Demand response has gained significant attention recently with the increasing penetration of renewable energy sources in power systems. Air conditioning loads are typical thermostatically controlled loads which can pl...Demand response has gained significant attention recently with the increasing penetration of renewable energy sources in power systems. Air conditioning loads are typical thermostatically controlled loads which can play an active role in ancillary services by regulating their aggregated power consumption. The aggregation of air conditioners is essential to the control of air conditioning loads. In this paper, linear state equations are proposed to aggregate air conditioning loads by solving coupled Fokker–Planck equations(CFPEs) using the finite difference method. By analyzing the numerical stability and convergence of the difference scheme, the grid spacings, including temperature step and time step, are properly determined according to the maximal principle. Stationary solutions of the CFPEs are obtained by analytical and numerical methods. Furthermore, a classification method using dimension reduction is proposed to deal with the problem of heterogeneous parameters and interval estimation is applied to describe the stochastic behavior of air conditioning loads. The simulation results verify the effectiveness of the proposed methods.展开更多
At this article studies of nonlinear viscoelastic fluid with one internal tensor parameter flow between parallel planes under a constant pressure gradient, taking into account the slipping phenomenon on the boundary. ...At this article studies of nonlinear viscoelastic fluid with one internal tensor parameter flow between parallel planes under a constant pressure gradient, taking into account the slipping phenomenon on the boundary. Numerically depending found on the components of the stress tensor and the flow velocity of the pressure gradient and the distance to the wall, enabled us to explain the emergence of non-parabolic profile of the flow velocity of the polymeric melt.展开更多
Optimal control system of state space is a conservative system, whose approximate method should be symplectic conservation. Based on the precise integration method, an algorithm of symplectic conservative perturbation...Optimal control system of state space is a conservative system, whose approximate method should be symplectic conservation. Based on the precise integration method, an algorithm of symplectic conservative perturbation is presented. It gives a uniform way to solve the linear quadratic control （LQ control） problems for linear timevarying systems accurately and efficiently, whose key points are solutions of differential Riccati equation （DRE） with variable coefficients and the state feedback equation. The method is symplectic conservative and has a good numerical stability and high precision. Numerical examples demonstrate the effectiveness of the proposed method.展开更多
A Bianchi type-V space time is considered with linear equation of state in the scalar tensor theory of gravitation proposed by Brans and Dicke. We use the assumption of constant deceleration parameter and power law re...A Bianchi type-V space time is considered with linear equation of state in the scalar tensor theory of gravitation proposed by Brans and Dicke. We use the assumption of constant deceleration parameter and power law relation between scalar field øand scale factor R to find the solutions. Some physical and kinematical properties of the model are also discussed.展开更多
基金supported by National Natural Science Foundation of China(No.51177093)
文摘Demand response has gained significant attention recently with the increasing penetration of renewable energy sources in power systems. Air conditioning loads are typical thermostatically controlled loads which can play an active role in ancillary services by regulating their aggregated power consumption. The aggregation of air conditioners is essential to the control of air conditioning loads. In this paper, linear state equations are proposed to aggregate air conditioning loads by solving coupled Fokker–Planck equations(CFPEs) using the finite difference method. By analyzing the numerical stability and convergence of the difference scheme, the grid spacings, including temperature step and time step, are properly determined according to the maximal principle. Stationary solutions of the CFPEs are obtained by analytical and numerical methods. Furthermore, a classification method using dimension reduction is proposed to deal with the problem of heterogeneous parameters and interval estimation is applied to describe the stochastic behavior of air conditioning loads. The simulation results verify the effectiveness of the proposed methods.
文摘At this article studies of nonlinear viscoelastic fluid with one internal tensor parameter flow between parallel planes under a constant pressure gradient, taking into account the slipping phenomenon on the boundary. Numerically depending found on the components of the stress tensor and the flow velocity of the pressure gradient and the distance to the wall, enabled us to explain the emergence of non-parabolic profile of the flow velocity of the polymeric melt.
基金Project supported by the National Natural Science Foundation of China (No.10202004)
文摘Optimal control system of state space is a conservative system, whose approximate method should be symplectic conservation. Based on the precise integration method, an algorithm of symplectic conservative perturbation is presented. It gives a uniform way to solve the linear quadratic control （LQ control） problems for linear timevarying systems accurately and efficiently, whose key points are solutions of differential Riccati equation （DRE） with variable coefficients and the state feedback equation. The method is symplectic conservative and has a good numerical stability and high precision. Numerical examples demonstrate the effectiveness of the proposed method.
文摘A Bianchi type-V space time is considered with linear equation of state in the scalar tensor theory of gravitation proposed by Brans and Dicke. We use the assumption of constant deceleration parameter and power law relation between scalar field øand scale factor R to find the solutions. Some physical and kinematical properties of the model are also discussed.
