Permanent Magnet Linear Generator Research Articles

Research on Decoupling Duty Cycle Optimization Control Method of a Multiport Converter for Dual-Port Direct Drive Wave Power Generation System

Dual-port direct drive wave energy power generation systems (DP-DDWEPGS) have received widespread attention due to their smooth and zero-free output power, compared to single-port direct drive wave energy power generation systems (SP-DDWEPGS) which have the disadvantage of large out-put power fluctuations. To further enhance the performance of the DP-DDWEPGS, optimal power capture control is proposed to achieve maximum power point tracking. Meanwhile, a multiport converter is applied to the DP-DDWEPGS to solve the problem caused by an excessive number of switching devices in the overall system converter. The multiport converter fulfills all the functional requirements of the DP-DDWEPGS while reducing the number of switching devices. However, switch multiplexing of the multiport converter also introduces coupling relationships between each port and the wave force exhibits time-varying characteristics, necessitating advanced control methods with superior fast-tracking capability. Therefore, in this paper, a decoupling duty cycle optimization model predictive control for DP-DDWEPGS is proposed. Based on the characteristics of switching multiplexing, NSC finite control set model predictive control (FCS-MPC) decouples the current prediction and the cost function, reduces the number of candidate voltage vectors in each operation, and shortens the operation time by 70%. To address the issues of high ripple value and increased error due to decoupling in FCS-MPC, duty cycle optimization control is added, greatly reducing the fluctuations in electromagnetic force and power of the permanent magnet linear generator (PMLG). Based on the established simulation model, the feasibility and superiority of the multiport converter and decoupling duty cycle optimization model predictive current control method are verified.

Non‐linear coordinated control of LPMG‐based direct drive wave energy conversion system with supplementary energy storage system based on feedback linearization

AbstractThe linear permanent magnet generator (LPMG)‐based direct drive wave energy conversion system (DDWECS) works under perpetual fluctuations of ocean waves. Short‐term energy storage, such as electrochemical energy storage, is usually adopted in a supplementary energy storage system (SESS) to buffer power fluctuations. Since the investigated DDWECS consists of various non‐linear components such as insulated gate bipolar transistors (IGBTs)‐based power electronic converters, the unremitting changes of system working conditions caused by ocean wave effects will degrade the dynamic performance with conventional linear controllers which are implemented via local linearization around a single working condition. This paper proposes the multiple feedback linearization based non‐linear coordinated control (MFLNCC) scheme for coordinating non‐linear plants in DDWECS with SESS such as the machine‐side converter (MSC), the grid‐side converter (GSC) and DC/DC converter in SESS. The enhanced dynamic performance of the proposed MFLNCC in DDWECS with SESS is validated under different scenarios.

Optimal hydraulic PTO and linear permanent magnet generator for a floating two-buoy wave energy converter

A fully coupled fluid-structure-power take-off model is used to investigate the optimal energy capture of a floating two-buoy wave energy converter excited by regular waves and irregular waves. The system incorporates hydraulic power take-off and a linear permanent magnet generator. By considering the coupling relationship between the power take-off parameters for regular waves, a power take-off parameter interval is determined for the optimization model. Parametric optimization of the hydraulic power take-off and linear permanent magnet generator systems is proposed, based on response surface methodology in conjunction with central combination design for sensitivity analysis and optimal configuration of different parameters. The methodology efficiently predicts optimal electric efficiency while reducing the requirement for multiple boundary element simulations. It is found that a model with predicted optimal configuration of the hydraulic power take-off system can achieve 10 % more electrical efficiency than that with linear permanent magnet generator. Comparison between the energy capacities of the different systems indicates that a device with linear permanent magnet generator attains higher energy conversion efficiency within a wider power take-off bandwidth. This study provides guidance for the design and selection of efficient power take-off systems for floating two-buoy wave energy converters.

Research on Maximum Power Control of Direct-Drive Wave Power Generation Device Based on BP Neural Network PID Method

Ocean wave energy is a new type of clean energy. To improve the power generation and wave energy conversion efficiency of the direct-drive wave power generation system, by addressing the issue of large output errors and poor system stability commonly associated with the currently used PID (proportional, integral, and derivative) control methods, this paper proposes a maximum power control method based on BP (back propagation) neural network PID control. Combined with Kalman filtering, this method not only achieves maximum power tracking but also reduces output ripple and tracking error, thereby enhancing the system’s control quality. This study uses a permanent magnet linear generator as the power generation device, establishes a system dynamics model, and predicts the main frequency of irregular waves through the Fast Fourier Transform method. It designs a desired current tracking curve that meets the maximum power strategy. On this basis, a comparative analysis of the control accuracy and stability of three control methods is conducted. The simulation results show that the BP neural network PID control method improves power generation and exhibits better accuracy and stability.

Modeling dynamic power generation from ocean waves in the Kingdom of Tonga: A comprehensive analysis using integrated mechanical and electrical framework

Globally, ocean wave energy can significantly reduce carbon dioxide emissions from the electricity generation sector. Wave energy converters (WECs) could be installed in the Kingdom of Tonga, which is surrounded by ocean, where the average wave energy flux is greater than 7 kW/m. There is a lack of feasibility studies in this area due to the unavailability of measured data on wave parameters and properties; hence, the potential of WEC is yet to be discovered or exploited. This study proposes an integrated mechanical and electrical modeling framework to analyze the impact of wave characteristics on dynamic power generation in three main islands of Tonga, including ‘Eua, Tongatapu, and Niuafo’ou. The mechanical simulation involves using a 2D Fourier wave model to identify the important factors that affect the power potential of ocean waves, such as wave height and period. The wave model is linked to a comprehensive electrical simulation model developed in Matlab Simulink, which includes a permanent magnet linear synchronous generator (PMLSG), rectifier, buck converter, inverter, and load to estimate the electrical power potential per 1 m2 of ocean area. According to the findings, in ‘Eua, the maximum annual generation intensity output is 90.45 kWh/m2, whereas in Niuafo'ou, the minimum is 48.5 kWh/m2. Applying this to a region (12.57 m2) where a WEC has been deployed in Australia, the highest yearly electricity generation in ‘Eua ranges between 926.41 and 1136.96 kWh/y, but in Tongatapu and Niuafo'ou, it ranges between around 610 and 899 kWh/y.

Electromagnetic–Thermal Characteristics Analysis of a Tubular Permanent Magnet Linear Generator for Free-Piston Engines

Temperature rise of the tubular permanent magnet linear generator (TPMLG) might lead to insulation failure and demagnetization of permanent magnets, affecting the safe and stable operation of other equipment and the entire system. Herein, a bidirectional electromagnetic–thermal coupling method for analyzing the electromagnetic loss and thermal characteristics of a TPMLG considering the effect of increased temperature on the permanent magnet was proposed. To study the electromagnetic–thermal characteristics of the TPMLG under stable power generation, a two-dimensional electromagnetic field model and a three-dimensional temperature field model were established and coupled. The temperature field of the TPMLG was numerically calculated using computational fluid dynamics over finite volume method under natural air cooling and forced air cooling conditions. Effects of loss and air flow velocity on the steady temperature field were investigated. Results indicated that copper loss increased by 24.5% considering the influence of temperature rise. The windings’ top central position in the TPMLG was the spot with the highest temperature of 127.8 °C and there was a potential demagnetization risk for the permanent magnets. Some reference for future research of clarifying thermal characteristics and cooling design was provided.

Nonlinear Optimal Control for a PMLSG-VSC Wave Energy Conversion Unit

This article aims to treat the nonlinear control problem for the complex dynamics of a wave energy unit (WEC) that consists of a Permanent Magnet Linear Synchronous Generator (PMLSG) and a Voltage Source Converter (VSC). The article has developed a globally stable nonlinear optimal control method for this wave power generation unit. The new method avoids complicated state-space model transformations and minimizes the energy dispersion by the control loop. A novel nonlinear optimal control method is proposed for the dynamic model of a wave energy conversion system, which includes a Permanent Magnet Linear Synchronous Generator (PMLSG) serially connected with an AC/DC three-phase voltage source converter (VSC). The dynamic model of this renewable energy system is formulated and differential flatness properties are proven about it. To apply the proposed nonlinear optimal control, the state-space model of the PMLSG-VSC wave energy conversion unit undergoes an approximate linearization process at each sampling instance. The linearization procedure relies on a first-order Taylor-series expansion and involves the computation of the system’s Jacobian matrices. It takes place at each sampling interval around a temporary operating point, which is defined by the present value of the wave energy conversion unit’s state vector and by the last sampled value of the control inputs vector. An H-infinity feedback controller is designed for the linearized model of the wave energy conversion unit. To compute the feedback gains of this controller, an algebraic Riccati equation is repetitively solved at each time step of the control algorithm. The global stability properties of the control scheme are proven through Lyapunov analysis.

Performance Characteristic of Permanent Magnet Linear Generator for Energy Conversion with Renewable Fuels on Free-Piston Engines

Renewable fuels attract more attention owing to reduction of both air pollution and greenhouse gas emissions compared to fossil fuels. The free-piston engine generator is a new energy conversion with compact structure, multifuel combustion mode possibility, and less friction loss, and it can be applied to a variety of renewable fuels. This study investigated the effect of operating parameters on power generation and motion characteristics for free-piston engine generator. A test bench and a detailed and validated numerical model of the free-piston engine generator were presented. Results show that with the increase of the average velocity, the output power root mean square (RMS) and efficiency of the generator gradually increase. The output power RMS grows rapidly, whereas the generator efficiency gradually stabilizes. Under the same average velocity but different strokes and frequencies, the generator power and efficiency are the same. This result means that the multiple-point operating condition can achieve the same output power and generator efficiency goals. Moreover, the optimal operating conditions can be selected comprehensively, considering factors such as fuel properties, combustion efficiency, and performance. The influence of the generator on motion characteristics of the system under pure resistive load and high-frequency operation should be noted.

Development of a Low Speed Linear Generator for use in a Wave Energy Converter

One of the main advantages of ocean waves as resource for electrical energy production is its high energy density. Several methods have been proposed for the conversion of ocean wave mechanical energy into electrical energy. One such method consists in the use of a direct drive linear generator enclosed inside a floating element. The generator is driven by a mass-spring system, which oscillates due to the ocean wave’s movement. In this paper are presented the study, development, and dynamic simulation of a linear tubular synchronous low speed permanent magnet generator, for use in a wave energy conversion system. The generator was dimensioned using a finite element analysis tool. The wave energy converter dynamic model, mechanical and electrical, was developed to evaluate its response. To validate the generator’s dimensioning and dynamic model, its prototype was built. The dynamic model simulation results and the prototype’s experimental results are presented.

Modeling and Analysis of Wave Power Generation using Permanent Magnet Linear Synchronous Generator

This paper describes ocean wave power generation by using permanent magnet linear synchronous generator. The preliminary analysis has shown that a linear generator enables substantial simplification of the mechanical system with respect to a dc generator case [1]. The linear motor has been adopted, taking into consideration the features of the incident waves and the behavior of the floating buoy. The floating buoy is placed on the ocean surface and connected to the generator. The wave energy is carried out from the movement of a buoy. An electrical conversion system is needed between the generator and the grid. For an analysis of the power system, the modeling of the linear generator and converter system was proceeded. This paper aims at studying the electrical part of the wave energy converter and study what impact the electrical system will have on the generator.

Operating characteristics and design parameter optimization of permanent magnet linear generator applied to free-piston energy converter

A tubular permanent magnet linear generator (PMLG) with axial magnetized is proposed for the free-piston engine generator (FPEG). The structures and test rigs of the PMLG and FPEG prototypes are introduced. The working characteristics of the PMLG in FPEG system are analyzed under ignition conditions. A 2D finite element model of the PMLG is designed and verified based on initial design parameters and test results. The influences of key operating parameters on the output performance of PMLG are studied. On these basis, when considering the actual motion characteristics of the PMLG in FPEG system, the effects of different structural parameters on the power generation performance and efficiency (h) are investigated. Results show that when the working frequency of the FPEG is relatively small, the displacement profile resembles a sinusoidal curve. As the working frequency and stroke length increase, the power generation increases rapidly. As the air gap length and back iron shaft diameter decrease, and the stator slot number increases, the output voltage (U), current (I), power (Pout), and total loss power (Ploss) show an approximately linear increasing trend. As the pole arc coefficient and stator tooth width increase, the U, I, Pout, and Ploss first increase and then decrease. As the stator yoke thickness increases, the U, I, and Pout increase rapidly and then tend to stabilize. Besides, these structural parameters have little impact on power generation efficiency of this PMLG.

Modeling of permanent magnet linear generator and state estimation based on sliding mode observer: A wave energy system application

Modeling of permanent magnet linear generator and state estimation based on sliding mode observer: A wave energy system application

A preliminary study of a novel wave energy converter of a Scotch Yoke mechanism-based power take-off

This work proposes a novel concept to harvest power from ocean waves using a Scotch Yoke mechanism to transmit the heave motion of the buoy into the rotation of an off-the-shelf rotary generator. The novel transmission mechanism is proposed to tackle some of the main obstacles of ocean waves energy harvesters associated with the reliance on resonance and the high expenses related to the large device dimensions and permanent magnet linear generators. The Scotch Yoke mechanism converts the linear wave motion of a harmonic nature into rotary generator motion, coinciding with the nature of ocean waves. A mathematical model is constructed relating the hydrodynamics of the float to the non-linear resistive forces of the power take-off. Simulations are conducted for two different devices, including a typical large-scale-up wave energy converter device and a relatively small scaled-down wave energy converter device that can be placed close to the shore. The simulation results showcase that the large scale device can have a peak harvesting efficiency of up to 42%, while the small scale device can have a peak harvesting efficiency of up to 34%. This is of great importance as the small device can be used with an off-the-shelf rotary generator, and can be placed close to the shoreline further lowering the cost of manufacturing, installation, and maintenance allowing easier access to the device. Also, to validate the concept, a small scaled-down device has been fabricated, and dry-tested. The tested power take-off is proven to be able to harvest energy from linear harmonic oscillating buoy motions with a peak efficiency of 49% (not including the hydrodynamic efficiency).

Optimal Energy Management System Control of Permanent Magnet Direct Drive Linear Generator for Grid-Connected FC-Battery-Wave Energy Conversion

The Wave Energy Conversion System (WECS) control strategy is presented in this study to make sure the system operates at its best under fluctuating wave resource situations. The suggested system consists of a MOPSO based MPC approach, a point absorber WEC oscillating in heave, back-to-back power converter for grid connections, and a linear permanent magnet generator. Despite the benefits of model predictive control, problems including switching frequency variations, steady-state errors, high processing costs, and constrained prediction horizons continue to exist. The article presents a method that incorporates the switching control action into the cost function while maintaining the finite nature of a model predictive control to handle the switching frequency issue. In order to minimise switching frequency variations while also addressing other control goals, such as regulating the direct current linked voltage and controlling the flow of active and reactive power, the switching control weight factors are optimised. In order to increase power quality, a fuel cell-based short-term energy storage system is also included to direct current link between the back-to-back converters.

Spectral-Domain Modelling of Wave Energy Converters as an Efficient Tool for Adjustment of PTO Model Parameters

The power take-off (PTO) system is a core component in WECs as it plays a critical role in power production. In numerical models the PTO systems are commonly represented and simplified through a combination of linear stiffness and damping terms in the equations of motion. These parameters are influential to the dynamic response and thus affect the power performance of WECs. In the preliminary design and optimization of WECs, proper tuning of the PTO damping and stiffness could reflect better the potential of the concept. In practice, the PTO damping and stiffness are tuned to maximize the absorbed power by achieving the desired velocity amplitude or phase of the velocity with respect to the excitation force. However, recent literature has indicated that the selection of PTO parameters for maximum mechanical power absorption is not necessarily optimal for the maximum production of electrical power when the conversion efficiency of the electrical machine is included. To obtain these parameters which maximize the delivered electrical power, wave-to-wire models are widely used. Nevertheless, wave-to-wire models are predominately established by using time-domain models which can be associated with large computational efforts from the perspective of early-stage design and concept evaluation. To tackle this challenge, a spectral-domain-based wave-to-wire model is proposed to cover both hydrodynamic and electrical responses. In this paper, a spherical heaving point absorber integrated with a linear permanent-magnet generator is used as reference. The relevant nonlinear effects are incorporated by statistical linearization using spectral-domain modelling. In particular, the nonlinear effects considered in this work include the viscous drag force, the electrical current saturation and the partial overlap between the translator and stator components of the linear generator. The model results are then verified against a nonlinear time-domain-based wave-to-wire model. Subsequently, the proposed model is applied to identify the PTO parameters for maximizing the electrical power in various wave states. The computational efficiency and accuracy of the proposed spectral-domain model are compared with the time-domain model, with regard to the identification of the proper PTO damping and stiffness. Based on the results, the advantage of using the spectral-domain-based wave-to-wire modeling in PTO tuning is demonstrated.

Sectional Modular Technology for Reducing Detent Force of Linear Unit in Linear-rotary Flux-switching Permanent-magnet Generator for Wind-wave Combined Energy Conversion

A linear-rotary flux-switching permanent magnet (FSPM) generator (LRFSPMG) is a potential candidate for a wind-wave combined energy conversion (WWCEC) system. The linear unit of the LRFSPMG is a tubular FSPM linear generator (TFSPMLG), which like other permanent magnet linear generators, has an inherent detent force problem. To alleviate this problem, a sectional modular technology scheme is investigated to reduce the detent force of the TFSPMLG. Firstly, the structure is briefly introduced and the detent force analyzed. Secondly, the sectional modular TFSPMLGs are presented and their feasibility verified with respect to the stator of the TFSPMLG being split into two and three sections, forming Modulars I and II, respectively. After that, the detent force suppression principle, and the effects that the sectional modular structures exert on the detent force are analyzed. According to the analysis results, two methods are presented to suppress the detent force: one is to suppress the magnetic coupling effect; the other is to reduce the remaining harmonics. Finally, the three TFSPMLGs, including the initial TFSPMLG, Modular I, and Modular II, are comparatively analyzed by finite-element analysis (FEA). The results show that both the detent forces are greatly reduced without sacrificing the back electromotive force (EMF) and average electromagnetic force, thereby proving the effectiveness of the TFSPMLG with a sectional modular structure.

An Innovative H-Type Flux Switching Permanent Magnet Linear Generator for Thrust Force Enhancement

In this paper, two H-type flux switching permanent magnet linear generators with outer-translator and inner-translator configurations are discussed and compared to a more conventional flux switching topology. The stators consist of H-Type modules housing circumferential coils and are surrounded by two annular permanent magnets. In conventional flux switching machines, the windings are orientated perpendicular to the direction of motion and the conductors twist around the magnets. In H-type topologies, the orientation of the windings is in the same plain as the magnets and parallel to the direction of motion, resulting in an increase in flux linkage. The proposed topologies are designed for a low operating speed and a large magnetic gap, as found in wave energy converters. All topologies are optimized using the Taguchi optimization approach with the goals of reducing force ripple and increasing the average thrust force and efficiency. The 2D finite element method (FEM) is used in the optimization stage to calculate the optimized parameters of the presented generators, after which the optimized structures are simulated using 3D FEM, and the results are extracted. The results of the optimization show that the H-type topologies deliver a 20% higher shear stress whilst offering an easier to assemble structure.

Study of a three-dimensional model simulation of a speed amplified flux switching linear generator for wave energy conversion and its design optimization in the ocean environment

This paper introduces a novel design of a speed amplified flux switching linear generator for the power take-off unit of an ocean wave energy converter. The design incorporates several innovative features, including semi-closed stator iron cores, four coil phases shifting, and a fixed pulley wheel mechanism. These enhancements aim to increase the generator's output power and reduce its cogging force. The fixed pulley wheel mechanism effectively doubles the relative speed of the translator with respect to the stators.The scientific originality of this work lies in the development of a comprehensive design methodology for wave energy converters, specifically focused on optimizing the power take-off design under different ocean environments. The proposed approach combines analytical techniques, hydrodynamic boundary element analysis, 3D electromagnetic finite element modeling, and machine learning methods. By synergistically employing these methods, the authors achieve an efficient and effective power take-off design.To facilitate the optimization process, a three-dimensional electromagnetic finite element model of the flux switching linear generator is developed. This model is refined and optimized to maximize the output power while minimizing the cogging force, using a regular sinusoidal wave motion as the excitation input.The experimental results confirm that the proposed flux switching linear generator outperforms conventional permanent magnet linear generators in terms of power output performance. Furthermore, the model is used to simulate and predict the generator's power output under various ocean environments, considering the hydrodynamics of the wave energy converter.In summary, this manuscript presents a significant contribution to the field of flux switching electromagnetic linear generator based wave energy harvesters. The novel generator design and the comprehensive design methodology offer valuable insights and advancements in the development of efficient wave energy converters.

Optimization design of Tubular Permanent Magnet Linear Generator based on entropy model for wave energy conversion

—The effective use of wave energy which has huge reserves is one of the ways to solve the climate problem and energy crisis. In this paper, a Tubular Permanent Magnet Linear Generator (TPMLG) is optimized by the combination of comprehensive sensitive parameters method and particle swarm optimization based on entropy model (EPSO). By introducing the information entropy model, the aggregation characteristics in the process of particle swarm search are accurately analyzed, which can effectively reduce the invalid iteration of particle swarm. Firstly, the main design parameters of TPMLG are designed using the basic initial principle of permanent magnet linear machines. Then, the two-dimensional parametric finite element analysis model of the TPMLG is established, and a comprehensive sensitivity index Sc is defined to calculate the sensitivity indices according to power density and thrust fluctuation. The strong sensitivity parameters are optimized Particle Swarm Optimization based on entropy model, and the Non-sensitivity parameters maintain the initial design values. Finally, an experimental prototype TPMLG was manufactured according to the optimized results. The speed of TPMLG was simulated by the universal testing machine MTS100kN, the experimental results show that the designed TPMLG can be effectively applied to the direct drive power take-off system.

A spectral-domain wave-to-wire model of wave energy converters

Wave-to-Wire models play an important role in the development of wave energy converters. They could provide insight into the complete operating process of wave energy converters, from the power absorption stage to the power conversion stage. In order to cover a set of relevant nonlinear effects, wave-to-wire models are predominately established in the time domain. However, the low computational efficiency of time-domain modeling is hindering the extensive application of wave-to-wire models, especially in early-stage design and optimization where a large number of iterations are required. To address this issue, a spectral-domain wave-to-wire model is proposed, and the nonlinear effects are incorporated by stochastic linearization. This model can significantly reduce the computational load and maintain good accuracy. The reference concept studied in this paper is defined as a heaving point absorber coupled with a linear permanent-magnet generator. Four representative nonlinear effects involved in both the hydrodynamic stage and the electrical stage of the concept are considered. The proposed model is verified against a corresponding nonlinear time-domain wave-to-wire model, and a good agreement is observed. The relative error of the proposed spectral-domain wave-to-wire model is around 2 % in typical operational regions and is still within 7 % for wave states with large significant wave heights, regarding the estimate of the power conversion efficiency. Meanwhile, the computational load of the spectral-domain wave-to-wire model is reduced by 2 to 3 orders of magnitudes compared with the conventional time-domain approach. Finally, a case study of tuning the PTO damping to maximize power production is conducted to demonstrate the performance of the proposed spectral-domain wave-to-wire model.