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Magnetic resonant coupling (MRC) is an efficient method for realizing the near-field wireless power transfer (WPT). Although the MRC enabled WPT (MRC-WPT) with a single pair of transmitter and receiver has been thoroughly studied in the literature, there is limited work on the general setup with multiple transmitters and/or receivers. In this paper, we consider a point-to-multipoint MRC-WPT system with one transmitter delivering wireless power to a set of distributed receivers. We aim to introduce new applications of signal processing and optimization techniques to the performance characterization and optimization in multiuser WPT via MRC. We first derive closedform expressions for the power drawn from the energy source at the transmitter and that delivered to the load at each receiver. We identify a "near-far" fairness issue in multiuser power transmission due to receivers' distancedependent mutual inductance with the transmitter. To tackle this issue, we propose a centralized charging control algorithm to jointly optimize the receivers' load resistance to minimize the total transmitter power drawn while meeting the given power requirement of each individual load. For ease of practical implementation, we also devise a distributed algorithm for the receivers to adjust their load resistance independently in an iterative manner. Last, we characterize the power region that constitutes all the achievable power-tuples of the loads via controlling their adjustable resistance. In particular, we compare the power regions without versus with the time sharing of users' power transmission, where it is shown that time sharing yields a larger power region in general. Extensive simulation results are provided to validate our analysis and corroborate our study on the multiuser MRC-WPT system.

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Energy storage systems (ESSs) are essential components of the future smart grids with high penetration of renewable energy sources. However, deploying individual ESSs for all energy consumers, especially in large systems, may not be practically feasible mainly due to high upfront cost of purchasing many ESSs and space limitation.As a result, the concept of shared ESS enabling all users charge/discharge to/from a common ESS has become appealing. In this paper, we study the energy management problem of a group of users with renewable energy sources and controllable (i.e., demand responsive) loads that all share a common ESS so as to minimize their sum weighted energy cost. Specifically, we propose a distributed algorithm to solve the formulated problem, which iteratively derives the optimal values of charging/discharging to/from the shared ESS, while only limited information is exchanged between users and a central controller; hence, the privacy of users is preserved. With the optimal charging and discharging values obtained, each user needs to independently solve a simple linear programming (LP) problem to derive the optimal energy consumption of its controllable loads over time as well as that of purchased from the grid. Using simulations, we show that the shared ESS can achieve lower energy cost compared to the case of distributed ESSs, where each user owns its ESS and does not share it with others. Next, we propose online algorithms for the real-time energy management, under non-zero prediction errors of load and renewable energy.The proposed algorithms differ in complexity and the information required to be shared between the users and central controller, where their performance is also compared via simulations. Index TermsShared energy storage system, energy management, distributed algorithm, online algorithm, renewable energy, convex optimization.

Abstract-In magnetic resonant coupling (MRC) enabled multiple-input multiple-output (MIMO) wireless power transfer (WPT) systems, multiple transmitters (TXs) each with one single coil are used to enhance the efficiency of simultaneous power transfer to multiple single-coil receivers (RXs) by constructively combining their induced magnetic fields at the RXs, a technique termed "magnetic beamforming". In this paper, we study the optimal magnetic beamforming design in a multi-user MIMO MRC-WPT system. We introduce the multi-user power region that constitutes all the achievable power tuples for all RXs, subject to the given total power constraint over all TXs as well as their individual peak voltage and current constraints. We characterize each boundary point of the power region by maximizing the sum-power deliverable to all RXs subject to their minimum harvested power constraints, which are proportionally set based on a given power-profile vector to ensure fairness. For the special case without the TX peak voltage and current constraints, we derive the optimal TX current allocation for the single-RX setup in closed-form as well as that for the multi-RX setup by applying the techniques of semidefinite relaxation (SDR) and time-sharing. In general, the problem is a non-convex quadratically constrained quadratic programming (QCQP), which is difficult to solve. For the case of one single RX, we show that the SDR of the problem is tight, and thus the problem can be efficiently solved. For the general case with multiple RXs, based on SDR we obtain two approximate solutions by applying the techniques of timesharing and randomization, respectively. Moreover, for practical implementation of magnetic beamforming, we propose a novel signal processing method to estimate the magnetic MIMO channel due to the mutual inductances between TXs and RXs. Numerical results show that our proposed magnetic channel estimation and adaptive beamforming schemes are practically effective, and can significantly improve the power transfer efficiency and multi-user performance trade-off in MIMO MRC-WPT systems compared to the benchmark scheme of uncoordinated WPT with fixed identical TX current.