Power Take-off System Research Articles

On the value of Fano resonance in wave energy converters

The article evaluates the potential of the Fano resonance operational principle in wave energy converters (WECs), using a 2-body loosely moored self-referenced WEC as an illustrative example. By leveraging Fano resonance, the point absorber buoy can remain relatively stationary with low loading on mooring lines, serving as an efficient wave energy transmitter while concurrently achieving resonance within the internal power take-off (PTO) system. This arrangement reduces the motion of the point absorber hull, thereby decreasing loads on the WEC structure, mooring lines, and anchors. As a result, operational and structural costs are minimised, further reducing the levelised costs of generated energy. Additionally, by ensuring minimal fluctuations in the WEC, confidence in using traditional linear mathematical models is increased, as commonly employed for WEC performance assessment and control design.The article presents a resonance study and introduces newly derived solutions in the frequency domain for the proposed operational concept. It analytically demonstrates the viability of employing the Fano resonance operational strategy for WECs, suggesting that this strategy has the potential to compete with traditional methods of wave energy transformation. Furthermore, the insights gained from the study contribute to identifying optimal parameters for a PTO system, as well as optimising the design of the heaving buoy.

Wave-to-wire modelling and hydraulic PTO optimization of a dense point absorber WEC array

We investigate the hydrodynamic interactions and power extraction efficiency of a dense array of Point Absorber (PA) Wave Energy Converters (WECs) clustered around the fixed pillar of a wind turbine –the Ocean Grazer device– with a standard hydraulic Power Take-Off (PTO) system. Using potential flow theory, a detailed wave-to-wire model is developed in WEC-Sim with four distinct hydraulic PTO designs: i) Multi PTO-with individual hydraulic PTO systems for each buoy, ii) Shared PTO V1-with a unified PTO system for the entire array, iii) Shared PTO V2-with the accumulator volume split into two segments, and iv) Shared PTO V3-with four strategically distributed segments. Key parameters such as the diameter of the hydraulic pistons, volume and pre-charged pressure of the high-pressure accumulators, hydraulic motor displacement and the speed of the electric generator are optimized with a genetic algorithm and a parametric analysis across various sea states. The results highlight that strategically allocating the accumulators across the floaters of a dense WEC array can yield significantly higher power production and should be considered at the early design stages.

Mechanical interactions modeling of inertial wave energy converters

Numerous technological solutions for wave energy converters (WECs), referred as inertial reaction mass (IRM) systems, incorporate a reacting mass within the floater, coupled with a power take-off (PTO) system, to shelter all electronic components from the hostile sea environment. While the overall complexity of the system increases, the current modeling procedures persist in considering only a limited number of modes of motion, neglecting relevant dynamical effects. In this context, this paper proposes a systematic procedure for defining the kinematic characteristics and overall analytical model for the dynamics of IRM WECs. The significance of the proposed procedure lies in the statement of the reaction mass-related dynamic equation, considering the floater’s parametric excitation in six degrees of freedom (DoF). Additionally, it introduces the procedure for defining the reaction forces that the inertial mass exerts on the floater, which are often neglected in the literature for the full simulation of such systems. Furthermore, the proposed analytical modeling procedure allows the definition of approximated models in more simplified nonlinear forms for dynamic analysis and ultimately in fully linear approximations. This enables the application of methodologies and techniques commonly used in the literature for linear systems. The development of the framework is kept generic, in order to introduce a versatile mathematical procedure, that can be easily adjusted, with minor modifications, to accurately capture and represent the mechanical interaction for a wide family of IRM WEC devices. Subsequently, a case study on a vertical-hinged pendulum WEC is analyzed, to showcase the effectiveness of the proposed methodology. Moreover, to test the reliability of the analytical framework, a comparison with the output of a commercial software is conducted.

Accounting for power take-off efficiency in optimal velocity tracking control of wave energy converters

There has been much research into how Wave Energy Converters (WECs) can capture energy from the waves and convert it into kinetic energy in the mechanical system (mechanical energy). However, because WECs typically generate power at high force and with low speed, the conversion of the mechanical energy into electrical energy can be inefficient. If Power Take-Off (PTO) efficiency is not accounted for in controller design then the efficiency of the WEC from wave energy to electrical energy can be poor. In this work, an adaptation of Optimal Velocity Tracking (OVT) control is presented, termed OVT-E, that accounts for PTO efficiencies in the controller formulation such that it converts more energy from the waves to electricity than traditional OVT approaches, termed OVT-M. Results show that, for an example WEC and PTO system in a simulation environment, OVT-E produces more efficient electrical energy conversion than OVT-M with lower forces through the drive-train. OVT-E is also shown to convert more electrical energy than an adaptive linear damping method. The methodology for designing OVT-E could have further applications when coupled with other controller implementations or if used alongside machine-learning for control co-design purposes.

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.

Real-time Wells turbine simulation on an oscillating-water-column wave energy converter physical model

Due to its simplicity and low cost, the Wells turbine is the most common choice for driving oscillating-water-column (OWC) wave energy converters (WECs) power take-off system. This turbine is characterized by a flow rate that is a linear function of the pressure head and inversely proportional to the rotational speed before the onset of hard stall conditions. The Wells turbine has been simulated in wave tanks using porous plugs, where the flow rate exhibits linear behaviour. However, numerical and experimental results have shown that rotational speed variations significantly influence the performance of OWC WECs. This work aims to develop a novel real-time simulator of a Wells turbine for use in physical models of OWC power plants. The proposed simulator consists of a diaphragm whose diameter is adjusted in real-time as a function of the pressure head measured in the laboratory and the rotational speed calculated by a hardware-in-the-loop model. In this way, it is possible to reproduce the full behaviour of the Wells turbine before and after a hard stall. Experimental results demonstrate the effectiveness of the simulator. A performance analysis was conducted to understand the device’s potential and compare the damping that Wells and impulse turbines introduce.

Comparative Study on the Performances of a Hinged Flap-Type Wave Energy Converter Considering Both Fixed and Floating Bases

The dynamical modeling and power optimization of floating wind–wave platforms, especially in regard to configurations based on constrained floating multi-body systems, lack in-depth systematic investigation. In this study, a floating wind-flap platform consisting of a flap-type wave energy converter and a floating offshore wind turbine is solved in the frequency domain considering the mechanical and hydrodynamic couplings of floating multi-body geometries and a model that suits the constraints of the hinge connection, which can accurately calculate the frequency domain dynamic response of the flap-type WEC. The results are compared with bottom-fixed flap-type wave energy converters in the absence of coupling with a floating wind platform. Moreover, combined with traditional optimization methods of power take-off systems for wave energy conversion, an optimization method is developed to suit the requirements of floating wind-flap platform configurations. The results are drawn for a specific operation site in the South China Sea, whereas a sensitivity analysis of the parameters is performed. It is found that the floating wind-flap platform has better wave energy absorption performance in the low-frequency range than the bottom-fixed flap-type wave energy converter; the average power generation in the low-frequency range can increase by up to 150 kW, mainly due to constructive hydrodynamic interactions, though it significantly fluctuates from the sea waves’ frequency range to the high-frequency range. Based on spectral analysis, operational results are drawn for irregular sea states, and the expected power for both types of flap-type WECs is around 30 kW, which points to a similar wave energy absorption performance when comparing the bottom-fixed flap with the flap within the hybrid configuration.

Wave energy converter with multiple degrees of freedom for sustainable repurposing of decommissioned offshore platforms: An experimental study

Targeting at the sustainable repurposing of decommissioned offshore platforms, a novel wave energy converter with a distinct mechanical-motion-rectifier power take-off system is developed to provide renewable energy. A scaled prototype is constructed and experimentally investigated in a large wave tank, as an essential step before sea trials. A new phenomenon of parametric oscillation is observed and explored, as physical evidence of chaotic instabilities of wave energy devices. Several advantages of the multi-degree-of-freedom device over its single-degree-of-freedom counterpart are disclosed physically for the first time. Releasing the pitch and roll degrees of freedom helps enlarge the heave amplitude of the energy-absorbing buoy, receive a larger hydrodynamic force from water waves to the power take-off system, reduce structural deflection and friction of the transmission machinery, and eliminate spiky and noisy vibrations of the internal force. Accordingly, the maximum efficiencies in the energy absorption and transmission stages increase from 45% and 11% to 90% and 30%, respectively; the overall efficiency of energy conversion is increased by up to three times in a broad spectrum of wave conditions.

Experimental Validation of a Modular All-Electric Power Take-Off Topology for Wave Energy Converter Enabling Marine Renewable Energy Interconnection

Power electronic converters are an enabling technology for the emerging marine energy applications, such as using ocean waves to produce electricity. This paper outlines the power take-off system and its key components used in a wave energy converter offering modularity and scalability to generate power efficiently. The proposed power take-off system was implemented based on a modular multilevel converter and could be deployed to convert any alternating current electrical energy to a different alternating current for interconnection to grid or non-grid applications. Examples of widespread deployment are supplying electricity to coastal communities or producing clean drinking water. The analysis using both the simulation tests and laboratory experiments verified the design objectives and basic functionality of the developed power take-off system. An acceptable response using a field programmable gate array-based controlled laboratory testbench was achieved, complying with guidelines specified in the prevalent industry standards. Seamless operation during steady-state and transients for the studied wave energy converter was achieved as supported by the obtained results. The key findings of this work were experimentally examined under different load conditions, direct current bus voltage fluctuations, and generator speed–torque regulation. The ability of the power take-off system to generate high-power quality of the waveforms, e.g., against adhering to the IEEE 519-2022 standard for total harmonic distortion limits, is also confirmed.

A Dual-Function Design of an Oscillating Water Column Integrated with a Slotted Breakwater: A Wave Flume Study

Wave energy conversion holds promise for renewable energy, but challenges like high initial costs hinder commercialization. Integrating wave-energy converters (WECs) into shore-protection structures creates dual-function structures for both electricity generation and coastal protection. Oscillating water columns (OWCs) have been well studied in the past with their simple generation mechanism and their out-of-water power take-off (PTO) system, which can minimize bio-fouling effects and maintenance costs compared to other submerged WECs. In addition, a slotted barrier allows for better circulation behind the breakwater while dissipating incoming wave energy through viscous damping. This study examines the performance of a new design which combines an OWC with a slotted breakwater. Small-scale (1:49) laboratory tests were performed with a piston-type wave generator. The performance is evaluated in terms of wave transmission, wave energy extraction, and wave loading under various wave conditions while focusing on the effects of the porosity of the slotted barrier and tide level changes. Results show that under larger waves, a decreasing wave transmission, increasing power extraction from the OWC, and energy dissipation from the slotted barrier are observed. On the other hand, under increasing wavelengths, wave transmission is observed to be constant; this is important for harbor design, which means that the breakwater is effective under a wider range of wavelengths. Porosity allows for more transmission while inducing less horizontal force on the structure.

Research on the design and optimal control of the power take-off (PTO) system for underwater eel-type power generators

Wave energy and ocean current energy are considered stable, reliable, and highly predictable renewable energy sources. The development of ocean current energy conversion technology is crucial in addressing power shortages. However, the low velocity of most ocean currents worldwide, typically less than 1.5 m/s, poses a challenge for traditional ocean current energy capture devices. Current estimations of power generation from underwater devices often significantly differ from actual results. This study presents an eel-type power generation device designed for underwater use, investigates the design and optimization of a hydraulic power take-off (PTO) system suitable for such devices, and examines key components of the hydraulic PTO system like variable hydraulic motors and generators. Analytical research was conducted to understand its operational characteristics, with a focus on components such as the accumulator, speed control valve, and energy storage flywheel. The article also delves into the hydrodynamic and energy conversion characteristics of the device under shallow water wave and current conditions, enhancing the hydraulic PTO system model and establishing an integrated calculation model for real-time data transmission during the calculation process. Through evaluations of pitch angle and power generation under varying sea conditions, the study explores the impact of hydraulic motor displacement and damping coefficient on the hydrodynamic and power generation characteristics of the device, further validated through sea trials. The study findings indicate a high level of parameter adaptation among the components of the hydraulic system. The addition of an accumulator to the system results in smoother output response curves, suggesting that the accumulator absorbs impacts and stabilizes the hydraulic power transmission system. The proposed comprehensive calculation method enables a more precise prediction of the performance of the eel power generation device in real marine environments, capturing its movement behavior and power generation characteristics. Adjusting the motor displacement or damping coefficient under specific conditions can optimize the total damping of the hydraulic PTO system for maximum power output. The optimal power point of the hydraulic power generation system varies for different sea conditions, with a potential power generation efficiency of up to 80.3% under certain circumstances.

Design of a Wave Generation System Using an Oscillating Paddle-Type Device Anchored to Fixed Structures on the Coast

Wave energy, a form of renewable energy, is derived from the movement of sea waves. Wave energy generation devices are technologies designed to harness this resource and convert it into electricity. These devices are classified based on their location, size, wave direction, and operating principle. This work presents the design of an oscillating device for harnessing wave energy. For this purpose, computational fluid dynamics and response surface methodology were employed to evaluate the influence of the percentage of the blade height submerged below the water surface (X1) and the distance from the device to the breakwater in terms of the percentage of the wave length (X2). The response variable studied was the hydrodynamic efficiency (η) of the device. Transient fluid dynamic simulations were carried out using Ansys Fluent software 2023 R1, with input conditions based on a wave spectrum characteristic of the Colombian Pacific Ocean. Analysis of variance determined that both factors and their interaction have significant effects on the response variable. Using the obtained regression model, the optimal point of the system was determined. Numerical results showed that the maximum η of the system was achieved when the device was submerged at 75% of its height and was positioned 10% of the wave length away from the vertical breakwater. Under this configuration, η was 64.8%. Experimental validations of the optimal configuration were conducted in a wave channel, resulting in a η of 45%. The difference in efficiencies can be attributed to mechanical losses in the power take-off system, which were not considered during the numerical simulations.

Hybrid Torque Coefficient Control of Average-to-Peak Ratio for Turbine Angular Velocity Reduction in Oscillating-Water-Column-Type Wave Energy Converter

Wave energy converters (WECs) have significant potential to meet the increasing energy demands and using an oscillating water column (OWC) is one of the most reliable ways to implement them. The OWC has a simple structure and excellent durability. However, control of the power take-off (PTO) system is difficult due to variability in the input wave energy. In particular, the design and control of the PTO system are complex, as the average-to-peak ratio of the output generation is large. Owing to the nature of the OWC, if the energy above the rating cannot be controlled, the power generated is inevitably reduced due to the decrease in operating time. We propose a method to reduce the angular speed of the turbine by dividing the section according to the input energy and correspondingly changing the torque coefficient, thereby increasing the operating time of the OWC. The control methods for the PTO system of OWC are verified through a 30 kW full-scale experimental device to be installed in a real sea area. The full-scale experimental device consists of an inverter that simulates the mechanical torque of an OWC based on the aerodynamic simulation of an impulse turbine, an induction motor, a permanent magnet synchronous generator, an AC/DC converter, and a battery for the energy storage system. The performance of conventional control methods and the proposed method are compared based on the results of numerical simulations and experiments. We show that the fluctuation in the turbine angular velocity in the proposed method is significantly reduced compared with that in the conventional control methods under regular and irregular wave conditions.

Neural network survivability approach of a wave energy converter considering uncertainties in the prediction of future knowledge

To tune the wave energy converter (WEC) controller parameters such as damping to reduce the line force during extreme wave conditions, future knowledge of the line force is required. To achieve this, the incoming wave and system state should be predicted for a few seconds in the future. It is rather an arduous task to predict the future knowledge of waves and the system’s dynamic when dealing with breaking and steep waves, and the system is subject to various nonlinear forces. The classical model-based control strategies often rely on linear assumptions to estimate the WEC dynamics for the sake of simplicity. Unlike the model-based, the data-driven approaches are free from modeling errors and the algorithms are trained over the true and noisy data to predict non-linear system behaviors. Using data-driven approaches, we are able to model nonlinear dynamics. However, new questions emerge on the accuracy of the future wave and system state predictions, and how this uncertainty propagates into the final prediction of the line force. As incorrect damping may lead to excessive line force and detrimental damage to the system, these are the knowledge gaps that need to be addressed. The main purpose of this paper is to answer these questions through a survivability strategy for wave energy converters by providing a realistic perspective on the implementation of the neural network approaches by accounting for the errors in the input data. For this purpose, a series of neural networks is designed that first predicts the surface elevation for 0.36 s ahead, i.e. corresponding to 2 s in the full-scale WEC. This future knowledge of the wave elevation is then used to predict the system state (i.e. power take-off (PTO) translator position) for the same prediction horizon based on the PTO damping. This information is then fed to a convolutional neural network (CNN) that predicts the peak line force 0.36 s ahead. This paper also evaluates the predictive capabilities of neural network (NN) models, comparing them to classical autoregressive (AR) and Kalman filter methods. While the AR model exhibits slightly higher accuracy in fixed PTO system configurations, it falters in providing real-time predictions when system parameters undergo variations. In contrast, the NN prediction model excels by establishing a robust relationship between system configuration and output signals. Especially noteworthy is its ability to outperform classical methods with minimal training on a selective set of system configurations. Then, the sensitivity of the peak line force prediction to the uncertainties in the input data from NN models and the prediction horizon is analyzed. The neural network models are trained over the experimental data subjected to extreme sea states for a point absorber wave energy converter. The results suggest that the accuracy of the surface elevation prediction has an insignificant direct effect on the peak force prediction model. However, these uncertainties are reflected in the PTO translator position prediction, and the model is considerably sensitive to the accuracy of this prediction. This sensitivity nonetheless is less notable for higher PTO damping values.

Optimal declutching control of hinged multiple floating bodies

In deep seas, there is an increasing utilisation of multiple floating structures as devices for harnessing renewable energy, such as hybrid wind-wave energy systems and multi-body wave energy converters. The control strategies have a great influence on the motion characteristics and energy conversion efficiency of these systems. The control technology brings more benefits to the system's performance, yet also introduces more complex challenges. This paper aims to fill the research gap in the control of multiple floating bodies and to propose a novel optimal declutching control method. Declutching control enables discontinuous loading and releasing of the force from power take-off system between bodies. It was found that the feasibility of the proposed method is highly dependent on the choice of objective functions, iteration numbers, and wave frequencies. With appropriate parameters, the declutching control can achieve a variety of objectives for a hinged floating multibody system, such as reducing pitch motion, improving extracted wave power, increasing relative rotational speed, and enhancing power extraction. The control effects on the velocity and the force-velocity phase relationship and how they benefit the objectives are discussed. All objective functions show a better control effect (at least 7.76%) on their respective performance indices than others.

Hydrodynamic Interactions and Enhanced Energy Harnessing amongst Many WEC Units in Large-Size Wave Parks

Interactions between wave energy converters (WECs) can significantly affect the overall energy-harnessing performance of a wave park. Although large-size wave parks with many WEC units are commonly considered in practical applications, it is challenging to simulate such parks due to huge computational costs. This paper presents a numerical model that uses the boundary element method (BEM) to simulate wave parks. Each wave energy converter (WEC) was modelled as a comprehensive system, including WEC buoys, power take-off, and mooring systems, with hydrodynamic interactions included. Two classical layouts for arranging 16 units were simulated using this numerical model. The energy-harnessing performance of these array layouts was analyzed for both regular waves and a selection of irregular sea state conditions with different wave directions, wave heights, wave periods and water depths. For each layout, three WEC separation distances were studied. An increase of up to 16% in the power performance of the WEC under regular waves was observed, which highlights the importance of interaction effects.

Multi-freedom effects on a raft-type wave energy convertor- hydrodynamic response and energy absorption

This research delves into the effects of multiple degrees of freedom on a raft-type wave energy converter (WEC), using both experimental and computational methods. The WEC features two interconnected floating bodies linked by a specialized parallelogram joint, allowing for distinct heave, pitch, and surge motions. The power take-off (PTO) system, integrating Coulomb damping, is analysed for its impact on energy absorption. Despite varying damping amplitudes, peak energy absorption is consistent across different wave periods, as shown in scaled model tests. Computational simulations further investigate the multi-freedom effects by imposing constraints on various degrees of freedom, thus elucidating their individual and combined influences on energy absorption. Preliminary results indicate that the addition of degrees of freedom can enhance the WEC's efficiency, especially through coordinated release of the bodies' relative pitch and surge motions. The study also finds that the energy absorption efficiency from pitch motion depends on the release of surge motion. Moreover, the energy distribution among each degree of freedom is significantly affected by the device's multi-freedom characteristics. This research provides valuable insights and practical guidelines for the development of advanced multi-freedom WEC technologies.

Numerical Study on the Swimming and Energy Self-Sufficiency of Multi-Joint Robotic Fish

Energy is one of the primary challenges in the long-term operation of robotic fish. The research on combining wave energy-harvesting technology with robotic fish for energy supplementation is not extensive, and there is insufficient comprehensive analysis on energy harvesting from waves and energy costs during swimming. Therefore, the energy self-sufficiency of multi-joint robotic fish is investigated by employing the coupling method of smoothed particle hydrodynamics (SPH) and multi-body dynamics in this study. A reversible energy conversion mechanism is applied to the robotic fish, serving as a driving system during swimming and as a power take-off (PTO) system during energy harvesting. The energy costs of the multi-joint robotic fish under various undulation parameters (including amplitude, frequency, and body wavelength) are analyzed, along with an examination of the influence of the PTO system on energy harvesting. The results show that, compared to the undulation amplitude and body wavelength, the undulation frequency has the greatest impact on swimming efficiency and energy costs, with low-frequency swimming being advantageous for efficient energy utilization. Additionally, the damping coefficient of the PTO system directly affects energy-harvesting efficiency, with higher energy-harvesting power achievable with an optimal PTO system parameter. Through a comprehensive analysis of energy costs and energy harvesting, it is concluded that the achievement of energy self-sufficiency for multi-joint robotic fish in marine environments is highly feasible.

A compressible degree of freedom as a means for improving the performance of heaving wave energy converters

A compressible degree of freedom (CDOF) can provide a means of improving wave power capture by adjusting the system stiffness and providing short-term energy storage, reducing or even eliminating the requirement for two-way electrical power flow as is typical in wave energy control systems. With the overarching goal of investigating and facilitating the application of a CDOF within wave energy converter (WEC) design, this paper focuses primarily on the case of heaving buoys, and on using air volumes to provide the compressible spring effect. Analytical formulae for the natural frequencies are used to gain fundamental insights into the main design considerations. Numerical methods are used to augment this understanding, helping to elucidate the effect of geometric parameters and scale on the required compressible volumes and the efficacy of the CDOF. Beginning with the WaveBot WEC, case studies are then used to demonstrate the design drivers in a more applied context, as well as highlighting the benefit of a self-reacting power take-off (PTO) system. The assimilation of these results with the findings of a detailed literature review culminates in a set of recommendations (or guiding principles) for designing a compressible degree of freedom to improve the performance of a heaving wave energy converter. These recommendations apply both to full-scale WECs, and to the design of scale physical modelling studies for validating the analytical and numerical models.

A novel oscillating wave surge converter by hollowing out the flap bottom: Numerical studies using smoothed particle hydrodynamics

Oscillating wave surge converters (OWSCs) have been extensively investigated. However, previous studies have mainly optimized their structural parameters, and the OWSC cost has seldomly been considered. The optimized OWSC may be uneconomical. Therefore, this study proposes an improved method by examining the fluid characteristics near the OWSC flap and by hollowing out the flap bottom. Such a design can not only enhance the OWSC, but can also save material making it economical. Furthermore, the capture factor (CF) per flap height (CFH) was proposed to evaluate the OWSC. The CFH considers a material cost that is positively correlated with flap height. The Sobol sensitivity analysis results show that only the wave period, water depth, power take-off system damping, flap hollow top height, and flap top height must be considered when optimizing the OWSC. This reduces half of the parameter dimensions to be optimized, further reducing the calculation cost and time. When optimizing the improved OWSC and the original OWSC to maximize the CFH, the CFH of the former one is 2.22 times larger than that of the latter, which indicates a significant improvement in OWSC economy. This implies that improved OWSC and CFH should be adopted in practical engineering applications.