Multi-Time Scale Operation and Simulation Strategy of the Park Based on Model Predictive Control

Due to the impact of source-load prediction power errors and uncertainties,the actual operation of the park will have a wide range of fluctuations compared with the expected state,resulting in its inability to achieve the expected economy.This paper constructs an operating simulation model of the park power grid operation considering demand response and proposes a multi-time scale operating simulation method that combines day-ahead optimization and model predictive control(MPC).In the day-ahead stage,an operating simulation plan that comprehensively considers the user’s side comfort and operating costs is proposed with a long-term time scale of 15 min.In order to cope with power fluctuations of photovoltaic,wind turbine and conventional load,MPC is used to track and roll correct the day-ahead operating simulation plan in the intra-day stage to meet the actual operating operation status of the park.Finally,the validity and economy of the operating simulation strategy are verified through the analysis of arithmetic examples.

Establishment of an astronomical time scale for the Shizigou Formation in the Qaidam Basin,Inner Asia and orbital forced evolution of lakes during The Pliocene

The Qaidam Basin,as the largest inland basin within the Tibetan Plateau,has accumulated more than 10,000 m of Cenozoic continental sediments.It serves as a crucial research area for documenting Cenozoic climate changes and plateau uplift processes in the Asian interior.Additionally,the basin holds vast reserves of oil and gas resources,making high-resolution drilling data invaluable for studying paleoclimate.In this study,the longsequence lacustrine deposits of JS1 drill core across the Shizigou Formation in the Yiliping Depression at the western center of the basin were studied,aiming to establish an astronomical timescale for the Shizigou Formation and investigate the characteristics of paleoclimatic changes during the late Miocene to the Pliocene for the Asian interior.The analysis was carried out using high-resolution natural gamma ray(GR)data sequences,employing techniques such as spectral analysis,filtering,and wavelet analysis in cyclostratigraphy.The results indicated the presence of a stable Milankovitch orbital signal was perfectly recorded in the Shizigou Formation,primarily influenced by eccentricity cycles,with weaker obliquity and precession cycles.Using the stable and continuous 405 ka eccentricity cycle in astronomical tuning,a"floating"astronomical timescale with a duration of 6.1 Ma for the Yiliping depression's Shizigou Formation has been established.With reference to previously established stratigraphic age anchor points,an absolute astronomical timescale(2.5–8.6 Ma)has been ultimately provided for the Shizigou Formation.Simultaneously,a clear 100 ka short eccentricity cycle record has been identified during the Pliocene(5.3–2.5 Ma),which corresponds in time with the aridification within the basin during this Pliocene period.In addition,a comparison of the Pliocene natural gamma ray curve of the Qaidam Basin with global ice volume variations indicated that the basin's aridification was influenced by global cooling,with eccentricity-modulated precession cycles controlling solar radiation and subsequently affecting the evolution of lakes in the arid region of Inner Asia.

A step to the decentralized real-time timekeeping network

The composite time scale(CTS) provides an accurate and stable time-frequency reference for modern science and technology. Conventional CTS always features a centralized network topology, which means that the CTS is accompanied by a local master clock. This largely restricts the stability and reliability of the CTS. We simulate the restriction and analyze the influence of the master clock on the CTS. It proves that the CTS's long-term stability is also positively related to that of the master clock, until the region dominated by the frequency drift of the H-maser(averaging time longer than ~10~5s).Aiming at this restriction, a real-time clock network is utilized. Based on the network, a real-time CTS referenced by a stable remote master clock is achieved. The experiment comparing two real-time CTSs referenced by a local and a remote master clock respectively reveals that under open-loop steering, the stability of the CTS is improved by referencing to a remote and more stable master clock instead of a local and less stable master clock. In this way, with the help of the proposed scheme, the CTS can be referenced to the most stable master clock within the network in real time, no matter whether it is local or remote, making democratic polycentric timekeeping possible.

Accelerated Primal-Dual Projection Neurodynamic Approach With Time Scaling for Linear and Set Constrained Convex Optimization Problems

The Nesterov accelerated dynamical approach serves as an essential tool for addressing convex optimization problems with accelerated convergence rates.Most previous studies in this field have primarily concentrated on unconstrained smooth con-vex optimization problems.In this paper,on the basis of primal-dual dynamical approach,Nesterov accelerated dynamical approach,projection operator and directional gradient,we present two accelerated primal-dual projection neurodynamic approaches with time scaling to address convex optimization problems with smooth and nonsmooth objective functions subject to linear and set constraints,which consist of a second-order ODE(ordinary differential equation)or differential conclusion system for the primal variables and a first-order ODE for the dual vari-ables.By satisfying specific conditions for time scaling,we demonstrate that the proposed approaches have a faster conver-gence rate.This only requires assuming convexity of the objective function.We validate the effectiveness of our proposed two accel-erated primal-dual projection neurodynamic approaches through numerical experiments.

A CNN-Based Single-Stage Occlusion Real-Time Target Detection Method

Aiming at the problem of low accuracy of traditional target detection methods for target detection in endoscopes in substation environments, a CNN-based real-time detection method for masked targets is proposed. The method adopts the overall design of backbone network, detection network and algorithmic parameter optimisation method, completes the model training on the self-constructed occlusion target dataset, and adopts the multi-scale perception method for target detection. The HNM algorithm is used to screen positive and negative samples during the training process, and the NMS algorithm is used to post-process the prediction results during the detection process to improve the detection efficiency. After experimental validation, the obtained model has the multi-class average predicted value (mAP) of the dataset. It has general advantages over traditional target detection methods. The detection time of a single target on FDDB dataset is 39 ms, which can meet the need of real-time target detection. In addition, the project team has successfully deployed the method into substations and put it into use in many places in Beijing, which is important for achieving the anomaly of occlusion target detection.

Noether symmetry and conserved quantity for dynamical system with non-standard Lagrangians on time scales

This paper focuses on studying the Noether symmetry and the conserved quantity with non-standard Lagrangians, namely exponential Lagrangians and power-law Lagrangians on time scales. Firstly, for each case, the Hamilton prin- ciple based on the action with non-standard Lagrangians on time scales is established, with which the corresponding Euler-Lagrange equation is given. Secondly, according to the invariance of the Hamilton action under the infinitesimal transformation, the Noether theorem for the dynamical system with non-standard Lagrangians on time scales is established. The proof of the theorem consists of two steps. First, it is proved under the infinitesimal transformations of a special one-parameter group without transforming time. Second, utilizing the technique of time-re-parameterization, the Noether theorem in a general form is obtained. The Noether-type conserved quantities with non-standard Lagrangians in both clas- sical and discrete cases are given. Finally, an example in Friedmann-Robertson-Walker spacetime and an example about second order Duffing equation are given to illustrate the application of the results.

Small-time scale network traffic prediction based on a local support vector machine regression model

In this paper we apply the nonlinear time series analysis method to small-time scale traffic measurement data. The prediction-based method is used to determine the embedding dimension of the traffic data. Based on the reconstructed phase space, the local support vector machine prediction method is used to predict the traffic measurement data, and the BIC-based neighbouring point selection method is used to choose the number of the nearest neighbouring points for the local support vector machine regression model. The experimental results show that the local support vector machine prediction method whose neighbouring points are optimized can effectively predict the small-time scale traffic measurement data and can reproduce the statistical features of real traffic measurements.

OSCILLATION FOR NONAUTONOMOUS NEUTRAL DYNAMIC DELAY EQUATIONS ON TIME SCALES

The article is concerned with oscillation of nonautonomous neutral dynamic delay equations on time scales. Sufficient conditions are established for the existence of bounded positive solutions and for oscillation of all solutions of this equation. Some results extend known results for difference equations when the time scale is the set Z^＋ of positive integers and for differential equations when the time scale is the set IR of real numbers.

Generalized Chaplygin equations for nonholonomic systems on time scales

The generalized Chaplygin equations for nonholonomic systems on time scales are proposed and studied. The Hamil- ton principle for nonholonomic systems on time scales is established, and the corresponding generalized Chaplygin equa- tions are deduced. The reduced Chaplygin equations are also presented. Two special cases of the generalized Chaplygin equations on time scales, where the time scales are equal to the set of real numbers and the integer set, are discussed. Finally, several examples are given to illustrate the application of the results.

A Floating Astronomical Time Scale for the Early Late Cretaceous Continental Strata in the Songliao Basin, Northeastern China

A continuous terrestrial succession was recovered from the Songke-2(SK-2)borehole in the Songliao Basin,Northeastern China.This borehole provides a unique material for further research on the continental paleoclimate during Cretaceous greenhouse period,following a series of achievements of the Songke-1(SK-1)core.In this study,thorium(Th)logging data were chosen as a paleoclimate proxy to conduct a detailed cyclostratigraphic analysis.The Th series varies quasi-periodically;power spectra and evolutionary fast Fourier transformation(FFT)analysis reveal significant cycles in the Quantou(K2 q),Qingshankou(K2 qn),Yaojia(K2 y)and Nenjiang(K2 n)formations.The ratio of cycle wavelengths in these stratigraphic units is approximately 20:5:2:1,corresponding to long orbital eccentricity(405 kyr),short orbital eccentricity(100 kyr),obliquity(37 kyr),and precession cycles(22.5 kyr and 18.4 kyr).The durations of the K2 n,K2 y,K2 qn and K2 q are estimated as 6.97,1.83,5.30 and 4.52 Myr,respectively,based on the constructed^18.62 Myr"floating"astronomical time scale(ATS).Comparison of the durations between the SK-1 s and SK-2 boreholes exhibits a slight difference of 0.06 Myr and 0.459 Myr for K2 qn and K2 y.Nevertheless,our ATS of K2 n supports the chronostratigraphic frame constructed by the CA-ID-TIMS data of the SK-1 s borehole.This new"floating"ATS provides precise numerical ages for stratigraphic boundaries,biozones and geological events in the Songliao Basin,and can serve as a basis for correlation of strata and events between marine and terrestrial systems.

Oscillation of Second-order Nonlinear Dynamic Equation on Time Scales

The oscillation for a class of second order nonlinear variable delay dynamic equation on time scales with nonlinear neutral term and damping term was discussed in this article. By using the generalized Riccati technique, integral averaging technique and the time scales theory, some new sufficient conditions for oscillation of the equation are proposed. These results generalize and extend many known results for second order dynamic equations. Some examples are given to illustrate the main results of this article.

Methods of reduction for Lagrange systems on time scales with nabla derivatives

The Routh and Whittaker methods of reduction for Lagrange system on time scales with nabla derivatives are studied.The equations of motion for Lagrange system on time scales are established, and their cyclic integrals and generalized energy integrals are given. The Routh functions and Whittaker functions of Lagrange system are constructed, and the order of differential equations of motion for the system are reduced by using the cyclic integrals or the generalized energy integrals with nabla derivatives. The results show that the reduced Routh equations and Whittaker equations hold the form of Lagrnage equations with nabla derivatives. Finally, two examples are given to illustrate the application of the results.

Oscillation of Third-order Delay Dynamic Equations on Time Scales

This paper is concerned with the oscillatory behavior of a class of third-order nonlinear variable delay neutral functional dynamic equations on time scale. By using the generalized Riccati transformation and inequality technique, we establish some new oscillation criteria for the equations. Our results extend and improve some known results, but also unify the oscillation of third-order nonlinear variable delay functional differential equations and functional difference equations with a nonlinear neutral term. Some examples are given to illustrate the importance of our results.

Generalized canonical transformation for second-order Birkhoffian systems on time scales

The theory of time scales,which unifies continuous and discrete analysis,provides a powerful mathematical tool for the study of complex dynamic systems.It enables us to understand more clearly the essential problems of continuous systems and discrete systems as well as other complex systems.In this paper,the theory of generalized canonical transformation for second-order Birkhoffian systems on time scales is proposed and studied,which extends the canonical transformation theory of Hamilton canonical equations.First,the condition of generalized canonical transformation for the second-order Birkhoffian system on time scales is established.Second,based on this condition,six basic forms of generalized canonical transformation for the second-order Birkhoffian system on time scales are given.Also,the relationships between new variables and old variables for each of these cases are derived.In the end,an example is given to show the application of the results.

Bursting oscillations in a hydro-turbine governing system with two time scales

A fast-slow coupled model of the hydro-turbine governing system （HTGS） is established by introducing frequency disturbance in this paper. Based on the proposed model, the performances of two time scales for bursting oscillations in the HTGS are investigated and the effect of periodic excitation of frequency disturbance is analyzed by using the bifurcation diagrams, time waveforms and phase portraits. We find that stability and operational characteristics of the HTGS change with the value of system parameter kd. Furthermore, the comparative analyses for the effect of the bursting oscillations on the system with different amplitudes of the periodic excitation a are carried out. Meanwhile, we obtain that the relative deviation of the mechanical torque mt rises with the increase of a. These methods and results of the study, combined with the performance of two time scales and the fast-slow coupled engineering model, provide some theoretical bases for investigating interesting physical phenomena of the engineering system.

Perturbation to Noether Quasi-Symmetry and Adiabatic Invariants for Nonholonomic Systems on Time Scales

Perturbation to Noether quasi-symmetry and adiabatic invariants for the nonholonomic system on time scales are studied. Firstly, some properties of time scale calculus are reviewed. Secondly, the differential equations of motion for the nonholonomic system on time scales, Noether quasi-symmetry and conserved quantity are given. Thirdly, perturbation to Noether quasi-symmetry and adiabatic invariants, which are the main results of this paper, are investigated. The main results are achieved by two steps, the first step is to obtain adiabatic invariants without transforming the time, and the next is to obtain adiabatic invariants under the infinitesimal transformations of both the time and the coordinates. And in the end, an example is given to illustrate the methods and results.

New Oscillation Criteria of Second-Order Nonlinear Delay Dynamic Equations on Time Scales

By using the generalized Riccati transformation and the integral averaging technique, the paper establishes some new oscillation criteria for the second-order nonlinear delay dynamic equations on time scales. The results in this paper unify the oscillation of the second-order nonlinear delay differential equation and the second-order nonlinear delay difference equation on time scales. The Theorems in this paper are new even in the continuous and the discrete cases.

Astronomical time scale of the Turonian constrained by multiple paleoclimate proxies

One of the clocks that record the Earth history is(quasi-) periodic astronomical cycles.These cycles influence the climate that can be ultimately stored in sedimentary rocks.By cracking these(quasi-) periodic sedimentation signals,high resolution astronomical time scale(ATS) can be obtained.Paleoclimate proxies are widely used to extract astronomical cycles.However different proxies may respond differently to astronomical signals and nonastronomical noises including tectonics,diagenesis,and measurement error among others.Astronomical time scale constructed based on a single proxy where its signal-to-noise ratio is low may have uncertainty that is difficult to evaluate but can be revealed by utilizing other proxies.Here,we test eight astronomical age models using two astrochro no logical methods from four paleoclimate proxies(i.e.,color reflection L~* and b~*,natural gamma radiation,and bulk density) from the Turonian to the Coniacian of the Cretaceous Period at the Demerara Rise in the equatorial Atlantic.The two astrochronological methods are time calibration using long eccentricity bandpass filtering(E1 bandpass) and tracking the long eccentricity from evolutive harmonic analysis(tracking EHA).The statistical mean and standard deviation of four age models from the four proxies are calculated to construct one integrated age model with age uncertainty in each method.Results demonstrate that extracting astronomical signals from multiple paleoclimate proxies is a valid method to estimate age model uncertainties.Anchored at the Cenomanian/Turonian boundary with an age of 93.9 ± 0.15 Ma from biostratigraphy,the ages for CC11/CC12(calcareous nannofossil zones),Turonian/Coniacian(CC12/CC13),CC13/CC14,and Coniacian/Santonian boundaries are 91.25±0.20 Ma,89.87±0.20 Ma,86.36±0.33 Ma,and 86.03±0.32 Ma in E1 bandpass method,compared with 91.17±0.36 Ma,89.74±0.38 Ma,86.13±1.31 Ma,and 85.80±1.33 Ma respectively in tracking EHA method.These results are consistent with previous studies within error and provide a reliable estimation of uncertainties of the ages.

Application of Time Scale to Parameters Tuning of Active Disturbance Rejection Controller for Induction Motor

Active disturbance rejection controller (ADRC) has good performance in induction motor (IM) control system, but controller parameter is difficult to tune. A method of tuning ADRC parameter by time scale is analyzed. The IM time scale is obtained by theoretical analysis. Combining the relations between scale time and ADRC parameters, ADRC parameter tuning in IM vector control based stator flux oriented is obtained. This parameter tuning method is validated by simulations and it provides a new technique for tuning of ADRC parameters of IM.