Showing papers on "AC power published in 2016"

Comparison of Dynamic Characteristics Between Virtual Synchronous Generator and Droop Control in Inverter-Based Distributed Generators

Abstract: In recent researches on inverter-based distributed generators, disadvantages of traditional grid-connected current control, such as no grid-forming ability and lack of inertia, have been pointed out. As a result, novel control methods like droop control and virtual synchronous generator (VSG) have been proposed. In both methods, droop characteristics are used to control active and reactive power, and the only difference between them is that VSG has virtual inertia with the emulation of swing equation, whereas droop control has no inertia. In this paper, dynamic characteristics of both control methods are studied, in both stand-alone mode and synchronous-generator-connected mode, to understand the differences caused by swing equation. Small-signal models are built to compare transient responses of frequency during a small loading transition, and state-space models are built to analyze oscillation of output active power. Effects of delays in both controls are also studied, and an inertial droop control method is proposed based on the comparison. The results are verified by simulations and experiments. It is suggested that VSG control and proposed inertial droop control inherits the advantages of droop control, and in addition, provides inertia support for the system.

Review of Power Sharing Control Strategies for Islanding Operation of AC Microgrids

Abstract: Microgrid is a new concept for future energy distribution system that enables renewable energy integration. It generally consists of multiple distributed generators that are usually interfaced to the grid through power inverters. For the islanding operation of ac microgrids, two important tasks are to share the load demand among multiple parallel connected inverters proportionately, and maintain the voltage and frequency stabilities. This paper reviews and categorizes various approaches of power sharing control principles. Simultaneously, the control schemes are graphically illustrated. Moreover, various control approaches are compared in terms of their respective advantages and disadvantages. Finally, this paper presents the future trends.

Integration of electric vehicles in smart grid: A review on vehicle to grid technologies and optimization techniques

Abstract: Energy crisis and environmental issues have encouraged the adoption of electric vehicle as an alternative transportation option to the conventional internal combustion engine vehicle. Recently, the development of smart grid concept in power grid has advanced the role of electric vehicles in the form of vehicle to grid technology. Vehicle to grid technology allows bidirectional energy exchange between electric vehicles and the power grid, which offers numerous services to the power grid, such as power grid regulation, spinning reserve, peak load shaving, load leveling and reactive power compensation. As the implementation of vehicle to grid technology is a complicated unit commitment problem with different conflicting objectives and constraints, optimization techniques are usually utilized. This paper reviews the framework, benefits and challenges of vehicle to grid technology. This paper also summarizes the main optimization techniques to achieve different vehicle to grid objectives while satisfying multiple constraints.

Small-Signal Modeling and Parameters Design for Virtual Synchronous Generators

Abstract: The concept of the virtual synchronous generator (VSG) is emerging as an attractive solution for controlling the grid-connected inverter when the renewable energy has a high penetration level into the grid. This paper focuses on the small-signal modeling and parameters design of the power loop of the VSG, and points out that the bandwidth of the power loop should be far less than twice the line frequency for the purpose of avoiding the VSG output voltage to be severely distorted. Consequently, the line-frequency-averaged small-signal model of the VSG is derived for system analysis and parameters design. Based on the model, the decoupling conditions between the active power loops (APLs) and the reactive power loops (RPLs) of the VSG are given. Finally, a step-by-step parameters design method is proposed to facilitate the design of the control parameters of the VSG. A 10-kVA prototype is built and tested in the laboratory, and the experimental results are given to verify the effectiveness of the theoretical analysis and the proposed parameters design method.

On the Existence and Linear Approximation of the Power Flow Solution in Power Distribution Networks

Abstract: We consider the problem of deriving an explicit approximate solution of the nonlinear power equations that describe a balanced power distribution network. We give sufficient conditions for the existence of a practical solution to the power flow equations, and we propose an approximation that is linear in the active and reactive power demands of the PQ buses. For this approximation, which is valid for generic power line impedances and grid topology, we derive a bound on the approximation error as a function of the grid parameters. We illustrate the quality of the approximation via simulations, we show how it can also model the presence of voltage controlled (PV) buses, and we discuss how it generalizes the DC power flow model to lossy networks.

Review of Active Power Decoupling Topologies in Single-Phase Systems

Abstract: Active power decoupling methods are developed to deal with the inherent ripple power at twice the grid frequency in single-phase systems generally by adding active switches and energy storage units. They have obtained a wide range of applications, such as photovoltaic (PV) systems, light-emitting diodes (LEDs) drivers, fuel cell (FC) power systems, and electric vehicle (EV) battery chargers, etc. This paper provides a comprehensive review of active power decoupling circuit topologies. They are categorized into two groups in terms of the structure characteristics: independent and dependent decoupling circuit topologies. The former operates independently with the original converter, and the latter, however, shares the power semiconductor devices with the original converter partially and even completely. The development laws for the active power decoupling topologies are revealed from the view of “duality principle,” “switches sharing,” and “differential connection.” In addition, the exceptions and special cases are also briefly introduced. This paper is targeted to help researchers, engineers, and designers to construct some new decoupling circuit topologies and properly select existing ones according to the specific application.

Voltage Stability and Reactive Power Sharing in Inverter-Based Microgrids With Consensus-Based Distributed Voltage Control

Abstract: We propose a consensus-based distributed voltage control (DVC) that solves the problem of reactive power sharing in autonomous inverter-based microgrids with dominantly inductive power lines and arbitrary electrical topology. Opposed to other control strategies available thus far, the control presented here does guarantee a desired reactive power distribution in steady state while only requiring distributed communication among inverters, i.e., no central computing nor communication unit is needed. For inductive impedance loads and under the assumption of small phase angle differences between the output voltages of the inverters, we prove that the choice of the control parameters uniquely determines the corresponding equilibrium point of the closed-loop voltage and reactive power dynamics. In addition, for the case of uniform time constants of the power measurement filters, a necessary and sufficient condition for local exponential stability of that equilibrium point is given. The compatibility of the DVC with the usual frequency droop control for inverters is shown and the performance of the proposed DVC is compared with the usual voltage droop control via simulation of a microgrid based on the Conseil International des Grands Reseaux Electriques (CIGRE) benchmark medium voltage distribution network.

Optimal Storage Planning in Active Distribution Network Considering Uncertainty of Wind Power Distributed Generation

Abstract: The penetration of renewable distributed generation (DG) sources has been increased in active distribution networks due to their unique advantages. However, non-dispatchable DGs such as wind turbines raise the risk of distribution networks. Such a problem could be eliminated using the proper application of energy storage units. In this paper, optimal planning of batteries in the distribution grid is presented. The optimal planning determines the location, capacity and power rating of batteries while minimizing the cost objective function subject to technical constraints. The optimal long-term planning is based on the short-term optimal power flow considering the uncertainties. The point estimate method (PEM) is employed for probabilistic optimal power flow. The batteries are scheduled optimally for several purposes to maximize the benefits. A hybrid Tabu search/particle swarm optimization (TS/PSO) algorithm is used to solve the problem. The numerical studies on a 21-node distribution system show the advantages of the proposed methodology. The proposed approach can also be applied to the realistic sized networks when some sensitive nodes are considered as candidate locations for installing the storage units.

A Modified Sequence-Domain Impedance Definition and Its Equivalence to the dq-Domain Impedance Definition for the Stability Analysis of AC Power Electronic Systems

Abstract: Representation of ac power systems by frequency-dependent impedance equivalents is an emerging technique in the dynamic analysis of power systems including power electronic converters. The technique has been applied for decades in dc-power systems, and it was recently adopted to map the impedances in ac systems. Most of the work on ac systems can be categorized into two approaches. One is the analysis of the system in the dq domain, whereas the other applies harmonic linearization in the phase domain through symmetric components. Impedance models based on analytical calculations, numerical simulation, and experimental studies have been previously developed and verified in both domains independently. The authors of previous studies discuss the advantages and disadvantages of each domain separately, but neither a rigorous comparison nor an attempt to bridge them has been conducted. This paper attempts to close this gap by deriving the mathematical formulation that shows the equivalence between the dq -domain and the sequence-domain impedances. A modified form of the sequence-domain impedance matrix is proposed, and with this definition the stability estimates obtained with the generalized Nyquist criterion become equivalent in both domains. The second contribution of this paper is the definition of a mirror frequency decoupled (MFD) system. The analysis of MFD systems is less complex than that of non-MFD systems because the positive and negative sequences are decoupled. This paper shows that if a system is incorrectly assumed to be MFD, this will lead to an erroneous or ambiguous estimation of the equivalent impedance.

Optimal Distributed Generation Allocation in Distribution Systems for Loss Minimization

Abstract: An efficient analytical (EA) method is proposed for optimally installing multiple distributed generation (DG) technologies to minimize power loss in distribution systems. Different DG types are considered, and their power factors are optimally calculated. The proposed EA method is also applied to the problem of allocating an optimal mix of different DG types with various generation capabilities. Furthermore, the EA method is integrated with the optimal power flow (OPF) algorithm to develop a new method, EA-OPF which effectively addresses overall system constraints. The proposed methods are tested using 33-bus and 69-bus distribution test systems. The calculated results are validated using the simulation results of the exact optimal solution obtained by an exhaustive OPF algorithm for both distribution test systems. The results show that the performances of the proposed methods are superior to existing methods in terms of computational speed and accuracy.

Fast Local Voltage Control Under Limited Reactive Power: Optimality and Stability Analysis

Abstract: High penetration of distributed energy resources presents several challenges and opportunities for voltage regulation in power distribution systems. A local reactive power (VAR) control framework will be developed that can fast respond to voltage mismatch and address the robustness issues of (de-)centralized approaches against communication delays and noises. Using local bus voltage measurements, the proposed gradient-projection based schemes explicitly account for the VAR limit of every bus, and are proven convergent to a surrogate centralized problem with proper parameter choices. This optimality result quantifies the capability of local VAR control without requiring any real-time communications. The proposed framework and analysis generalize earlier results on the droop VAR control design, which may suffer from under-utilization of VAR resources in order to ensure stability. Numerical tests have demonstrated the validity of our analytical results and the effectiveness of proposed approaches implemented on realistic three-phase systems.

Networked Microgrids for Self-Healing Power Systems

Abstract: This paper proposes a transformative architecture for the normal operation and self-healing of networked microgrids (MGs). MGs can support and interchange electricity with each other in the proposed infrastructure. The networked MGs are connected by a physical common bus and a designed two-layer cyber communication network. The lower layer is within each MG where the energy management system (EMS) schedules the MG operation; the upper layer links a number of EMSs for global optimization and communication. In the normal operation mode, the objective is to schedule dispatchable distributed generators (DGs), energy storage systems (ESs), and controllable loads to minimize the operation costs and maximize the supply adequacy of each MG. When a generation deficiency or fault happens in an MG, the model switches to the self-healing mode and the local generation capacities of other MGs can be used to support the on-emergency portion of the system. A consensus algorithm is used to distribute portions of the desired power support to each individual MG in a decentralized way. The allocated portion corresponds to each MG’s local power exchange target, which is used by its EMS to perform the optimal schedule. The resultant aggregated power output of networked MGs will be used to provide the requested power support. Test cases demonstrate the effectiveness of the proposed methodology.

A Two-Stage Robust Reactive Power Optimization Considering Uncertain Wind Power Integration in Active Distribution Networks

Abstract: Traditional reactive power optimization aims to minimize the total transmission losses by control reactive power compensators and transformer tap ratios, while guaranteeing the physical and operating constraints, such as voltage magnitudes and branch currents to be within their reasonable range. However, large amounts of renewable resources coming into power systems bring about great challenges to traditional planning and operation due to the stochastic nature. In most of the practical cases from China, the wind farms are centrally integrated into active distribution networks. By the use of conic relaxation based branch flow formulation, the reactive optimization problem in active distribution networks can be formulated as a mixed integer convex programming model that can be tractably dealt with. Furthermore, to address the uncertainties of wind power output, a two-stage robust optimization model is proposed to coordinate the discrete and continuous reactive power compensators and find a robust optimal solution that can hedge against any possible realization within the uncertain wind power output. Moreover, the second order cone programming-based column-and-constraint generation algorithm is employed to solve the proposed two-stage robust reactive power optimization model. Numerical results on 33-, 69- and 123-bus systems and comparison with the deterministic approach demonstrate the effectiveness of the proposed method.

Droop-Based Distributed Cooperative Control for Microgrids With Time-Varying Delays

Abstract: This paper develops a droop-based distributed cooperative control scheme for microgrids under a switching communication network with non-uniform time-varying delays. We first design a pinning-based frequency/voltage controller containing a distributed voltage observer and then design a consensus-based active/reactive power controller, which are employed into the secondary control stage to generate the nominal set points used in the primary control stage for different distributed generators (DGs). By this approach, the frequencies and the weighted average value of all DGs’ voltages can be pinned to the desired values while maintaining the precise active and reactive power sharing. With the proposed scheme, each DG only needs to communicate with its neighbors intermittently, even if their communication networks are local and time-varying, and their variant delays may be non-uniform. Sufficient conditions on the requirements for the network connectivity and the delay upper bound that guarantee the stability and reliability of the microgrid are presented. The effectiveness of the proposed control scheme is verified by the simulation of a microgrid test system.

Coordinated Control of Distributed Energy-Storage Systems for Voltage Regulation in Distribution Networks

Abstract: In this paper, distributed energy-storage systems (ESSs) are proposed to solve the voltage rise/drop issues in low-voltage (LV) distribution networks with a high penetration of rooftop photovoltaics (PVs). During the peak PV generation period, the voltages are mitigated by charging the ESSs, and the stored energy is discharged for voltage support during the peak load period. The impact of storage devices integrated with the PV source on feeder voltages is investigated in detail. A coordinated control method, which includes distributed and localized controls, is proposed for distributed ESSs. The distributed control using the consensus algorithm regulates the feeder voltages within the required limits, while the localized control regulates the state of charge (SoC) of each ESS within the desired SoC range. The entire control structure ensures voltage regulation while effectively utilizing storage capacity under various operation conditions. The proposed control method is evaluated in LV distribution networks, and the simulation results validate the effectiveness of this method.

Active Management of Low-Voltage Networks for Mitigating Overvoltages Due to Photovoltaic Units

Abstract: In this paper, the overvoltage problems that might arise from the integration of photovoltaic (PV) panels into low-voltage (LV) distribution networks is addressed. A distributed scheme is proposed that adjusts the reactive and active power output of inverters to prevent or alleviate such problems. The proposed scheme is model-free and makes use of limited communication between the controllers in the form of a distress signal only during emergency conditions. It prioritizes the use of reactive power, while active power curtailment is performed only as a last resort. The behavior of the scheme is studied using dynamic simulations on a single LV feeder and on a larger network composed of 14 LV feeders. Its performance is compared with a centralized scheme based on the solution of an optimal power flow (OPF) problem, whose objective function is to minimize the active power curtailment. The proposed scheme successfully mitigates overvoltage situations due to high PV penetration and performs almost as well as the OPF-based solution with significantly less information and communication requirements.

A Fully Distributed Reactive Power Optimization and Control Method for Active Distribution Networks

Abstract: This paper presents a fully distributed reactive power optimization algorithm that can obtain the global optimum solution of nonconvex problems for distribution networks (DNs) without requiring a central coordinator. Second-order conic relaxation is used to achieve exact convexification. A fully distributed second-order cone programming solver (D-SOCP) is formulated corresponding to the given division of areas based on the alternating direction method of multipliers (ADMM) algorithm, which is greatly simplified by exploiting the structure of active DNs. The problem is solved for each area with very little interchange of boundary information between neighboring areas. D-SOCP is extended by using a varying penalty parameter to improve convergence. A proof of its convergence is also given. The effectiveness of the method is demonstrated via numerical simulations using the IEEE 69-bus, 123-bus DNs, and a real 1066-bus distribution system.

Comparison Study on SS and Double-Sided LCC Compensation Topologies for EV/PHEV Wireless Chargers

Abstract: This paper compares the characteristics of the series–series and double-sided Inductor-Capacitor-Capacitor (LCC) compensation topologies for electric vehicle (EV) wireless chargers. Both the well-tuned and mistuned topologies for the two compensation methods are analyzed in detail. The mistuning considered here is mainly caused by the variations of the relative position between the primary and secondary sides. The output power displacements caused by mistuning are compared for both compensation topologies, as well as the impacts of the load variations on the performances of the mistuned topologies. The voltage and current stresses on components are also studied. The comparative result shows that the double-sided LCC compensation topology is less sensitive to mistuning. A double-sided LCC-compensated EV wireless charger system with up to 7.7-kW output power is built to verify the analysis results. A peak efficiency of 96% from dc power source to battery load is achieved.

Microgrid Scheduling With Uncertainty: The Quest for Resilience

Abstract: In recent years, natural disasters around the world have underscored the need for operative solutions that can improve the power grid resilience in response to low-probability high-impact incidents. The advent of microgrids (MGs) in modern power systems has introduced promising measures that can fulfil the power network resiliency requirements. This paper presents a two-stage stochastic programing approach to the optimal scheduling of a resilient MG. The impact of natural disasters on the optimal operation of MGs is modeled using a stochastic programming process. Other prevailing uncertainties associated with wind energy, electric vehicles, and real-time market prices are also taken into account. The proposed hourly scheme attempts to mitigate damaging impacts of electricity interruptions by effectively exploiting the MG capabilities. Incorporating AC network constraints in the proposed model offers a better solution to the security-constrained operation of MGs. The proposed model is linearized which offers robustness, simplicity, and computational efficiency in optimizing the MG operation. The effectiveness of proposed approach is illustrated using a large-scale MG test bed with a realistic set of data.

Droop-Free Distributed Control for AC Microgrids

Abstract: A cooperative distributed secondary/primary control paradigm for AC microgrids is proposed. This solution replaces the centralized secondary control and the primary-level droop mechanism of each inverter with three separate regulators: voltage, reactive power, and active power regulators. A sparse communication network is spanned across the microgrid to facilitate limited data exchange among inverter controllers. Each controller processes its local and neighbors' information to update its voltage magnitude and frequency (or, equivalently, phase angle) set points. A voltage estimator finds the average voltage across the microgrid, which is then compared to the rated voltage to produce the first-voltage correction term. The reactive power regulator at each inverter compares its normalized reactive power with those of its neighbors, and the difference is fed to a subsequent PI controller that generates the second-voltage correction term. The controller adds the voltage correction terms to the microgrid rated voltage (provided by the tertiary control) to generate the local voltage magnitude set point. The voltage regulators collectively adjust the average voltage of the microgrid at the rated voltage. The voltage regulators allow different set points for different bus voltages and, thus, account for the line impedance effects. Moreover, the reactive power regulators adjust the voltage to achieve proportional reactive load sharing. The third module, the active power regulator, compares the local normalized active power of each inverter with its neighbors' and uses the difference to update the frequency and, accordingly, the phase angle of that inverter. The global dynamic model of the microgrid, including distribution grid, regulator modules, and the communication network, is derived, and controller design guidelines are provided. Steady-state performance analysis shows that the proposed controller can accurately handle the global voltage regulation and proportional load sharing. An AC microgrid prototype is set up, where the controller performance, plug-and-play capability, and resiliency to the failure in the communication links are successfully verified.

Optimal Reactive Power Dispatch for Voltage Regulation in Unbalanced Distribution Systems

Abstract: In this paper, we propose a method to optimally set the reactive power contributions of distributed energy resources (DERs) present in distribution systems with the goal of regulating bus voltages. For the case when the network is balanced, we use the branch power flow modeling approach for radial power systems to formulate an optimal power flow (OPF) problem. Then, we leverage properties of the system operating conditions to relax certain nonlinear terms of this OPF, which results in a convex quadratic program (QP). To efficiently solve this QP, we propose a distributed algorithm based on the Alternating Direction Method of Multipliers (ADMM). Furthermore, we include the unbalanced three-phase formulation to extend the ideas introduced for the balanced network case. We present several case studies to demonstrate the method in unbalanced three-phase distribution systems.

Virtual Synchronous Machines: A unified interface for grid integration

Abstract: Power systems are going through a paradigm change from centralized generation to distributed generation and further on to smart grids. More and more renewable-energy sources, electric vehicles, energy storage systems, and so forth are being connected to power systems through power electronic converters. Moreover, the majority of loads are expected to connect to the grid through power electronic converters as well. This article shows that these converters, either on the supply side or on the load side, can all be controlled to behave like virtual synchronous machines (VSMs) and possess the dynamics of synchronous machines, providing a unified interface for smart grid integration. Synchroconverter technology and its developments are the focus of this article because the mathematical model of synchronous machines is embedded in the controller of synchronverters to provide close imitation.

Operation Modes for the Electric Vehicle in Smart Grids and Smart Homes: Present and Proposed Modes

Abstract: This paper presents the main operation modes for an electric vehicle (EV) battery charger framed in smart grids and smart homes, i.e., present-day and new operation modes that can represent an asset toward EV adoption are discussed and proposed, respectively. Apart from the well-known grid-to-vehicle (G2V) and vehicle-to-grid (V2G) operation modes, this paper proposes two new operation modes: home-to-vehicle (H2V), where the EV battery charger current is controlled according to the current consumption of the electrical appliances of the home (this operation mode is combined with G2V and V2G), and vehicle-for-grid (V4G), where the EV battery charger is used for compensating current harmonics or reactive power, simultaneously with the G2V and V2G operation modes. The vehicle-to-home (V2H) operation mode, where the EV can operate as a power source in isolated systems or as offline uninterruptible power supply to feed priority appliances of the home during power outages of the electrical grid, is presented in this paper and framed with the other operation modes. These five operation modes were validated through experimental results using a developed 3.6-kW bidirectional EV battery charger prototype, which was specially designed for these operation modes. This paper describes the developed EV battery charger prototype, detailing the power theory and the voltage and current control strategies used in the control system. This paper also presents experimental results for the various operation modes, both in steady state and during transients.

A Novel Approach to Solve Power Flow for Islanded Microgrids Using Modified Newton Raphson With Droop Control of DG

Abstract: The study of power flow analysis for microgrids has gained importance where several methods have been proposed to solve these problems. However, these schemes are complicated and not easy to implement due to the absence of a slack bus as well as the dependence of the power on frequency as a result of the droop characteristics. This paper proposes simple and effective modifications to the conventional method (Newton Raphson) to compute the power flow for microgrids. The presented method provides a simple, easy to implement, and accurate approach to solve the power flow equations for microgrids. The proposed method is applied to two test systems: a 6-bus system and a 38-bus system. The results are compared against simulation results from PSCAD/EMTDC which validate the effectiveness of the developed method. The proposed technique can be easily integrated in current commercially available power system software and can be applied for power system studies.

A Bidirectional Nonisolated Multi-Input DC–DC Converter for Hybrid Energy Storage Systems in Electric Vehicles

Abstract: To process the power in hybrid energy systems using a reduced part count, researchers have proposed several multiinput dc–dc power converter topologies to transfer power from different input voltage sources to the output. This paper proposes a novel bidirectional nonisolated multi-input converter (MIC) topology for hybrid systems to be used in electric vehicles composed of energy storage systems (ESSs) with different electrical characteristics. The proposed converter has the ability to control the power of ESSs by allowing active power sharing. The voltage levels of utilized ESSs can be higher or lower than the output voltage. The inductors of the converter are connected to a single switch; therefore, the converter requires only one extra active switch for each input, unlike its counterparts, hence resulting in reduced element count. The proposed MIC topology is compared with its counterparts concerning various parameters. It is analyzed in detail, and then, this analysis is validated by simulation and through a 1-kW prototype based on a battery/ultracapacitor hybrid ESS.

Voltage collapse in complex power grids

Abstract: A large-scale power grid's ability to transfer energy from producers to consumers is constrained by both the network structure and the nonlinear physics of power flow. Violations of these constraints have been observed to result in voltage collapse blackouts, where nodal voltages slowly decline before precipitously falling. However, methods to test for voltage collapse are dominantly simulation-based, offering little theoretical insight into how grid structure influences stability margins. For a simplified power flow model, here we derive a closed-form condition under which a power network is safe from voltage collapse. The condition combines the complex structure of the network with the reactive power demands of loads to produce a node-by-node measure of grid stress, a prediction of the largest nodal voltage deviation, and an estimate of the distance to collapse. We extensively test our predictions on large-scale systems, highlighting how our condition can be leveraged to increase grid stability margins.

Wireless Power Transfer by Electric Field Resonance and Its Application in Dynamic Charging

Abstract: In this paper, the electric field resonance (EFR) method, similar to the four-coil configuration of the magnetic field resonance wireless power transfer, is proposed for the capacitive coupling power transfer. The characteristics of the proposed method are derived and analyzed. With the EFR method, not only unity power factor for the power source is achieved, but also high power factor and low reactive power for the capacitive coupling stage are achieved. Effective power transfer is realized by the EFR method. Based on the proposed method, a dynamic charging concept for railway vehicles is then proposed. A prototype powering system is designed and built to prove the validity of the proposed method. Analytical, simulation, and experimental results are given and compared. A 23-cm model vehicle is put on a 150-cm track. It is shown that about 700-W power is transferred through a 24-pF coupling capacitor. The proposed method reaches 91% dc–dc overall efficiency at switching frequency 2 MHz.