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To provide a numerical technique for the quick and simple determination of the switching time instants for field‐circuit coupled problems with switching elements.

3D magnetic vector potential formulation coupled to an electrical circuit with switching elements, for example, diodes, is presented. The change of the state of the switching elements is implemented as a modification of the model topology.

Since every step of the singly diagonally implicit Runge‐Kutta methods delivers not only the solution of this time step but also its stage derivatives, they can be efficiently employed to construct a dense‐output‐based interpolation polynomial, with their roots approximating the switching time instants.

This paper presents a computationally cheap interpolation approach for quick and accurate determination of switching time instances for field‐circuit coupled problems with switching elements. The proposed technique can be successfully incorporated into software packages designed to model coupled problems of different nature, where sudden changes of quality may take place.

To provide a reliable numerical technique for the time integration of the electromagnetic models with sinusoidal excitation.

The numerical integration of an electrotechnical problem is commonly carried out using adaptive time stepping. For one particular selected time step, Runge‐Kutta (RK) adaptive integration methods deliver two approximations to the solution with different order of approximation. The difference between both is used to estimate the local error.

Standard error‐controlled RK time integration fails for electromagnetic problems with sinusoidal excitation when the adaptive time step selection relies upon the comparison of a main solution and an embedded solution where the difference of orders is one. This problem is overcome when the embedded solution differs by two orders of approximations. Such embedded solution is efficiently constructed by putting appropriate order conditions on the coefficients of the Butcher table.

Using the technique proposed in the paper, electromagnetic problems with sinusoidal dynamics can also be effectively tackled.

The coupling between a 3D modified magnetic vector potential formulation discretized by the finite integration technique and an electrical circuit that includes solid and stranded conductors is presented. This paper describes classical time integration methods and the implicit Runge‐Kutta methods, the latter being an appropriate alternative to the first ones to solve effectively index 1 differential‐algebraic equations arising from combined simulation of electromagnetic fields and electrical circuits.