Hans-Dieter Lang

Convex Optimization of Wireless Power Transfer Systems With Multiple Transmitters

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.

Optimization and design sensitivity of SISO and MISO wireless power transfer systems

The maximum achievable power transfer efficiency (PTE) of a multi-transmitter wireless power transfer (WPT) system can be obtained directly from its impedance matrix and the load at the receiver through closed-form expressions. This opens the way to both evaluating the performance of a system or an operating mode as well as relating permissible performance degradation to component tolerances. The latter also gives insight into the complexity of realizing and optimally operating a particular system in practice.

Semidefinite Relaxation-Based Optimization of Multiple-Input Wireless Power Transfer Systems

An optimization procedure for multitransmitter multiple-input single-output (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, semianalytical, 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 SDR, 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.

Optimization of Wireless Power Transfer Systems Enhanced by Passive Elements and Metasurfaces

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.

Broadband sensitivity analysis in a single FDTD simulation with the complex step derivative approximation

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 numerical 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.

Magnetic near-field focusing and optimal wireless power transfer

The relation between subwavelength focusing near-field arrays and arrays designed to maximize power transfer efficiency is investigated. The intuitive expectation that magnetic field focusing around the receiver may maximize power transfer efficiency is not confirmed, when the fields of capacitively loaded loop arrays, designed for optimal power transfer efficiency, are analyzed. The significant role of loss is outlined and interesting aspects of the underlying physics are illustrated.

Optimal performance enhancement of WPT systems by passive intermediate couplers

Using passive intermediate relay elements can lead to substantial performance enhancement of wireless power transfer (WPT) systems. However, it is challenging to fully optimize such systems rigorously, as the underlying problem is nonconvex; meaning such optimization problems are generally unsolvable. The optimization method based on tight semidefinite relaxation presented herein puts the problem in an efficiently and reliably solvable convex form. Simulation results pinpoint the difficulties, prove the capability of the method and indicate its possibilities.

Closed-form optimization of multi-transmitter wireless power transfer systems

While the physical limitations of single-transmitter wireless power transfer (WPT) systems are well-known, systems with multiple transmitters prove difficult to optimize, in order to find their maximum achievable performance. The optimization process leading to a convex quadratic program is outlined and closed-form expressions solving that problem analytically are reviewed. Comparison of results obtained from these formulations and others aquired from analytical modeling show perfect agreement; thus, it is verified that the formulations are equivalent. Hence, they offer a compact and insightful analytical framework for the design and optimization of emerging multi-transmitter WPT topologies.

Maximum transfer efficiency and optimal loads for WPT systems with multiple transmitters

Wireless power transfer (WPT) systems with multiple transmitters promise advantages over single transmitter systems, most predominantly a higher transfer efficiency. Using closed-form expressions obtained from convex optimization, the maximum achievable transfer efficiency and the required load resistance (impedance matching) values are investigated and compared against the single transmitter reference.

From optimization of near-field WPT systems to far-field antenna arrays

A semidefinite relaxation-based optimization framework developed for near-field wireless power transfer systems is adopted for far-field applications. As shown via simulation results, the framework can be used to maximize gain by using optimal reactive loading as well as to iteratively optimize the geometry for self-resonant maximal-gain array antennas.