Under the partial shading conditions(PSC)of Photovoltaic(PV)modules in a PV hybrid system,the power output curve exhibits multiple peaks.This often causes traditional maximum power point tracking(MPPT)methods to fall ...Under the partial shading conditions(PSC)of Photovoltaic(PV)modules in a PV hybrid system,the power output curve exhibits multiple peaks.This often causes traditional maximum power point tracking(MPPT)methods to fall into local optima and fail to find the global optimum.To address this issue,a composite MPPT algorithm is proposed.It combines the improved kepler optimization algorithm(IKOA)with the optimized variable-step perturb and observe(OIP&O).The update probabilities,planetary velocity and position step coefficients of IKOA are nonlinearly and adaptively optimized.This adaptation meets the varying needs of the initial and later stages of the iterative process and accelerates convergence.During stochastic exploration,the refined position update formulas enhance diversity and global search capability.The improvements in the algorithmreduces the likelihood of falling into local optima.In the later stages,the OIP&O algorithm decreases oscillation and increases accuracy.compared with cuckoo search(CS)and gray wolf optimization(GWO),simulation tests of the PV hybrid inverter demonstrate that the proposed IKOA-OIP&O algorithm achieves faster convergence and greater stability under static,local and dynamic shading conditions.These results can confirm the feasibility and effectiveness of the proposed PV MPPT algorithm for PV hybrid systems.展开更多
微积分的一个重要应用就是微分方程,在工科院校的高等数学的课程当中,对于二阶常微分方程会花非常大的力气在二阶常系数线性常微分方程的求解中,对于其余的二阶常微分方程尤其是非线性的常微分方程很少涉及。本文通过对Kepler三大行星...微积分的一个重要应用就是微分方程,在工科院校的高等数学的课程当中,对于二阶常微分方程会花非常大的力气在二阶常系数线性常微分方程的求解中,对于其余的二阶常微分方程尤其是非线性的常微分方程很少涉及。本文通过对Kepler三大行星运动定律的数学推导,来说明非线性常微分方程才是实际当中碰到的大多数,以及微积分作为人类历史上的一项伟大发现的重要意义。An important application of calculus is differential equations. In the advanced mathematics courses of engineering colleges, a lot of effort is spent on solving second-order linear differential equations with constant coefficients, while other second-order differential equations, especially nonlinear differential equations, are rarely involved. This paper uses the mathematical derivation of Kepler’s three laws of planetary motion to illustrate that nonlinear differential equations are the majority of ordinary differential equations encountered in practice, and the importance of calculus as a great discovery in human history.展开更多
Possible bulk compositions of the super-Earth exoplanets CoRoT-7b, Kepler-9d, and Kepler-10b are investigated by applying a commonly used silicate model and a non-standard carbon model. Their internal structures are d...Possible bulk compositions of the super-Earth exoplanets CoRoT-7b, Kepler-9d, and Kepler-10b are investigated by applying a commonly used silicate model and a non-standard carbon model. Their internal structures are deduced using a suitable equation of state for the materials. The degeneracy problems of their compo- sitions can be partly overcome, based on the fact that all three planets are extremely close to their host stars. By analyzing the numerical results, we conclude： 1） the iron core of CoRoT-7b is not more than 27% of its total mass within lc~ mass-radius error bars, so an Earth-like composition is less likely, but its carbon rich model can be com- patible with an Earth-like core/mantle mass fraction; 2） Kepler-10b is more likely to have a Mercury-like composition, with its old age implying that its high iron content may be a result of strong solar wind or giant impact; 3） the transiting-only super-Earth Kepler-9d is also discussed. Combining its possible composition with the formation theory, we can place some constraints on its mass and bulk composition.展开更多
Beginning with a Lagrangian, we derived an approximate relativistic orbit equation which describes relativistic corrections to Keplerian orbits. The critical angular moment to guarantee the existence of periodic orbit...Beginning with a Lagrangian, we derived an approximate relativistic orbit equation which describes relativistic corrections to Keplerian orbits. The critical angular moment to guarantee the existence of periodic orbits is determined. An approximate relativistic Kepler’s elliptic orbit is illustrated by numerical simulation via a second-order perturbation method of averaging.展开更多
The present study deals with a traditional physical problem: the solution of the Kepler’s equation for all conics (ellipse, hyperbola or parabola). Solution of the universal Kepler’s equation in closed form is obtai...The present study deals with a traditional physical problem: the solution of the Kepler’s equation for all conics (ellipse, hyperbola or parabola). Solution of the universal Kepler’s equation in closed form is obtained with the help of the two-dimensional Laplace technique, expressing the universal functions as a function of the universal anomaly and the time. Combining these new expressions of the universal functions and their identities, we establish one biquadratic equation for universal anomaly (χ) for all conics;solving this new equation, we have a new exact solution of the present problem for the universal anomaly as a function of the time. The verifying of the universal Kepler’s equation and the traditional forms of Kepler’s equation from this new solution are discussed. The plots of the elliptic, hyperbolic or parabolic Keplerian orbits are also given, using this new solution.展开更多
基金funding from the Graduate Practice Innovation Program of Jiangsu University of Technology(XSJCX23_58)Changzhou Science and Technology Support Project(CE20235045)Open Project of Jiangsu Key Laboratory of Power Transmission&Distribution Equipment Technology(2021JSSPD12).
文摘Under the partial shading conditions(PSC)of Photovoltaic(PV)modules in a PV hybrid system,the power output curve exhibits multiple peaks.This often causes traditional maximum power point tracking(MPPT)methods to fall into local optima and fail to find the global optimum.To address this issue,a composite MPPT algorithm is proposed.It combines the improved kepler optimization algorithm(IKOA)with the optimized variable-step perturb and observe(OIP&O).The update probabilities,planetary velocity and position step coefficients of IKOA are nonlinearly and adaptively optimized.This adaptation meets the varying needs of the initial and later stages of the iterative process and accelerates convergence.During stochastic exploration,the refined position update formulas enhance diversity and global search capability.The improvements in the algorithmreduces the likelihood of falling into local optima.In the later stages,the OIP&O algorithm decreases oscillation and increases accuracy.compared with cuckoo search(CS)and gray wolf optimization(GWO),simulation tests of the PV hybrid inverter demonstrate that the proposed IKOA-OIP&O algorithm achieves faster convergence and greater stability under static,local and dynamic shading conditions.These results can confirm the feasibility and effectiveness of the proposed PV MPPT algorithm for PV hybrid systems.
文摘微积分的一个重要应用就是微分方程,在工科院校的高等数学的课程当中,对于二阶常微分方程会花非常大的力气在二阶常系数线性常微分方程的求解中,对于其余的二阶常微分方程尤其是非线性的常微分方程很少涉及。本文通过对Kepler三大行星运动定律的数学推导,来说明非线性常微分方程才是实际当中碰到的大多数,以及微积分作为人类历史上的一项伟大发现的重要意义。An important application of calculus is differential equations. In the advanced mathematics courses of engineering colleges, a lot of effort is spent on solving second-order linear differential equations with constant coefficients, while other second-order differential equations, especially nonlinear differential equations, are rarely involved. This paper uses the mathematical derivation of Kepler’s three laws of planetary motion to illustrate that nonlinear differential equations are the majority of ordinary differential equations encountered in practice, and the importance of calculus as a great discovery in human history.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10833001 and 10925313)Ph.D traininggrant of China (20090091110002)+1 种基金Fundamental Research Funds for the Central Universities(No. 1112020102)support from the Shandong Provincial Natural Science Foundation,China (ZR2010AQ023)
文摘Possible bulk compositions of the super-Earth exoplanets CoRoT-7b, Kepler-9d, and Kepler-10b are investigated by applying a commonly used silicate model and a non-standard carbon model. Their internal structures are deduced using a suitable equation of state for the materials. The degeneracy problems of their compo- sitions can be partly overcome, based on the fact that all three planets are extremely close to their host stars. By analyzing the numerical results, we conclude： 1） the iron core of CoRoT-7b is not more than 27% of its total mass within lc~ mass-radius error bars, so an Earth-like composition is less likely, but its carbon rich model can be com- patible with an Earth-like core/mantle mass fraction; 2） Kepler-10b is more likely to have a Mercury-like composition, with its old age implying that its high iron content may be a result of strong solar wind or giant impact; 3） the transiting-only super-Earth Kepler-9d is also discussed. Combining its possible composition with the formation theory, we can place some constraints on its mass and bulk composition.
文摘Beginning with a Lagrangian, we derived an approximate relativistic orbit equation which describes relativistic corrections to Keplerian orbits. The critical angular moment to guarantee the existence of periodic orbits is determined. An approximate relativistic Kepler’s elliptic orbit is illustrated by numerical simulation via a second-order perturbation method of averaging.
文摘The present study deals with a traditional physical problem: the solution of the Kepler’s equation for all conics (ellipse, hyperbola or parabola). Solution of the universal Kepler’s equation in closed form is obtained with the help of the two-dimensional Laplace technique, expressing the universal functions as a function of the universal anomaly and the time. Combining these new expressions of the universal functions and their identities, we establish one biquadratic equation for universal anomaly (χ) for all conics;solving this new equation, we have a new exact solution of the present problem for the universal anomaly as a function of the time. The verifying of the universal Kepler’s equation and the traditional forms of Kepler’s equation from this new solution are discussed. The plots of the elliptic, hyperbolic or parabolic Keplerian orbits are also given, using this new solution.
