S.O. Baryshnikov1, V.V. Sakharov2, A.A. Chertkov3, A.A. Zhilenkov4, T.D. Kainova5, O.Yu. Kichigina6

1–3 Admiral Makarov State University of Maritime and Inland Shipping (St. Petersburg, Russia)

4–6 Saint Petersburg State Marine Technical University (St. Petersburg, Russia)

4zhilenkovanton@gmail.com, 5marine_electronics@smtu.ru, 6olga1986kichigina@gmail.com

For electric circuits with complex topology, especially those containing switching elements, the problem of calculating energy distribution and steady-state operating conditions under topological constraints is of practical importance. However, as the structure becomes more complex, the dimensionality grows, and switching is introduced, conventional manual circuit-equation calculations become cumbersome and scale poorly. Therefore, a formal computational approach is required that encodes constraints via circuit topology, reduces the problem to an extremum formulation, and obtains the solution using numerical optimization methods. To develop an algorithm for calculating energy distribution and voltages in conservative multi-loop capacitive circuits, as well as for evaluating the steady-state conditions of switched-capacitor converters, using the principle of least (stationary) action and CVX-based convex optimization tools in MATLAB. A method is proposed in which the energy distribution in a multi-loop capacitive circuit is obtained from an extremum formulation: the objective function is written in terms of electric-field energy, and the unknowns are the capacitor voltages. Topological relations and switching states are represented as a set of constraints formed from Kirchhoff’s laws in matrix form, after which the problem is solved in MATLAB using CVX as a convex optimization problem. It is shown that the approach is applicable to circuits with switches and can represent structural changes by modifying the constraints. For switched-capacitor converters, a procedure is presented for computing the no-load steady-state operating mode: a system of linear equations is assembled from the generalized cycle matrix and solved to determine the input-output relationship. The algorithm and its software implementation can be used for the analysis and synthesis of capacitive networks and switched-capacitor converters with high dimensionality and variable topology, as well as for digitalization of calculations, resource saving, and multi-criteria design of electrical engineering systems.

Baryshnikov S.O., Sakharov V.V., Chertkov A.A., Zhilenkov A.A., Kainova T.D., Kichigina O.Yu. Algorithm for estimating energy distribution in multi-loop electric circuits using CVX technologies. Electromagnetic waves and electronic systems. 2026. V. 31. № 2. P. 14−24. DOI: https://doi.org/10.18127/j15604128-202602-03 (in Russian)

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