Un operador de subestación miró su medidor electrónico hoy cuando llegó una tormenta eléctrica y cambió la línea de 110 kV de potencia de 108 kV a 116 kV. A pesar de eso, el bus de 20 kV en el lado secundario mostró valores entre 19.9 y 20.1 kV al mismo tiempo. El instrumento que trabaja allí se llama cambiador de tomas bajo carga: la relación de transformación se corrige paso a paso.
El artículo interpreta qué es la relación de transformación, cómo se calcula, cuál es la relación entre la relación de transformación y la estabilidad de voltaje, cómo los cambiadores de tomas hacen que la relación de transformación sea estable en ese mismo momento, y qué consecuencias se pueden obtener si hay un error en la relación de transformación. Se proporcionan ejemplos de cálculos en el documento junto con referencias a las normas IEC 60076 y IEEE C57, rango típico de tomas, el costo de los cambiadores de tomas, y otros.
¿Qué es la relación de transformación? (Definición y fórmula)
La relación de transformación o relación de vueltas define la relación de vueltas del devanado primario al número de vueltas del devanado secundario. Es igual a la relación de voltaje primario a voltaje secundario y la relación inversa de las corrientes primarias a secundarias en el caso teórico.
N1/N2 = V1/V2 = I2/I1.
Los transformadores reales no son ideales. En los transformadores reales, la reactancia de fuga y la resistencia del devanado dan lugar a caídas de voltaje, haciendo que el voltaje real sea más bajo que el voltaje en vacío. La diferencia en el voltaje en porcentaje se llama regulación de voltaje que está alrededor de 2%-6% dependiendo de las características de los transformadores.
La siguiente definición se utiliza de manera intercambiable en los contratos:
| Término | Significado | Ejemplo |
|---|---|---|
| Relación de vueltas | N1 / N2 (geometría de devanado puro) | 550 / 100 = 5.5 |
| Relación de voltaje | V1 / V2 en vacío | 110 kV / 20 kV = 5.5 |
| Regulación | Caída de voltaje de vacío a carga completa | 2.5%–6% |
Cómo calcular la relación de transformación: ejemplos resueltos
Determinar la relación es fácil si se conoce el voltaje o el número de vueltas.
Por ejemplo:
Un transformador de voltaje de 110 kV/20 kV tiene 110:20 con 2200 vueltas en el primario, lo que significa que hay 400 vueltas en el secundario.
En el caso de un transformador de mayor voltaje, 18 kV – 400 kV, la relación se convierte en (400/18 = 22.2).
Un transformador de distribución generalmente tiene una relación de voltaje de 11 kV/0.4 kV, lo que significa que la relación es 11/0.4 = 27.5:1.
Debido a la construcción del autotransformador, que comparte una parte del sistema de devanado, tiene un menor número de vueltas para la misma relación de voltaje de 2:1.
En el caso de transformadores que operan en un sistema trifásico, se debe utilizar el voltaje línea a línea, mientras que el grupo vectorial (Dyn11, YNd11) es importante en términos de determinar la relación del desplazamiento de fase y la relación de magnitud del sistema.
Por qué la relación es la válvula reguladora de la red.
Las fluctuaciones de voltaje en una línea de transmisión ocurren debido a varios factores, a saber, modificaciones en la carga, fallos de generador, pérdidas de potencia reactiva y distancia de la fuente. Sin ajuste al ratio, un alimentador puede experimentar fluctuaciones de voltaje de 5% a 10% a lo largo de un solo día. El ratio del transformador actúa como el medio práctico para compensar las ventajas de la variabilidad del voltaje, ya que existe una relación directa entre las vueltas y el voltaje de salida, con cualquier cambio que conduce a fluctuaciones correspondientes.
Los operadores del sistema deben mantener el voltaje dentro de los límites legales establecidos por las regulaciones, que requieren mantener el voltaje en ± 5% en el sector de distribución y ± 10% en el sector de transmisión. El método más utilizado en este proceso es el OLTC, que ajusta el ratio del transformador. De hecho, el OLTC es tan ampliamente utilizado que tener un transformador sin OLTC necesita una justificación por escrito.
Cambiadores de tomas: El mecanismo que ajusta el ratio
Existen dos familias de cambiadores de tomas, y elegir entre ellas es principalmente una cuestión de ciclo de trabajo:
| Aspecto | Fuera de circuito (DETC) | Bajo carga (OLTC) |
|---|---|---|
| Operación | Desenergizado solamente | Bajo carga, automatizado |
| Rango típico de tomas | ±2.5% a ±5% | ±10% a ±16% |
| Pasos | 3–5 | 13–17 (1.25%–2.5% cada uno) |
| Capacidad de regulación | Solo estacional | Continua, automática (±2% de mantenimiento) |
| Prima de precio | Línea base | +$15,000–$60,000 depending on rating |
| Common on | Distribution transformers | Power transformers ≥5 MVA |
While OLTCs are operating with electrical current, they use resistors or reactors and fast vacuum interrupters in order to minimize electrical arcing on the main contacts in the process of switching from fixed taps. A contemporary motor-controlled OLTC takes approximately 2 to 10 seconds to finish a cycle. It can be noted that the controller in this case uses voltage feedback from the secondary side of the transformer.
Ratio Matching for Parallel Operation
When using two transformers to supply the same bus simultaneously, the ratios need to be adjusted to be closely matched. A difference in ratios of Δ% generates a so-called circulating current (participating in the circuit even in idle condition).
One advice is to make sure we keep the circulating current below 10% of the capacity of the smaller transformer.
The effect of a 1% difference in ratio is usually a circulating current of 2%-5% of the capacity of two transformers with capacity of 20 MVA / 110 kV, which depends on impedance (normally 10%).
The transformers should be operated in accordance with some basic conditions for this, namely: same group of vector, ratio must match, and impedance should not vary more than 10%, if at all.
To account for this, operators need to change the tap position for each transformer to make those equal, and many of modern AVRs have a master-follower scheme for this purpose.
Effects of Wrong Ratio: Circulating Current & Protection Issues
Relaying misoperation, due to relay rating, can lead to malfunctioning of protections with erroneous relay settings resulting in either protector operation without proper fault or failure to detect real internal defects because of 2%-5% errors.
Voltage changes can force the voltage along the creek into outside limits.
Imbalance in load situation implies that a unit with a higher ratio consumes a considerable share of both active and reactive power leading to acceleration of its aging.
That is why ratio check became one of the steps of commissioning according to IEC 60076-1 requirements stating that the voltage ratio on the main tapping must differ by no more than ±0.5% from design value and every tap must be verified against the nameplate data.
Ratio Testing Methods & Standards
The standard field test is the turns-ratio test performed with a transformer turns ratio (TTR) meter:
| Method | Principle | Precisión | Uso Típico |
|---|---|---|---|
| TTR meter (TTR test) | Compares injected and induced voltage on each tap | ±0.1% | Commissioning, routine maintenance |
| Voltage ratio check at no load | Apply reduced voltage, measure both sides | ±0.3% | On-site verification |
| Capacitance ratio / low-voltage test | Equivalent ratio via capacitive coupling | ±0.5% | Factory type tests |
Both factory tests and site tests originate from IEC 60076-1 and IEEE C57.12.90. The TTR test is considered a primary diagnostic test as the movement in the ratio between different tests done on the same unit oftentimes signifies a shorted turn in the winding, making yearly ratio tests an essential element of monitoring.
Typical Ratios and Tap Ranges by Application
| Aplicación | Typical Ratio | Tap Range | Tap Changer |
|---|---|---|---|
| GSU at a power plant | 18/400 kV (22.2:1) | ±7.5% in 5 steps | Off-circuit, sometimes OLTC |
| Transmission substation | 220/110 kV (2:1) | ±16% in 17 steps | OLTC |
| Sub-transmission | 110/20 kV (5.5:1) | ±12% in 13 steps | OLTC |
| Industrial power | 33/11 kV (3:1) | ±10% in 9 steps | OLTC or off-circuit |
| Distribution | 11/0.4 kV (27.5:1) | ±2.5% off-circuit | Off-circuit |
Distribution transformers require only periodic adjustments, so off-load taps in steps of ±2.5% and ±5% are adequate to account for seasonal load variation. By contrast, transmission and sub-transmission transformers areconfigured with OLTC because large groups of customers are directly affected by the action of the transmission voltage on them.
Tap Changer & Transformer Price Impact
Tap-changer choice is a real line item in any transformer budget. Planning ranges:
| Transformador | Without OLTC | With OLTC | Premium |
|---|---|---|---|
| 5 MVA / 33 kV | $55,000–$90,000 | $75,000–$130,000 | +$15,000–$40,000 |
| 20 MVA / 110 kV | $150,000–$260,000 | $175,000–$320,000 | +$20,000–$60,000 |
| 50 MVA / 110 kV | $360,000–$700,000 | $400,000–$800,000 | +$25,000–$90,000 |
The charges differ according to the type of specifications, the brand, and the area. The high expense involved in grid-tied units pays off in short time: the On-load tap changer (OLTC) can recover the cost quickly because it keeps the voltage regulated and diminishes the energy losses in feeders.
Brands & How Ratio Design Differs
Ratio mathematics remains the same irrespective of the originating company — physics is not up for negotiation; however, manufacturers distinguish themselves based on the type of tap-changer design, control, quality management, and pricing. Reliability benchmarks are set by the MR (Maschinenfabrik Reinhausen) and ABB tap changers as Asian companies increasingly make use of licensed or self-developed OLTC designs at cheaper rates.
| Marca | País | Tap-Changer Strengths | Indicative Price (20 MVA/110 kV, with OLTC) |
|---|---|---|---|
| Hitachi Energy | Suiza/Japón | Proprietary OLTC, AVR integration | $450,000–$700,000 |
| Siemens Energy | Alemania | MR OLTC options, digital control | $430,000–$680,000 |
| Schneider Electric | Francia | Distribution focus, MV units | $280,000–$450,000 |
| TBEA | China | In-house OLTC, scale | $180,000–$320,000 |
| Jiangsu Subian Electric Power | China | Custom ratios & taps, MR or in-house OLTC | $160,000–$300,000 |
The cost is determined by specification and area. In projects that require customized ratio and tap specifications – unique vector groups, special tap ranges, or particular brands of OLTC – Jiangsu Subian Electric Power is a reliable partner: it manufactures distribution and power transformers with capacity from 50 kva to 220 kV, provides quotes for individual tap configurations, and installs the required MR or similar on-load tap changers. Each unit is delivered with ratio test records on all taps under the IEC 60076-1 standard, and factory prices are usually 30%-50% lower than prices for European companies.
Preguntas Frecuentes
How is transformer ratio calculated?
The transformer ratio is determined by the number of turns in the primary coil divided by the number of turns in the secondary coil (N1/N2), which is equal to the no-load voltage ratio (V1/V2). For example, the transformer applied at 110 kV/20 kV will have a 5.5:1 ratio, while for the 11 kV/0.4 kV transformer the ratio is 27.5:1. Because of the inverse relationship, it is evident that in a step-up transformer (ratio smaller than one; such as 0.045 for the transformer with 18/400 kV voltage), the output voltage will be high while the output current is low.
What is the tolerance on transformer ratio?
Per IEC 60076-1, the ratio at the principal tap must be within ±0.5% of the nameplate value, and the same tolerance applies at every tap position unless otherwise specified. Field TTR meters measure to ±0.1%, so a deviation beyond 0.5% on a commissioning test warrants investigation for shorted turns or a wrong connection.
Why do transformers need tap changers for voltage regulation?
Due to fluctuations in line voltage based on load, generation, and distance from the source, without the ratio adjustment, the distribution feeder can fluctuate 5%–10% throughout the day. OLTC varies the ratio by 1.25%–2.5% in steps within a range of ±10% to ±16% to provide a secondary voltage of about ±2% automatically. This ensures the motors, electronics, and the customer equipment are safe from overvoltage and undervoltage.
What happens if two transformers in parallel have different ratios?
An electric current circulates between the two units, even when there is no load coming from outside. In other words, a circulating current flows in a transformer even when it is on standby mode. When we take the case of 20 MVA/110 kV units, even a 1%-ratio mismatch will cause a circulating current of around 2%-5% of full-load rated current. Moreover, if the mismatch increases, the circulating current will also increase accordingly. The action of operators, who equalize the ratio through the tap selection process, will prevent circulating currents from rising more than 10% of the rating of the small transformer.
How much does an on-load tap changer add to transformer cost?
OLTC generally makes it possible to add between $15,000 and $60,000 to the cost of power transformers rated between 5 MVA and 50 MVA, with higher rated transformers costing more. The investment usually pays off due to better voltage control and lower losses of power as well as absence of equipment failures.
Referencias
- IEC 60076-1: Power Transformers — General — Defines ratio, tolerances, taps, and testing requirements.
- IEC 60076-8: Application Guide — Guidance on tapping, parallel operation, and application of power transformers.
- IEEE C57.12.00: General Requirements for Liquid-Immersed Transformers — North American requirements for ratio and tap specifications.
- Maschinenfabrik Reinhausen (MR) — Industry reference for on-load tap changer design and control.
- IEEE C57.12.90: Test Code for Liquid-Immersed Distribution, Power, and Regulating Transformers — The test procedures including ratio tests.
- US EPA: Transformer Efficiency Programs — Background on why voltage control and efficient transformers matter at scale.
Conclusión
The transformer ratio functions like a control device in the power system – a tiny, accurate change in the turns ratio made by tap changers allows to maintain voltage within the legal limits while securing power supply across hundreds of kilometers of power lines. Knowledge of ratio measurement, its limits, and parallel operation is crucial for all professionals who specify, test, or service transformers.
The ratio is also no-load voltage ratio. Distribution transformers may work with 5.5:1 up to 27.5:1.
Transformers with on-load tap changers modify the ratio from -10% to +16% and position the tap lever in 13-17 steps.
Transformers should have the same ratio and impedance in order to prevent circulation of the current. Ratio test is obligatory (IEC 60076-1, tolerance of ±0.5%) and allows detecting shorted turns.
If your project requires a transformer with a specific ratio, tap range, or OLTC configuration, Jiangsu Subian Electric Power can engineer and supply distribution and power transformers from 50 kVA to 220 kV class, with full ratio test reports on every unit.