Optimizing Regenerative Braking: A Variational Calculus Approach

We begin by analyzing, using basic physics considerations, under what conditions it becomes energetically favorable to use aggressive regenerative braking to reach a lower speed over “coasting” where one relies solely on air drag to slow down. We then proceed to reformulate the question as an optimization problem to find the velocity profile that maximizes battery charge. Making a simplifying assumption on battery-charging efficiency, we express the recovered energy as an integral quantity, and we solve the associated Euler–Lagrange equation to find the optimal braking curves that maximize this quantity in the framework of variational calculus. Using Lagrange multipliers, we also explore the effect of adding a fixed-displacement constraint.

On the Definition of Energy Flux in One-Dimensional Chains of Particles

We review two well-known definitions present in the literature, which are used to define the heat or energy flux in one dimensional chains. One definition equates the energy variation per particle to a discretized flux difference, which we here show it also corresponds to the flux of energy in the zero wavenumber limit in Fourier space, concurrently providing a general formula valid for all wavelengths. The other relies somewhat elaborately on a definition of the flux, which is a function of every coordinate in the line. We try to shed further light on their significance by introducing a novel integral operator, acting over movable boundaries represented by the neighboring particles’ positions, or some combinations thereof. By specializing to the case of chains with the particles’ order conserved, we show that the first definition corresponds to applying the differential continuity-equation operator after the application of the integral operator. Conversely, the second definition corresponds to applying the introduced integral operator to the energy flux. It is, therefore, an integral quantity and not a local quantity. More worryingly, it does not satisfy in any obvious way an equation of continuity. We show that in stationary states, the first definition is resilient to several formally legitimate modifications of the (models of) energy density distribution, while the second is not. On the other hand, it seems peculiar that this integral definition appears to capture a transport contribution, which may be called of convective nature, which is altogether missed by the former definition. In an attempt to connect the dots, we propose that the locally integrated flux divided by the inter-particle distance is a good measure of the energy flux. We show that the proposition can be explicitly constructed analytically by an ad hoc modification of the chosen model for the energy density.

An Improved Frequency Dead Zone with Feed-Forward Control for Hydropower Units: Performance Evaluation of Primary Frequency Control

Due to the integration of more intermittent renewable energy into the power grid, the demand for frequency control in power systems has been on the rise, and primary frequency control of hydropower units plays an increasingly important role. This paper proposes an improved frequency dead zone with feed-forward control. The aim is to achieve a comprehensive performance of regulating rapidity, an assessment of integral quantity of electricity, and the wear and tear of hydropower units during primary frequency control, especially the unqualified performance of integral quantity of electricity assessment under frequency fluctuations with small amplitude. Based on a real hydropower plant with Kaplan units in China, this paper establishes the simulation model, which is verified by comparing experimental results. After that, based on the simulation of real power grid frequency fluctuations and a real hydropower plant case, the dynamic process of primary frequency control is evaluated for three aspects, which include speed, integral quantity of electricity, and wear and tear. The evaluation also includes the implementations of the three types of dead zones: common frequency dead zone, the enhanced frequency dead zone, and the improved frequency dead zone. The results of the study show that the improved frequency dead zone with feed-forward control increases the active power output under small frequency fluctuations. Additionally, it alleviates the wear and tear problem of the enhanced frequency dead zone in the premise of guaranteeing regulation speed and integral quantity of electricity. Therefore, the improved frequency dead zone proposed in this paper can improve the economic benefit of hydropower plants and reduce their maintenance cost. Accordingly, it has been successfully implemented in practical hydropower plants in China.

Assessment of Factors Affecting the Final Value of «Volume Loss» by TBM Tunneling

This paper covers design diagrams and algorithms for determining the strain state of soil mass in case of its underworking. When tunnels are constructed in restrained urban conditions peculiar to megapolises, there is an acute problem related to the assessment of their influence on the existing above-and underground facilities. The strains of buildings and structures that occur as a result of underground construction work may have an impact on the operation reliability of these facilities. Russian regulatory documents in the area of underground urban construction strictly govern the basic parameters of the subsidence trough, such as maximum vertical subsidence, curvature, inclination, etc., for most of the existing underworked structures. Such facilities include both buildings and structures of various purposes above ground and different types of utilities (roads and railways, pipelines, cable lines, etc.). The method described in the paper offers the use of an integral quantity of "volume loss" when tunneling is performed by tunnel-boring machines. The "volume loss" term shall be understood to mean the distance between tunnel lining and soil mass, which initially occurs due to the difference between rotor diameter and lining outside diameter. There are also a number of other technology factors affecting the increase of this parameter, and their quantitative assessment is given in this paper. The method proposed in this paper makes it possible to promptly assess the impact of tunneling operations on the existing underworked structures with account of basic influencing factors.

Simplification of State Transition Diagrams in Average Unavailability Analysis by Using Generalized Perturbation Theory

Safety analysis studies in nuclear engineering, more specifically system reliability, usually handle a great number of components, so that computational difficulties may arise. To face the problem of many component systems a method for simplifying the state transition diagram in Markovian reliability analyses has been proposed, using the edges which can be cut, since these latter have a smaller influence on system failure probability. In order to extend the application of GPT (Generalized Perturbation Theory), this work uses GPT formalism to reduce the number of states in a transition diagram, not considering the state probability as the integral quantity of interest, but the mean system unavailability instead. Therefore, after simplifying the original diagram, the mean unavailability for the new system was calculated and the results were very close to those of the original diagram integral quantity (giving a relative error of about 2%), showing that the proposed simplification is quite reasonable and simple to apply.

Stochastic Space–Time Disaggregation of Rainfall into DSD fields

A stochastic method to disaggregate rain rate fields into drop size distribution (DSD) fields is proposed. It is based on a previously presented DSD simulator that has been modified to take into account prescribed block-averaged rain rate values at a coarser scale. The integral quantity used to drive the disaggregation process can be the rain rate, the radar reflectivity, or any variable directly related to the DSD. The proposed method is illustrated and qualitatively evaluated using radar rain rate data provided by MeteoSwiss for two rain events of very contrasted type (stratiform versus convective). The evaluation shows that both types of rainfall are correctly disaggregated, although the general agreement in terms of rain rate distributions, intermittency, and space–time structures is much better for the stratiform case. Possible extensions and generalizations of the technique (e.g., using radar reflectivities at two different frequencies or polarizations to drive the disaggregation process) are discussed at the end of the paper.

Identification for Chaos and Subharmonic Responses in Coupled Forced Duffing's Oscillators

ABSTRACTIn this paper, a response integral quantity method is proposed. This technique provides a quantitative characterization of system responses and can assist the role of the traditional stroboscopic technique (Poincaré section method) in observing bifurcations and chaos of the nonlinear oscillators. We numerically analyze and identify the chaos and subharmonic responses in the forced coupled Duffing's oscillators in which we find that chaotic behaviors and high-order subharmonic responses exist. Due to the signal response contamination of system, it is difficult to identify the high-order responses of the subharmonic motion because of the sampling points on Poincaré map being very close to each other. Even the system responses are subject to misjudgments. The simulation results, however, show that the highorder subharmonic and chaotic responses and their bifurcations can be observed effectively.

GLOBAL TANGENCY AND TRANSVERSALITY OF PERIODIC FLOWS AND CHAOS IN A PERIODICALLY FORCED, DAMPED DUFFING OSCILLATOR

This paper presents how to apply a newly developed general theory for the global transversality and tangency of flows in n-dimensional nonlinear dynamical systems to a 2-D nonlinear dynamical system (i.e. a periodically forced, damped Duffing oscillator). The global tangency and transversality of the periodic and chaotic motions to the separatrix for such a nonlinear system are discussed to help us understand the complexity of chaos in nonlinear dynamical systems. This paper presents the concept that the global transversality and tangency to the separatrix are independent of the Melnikov function (or the energy increment). Chaos in nonlinear dynamical systems makes the exact energy increment quantity to be chaotic no matter if the nonlinear dynamical systems have separatrices or not. The simple zero of the Melnikov function cannot be used to simply determine the existence of chaos in nonlinear dynamical systems. Through this paper, the expectation is that, from now on, one can use the alternative aspect to look into the complexity of chaos in nonlinear dynamical systems. Therefore, in this paper, the analytical conditions for global transversality and tangency of 2-D nonlinear dynamical systems are presented. The first integral quantity increment (i.e. the energy increment) for a certain time interval is achieved for periodic flows and chaos in the 2-D nonlinear dynamical systems. Under the perturbation assumptions and convergent conditions, the Melnikov function is recovered from the first integral quantity increment. A periodically forced, damped Duffing oscillator with a separatrix is investigated as a sampled problem. The corresponding analytical conditions for the global transversality and tangency to the separatrix are obtained and verified by numerical simulations. The switching planes and the corresponding local and global mappings are defined on the separatrix. The mapping structures are developed for local and global periodic flows passing through the separatrix. The mapping structures of global chaos in the damped Duffing oscillator are also discussed. Bifurcation scenarios of the damped Duffing oscillator are presented through the traditional Poincaré mapping section and the switching planes. The first integral quantity increment (i.e. L-function) is presented to observe the periodicity of flows. In addition, the global tangency of periodic flows in such an oscillator is measured by the G-function and G(1)-function, and is verified by numerical simulations. The first integral quantity increment of periodic flows is zero for their complete periodic cycles. Numerical simulations of chaos in such a Duffing oscillator are carried out through the Poincaré mapping sections. The conservative energy distribution, G-function and L-function along the displacement of Poincaré mapping points are presented to observe the complexity of chaos. The first integral quantity increment (i.e. L-function) of chaotic flows at the Poincaré mapping points is nonzero and chaotic. The switching planes of chaos are presented on the separatrix for a better understanding of the global transversality to the separatrix. The switching point distribution on the separatrix is presented and the switching G-function on the separatrix is given to show the global transversality of chaos on the separatrix. The analytical conditions are obtained from the new theory rather than the Melnikov method. The new conditions for the global transversality and tangency are more accurate and independent of the small parameters.