 93 percent of its rating; the pair can supply only 33.3 MVA before the larger unit reaches its rating. Cooling stages add a trap. Two units rated 60/80 MVA and 60/80/100 MVA, each with 8 percent impedance on its 60 MVA self-cooled rating, have equal impedances in ohms and share load equally, so the first reaches its 80 MVA top rating when the pair carries 160 MVA, not 180 MVA.

Circulating Current

A difference in voltage ratio acts as a voltage source in the loop formed by the two units and drives a current, in per unit, limited only by their series impedances and independent of the load:

I_c = Δv / (z_A + z_B)

Two identical 20 MVA units with 8 percent impedance whose ratios differ by an illustrative 1.25 percent tap step circulate 0.078 per unit, about 65 A at 13.8 kV, almost purely reactive. A difference in phase displacement is far worse: paralleling a Yy0 unit with a Dy1 unit puts 30° between their secondary voltages, a driving voltage of |1 − e^−j30°| = 0.518 per unit, which circulates 3.2 per unit, a sustained fault. Unequal X/R ratios matter much less. Two units of equal 8 percent impedance with X/R ratios of 16 and 4 each carry 50.2 percent of the load current, only 0.4 percent more in total than the load current itself.

Clock Numbers 1 and 11

Connected directly, units with clock numbers 1 and 11 put 60° between their secondary voltages, a driving voltage of 1.0 per unit that would circulate 6.25 per unit through two 8 percent units. They can still run in parallel if the same two phases are interchanged at both the high-voltage and the low-voltage terminals of the Dyn11 unit: it then sees negative sequence in its own terminal order, its shift reverses, and relative to the system it behaves as Dyn1. Every drawing, relay, and meter must then follow the new phase assignment.

Cooling Classes and Thermal Limits

Losses become heat, and insulation life depends on how hot the hottest part of the winding runs. A liquid-immersed transformer moves that heat to air or water by circulating its liquid through radiators or coolers.

The Four-Letter Code

IEC 60076-2:2011, the IEC standard on temperature rise for liquid-immersed transformers, identifies the cooling method with a four-letter code:

ONAN is therefore oil natural, air natural: a tank and radiators with no moving parts. ONAF adds fans, OFAF adds oil pumps, and ODAF directs the pumped oil into the windings. A unit with several cooling stages lists them in rising order of cooling capacity, and its rated power is the power at the highest stage, as in a 60/80/100 MVA ONAN/ONAF/ONAF nameplate.

IEEE Designations, Old and New

IEEE C57.12.00 now uses the same codes. Older North American nameplates carry the designations they replaced, which the standard's 2000 edition tabulated: OA for ONAN, FA for ONAF, FOA for OFAF or, with directed oil flow, ODAF, and FOW for OFWF or ODWF.

Temperature-Rise Limits

For windings with class 105 °C solid insulation in mineral oil at continuous rated power, IEC 60076-2 limits the top-liquid rise to 60 K, the average winding rise to 65 K for ON and OF cooling and 70 K for OD cooling, and the hot-spot winding rise to 78 K. The limits assume air no hotter than 40 °C at any time, 30 °C as the monthly average of the hottest month, and 20 °C as the yearly average; at that yearly average, the hot-spot limit corresponds to 98 °C. IEEE C57.12.00 rates North American units for a 65 °C average winding rise.

Aging and Loading Guides

Cellulose insulation ages faster the hotter it runs. The loading guides, IEEE C57.91 and IEC 60076-7:2018, calculate hot-spot temperature from the load cycle and ambient temperature, convert it to a relative aging rate, and permit loads above nameplate rating when periods of fast aging are balanced by periods of slow aging. The 2018 edition of IEC 60076-7 also models how moisture and oxygen accelerate aging.

Inrush Current

Switching on an unloaded transformer can draw a current several times its rating for a fraction of a second or longer, because Faraday's law ties the core flux to the integral of the applied voltage.

Why the Core Saturates

In steady state the flux lags the voltage by 90°, reaching its peak Φ_m at a voltage zero. A transformer switched on at a voltage zero, however, starts from whatever residual flux Φ_r its core kept when last switched off, and over the next half-cycle the flux changes by 2Φ_m, reaching Φ_r + 2Φ_m. A line-frequency core already runs near saturation, so this excursion drives it deep into saturation, and the energized winding's inductance collapses toward its air-core value. The current flows in tall, one-sided pulses once each cycle. Switching at a voltage peak with no residual flux starts the flux where steady state would have it, and no transient occurs.

An Estimate of the First Peak

Beyond saturation, the extra flux linkage must be supplied through the air-core inductance of the energized winding. With b_r and b_s the residual and saturation flux as multiples of the normal peak flux, and x_ac the per-unit air-core reactance of the winding plus the source reactance, the first peak, as a multiple of rated RMS current, is roughly

i_peak ≈ √2 (2 + b_r − b_s) / x_ac

The estimate assumes switching at a voltage zero, residual flux in the direction of the first excursion, sharp saturation, and negligible resistance during the first half-cycle. Illustrative values of b_r = 0.8, b_s = 1.2, and x_ac = 0.25 give about 9 times rated RMS current, and about 4.5 times with no residual flux. A winding farther from the core encloses more area and has a larger air-core reactance, so energizing it draws less.

Decay, Sympathetic Inrush, and Mitigation

Resistance consumes the flux offset, so the peaks decay within cycles to seconds, most slowly in large units with a high X/R ratio. Inrush current is rich in second harmonic and flows only on the energized side, so it resembles an internal fault to a differential relay; Power System Protection explains how relays restrain against it. Energizing one transformer can also saturate a paralleled unit already in service, because the DC component of the inrush current, flowing through the shared source resistance, offsets the voltage both units see. Controlled switching, which closes each breaker pole at the instant that suits the residual flux, and closing resistors both reduce inrush.

Efficiency Regulations

Transformers run continuously for decades, so small differences in loss add up across a fleet. The U.S. and European rules limit those losses in different ways.

United States

The U.S. Department of Energy sets energy conservation standards for distribution transformers in 10 CFR 431.196. Its definition, in 10 CFR 431.192, covers 60 Hz transformers with an input line voltage of 34.5 kV or less and an output line voltage of 600 V or less, rated from 10 kVA for liquid-immersed units or 15 kVA for dry-type units up to 5,000 kVA, and it excludes autotransformers and grounding, rectifier, regulating, and several other special types. The standards set a minimum efficiency at 50 percent of nameplate load for liquid-immersed and medium-voltage dry-type units and at 35 percent for low-voltage dry-type units. The levels in force apply to units manufactured from January 1, 2016, and a final rule published on April 22, 2024, raises them for units manufactured on or after April 23, 2029. For a three-phase, liquid-immersed 1,000 kVA unit, the minimum rises from 99.43 to 99.46 percent, though submersible units keep the earlier level; if the output at the test point is taken as 500 kW, the allowed loss falls from 2,866 W to 2,715 W, a cut of 5 percent. For a three-phase, low-voltage dry-type 75 kVA unit, the minimum rises from 98.60 to 98.95 percent.

European Union

Commission Regulation (EU) No 548/2014, adopted on May 21, 2014, sets ecodesign requirements for power transformers of at least 1 kVA used in 50 Hz transmission and distribution networks or in industrial applications. Medium power transformers have a highest voltage for equipment above 1.1 kV and up to 36 kV and a rated power from 5 kVA to less than 40 MVA; up to 3,150 kVA they must stay within maximum load and no-load losses, and above it they must reach a minimum peak efficiency index (PEI). Large power transformers, above 36 kV or of 40 MVA or more, must also reach a minimum PEI. Tier 1 applied from July 1, 2015, and Tier 2 from July 1, 2021. For a 1,000 kVA three-phase liquid-immersed unit with a highest voltage for equipment of 24 kV or less on one winding and 1.1 kV or less on the other, Tier 1 allows 10,500 W of load loss and 770 W of no-load loss, and Tier 2 allows 7,600 W and 693 W. Instrument, rectifier, furnace, traction, earthing, and welding transformers are among the exemptions.

The regulation defines PEI as the maximum value of the ratio of the transmitted apparent power minus the electrical losses to the transmitted apparent power. With a constant loss plus a load loss that grows with the square of load, that maximum falls where load loss equals no-load loss plus the cooling power drawn at no load, the condition derived earlier. For the Tier 2 limits of the 1,000 kVA unit with no cooling power, it falls at 30.2 percent load and equals 99.54 percent.

Commission Regulation (EU) 2019/1783, adopted on October 1, 2019, amended the rules. It set separate loss limits for one-for-one replacements of pole-mounted units from 25 to 400 kVA, required only Tier 1 of a replacement medium transformer whose installation at Tier 2 would bring disproportionate costs, and gave large transformers fall-back requirements in similar cases. It also prohibited designs that detect a test and alter their performance, and it called for a review by July 1, 2023, including whether to introduce a stricter Tier 3.

Comparing the Two

The regimes differ: the U.S. rules fix efficiency at one load point, while the EU caps two losses for smaller units and sets a minimum peak efficiency for larger ones. Compliance with either comes down to the same trade: lower core loss through better core steel or lower flux density, and lower load loss through more conductor material.

Condition Monitoring and Dissolved-Gas Analysis

A large power transformer is costly and slow to replace: in 2000, the U.S. Bureau of Reclamation's maintenance manual FIST 3-30 put a realistic replacement time at 18 months to 2 years and expected lead times to grow. Owners therefore track each unit's condition and act on the evidence before a failure.

Dissolved-Gas Analysis

Electrical and thermal faults break chemical bonds in the oil and paper, and the fragments recombine into gases that dissolve in the oil. IEC 60599:2022, the fourth edition of the IEC guide to interpreting dissolved and free gases, explains the chemistry: low-energy faults, such as corona partial discharges, break the weakest carbon–hydrogen bonds and yield mainly hydrogen, while higher energies and temperatures break carbon–carbon bonds and form ethane, ethylene, and finally acetylene. Hydrogen and the hydrocarbon gases come mainly from the oil, while carbon monoxide and carbon dioxide point to cellulose. Field samples go to a laboratory for gas chromatography, following guidance such as IEC 60567, and online monitors track some gases continuously.

IEC 60599 classifies faults as partial discharges (PD), discharges of low energy (D1), discharges of high energy (D2), and thermal faults below 300 °C (T1), between 300 and 700 °C (T2), and above 700 °C (T3). It identifies them from gas ratios and graphical methods, among them Duval's triangle, named for Michel Duval, whose 2002 review in IEEE Electrical Insulation Magazine surveyed the faults that gas-in-oil analysis can detect. The triangle plots the relative proportions of methane, ethylene, and acetylene and divides the plot into fault zones; IEC 60599 gives one version for transformers, bushings, and cables and another for on-load tap-changers. IEEE C57.104-2019 is the North American guide to interpreting these gases in mineral oil-immersed transformers. The Bureau of Reclamation's manual stresses that a sudden increase in key gases and the rate of gas production matter more than the amount of gas, except for acetylene: more than a few parts per million indicates high-energy arcing, although a very hot thermal fault can produce traces.

Oil, Paper, and Electrical Tests

Oil tests track moisture, dielectric strength, acid number, and interfacial tension, which show whether the oil still insulates and whether it is oxidizing toward sludge. Furanic compounds, formed as paper degrades, give an indirect measure of the paper, which cannot be renewed without rebuilding the unit. Offline electrical tests compare winding resistance, turns ratio, excitation current, leakage reactance, and the power factor and capacitance of the insulation and bushings with a baseline. Frequency response analysis, whose measurement technique IEC 60076-18 standardizes, compares a winding's response over a wide frequency range with earlier results or a sister unit and reveals winding movement after a through-fault or transport. Infrared thermography finds overheated connections and blocked radiators.

Online Monitoring and Protective Devices

Top-oil and winding temperature indicators and fiber-optic sensors at the expected hot spot track the thermal state. On a transformer with a conservator, a Buchholz relay in the pipe to the conservator collects gas from slowly developing faults to raise an alarm and trips the transformer on an oil surge or a loss of oil, and a sudden-pressure relay detects the rapid pressure rise of an internal arc. Power System Protection places these devices in the protection scheme.

Summary

Open-circuit and short-circuit tests measure a power transformer's equivalent circuit, and its percent impedance trades fault current against voltage drop. Regulation is approximately n(r cos φ + x sin φ) plus a small quadrature term, and efficiency peaks where load loss equals no-load loss. IEC 60076-1 writes winding connections with clock numbers, IEEE C57.12.00 makes standard delta–wye and wye–delta units clock number 1, and the placement of grounded wyes and deltas decides ground sources and the need for tertiaries.

Autotransformers need windings rated at only the co-ratio times the throughput, at the cost of isolation. Tap changers adjust the ratio off circuit or under load, and paralleled units need matching displacements and ratios and similar impedances on a common base. Cooling codes, temperature-rise limits, and loading guides govern thermal capacity. U.S. and EU rules cap losses in different ways, and dissolved-gas analysis, interpreted with tools such as Duval's triangle, gives early warning of internal faults.

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