Linear dynamic modeling method and system based on generalized momentum and koopman theory

Abstract

The application discloses a kind of linear dynamic modeling method and system based on generalized momentum and Koopman theory, for the interaction and operation law of multiple energy in wisdom transformer area system, construct the mathematical model of wisdom transformer area system including a variety of different energy, power electronic equipment control logic and power flow equation;Comprehensively consider multiple constraints, construct the constraint condition set of the mathematical model of wisdom transformer area system;By introducing momentum base state space representation, linear decoupling is carried out from state-dependent dynamics to control input channel, a linear Koopman dynamic model only needs to learn unexcited dynamics, which significantly reduces model complexity and improves data efficiency;Further integrate linear generalized extended state observer, realize real-time estimation and compensation to external disturbance and unmodeled dynamic characteristics of system;The proposed method is applied to the actual data of wisdom transformer area system, while improving the accuracy of dynamic characteristic extraction, significantly enhances the stability and robustness of the system under uncertain conditions.

Description

Technical Field

[0001] This invention belongs to the field of smart transformer substation energy system technology, and particularly relates to a linear dynamic modeling method and system based on generalized momentum and Koopman theory. Background Technology

[0002] With the continuous advancement of integrated power system construction, smart distribution areas, as an important component of modern power systems, are facing increasingly complex nonlinear dynamic characteristics and modeling challenges. While smart distribution areas improve the intelligence level of energy management by integrating various distributed energy sources and advanced power electronics technologies, their strong nonlinearity, multiple uncertainties, and complex coupling between source, grid, load, and storage pose significant difficulties for accurate system modeling and robust control.

[0003] Traditional physical mechanism-based modeling methods suffer from problems such as complex parameter tuning and poor model adaptability when describing the nonlinear dynamics of smart distribution areas. While existing data-driven methods can characterize system nonlinearity to some extent, they often face limitations such as high model complexity, heavy computational burden, and insufficient robustness to uncertainties and external disturbances. In particular, with the high proportion of renewable energy integration, the system operating point changes frequently, further increasing the difficulty of dynamic modeling and control.

[0004] To address these challenges, there is an urgent need to develop a smart transformer area dynamic modeling and control method that can balance model accuracy and computational efficiency while possessing strong robustness. This would enable efficient energy management and optimized control of the system under complex operating conditions, improve power quality and supply reliability, promote the efficient consumption of a high proportion of renewable energy, and contribute to the low-carbon transformation of the energy system. Summary of the Invention

[0005] This invention provides a linear dynamic modeling method and system based on generalized momentum and Koopman theory to solve the problem of dynamic accurate modeling and robust control of smart distribution transformers under the complex interaction of uncertainties in renewable energy output, load fluctuations and power electronic equipment.

[0006] In a first aspect, the present invention provides a linear dynamic modeling method based on generalized momentum and Koopman theory, comprising:

[0007] To address the interaction and operational patterns of multiple energy sources within a smart distribution transformer system, a mathematical model of the smart distribution transformer system is constructed, incorporating various energy sources, power electronic equipment control logic, and power flow equations.

[0008] Taking into account multiple constraints, a set of constraints is constructed for the mathematical model of the smart transformer substation system;

[0009] A linear Koopman dynamic model is constructed based on momentum-based state-space representation, and the state variables in the mathematical model of the smart transformer substation system are defined as a combination of generalized position coordinates and generalized momentum coordinates.

[0010] The integrated linear generalized extended state observer (GESO) is used to estimate and compensate for external disturbances and unmodeled dynamic features in the smart distribution area system in real time.

[0011] Based on actual data from the smart distribution transformer system, the power flow equations are solved and the spatiotemporal voltage response is obtained. Based on the constructed linear Koopman dynamic model and linear generalized extended state observer, the nonlinear dynamic characteristics of the smart distribution transformer system are modeled and controlled.

[0012] Secondly, the present invention provides a linear dynamic modeling system based on generalized momentum and Koopman theory, including a smart transformer area mathematical model construction module, a smart transformer area constraint condition set construction module, a linear Koopman dynamic model construction module, a disturbance observation and compensation module, and a closed-loop control module.

[0013] Smart Distribution Area Mathematical Model Construction Module: Used to construct a mathematical model of the smart distribution area system that includes various energy sources, power electronic equipment control logic, and power flow equations, based on the interaction and operation patterns of multiple energy sources within the smart distribution area system.

[0014] Smart Transformer Area Constraint Set Construction Module: Used to comprehensively consider multiple constraints and construct the constraint set for the mathematical model of the smart transformer area system;

[0015] Linear Koopman Dynamic Model Construction Module: Used to construct linear Koopman dynamic models based on momentum-based state-space representation, defining the state variables in the mathematical model of the smart transformer substation system as a combination of generalized position coordinates and generalized momentum coordinates;

[0016] Disturbance Observation and Compensation Module: Used to integrate a linear generalized extended state observer to perform real-time estimation and compensation for external disturbances and unmodeled dynamic features in the smart distribution area system;

[0017] Closed-loop control module: used to solve the power flow equation and obtain the spatiotemporal voltage response based on the actual data of the smart distribution area system. Based on the constructed linear Koopman dynamic model and linear generalized extended state observer, it realizes the modeling and control of the nonlinear dynamic characteristics of the smart distribution area system.

[0018] Thirdly, an electronic device is provided, comprising: at least one processor, and a memory communicatively connected to the at least one processor, wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform the steps of the linear dynamic modeling method based on generalized momentum and Koopman theory described above.

[0019] Fourthly, the present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the above-described linear dynamic modeling method based on generalized momentum and Koopman theory.

[0020] The technical effects and advantages provided by the present invention in the above technical solution are as follows:

[0021] This application proposes a linear dynamic modeling method and system based on generalized momentum and Koopman theory, which demonstrates significant advantages in several aspects for smart distribution areas facing challenges such as fluctuations in renewable energy output, random load changes, and complex interactions with power electronic equipment.

[0022] By introducing momentum-based state-space representation, this invention achieves linear decoupling between control input and state-dependent dynamics, enabling the constructed linear Koopman dynamic model to learn only the unexcited dynamic part of the system, significantly reducing the number of model parameters, improving data utilization efficiency and training speed, and effectively reducing model complexity.

[0023] Compared with traditional nonlinear modeling and conventional dimensionality increase methods, the linear Koopman dynamic model obtained by this invention is not only simple in structure and easy to analyze, but also has better prediction accuracy than the traditional bilinear model. At the same time, it effectively preserves the dominant dynamic modes of the system and avoids excessive decay of key dynamic characteristics, laying a reliable foundation for system stability analysis and control.

[0024] By integrating a linear generalized extended state observer, this invention can estimate and actively compensate for uncertainties such as load mutations and renewable energy fluctuations in smart distribution areas in real time. Combined with a linear model predictive control framework, it significantly enhances the voltage stability, frequency support capability, and overall operational robustness of the system under uncertain operating conditions while maintaining the linear structure of the controller.

[0025] In summary, this invention provides a high-precision, efficient, and robust dynamic modeling and control solution for smart distribution transformers by organically integrating momentum-based state-space representation, linear Koopman dynamic modeling, and linear generalized extended state observer (GESO)-model predictive controller (MPC controller). This provides effective technical support for the real-time optimized scheduling and safe and stable operation of smart distribution transformers. Attached Figure Description

[0026] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0027] Figure 1 A flowchart illustrating a linear dynamic modeling method based on generalized momentum and Koopman theory, provided as an embodiment of the present invention;

[0028] Figure 2 A structural block diagram of a linear dynamic modeling system based on generalized momentum and Koopman theory is provided as an embodiment of the present invention.

[0029] Figure 3 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0030] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0031] Please see Figure 1 As shown, one embodiment of the present invention provides a linear dynamic modeling method based on generalized momentum and Koopman theory, specifically including the following steps:

[0032] Step S101 involves constructing a mathematical model of the smart distribution transformer system, encompassing various energy sources, power electronic equipment control logic, and power flow equations, addressing the complex interactions and operational patterns of diverse energy sources within the system. This mathematical model is based on renewable energy power generation systems such as solar photovoltaic (PV) and wind power systems. It integrates the regulation capabilities provided by solar PV power sources, wind turbines, battery energy storage systems (BESS), hydrogen fuel cells (HFC), and synchronous generators (SG), and incorporates the control characteristics of power electronic equipment, enabling real-time feedback control of the smart distribution transformer system's operational status.

[0033] (1) The solar photovoltaic power generation system constructs a continuous-time function using pre-collected discrete-time power data. Assume the set of measurement data for 24 hours a day is... , express The measured power output of solar photovoltaic (PV) power generation at any given time can be calculated using linear interpolation. This approach aims to transform discrete, hourly measurement data into a continuous power curve, enabling more refined analysis and calculations at any given time.

[0034] Define a periodic function as 24 hours, and implement the loop using the modulo operation method. Its expression is:

[0035] ,

[0036] ,

[0037] In the formula, For continuous time; Indicating that the smart district is in The power generation capacity of solar photovoltaic at any given time; This indicates that the output is calculated using linear interpolation.

[0038] (2) The 24-hour measurement data set of the wind power generation system is as follows: , express The measured power output of wind power generation at any given time. Wind power output is calculated using linear interpolation. This approach aims to transform discrete, hourly measurement data into a continuous power curve, enabling more refined analysis and calculations at any given time.

[0039] Define a periodic function as 24 hours, and implement the loop using the modulo operation method. Its expression is:

[0040] ,

[0041] ,

[0042] In the formula, For continuous time; Indicating that the smart district is in The output power of wind power generation at any given time; This indicates that the output is calculated using linear interpolation.

[0043] (3) The goal of a battery energy storage system (BESS) is to compensate for the power gap in a smart distribution area caused by the mismatch between load and distributed power generation. Its expression is:

[0044] ,

[0045] In the formula, This indicates a power shortage in the smart distribution area system; Indicating that the smart district is in The power demand of the load at any given time.

[0046] Based on different time periods, charging and discharging strategies are selected. During periods of sufficient photovoltaic power, when the smart distribution area has remaining power, BESS prioritizes charging operations, the expression of which is:

[0047] ,

[0048] In the formula, Indicates in BESS charging power at all times; This indicates the maximum allowable charge and discharge power of BESS.

[0049] During peak load periods, when a power shortage occurs in a smart distribution area, the BESS prioritizes discharge operations, the expression of which is:

[0050] ,

[0051] In the formula, Indicates in The discharge power of BESS at any given time.

[0052] (4) In the smart distribution system, HFC is designed as a supplementary power source to make up for the insufficient power of the system after BESS regulation. Specifically, when solar photovoltaic, wind power and BESS cannot fully meet the load demand, the remaining power gap will be shared by HFC and SG.

[0053] Smart Transit Area The load demand power at time is The sum of wind and solar power output and the power provided by BESS for:

[0054] ,

[0055] The remaining power deficit in a smart distribution area is defined as:

[0056] ,

[0057] In the formula, This indicates the remaining power deficit after BESS regulation. When the value is positive, it indicates that the system has insufficient power supply and needs to be supplemented by HFC; otherwise, no additional supplementation is required.

[0058] Based on the aforementioned power gap, there are two different methods for calculating the actual output power of HFC, each corresponding to a different scheduling strategy:

[0059] 1) In establishing the linear Koopman dynamic model of the smart distribution transformer system, the output expression of HFC is:

[0060] ,

[0061] In the formula, Indicates in The output power of HFC in the linear Koopman dynamic model at time t; Indicates in The maximum output limit of HFC in the linear Koopman dynamic model at time t.

[0062] 2) In the load-sharing strategy used in power flow calculations, the output of the HFC (High-Power Controller) proportionally covers a portion of the power deficit, as expressed in the following expression:

[0063] ,

[0064] In the formula, Indicates in The output power of the load-sharing strategy adopted by HFC in power flow calculation at any given time; Indicates in The maximum output limit of the load-sharing strategy adopted by HFC in power flow calculation at any given time.

[0065] The practical significance of adopting two different implementation methods lies in meeting the requirements of global scheduling and dynamic simulation, reflecting the collaborative control mechanism between devices, and enhancing the overall flexibility and robustness of the smart distribution area system. The former ensures rapid response of the energy management layer in the face of gaps, while the latter, through proportional sharing in power flow simulation, more realistically simulates the collaborative optimization between devices, providing richer evidence for subsequent system optimization and control strategy research.

[0066] (5) As an important traditional regulating and backup energy device, SG plays a supplementary and stable power supply role in smart distribution areas. Its main task is to meet the energy demand of the smart distribution area system by adjusting the output power when the load demand exceeds the capacity provided by solar photovoltaic power generation, wind power generation, BESS, and HFC, and plays a key role in balancing power supply and demand and maintaining system frequency and voltage stability during transient and steady-state processes. Its expression is:

[0067] ,

[0068] In the formula, This indicates the remaining power gap after BESS and HFC regulation; Indicates in The charging and discharging power of BESS at any given time is negative when charging and positive when discharging. Indicates in The output power of SG in the linear Koopman dynamic model at time 1; Indicates in The maximum output limit of SG in the linear Koopman dynamic model at time 1.

[0069] In power flow calculation, SG and HFC work together. Their expression is:

[0070] ,

[0071] In the formula, Indicates in The output power of SG in the power flow calculation using the sharing strategy; Indicates in The maximum output limit of the load-sharing strategy adopted by SG in power flow calculation at time SG.

[0072] (6) To improve the stability of the smart distribution transformer system, this invention employs a virtual synchronous generator (VSG) control strategy for power electronic devices such as photovoltaic, energy storage, and HFC. This control strategy uses a droop control mechanism to convert the power deviation of the smart distribution transformer system into frequency and voltage adjustments. The expression for frequency droop is:

[0073] ,

[0074] In the formula, This indicates the frequency adjustment amount caused by the active power deviation; Indicates the frequency droop factor; This represents the active power injected by the node; This indicates the reference power of the smart distribution area system.

[0075] The expression for voltage droop is:

[0076] ,

[0077] In the formula, This indicates the voltage adjustment caused by reactive power deviation; Indicates the voltage droop factor; This represents the reactive power injected by the node.

[0078] After obtaining the frequency and voltage adjustments, an additional damping term is introduced to correct the VSG's response under control, simulating the inertial response and damping characteristics of a physical synchronous machine. Its expression is:

[0079] ,

[0080] In the formula, This indicates the actual frequency of the VSG under control; This represents the damping coefficient, used to suppress system oscillations and enhance the stability of the control response; This indicates the voltage setting value of the VSG under control; Indicates the rated voltage of the smart distribution area system; This indicates the rated frequency of the smart distribution area system.

[0081] Finally, under the VSG-based control strategy, the node voltage The dynamic state equation expression is as follows:

[0082]

[0083] In the formula, , These represent the real and imaginary parts of the node voltage, respectively. , They represent the target voltages respectively. The real and imaginary parts.

[0084] The power flow equations of the mathematical model of the smart distribution transformer system are as follows:

[0085] Smart Transformer Area System Admittance Matrix During construction, a diagonally dominant matrix is ​​used to ensure numerical stability, expressed as:

[0086] ,

[0087] In the formula, Represents a random complex matrix; express The first in the matrix Line 1 The elements of the column, where N is the number of nodes;

[0088] No. Injected current at each node for:

[0089] ,

[0090] In the formula, Indicates the first The voltage injected into each node;

[0091] No. Complex power of each node for:

[0092] ,

[0093] In the formula, Indicates the first Voltage injected at each node, for The conjugate of complex numbers.

[0094] In summary, in response to the complex interactions and operational patterns of multiple energy sources within a smart distribution network system, this invention constructs a mathematical model that includes various energy sources, power electronic equipment control logic, and power flow equations. This model effectively characterizes the dynamic coupling between the components, providing solid data support for system scheduling optimization and energy efficiency management.

[0095] Step S102: Based on the above mathematical model, and taking into account multiple factors, construct a set of constraints for the mathematical model of the smart distribution area system, providing basic support for the safe and stable operation and efficient scheduling of the smart distribution area system.

[0096] To ensure that the BESS operates within a safe range, the charging and discharging power of the BESS must meet the following constraints:

[0097] ,

[0098] The state of charge (SOC) of a battery in a BESS reflects the current energy level stored in the battery, and its expression is:

[0099] ,

[0100] In the formula, Indicates in The state of charge of BESS at time 10:00. Indicates in The state of charge of BESS at time t, ranging from ; Indicates in The charging and discharging power of BESS at any given time is negative when charging and positive when discharging. This is the discrete time step, used to calculate the state changes of the BESS. This indicates the rated energy capacity of BESS.

[0101] To ensure that the BESS can meet regulation requirements during long-term operation while protecting the battery from extreme operating conditions, thereby extending battery life and ensuring the safe operation of the smart distribution area, its SOC must meet upper and lower limits:

[0102] ,

[0103] In the formula, This indicates the minimum energy level of the battery to prevent over-discharge. This indicates the maximum energy limit of the battery to prevent overcharging.

[0104] The set of constraints will serve as the state and input constraints in the linear Koopman dynamic model and model predictive control framework, ensuring that the system achieves optimized scheduling and robust control within a safe operating range.

[0105] Step S103: Based on the above mathematical model, construct a linear Koopman dynamic model based on the momentum-based state space representation, and redefine the state variables in the mathematical model of the smart transformer substation system as a combination of generalized position coordinates and generalized momentum coordinates.

[0106] Using momentum-based state-space representation, the state variables in the mathematical model of the smart distribution transformer system are defined as follows: ,in It represents generalized position coordinates, including electrical quantities such as the real and imaginary parts of node voltages; Represents the generalized momentum coordinates, defined as the integral or virtual momentum related to power and current; Indicates transpose;

[0107] Based on momentum-based state-space representation, the dynamic characteristics of a smart distribution transformer system can be described as follows:

[0108] ,

[0109] In the formula, To control the input, it acts on the system in a linear form, and only the unexcited dynamic part needs to be learned through the neural network architecture. The corresponding Koopman embedding.

[0110] Constructing a linear Koopman dynamic model:

[0111] ,

[0112] ,

[0113] In the formula, These represent the Koopman states at times k and k+1, respectively. This represents the control input vector applied to the smart distribution system at time k; This represents the state vector of the intelligent distribution area system at time k; The matrix of the Koopman system to be learned; Given a known input matrix; This is the state reconstruction matrix.

[0114] By collecting system operation data, a loss function is designed based on prediction error and consistency improvement. A high-precision linear dynamic model is obtained by training the unexcited dynamic part using a neural network.

[0115] Step S104: Integrate a linear generalized extended state observer to perform real-time estimation and compensation for external disturbances and unmodeled dynamic features in the smart transformer substation system.

[0116] Load fluctuations, renewable energy power generation fluctuations, and unmodeled line losses in the smart distribution transformer system are uniformly defined as lumped disturbances acting on the system. Based on this, a linear generalized extended state observer is introduced to handle lumped disturbances. Perform dynamic estimation;

[0117] The design of the linear generalized extended state observer is based on an augmented system model, which incorporates lumped disturbances. Considered as an additional state of the system, its dynamic equation is:

[0118] ,

[0119] ,

[0120] In the formula, , The Koopman system matrix and control matrix are in continuous time. These are the observed values ​​of the state variables; The derivative of the observed values ​​of the state variable; These are perturbation observations; The derivative of the perturbation observation; This represents the upgraded Koopman state. For disturbance compensation control law; , This is the observer gain coefficient, and by configuring the poles, we can ensure that the estimation error converges quickly.

[0121] Disturbance observations The disturbance compensation control law is fed forward to the input of the linear Koopman dynamic model predictive controller (MPC).

[0122] ,

[0123] In the formula, The nominal control quantity calculated for the predictive controller of the linear Koopman dynamic model. To control the pseudo-inverse of the input matrix, this compensation function can correct the control commands of BESS, HFC and other equipment in real time when the load fluctuates or the photovoltaic output changes randomly, thereby suppressing voltage deviation and frequency fluctuation.

[0124] The linear generalized extended state observer is directly embedded in the linear Koopman dynamic model predictive control framework. Without disrupting the linear structure of the controller, it enables proactive disturbance rejection of multiple uncertainties in the smart distribution area, effectively enhancing the power supply quality and operational robustness of the smart distribution area system under non-ideal operating conditions.

[0125] Step S105: Solve the power flow equation and obtain the spatiotemporal voltage response based on the actual data of the smart distribution transformer system. Based on the constructed linear Koopman dynamic model and linear generalized extended state observer, realize the modeling and control of the nonlinear dynamic characteristics of the smart distribution transformer system.

[0126] Based on real-time operation data of the smart distribution area system collected by SCADA or PMU, a training dataset is constructed, which includes node voltage, injected power, BESS charging and discharging status and new energy output. The training dataset is mapped to generalized position-generalized momentum state pairs through momentum-based state space representation.

[0127] The linear Koopman dynamic model is trained end-to-end using the training dataset. By minimizing the multi-step prediction error and state reconstruction loss, the trained linear Koopman dynamic model is obtained, which can accurately describe the dynamic evolution of the smart distribution area system.

[0128] The trained linear Koopman dynamic model and the linear generalized extended state observer are integrated into the model predictive control framework to construct a closed-loop control system. Within each control cycle, the Koopman state is initialized based on real-time measurement data, and the optimal control sequence is calculated by solving the following optimization problem:

[0129] ,

[0130] ,

[0131] ,

[0132] ,

[0133] In the formula, To optimize decision variables; For prediction in the time domain; This is the weight matrix; The reference trajectory for the state, Real-time perturbation estimation provided for linear generalized extended state observers; Sampling time; , These are the upper and lower limits of the state constraints; , To control the upper and lower limits of input constraints.

[0134] Through a closed-loop control system, coordinated scheduling of regulation resources such as BESS, HFC, and SG is achieved. Under the premise of ensuring stable node voltage and qualified frequency, the fluctuations of new energy sources are effectively mitigated, and the robustness of smart distribution area operation and energy absorption capacity are improved.

[0135] In summary, the method presented in this embodiment proposes a linear dynamic modeling approach based on generalized momentum and Koopman theory. By constructing a mathematical model of a smart distribution transformer area that integrates multi-energy characteristics and power electronic control logic, it accurately characterizes the multi-element dynamic coupling relationships within the smart distribution transformer area system. Employing momentum-based state-space representation linearly decouples the control input from state-dependent dynamics, significantly reducing model complexity and improving data efficiency. Furthermore, by integrating a linear generalized extended state observer and a model predictive control framework, it achieves real-time estimation and proactive compensation for external disturbances and unmodeled dynamic characteristics of the smart distribution transformer area system. Under the conditions of ensuring voltage stability and frequency compliance, it effectively improves the operational robustness and control performance of the smart distribution transformer area system in scenarios involving new energy fluctuations and load changes.

[0136] In summary, this application addresses the dynamic characteristics and stable control problems faced by smart distribution transformer areas under the uncertainty of renewable energy output and the control interaction of power electronic equipment. It proposes a linear dynamic modeling method based on generalized momentum and Koopman theory, providing effective theoretical basis and technical support for the real-time optimized scheduling and safe and stable operation of smart distribution transformer areas. Furthermore, considering the complex interactions and operational patterns of multiple energy sources within the smart distribution transformer system, this invention constructs a mathematical model encompassing various energy sources, power electronic equipment control logic, and power flow equations. This model effectively characterizes the dynamic coupling between the components, providing solid data support for system scheduling optimization and energy efficiency management.

[0137] Please see Figure 2 As shown, another embodiment of the present invention provides a linear dynamic modeling system based on generalized momentum and Koopman theory, including a smart transformer area mathematical model construction module 201, a smart transformer area constraint condition set construction module 202, a linear Koopman dynamic model construction module 203, a disturbance observation and compensation module 204, and a closed-loop control module 205.

[0138] Smart Distribution Area Mathematical Model Construction Module 201: Used to construct a mathematical model of the smart distribution area system that includes multiple different energy sources, power electronic equipment control logic, and power flow equations, based on the interaction and operation patterns of multiple energy sources within the smart distribution area system.

[0139] Smart Transformer Area Constraint Set Construction Module 202: Used to comprehensively consider multiple constraints and construct a set of constraints for the mathematical model of the smart transformer area system;

[0140] Linear Koopman Dynamic Model Construction Module 203: Used to construct a linear Koopman dynamic model based on momentum-based state space representation, defining the state variables in the mathematical model of the smart transformer substation system as a combination of generalized position coordinates and generalized momentum coordinates;

[0141] Disturbance Observation and Compensation Module 204: Used to integrate a linear generalized extended state observer to perform real-time estimation and compensation for external disturbances and unmodeled dynamic features in the smart distribution area system;

[0142] Closed-loop control module 205: It is used to solve the power flow equation and obtain the spatiotemporal voltage response based on the actual data of the smart distribution area system. Based on the constructed linear Koopman dynamic model and linear generalized extended state observer, it realizes the modeling and control of the nonlinear dynamic characteristics of the smart distribution area system.

[0143] It should be understood that Figure 2 The modules and references described in the document Figure 1 The steps described in the text correspond to those in the method described above. Therefore, the operations, features, and corresponding technical effects described above also apply to the method described in the text. Figure 2 The various modules in the document will not be described in detail here.

[0144] In other embodiments, the present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, the processor performs the linear dynamic modeling method based on generalized momentum and Koopman theory in the above method embodiments.

[0145] In one implementation, a computer-readable storage medium may include a stored program area and a stored data area, wherein the stored program area may store an operating system and an application program required for at least one function; the stored data area may store data created based on the use of a linear dynamic modeling system based on generalized momentum and Koopman theory, etc. Furthermore, the computer-readable storage medium may include high-speed random access memory and may also include non-volatile memory, such as at least one disk storage device, flash memory device, or other non-volatile solid-state storage device. In some embodiments, the computer-readable storage medium may optionally include memory remotely located relative to a processor, which can be connected to the linear dynamic modeling system based on generalized momentum and Koopman theory via a network. Examples of such networks include, but are not limited to, the Internet, corporate intranets, local area networks, mobile communication networks, and combinations thereof.

[0146] Figure 3 This is a schematic diagram of the structure of the electronic device provided in the embodiment of the present invention, such as... Figure 3As shown, the device includes a processor 310 and a memory 320. The electronic device may also include an input device 330 and an output device 340. The processor 310, memory 320, input device 330, and output device 340 can be connected via a bus or other means. Figure 3 Taking a bus connection as an example, memory 320 is the computer-readable storage medium described above. Processor 310 executes various server functions and data processing by running non-volatile software programs, instructions, and modules stored in memory 320, thereby implementing the linear dynamic modeling method based on generalized momentum and Koopman theory described in the above embodiment. Input device 330 can receive input digital or character information and generate key signal inputs related to user settings and function control of the linear dynamic modeling system based on generalized momentum and Koopman theory. Output device 340 may include a display screen or other display device.

[0147] The aforementioned electronic device can execute the method provided in the embodiments of the present invention, and has the corresponding functional modules and beneficial effects for executing the method. Technical details not described in detail in this embodiment can be found in the method provided in the embodiments of the present invention.

[0148] In one implementation, the above-described electronic device is applied to a linear dynamic modeling system based on generalized momentum and Koopman theory, for a client, comprising: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to execute the instructions stored in the computer-readable storage medium.

[0149] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., including several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods of various embodiments or some parts of embodiments.

[0150] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A linear dynamic modeling method based on generalized momentum and Koopman theory, characterized in that, include: To address the interaction and operational patterns of multiple energy sources within a smart distribution transformer system, a mathematical model of the smart distribution transformer system is constructed, incorporating various energy sources, power electronic equipment control logic, and power flow equations. Taking into account multiple constraints, a set of constraints is constructed for the mathematical model of the smart transformer substation system; A linear Koopman dynamic model is constructed based on momentum-based state-space representation, and the state variables in the mathematical model of the smart transformer substation system are defined as a combination of generalized position coordinates and generalized momentum coordinates. An integrated linear generalized extended state observer is used to estimate and compensate for external disturbances and unmodeled dynamic features in the smart distribution area system in real time. Based on the actual data of the smart distribution transformer system, the power flow equations are solved and the spatiotemporal voltage response is obtained. Based on the constructed linear Koopman dynamic model and linear generalized extended state observer, the nonlinear dynamic characteristics of the smart distribution transformer system are modeled and controlled. The construction of the linear Koopman dynamic model based on momentum-based state-space representation includes: Using momentum-based state-space representation, the state variables in the mathematical model of the smart distribution transformer system are defined as follows: ,in Represents generalized position coordinates, including the real and imaginary parts of the node voltage; Represents the generalized momentum coordinates, defined as the integral or virtual momentum related to power and current; Indicates transpose; Based on momentum-based state-space representation, the dynamic characteristics of a smart distribution transformer system can be described as follows: , In the formula, To control the input, it acts linearly on the smart distribution area system, and only needs to learn the unexcited dynamic part through a neural network architecture. The corresponding Koopman embedding; Constructing a linear Koopman dynamic model: ， ， In the formula, These represent the Koopman states at times k and k+1, respectively. This represents the control input vector applied to the smart distribution system at time k; This represents the state vector of the intelligent distribution area system at time k; The matrix of the Koopman system to be learned; Given a known input matrix; The state reconstruction matrix; The integrated linear generalized extended state observer performs real-time estimation and compensation for external disturbances and unmodeled dynamic features in the smart distribution network system, including: Load fluctuations, renewable energy power generation fluctuations, and unmodeled line losses in the smart distribution transformer system are uniformly defined as lumped disturbances acting on the system. Introducing a linear generalized extended state observer for lumped disturbances Perform dynamic estimation; The design of the linear generalized extended state observer is based on an augmented system model, which incorporates lumped disturbances. Considered as an additional state of the system, its dynamic equation is: ， ， In the formula, , The Koopman system matrix and control matrix are in continuous time. These are the observed values ​​of the state variables; The derivative of the observed values ​​of the state variable; These are perturbation observations; The derivative of the perturbation observation; , The observer gain coefficient; This represents the upgraded Koopman state. For disturbance compensation control law; Disturbance observations The disturbance compensation control law is fed forward to the input of the linear Koopman dynamic model predictive controller. ， In the formula, The nominal control quantity calculated for the predictive controller of the linear Koopman dynamic model. To control the pseudo-inverse of the input matrix.

2. The linear dynamic modeling method based on generalized momentum and Koopman theory according to claim 1, characterized in that, The mathematical model of the intelligent distribution area system is based on the solar photovoltaic power generation system and the wind power generation system. It combines the regulation capabilities provided by the solar photovoltaic power source, wind turbine, battery energy storage system (BESS), hydrogen fuel cell (HFC) and synchronous generator (SG), and incorporates the control characteristics of power electronic equipment to provide real-time feedback control of the operating status of the intelligent distribution area system. The set of 24-hour measurement data for a solar photovoltaic power generation system is , express The measured power of solar photovoltaic power generation at any given time is calculated using linear interpolation for the smart distribution area. The power generation capacity of solar photovoltaic at any given time is ; The 24-hour measurement data set of a wind power generation system is , express The measured power output of wind power generation at any given time is calculated using linear interpolation for the smart distribution area. The output power of wind power generation at any time is ; The goal of a Battery Energy Storage System (BESS) is to compensate for the power gap in smart distribution areas caused by the mismatch between load and distributed generation. Its expression is: ， In the formula, This indicates a power shortage in the smart distribution area system. Indicating that the smart district is in The load power demand at any given time; Hydrogen fuel cells (HFCs) serve as supplementary power sources to compensate for the insufficient power in the smart distribution area system after BESS regulation. The expression is as follows: ， In the formula, This indicates the remaining power deficit after BESS regulation. This represents the sum of power output from wind and solar power and the power provided by BESS. The synchronous generator SG is used to meet the energy demand of the smart distribution area system when the load demand exceeds the capacity provided by solar photovoltaic power generation, wind power generation, BESS, and HFC. The expression is as follows: ， In the formula, This indicates the remaining power gap after BESS and HFC regulation; Indicates in The charging and discharging power of BESS at any given time is negative when charging and positive when discharging. Indicates in The output power of HFC in the linear Koopman dynamic model at time t; Indicates in The output power of SG in the linear Koopman dynamic model at time 1; Indicates in The upper limit of the maximum output of SG in the linear Koopman dynamic model at time 1; For the control strategy of using a virtual synchronous generator (VSG) for power electronic equipment, a droop control mechanism is adopted to convert the power deviation of the smart distribution system into frequency and voltage adjustment quantities. The expression for frequency droop is: ， In the formula, This indicates the frequency adjustment amount caused by active power deviation; Indicates the frequency droop factor; This represents the active power injected by the node; Indicates the reference power of the smart distribution area system; The expression for voltage droop is: ， In the formula, This indicates the voltage adjustment caused by reactive power deviation; Indicates the voltage droop factor; This represents the reactive power injected by the node; After obtaining the frequency and voltage adjustment values, an additional damping term is introduced to correct the VSG's response under control, expressed as: ， In the formula, This indicates the actual frequency of the VSG under control; Indicates the damping coefficient; This indicates the voltage setting value of the VSG under control; Indicates the rated voltage of the smart distribution area system; Indicates the rated frequency of the smart distribution area system; Node voltage under VSG-based control strategy The dynamic state equation expression is as follows: ， In the formula, , These represent the real and imaginary parts of the node voltage, respectively. , They represent the target voltages respectively. The real and imaginary parts.

3. The linear dynamic modeling method based on generalized momentum and Koopman theory according to claim 1, characterized in that, The power flow equations of the mathematical model of the smart distribution transformer system are as follows: Smart Transformer Area System Admittance Matrix During construction, a diagonally dominant matrix is ​​used to ensure numerical stability, expressed as: ， In the formula, Represents a random complex matrix; express The first in the matrix Line number The elements of the column, where N is the number of nodes; No. Injected current at each node for: ， In the formula, Indicates the first The voltage injected into each node; No. Complex power of each node for: ， In the formula, Indicates the first Voltage injected at each node, for The conjugate of complex numbers.

4. The linear dynamic modeling method based on generalized momentum and Koopman theory according to claim 2, characterized in that, The set of constraints for constructing the mathematical model of the smart transformer substation system, taking into account multiple constraints, includes: BESS's charging and discharging power meets the constraints: ， In the formula, Indicates in BESS's charging power at all times. Indicates in The discharge power of BESS at any given time. This indicates the maximum allowable charge and discharge power of BESS; The State of Charge (SOC) of a Battery Estimated Energy Storage System (BESS) reflects the current energy level stored in the battery, and its expression is: ， In the formula, Indicates in The state of charge of BESS at time 10:

00. Indicates in The state of charge of BESS at time t, ranging from ; Indicates in The charging and discharging power of BESS at any given time is negative when charging and positive when discharging. This is the discrete time step, used to calculate the state changes of the BESS. This indicates the rated energy capacity of BESS; BESS's battery state of charge (SOC) meets the upper and lower limits: ， In the formula, Indicates the minimum energy level of the battery; This indicates the maximum energy limit of the battery.

5. The linear dynamic modeling method based on generalized momentum and Koopman theory according to claim 1, characterized in that, The process involves solving the power flow equations and obtaining the spatiotemporal voltage response based on actual data from the smart distribution transformer system. Then, based on the constructed linear Koopman dynamic model and linear generalized extended state observer, it enables the modeling and control of the nonlinear dynamic characteristics of the smart distribution transformer system, including: Based on the real-time operation data of the smart distribution area system collected by SCADA or PMU, a training dataset containing node voltage, injected power, BESS charging and discharging status and new energy output is constructed. The training dataset is mapped to generalized position-generalized momentum state pairs through momentum-based state space representation. The linear Koopman dynamic model is trained end-to-end using the training dataset. By minimizing the multi-step prediction error and state reconstruction loss, the trained linear Koopman dynamic model is obtained. The trained linear Koopman dynamic model and the linear generalized extended state observer are integrated into the model predictive control framework to construct a closed-loop control system. Within each control cycle, the Koopman state is initialized based on real-time measurement data, and the optimal control sequence is calculated by solving the following optimization problem: ， ， ， ， In the formula, To optimize decision variables; For prediction in the time domain; This is the weight matrix; The reference trajectory for the state, Real-time perturbation estimation provided for linear generalized extended state observers; Sampling time; , These are the upper and lower limits of the state constraints; , To control the upper and lower limits of input constraints.

6. A linear dynamic modeling system based on generalized momentum and Koopman theory, used to implement the modeling method described in any one of claims 1-5, characterized in that, It includes a smart transformer area mathematical model construction module, a smart transformer area constraint set construction module, a linear Koopman dynamic model construction module, a disturbance observation and compensation module, and a closed-loop control module; Smart Distribution Area Mathematical Model Construction Module: Used to construct a mathematical model of the smart distribution area system that includes various energy sources, power electronic equipment control logic, and power flow equations, based on the interaction and operation patterns of multiple energy sources within the smart distribution area system. Smart Transformer Area Constraint Set Construction Module: Used to comprehensively consider multiple constraints and construct the constraint set for the mathematical model of the smart transformer area system; Linear Koopman Dynamic Model Construction Module: Used to construct linear Koopman dynamic models based on momentum-based state-space representation, defining the state variables in the mathematical model of the smart transformer substation system as a combination of generalized position coordinates and generalized momentum coordinates; Disturbance Observation and Compensation Module: Used to integrate a linear generalized extended state observer to perform real-time estimation and compensation for external disturbances and unmodeled dynamic features in the smart distribution area system; Closed-loop control module: used to solve the power flow equation and obtain the spatiotemporal voltage response based on the actual data of the smart distribution area system. Based on the constructed linear Koopman dynamic model and linear generalized extended state observer, it realizes the modeling and control of the nonlinear dynamic characteristics of the smart distribution area system.

7. An electronic device, characterized in that, include: At least one processor, and a memory communicatively connected to the at least one processor, wherein the memory stores instructions executable by the at least one processor to enable the at least one processor to perform the steps of the modeling method according to any one of claims 1 to 5.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the modeling method according to any one of claims 1 to 5.

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