213 results about "Algebraic equation" patented technology

The invention discloses a parallel iteration Runge-Kutta method for simulating a second-order nonlinear differential equation. The parallel iteration Runge-Kutta method comprises the steps that a simulated ordinary differential equation is converted into a target nonlinear implicit differential equation, and a system differential algebraic equation is established; judging whether a system matrix and a decomposition iteration matrix in the system differential algebraic equation are updated or not; a four-order extrapolation method is adopted to obtain a predicted differential variable derivative, and if a prediction result is not converged, parallel iterative operation is carried out through a four-stage four-order Runge-Kutta method; after the iteration process is converged, judging whether an operation result accords with a preset error range, if not, updating a system matrix according to a step size reduction strategy and re-decomposing an iteration matrix, and if yes, updating the operation result; and storing and displaying an operation result when judging that simulation is finished. The algorithm stability and the calculation efficiency of the rigidity problem can be considered.

The invention relates to a fault current analysis method based on first-order Taylor expansion, and the method comprises the following steps: 1, determining a system control strategy which is a network construction type control strategy and comprises a power loop, a virtual impedance link and a voltage and current loop; the power loop comprises an active power control loop and a reactive power control loop; 2, constructing a differential algebraic equation set model capable of representing the dynamic state of the system; 3, according to the characteristic that the integral value does not suddenly change at the moment before and after the fault occurs, the steady state before the fault is utilized to solve and obtain an instant state variable value after the fault, and then an instant dq-axis current value after the fault and an instant current amplitude value after the fault are obtained; 4, performing first-order Taylor expansion on the constructed differential algebraic equation set at the solved post-fault instant state variable value and the dq-axis current value, and converting a nonlinear differential algebraic equation set model into a linear differential algebraic equation set; and 5, analyzing the fault current.

The invention discloses a helicopter rotor system dynamics simulation efficient solving method based on a three-dimensional entity unit, and belongs to the technical field of helicopter rotor system dynamics simulation analysis. Comprising the following steps: dividing a helicopter rotor geometric model into three-dimensional entity finite element models, and endowing unit attributes; and according to the finite element model, dividing co-rotation analysis components, and realizing effective butt joint among the components. Establishing a dynamic differential algebraic equation of the rotor system, and discretizing the dynamic differential algebraic equation; two key items in the efficient solving process are calculated, calculation of iteration increments is completed, and the dynamic time-history response of the rotor system is obtained. According to the thought of a component-level co-rotation coordinate method, extracting the elastic deformation of the rotor component, completing the stress tensor calculation of the rotor structure, and outputting a stress nephogram. According to the method, each iteration step linearized equation set is solved by adopting a Schel complement method, so that the solving efficiency of the large-scale linear equation set is improved; on the premise of keeping high precision, the dynamic simulation analysis of the finite element model of the large-scale rotor system can be efficiently completed.

The invention discloses an inner-layer process dynamic optimization method based on an RBF coherent method. The inner-layer process dynamic optimization method comprises the following steps: giving a control variable initial value u0, a state variable initial value x0, optimization time t0 and te and boundary constraints of all variables; performing variable discretization; simulation of a DAE model equation is carried out once in each optimization iteration, and model calculation is carried out on a discrete nonlinear algebraic equation set in a simulation layer by adopting a Newton iteration method to obtain a value of a state variable; during model calculation, obtaining a sensitivity information matrix of a state variable to a control variable and a time variable; and in each optimization iteration process, the previous steps are repeated, and an NLP solver is utilized to solve the nonlinear programming problem processed by the simulation layer until the convergence precision of optimization iteration is achieved, and an optimal solution is found. According to the method, optimal scheduling of the fast climbing ability of the CHP unit is considered, wind power consumption can be promoted on the premise of ensuring the feasibility of a CEHS scheduling scheme, and the operation cost is saved.

The invention relates to the technical field of water supply pipe networks, and discloses a multi-pump-room collaborative intelligent water supply frequency conversion regulation and control method, which comprises the following steps: initializing sensor calibration and data acquisition, generating a standardized data packet by using Kalman filtering, constructing a differential algebraic equation model, and online updating a pipe network topological characteristic matrix in combination with a mixed basis function observer. Layered optimization control and frequency conversion cooperative regulation and control are driven, 30-100ms-level real-time solution of a differential equation is realized by means of a hardware acceleration module, a three-dimensional pressure cloud picture is finally generated, and early warning is triggered based on a current harmonic threshold value. The transient fault capturing capability is enhanced by dynamically adjusting the data acquisition frequency, and the problem of signal distortion caused by traditional fixed sampling is solved; resource allocation is optimized and calculated in combination with a pipe network topology model dimension reduction technology, and calculation power waste in large-scale monitoring is reduced; and dynamic reconstruction of the model is driven by abnormal data to realize system self-adaption, so that manual parameter adjustment deviation is avoided, and the prediction precision and the diagnosis reliability are remarkably improved.

The invention relates to the field of fractional calculus and partial differential equation solving, and discloses a novel fractional sub-equation neural network analysis solver, which comprises the following steps: constructing a full-connection neural network model, and substituting the formula into a fractional partial differential equation to obtain a fractional sub-equation neural network analysis solver; and a Riemann-Liouville fractional derivative is corrected by utilizing Jumarie which meets a chain rule, so that the problem is converted into an algebraic equation form. Unknown variables and coefficients of the integer order partial differential equation are extracted by using a symbol calculation tool, an overdetermined nonlinear algebraic equation set is generated, and the weight and bias of the neural network are obtained by solving the equation set. And finally, optimizing the preliminary analytical solution in combination with a special solution of a fractional order Riccati equation, and generating a final analytical solution comprising a generalized fractional order hyperbolic function, a generalized fractional order trigonometric function and a Mittag-Leffler function form. According to the method, the analytic solution efficiency is improved, the expression range of understanding is expanded, and meanwhile, the mathematical characteristics of fractional derivatives are reserved.

The invention relates to the technical field of robot control, in particular to a mounting type power transmission line inspection robot self-adaptive control method, system and device based on deep reinforcement learning and a storage medium. Establishing a multi-modal fusion state vector by synchronously collecting visual sensing, inertial measurement and actuator feedback data, and inputting the multi-modal fusion state vector into a deep reinforcement learning strategy network to dynamically generate a state weight and a control weight adjustment amount of a linear quadratic controller; performing positive qualitative verification, amplitude limitation adjustment and constraint projection processing on the candidate weight matrix; a feedback gain matrix is obtained by solving an algebraic Riccati equation, and control output is calculated according to the state deviation to drive the double mechanical arms to execute inspection actions; designing a multi-target reward function of the comprehensive task completion quality and the energy consumption efficiency, and iteratively updating strategy network parameters by adopting a near-end strategy optimization algorithm; the problem that a fixed weight controller is difficult to adapt to dynamic working conditions of a power transmission line is solved, and a technical scheme is provided for intelligent control of a power inspection robot.

The invention discloses a copper recovery processing system and method for flameless combustion of copper-containing sludge, and relates to the technical field of intelligent control. A distributed sensor network is deployed, multi-source combustion data in a combustion furnace are acquired in real time, a hybrid convolution-long and short-term memory network model is constructed, cross-modal feature fusion is performed on the multi-source combustion data, and the copper recovery processing system and method for flameless combustion of the copper-containing sludge are obtained. The method comprises the following steps: extracting a multi-dimensional combustion feature vector, correcting system parameters of a differential-algebraic equation on line based on the multi-dimensional combustion feature vector, solving a real-time system state variable after the system parameters are corrected, and constructing a constraint condition by using the system state variable. A multi-agent reinforcement learning model is constructed based on the multi-source combustion data and the multi-dimensional combustion feature vectors, dynamic combustion parameters are optimized in parallel by adopting a multi-agent depth deterministic strategy gradient algorithm, and the dynamic combustion parameters are sent to a combustion execution mechanism for combustion parameter updating; the stability and the environmental protection performance in the combustion process are obviously improved.

The invention discloses a Bernstein polynomial-based multi-region frequency safety unit scheduling method and device, and the method comprises the steps: constructing a multi-region frequency response model based on the dynamic primary frequency modulation response of a synchronous generator, and the optimal distribution of a speed regulator dead zone and frequency modulation reserve; carrying out approximation on an integral-differential algebraic equation of the multi-region frequency response model through a Bernstein polynomial to obtain a dynamic algebraic expression of the multi-region frequency, and constructing a multi-region frequency security constraint according to the dynamic algebraic expression of the multi-region frequency; embedding the multi-region frequency security constraint into a unit commitment problem, and constructing a multi-region frequency security constraint unit commitment model; decomposing a mixed integer programming problem of the multi-region frequency security constraint unit commitment model into a main problem and a sub-problem through an adaptive double-layer decomposition algorithm; and solving to obtain a multi-region frequency safety unit scheduling scheme. According to the method, the frequency dynamic difference between the regions is accurately captured, and the frequency safety of the high-proportion new energy power system is improved.

Compiler systems and methods that solve the DAE transformation problem by simulating DAEs using general-purpose compilers are disclosed herein. The compiler systems and methods extend an existing general-purpose intermediate representation (IR) with a minimal set of intrinsics to represent the model function, which allows leveraging existing compiler technology. A first compiler input is a model of a physical system from source modeling languages. A second compiler input is a first IR for each subroutine specific to the model. The model is compiled to a second IR that is universal across multiple source modeling languages. The IR maps each primitive of the source modeling language to a subroutine call specific to the source modeling language from which the primitive is derived. The first and second IRs are combined into a third IR that describes the model in terms of intrinsics of the third IR.

The invention belongs to the technical field of photoelectricity, and relates to a detector moving laser irradiation damage assessment method and system. The evaluation method comprises the following steps: determining mobile laser parameters and detector structure material attribute parameters; constructing a detector solid heat transfer transient model; setting physical field boundary conditions of the solid heat transfer transient model and performing grid division; setting solver parameters, specifically, inputting the moving laser pulse width and the moving laser frequency into a pre-trained linear neural network model, and calculating by applying an expression of the model to obtain the solver parameters; and based on the solver parameters, solving the solid heat transfer transient model in the solver, judging the thermal damage condition of the detector by calling domain ordinary differential and differential algebraic equation modules, and if it is determined that the detector is damaged, calculating the damage area and volume of the detector to obtain the spatial distribution condition of the damage area of the detector.

The embodiment of the invention discloses a negative damping elimination method, device and equipment based on SVG and a storage medium, and the method comprises the steps: carrying out the impedance scanning of the SVG in a range of 1-3000Hz, obtaining the positive-sequence impedance and negative-sequence impedance of the SVG under different operation conditions, and determining the leading operation condition of the SVG impedance; determining the positive sequence equivalent impedance and the negative sequence equivalent impedance of the SVG grid-connected point according to the positive sequence dominant impedance and the negative sequence dominant impedance of the SVG under the dominant operation condition; determining the value ranges of the positive sequence damping correction value and the negative sequence damping correction value of the SVG; the maximum value of the intersection of the two value ranges is determined as SVG compensation damping, and the SVG compensation damping is merged into an SVG grid-connected point port; according to the scheme, only two unknown parameters including the positive sequence damping correction value and the negative sequence damping correction value are involved, the parameters can be calculated based on an analytic formula pure algebraic equation, the calculation mode is simple, the port impedance characteristic negative damping of the SVG in the full frequency band within the range of 1-3000 Hz can be eliminated, and the problem of high-frequency oscillation is thoroughly solved.

The invention provides a method and a system for selecting an input signal of a damping controller of a synchronous phase modifier. The method comprises the following steps: establishing a differential equation and an algebraic equation of the whole system based on a dynamic model of a grid-connected system; linearizing a differential equation and an algebraic square of the whole system at a stable operation point, and establishing a small-signal linearization model of the whole system; solving a system state matrix based on the small signal linearization model, calculating a characteristic value, a left characteristic vector and a right characteristic vector of the system state matrix, and determining different oscillation modes of the system according to a characteristic value calculation result of the system state matrix; calculating participation factors in different oscillation modes by combining the left feature vector and the right feature vector of the system, and constructing a participation factor matrix; and in combination with the participation factor matrix, aiming at a certain oscillation mode of the system, the size of the participation factors between the oscillation mode and different state variables is compared and analyzed, and the state variable with the maximum participation factor is used as an input signal of the damping controller of the synchronous phase modifier.

The invention discloses a multi-converter parameter collaborative optimization method for improving the small interference stability of an active power distribution network, and belongs to the technical field of power systems, and the method comprises the steps: building a differential algebraic equation model, and carrying out the linearization of a steady-state operation point, and obtaining a state space model; and a control parameter optimization problem taking the minimization of the spectrum intercept construction as a target is defined, and control parameters are a GFL converter phase-locked loop parameter and a GFM converter virtual damping parameter. First-order sensitivity and second-order sensitivity of eigenvalues to control parameters are calculated based on a matrix perturbation theory and are converted into local quadratic constraint sub-problems. And performing convexity solution by adopting a positive semidefinite relaxation method, adjusting the step length in combination with a line search mechanism, iteratively updating control parameters, and outputting an optimization result after a convergence condition is met. According to the method, the spectral intercept is reduced through multi-converter parameter collaborative optimization, and the weak stability characteristic is improved; the convergence and solvability are improved by utilizing matrix perturbation and positive semidefinite relaxation; and the stability is enhanced and optimized by adopting line search step length adjustment.

According to the cluster system simulation solving method and device, the storage medium and the computer equipment provided by the invention, during simulation solving, the cluster system is divided into the multiple independent subsystems according to the topological structure of the cluster system, and the digital model of each subsystem is constructed, so that the model matrix dimension is reduced, and the single-step calculation amount is reduced; and then differential solution is carried out on the digital model of each subsystem to obtain a differential solution result, and then algebraic solution is carried out, so that mutual containment of the two subsystems is avoided, and the speed is increased. Before algebraic solution, dependence parameters of the cluster system are determined according to the controlled relationship among the subsystems, and whether the cluster system has an algebraic ring is determined and judged based on the dependence parameters; if yes, carrying out iterative solution on each digital model by adopting a Newton-Raphson iterative algorithm to avoid error accumulation caused by closed-loop dependence; and if not, sequentially solving the algebraic equations in the digital models by adopting a display function, and improving the solving efficiency to a millisecond level.

A balance, having an indicator with clearly marked inequalities, provides feedback to a user where the user determines whether they have created an equality or inequality and whether an adjustment is necessary. Users connect mathematical statements with a correct equality or inequality symbol. The indicator provides users with a physical representation of basic math operations, including addition, subtraction, multiplication, and division, as well as fractions, negative numbers, and algebraic equations. Physical adjustments to the balance system correspond to conventional mathematic / algebraic written representation. Constant cubes include several different sets of unit weight. Other cubes or objects are labeled with colored symbols and are provided in a variety of weights and quantities. Opposite chips are labeled with negative signs; line chips are labeled with “x” and “y.” Combinations of the constant cubes, cubes or objects labeled with colored symbols, opposite chips, and line chips are arranged on removable pans on the balance to teach mathematical functions.

The invention relates to the technical field of automobile steer-by-wire system control, in particular to a trajectory tracking control method based on data-driven fuzzy value iteration. For nonlinearity and uncertainty of a steer-by-wire (SBW) system, a T-S fuzzy technology is adopted to construct a local linear model of the SBW system. Constructing a fuzzy augmented tracking system by introducing a reference signal; secondly, a fuzzy discount coupling algebraic Riccati equation based on a Hamilton-Jacobi-Bellman equation is deduced; and a data-driven fuzzy tracking value iteration (VI) algorithm is designed, and the tracking control problem of the system is solved through online iteration. The algorithm has the prominent characteristics that the dependence on system dynamics information is completely eliminated, and closed-loop trajectory tracking control can be realized without an initial stable control strategy. The method can be widely applied to the fields of intelligent driving, automatic driving steering control and the like, and is particularly suitable for scenes with uncertain system models and difficult control initialization.

The invention provides a three-dimensional geological modeling method, system and equipment based on a particle dynamics system. The method comprises the following steps: carrying out data preprocessing on a drilling data set of a to-be-built geological model region to obtain a stratum attribute known point set; discretizing the to-be-built geologic model area, and performing stratum parameter initialization processing on each spatial discrete coordinate point in the to-be-built geologic model area according to the stratum attribute known point set to obtain initial stratum parameters of a to-be-built geologic model; based on the initial stratum parameters and the drilling data set, a weight function expressed by spatial distribution information is established; establishing a link relation information matrix according to grid division and section discontinuity information of the to-be-established geological model area; based on a particle dynamics theory, establishing a system dynamics equation in a differential algebraic equation form by applying the initial stratum parameters, the weighting function and the link relation information matrix; and solving the system kinetic equation to establish a three-dimensional geological model of the to-be-established geological model area.

The invention discloses a deep and far sea wind power time-varying impedance model grid connection analysis method based on a time domain residual error method, relates to the technical field of power system modeling simulation, and can efficiently and accurately analyze deep and far sea wind power grid connection. The method comprises the following steps: establishing a differential algebraic equation set containing high-capacity submarine cable impedance and a plurality of nonlinear links, and constructing a recursive coefficient matrix; dividing a preset global time domain into a plurality of time domain subintervals, and solving the recursion coefficient matrix in each time domain subinterval by referring to a universal analytic solution represented by a power series explicit operator to generate a global time domain explicit solution corresponding to the preset global time domain; performing discrete Fourier transform on the global time domain explicit solution to obtain a time-frequency domain spectrum result; and constructing a time-varying impedance model according to the differential algebraic equation, setting the time-varying impedance model by adopting a time-frequency domain spectrum result, and analyzing the deep and far sea wind power grid-connected control system by utilizing the set time-varying impedance model.

The invention discloses a neural network construction method and system for solving a high-index differential algebraic equation, and the method achieves the efficient and precise solving of the high-index differential algebraic equation through the preprocessing of an equation, the construction of a physical information neural network model, the definition of a loss function, the setting of training parameters and data, and the iterative training through an L-BFGS algorithm. And finally, the trained neural network model is used for solving a differential algebraic equation of the constrained mechanical arm system, variable values are uniformly selected in a definition domain and input into the trained model, so that a solution of the system is obtained, in addition, a predicted solution and an actual solution of the neural network are compared and analyzed, and the optimal solution is obtained. By means of the mode, the nonlinear high-index differential algebraic equation problem in the constrained mechanical arm system can be efficiently and accurately solved.

The invention discloses a homogenization dimension reduction decoupling method for collaborative recovery of a large-scale heterogeneous non-constant multi-energy system. Comprising the following steps: constructing an electricity-gas-water multi-energy post-disaster load recovery time sequence decision double-layer optimization model under the multi-coupling non-constant partial differential constraint based on a power grid dynamic reconstruction model, a gas grid compressible dynamic energy flow model and a water grid non-constant water power energy flow model; performing space-time grid discretization on the power grid dynamic reconstruction model, the gas grid compressible dynamic energy flow model and the water grid non-constant hydrodynamic energy flow model to form a coupling algebraic equation set; based on the coupling algebraic equations of the power grid, the gas grid and the water grid, constructing a power-gas-water multi-energy post-disaster load recovery time sequence decision optimization dimensionality reduction model in the modal space; and decoupling the power-gas-water multi-energy post-disaster load recovery time sequence decision optimization dimensionality reduction model into three mutually independent scheduling sub-models with different time scales, and solving to obtain an optimal solution of the original power-gas-water multi-energy post-disaster load recovery time sequence decision optimization dimensionality reduction model.

The invention discloses a frequency lowest point evaluation method considering a low-voltage ride-through process of a new energy unit, and belongs to the technical field of power systems. The method comprises the following steps: establishing a whole-system quasi-steady-state model, respectively constructing models for a synchronous machine, a new energy unit and a load, and replacing a differential equation of power electronic equipment such as the new energy unit with a nonlinear algebraic equation; based on the model, node voltage and injection current are updated through an alternate iteration method, key quasi-steady-state points when the new energy unit enters a low-voltage ride-through state and is in an off-network state are identified, and overall unbalanced power of the system is output; inputting the unbalanced power of each key quasi-steady-state point into the ASF model, and fitting a system frequency curve to obtain the lowest point of the frequency by considering the power vacancy of the low-voltage ride-through and off-network stages. The method does not need to depend on time domain simulation, can quickly and accurately evaluate the lowest point of the frequency, and is suitable for online stability evaluation of the power system.

The invention relates to the field of electric power, discloses a thermal power generating unit APS automatic start-stop full-process control method and system, and is used for solving the contradiction among safety, economy and rapidity of a traditional APS system. The method comprises the steps of establishing a differential algebraic equation system based on unit physical parameters to generate a unified model constraint set; generating a reference trajectory representing energy conversion efficiency and power in a differential flat space according to the start-stop target curve; predicting a thermal stress change rate through a fractional order differential operator based on the metal temperature to generate a safety margin instruction; generating an energy coordination correction instruction according to the Hamiltonian energy network balance point of the boiler heat storage and steam turbine kinetic energy solving port; and mapping the reference trajectory into a control instruction, integrating thermal stress constraint and energy coordination correction, and then distributing and executing. Safe and efficient start-stop control under full-process physical constraints is achieved, start-stop safety and economy are improved, and the service life of equipment is prolonged.

The invention relates to the technical field of power system simulation, and discloses a power system time sequence simulation system considering security constraints. The system comprises a power grid topology analysis unit, a dynamic security domain calculation unit, a time sequence constraint modeling unit, a simulation track generation unit and a check feedback unit. The power grid topology analysis unit obtains element connection relations and electrical parameters, and generates a topology description file containing a node admittance matrix; the dynamic safety domain calculation unit obtains the voltage stability limit and the power angle stability boundary of each working condition, and forms a safety domain boundary set; a time sequence constraint modeling unit combines the set with a predefined time interval to build a security constraint time sequence model containing a transient process; the simulation trajectory generation unit solves a differential algebraic equation set by using an implicit trapezoidal integral method, and outputs a state variable trajectory with a timestamp; and the check feedback unit compares the track with the security domain boundary, marks an abnormal segment and generates a correction instruction. The system realizes fusion of security constraint and time sequence simulation.

The invention discloses a unit commitment optimization method and system containing transient voltage security constraints, and belongs to the field of transient security evaluation and control of a power system. The method comprises the following steps: constructing a unit commitment model according to transient voltage safety constraint conditions; simplifying an embedded differential-algebraic equation set constraint in the unit commitment model through a trajectory sensitivity algorithm to obtain an optimization model under transient voltage under multiple time scales; decomposing the optimization model according to a generalized Benders decomposition algorithm to obtain a mixed integer linear programming problem which does not contain alternating current power flow calculation and a nonlinear programming problem which meets transient voltage constraint after iteration; and respectively solving the mixed integer linear programming problem and the nonlinear programming problem through a solver to obtain an optimal solution of the unit commitment model. Therefore, by simplifying the constraint of the embedded differential-algebraic equation set, the model is decomposed into the main problem and the sub-problem with different emphasis, and the main problem and the sub-problem are solved respectively, so that the efficiency of solving the original problem is greatly improved.

The invention provides a dynamic grouping method and device for a heterogeneous direct current delivery system, and relates to the technical field of dynamic analysis and control of a power system, and the method comprises the steps: deducing a linear time-varying variation equation which is satisfied by the trajectory sensitivity of a system state trajectory to a system parameter vector based on a parameterized differential-algebraic equation model; calculating the track sensitivity of each device to a system parameter vector, projecting the track sensitivity to a common connection point corresponding to each device, and constructing a unified sensitivity feature vector of each device; calculating the dynamic similarity between the devices based on the unified sensitivity feature vector, and constructing a mixed similarity matrix in combination with the electrical distance similarity between the devices; and feature decomposition and feature vector clustering are carried out based on the mixed similarity matrix, and dynamic clustering of heterogeneous equipment is realized. According to the dynamic grouping method provided by the invention, unified grouping of heterogeneous equipment such as a synchronous machine and a converter can be realized in a heterogeneous power system containing high-proportion new energy and direct-current power transmission.

The application relates to the technical field of power electronics, and discloses a press-contact type IGBT device packaging structure optimization method and system. The method comprises the following steps: constructing an equivalent model of a press-contact type IGBT device; constructing a differential algebraic equation for uniformly describing the equivalent model of the press-contact type IGBT device and circuit port variables; converting the differential algebraic equation into a nonlinear algebraic equation group through time domain discretization, and constructing an iteration matrix with a global state vector as a derivation object according to a solving mode of the nonlinear algebraic equation group; performing low-dimensional subspace projection on the iteration matrix based on a Krylov subspace, and combining residual minimization to solve a linear subproblem of the iteration matrix, so that current uniformity characteristic results of the press-contact type IGBT device are obtained; and the packaging structure of the press-contact type IGBT device is optimized based on current density distribution reflected by the current uniformity characteristic results. The application can improve the current uniformity and operation reliability of the system.

The invention discloses a multi-stage separation unit initialization method and system based on a virtual transient model and application, and relates to the technical field of chemical process simulation, and the method comprises the steps: constructing a virtual transient differential equation of a multi-stage separation unit; constructing a virtual differential variable associated equation of the multi-stage separation unit; constructing a virtual transient model of the whole tower of the multistage separation unit; solving the virtual transient model; and outputting the initial estimation value. According to the multi-stage separation unit initialization method and system based on the virtual transient model and the application, when a dynamic process differential algebraic equation model is constructed, the use of a complex hydraulics association formula and structural information of the separation unit is avoided, the time-varying item is virtual, the method does not need to be based on a real physical process, and the time-varying item is saved. However, the integral is completely equivalent to the algebraic equation model when reaching the steady state, so that the initialization process of the multi-stage separation unit based on the virtual transient model is easier to solve, and the method has the advantages of high calculation efficiency and higher robustness.

A method for calibrating the feedback gain of an LQI controller implemented in an electronic control unit (25) operatively connected for controlling the operation of a physical electrical or electromechanical device (26) of a dynamic physical system (28), in particular a vehicle powertrain (4), wherein the method of calibrating the LQI controller comprises: obtaining values of various physical parameters of the dynamic physical system (28); substituting the obtained value of the physical parameter into a predetermined equation for calculating the value of each term of a P matrix, where the P matrix is a solution to the algebraic Riccati equation, and where the predetermined equation comprises the physical parameter of the system (28); and calculating a new feedback gain of the LQI controller based on the arbitrary selected positive value of r based on the matrix equation, wherein terms of the matrix K correspond to the feedback gain.

The invention discloses a distributed photovoltaic aggregation frequency modulation standby optimal configuration method considering node frequency security constraints under transmission and distribution cooperation. The method comprises the following steps: describing uncertainty of photovoltaic aggregation frequency modulation capability by using a Gaussian mixture model, and establishing a power transmission network node frequency response model containing frequency space distribution characteristics; taking minimization of system power generation and frequency modulation reserve cost as a target, and combining opportunity constraint planning to construct an optimal configuration model; a response model is reduced based on a frequency divider theory, a Bernstein polynomial approximates frequency dynamics, and a differential algebraic equation is converted into an algebraic equation; then, binary expansion and Gaussian mixture model linear invariance are utilized to convert the model into a mixed integer linear programming model, and Bernstein polynomial convex hull property tightening constraint is combined; and finally, solving the model to obtain the optimal photovoltaic aggregation frequency modulation reserve capacity and control parameters. The frequency space distribution is accurately described, the problem of insufficient frequency safety risk identification is solved, and the frequency safety level of a power system is improved.