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This paper presents implementation details of coupling circuit equations and motion with two dimensional finite element models for transient magnetic analysis. Finite elements with incomplete shape functions are used in a novel way to handle the interface between the moving and stationary parts of the mesh. The final system of equations can then be solved using adaptive time stepping.Two examples are presented, a generator, which is coupled to motion and a motor, which is coupled to external circuits.

To meet unbalanced demand, an energy provider has to include costly generation technologies, which in turn results in high residential electricity prices. Our work is devoted to the application of a bilevel optimisation, a challenging class of optimisation problems, in electricity market. We propose an original demand-side management model, adapt a solution approach based on complementary slackness conditions, and provide the computational results on illustrative and real data. The goal is to optimise hourly electricity prices, taking into account consumers' behaviour and minimizing energy generation costs. By choosing new pricing policy and shifting electricity consumption from peak to off-peaks hours, the consumers might decrease their electricity payments and eventually, decrease the energy generation costs.