83 results about "Differential algebraic equation" patented technology

The invention relates to the technical field of hydroelectric generating set fault diagnosis, in particular to a hydroelectric generating set fault diagnosis method and system based on a DdAE (Difference Differential Algebraic Equations) deep learning model. The method and the system are established on the basis of the analysis of the original vibration data of the hydroelectric generating set, adeep learning characteristic extraction method based on a multilayer neural network model is adopted, a complex manual processing and feature extraction process is not required, an ASFA (Aquatic Sciences and Fisheries Abstracts) method based on random search is adopted to carry out the structural parameter adjustment and optimization of the DdAE to achieve a purpose of strategy optimization. A deep denoising automatic encoder model is used for realizing the distributed expression of original data, and reconstruction data subjected to feature extraction is input into a Softmax regression modelto judge the work state and the fault type of the hydroelectric generating set. The analysis of a network experiment result indicates that the method can be effectively applied to the hydroelectric generating set fault diagnosis.

A new method for simulation of general electrical circuits on parallel computing platforms is disclosed. Parallel simulation of general time-domain circuits that are represented by nonlinear / linear differential algebraic equations is accomplished by partitioning them into smaller subcircuits via a novel combination of the companion form representation of the given circuit and an efficient form of node splitting, during Newton Raphson iterations, at any time point. The new invention formulates the interface vectors between partitions, through purely binary vectors, leading to a high degree of parallelism, scalability and reduced computational and communication costs for synchronizing the solutions between various partitions. Parallel platforms considered can be diverse such as (including but not restricted to) multicore CPUs, distributed systems of computers. The new invention also provides for scalable parallel simulation of mixed-domain formulations, such as (including but not restricted to), integrated circuits, electronic packages, PCBs, electromagnetic modules, MEMS and optical components etc.

Provided is a simulation analysis method of the electromechanical transient process of an electrical power system. An electromechanical transient system model of the electrical power system is established, the electromechanical transient of the electrical power system is simulated through network dividing and solving of differential algebraic equations, simulating calculation is performed according to the simulation process, the electromechanical transient of the electrical power system is analyzed through simulation modeling, and therefore stability and safety of the electric power system are guaranteed.

The invention discloses a nuclear power unit steam generator mechanism model building method and a system thereof; the method comprises the following steps: building mechanism models for nuclear powerunit steam generator segments; integrally processing the built segment models; dynamic model structure processing; dynamic model verification, respectively step disturbance for three inputs includingfeed water flow, steam flow and coolant temperature, analyzing to obtain a response curve, determining whether the curve trends is consistent with theory or not, and verifying the model building rationality and accuracy. The method combines segment and lumped parameters to carry out mechanism modeling, uses a special solution aiming at a DAE differential equation in a MATLAB, redistributes ODE resolver quality matrix parameters, and converts the differential algebraic equation into a non-linear state space form, thus realizing differential algebraic equation accurate solving, and finally verifying the accuracy of the built models.

The invention provides a global optimization method for control parameters of a photovoltaic power generation system. The method comprises the following steps: firstly, an established differential-algebraic equation of a photovoltaic plant power generation system is linearized at a steady-state value to obtain a state matrix used for analyzing the small disturbance stability of the system; then the influence on the system small disturbance stability of the system caused by control parameters is analyzed by calculating the eigenvalue, the damping ratio and participation factors of the state matrix to further determine the reasonable variation range of the control parameters; and finally, a quantitative model is introduced to serve as a parameter optimization objective function and the optimization algorithm is utilized to achieve global optimization of the control parameters of the photovoltaic plant power generation system. According to the invention, as for the small disturbance stability of the system, a scientific and reasonable quantification standard is established, and the problem of difficult single optimization due to mutual coupling of the system control parameters is solved. By adopting the method for parameter optimization, global optimization of the control parameters can be realized, and the small disturbance stability of the photovoltaic plant power generation system is improved.

A method and apparatus are provided for solving a set of differential-algebraic equation arising in a circuit simulation is provided. A collocation method is applied to each differential-algebraic equation to discretize the set of differential-algebraic equations. A solution to the set of differential-algebraic equations based on the discretized differential-algebraic equation is then formed.

The invention discloses a small-interference stability rapid analysis method targeted at a large scale electric power system. According to the method, an electric power system network, network parameters, a dynamic element model and model parameters are firstly obtained to form a differential algebraic equation set DAE of a system. Linearization of the DAE is carried out at a system steady state point (x0, y0) to obtain a corresponding linear dynamic system. A system key oscillation modal characteristic value is computed in parallel. Finally, based on the obtained key oscillation modal characteristic value computing result, a damping ratio of the system key oscillation modal is obtained. Through comparison with a damping ratio critical value zeta0, the stability of the system is determined. If a non-stable oscillation modality exists, participation factors of system variables in the modality can be calculated according to the characteristic value obtained through calculating and a characteristic vector thereof so as to further determine dynamic elements strongly related to the non-stable oscillation modality. The method can carry out rapid analysis on small-interference stability of the large scale electric power system so as to satisfy real-time requirements.

Animating strands (such as long hair), for movies, videos, etc. is accomplished using computer graphics by use of differential algebraic equations. Each strand is subject to simulation by defining its motion path, then evaluating dynamic forces acting on the strand. Collision detection with any objects is performed, and collision response forces are evaluated. Then for each frame a differential algebraic equations solver is invoked to simulate the strands.

The invention discloses an operation optimization method of a full flow roll type reverse osmosis seawater desalination system. According to the reverse osmosis mechanism of the seawater desalination system and structure of the whole process, the method establishes an accurate model of whole process reverse osmosis water production and storage process in a strict mechanism mode, the model is described by differential algebraic equations, the water production process and the water supply process are connected, and buffer action of the reservoir and step change of power price are used to reduce overall operating costs. In order to solve the optimized proposition described in a differential algebraic form brought by precise modeling, simultaneous solution technique is employed to solve the optimized proposition. The invention integrally considers a variety of variable parameters influencing factors of the seawater desalination system, a whole process system process model with variable parameters is established, and simultaneous solution technique is used for researching operation optimization of the seawater desalination system, so as to further reduce the operation cost of the seawater desalination system.

The invention discloses a dynamic response analyzing method of an aggregation type tensegrity structure based on a sliding rope unit of a multi-body system. The method comprises the following steps that firstly, a traditional tensegrity structure system is transformed into the multi-body system; secondly, based on a traditional rope unit of the multi-body system, the sliding rope unit of the multi-body system is built; thirdly, a multi-body dynamical system equivalence model of the aggregation type tensegrity structure is built by using the sliding rope unit in the second step; fourthly, a differential algebra equation set of multi-body dynamics is solved so as to get the dynamic response of the aggregation type tensegrity structure. In the dynamic response analyzing method, a new strategyof statics and dynamics analysis of the aggregation type tensegrity structure is provided. Compared with an existing non-linear finite element method, the multi-body dynamics modeling analysis is adopted, the modeling process is simple and universal, the operation is simple, and the modeling process is more suitable for the objective physical motion properties of the tensegrity structure system.

The invention discloses a multi-body-dynamics-equation solving method based on a Bathe integration strategy. The method includes: establishing a corresponding coordinate system in a multi-body dynamics system, and using a relative-coordinate method and a Lagrangian-multiplier method to obtain dynamics equations according to a virtual-power principle; seeking a second derivative of a constraint equation with respect to time to obtain differential-algebraic equations of an index -1, and adding constraint stability terms to form a general form of the dynamics equations with complete constraints;carrying out integration iteration solving on the general form of the dynamics equations with the complete constraints on a time step [t, t+h / 2] to obtain motion parameters of a moment t+h / 2; carryingout integration iteration solving on a time step [t+h / 2, t+h] to obtain the motion parameters of a moment t+h; and carrying out repeated iteration calculation, outputting values of generalized displacement, velocity and acceleration, which are of a system and are changed over time, when calculation time reaches set total simulation time, and thus analyzing motion status of the multi-body process-closed-loop dynamics system in certain time. The method can also achieve better precision in a case of larger integration step length.

The invention discloses a power grid multi-disaster coupling cascading failure analysis method and system, and the method comprises the steps: obtaining a power grid primary parameter and a power gridsecondary parameter, and building a dynamic power grid system model; obtaining external environment data, inputting the external environment data into the dynamic power grid system model, judging whether an external power grid fault event exists, and obtaining a sequence of power grid element faults caused by an external environment in an initial power grid operation mode; establishing a power grid hybrid differential algebraic equation; simulating the dynamic power grid system model according to initial conditions of power grid cascading failure simulation analysis and the established powergrid hybrid differential algebraic equation; during simulation, judging whether the power grid is disconnected according to the admittance matrix Ybus, and if the power grid is not disconnected, continuing operation; judging whether simulation is finished or not; forming a power grid successive fault accident chain; outputting simulation data, and comprehensively evaluating the operation risk of the power grid. According to the method, the influence of multi-disaster coupling cascading faults of relay protection action characteristics on power grid elements can be considered.

Methods for modeling and executing systems in a linearly-implicit formulation of ordinary differential equations (ODEs) or differential algebraic equations (DAEs) are provided in modeling environments. The modeling environments may include block diagram modeling environments, such as time-based block diagram modeling environments. The block diagram modeling environments may include or be coupled to other modeling environments, such as physical modeling environments, so that models created in other modeling environments may also be introduced and solved in the linearly-implicit formulation of ODEs or DAEs in the block diagram modeling environments. Models describing the systems in the linearly-implicit formulation of ODEs or DAEs may also be created directly by users using user-defined blocks in the block diagram modeling environments. The present invention provides solvers for solving the system described in the linearly-implicit formulation of DAEs as well as ODEs in the block diagram modeling environment.

The invention provides a transient response analytic calculation method for a high-voltage direct current power transmission system. The method comprises the following steps that: A, a smoothing reactor, a direct current filter and a direct current power transmission circuit of the high-voltage direct current power transmission system are combined with a voltage current relationship to obtain a differential algebraic equation set of the high-voltage direct current power transmission system under different operation work conditions according to a circuit principle; according to the logic relationship of a control system, a differential equation of the control system is built, and a state equation (shown as the accompanying drawing) of the high-voltage direct current power transmission system is finally formed, wherein the differential algebraic equation set is a constant-coefficient nonhomogeneous linear differential equation set, x is the state quantity under the i-th operation work condition, Ai is a state matrix, Bi is an input matrix, the input u(t) is a rectifier-side and inverter-side three-phase voltage instantaneous expression, and Ci is a component after the addition of the control system; B, through the steady state response calculation on the high-voltage direct current power transmission system, the relationship x(t) of the state quantity of the high-voltage direct current power transmission system varying with time and initial values of each operation quantity of the control system are obtained; C, under the alternate current voltage change, the direct current transient response calculation is carried out; and D, the calculation is completed.

The invention provides a wind power farm tripping method and device for preventing transient voltage instability. The method comprises steps as follows: acquiring a dynamic grid model, and setting a wind power farm model in the dynamic grid model to be a constant-power source so as to obtain a differential-algebraic equation set of the dynamic grid model; performing time-domain simulation on the differential-algebraic equation set under the condition of preset faults to acquire a singular point for terminating the time-domain simulation; acquiring a partial derivative matrix of the differential-algebraic equation set, and calculating the minimum modulus characteristic value of the partial derivative matrix at the singular point and a corresponding left characteristic vector of the partialderivative matrix at the singular point; determining an active balance equation in the left characteristic vector and an element wk corresponding to the active balance equation; performing tripping onthe wind power farm with the maximum element wk modulus value under the condition of preset fault. Control performance parameters of the wind power farms are acquired by the aid of left characteristic vector information at the singular point, the wind power farm with the best control effect is selected for implementation of tripping emergency control, and stability of a grid system is guaranteedwith the minimum tripping price.

The invention discloses a power system transient stability simulation method based on explicit numerical integration, which is suitable for a generator to adopt a second order model, and overcomes the shortcomings of a conventional power system transient stability numerical integration method that the computing quantity is large and the computing speed can not meet the on-line computing requirement of a power system. Compared with the conventional power system transient stability numerical integration method, in the power system transient stability simulation method provided by the invention,the characteristic that analytical expression exists in a second derivative d<2>Delta / dt<2> of a power angle Delta is utilized to deduce the explicit second-order single-step integration formula of the motion equation of a generator rotor, which has the local truncation error of O(h<3>), and the computing quantity is equivalent to the explicit Euler method with the local truncation error of O (h<2>); and the characteristic that when the generator adopts the second order model to describe, only the power angle is required to be obtained during solving the network algebraic equation set is alsoutilized, and the differential-algebraic equation is only required to be solved at one time in each integration step. By adopting the invention, the speed of the transient stability simulation computation based on explicit numerical integration is remarkably increased, and the method is equivalent to half of the improved Euler method.

The invention relates to a multi-body simulation data interaction method for a launch vehicle. The method comprises the following steps: step (1), establishing a finite element model of the launch vehicle; step (2), performing shutdown analysis of the launch vehicle, updating or acquiring the current time sequence; step (3), performing time series analysis for each component of the launch vehicle and acquiring the status of each component of the launch vehicle through the time sequence and a preset offset value; step (4), configuring status parameters for each component of the launch vehicle, establishing interactive data cards between various components, and filling the interactive data cards with output parameters of the various components under the current status; and step (5), using a Lagrange equation of the first kind to discretize the finite element model established in the step (1) and external forces generated by the various components in the step (4) into differential-algebraic equations, solving the equations, and obtaining the displacement and load of each node in the finite element model of the launch vehicle. The multi-body simulation data interaction method for the launch vehicle provided by the invention realizes the general dynamics simulation of the launch vehicle, and realizes the calculation of the flight trajectory, attitude and load of the launch vehicle.

The invention discloses a power system transient stability simulation method based on network node numbering optimization. A sparse vector technology is widely applied to power system calculation. However, existing network node numbering methods applied to sparse vectors aim to achieve the purpose that the average forward and backward substitution calculation amount of all nodes is the smallest, and the characteristic that forward and backward substitution only needs to be conducted on active nodes during transient stability simulation is not taken into consideration. According to the power system transient stability simulation method, the characteristic that the sparse structure of an independent vector of a network algebraic equation and the sparser structure of a solution vector are identical and decided during transient stability simulation is fully considered, the network nodes are divided into active nodes and passive nodes, the out-degrees of the nodes, the number of active precursor nodes and the number of the precursor nodes are fully considered, the network nodes are numbered, under the condition that the number of newly increased elements of a factor table is small, the average path length of the active nodes is made the smallest, and no requirement for the path tree lengths of the passive nodes exists. By the adoption of the power system transient stability simulation method, the calculation amount of solving a differential algebra equation set during transient stability simulation of a power system can be remarkably reduced.

An example method of simplifying a system expressed as differential algebraic equations includes transforming the differential algebraic equations into Hessenberg form, the Hessenberg form including algebraic equations and differential equations, using the algebraic equations to express a constraint manifold, and using a combination of differentiation and projections onto the normal and tangential spaces of the constraint manifold to simplify the differential equations.

A computer-implemented method computes the steady-state and control voltage of a voltage controlled oscillator, given a known frequency or a known period of oscillation of the voltage controlled oscillator. Differential algebraic equations representative of the voltage controlled oscillator are generated, where the differential algebraic equations includes a known period or frequency of oscillation and an unknown control voltage of the voltage controlled oscillator. The differential algebraic equations are modified using a finite difference method, a shooting method, or a harmonic balance method, to obtain a set of matrix equations corresponding to the differential algebraic equations. A solution to the matrix equations is obtained using a Krylov subspace method, using a preconditioner for the Krylov subspace method that is derived from a Jacobian matrix corresponding to the matrix equations, where the solution includes the control voltage of the voltage controlled oscillator in steady state.

The invention discloses a power system transient stability simulation method based on multiple sparse vector road sets. In power system transient stability calculation, the sparse vector technology of the sparse structure of network algebraic equation independent vectors and solution vectors is widely applied. In the existing sparse vector technology, close attention is only paid on the high sparsity of the network algebraic equation independent vectors and the solution vectors, an active node road set is formed to conduct solving, and the characteristics that different solution vectors are needed in different stages of iteration solving of the network algebraic equation in the transient stability calculation process are not taken into consideration. According to the power system transient stability simulation method, the characteristics of active nodes in the network are taken into full consideration, the active nodes are divided into two types, three different sparse vector road sets are formed, different sparse vector road sets are adopted in different steps in the solving process, and thus unnecessary calculation is further avoided. By means of the power system transient stability simulation method, the calculated amount of solving the differential and algebraic equation can be obviously reduced in the power system transient stability simulation.

The invention belongs to the technical field of non-imaging optical lenses, and particularly relates to a total internal reflection lens design method for custom lighting. According to the method, based on a Snell law and an edge light theory, in combination with the law of conservation of energy, a total internal reflection aspheric mathematical model and a transmission aspheric mathematical model are established, two sets of differential algebraic equations are obtained to represent contour curves of two aspheric surfaces, and aspheric surface type data are obtained through solving; an irradiance distribution problem of customized light spots is converted into a free-form surface solving problem, a group of nonlinear equations is established, and a lens boundary free-form surface contouris obtained by solving the equations; and the aspheric surface and the free-form surface are combined into a lens by using a software tool. The optical device designed by the invention has good lightdistribution performance, can customize the shape of the illumination light spots, is good in irradiation uniformity, has a relatively high energy utilization rate, and overcomes a problem that a traditional total internal reflection lens cannot generate a customized shape and high-efficiency uniform illumination light spots on a target surface.

The invention discloses a method for carrying out modeling on an information physical fusion system by using AADL-Modelica. An information system and a physical system of the information physical fusion system are respectively modeled by using the AADL and the Modelica. Aiming at the problem that AADL cannot describe inter-state probability migration and inter-component detailed communication, a probability behavior attachment is provided. As a supplement of the AADL, the Modelica language uses a differential algebraic equation to model the continuous dynamics of the physical system. The method comprises the following steps: according to a mapping rule of AADL and Modelica; and correspondingly expanding the attribute set of the AADL, converting the model established by Modelica into an AADL model, fusing an information system and a physical system in the information physical fusion system, and analyzing the delay time in the information physical fusion system by using Osate. On the basis of Modelica and AADL modeling, Z specifications are adopted to carry out formalized constraint on a large amount of data generated in the system interaction process.

The invention discloses a method for improving system damping and modeling based on double-fed fan rapid active power modulation. According to the method for improving the system damping, on the basisof an existing fan double-closed-loop control structure, the increment [delta][omega] of the angular speed of a generator is selected as an input signal of damping control, the increment [delta]P ofthe rotor power of a DFIG serves as an output signal and is added to a double-fed draught fan active power control loop to improve the damping of a system, and the dynamic behavior of the system is improved; the problems that in the prior art, the stability of a fan grid-connected system is researched, but a control system of a converter is complex and active and reactive coupling exists are solved; and the technical problems that a complete mathematical model does not exist, and a detailed differential algebraic equation set of the system is given exist.

The invention relates to the technical field of dynamics system optimization, and provides a flexible multi-body system dynamics semi-analytical sensitivity analysis method based on absolute node coordinate description. The method comprises the following steps: firstly, establishing a mass matrix, a rigidity matrix and a generalized force array of the flexible multi-body system based on an absolute node coordinate method; secondly, establishing a kinetic equation and an optimization objective function of the flexible multi-body system; thirdly, based on a direct differential method or an adjoint variable method, establishing a semi-analytical sensitivity calculation formula of the flexible multi-body system dynamics; and finally, solving the dynamic differential algebraic equation of the flexible multi-body system to obtain a sensitivity calculation result. The method is based on an absolute node coordinate method and a multi-body system dynamics theory. A semi-analytical sensitivity calculation formula of the flexible multi-body system is established to solve the sensitivity analysis problem of dynamics of the flexible multi-body system, a set of new strategy for sensitivity analysis of the flexible multi-body system is provided, and convenience is provided for sensitivity calculation of the large-scale complex flexible multi-body system.

The invention discloses a short-term-voltage stability control method for an electric power system. In the method, firstly, through an on-site measurement mutual inductor, the operation state of the electric power system is measured and through state estimation calculation, steady-state operation data of system operation is obtained and a reactive optimization non-linear programming model based on an optimal power flow is constructed and then system dynamic data is extracted from a stability database of the electric power system; and a differential-algebraic equation set which describes system dynamic characteristics and an initial value equation thereof are constructed and according to the steady-state data and the dynamic data, modeling is carried out on a dynamic reactive compensation device and then a dynamic optimization model is constructed and finally the dynamic reactive optimization model based on the stability-constraining optimal power flow is solved. A reactive standby optimization result is coded into a control instruction and transmitted to an on-site generator and the reactive compensation device through a remote control system of the electric power system. The short-term-voltage stability control method for the electric power system is capable of accurately calculating an optimal dynamic reactive standby scheduling scheme during system operation and improving the short-term-voltage stability of system operation.

The invention discloses a rolling type stochastic projection integration method suitable for dynamic simulation of active power distribution networks. According to the method, the stochastic characteristic and multi-time scale characteristic in the operation process of active power distribution systems are fully considered, and a stochastic differential-algebraic equation-based active power distribution system dynamic simulation model is solved through combining a deterministic projection integration algorithm with a hybrid stochastic numerical integration algorithm and fusing a thought of rolling type multi-stochastic trajectory simulation; the method is suitable for the stochastic dynamic simulation calculation under system fault or operation conditions. Compared with the traditional stochastic numerical integration algorithm, the method disclosed in the invention has approximate strong convergence and weak convergence, can be used for greatly improving the simulation calculation efficiency under same Monte Carlo simulation times, and is particularly suitable for the stochastic operation simulation and analytical calculation of active power distribution systems with various distributed power supplies and loads.

The invention relates to a rapid assessment method for transient stability of a super-large urban power grid based on dynamic security domains, and the technical feature thereof is that the method comprises the following steps: step 1, determine system data in a potential operation mode of the system to form a system differential algebraic equation; step 2, according to the system flow section under the large operation mode, screening heavy-duty lines and substations, and supplementing high-power nodes to solve the pre-fault equilibrium point and form a large disturbance expected accident set;step 3, after generating a transient stability assessment scene set, numbering the assessment scenes and starting the assessment of the dynamic security domains; step 4, determining the measures andfault response time for the expected accidents, searching for a transient stability critical equilibrium point, and calculating the dynamic security domains for each transient stability assessment scene; and step 5, assessing the transient stability of the power grid after the occurrence of the expected accident on the system, and calculating the stability margin. The method can shorten the assessment time of the transient stability of the system and can give a stability margin.

According to the method of the invention, the estimation of the angular position is obtained by calculating at least one first estimator as solution of a differential algebraic equation whose coefficients depend on electric parameters of the rotating electric machine comprising first and second inductances of a stator respectively along a direct axis and a quadrature axis with respect to a magnetic flux produced by the rotor of the machine, a resistance of a phase winding and the magnetic flux produced by the rotor. The coefficients also depend on a reference voltage of a vector pulse width modulation (10) applied to the stator of the machine, on phase currents and on first derivatives with respect to time of these phase currents. The estimation of the speed of rotation is obtained by calculating a second estimator obtained by a calculation of first derivative of the first estimator with respect to time.

A new method for simulation of general electrical circuits on parallel computing platforms is disclosed. Parallel simulation of general time-domain circuits that are represented by nonlinear / linear differential algebraic equations is accomplished by partitioning them into smaller subcircuits via a novel combination of the companion form representation of the given circuit and an efficient form of node splitting, during Newton Raphson iterations, at any time point. The new invention formulates the interface vectors between partitions, through purely binary vectors, leading to a high degree of parallelism, scalability and reduced computational and communication costs for synchronizing the solutions between various partitions. Parallel platforms considered can be diverse such as (including but not restricted to) multicore CPUs, distributed systems of computers. The new invention also provides for scalable parallel simulation of mixed-domain formulations, such as (including but not restricted to), integrated circuits, electronic packages, PCBs, electromagnetic modules, MEMS and optical components etc.