19 results about "Nonlinear differential equations" patented technology

The application discloses a kind of network type converter transient power angle nonlinear mathematical analysis modeling methods, this method is directed to the power system containing network type converter, lack of the mathematical analysis model of its transient power angle characteristic problem and proposes.The specific steps realized by the method are as follows: the system model of network type converter single-machine infinite system is constructed;Transient power angle nonlinear mathematical model of network type converter single-machine infinite system is established;Least square method is applied to fitting nonlinear differential equation;Transient power angle nonlinear differential equation after fitting is solved based on multiscale method.The application deduces the mathematical analysis model of network type converter transient power angle using circuit theorem, least square method and multiscale method, can predict the transient power angle response process of network type converter system in advance, compared with traditional phase diagram method, the mathematical analysis model can be analyzed network type converter transient power angle characteristic under different system parameters in large disturbance process.

This invention relates to the field of asynchronous motor control technology, specifically to an asynchronous motor speed control method and system based on an improved Super-Twisting sliding mode algorithm. The method includes: (1) deriving the fourth-order nonlinear differential equation of a three-phase squirrel-cage asynchronous motor in a rotating coordinate system d-q based on rotor magnetic field orientation theory; (2) designing a linear sliding surface based on the error between the set speed and the feedback speed; (3) using the first-order differential equation of rotor speed in step (1) and the linear sliding surface described in step (2), and introducing a variable proportional differential term based on the traditional Super-Twisting sliding mode algorithm to design a fast Super-Twisting sliding mode speed controller; (4) constructing a variable exponential switching function to replace the sign function in the fast Super-Twisting sliding mode speed controller described in step (3), thus completing the design of the improved Super-Twisting sliding mode speed controller. This solution effectively solves the problems of slow response speed and poor control accuracy in existing systems, thereby improving the overall robustness of asynchronous motor control.

This invention relates to a method for constructing a curved solar concentrator with uniform light reception on the absorber surface, belonging to the field of solar photovoltaic and photothermal technology. This invention utilizes differential geometry theory to construct a system of first-order nonlinear differential equations relating the concentrator's reflective surface (x and y coordinates) to the radius r of the circular absorber. The reflective surface profile parameters are obtained through iterative solutions. A discrete point lattice is obtained, with the spatial straight-line distance and maximum deviation between adjacent iteration coordinate points not exceeding 2 mm as the convergence criterion. A curved concentrator model is then generated through spline curve fitting. The energy flux density distribution on the absorber surface is obtained using the ray tracing software Tracepro, and the uniformity of the energy flux distribution is verified using a relative deviation not exceeding ±10% of the average value. This invention achieves uniform distribution of incident solar radiation on the absorber surface, eliminates local hot spots, significantly reduces thermal stress gradients, and improves the photothermal conversion efficiency and operational stability of the solar concentrator system.

The invention provides a layered dynamic thermodynamic modeling method for a salt cavern gas storage for compressed air energy storage, and belongs to the technical field of compressed air energy storage. The core idea of the method is spatial discretization and layered solution, N control bodies are divided in the vertical direction according to the geometric characteristics of the salt cavern, then a mass conservation equation, an energy conservation equation and a Redl ich-Kwong real gas state equation are established for each control body, and finally all the control body equations are coupled into a nonlinear differential equation set. After initial conditions and boundary conditions are given, a numerical method is adopted for solving. According to the method, the temperature and pressure layering characteristics in the salt cavern can be accurately described, the problems that a traditional single-tank model underestimates the energy storage capacity and energy loss calculation is inaccurate are solved, high-precision model support is provided for compressed air energy storage power station power dispatching and system optimization, and high practicability and popularization value are achieved.

This invention belongs to the field of mechanical analysis technology and provides a method and system for elastic beam deformation analysis based on fourth-order nonlinear differential equations. The method includes: obtaining the stress-strain relationship and lateral displacement function of the elastic beam; constructing a fourth-order nonlinear mechanical response function of the elastic beam based on the obtained stress-strain relationship and lateral displacement function; solving the constructed fourth-order nonlinear mechanical response function to identify the local buckling location and higher-order shear effects of the elastic beam; taking the minimum weight of the elastic beam as the objective function, considering the displacement and stress constraints of the elastic beam, performing sensitivity analysis of the elastic beam based on the obtained local buckling location and higher-order shear effects, adjusting the nonlinear coefficient of the elastic beam, and completing the elastic beam deformation analysis based on fourth-order nonlinear differential equations.

The invention relates to a high-dimensional complex nonlinear differential equation periodic response efficient universal easy-to-use solving method, which is characterized in that an automatic differential technology and a harmonic balance method are fused, and the method comprises the following steps: step 1, solution setting: representing the periodic response of a system by using discrete Fourier series; step 2, harmonic balance: substituting periodic response in a Fourier series form of the system back to a system kinetic equation, and converting a differential equation into an algebraic equation through a harmonic balance program; 3, calculating a Jacobian matrix, namely, quickly obtaining an accurate Jacobian matrix of the algebraic equation after harmonic balance by utilizing an automatic differential technology; and 4, solving an algebraic equation, namely calculating by using a Newton-Raphson method to obtain a system periodic response. The method solves the problems that a high-dimensional complex nonlinear differential equation response solving method is low in efficiency, not universal and not easy to use, can be widely applied to calculation of high-dimensional complex nonlinear system dynamic response, and has the advantages of being efficient, universal, capable of being used immediately after being opened and modularized.

The invention discloses a GFL-VSC transient stability analysis method and system considering LVRT control, and belongs to the technical field of power system safety and stability analysis. The method comprises the following steps: decomposing a full-order model into a low-order fast subsystem and a low-order slow subsystem by using small parameters based on a singular perturbation theory according to a time scale difference between a current loop and a phase-locked loop; in the slow subsystem, solving a nonlinear differential equation of a phase-locked loop by using a multi-scale method to obtain an approximate analytical solution based on initial conditions, system parameters and fault depth, and establishing a stable boundary criterion according to the approximate analytical solution; and in the fast subsystem, establishing a dynamic model comprising a time-varying item, solving to obtain an analytic solution of the dynamic model, and determining the transient stability of the GFL-VSC under the influence of the current loop control parameters according to the stability boundary criterion and the analytic solution. According to the method, the transient stability of the GFL-VSC considering the LVRT control can be effectively analyzed.

The invention provides a signal processing method and system of a pan-tilt motor, electronic equipment and a storage medium, and relates to the technical field of signal processing, a stator of the pan-tilt motor is provided with two linear Hall sensors, and the method comprises the following steps: respectively collecting Hall signals of the two linear Hall sensors; performing signal processing on the two Hall signals to obtain two Hall voltage signals; respectively carrying out noise extraction on the two Hall voltage signals based on a steepest control comprehensive function of a discrete system to obtain two standard voltage signals; and calculating the electrical angle of the pan-tilt motor according to the two standard voltage signals. Based on the steepest control comprehensive function of the discrete system, adaptive balance of noise suppression and phase lag is realized through the nonlinear differential equation, the electrical angle error of the pan-tilt motor is effectively reduced, the dynamic response speed of the pan-tilt motor system is improved, and the stability and real-time performance of a live broadcast picture are guaranteed.

The invention discloses a multi-core optical cable shape reconstruction method based on fourth-order step integral and GOC compensation, and belongs to the technical field of structure health monitoring, and the technical key points are that the method comprises the steps: solving a curvature vector through the central wavelength change data of a fiber grating sensor in a multi-core optical cable; obtaining a geometric information matrix of the multi-core optical cable; constructing a multi-core optical cable shape reconstruction algorithm, carrying out numerical solution on a nonlinear differential equation of a tangent vector by adopting a four-order step integration method, substituting the obtained tangent vector into a geometric information matrix of the multi-core optical cable, and combining curvature information of the multi-core optical cable to obtain an ideal shape of the multi-core optical cable; and constructing a fiber core position geometrical optical compensation model, analyzing a geometrical relationship between an actual deviation fiber core position and a fiber core position of an ideal multi-core optical cable shape, and correcting a multi-core optical cable wavelength variation error caused by fiber core position deviation, so as to at least have the technical effect of improving the shape reconstruction precision of the multi-core optical cable.

The invention relates to a light-hydrogen capacity ratio configuration method and a light-hydrogen capacity ratio configuration system considering the internal durability of a proton exchange membrane electrolytic cell and the photovoltaic rapid fluctuation power, and the method comprises the steps: building a photovoltaic power fluctuation model, an electrolytic cell response model and an equivalent circuit model; a nonlinear differential equation system that the cell voltage is influenced by photovoltaic capacity, electrolytic cell capacity and fluctuation parameters is derived, and electrical constraint conditions based on the durability of the electrolytic cell are set, such as the cell voltage is 1.8-2.5 V, the anode overpotential is less than or equal to 2.2 V, and the voltage change rate is less than or equal to 150mV / s, so that the optimization range of the light-hydrogen capacity ratio k = Cpv / Pelrate is quickly determined. According to the method, the algorithm complexity is effectively reduced, the calculation efficiency is improved, meanwhile, the durability of the membrane and the catalyst in the electrolytic cell is guaranteed, and the economical efficiency and reliability of system equipment are improved.

The application discloses a frequency index equivalent-based energy storage equivalent synchronous machine frequency modulation parameter evaluation method, belongs to the equivalent frequency modulation capacity evaluation field of new energy station, and comprises the following steps: S1, establishing a nonlinear differential equation set of a synchronous generator unit and a new energy power system considering a dead zone link; S2, defining key parameters of the synchronous generator unit and key parameters of the new energy power system; S3, determining that the system average frequency change rate is a frequency response index equivalent target; S4, simulating; S5, constructing a three-dimensional curved surface; S6, searching for energy storage equivalent synchronous generator unit frequency modulation control parameters on the three-dimensional curved surface; and S7, outputting an energy storage frequency modulation capacity quantitative evaluation report. The frequency index equivalent-based energy storage equivalent synchronous machine frequency modulation parameter evaluation method has important guiding significance by using the known frequency modulation characteristics of the synchronous generator to inversely quantify the unknown frequency modulation capacity of the energy storage and considering nonlinear factors in actual operation.

The application discloses a parameter-unknown chaotic system adaptive synchronization control method based on DNA strand displacement, and comprises the following steps: a chemical reaction module of a nonlinear differential equation with square terms and product terms is obtained by describing emergent reactions, trigger reactions and degradation reaction processes through double-molecule chemical reactions; a Yang chaotic system is constructed by using a DNA strand displacement reaction; an adaptive controller capable of realizing synchronization and an adaptive law expression for unknown parameter estimation are obtained; and the effectiveness of the adaptive controller is verified according to the Lyapunov stability principle. Through the DNA strand displacement mechanism, an internal synchronization mode without the participation of an external chaotic system, i.e. the synchronization between subsystems in a chaotic system, is realized; and under random reactions or other disturbances, the synchronization between the subsystems and the estimation of the unknown parameters by the adaptive law are verified. The method has robustness to parameter deviation, and through triggering a series of DNA reactions, different one-to-one and one-to-many combinations between the subsystems are synchronized.

The invention relates to the technical field of energy storage system modeling, in particular to a compressed air energy storage side all-working-condition dynamic modeling method which comprises the steps that a third-order nonlinear differential equation set and a compressor characteristic model are built based on the pressure, mass flow and angular speed of a compressor pressurizing chamber of a compressed air energy storage system; a gas-machine-heat dynamic model of the compressor is established; determining control input based on the motor driving torque, constructing a motor driving torque model, constructing an inlet guide vane dynamic model, and constructing a gas storage throttle valve model so as to establish a controller model; and establishing a gas storage inlet pipeline pressure dynamic model and a gas pressure and temperature dynamic equation so as to establish a gas storage joint model. Therefore, the problem that the reliability of the operation state evaluation of the advanced adiabatic compressed air energy storage system is influenced due to insufficient accuracy and robustness of the model caused by insufficient consideration of a coupling mechanism among multi-dimensional state variables in the system in a modeling method in the related technology is solved.

This application relates to a stability analysis method for high-voltage direct current (HVDC) transmission systems and a nonlinear modeling method, apparatus, and equipment for grid-connected converters. The nonlinear modeling method for grid-connected converters first determines voltage differential equations, voltage differential data, current differential equations, and current differential data by obtaining electrical quantity data. Then, it sequentially determines the main loop dynamic equations and periodic differential equations. By combining the voltage and current differential equations of the control loop dynamics with the main loop dynamic equations and periodic differential equations, a nonlinear differential equation for analyzing the stability of the HVDC transmission system is obtained. This nonlinear differential equation is used to analyze the stability of the HVDC transmission system, solving the problems of existing HVDC transmission systems based on modular multilevel converters where periodic time-varying dynamics and strongly nonlinear limiting behavior induce dynamic bifurcation leading to system instability, and the lack of a universal nonlinear mathematical model and efficient and accurate analysis method.

A method for automatically path planning for optimizing a path of a machinery moving in an area, comprises the steps of: taking coordinates of an area contour, a working width of the machinery operating in the area, a mathematical description of the dynamics of the machinery operating in the area in form of a system of nonlinear differential equations, determines segments along the headland path which are not feasible with respect to dynamics of the machinery or whose traversal would result in area coverage gaps. A mathematical algorithm is used with a hierarchical two-step framework in combination with a special coordinate transformation from a time into a spatial domain to formulate geographic high-precision constraints. The hierarchical two-step framework addresses two objectives: a generation of headland paths and a generation of smooth transitions between headland path and mainfield lanes, whereby the first hierarchical step varies for the two objectives.

The invention relates to the technical field of intelligent control, in particular to an uncertain nonlinear intelligent agent obstacle avoidance control method based on tracking. According to the method, an intelligent agent is modeled into an uncertain nonlinear model and converted into an uncertain nonlinear differential equation, a dynamic tracking controller is designed based on input state stability, and an obstacle avoidance controller is designed based on feasible set projection. The invention provides an uncertain nonlinear intelligent agent obstacle avoidance control method based on tracking, and solves or at least alleviates the problems that an existing intelligent agent obstacle avoidance control method is adaptive to an uncertain nonlinear dynamic model and a complex environment, is easy to fall into local optimum, is poor in real-time performance and the like, so that the requirement of obstacle avoidance control on a system is reduced, and the system reliability is improved. And moreover, the obstacle avoidance controller is designed based on the first-order integrator, so that the design process of the obstacle avoidance controller is simplified, and a simple low-order system can control a complex high-order intelligent agent.

The application discloses a DC power transmission subsequent commutation failure prediction method and optimization method based on a turn-off angle dynamic equation, and the prediction method comprises the following steps: obtaining the turn-off angle of the LCC-HVDC inverter side based on the turn-off angle output characteristics of the LCC-HVDC inverter side; analyzing the process of the first commutation failure and the subsequent commutation failure of the LCC-HVDC system based on the inverter side DC current control, the low-voltage current limiting control, the fixed turn-off angle control and the current deviation control; obtaining the transient nonlinear differential equation about the turn-off angle by analyzing the dynamic characteristics of the DC current and the trigger advance angle during the first commutation failure recovery in combination with the control characteristics of the low-voltage current limiting control and the fixed turn-off angle control; and drawing the phase diagram curve of the turn-off angle under different AC voltages and AC voltage change rates based on the transient nonlinear differential equation about the turn-off angle, and obtaining the criterion for predicting the occurrence of the subsequent commutation failure by analyzing the phase diagram curve. The application improves the stability and operation reliability of the system.

The invention relates to the technical field of power system automation, in particular to a complex power grid electric energy quality unified detection method and system.The method comprises the steps that an electric energy quality disturbance unified representation model is built, and the output quantity is a disturbance characteristic core index set; establishing a nonlinear adaptive filtering dynamic adjustment architecture, and constructing a nonlinear differential equation of the dynamic adjustment architecture based on the unified representation model; filtering the power grid real-time signal based on the dynamic adjustment architecture and outputting an original disturbance feature set; regulating and controlling the value of a dynamic response parameter group in the dynamic regulation framework according to a nonlinear differential equation; a multi-objective optimization algorithm is adopted to execute parameter synchronous optimization processing; and inputting the original disturbance feature set into the unified representation model to generate a disturbance feature core index set. According to the method, the technical contradiction that the dynamic response capability is insufficient due to offline parameter setting in a complex multi-disturbance power grid scene, and cooperative optimization of electric energy quality high-precision measurement and relay protection rapid decision cannot be met at the same time is effectively solved.

A method for automatically path planning for optimizing a path of a machinery moving in an area, comprises the steps of: taking coordinates of an area contour, a working width of the machinery operating in the area, a mathematical description of the dynamics of the machinery operating in the area in form of a system of nonlinear differential equations, determines segments along the headland path which are not feasible with respect to dynamics of the machinery or whose traversal would result in area coverage gaps. A mathematical algorithm is used with a hierarchical two-step framework in combination with a special coordinate transformation from a time into a spatial domain to formulate geographic high-precision constraints. The hierarchical two-step framework addresses two objectives: a generation of headland paths and a generation of smooth transitions between headland path and mainfield lanes, whereby the first hierarchical step varies for the two objectives.