A detailed analysis is presented for a boundary value problem of circular coils with parallel axes shielded by a cuboid of high permeability. Field solutions are given by establishing a suitable ansatz of the magnetic scalar potential, which can satisfy the boundary conditions on six surfaces of the cuboid without difficulty. Analytic expressions are also given for the self and mutual inductance of shielded circular coils with rectangular cross section. By differentiating the self-and mutual magnetic energy with respect to the centre coordinates of the shielded coils, the total forces exerted on them are further obtained, which consist of self and mutual force components. Finally, the numerical results of the proposed method are compared with those of the finite-element method simulations, and the proposed method proves to be accurate and efficient enough for practical applications.

Coaxial iron-core coil system shielded by a magnetic screen is a complex model for analytical calculation, because a complicated boundary value problem must be tackled for obtaining inductances of the coils in this situation. Truncated region eigenfunction expansion method is a suitable way to work out such a problem containing complex boundary conditions. Three different models are taken into consideration in this study. Starting with coil system shielded by two infinitely large plates, the basic steps of the proposed method are introduced carefully. Then the relevant techniques and conclusions are applied to the iron-core coils shielded by a fully enclosed cylindrical screen of high permeability and a lidless one. The effectiveness of the proposed method is verified by comparing with finite element method software and experiments. From relevant data, it is evident that the proposed method is much faster and can be easily used for forecast and evaluation of new schemes in device design process.

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This paper presents a multi-objective Pareto optimal method for allocation of fault current limiters based on an immune algorithm, which takes into account two objectives of the cost and fault current mitigation effect. A sensitivity factor calculation method based on the rate of fault current mitigation is proposed to reduce the search space and improve the efficiency of the algorithm. In this approach, the objective functions related to the cost and fault current mitigation effect are established. A modified inversion operator based on equal cost is proposed to converge to global optimal solutions more effectively. The proposed algorithm is tested on the IEEE 39-bus system, and obtains the Pareto optimal solutions, from which the user can select the most suitable solutions according to the preferences and relative importance of the objective functions. Simulation results are used to verify the proposed method.