Wireless power transfer systems with multiple transmitters promise advantages of higher transfer efficiencies and focusing effects over single-transmitter systems. From the standard formulation, straightforward maximization of the power transfer efficiency is not trivial. By reformulating the problem, a convex optimization problem emerges, which can be solved efficiently. Further, using Lagrangian duality theory, analytical results are found for the achievable maximum power transfer efficiency and all parameters involved. With these closed-form results, planar and coaxial wireless power transfer setups are investigated.Index Terms-Convex optimization, maximum transfer efficiency, multiple transmitters, wireless power transfer.
Abstract-This paper presents a rigorous optimization technique for wireless power transfer (WPT) systems enhanced by passive elements, ranging from simple reflectors and intermediate relays all the way to general electromagnetic guiding and focusing structures, such as metasurfaces and metamaterials. At its core is a convex semidefinite relaxation formulation of the otherwise nonconvex optimization problem, of which tightness and optimality can be confirmed by a simple test of its solutions. The resulting method is rigorous, versatile, and general -it does not rely on any assumptions. As shown in various examples, it is able to efficiently and reliably optimize such WPT systems in order to find their physical limitations on performance, optimal operating parameters and inspect their working principles, even for a large number of active transmitters and passive elements.
An optimization procedure for multi-transmitter (MISO) wireless power transfer (WPT) systems based on tight semidefinite relaxation (SDR) is presented. This method ensures physical realizability of MISO WPT systems designed via convex optimization -a robust, semi-analytical and intuitive route to optimizing such systems. To that end, the nonconvex constraints requiring that power is fed into rather than drawn from the system via all transmitter ports are incorporated in a convex semidefinite relaxation, which is efficiently and reliably solvable by dedicated algorithms. A test of the solution then confirms that this modified problem is equivalent (tight relaxation) to the original (nonconvex) one and that the true global optimum has been found. This is a clear advantage over global optimization methods (e.g. genetic algorithms), where convergence to the true global optimum cannot be ensured or tested. Discussions of numerical results yielded by both the closed-form expressions and the refined technique illustrate the importance and practicability of the new method. It, is shown that this technique offers a rigorous optimization framework for a broad range of current and emerging WPT applications.
A new sensitivity analysis approach that can be easily embedded in the Finite-Difference Time-Domain (FDTD) method, in order to accurately and efficiently compute broadband sensitivities in a single simulation, is introduced. The main element of the proposed technique is the use of the complex step derivative (CSD) approximation, which allows for the numeri cal computation of derivatives without relying on error-prone finite-difference expressions. The mathematical derivation of this CSD-FDTD technique is accompanied by a three-dimensional microstrip circuit example.
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