Optimal design of transformers

By Nigel Atkinson

With the growing requirement to improve the design of tomorrow’s transformers, many designers and engineers are finding they need to investigate new types of transformer, with higher ratings or smaller footprint. Or quite simply, they need to improve their device’s efficiency. Engineers who have taken their designs as far as possible with hand calculations, test-based processes and analytical methods often require more accurate and versatile techniques to provide necessary insights to design better transformers.

If you are already active in the field of transformer design you probably have some analytical tools to hand. Given a transformer power rating it quickly delivers some approximate sizing recommendations for your device. With tools like this you might get, say, a 90-something % efficient transformer. They are good for very quickly getting in the ballpark. But analytical tools are not using accurate material data or precisely representing stray flux leakage. Maybe you want to switch to using, say, grain-oriented steels for the first time. Or you had to comply with the EU Ecodesign directive.

You’ll only achieve that innovative leap cost-effectively with finite element analysis. FEA is best deployed, because of its computational resource requirement, in getting from that initial over-engineered sizing approximation to a class-leading design. Go back a decade or so and industry primarily used the traditional make it-test it-measure it-break it approach to new product development. New designs would be coupled up to circuits in the laboratory and key parameters would be measured across the desired operating range.

Simulation provides designers with the means to replicate tests virtually, saving time and money. It also allows effects to be separated  – in the past designers would only have been able to measure a limited number of samples of operating temperature, but simulation allows them to see which types of loss are generating the most heat. Because of the variety of advanced post-processing techniques designers can see what’s happening inside the device – where the problems or inefficiencies are arising, as well as where flux leakage is occurring, where structures are saturated and at what position problems could occur.

Once designers have built a model of the base design, “what-if” scenarios are far easier and quicker to run virtually than in the lab. These designs offer robustness against potential manufacturing issues (dimensional tolerances), material supply dependencies (does it only work with one type of steel) or its performance at different environmental temperatures. When designers have developed a functional design, automated optimization techniques can be employed to refine the design even further.

To start with the very basics of transformers, in an ideal world different windings on primary and secondary circuits produce transformed voltages and currents on the output compared to the input according to very simple calculations. But in the real world there is less than 100% flux linkage. Hence designers have to consider flux leakages in both the primary and secondary. When designing a real-life transformer a certain amount of leakage may be desirable, say when designing air-gaps or magnetic bypass shunts to limit short-circuit currents.

In addition to the leakage flux, coils will be made of less than perfect conductors, therefore there are copper losses to deal with. In the core there will be magnetising reactance and losses from the iron. All these deviations from the perfect transformer can be expressed as equivalent circuit parameters and are often used in transformer specification. In the diagram below, V1 represents the primary voltage.

The resistances R1 and R2 represent the copper losses in primary and secondary windings respectively. The primary and secondary windings don’t share exactly the same flux, instead there is some flux leakage. However, this leakage doesn’t cause power losses, rather it causes a phase change between the voltages and currents, and the effect can be modelled using the reactances L1 and L2 for the primary and secondary flux leakages respectively. The resistance R3 represents the iron losses, i.e. the hysteresis and eddy current losses in the core. A transformer with finite permeability needs a small magnetizing current. This current is in phase with the core flux, but not with the induced voltage. This effect is modelled by the reactance L3.

When it comes to assessing the performance of a prospective transformer, three tests are commonly carried out. These can be reproduced in the virtual world using simulation to calculate the parameters that we see here.

1) Open Circuit test

In the Open circuit test the secondary windings are not connected to load. When there is no load at the secondary windings of the transformer, no current flows through the ideal transformer windings. The impedances R1 and L1 are usually much smaller than the impedances R3 and L3 so the transformer equivalent circuit can be approximated.

Once the model is solved:

  • Lorentz forces are calculated on the primary and secondary windings using Integrals over Conductors;
  • Eddy Current and Iron losses can be calculated.
  • No load losses can be calculated as the sum of the eddy current, iron and resistive losses; and
  • The active power Pm is obtained from the iron loss calculation on the core. The apparent power (V1 I1) is calculated from the rms values of the voltage and current in the primary. Hence, the reactive power Qm, the iron loss resistance R3 and the inductance L3 are calculated.

2) Short Circuit test

During this test, one phase of the transformer secondary is short-circuited and the primary is connected to a power supply. The current in the primary is increased, until the current in the secondary reaches the rated value.  This allows the short-circuit impedance of the transformer to be calculated by the simulation.

Once the model is solved:

  • Lorentz forces and Eddy Current and Iron losses can be calculated.
  • The active power Pm is obtained from the resistive loss calculation in the windings. The apparent power (V1*I1) is calculated from the rms values of the voltage and current in the primary. Hence, the reactive power Qm, the resistance R1 + R’2 and the inductance L1 + L’2 are calculated from the equations.

3) Inrush test

In this test either the voltage or the frequency is ramped up to the rated value at the rated current. Here we are interested in the voltages and currents in the circuits and the forces on the coils.

Once the model is solved:

  • Lorentz forces can be calculated on the primary and secondary windings, and Eddy current and Iron losses can be calculated, as can the efficiency of the transformer.