Genetic Algorithm Sculpts Compact High-Frequency Transformer for Solid-State Power Conversion

Solid-state transformers offer one possible approach for managing the power flows that come with renewable generation, distributed energy resources, and battery storage, combining power electronic converters with a high-frequency isolation stage instead of relying solely on conventional line-frequency magnetics. At the heart of such a system sits a deceptively simple component: a high-frequency transformer that isolates the high-voltage side from the low-voltage side while shuttling energy back and forth tens of thousands of times per second. A new study now shows how a carefully tuned genetic algorithm can design one of these transformers from the ground up, balancing size, losses, heat, and manufacturability in a single optimization sweep, and then prove the result on a working laboratory prototype.

The research, conducted at A. D. Patel Institute of Technology in Vallabh Vidyanagar, India, targets the dual active bridge (DAB) converter, widely regarded as a suitable topology for the isolated DC-DC stage of a solid-state transformer. In a DAB, two full-bridge circuits face each other across the transformer, and the phase shift between their switching waveforms dictates both the magnitude and direction of power flow. Because the transformer operates at 20 kilohertz rather than the 50 or 60 hertz of a conventional unit, its magnetic core and windings shrink considerably.

But high-frequency operation is a double-edged sword: it magnifies core losses, skin-effect losses in the copper, and the thermal stresses that come with packing power into a small volume. What makes the transformer design problem so stubborn is that every parameter pulls against the others. Raising the flux density shrinks the core but inflates hysteresis and eddy-current losses.

Increasing current density reduces conductor volume yet raises copper loss and temperature. Bringing the primary and secondary windings closer together lowers leakage inductance, which sounds desirable until you realize that in a DAB converter, leakage inductance is not a nuisance at all. It is the very element that shapes power transfer and enables zero-voltage switching, the soft-switching technique that lets transistors turn on when the voltage across them is nearly zero, slashing switching losses.

Design the leakage inductance correctly and the converter needs no external series inductor; get it wrong and either the power transfer collapses or the current stress soars. Conventional design procedures handle these couplings through sequential, rule-based calculations, which the authors argue becomes difficult when electromagnetic, thermal, insulation, and converter-level requirements interact so strongly. Their answer is a constraint-driven multi-objective framework that minimizes three quantities simultaneously: the area product, a standard proxy for magnetic size; copper loss; and core loss.

Around these objectives they wrap a set of hard constraints, including a minimum predicted transformer efficiency of 99 percent, a leakage inductance at least equal to the value the DAB power-transfer equation demands, a temperature-rise ceiling, window utilization kept below 60 percent to preserve insulation and cooling margins, and conductor radii limited by the skin depth at the switching frequency. To test whether their chosen optimizer actually deserved the job, the team ran a bake-off. Six metaheuristic algorithms, namely a genetic algorithm (GA), particle swarm optimization, NSGA-II, the multi-objective grey wolf optimizer, simulated annealing, and the whale optimization algorithm, were set loose on the identical problem with the same variable bounds, constraints, and computational budgets.

Each ran 20 independent times. The genetic algorithm delivered the highest mean analytical efficiency of 99.7893 percent, and a Kruskal-Wallis test confirmed the differences among algorithms were statistically significant, with post-hoc comparisons surviving Holm correction. On Pareto-front quality, NSGA-II edged ahead on hypervolume at 0.92 while the GA posted the best spread at 0.88, a balance of convergence and diversity that led the researchers to keep the GA as their principal method, though they are careful to note this does not make it universally superior for every criterion.

Against a reference design built by the classical area-product method, the optimized transformer cut total loss from 3.37 watts to 0.55 watts while shrinking the magnetic structure. Crucially, the team did not stop at numbers on a screen. They screened commercial cores against the optimized window area of 4.30 times ten to the minus four square metres and found a nanocrystalline core, a VITROPERM 500F UI core, whose window area of 4.37 times ten to the minus four square metres matched almost exactly, proving the solution could actually be built.

Finite-element analysis in ANSYS then stress-tested the analytical predictions. The simulated peak flux density of 0.288 tesla deviated from the analytical 0.280 tesla by only 2.9 percent. A counter-magnetomotive-force excitation, which cancels the main magnetizing field to expose the leakage paths alone, allowed the finite-element model to extract a primary-referred leakage inductance of about 577 microhenries, within 2.7 percent of the analytical 562 microhenries.

A steady-state thermal simulation predicted a maximum temperature of 52.81 degrees Celsius at roughly 30 degrees ambient, comfortably below the 80-degree constraint. The two-dimensional models do carry limitations, since end-turn effects, terminals, and non-uniform cooling are not resolved, but the agreement was strong enough to justify building hardware. That hardware was a 150-watt, 120-volt to 12-volt, 20-kilohertz DAB prototype wound with Litz wire, one hundred strands of 0.1-millimetre copper, in a 20-to-2 turn arrangement.

The measured leakage inductance came in at 585 microhenries, within about 4 percent of the analytical estimate. At rated load, oscilloscope-based power analysis yielded a transformer-side efficiency of approximately 98.75 percent, about 0.88 percentage points below the analytical prediction, a gap the authors attribute to practical winding losses, high-frequency effects, modelling assumptions, and measurement uncertainty rather than claiming a precise loss breakdown. A zoomed view of the switching transition showed markedly reduced voltage-current overlap, consistent with zero-voltage switching at the tested operating point, achieved through the transformer's designed leakage inductance with no external inductor, though the authors emphasize that soft switching is operating-point dependent and was verified only at representative conditions.

The converter also had to stay stable when the world around it changed. A linearized small-signal model of the voltage-control loop, closed with a digital PI controller, showed a phase margin of about 90.44 degrees at the nominal operating point, with both closed-loop poles safely in the left half of the complex plane. A robustness analysis then perturbed the leakage inductance, load resistance, and output capacitance each by plus or minus 20 percent.

Poles never crossed into instability, and the phase margin stayed between roughly 88 and 93 degrees. On the bench, load steps and input-voltage steps produced brief deviations of a few percent that settled within tens of milliseconds, with the measured transients slightly larger than simulation predicted, as parasitics and sensing delays in real hardware tend to ensure. Infrared thermography delivered perhaps the most visually satisfying verdict: while the external load resistors reached about 122 degrees Celsius, the transformer surface sat near 35 degrees, barely above ambient.

The authors are candid that their validation covers only this 150-watt laboratory scale; scaling to kilowatt-level solid-state transformers will require recalculating the leakage-inductance requirement, reworking insulation coordination, and rethinking cooling, since the required inductance depends directly on power, voltage ratio, and switching frequency. Still, the study demonstrates a complete chain, from competing objectives and coupled constraints, through statistical comparison of optimizers, finite-element verification, and converter simulation, to a working prototype, offering a template for designing the magnetic components of future solid-state conversion systems rather than guessing at them.

Subject of Research: Multi-objective optimization and experimental validation of a high-frequency transformer for dual active bridge converters in solid-state transformer applications

Article Title: Constraint-driven multi-objective design and experimental validation of a high-frequency transformer for dual active bridge converters in solid-state transformer applications

Article References: Solanki, J. B., Chudasama, K. J., & Paghdar, H. V. (2026). Constraint-driven multi-objective design and experimental validation of a high-frequency transformer for dual active bridge converters in solid-state transformer applications. Cleaner Engineering and Technology, Article 101339. https://doi.org/10.1016/j.clet.2026.101339

Image Credits: AI Generated

DOI: 10.1016/j.clet.2026.101339

Keywords: solid-state transformer, high-frequency transformer, dual active bridge converter, genetic algorithm, multi-objective optimization, nanocrystalline core, leakage inductance, zero-voltage switching, finite-element analysis, power electronics, renewable energy, small-signal stability