Modeling dynamic demand response using Monte Carlo simulation and interval mathematics for boundary estimation

With the rapid development of various technologies and applications in smart grid implementation, demand response has attracted growing research interests because of its potentials in enhancing power grid reliability with reduced system operation costs. This paper presents a new demand response model with elastic economic dispatch in a locational marginal pricing market. It models system economic dispatch as a feedback control process, and introduces a flexible and adjustable load cost as a controlled signal to adjust demand response. Compared with the conventional “one time use” static load dispatch model, this dynamic feedback demand response model may adjust the load to a desired level in a finite number of time steps and a proof of convergence is provided. In addition, Monte Carlo simulation and boundary calculation using interval mathematics are applied for describing uncertainty of end-user's response to an independent system operator's expected dispatch. A numerical analysis based on the modified Pennsylvania-Jersey-Maryland power pool five-bus system is introduced for simulation and the results verify the effectiveness of the proposed model. System operators may use the proposed model to obtain insights in demand response processes for their decision-making regarding system load levels and operation conditions.

Nonlinear static and dynamic damped response of a composite rectangular plate resting on a two-parameter elastic foundation

Nonlinear static and dynamic response analyses of a clamped. rectangular composite plate resting on a two-parameter elastic foundation have been studied using von Karman's relations. Incorporating the material damping, the governing coupled, nonlinear partial differential equations are obtained for the plate under step pressure pulse load excitation. These equations have been solved by a one-term solution and by applying Galerkin's technique to the deflection equation. This yields an ordinary nonlinear differential equation in time. The nonlinear static solution is obtained by neglecting the time-dependent variables. Thc nonlinear dynamic damped response is obtained by applying the ultraspherical polynomial approximation (UPA) technique. The influences of foundation modulus, shear modulus, orthotropy, etc. upon the nonlinear static and dynamic responses have been presented.

Seismic characterization and dynamic site response of a municipal solid waste landfill in Bangalore, India

Seismic design of landfills requires an understanding of the dynamic properties of municipal solid waste (MSW) and the dynamic site response of landfill waste during seismic events. The dynamic response of the Mavallipura landfill situated in Bangalore, India, is investigated using field measurements, laboratory studies and recorded ground motions from the intraplate region. The dynamic shear modulus values for the MSW were established on the basis of field measurements of shear wave velocities. Cyclic triaxial testing was performed on reconstituted MSW samples and the shear modulus reduction and damping characteristics of MSW were studied. Ten ground motions were selected based on regional seismicity and site response parameters have been obtained considering one-dimensional non-linear analysis in the DEEPSOIL program. The surface spectral response varied from 0.6 to 2g and persisted only for a period of 1s for most of the ground motions. The maximum peak ground acceleration (PGA) obtained was 0.5g and the minimum and maximum amplifications are 1.35 and 4.05. Amplification of the base acceleration was observed at the top surface of the landfill underlined by a composite soil layer and bedrock for all ground motions. Dynamic seismic properties with amplification and site response parameters for MSW landfill in Bangalore, India, are presented in this paper. This study shows that MSW has less shear stiffness and more amplification due to loose filling and damping, which need to be accounted for seismic design of MSW landfills in India.

Seismic characterization and dynamic site response of a municipal solid waste landfill in Bangalore, India

Seismic design of landfills requires an understanding of the dynamic properties of municipal solid waste (MSW) and the dynamic site response of landfill waste during seismic events. The dynamic response of the Mavallipura landfill situated in Bangalore, India, is investigated using field measurements, laboratory studies and recorded ground motions from the intraplate region. The dynamic shear modulus values for the MSW were established on the basis of field measurements of shear wave velocities. Cyclic triaxial testing was performed on reconstituted MSW samples and the shear modulus reduction and damping characteristics of MSW were studied. Ten ground motions were selected based on regional seismicity and site response parameters have been obtained considering one-dimensional non-linear analysis in the DEEPSOIL program. The surface spectral response varied from 0.6 to 2g and persisted only for a period of 1s for most of the ground motions. The maximum peak ground acceleration (PGA) obtained was 0.5g and the minimum and maximum amplifications are 1.35 and 4.05. Amplification of the base acceleration was observed at the top surface of the landfill underlined by a composite soil layer and bedrock for all ground motions. Dynamic seismic properties with amplification and site response parameters for MSW landfill in Bangalore, India, are presented in this paper. This study shows that MSW has less shear stiffness and more amplification due to loose filling and damping, which need to be accounted for seismic design of MSW landfills in India.

Generalization of Response Number for Dynamic Plastic Response of Shells Subjected to impulsive Loading

A dimensionless number, termed as response number in Zhao [Archive of Applied Mechanics 68 (1998) 524], has been suggested for the dynamic plastic response of beams and plates made up of rigidly perfect plastic materials subjected to dynamic loading. Many theoretical and experimental results can be reformulated into new concise forms with the response number. The concept of a new dimensionless number, response number, termed as Rn(n), is generalized in Zhao [Forschung im Ingenieurwesen 65 (1999) 107] to study the elastic, plastic, dynamic elastic as well as dynamic plastic buckling problems of columns, plates as well as shells. The response number Rn(n) is generalized to the dynamic behaviour of shells of various shapes in the present paper.

Application of response number for dynamic plastic response of plates subjected to impulsive loading

A dimensionless number, termed response number, is applied to the dynamic plastic response of plates subjected to dynamic loading. Many theoretical and experimental results presented by different researchers are reformulated into new concise forms with the response number. The advantage of the new forms is twofold: (1) they are more physically meaningful, and (2) they are independent of the choice of units, thus, they have wider range of applications.

Suggestion of a new dimensionless number for dynamic plastic response of beams and plates

A dimensionless number, termed response number in the present paper, is suggested for the dynamic plastic response of beams and plates made of rigid-perfectly plastic materials subjected to dynamic loading. It is obtained at dimensional reduction of the basic governing equations of beams and plates. The number is defined as the product of the Johnson's damage number and the square of the half of the slenderness ratio for a beam; the product of the damage number and the square of the half of the aspect ratio for a plate or membrane loaded dynamically. Response number can also be considered as the ratio of the inertia force at the impulsive loading to the plastic limit load of the structure. Three aspects are reflected in this dimensionless number: the inertia of the applied dynamic loading, the resistance ability of the material to the deformation caused by the loading and the geometrical influence of the structure on the dynamic response. For an impulsively loaded beam or plate, the final dimensionless deflection is solely dependent upon the response number. When the secondary effects of finite deflections, strain-rate sensitivity or transverse shear are taken into account, the response number is as useful as in the case of simple bending theory. Finally, the number is not only suitable to idealized dynamic loads but also applicable to dynamic loads of general shape.