A method for constructing a discrete state space model of a power system and related equipment

Abstract

The application relates to the technical field of power system simulation, in particular to a discrete state space model construction method of a power system and related equipment, which is characterized in that a continuous state space model is constructed based on the operation state of the power system. The continuous model is discretized by using an explicit integration method and an implicit integration method to obtain a first discretized model and a second discretized model. The transformation relationship between the two discretized models is analyzed, and a dissipative continuous system related to the original state space model is derived. The dissipative continuous system is discretized again by using the explicit integration method, and finally, a target discrete state space model is obtained. The method realizes the accurate discretization of the continuous model of the power system, and provides theoretical support for system stability analysis and control strategy design.

Description

Technical Field

[0001] This invention relates to the field of power system simulation technology, specifically to a method for constructing a discrete state-space model of a power system and related equipment. Background Technology

[0002] With the large-scale integration of new energy sources, the transient characteristics of power systems exhibit complex features across a wide frequency range, including both low-frequency transients of synchronous machines and high-frequency electromagnetic transients of power electronic devices, posing a dual challenge to simulation accuracy and speed. Numerical simulation, as a core tool for analyzing transient / steady-state power systems, needs to improve speed while ensuring computational accuracy to meet the requirements of large-scale systems and hardware-in-the-loop testing.

[0003] Current electromagnetic transient simulations primarily employ nodal analysis (based on nodal network equations, fast and convenient but with poor scalability) and state variable methods (based on state-space differential equations, directly reflecting the dynamic essence of the system). Among discrete methods, the forward Euler method, as an explicit method, is simple and easy to use, suitable for nonlinear system simulation, but has poor convergence and requires extremely small step sizes to maintain stability, resulting in slow speed. The trapezoidal rule, as an implicit method, has better convergence and can maintain system stability, but has high computational complexity. Therefore, existing methods struggle to balance accuracy and speed: high accuracy requires small step sizes to capture wideband transients, but significantly increases the computational load; low-precision methods, while fast, cannot accurately reconstruct complex dynamics. This contradiction is further exacerbated in new energy scenarios, hindering the development of large-scale system simulation and hardware-in-the-loop testing. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a method and related equipment for constructing a discrete state-space model of a power system, which addresses the shortcomings of the prior art and solves the technical problem that existing simulation methods cannot balance accuracy and speed.

[0005] The objective of this invention is achieved through the following technical solutions: In a first aspect, the present invention provides a method for constructing a discrete state-space model of a power system, comprising: Establish a state-space model based on the operating status of the power system; Based on the first discretization method and the second discretization method, the state space model is discretized respectively to obtain the first discretized model and the second discretized model. The first discretization method is an explicit integration method, and the second discretization method is an implicit integration method. Analyze the transformation relationship between the first discretization model and the second discretization model, and obtain the dissipative continuous system corresponding to the state space model based on the transformation relationship; The dissipative continuous system is discretized using the first discretization method to obtain the target discrete state-space model.

[0006] As a further improvement of the present invention, the step of establishing a state-space model based on the operating state of the power system includes: Sub-state space models of each power device in the power system and a sub-state space model of the power network topology are established respectively; the sub-state space models of the power devices are obtained based on the operating states of the power devices. Obtain the interconnection feedback relationship between the sub-state space models of each power device and the sub-state space model of the power network topology; Based on the aforementioned interconnection feedback relationship, the sub-state space models of each power device and the sub-state space model of the power network topology are integrated to obtain the state space model of the power system.

[0007] As a further improvement of the present invention, the first discretization method is the forward Euler method; the second discretization method is the trapezoidal method.

[0008] As a further improvement of the present invention, the transformation relationship between the first discretization model and the second discretization model is analyzed, including: The first discretized model and the second discretized model are respectively mapped from the time domain to the complex frequency domain, and the first complex frequency domain transformation operator and the second complex frequency domain transformation operator are obtained accordingly. Construct an algebraic relationship between the first complex frequency domain transform operator and the second complex frequency domain transform operator, wherein the algebraic relationship is the transform relationship.

[0009] As a further improvement of the present invention, a dissipative continuous system corresponding to the state-space model is obtained based on the transformation relationship, including: Mapping the state-space model of the power system to the complex frequency domain; Substituting the transformation relationship into the mapped state-space model yields a dissipative continuous system represented in the complex frequency domain; After inverse transformation of the dissipative continuous system, a state-space model of the time-domain representation of the dissipative continuous system is obtained.

[0010] As a further improvement of the present invention, the dissipative continuous system is:

[0011] In the formula, For the state variables of the power system, For the output of the power system, The sampling period is For the input of the power system, Let be the state function of the power system. This is the output function of the power system.

[0012] As a further improvement of the present invention, after determining the dissipative continuous system corresponding to the state-space model, the method further includes: The state-space model of the dissipative continuous system is linearized to obtain a linearized dissipative system. The equivalent dissipation resistance parameters are analyzed from the linearized dissipation system. The state-space model of the power system is compensated using the dissipation resistance parameters. The compensated power system is then discretized to obtain the target discrete state-space model.

[0013] Secondly, this invention provides a system for constructing a discrete state-space model of a power system, comprising: The model acquisition module is used to establish a state-space model based on the operating state of the power system. The discretization processing module is used to discretize the state space model based on a first discretization method and a second discretization method, respectively, to obtain a first discretized model and a second discretized model. The first discretization method is an explicit integration method, and the second discretization method is an implicit integration method. The dissipative system construction module is used to perform analysis on the transformation relationship between the first discretized model and the second discretized model, and to determine the dissipative continuous system corresponding to the state space model based on the transformation relationship; The target discretization module is used to discretize the dissipative continuous system using a first discretization method to obtain a target discrete state-space model.

[0014] Thirdly, the present invention provides a computer-readable storage medium storing a computer program adapted to be loaded by a processor and executed as described above in the method for constructing a discrete state-space model of a power system.

[0015] Fourthly, the present invention provides a computer device, comprising: a processor and a computer-readable storage medium; A processor, adapted to execute computer programs; A computer-readable storage medium storing a computer program, which, when executed by the processor, implements the discrete state-space model construction method for a power system as described above.

[0016] The beneficial effects of this invention are as follows: This invention provides a method for constructing a discrete state-space model of a power system. A state-space model is established based on the operating state of the power system, and the model is discretized using both explicit and implicit integration methods to obtain a first discretized model and a second discretized model. By analyzing the transformation relationship between the two discretized models, the dissipative continuous system corresponding to the state-space model is determined. Finally, the dissipative continuous system is discretized using an explicit integration method to obtain the target discrete state-space model. The explicit integration method has high computational efficiency due to its direct solution, while the implicit integration method, due to its unconditional stability, guarantees the stability of the discretization process. The discretization results of both methods, through transformation relationship analysis, can accurately derive the mathematical characteristics of the dissipative continuous system. Finally, when using the explicit integration method to discretize the dissipative continuous system, it inherits the high efficiency of the explicit method while avoiding numerical oscillations through the characteristic constraints of the dissipative continuous system, achieving a synergistic optimization of computational efficiency and system stability. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. 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.

[0018] Figure 1 This is a diagram showing the relationship between the dissipative system and the original system based on the improved Euler discretization method proposed in this invention. Figure 2 This invention is a dissipative-based improved Euler discretization method. A The relationship between the dissipative system with =0 and the original system.

[0019] Figure 3 This is a diagram showing the relationship between the dissipative system and the original system in Example 1 (taking an inductor as an example) of Embodiment 2 of the improved Euler discretization method based on dissipation proposed in this invention.

[0020] Figure 4 These are waveform diagrams of three methods in Example 1 (taking an inductor as an example) of Embodiment 2 of the improved Euler discretization method based on dissipation proposed in this invention.

[0021] Figure 5 This is the circuit diagram of Case 2 (grid inverter-infinite grid system) in Embodiment 2 of the improved Euler discretization method based on dissipation proposed in this invention.

[0022] Figure 6This is a diagram showing the closed-loop pole distribution of the dissipative system and the original system in Example 2 (grid-type inverter-infinite grid system) of the improved Euler discretization method based on dissipation proposed in this invention.

[0023] Figure 7 The waveform diagrams are shown for three methods in Example 2 (grid inverter-infinite grid system) of the improved Euler discretization method based on dissipation proposed in this invention.

[0024] Figure 8 This is an internal structure diagram of the electronic device mentioned in the embodiments of the present invention. Detailed Implementation

[0025] To make the objectives and technical solutions of this invention clearer and easier to understand, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. The specific embodiments described herein are for illustrative purposes only and are not intended to limit the invention.

[0026] The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings and specific embodiments. The described embodiments are only some embodiments of the present invention, and not all embodiments.

[0027] Example 1 In existing electromagnetic transient simulations of power systems, the state-space equation method based on state variables is the core modeling method for revealing the dynamic nature of the system. The forward Euler method and the trapezoidal rule are the two most widely used discretization methods. The forward Euler method, as an explicit integration method, has the advantages of simple structure and adaptability to simulations of complex nonlinear systems, but its convergence is poor. Systems discretized using this method are prone to instability, requiring extremely small sampling steps to maintain system stability, significantly reducing simulation speed. The trapezoidal rule, as an implicit integration method, has excellent convergence and can maintain the stability of the original continuous system, but its implicit structure leads to high computational complexity and numerous iterative calculations, also affecting simulation efficiency. Currently, no discretization modeling method can simultaneously combine the computational speed advantage of the forward Euler method with the convergence and stability advantages of the trapezoidal rule, making it difficult to meet the high-efficiency simulation requirements of large-scale power system simulations and hardware-in-the-loop testing scenarios.

[0028] Therefore, this application provides a method for constructing a discrete state-space model of a power system. By finding the essential connection between two discretization methods through two discretized state-space models, a dissipative system can be obtained. This makes the dissipative system discretized by the forward Euler method equivalent to the original power system discretized by the trapezoidal method, indirectly improving the convergence and stability of the explicit method while retaining its computational efficiency advantage. The following section elaborates on the method for constructing a discrete state-space model of a power system described in this application, with specific technical solutions.

[0029] S1: Establish a state-space model based on the operating state of the power system.

[0030] It should be noted that the state-space model in this embodiment is a mathematical model that describes the dynamic relationship between the state variables, input variables, and output variables of the power system. It serves as the basis for the discretization simulation of the power system. The power system operating state mentioned in this step includes core information such as the operating electrical quantities of each power device in the power system, the topological connection relationship of the power network, and network operating parameters. The electrical quantities specifically include voltage, current, and power, while the network operating parameters specifically include impedance, admittance, and transmission parameters.

[0031] In this step, the power system is decomposed into two main components: power equipment and power network topology. Sub-state space models are established for each component. Then, based on the actual operating characteristics of the power system, the interconnection and feedback relationships between the sub-models are explored. Finally, based on these relationships, the sub-models are integrated to obtain a state space model that can accurately represent the dynamic operating characteristics of the entire power system.

[0032] In some embodiments of this application, establishing a state-space model of a power system specifically includes: First, establishing sub-state-space models for each power device and a sub-state-space model for the power network topology. The sub-state-space models for power devices are obtained based on the real-time operating states of the devices. Different types of power devices correspond to different sub-state-space models. For example, sub-models for passive devices such as inductors and capacitors are established based on the physical laws of electromagnetic induction and charge storage; sub-models for active devices such as inverters and synchronous machines are established based on the control strategies and electrical characteristics of the devices; and the sub-state-space model for the power network topology is established based on Kirchhoff's laws and the topology connection matrix of the network. Second, obtaining the sub-state-space models for each power device... The interconnection and feedback relationship between the sub-state space models of the equipment and the sub-state space model of the power network topology characterizes the interaction law of electrical quantities between the power equipment and the power network. For example, the output current of the power equipment serves as the input of the power network, and the node voltage of the power network serves as the input of the power equipment, forming a bidirectional feedback relationship. Finally, based on the interconnection and feedback relationship, the sub-state space models of each power equipment and the sub-state space model of the power network topology are integrated. Through mathematical methods such as variable substitution and simultaneous equations, the internal interaction variables between the sub-models are eliminated, resulting in a state space model with the state quantities, input quantities, and output quantities of the entire power system as its core. Its mathematical expression is:

[0033] In the formula, For the state variables of the power system, For the state variables of the power system, For the input of the power system, For the output of the power system, Let be the state function of the power system. This is the output function of the power system.

[0034] By breaking down the complex power system into multiple simple subsystems, the modeling difficulty of a single model is reduced while ensuring the accuracy of each sub-model. The integration method based on actual interconnection and feedback relationships ensures that the final state-space model is highly matched with the actual operating characteristics of the power system, providing an accurate basic model for subsequent discretization processing and effectively improving the accuracy of subsequent discretization simulation.

[0035] S2: Based on the first discretization method and the second discretization method, the state space model is discretized respectively to obtain the first discretization model and the second discretization model.

[0036] The first discretization method described in this step is an explicit integration method, in which the discretized state variables can be directly calculated from the state variables and input variables of the previous time step without iteration. The second discretization method is an implicit integration method, in which the discretized state variables appear on both sides of the equation, requiring iterative solution. Both discretization methods process the continuous state-space model of the power system. The core principle is to transform the differential equations in the continuous time domain into difference equations in the discrete time domain through numerical integration, thereby achieving a discretized representation of the dynamic behavior of the power system.

[0037] Specifically, in some embodiments of this application, the first discretization method is the forward Euler method, and the second discretization method is the trapezoidal method. These two are the most typical explicit and implicit integration methods in power system simulation, which are suitable for the discretization processing requirements of power system state space models.

[0038] The specific process of discretizing the state-space model using the forward Euler method is as follows: The power system is sampled at a fixed sampling period T, where the step index is denoted as k. k and k+1 represent two adjacent sampling times, respectively. Based on the explicit integration rule of the forward Euler method, the derivatives of the power system's state variables are approximated by the differences between state variables at adjacent times, ultimately yielding the first discretized model, whose corresponding mathematical expression is:

[0039] In the formula, Let k be the state variables of the power system at time k. Let be the state variables of the power system at time k+1. Let k be the power system input at time k. Let K be the power system input at time k+1. This is the system output at time k+1.

[0040] The specific process of discretizing the state-space model using the trapezoidal method is as follows: Sampling is performed with a sampling period T. Based on the implicit integration rule of the trapezoidal method, the state integral of the continuous system is approximated by the area of ​​a trapezoid. The state function values ​​at times k and k+1 are fused for calculation, ultimately yielding the second discretized model, whose mathematical expression is:

[0041] In the formula, Let k be the state variables of the power system at time k. Let be the state variables of the power system at time k+1. Let k be the power system input at time k. Let K be the power system input at time k+1. This is the system output at time k+1.

[0042] S3: Analyze the transformation relationship between the first discretization model and the second discretization model, and determine the dissipative continuous system corresponding to the state-space model based on the transformation relationship.

[0043] This embodiment first analyzes the transformation relationship between the first and second discretization models. The corresponding working principle is as follows: the time-domain discretization model is mapped to the complex frequency domain, and the transformation operators in the complex frequency domain are used to characterize the mathematical essence of the discretization method. By constructing the algebraic relationship between different transformation operators, the essential transformation relationship between the two discretization models is obtained. In addition, a dissipative continuous system is constructed based on this transformation relationship. The corresponding working principle is as follows: the transformation relationship in the complex frequency domain is substituted into the state-space model of the power system in the complex frequency domain. Through mathematical transformation and inverse transformation, the dissipative system in the time domain is obtained. This system is an equivalent transformation of the original continuous power system.

[0044] In some embodiments of this application, analyzing the transformation relationship between the first discretization model and the second discretization model specifically includes two sub-steps: First, the first discretization model and the second discretization model are mapped from the time domain to the complex frequency domain, respectively, and corresponding first and second complex frequency domain transformation operators are obtained. The complex frequency domain mapping adopts a joint transformation method of Laplace transform and Z transform, wherein the Laplace operator s represents the complex frequency domain characteristics of the continuous system, and the Z transform operator z represents the complex frequency domain characteristics of the discrete system. For the first discretization model corresponding to the forward Euler method, its complex frequency domain transformation relationship is as follows: In the formula: It is the Laplace operator. yes Transformation operator, This is the sampling period. This formula is the first complex frequency domain transform operator; for the second discretized model corresponding to the trapezoidal method, its complex frequency domain transform relationship is: This formula is the second complex frequency domain transform operator.

[0045] Secondly, an algebraic relationship is constructed between the first and second complex frequency domain transformation operators. The z in the first complex frequency domain transformation operator is represented by s and substituted into the second complex frequency domain transformation operator. Through mathematical operations such as elimination and simplification, the essential transformation relationship between the trapezoidal method and the forward Euler method in the complex frequency domain is obtained as follows: This algebraic relationship is the transformation relationship between the first and second discretized models.

[0046] Determining the dissipative continuous system based on the above transformation relationship involves three sub-steps: First, the state-space model of the power system is mapped to the complex frequency domain. The mathematical expression of the state-space model in the complex frequency domain is:

[0047] In the formula, X , U , Y These represent the system's state variables, input variables, and output variables in the complex frequency domain, respectively. F(X,U) , G(X,U) These are the system's state function and output function in the complex frequency domain, respectively.

[0048] Secondly, substituting the above transformation relationship in the complex frequency domain into the mapped state-space model, we obtain the dissipative continuous system represented in the complex frequency domain. The expression after substitution is:

[0049] After rearranging the formula, it is rewritten as follows: Finally, the dissipative continuous system is subjected to an inverse transform, restoring the mathematical relationships in the complex frequency domain to the time domain, resulting in the state-space model of the dissipative continuous system in the time domain, where the state transformation relationship in the time domain is: The mathematical expression for the state-space model in the time domain is:

[0050] This model is the dissipative continuous system corresponding to the original state-space model of the power system, where State function For state variables The partial derivatives of the state function characterize the rate of change of the state function. For example... Figure 1 As shown, the system model obtained by discretizing the dissipative continuous system model using the first discretization method is equivalent in numerical stability to the system model obtained by discretizing the power system model using the second discretization method.

[0051] Therefore, by analyzing the transformation relationship between the two discretization models through the complex frequency domain transformation operator, we can strip away the surface features of time-domain discretization and uncover the essential mathematical connection between the two methods, providing a precise theoretical basis for constructing a dissipative continuous system. The dissipative continuous system is constructed by substituting and inversely transforming the complex frequency domain transformation relationship. The mathematical derivation process is rigorous, and at the same time, the dissipative continuous system has the characteristic of compensating for the convergence defects of the first discretization method.

[0052] S4: The dissipative continuous system is discretized using the first discretization method to obtain the target discrete state-space model.

[0053] The constructed dissipative continuous system is used as the discretization object. The first discretization method (explicit integration method) is used for numerical discretization. Since the dissipative continuous system has achieved improved convergence and stability through the transformation of the original system, when discretizing it using the explicit integration method, there is no need to select an extremely small sampling step size, and there will be no system instability problem. The final target discrete state space model retains the advantages of the first discretization method, such as fast calculation speed and simple structure, and also has the advantages of the second discretization method, such as good convergence and strong stability.

[0054] In some embodiments of this application, after determining the dissipative continuous system, the dissipative continuous system can be linearized. Based on the linearization result, the first discretization method is improved, and then the improved first discretization method is used to discretize the dissipative continuous system, further improving the accuracy and adaptability of the target discrete state space model. The specific process is as follows: First, the state space model of the dissipative continuous system is linearized to obtain a linearized dissipative system. The core of linearization is to perform a Taylor expansion of the nonlinear function in the dissipative continuous system at the operating point and ignore higher-order small terms. Finally, the mathematical expression of the linearized dissipative system is obtained as follows:

[0055] In the formula, , , , These are the matrix coefficients of the original system. They are the state matrix, input matrix, output matrix, and direct transfer matrix, respectively. Next, the linearized dissipative system is simplified. After simplification, we can further obtain:

[0056] in,

[0057]

[0058]

[0059]

[0060] After simplification, a linearized model is obtained, represented by the coefficients of the dissipative system matrix. Then, the equivalent dissipative resistance parameters are analytically derived from the linearized dissipative system. Dissipation resistance is a core characteristic parameter of dissipative continuous systems, characterizing the energy dissipation properties of the system. The corresponding analytical process involves separating the dissipation resistance-related terms from the output equation of the linearized dissipative system through matrix inversion, transformation, and other operations, ultimately obtaining the mathematical expression for dissipation resistance as follows:

[0061] In the formula, I is the identity matrix. For example... Figure 2 As shown, it demonstrates when The relationship between dissipative systems and power systems. From a signal form perspective, a dissipative system is equivalent to the original system plus a gain from input to output. From a circuit perspective, a dissipative system is equivalent to a power system with a dissipative resistor connected in parallel on the input side.

[0062] Finally, the forward Euler method is improved by using the dissipation resistance parameter. The energy dissipation characteristics of the dissipation resistance are incorporated into the discretization calculation process of the forward Euler method. Based on the improved forward Euler method, the dissipation continuous system is discretized to obtain the target discrete state space model.

[0063] By linearizing the dissipative resistance parameters, the characteristics of dissipative continuous systems can be quantified into specific electrical parameters, which is more in line with the engineering analysis habits of power systems and facilitates engineering applications. Improving the forward Euler method using dissipative resistance parameters can further optimize the discretization characteristics of the explicit integration method, making the improved forward Euler method more adaptable to dissipative continuous systems. The resulting target discrete state-space model has better simulation accuracy and stability, while still retaining the core advantages of the forward Euler method, such as no iteration and fast calculation speed.

[0064] In addition, this application also includes further deriving the state-space model in the complex frequency domain to obtain the characteristic roots of the power system. The dissipative system in the complex frequency domain is characterized as follows:

[0065] Further derivation yields the characteristic roots of the dissipative system as follows: .

[0066] Let the characteristic roots of the original power system be The characteristic roots of the dissipative system are This verifies the relationship between the two as follows: .

[0067] Therefore, this method effectively solves the technical problem that traditional discretization methods cannot balance computational accuracy and speed. It can meet the high-efficiency simulation requirements of large-scale power system simulation, hardware-in-the-loop testing and other scenarios, and provides a new approach for electromagnetic transient simulation of power systems. It has significant application advantages in the simulation of complex power systems containing new energy power electronic devices, and can effectively reduce the computational load of simulation and improve the overall efficiency and accuracy of simulation.

[0068] Example 2 Based on the discrete state-space model construction method for power systems provided in Example 1, this example uses two cases for specific illustration.

[0069] This embodiment uses two case studies—an inductor and a grid-connected inverter-infinite grid system—to verify the correctness and rationality of the proposed improved Euler discretization method based on dissipation. This method is applicable not only to electrical components such as inductors and capacitors but also to various large-scale power systems. It should be noted that in this embodiment, the original system discretized by the forward Euler method is simply referred to as the forward Euler method, the original system discretized by the trapezoidal method is simply referred to as the trapezoidal method, and the dissipative system discretized by the forward Euler method is simply referred to as the proposed method.

[0070] Case 1: Using electric current For output, voltage The state-space model of the inductor for the input is as follows: ; Based on the derivation in Example 1, the inductor's dissipation system is as follows: .

[0071] like Figure 3 The diagram illustrates the relationship between the dissipation system of an inductor and the original system (inductor). The dissipation system of an inductor consists of an inductor connected in parallel with a resistor of [value missing]. The dissipation resistance.

[0072] The test is conducted by constructing a single-phase AC system (AC voltage source in series with an inductor), such as... Figure 4 As shown, the waveforms of the three methods in Case 1 (taking an inductor as an example) are displayed. From the simulation diagram, it can be seen that the current waveform of the method proposed in this embodiment almost overlaps with that of the trapezoidal method, and is clearly different from the current waveform of the forward Euler method. Although the inductor case does not demonstrate that the stability of the proposed method is consistent with that of the trapezoidal method, it is at least the same in form or in terms of the simulated waveform.

[0073] Case 2: The correctness of the proposed method is verified using a grid-connected inverter-infinite grid system. In this case, the outer loop of the grid-connected converter's control section employs phase-locked loop control, while the inner loop uses current closed-loop control. For example... Figure 5As shown, it illustrates the test circuit for Case 2 (grid-connected inverter-infinite grid system) in an embodiment of the improved Euler discretization method based on dissipation proposed in this invention. Specifically, the grid-connected inverter is directly connected to the power grid through line impedance. To verify the correctness of the theory, three aspects will be tested below: state-space modeling (pole plot), MATLAB / Simulink simulation, and maximum allowable sampling step size.

[0074] (1) State-space modeling (pole plot) like Figure 6 The figure shows the closed-loop pole distributions of the dissipative system and the original system in a grid-connected inverter-infinite grid system. As can be seen from the figure, the dissipative system changes with the sampling step size; the smaller the sampling step size, the closer the dissipative system is to the original system. Conversely, as the sampling step size increases, the difference between the dissipative system and the original system becomes larger. It can be seen that the high-frequency poles of the dissipative system are moving towards the left half-plane, meaning the system is becoming more stable. In other words, improving the stability of the original system compensates for the convergence difference between the forward Euler method and the trapezoidal method. This is consistent with theoretical analysis.

[0075] (2) MATLAB / Simulink simulation To better compare the forward Euler method, trapezoidal method, and the proposed method, a transient load (small disturbance) was applied to the output side of the grid-connected inverter at 0.1s to observe the transient process. Figure 7 The simulation waveforms of three methods for a grid-connected inverter-infinite grid system are shown. To ensure stability using the forward Euler method, the sampling step size must be very small. However, when the sampling step size is small, the differences between the discrete methods themselves are also small, resulting in almost identical simulation waveforms for the three methods from a macroscopic perspective. However, when the initial transient and small-disturbance transients are magnified, it is found that the transient of the forward Euler method is significantly larger, while the proposed method almost overlaps with the trapezoidal method. This verifies the correctness of the proposed method, and its disturbance rejection capability is almost identical to that of the trapezoidal method.

[0076] (3) Maximum allowable sampling step size Table 1 shows the order of magnitude of the maximum allowable step size for the three methods of the grid-type inverter-infinite grid system.

[0077] Table 1. Order of magnitude of the maximum allowable step size for the three methods in Case 2 (grid-based inverter-infinite grid system)

[0078] As can be seen, the maximum allowable step size of the method proposed in this invention is on the same order of magnitude as that of the trapezoidal method, and is much larger than that of the forward Euler method. This indicates that the stability of the proposed method is almost the same as that of the trapezoidal method.

[0079] Example 3 This embodiment provides a discrete state-space model construction system for a power system, including: The model acquisition module is used to establish a state-space model based on the operating state of the power system. The discretization processing module is connected to the model acquisition module and is used to discretize the state space model based on the first discretization method and the second discretization method respectively, to obtain the first discretized model and the second discretized model. The first discretization method is an explicit integration method and the second discretization method is an implicit integration method. The dissipative system construction module communicates with the discretization processing module and is used to perform analysis on the transformation relationship between the first discretization model and the second discretization model, and determine the dissipative continuous system corresponding to the state space model based on the transformation relationship. The target discretization module communicates with the dissipative system construction module and the discretization processing module. It is used to discretize the dissipative continuous system using the first discretization method to obtain the target discrete state space model.

[0080] Specific limitations regarding the discrete state-space model construction system for power systems can be found in the limitations of the discrete state-space model construction method for power systems described above; the corresponding technical effects are equivalent and will not be repeated here. Each module in the aforementioned discrete state-space model construction system for power systems can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device, or stored in the memory of a computer device as software, so that the processor can call and execute the operations corresponding to each module.

[0081] Example 4 Figure 8 An internal structural diagram of a computer device is shown in one embodiment. This computer device may specifically be a terminal or a server. Figure 8As shown, the computer device includes a processor, memory, network interface, display, camera, and input device connected via a system bus. The processor provides computing and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage media. The network interface is used to communicate with external terminals via a network connection. When executed by the processor, the computer program implements a battery state prediction method. The display screen can be an LCD screen or an e-ink display. The input device can be a touch layer covering the display screen, buttons, a trackball, or a touchpad on the computer device's casing, or an external keyboard, touchpad, or mouse.

[0082] As will be understood by those skilled in the art, computer equipment Figure 8 The structure shown is merely a block diagram of a portion of the structure related to the present invention and does not constitute a limitation on the computer device to which the present invention is applied. A specific computing device may include more or fewer components than those shown in the figure, or combine certain components, or have the same component arrangement.

[0083] In one embodiment, a computer device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the method described above.

[0084] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the steps of the above-described method.

[0085] In summary, the discrete state-space model construction method, system, computer equipment, and storage medium for a power system provided in this application construct a dissipative continuous system through the discretization model transformation relationship of explicit and implicit integration methods, and then discretize the dissipative continuous system using explicit integration methods, thus achieving a fusion of the advantages of explicit and implicit integration methods. This method only involves the mathematical transformation of the original power system state-space model, and the transformation process is a simple matrix operation and complex frequency domain / time domain conversion, without the need to reselect state variables. The calculation process is concise and efficient, bypassing the large number of iterative calculations caused by the implicit structure of implicit integration methods, significantly improving the simulation calculation speed. Simultaneously, the constructed dissipative continuous system compensates for the convergence defects of explicit integration methods, enabling the target model discretized using explicit integration methods to maintain the same convergence and stability as implicit integration methods, without the need to select extremely small sampling step sizes, further improving simulation efficiency.

[0086] The various embodiments in this specification are described in a progressive manner. For directly identical or similar parts of the embodiments, refer to each other. Each embodiment focuses on its differences from other embodiments. In particular, the system embodiments are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions in the method embodiments. It should be noted that the technical features of the above embodiments can be combined arbitrarily. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as the combination of these technical features does not contradict each other, it should be considered within the scope of this specification.

[0087] The above-described embodiments are merely preferred embodiments of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various improvements and substitutions without departing from the principles of the present invention, and these improvements and substitutions should also be considered within the scope of protection of the present invention. Therefore, the scope of protection of this invention should be determined by the scope of the claims.

Claims

1. A method for constructing a discrete state space model of a power system, characterized by, include: Establish a state-space model based on the operating status of the power system; Based on the first discretization method and the second discretization method, the state space model is discretized respectively to obtain the first discretized model and the second discretized model. The first discretization method is an explicit integration method, and the second discretization method is an implicit integration method. Analyze the transformation relationship between the first discretization model and the second discretization model, and obtain the dissipative continuous system corresponding to the state space model based on the transformation relationship; The dissipative continuous system is discretized using the first discretization method to obtain the target discrete state-space model.

2. The discrete state space model construction method of a power system according to claim 1, wherein, The establishment of a state-space model based on the operating state of the power system includes: Sub-state space models of each power device in the power system and a sub-state space model of the power network topology are established respectively; the sub-state space models of the power devices are obtained based on the operating states of the power devices. Obtain the interconnection feedback relationship between the sub-state space models of each power device and the sub-state space model of the power network topology; Based on the aforementioned interconnection feedback relationship, the sub-state space models of each power device and the sub-state space model of the power network topology are integrated to obtain the state space model of the power system.

3. The method of claim 1, wherein The first discretization method is the forward Euler method; the second discretization method is the trapezoidal method.

4. The method of claim 1, wherein The transformation relationship between the first discretization model and the second discretization model is analyzed, including: The first discretized model and the second discretized model are respectively mapped from the time domain to the complex frequency domain, and the first complex frequency domain transformation operator and the second complex frequency domain transformation operator are obtained accordingly. Construct an algebraic relationship between the first complex frequency domain transform operator and the second complex frequency domain transform operator, wherein the algebraic relationship is the transform relationship.

5. The method of claim 4, wherein, Based on the transformation relationship, a dissipative continuous system corresponding to the state-space model is obtained, including: Mapping the state-space model of the power system to the complex frequency domain; Substituting the transformation relationship into the mapped state-space model yields a dissipative continuous system represented in the complex frequency domain; After inverse transformation of the dissipative continuous system, a state-space model of the time-domain representation of the dissipative continuous system is obtained.

6. The method of claim 5, wherein, The dissipative continuous system is: In the formula, For the state variables of the power system, For the output of the power system, The sampling period is For the input of the power system, Let be the state function of the power system. This is the output function of the power system.

7. The method for constructing a discrete state-space model of a power system according to any one of claims 1 to 6, characterized in that, After determining the dissipative continuous system corresponding to the state-space model, the process further includes: The state-space model of the dissipative continuous system is linearized to obtain a linearized dissipative system. The equivalent dissipation resistance parameters are analyzed from the linearized dissipation system. The state-space model of the power system is compensated using the dissipation resistance parameters. The compensated power system is then discretized to obtain the target discrete state-space model.

8. A system for constructing a discrete state-space model of a power system, characterized in that, include: The model acquisition module is used to establish a state-space model based on the operating state of the power system. The discretization processing module is used to discretize the state space model based on a first discretization method and a second discretization method, respectively, to obtain a first discretized model and a second discretized model. The first discretization method is an explicit integration method, and the second discretization method is an implicit integration method. The dissipative system construction module is used to perform analysis on the transformation relationship between the first discretized model and the second discretized model, and to determine the dissipative continuous system corresponding to the state space model based on the transformation relationship; The target discretization module is used to discretize the dissipative continuous system using a first discretization method to obtain a target discrete state-space model.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program adapted to be loaded by a processor and executed as described in any one of claims 1 to 7 for constructing a discrete state-space model of a power system.

10. A computer device, characterized in that, include: Processor and computer-readable storage media; A processor, adapted to execute computer programs; A computer-readable storage medium storing a computer program, which, when executed by the processor, implements the method for constructing a discrete state-space model of a power system as described in any one of claims 1 to 7.

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