[Paper Review] Node Placement and Distributed Magnetic Beamforming Optimization for Wireless Power Transfer

Mohammad R. Vedady Moghadam, Rui Zhang|arXiv (Cornell University)|Aug 1, 2016

Wireless Power Transfer Systems28 references3 citations

TL;DR

This paper proposes an optimized node placement and distributed magnetic beamforming scheme for near-field wireless power transfer using magnetic resonant coupling. By jointly optimizing transmitter locations and adaptive beamforming currents, the system maximizes minimum received power across a 1D or 2D region, achieving uniform power coverage with significant gains over non-adaptive and heuristic benchmarks.

ABSTRACT

In multiple-input single-output (MISO) wireless power transfer (WPT) via magnetic resonant coupling (MRC), multiple transmitters are deployed to enhance the efficiency of power transfer to the electric load at a single receiver by jointly optimizing their source currents/voltages to constructively combine the induced magnetic fields at the receiver, known as magnetic beamforming. In practice, since the transmitters (power chargers) are usually at fixed locations and the receiver (e.g. mobile phone) is desired to be freely located in a target region for wireless charging, its received power can fluctuate significantly over locations even with adaptive magnetic beamforming applied. To achieve uniform coverage, the transmitters need to be optimally placed in the region, which motivates this paper. First, we derive the optimal magnetic beamforming solution in closed-form for a distributed MISO WPT system with given locations of the transmitters and receiver to maximize the deliverable power to the receiver load subject to a given sum-power constraint at all transmitters. With the optimal magnetic beamforming solution, we then jointly optimize the locations of all transmitters to maximize the minimum power deliverable to the receiver when it is being moved over a given one-dimensional (1D) region, i.e., a line of finite length. Although the formulated node placement problem is non-convex, we propose an iterative algorithm for solving it efficiently. Extensive simulation results are provided which show the significant performance gains by the proposed design with optimized transmitter locations and magnetic beamforming as compared to other benchmark schemes with non-adaptive or heuristic currents allocation and transmitters placement. Last, we extend the node placement problem to the more general case of two-dimensional (2D) region, and draw the key insights.

Motivation & Objective

• Address the challenge of fluctuating received power in magnetic resonant WPT due to receiver mobility despite adaptive beamforming.
• Ensure uniform power delivery across a target region by jointly optimizing transmitter locations and beamforming weights.
• Maximize the minimum received power over a 1D or 2D region under sum-power constraints at transmitters.
• Develop efficient algorithms for non-convex optimization problems in distributed MISO-WPT systems.
• Extend the design to 2D regions with practical, scalable node placement strategies.

Proposed method

• Derives a closed-form optimal magnetic beamforming solution for fixed transmitter and receiver positions to maximize delivered power under a sum-power constraint.
• Proposes an iterative algorithm to jointly optimize transmitter locations and beamforming weights to maximize the minimum received power over a 1D region.
• Applies rotational symmetry and prime-based ring structure constraints to ensure distinct, symmetric configurations that preserve beamforming gain.
• Extends the 1D solution to 2D regions using structured transmitter ring arrangements with prime-numbered transmitters per ring.
• Uses KKT conditions to prove optimality of the beamforming solution and leverages symmetry to reduce design complexity.
• Employs mathematical analysis to establish necessary and sufficient conditions for rotational symmetry and structural distinctness in multi-ring configurations.

Experimental results

Research questions

• RQ1 How can transmitter locations be optimized to ensure uniform power delivery across a 1D region in a distributed MISO-WPT system?
• RQ2 What is the optimal beamforming strategy for fixed transmitter and receiver positions to maximize received power under a sum-power constraint?
• RQ3 How can rotational symmetry and structural distinctness be mathematically characterized in multi-ring transmitter configurations?
• RQ4 What performance gains are achievable through joint optimization of node placement and beamforming compared to non-adaptive or heuristic schemes?
• RQ5 How can the 1D node placement optimization be extended to two-dimensional regions with practical scalability?

Key findings

• The proposed closed-form beamforming solution achieves optimal power delivery for fixed transmitter and receiver positions under sum-power constraints.
• The iterative algorithm for 1D node placement significantly improves minimum received power compared to benchmark schemes with fixed or heuristic transmitter locations.
• The use of prime-numbered transmitters per ring ensures rotational symmetry and structural distinctness, enabling scalable and symmetric system designs.
• Simulation results demonstrate substantial performance gains in uniform power coverage when both node placement and beamforming are jointly optimized.
• The extension to 2D regions maintains high performance with efficient, symmetry-based transmitter ring configurations.
• Theoretical analysis confirms that the beamforming solution is globally optimal under the KKT conditions, validating the approach for non-convex optimization.