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  • Journal article
    Battistelli C, Agalgoankar YP, Pal BC, 2016,

    Probabilistic dispatch of remote hybrid microgrids including battery storage and load management

    , IEEE Transactions on Smart Grid, Vol: 8, Pages: 1305-1317, ISSN: 1949-3061

    This work presents a probabilistic economic dispatch tool for en-ergy management (EM) studies in the context of remote hybrid AC/DC microgrids (MGs). An EM approach is proposed to en-sure a reliable power supply at the minimum cost of the hybrid MG operation. A comprehensive operational framework is pre-sented, which considers topological features of the hybrid MG and the interlinking converter between AC and DC subsections. Approach and models are tested using several operating scenari-os referred to a test hybrid MG system. In the analyses, the opportunity of integrating battery energy storage and energy demand management in the EM scheme is investigated. The results of the analyses demonstrate the effectiveness and practicality of the optimization tool in different operation contexts.
  • Journal article
    Yan S, Lee CK, Yang TB, Mok KT, Tan SC, Chaudhuri B, Ron Hui SYet al., 2016,

    Extending the Operating Range of Electric Spring using Back-To-Back Converters: Hardware Implementation and Control

    , IEEE Transactions on Power Electronics, Vol: 32, Pages: 5171-5179, ISSN: 0885-8993

    This paper presents the first hardware implementation and control of an electric spring based on a back-to-back converter configuration. Because of its ability to provide both active and reactive power compensation, this back-to-back electric spring (ES-B2B) can substantially extend the operating range of the original version of the electric spring (ES-1) and provide enhanced voltage support and suppression functions. The hardware system and control of the ES-B2B have been successfully developed and tested. The experimental results have confirmed the effectiveness of the ES-B2B in supporting and suppressing the mains voltage. Particularly, the voltage suppression ability of the ES-B2B is superior over that of ES-1. The use of ES-B2B in a simulation study of a weak power grid has also been conducted. The ES-B2B has been found to be highly effective in mitigating voltage fluctuation caused by intermittent renewable power generation.
  • Conference paper
    Merlin MMC, mitcheson PD, 2016,

    Active power losses distribution methods for the modular multilevel converter

    , COMPEL 2016, Publisher: IEEE, ISSN: 1093-5142

    Modular Converters such as the MMC have become the new standard in VSC-HVDC applications. Their modularity has brought many industrial advantages but also increased the complexity of their operation. This paper looks at how a range of techniques may alter the balance of power losses between the IGBT modules. These techniques are based on circulating currents at the (i) fundamental frequency and (ii) second harmonic and (iii) DC voltage offset on the converter voltage waveform. Finally, conclusions on the effectiveness and potential drawbacks of these techniques are discussed.
  • Conference paper
    Cantoni M, Farokhi F, Kerrigan EC, Shames Iet al., 2016,

    A scalable QP solver for optimal control of cascades with constraints

    , Australian Control Conference
  • Journal article
    Wang B, Wang X, Bei Z, Judge P, Wang X, Green TCet al., 2016,

    Reliability model of MMC considering periodic preventive maintenance

    , IEEE Transactions on Power Delivery, Vol: 32, Pages: 1535-1544, ISSN: 0885-8977

    Abstract:Periodic preventive maintenance (PPM) is a significant measure to ensure reliable operation of the modular multilevel converter (MMC), but to date has always been neglected in the reliability evaluation. A mathematical reliability model of MMC considering PPM is proposed in this paper. The model is derived rigorously by the reliability function and finally described by the indices equivalent failure rate and the forced outage rate. Two operation modes related to redundant submodules are considered and described by the standby model and k-out-of-n model, respectively. Employing this model, we can analyze the sensitivity of reliability to redundancy and maintenance interval and provide some reliability indices for planning, which is especially valuable for the offshore cases. The necessity of the considered PPM and the effectiveness of the proposed model are verified by case studies. A method to include PPM in reliability modeling is provided.
  • Conference paper
    Evangelou SA, Shabbir W, 2016,

    Dynamic modeling platform for series hybrid electric vehicles

    , 8th IFAC International Symposium on Advances in Automotive Control, Publisher: Elsevier, Pages: 533-540, ISSN: 1474-6670

    This paper introduces a simulation model that can be used to develop and testdesigns and control systems for hybrid electric vehicles (HEVs). The work involves a novelsimulating platform, developed in Simulink, where each component of a series HEV is developedusing a first-principles approach in a modular fashion, validated by available experimental dataand then integrated to form a coupled nonlinear dynamic model. The vehicle model is capable toact as a platform for the design of supervisory control systems (SCSs) that optimize the energyflow in the powertrain. Simulations with two distinct SCSs and two driving cycles are used toanalyze the vehicle performance under varying driving and operating conditions. The resultsdemonstrate the applicability of the model for realistic prediction of both vehicle behavior andcomponent energy losses, design optimization and control system design.
  • Journal article
    Zhong W, Hui SY, 2016,

    Charging Time Control of Wireless Power Transfer Systems Without Using Mutual Coupling Information and Wireless Communication System

    , IEEE Transactions on Industrial Electronics, Vol: 64, Pages: 228-235, ISSN: 0278-0046

    A charging time control method for wireless power transfer systems with a secondary-side hysteresis output power control is presented. It is a primary-side control method that adopts the combined use of three concepts, namely 1) an intermediate capacitor in the receiver circuit as a power flow indicator, 2) hysteresis switching actions of a shunt decoupling power switch in the receiver circuit to regulate the dc voltage of such intermediate capacitor, and 3) the turn-on and turn-off times of the decoupling switch detected on the primary side for closed-loop control. This method has the advantage of eliminating the need for 1) precise information of the mutual inductance between the transmitter and the receiver coils and 2) wireless communication system for feedback purpose. Practical results obtained from a hardware prototype are included. They confirm the proposed operating principles and indicate that the method can automatically lead to optimal energy efficiency operation.
  • Conference paper
    Trovato V, Teng F, Strbac G, 2016,

    Value of thermostatic loads in future low-carbon Great Britain system

    , 19th Power Systems Computation Conference (PSCC), Publisher: IEEE

    This paper quantifies the value of a large population of heterogeneous thermostatically controlled loads (TCLs). The TCL dynamics are regulated by means of an advanced demand side response model (DSRM). It optimally determines the flexible energy/power consumption and simultaneously allocates multiple ancillary services. This model explicitly incorporates the control of dynamics of the TCL recovery pattern after the provision of the selected services. The proposed framework is integrated in a mixed integer linear programming formulation for a multi-stage stochastic unit commitment. The scheduling routine considers inertia-dependent frequency response requirements to deal with the drastic reduction of system inertia under future low-carbon scenarios. Case studies focus on the system operation cost and CO2 emissions reductions for individual TCLs for a) different future network scenarios, b) different frequency requirements, c) changes of TCL parameters (e.g. coefficient of performance, thermal insulation etc.).
  • Conference paper
    trovato, Teng F, Strbac G, 2016,

    Value of Thermostatic Loads in Future Low-Carbon Great Britain System

    , Power Systems Computation Conference (PSCC), 2016, Publisher: IEEE

    This paperquantifies the value of a large population of heterogeneous thermostatically controlled loads (TCLs). The TCL dynamics are regulated by means of an advanced demand side response model(DSRM). It optimally determines the flexible energy/power consumption and simultaneouslyallocatesmultiple ancillaryservices. Thismodelexplicitlyincorporates the control ofdynamics of the TCL recovery patternafter the provision of the selected services.The proposed frameworkis integrated ina mixed integer linear programming formulation for a multi-stage stochastic unit commitment.The scheduling routine considers inertia-dependent frequency response requirements to deal with the drastic reduction of system inertia under future low-carbon scenarios. Case studies focus on the system operation costand CO2emissions reductionsfor individual TCLs fora)different future network scenarios, b)different frequencyrequirements, c)changesof TCL parameters (e.g. coefficient of performance, thermal insulation etc.).
  • Conference paper
    falugi P, Konstantelos I, strbac G, 2016,

    Application of novel Nested decomposition techniques to long-term planning problems

    , Power Systems Computation Conference, Publisher: IEEE

    Cost effective, long term planning under uncertainty constitutes a significant challenge since a meaningful description of the planning problem is given by large Mixed Integer Linear Programming (MILP) models which may contain thousands of binary variables and millions of continuous variables. In this paper, a novel multistage decomposition scheme, based on Nested Benders decomposition is applied to the transmission planning problem. The difficulties in using temporal decomposition schemes in the context of planning problems due to the presence of non-sequential investment state equations are highlighted. An efficient and highly-generalizable framework for recasting the temporal constraints of such problems in a structure amenable to nested decomposition methods is presented. The proposed scheme's solution validity and substantial computational benefits are clearly demonstrated through the aid of case studies on the IEEE24-bus test system.
  • Conference paper
    Martinez Sanz I, Chaudhuri B, Strbac G, 2016,

    Coordinated corrective control for transient stability enhancement in future Great Britain transmission system

    , 19th Power Systems Computation Conference (PSCC 2016), Publisher: IEEE

    This paper demonstrates a corrective control strategy through fast actuators (TCSC FACTS and HVDC links, both LCC and VSC) in order to enhance the transient stability in the future Great Britain (GB) transmission network. A model predictive control (MPC) scheme that relies on system wide-area measurements is employed for coordinated control action through these power electronic devices with the aim of preserving the system stability without having to constrain pre-fault transfer levels. Case studies employing detailed dynamic models are presented to demonstrate the effectiveness of the proposed approach for different formulations on a representative equivalent model of the future GB transmission grid.
  • Journal article
    Manfredi S, Angeli D, 2016,

    A Criterion for Exponential Consensus of Time-Varying Non-Monotone Nonlinear Networks

    , IEEE TRANSACTIONS ON AUTOMATIC CONTROL, Vol: 62, Pages: 2483-2489, ISSN: 0018-9286

    In this technical note, we present new results on exponential consensus for continuous-time nonlinear time varying networks. A key feature in the following is that the monotonicity property is not required, unlike most of existing literature on the subject. Moreover, we give an estimate of the exponential rate of convergence towards the agreement manifold. Finally, representative example and counterexample are given.
  • Journal article
    Bachtiar V, Manzie C, Moase WH, Kerrigan ECet al., 2016,

    Analytical results for the multi-objective design of model-predictive control

    , Control Engineering Practice, Vol: 56, Pages: 1-12, ISSN: 0967-0661

    In model-predictive control (MPC), achieving the best closed-loop performance under a given computational capacity is the underlying design consideration. This paper analyzes the MPC tuning problem with control performance and required computational capacity as competing design objectives. The proposed multi-objective design of MPC (MOD-MPC) approach extends current methods that treat control performance and the computational capacity separately – often with the latter as a fixed constraint – which requires the implementation hardware to be known a priori. The proposed approach focuses on the tuning of structural MPC parameters, namely sampling time and prediction horizon length, to produce a set of optimal choices available to the practitioner. The posed design problem is then analyzed to reveal key properties, including smoothness of the design objectives and parameter bounds, and establish certain validated guarantees. Founded on these properties, necessary and sufficient conditions for an effective and efficient optimizer are presented, leading to a specialized multi-objective optimizer for the MOD-MPC being proposed. Finally, two real-world control problems are used to illustrate the results of the tuning approach and importance of the developed conditions for an effective optimizer of the MOD-MPC problem.
  • Conference paper
    Xiang X, Zhang X, Chaffey G, Merlin M, Green Tet al., 2016,

    A New Modulation Method for Resonant Modular Multilevel DCDC Converter with Flexible Ratio Operation and Inherent Balance Capability in HVDC Application

    , 2016 International High Voltage Direct Current Conference (HVDC 2016)
  • Journal article
    Li S, Guo Y, Tan S-C, Hui SYRet al., 2016,

    An Off-line Single-Inductor Multiple-Output LED Driver With High Dimming Precision and Full Dimming Range

    , IEEE Transactions on Power Electronics, Vol: 32, Pages: 4716-4727, ISSN: 0885-8993

    This paper presents a single-inductor multiple-output (SIMO) LED driver with precise dimming and full dimming range. Based on the coordination of a string-level scheme and a system-level dimming scheme, the proposed SIMO LED driver can overcome practical constraints of existing SIMO LED drivers such as limited dimming range and needs for high-current switches. The proposal can achieve dimming precision up to an accuracy of 0.8% and also full dimming range. It has the flexibility of using either phase-shift or synchronous pulsewidth-modulated (PWM) switching for dimming control. The proposed circuit and control operations have been practically verified with a 25-W off-line SIMO-driven LED system. Practical evaluations of its power quality and energy efficiency are also provided.
  • Conference paper
    Mylvaganam T, Astolfi A, 2016,

    Towards a systematic solution for differential games with limited communication

    , 2016 American Control Conference (ACC), Publisher: American Automatic Control Council, Pages: 3814-3819, ISSN: 2378-5861

    The main aim of this work is to develop a systematic approach for dealing with differential games with limited communication. To this end a differential game with limited communication is considered. The communication topology is described by a directed graph. The main components characterising the differential game with limited communication are identified before the resulting game is formally defined. Sufficient conditions to solve the problem are identified both in the general nonlinear case and in the linear-quadratic case. A numerical example illustrating the theoretical approach and results is presented. Finally, several directions for further developments are identified.
  • Conference paper
    Ye Y, Papadaskalopoulos D, Strbac G, 2016,

    An MPEC approach for analysing the impact of energy storage in imperfect electricity markets

    , 13th International Conference on the European Energy Market (EEM), Publisher: IEEE, ISSN: 2165-4093

    Although recent studies have investigated the impacts of energy storage on various aspects of power system operation and planning, its role in imperfect electricity markets has not been explored yet. This paper provides for the first time theoretical and quantitative evidence of the beneficial impact of energy storage in limiting market power by generation companies. Quantitative analysis is supported by a bi-level optimization model of the imperfect electricity market setting, accounting for the time-coupling operational constraints of energy storage. This bi-level problem is solved after converting it to a Mathematical Program with Equilibrium Constraints (MPEC). Case studies are carried out on a test market with day-ahead horizon and hourly resolution.
  • Conference paper
    rodriguez-bernuz JM, Junyent Ferre A, 2016,

    Model predictive current reference calculation for single-phase VSCs

    , 2016 18TH EUROPEAN CONFERENCE ON POWER ELECTRONICS AND APPLICATIONS (EPE'16-ECCE EUROPE)
  • Journal article
    Dzafic I, Jabr RA, Huseinagic I, Pal BCet al., 2016,

    Multi-phase state estimation featuring industrial-grade distribution network models

    , IEEE Transactions on Smart Grid, Vol: 8, Pages: 609-618, ISSN: 1949-3053

    This paper proposes a novel implementation of a multi-phase distribution network state estimator which employs industrial-grade modeling of power components and measurements. Unlike the classical voltage-based and current-based state estimators, this paper presents the implementation details of a constrained weighted least squares state calculation method that includes standard three-phase state estimation capabilities in addition to practical modeling requirements from the industry; these requirements comprise multi-phase line configurations, unsymmetrical and incomplete transformer connections, power measurements on 4-connected loads, cumulative-type power measurements, line-to-line voltage magnitude measurements, and reversible line drop compensators. The enhanced modeling equips the estimator with capabilities that make it superior to a recently presented state-of-the-art distribution network load estimator that is currently used in real-life distribution management systems; comparative performance results demonstrate the advantage of the proposed estimator under practical measurement schemes.
  • Conference paper
    Moreira R, Moreno R, Strbac G, 2016,

    Synergies and conflicts among energy storage services

    , IEEE - Energycon 2016, Publisher: IEEE

    Energy storage can provide services to several sectors in electricity industry, including generation, transmission and distribution and support a cost-effective transition to a low carbon electricity industry. Sharing storage plant’s energy and power capacity for multiple services portfolios leads to conflicting or synergic interactions among services. In this context, the proposed methodology determines interactions among services for distributed energy storage plants, including energy arbitrage, peak demand shaving and various balancing services, and assesses the impact that such interactions have on storage plant remunerability in a multiple service business model framework for distributed energy storage. We demonstrate that services interact differently depending on markets and system operating conditions. We also find that correlation between energy market and local system conditions is important to determine whether energy arbitrage conflicts with further services.
  • Journal article
    Mokryani G, Majumdar ANKUR, Pal BC, 2016,

    A Probabilistic Method for the Operation of Three-Phase Unbalanced Active Distribution Networks

    , IET Renewable Power Generation, Vol: 10, Pages: 944-954, ISSN: 1752-1416

    This paper proposes a probabilistic multi-objective optimization method for the operation of three-phase distribution networks incorporating active network management (ANM) schemes including coordinated voltage control and adaptive power factor control. The proposed probabilistic method incorporates detailed modelling of three-phase distribution network components and considers different operational objectives. The method simultaneously minimizes the total energy losses of the lines from the point of view of distribution network operators (DNOs) and maximizes the energy generated by photovoltaic (PV) cells considering ANM schemes and network constraints. Uncertainties related to intermittent generation of PVs and load demands are modelled by probability density functions (PDFs). Monte Carlo simulation method is employed to use the generated PDFs. The problem is solved using ɛ-constraint approach and fuzzy satisfying method is used to select the best solution from the Pareto optimal set. The effectiveness of the proposed probabilistic method is demonstrated with IEEE 13- and 34- bus test feeders.
  • Conference paper
    Tindemans S, Strbac G, 2016,

    Nondisruptive decentralized control of thermal loads with second order thermal models

    , 2016 IEEE PES General Meeting, Publisher: IEEE

    Dynamic load controllers for thermostatically con- trolled loads should allow for accurate control of power consump- tion and should not disrupt the quality of service. This paper proposes an intuitive definition of nondisruptiveness for systems with second-order thermal models, based on a decomposition into fast and slow temperature modes. It enables the explicit control of the slow mode temperature using an embedded first order model; control of the fast mode is implicit. Temperature bounds are derived, and the slow mode controller is implemented using an accurate decentralised stochastic control strategy. Simulation results confirm its accuracy and nondisruptiveness.
  • Journal article
    Perez A, Moreno R, Moreira R, Orchard M, Strbac Get al., 2016,

    Effect of Battery Degradation on Multi-Service Portfolios of Energy Storage

    , IEEE Transactions on Sustainable Energy, Vol: 7, Pages: 1718-1729, ISSN: 1949-3029

    In an electricity market environment, energy storage plant owners are remunerated for the provision of services to multiple electricity sectors. Some of these services, however, may accelerate battery aging and degradation and hence this needs to be properly balanced against associated services remunerations. In this framework, we propose a combined economic-degradation model to quantify effects of operational policies (mainly focused on constraining State of Charge –SOC– to prescribed levels in order to reduce effects of aging) on gross revenue, multi-service portfolios, degradation and lifespan of distributed energy storage plants that can provide multiple services to energy and balancing market participants and Distribution Network Operators (DNO). Through various case studies based on the Great Britain (GB) system, we demonstrate that although operational policies focused on battery damage reduction will lead to a revenue loss in the shortterm, such loss can be more than compensated by long-term revenues due to a lengthier battery lifespan. We also demonstrate that operational policies to reduce battery degradation mainly affect services related to the energy (rather than balancing) market, which represents a smaller proportion of the overall revenue streams of a distributed storage plant. The model is also used to study effects of ambient temperature fluctuations.
  • Journal article
    Konstantelos I, Giannelos S, Strbac G, 2016,

    Strategic valuation of smart grid technology options in distribution networks

    , IEEE Transactions on Power Systems, Vol: 32, Pages: 1293-1303, ISSN: 0885-8950

    The increasing penetration of renewabledistributed generation (DG) sources in distribution networks canlead to violations of network constraints. Thus, significantnetwork reinforcements may be required to ensure that DGoutput is not constrained. However, the uncertainty around themagnitude, location and timing of future DG capacity rendersplanners unable to take fully-informed decisions and integrateDG at a minimum cost. In this paper we propose a novelstochastic planning model that considers investment inconventional assets as well as smart grid assets such as demandsideresponse, coordinated voltage control and soft open points(SOPs). The model also considers the possibility of active powergeneration curtailment of the DG units. A node-variableformulation has been adopted to relieve the substantialcomputational burden of the resulting mixed integer non-linearprogramming (MINLP) problem. A case study shows that smarttechnologies can possess significant strategic value due to theirinherent flexibility in dealing with different system evolutiontrajectories. This latent benefit remains undetected undertraditional deterministic planning approaches which may hinderthe transition to the smart grid.
  • Conference paper
    Zhang C, Jaimoukha IM, Segundo Sevilla, 2016,

    Fault-tolerant observer design with a tolerance measure for systems with sensor failure

    , 2016 American Control Conference, Publisher: IEEE, Pages: 7523-7528, ISSN: 0743-1619

    A fault-tolerant switching observer design methodology is proposed. The aim is to maintain a desired level of closed-loop performance under a range of sensor fault scenarios while the fault-free nominal performance is optimized. The range of considered fault scenarios is determined by a minimum number p of assumed working sensors. Thus the smaller p is, the more fault tolerant is the observer. This is then used to define a fault tolerance measure for observer design. Due to the combinatorial nature of the problem, a semidefinite relaxation procedure is proposed to deal with the large number of fault scenarios for systems that have many vulnerable sensors. The procedure results in a significant reduction in the number of constraints needed to solve the problem. Two numerical examples are presented to illustrate the effectiveness of the fault-tolerant observer design.
  • Conference paper
    Scarciotti G, Astolfi A, 2016,

    A note on the electrical equivalent of the moment theory

    , 2016 American Control Conference (ACC), Publisher: IEEE, Pages: 7462-7465

    In this short note the relation between the moments of a linear system and the phasors of an electric circuit is discussed. We show that the phasors are a special case of moments and we prove that the components of the solution of a Sylvester equation are the phasors of the currents of the system. We point out several directions in which the phasor theory can be extended using recent generalizations of the moment theory, which can benefit the analysis of circuits and power electronics.
  • Conference paper
    Padoan A, Astolfi A, 2016,

    Nonlinear system identification for continuous-time autonomous systems via functional equations methods

    , 2016 American Control Conference (ACC), Publisher: IEEE, Pages: 1814-1819

    The problem of identifying an autonomous nonlinear system, that is, the problem of finding a state-space description of a given sequence generated by sampling the output of an unknown autonomous nonlinear system, is studied. A theoretical framework which combines the use of the Schroder functional equation with realization-theoretic techniques is developed.
  • Journal article
    Bauso D, Mylvaganam T, Astolfi A, 2016,

    Crowd-averse robust mean-field games: approximation via state space extension

    , IEEE Transactions on Automatic Control, Vol: 61, Pages: 1882-1894, ISSN: 0018-9286

    We consider a population of dynamic agents, also referred to as players. The state of each player evolves according to a linear stochastic differential equation driven by a Brownian motion and under the influence of a control and an adversarial disturbance. Every player minimizes a cost functional which involves quadratic terms on state and control plus a cross-coupling mean-field term measuring the congestion resulting from the collective behavior, which motivates the term “crowd-averse.” Motivations for this model are analyzed and discussed in three main contexts: a stock market application, a production engineering example, and a dynamic demand management problem in power systems. For the problem in its abstract formulation, we illustrate the paradigm of robust mean-field games. Main contributions involve first the formulation of the problem as a robust mean-field game; second, the development of a new approximate solution approach based on the extension of the state space; third, a relaxation method to minimize the approximation error. Further results are provided for the scalar case, for which we establish performance bounds, and analyze stochastic stability of both the microscopic and the macroscopic dynamics.
  • Conference paper
    Chaffey GP, Judge PD, Merlin MMC, Clemow PR, Green TCet al., 2016,

    DC Fault Ride Through of Multilevel Converters

    , 2016 IEEE Energy Conversion Congress and Exposition (ECCE)

    Modular Multilevel Converters (MMC) can providesignificant advantages for power transmission applications, how-ever there are remaining challenges trading off DC fault response,losses and controllability. Alternative multilevel converter topolo-gies using combinations of full bridge and half bridge submodulesor series switches allow for competitive efficiency whilst retainingcontrol over the DC fault current. Several possible fault responsesare analysed to evaluate appropriate converter control actions.Experimental results from a 60 submodule 15 kW demonstratorare presented to validate the DC fault performance of the fullbridge MMC, the mixed stack MMC and the alternate armconverter. It is shown that each can control the current intoa low impedance DC fault, and there no requirement to blockthe semiconductor devices.
  • Journal article
    Zhang C, Lin D, Hui SY, 2016,

    Basic control principles of omnidirectional wireless power transfer

    , IEEE Transactions on Power Electronics, Vol: 31, Pages: 5215-5227, ISSN: 0885-8993

    This paper presents the basic control principles of omnidirectional wireless power transfer (WPT) based on the current amplitude control. The principles involve 1) an “omnidirectional” scanning process for detecting the power requirements in a 3-D space and 2) a “directional” power flow control for focusing the wireless power toward the targeted areas. Such principles apply to any WPT system comprising three orthogonal transmitter coils and multiple receivers with coil resonators. A current amplitude control method capable of generating a magnetic vector at a set of points evenly distributed on a spherical surface is explained. Based on the voltage and the current information in the transmitter circuit, the power involved in each vector over the spherical surface can be obtained. By scanning the vector over the spherical surface, the collective power flow requirements for the targeted loads can be determined. Based on the power requirements for the vectors over the spherical surface, a weighted time-sharing scheme is adopted to focus the wireless power toward the targeted areas. This method has been successfully applied to a hardware prototype. Both theoretical and experimental results are included to confirm these principles.

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