摘要
研究了一种振荡浮子式波浪能发电装置的运动以及阻尼器系数对发电效能的影响,并根据装置平衡与垂荡运动时的受力条件,建立二元二阶微分方程组模型.对阻尼系数恒定和不恒定两种情况分别求解,前者采用拉氏变换法可以得到微分方程组的解析解,后者采用四阶Runge-Kutta法可以得到数值解.在求解阻尼系数恒定时的最大功率时,采用力电比拟法,即将力学方程比拟成电学方程,应用相量法将阻尼器的输出功率转化为电阻的最大功率进行求解.经计算,在设定的波浪条件和阻尼系数下,1 m量级的发电装置功率可以达到229.34 W,与同等量级的太阳能电池板相当.
The convertion of the kinetic energy and potential energy of ocean surface waves into mechanical energy for power generation is one of the important research fields of renewable energy.This paper looks into a kind of wave energy generator,as well as how the damping coefficient contribute to power generation.In regard to different mechanics conditions,differential equations of the second order of two independent variates are applied.For the two cases of constant damping coefficient and inconstant damping coefficient,the former can be solved analytically by using Laplace transform method,and the latter can be tackled numerically by using the fourth order Runge Kutta method.When calculating the maximum power under the condition that the damping coefficient is constant,we use the Dynamics-Electricity Analogy Method,that is,the dynamical equations are compared to the electrical equation.Furthermore,the phasor method is used to convert the output power of the damper into the maximum power of the resistance.According to the results,under the set wave conditions and damping coefficient,the power of the one-meter-scale wave power generation device can reach 229.34 Watt,equivalent to the solar panel of the same level.
作者
宋昊天
夏天乐
张烨阳
贺丹
SONG Haotian;XIA Tianle;ZHANG Yeyang;HE Dan(School of Information Science and Engineering,Southeast University,Nanjing,Jiangsu 211102,China;School of Physics,Southeast University,Nanjing,Jiangsu 211102,China;School of Mathematice,Southeast University,Nanjing,Jiangsu 211102,China)
出处
《数学建模及其应用》
2023年第1期35-43,113,共10页
Mathematical Modeling and Its Applications
基金
东南大学教改项目“四新”背景下数学建模创新能力培养研究
东南大学教改项目《工科数学分析》课程思政的探索与实践。
关键词
波浪发电装置
力电比拟法
拉普拉斯变换
龙格库塔法
wave power generation
dynamics-electricity analogy method
Laplace transform
Runge Kutta method
