Stochastic programming based coordinated expansion planning of generation,transmission,demand side resources,and energy storage considering the DC transmission system

With the increasing penetration of wind and solar energies,the accompanying uncertainty that propagates in the system places higher requirements on the expansion planning of power systems.A source-grid-load-storage coordinated expansion planning model based on stochastic programming was proposed to suppress the impact of wind and solar energy fluctuations.Multiple types of system components,including demand response service entities,converter stations,DC transmission systems,cascade hydropower stations,and other traditional components,have been extensively modeled.Moreover,energy storage systems are considered to improve the accommodation level of renewable energy and alleviate the influence of intermittence.Demand-response service entities from the load side are used to reduce and move the demand during peak load periods.The uncertainties in wind,solar energy,and loads were simulated using stochastic programming.Finally,the effectiveness of the proposed model is verified through numerical simulations.

A coordinated operation method of wind-PV-hydrogenstorage multi-agent energy system

Wind-photovoltaic(PV)-hydrogen-storage multi-agent energy systems are expected to play an important role in promoting renewable power utilization and decarbonization.In this study,a coordinated operation method was proposed for a wind-PVhydrogen-storage multi-agent energy system.First,a coordinated operation model was formulated for each agent considering peer-to-peer power trading.Second,a coordinated operation interactive framework for a multi-agent energy system was proposed based on the theory of the alternating direction method of multipliers.Third,a distributed interactive algorithm was proposed to protect the privacy of each agent and solve coordinated operation strategies.Finally,the effectiveness of the proposed coordinated operation method was tested on multi-agent energy systems with different structures,and the operational revenues of the wind power,PV,hydrogen,and energy storage agents of the proposed coordinated operation model were improved by approximately 59.19%,233.28%,16.75%,and 145.56%,respectively,compared with the independent operation model.

Curve integral with path independent in orthogonal curvilinear coordinate system

It is explored that the line integral is a path independent in two or three arbitrary dimensional orthogonal curvilinear coordinate systems, which is based on the integral condition with the path independent in two or three dimensional rectangular coordinate systems. Firstly, according to the coordinate transformation, the condition that the line integral is the path independent in the polar coordinate system is obtained easily from the Green's theorem in two-dimensional rectangular coordinate system and the condition is extended to arbitrary two-dimension orthogonal curvilinear coordinates. Secondly, through the coordinate transformation relationship and the area projection method, the Stokes formula in three-dimensional rectangular coordinate system is promoted to the spherical coordinate system and cylindrical coordinate system, and the condition that the line integral is a path independent is obtained. Furthermore, the condition is extended to arbitrary three-dimension orthogonal curvilinear coordinates. Lastly, the conclusions are made.

Generalization of the Second Order Vector Potential Formulation for Arbitrary Non-Orthogonal Curvilinear Coordinates Systems from the Covariant Form of Maxwell's Equations

A great number of semi-analytical models, notably the representation of electromagnetic fields by integral equations are based on the second order vector potential (SOVP) formalism which introduces two scalar potentials in order to obtain analytical expressions of the electromagnetic fields from the two potentials. However, the scalar decomposition is often known for canonical coordinate systems. This paper aims in introducing a specific SOVP formulation dedicated to arbitrary non-orthogonal curvilinear coordinates systems. The electromagnetic field representation which is derived in this paper constitutes the key stone for the development of semi-analytical models for solving some eddy currents moelling problems and electromagnetic radiation problems considering at least two homogeneous media separated by a rough interface. This SOVP formulation is derived from the tensor formalism and Maxwell’s equations written in a non-orthogonal coordinates system adapted to a surface characterized by a 2D arbitrary aperiodic profile.

Explicit structure-preserving geometric particle-in-cell algorithm in curvilinear orthogonal coordinate systems and its applications to whole-device 6D kinetic simulations of tokamak physics

Explicit structure-preserving geometric particle-in-cell(PIC)algorithm in curvilinear orthogonal coordinate systems is developed.The work reported represents a further development of the structure-preserving geometric PIC algorithm achieving the goal of practical applications in magnetic fusion research.The algorithm is constructed by discretizing the field theory for the system of charged particles and electromagnetic field using Whitney forms,discrete exterior calculus,and explicit non-canonical symplectic integration.In addition to the truncated infinitely dimensional symplectic structure,the algorithm preserves exactly many important physical symmetries and conservation laws,such as local energy conservation,gauge symmetry and the corresponding local charge conservation.As a result,the algorithm possesses the long-term accuracy and fidelity required for first-principles-based simulations of the multiscale tokamak physics.The algorithm has been implemented in the Sym PIC code,which is designed for highefficiency massively-parallel PIC simulations in modern clusters.The code has been applied to carry out whole-device 6 D kinetic simulation studies of tokamak physics.A self-consistent kinetic steady state for fusion plasma in the tokamak geometry is numerically found with a predominately diagonal and anisotropic pressure tensor.The state also admits a steady-state subsonic ion flow in the range of 10 km s-1,agreeing with experimental observations and analytical calculations Kinetic ballooning instability in the self-consistent kinetic steady state is simulated.It is shown that high-n ballooning modes have larger growth rates than low-n global modes,and in the nonlinear phase the modes saturate approximately in 5 ion transit times at the 2%level by the E×B flow generated by the instability.These results are consistent with early and recent electromagnetic gyrokinetic simulations.

MULTI-FIGHTER COORDINATED MULTI-TARGET ATTACK SYSTEM

A definition of self-determined priority is used in airfight decision firstly. A scheme of grouping the whole fighters is introduced, and the principle of target assignment and fire control is designed. Based on the neutral network, the decision algorithm is derived and the whole coordinated decision system is simulated. Secondly an algorithm for missile-attacking area is described and its calculational result is obtained under initial conditions. Then the attacking of missile is realized by the proportion guidance. Finally, a multi-target attack system. The system includes airfight decision, estimation of missile attack area and calculation of missile attack procedure. A digital simulation demonstrates that the airfight decision algorithm is correct. The methods have important reference values for the study of fire control system of the fourth generation fighter.

Combined Method of Datum Transformation Between Different Coordinate Systems

The similarity transformation model between different coordinate systems is not accurate enough to describe the discrepancy of them.Therefore,the coordinate transformation from the coordinate frame with poor accuracy to that with high accuracy cannot guarantee a high precision of transformation.In this paper,a combined method of similarity transformation and regressive approximating is presented.The local error accumulation and distortion are taken into consideration and the precision of coordinate system is improved by using the recommended method

Measurement of Coordinate Parameter by Multi-baseline Digital Close-range Photogrammetry System and Data Analysis for Jujube

[Objective] The aim was to explore the measurement of coordinate parameter by multi-baseline digital close-range photogrammetry system.[Method] The 3-dimensional coordinate of 8-year-old Jujube was measured by using Lensphoto multi-baseline digital close-range photogrammetry system,and through comparing with measured data of Total Station,the error and accuracy of photogrammetry data were analyzed.[Result] The absolute error of X,Y and Z coordinate was 0-0.014,0-0.018 and 0-0.004 m respectively,and the relative error of X,Y and Z coordinate was less than 0.145%.The significance test of pairs for the photogrammetry data and measured data of Total Station indicated that the space coordinate data of stumpage were accurately measured by using the multi-baseline digital close-range photogrammetry method,and the photogrammetry data meet the need of space coordinate measurement for virtual plant growth simulation.[Conclusion] This study had provided theoretical basis for the growth measurement of virtual plant growth simulation.

Applied Mode Coordinate to Solve Dynamic Responses of Antenna Mechanic System

Based on the Lagrange s equation and the finite element method, this paper establishes the dynamic equation of a radar antenna mechanic system which is a high accuracy system and consists of two flexible bodies. Mode coordinates are used to reduce the orders of equation. Finally, the calculation method and engineering example are given when the rotational velocity of antenna is invariable and the wind velocity is 25?m/s. The error of antenna mechanic system can be estimated using the calculation results.

Application of a compound controller based on fuzzy control and support vector machine to ship's boiler-turbine coordinated control system

Multivariables, strong coupling, nonlinearity, and large delays characterize the boiler-turbine coordinated control systems for ship power equipment. To better deal with these conditions, a compound control strategy based on a support vector machine （SVM） with inverse identification was proposed and applied to research simulating coordinated control systems. This method combines SVM inverse control and fuzzy control, taking advantage of the merits of SVM inverse controls which can be designed easily and have high reliability, and those of fuzzy controls, which respond rapidly and have good anti-jamming capability and robustness. It ensures the controller can be controlled with near instantaneous adjustments to maintain a steady state, even if the SVM is not trained well. The simulation results show that the control quality of this fuzzy-SVM compound control algorithm is high, with good performance in dynamic response speed, static stability, restraint of overshoot, and robustness.

Lie Symmetries and Conserved Quantities of Holonomic Systems with Remainder Coordinates

Aim To study the Lie symmetries and the consered quantities of the holonomic systems with remainder coordinates. Methods Using the invariance of the ordinary differential equations under the infinitesimal transformations to establish the determining equations and the restriction equations of the Lie symmetries of the systems. Results and Conclusion the structure equation and the form of conserved quantities were obtained. An example was given to illustrate the application of the result.

Computation of strain and rotation tensor as well as their uncertainties for small arrays in spherical coordinate system

Based on Taylor series expansion and strain components expressions of elastic mechanics, we derive formulae of strain and rotation tensor for small arrays in spherical coordinates system. By linearization process of the formulae, we also derive expressions of strain components and Euler vector uncertainties respectively for subnets using the law of error propagation. Taking GPS velocity field in Sichuan-Yunnan area as an example, we compute dilation rate and maximum shear strain rate field using the above procedure, and their characteristics are preliminarily car- ried on. Limits of the strain model for small array are also discussed. We make detailed explanations on small array method and the choice of small arrays. How to set weights of GPS observations are further discussed. Moreover relationship between strain and radius of GPS subnets is also analyzed.

Numerical Modeling of the Hyperbolic Mild-Slope Equation in Curvilinear Coordinates

The mild-slope equation is familiar to coastal engineers as it can effectively describe wave propagation in nearshore regions. However, its computational method in Cartesian coordinates often renders the model inaccurate in areas with irregular shorelines, such as estuaries and harbors. Based on the hyperbolic mild-slope equation in Cartesian coordinates, the numerical model in orthogonal curvilinear coordinates is developed. The transformed model is discretized by the finite difference method and solved by the ADI method with space-staggered grids. The numerical predictions in curvilinear co- ordinates show good agreemenl with the data obtained in three typical physical expedments, which demonstrates that the present model can be used to simulate wave propagation, for normal incidence and oblique incidence, in domains with complicated topography and boundary conditions.

Numerical Simulation of Wave-Induced Currents Combined with Parabolic Mild-Slope Equation in Curvilinear Coordinates

Researches on breaking-induced currents by waves are summarized firstly in this paper. Then, a combined numerical model in orthogonal curvilinear coordinates is presented to simulate wave-induced current in areas with curved boundary or irregular coastline. The proposed wave-induced current model includes a nearshore current module established through orthogonal curvilinear transformation form of shallow water equations and a wave module based on the curvilinear parabolic approximation wave equation. The wave module actually serves as the driving force to provide the current module with required radiation stresses. The Crank-Nicolson finite difference scheme and the alternating directions implicit method are used to solve the wave and current module, respectively. The established surf zone currents model is validated by two numerical experiments about longshore currents and rip currents in basins with rip channel and breakwater. The numerical results are compared with the measured data and published numerical results.

3D Numerical Simulation of Overbank Flow in Non-Orthogonal Curvilinear Coordinates

The velocity field in meandering compound channels with overhank flow is highly three dimensional. To date, its features have been investigated experimentally and little research has been undertaken to investigate the feasibility of reproducing these velocity fields with computer models. If computer modeling were to prove successful in this context, it could become a useful prediction technique and research tool to enhance our understanding of natural river dynamics. A 3-D k-E turbulence hydrodynamic model in curvilinear coordinates is established to simulate the overhank flow. The bodyfitted coordinate is adopted in the horizontal plane, the part grid is adopted in the vertical direction, and the wall-function method is employed to simulate the bed resistance. The model is applied to the simulation of the meandering channel with straight flood plain banks, and the main velocities and secondary velocities for both the longitudinal and cross sections are presented. Comparison and analysis show that the results of simulation are fit to reflect the results of experiment. These results show the application value of the model to 3D overhank flow.

A Numerical Model of Nonlinear Wave Propagation in Curvilinear Coordinates

For the simulation of the nonlinear wave propagation in coastal areas with complex boundaries, a numerical model is developed in curvilinear coordinates. In the model, the Boussinesq-type equations including the dissipation terms are em- ployed as the governing equations. In the present model, the dependent variables of the transformed equations are the free surface elevation and the utility velocity variables, instead of the usual primitive velocity variables. The introduction of utility velocity variables which are the products of the contravariant components of the velocity vector and the Jacobi ma- trix can make the transformed equations relatively concise, the treatment of lateral boundary conditions easier and the de- velopment of the program simpler. The predictor-corrector method and five-point finite-difference scheme are employed to discretize the time derivatives and the spatial ones, respectively. The numerical model is tested for three cases. It is found that the numerical results are in good agreement with the analytical results and experimental data.

SPACE-TIME CONSERVATION SCHEME IN NONORTHOGONAL CURVILINEAR COORDINATES

A scheme of space time conservation (STC) based on the method of space time conservation element and solution element (CE/SE) is represented in a nonorthogonal curvilinear coordinate system. The corresponding initial and boundary conditions are discussed. It is seen that in the nonorthogonal coordinates the scheme maintains the advantages of the STC method, and is noted for its simple structure, clear physical meaning, rapid calculation and high accuracy. It is easy to extend to the multidimensional flow. The numerical results for a 2D Euler equation show good agreement with those from other computational methods and the experiment.

Earth crust vertical movements according to ITRF2000, ITRF2005,ITRF2008 and ITRF2014 coordinate systems and their comparing analysis

The analysis of Earth’s crust movement vertical velocities was made both for separate regions, and averaged on regions. As input data coordinates and velocities of earth crust points, obtained in International Coordinate Systems ITRF2000, ITRF2005,ITRF2008 on the base of processing radio interferometric(VLBI), laser(SLR), Doppler(DORIS) and GPS observations was used. For the purpose of global analysis all input velocity values were averaged in the x trapezoids. For filling trapezoids the spherical function expansion to N=36 was made. Expansion harmonic coefficients allowed determine the global characteristics of earth crust movements both for all Earth, and for separate hemispheres, polar and equatorial regions, continents and oceans. It appears, that polar regions were risen, and equatorial ones were lowered, that can indicate the modern Earth oblateness reduction. The constructed maps of vertical velocities were compared with obtained by us map of earth crust strain distribution. It is appeared, that regions of modern earth surface rising(Fennoscandia, Canada, Antarctica) coincide with regions of vertical extension strain, and the lowering regions-with compression regions. Simultaneously with the determination of harmonious coefficients the mean-square error of approximation for expansion of power n=1 N and power dispersion were determined. Whereas the results converge badly and dispersion increased with the n grows, hence we can concludes, that vertical movements do not characterized global earth crust movement and denotes the unrelated character of these movement. Seemingly, the main cause of such movement origin is the local seismic events(earthquake, volcanic eruption and so on). It confirms by our conclusions about correspondence of vertical strain maximal gradient(and therefore vertical velocities) map of the earthquake distribution. In work the detailed analysis of obtained results for separate Earth’s regions was made.

Sensitivity Analysis Approach to Multibody Systems Described by Natural Coordinates

The classical natural coordinate modeling method which removes the Euler angles and Euler parameters from the governing equations is particularly suitable for the sensitivity analysis and optimization of multibody systems. However, the formulation has so many principles in choosing the generalized coordinates that it hinders the implementation of modeling automation, A first order direct sensitivity analysis approach to multibody systems formulated with novel natural coordinates is presented. Firstly, a new selection method for natural coordinate is developed. The method introduces 12 coordinates to describe the position and orientation of a spatial object. On the basis of the proposed natural coordinates, rigid constraint conditions, the basic constraint elements as well as the initial conditions for the governing equations are derived. Considering the characteristics of the governing equations, the newly proposed generalized-ct integration method is used and the corresponding algorithm flowchart is discussed. The objective function, the detailed analysis process of first order direct sensitivity analysis and related solving strategy are provided based on the previous modeling system Finally, in order to verify the validity and accuracy of the method presented, the sensitivity analysis of a planar spinner-slider mechanism and a spatial crank-slider mechanism are conducted. The test results agree well with that of the finite difference method, and the maximum absolute deviation of the results is less than 3%. The proposed approach is not only convenient for automatic modeling, but also helpful for the reduction of the complexity of sensitivity analysis, which provides a practical and effective way to obtain sensitivity for the optimization problems of multibody systems.

Simulation of Surface Wave with Large Eddy Simulation in σ-Coordinate System

A three dimensional numerical model in the σ coordinate system is developed to study the problem of waves. Turbulence effects are modeled by a subgrid scale (SGS) model with the concept of large eddy simulation (LES). The σ coordinate transformation is introduced to map the irregular physical domain of the wavy free surface and uneven bottom onto the regular computational domain of the shape of rectangular prism. The operator splitting method, which splits the solution procedure into the advection, diffusion, and propagation steps, is used to solve the modified Navier Stokes Equation. The model is used to simulate the propagation of solitary wave and wave passing over a submerged breakwater. Numerical results are compared with available analytical solutions and experimental data in terms of velocity profiles, free surface displacement, and energy conservation. Good agreement is obtained. The method is proved to be of high accuracy and efficiency in simulating surface wave propagation and wave structure interaction. It is suitable for the large and irregular physical domain, and requiring the non uniform grid system. The present work provides a foundation for further studies of random waves, wave structure interaction, wave discharge interaction, etc.