Methods and related devices for establishing nonlinear mathematical models of hybrid DC transmission systems considering discontinuous characteristics

Abstract

This invention provides a method and related apparatus for establishing a nonlinear mathematical model of a hybrid DC transmission system considering discontinuous characteristics. The method includes: representing the dynamic processes of discontinuous components in the main and control loops of the hybrid DC transmission system using a step function; approximating the step function as a continuous function using a linear combination of hyperbolic tangent functions to obtain a continuous expression; obtaining modular nonlinear differential equations for the rectifier, inverter, and AC / DC networks, and replacing the discontinuous dynamic parts involved in the equations with the continuous expression; and interconnecting the modules according to their input-output relationships to obtain a complete nonlinear mathematical model of the hybrid DC transmission system. This invention establishes a nonlinear mathematical model of a hybrid DC transmission system that accurately reflects discontinuous dynamic characteristics by employing the continuous approximation method using step functions and hyperbolic tangent functions, thereby improving the accuracy and practicality of system modeling.

Description

Technical Field

[0001] This invention belongs to the field of power system modeling technology, specifically relating to a method and related apparatus for establishing a nonlinear mathematical model of a hybrid DC transmission system that considers discontinuous characteristics. Background Technology

[0002] To address the energy consumption problem caused by the inverse distribution of primary energy bases and actual load demand, and to achieve large-capacity, long-distance power transmission, high-voltage direct current (HVDC) transmission technology has been extensively developed. Currently, HVDC transmission mainly employs two types of converters: line commutated converters (LCCs) and voltage source converters (VSCs). LCCs use semi-controlled semiconductor devices as the core components of the converter, which suffers from commutation failure issues. However, due to their mature technology, relatively low cost, and large transmission capacity, they will continue to be widely used in the future. VSCs have evolved from two-level and three-level converters to modular multilevel converters (MMCs). MMCs use fully controlled semiconductor devices, offering significant advantages in controllability, adaptability, and harmonic levels. Hybrid HVDC transmission systems combine the advantages of both types, possessing significant advantages and broad development potential and application prospects.

[0003] However, with the continuous deepening of power electronics, various instability problems in DC transmission systems have become increasingly prominent. Numerous unstable oscillation events have occurred in existing high-voltage DC projects. The analysis and management of these problems rely on establishing accurate mathematical models.

[0004] For the modeling problem of hybrid DC transmission systems, existing technical solutions are usually carried out within a continuous nonlinear time-invariant framework, characterizing the dynamic behavior of LCC and MMC in an average manner. However, such methods still have the following problems:

[0005] First, it cannot take into account the inherent discontinuous switching characteristics of power electronic devices such as thyristors in LCCs and sub-modules in MMCs.

[0006] Second, it cannot characterize the impact of discrete processes such as amplitude limiting and multi-controller switching on the dynamic process of the actual control system.

[0007] Third, it cannot reveal the typical periodic time-varying behavior of hybrid DC transmission systems. Summary of the Invention

[0008] In view of this, the present invention provides a method and related apparatus for establishing a nonlinear mathematical model of a hybrid DC transmission system that considers discontinuous characteristics, so as to solve the above-mentioned problems existing in the modeling methods of existing hybrid DC transmission systems.

[0009] To achieve the above objectives, the technical solution provided by the present invention is as follows:

[0010] In a first aspect, the present invention provides a method for establishing a nonlinear mathematical model of a hybrid DC transmission system considering discontinuous characteristics, comprising the following steps:

[0011] The dynamic process of discontinuous links in the main circuit and control circuit of a hybrid DC transmission system is represented by a step function;

[0012] By using a linear combination of hyperbolic tangent functions to approximate the step function as a continuous function, a continuous expression of the function is obtained.

[0013] Modular nonlinear differential equations for the rectifier side, inverter side, and AC / DC side networks are obtained, and the discontinuous dynamic parts involved in the modular nonlinear differential equations are replaced by corresponding continuous functional expressions.

[0014] By interconnecting the modules according to their input-output relationships, a complete nonlinear mathematical model of the hybrid DC transmission system considering discontinuous characteristics is obtained.

[0015] Furthermore, the discontinuous element in the main circuit is a thyristor. The dynamic process of the discontinuous element in the main circuit of the hybrid DC transmission system is represented by a step function, including:

[0016] Using S th Characterizing the switching function of a thyristor, we have:

[0017]

[0018] In the formula, S f and S i These represent whether the trigger signal has arrived and whether the forward current is less than the holding current, respectively, and can be expressed using a step function as follows:

[0019]

[0020] In the formula, φ is the firing angle, φ is the synchronization phase, i is the forward current, and I is the forward current. hold To maintain the current; and the step function H(x) is expressed as:

[0021] .

[0022] Furthermore, the discontinuous elements in the control loop are limiting elements and switching elements. The dynamic process of the discontinuous elements in the control loop of the hybrid DC transmission system is represented by a step function, including:

[0023] The discontinuities in the limiting and switching stages are characterized by the following formulas:

[0024]

[0025]

[0026] In the formula, α in / min / max These represent the input / output lower limit / output upper limit of the firing angle of the constant current limiting circuit, respectively; u dc / min / max These represent the DC voltage input to the low-voltage current limiting unit, the lower limit of the DC voltage, and the upper limit of the DC voltage, respectively; I ord This is the output current command value; Let H(x) represent the lower and upper limits of the output current command, respectively; and let the step function H(x) be expressed as:

[0027] .

[0028] Furthermore, the step function is approximated as a continuous function using a linear combination of hyperbolic tangent functions, as follows:

[0029]

[0030] In the formula, h(x) is a linear combination of hyperbolic tangent functions, tanh is a hyperbolic tangent function, and k is an adjustable coefficient.

[0031] Furthermore, for the rectifier-side main circuit module, the discontinuous dynamic parts involved in the modular nonlinear differential equations are replaced with corresponding continuous functional expressions, including:

[0032] Based on the characteristics of thyristor switching, the mathematical model of the differential equation between the port voltage and current of the rectifier-side main circuit module is determined as follows:

[0033]

[0034] In the formula, L t For transformer inductance, i a / b / c For phases A, B, and C, , , and These are the switching functions for the upper and lower bridge arms of phase j, respectively.

[0035] The bridge arm switching function, after being approximated by the hyperbolic tangent function, replaces the original bridge arm switching function. and A new differential equation mathematical model for the rectifier-side main circuit module is obtained.

[0036] Furthermore, for the rectifier-side constant current control loop, the discontinuous dynamic parts involved in the modular nonlinear differential equations are replaced with corresponding continuous functional expressions, including:

[0037] The mathematical model of the differential equations for the control loop is determined as follows:

[0038]

[0039] In the formula, x 1,dc and x 2,dc T is a state variable. m and G m Let i be the time constant and proportional coefficient of the first-order inertial filter element. dc k is the DC current on the rectifier side. i I is the integral coefficient in the proportional-integral system. ord This is the current command value;

[0040] The current command value, I, is replaced by the current command value that has been approximated as a continuous function using the hyperbolic tangent. ord ;

[0041] The firing angle α is determined based on the current command value through continuous approximation, and then continuously approximated as follows:

[0042]

[0043] In the formula, α in / min / max Let h(x) represent the input / output lower limit and output upper limit of the constant current limiting circuit, respectively. h(x) is a linear combination of hyperbolic tangent functions, and k... p This is the proportional coefficient in the proportional-integral process.

[0044] Furthermore, the expression for the complete nonlinear mathematical model of the hybrid DC transmission system is as follows:

[0045]

[0046] In the formula, x is the system state variable, that is, the differential component in the modular nonlinear differential equation, and N is the total number of system state variables. It is a nonlinear vector field.

[0047] Secondly, the present invention provides a device for establishing a nonlinear mathematical model of a hybrid DC transmission system considering discontinuous characteristics, comprising:

[0048] The first processing module is used to represent the dynamic process of discontinuous links in the main circuit and control circuit of the hybrid DC transmission system using step functions;

[0049] The second processing module is used to approximate the step function as a continuous function by using a linear combination of hyperbolic tangent functions to obtain a continuous function expression.

[0050] The third processing module is used to obtain the modular nonlinear differential equations of the rectifier side, inverter side and AC / DC side networks, and to replace the discontinuous dynamic parts involved in the modular nonlinear differential equations with corresponding continuous functional expressions.

[0051] The model building module is used to interconnect the various modules according to the input-output relationship to obtain a complete nonlinear mathematical model of the hybrid DC transmission system that takes into account discontinuous characteristics.

[0052] Thirdly, the present invention provides a computer device, the device including a processor and a memory:

[0053] The memory is used to store computer programs and send the instructions of the computer programs to the processor;

[0054] The processor executes instructions from the computer program, such as the method for establishing a nonlinear mathematical model of a hybrid DC transmission system considering discontinuous characteristics, as described in the first aspect.

[0055] Fourthly, the present invention provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements a method for establishing a nonlinear mathematical model of a hybrid DC transmission system considering discontinuous characteristics, as described in the first aspect.

[0056] In summary, this invention provides a method and related apparatus for establishing a nonlinear mathematical model of a hybrid DC transmission system considering discontinuous characteristics. The method includes: representing the dynamic processes of discontinuous components in the main circuit and control circuit of the hybrid DC transmission system using a step function; approximating the step function with a continuous expression using a linear combination of hyperbolic tangent functions to obtain a continuous functional expression; obtaining modular nonlinear differential equations for the rectifier side, inverter side, and AC / DC side networks, and correspondingly replacing the discontinuous dynamic parts involved in the modular nonlinear differential equations with the continuous functional expression; and interconnecting the modules according to their input-output relationships to obtain a complete nonlinear mathematical model of the hybrid DC transmission system considering discontinuous characteristics. This invention, by employing the continuous approximation method using step functions and hyperbolic tangent functions, establishes a nonlinear mathematical model of a hybrid DC transmission system that accurately reflects discontinuous dynamic characteristics, thereby improving the accuracy and practicality of system modeling. Attached Figure Description

[0057] 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 only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0058] Figure 1 A flowchart illustrating a method for establishing a nonlinear mathematical model of a hybrid DC transmission system considering discontinuous characteristics, provided in an embodiment of the present invention;

[0059] Figure 2 This is a topology diagram of a hybrid DC transmission system provided in an embodiment of the present invention;

[0060] Figure 3 A comparison chart of AC current, DC current, and DC voltage on the rectifier side during the process of the DC current command value of the constant current controller provided in the embodiment of the present invention suddenly dropping from 1 pu to 0.5 pu;

[0061] Figure 4 A comparison chart of inverter-side AC current, DC current, and DC voltage during the process of the constant current controller DC current command value suddenly dropping from 1 pu to 0.5 pu, provided for an embodiment of the present invention.

[0062] Figure 5 A block diagram of a device for establishing a nonlinear mathematical model of a hybrid DC transmission system considering discontinuous characteristics, provided in an embodiment of the present invention;

[0063] Figure 6 This is a block diagram of a computer device provided in an embodiment of the present invention. Detailed Implementation

[0064] To make the objectives, features, and advantages of this invention more apparent and understandable, the technical solutions of the embodiments of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the embodiments described below are only some embodiments of this invention, and not all embodiments. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0065] Please see Figure 1 This embodiment provides a method for establishing a nonlinear mathematical model of a hybrid DC transmission system considering discontinuous characteristics, including the following steps:

[0066] S1: The step function is used to represent the dynamic process of discontinuous links in the main circuit and control circuit of the hybrid DC transmission system.

[0067] It should be noted that the step function is a discontinuous function, typically used to represent sudden changes in the state of a signal or system. It jumps from one value to another at a certain point, remaining constant before and after that point.

[0068] Some components in hybrid DC transmission systems, such as thyristor switches and submodule switching, exhibit significant switching characteristics. Step functions can effectively simulate these instantaneous changes. For example, a step function of 1 can be used to represent the conduction of a thyristor, while a step function of 0 can be used to represent the turn-off of a thyristor. By using step functions, these discontinuous processes can be transformed into part of a mathematical model.

[0069] S2: The step function is approximated as a continuous function by using a linear combination of hyperbolic tangent functions to obtain a continuous expression of the function.

[0070] It should be noted that the hyperbolic tangent function (tanh(x)) is a function with a smooth transition, and its graph presents an S-shaped curve. The linear combination of the hyperbolic tangent function 0.5·[1+tanh(k·x)] approaches 0 and 1 respectively in the limiting case, but is continuous and smooth in the middle part.

[0071] Although the step function accurately describes discontinuous phenomena, it is not ideal for simulation, numerical solutions, or mechanistic analysis of system dynamics. To overcome this problem, the hyperbolic tangent function can be used to approximate the step function. Specifically, by adjusting the parameter k in the linear combination of the hyperbolic tangent function, its shape can be made close to that of the step function while preserving good mathematical properties such as differentiability and continuity. The resulting function numerically approximates the behavior of the step function while ensuring stability and accuracy in the computational process.

[0072] S3: Obtain the modular nonlinear differential equations of the rectifier side, inverter side and AC / DC side networks, and replace the discontinuous dynamic parts involved in the modular nonlinear differential equations with corresponding continuous function expressions.

[0073] It should be noted that modular nonlinear differential equations refer to decomposing the entire system into several subsystems (modules), each with its own nonlinear differential equations describing its dynamic behavior. Discontinuous dynamics refer to non-smooth changes occurring in the system, such as the transient changes in the vector field caused by switching actions.

[0074] For different parts of the hybrid DC transmission system, such as the rectifier side, inverter side, and AC / DC network, their nonlinear differential equations are established respectively. Then, in these equations, wherever discontinuous dynamics represented by step functions are involved, they are replaced with the continuous hyperbolic tangent function expression obtained in step S2. This not only ensures that the dynamic behavior within each subsystem is accurately described, but also makes the overall system model more mathematically consistent and easier to handle.

[0075] S4: Interconnect the modules according to their input-output relationships to obtain a complete nonlinear mathematical model of the hybrid DC transmission system that takes into account discontinuous characteristics.

[0076] It should be noted that, based on the existing modular nonlinear differential equations and after all discontinuous parts have been made continuous, the next step is to define the input-output relationships between the modules according to the actual physical connections. This step involves determining which variables are shared and how to correctly pass the output of one module to the next as input. The final result is a complete system-level nonlinear mathematical model that reflects the actual operating conditions of the hybrid DC transmission system, including all its discontinuous characteristics.

[0077] This embodiment provides a method for establishing a nonlinear mathematical model of a hybrid DC transmission system that considers discontinuous characteristics. By using the continuous approximation method of step function and hyperbolic tangent function, a nonlinear mathematical model of the hybrid DC transmission system that can accurately reflect the discontinuous dynamic characteristics is established, thereby improving the accuracy and practicality of system modeling.

[0078] In one embodiment, the discontinuous element in the main circuit is a thyristor, and two scenarios need to be considered: turn-on due to a trigger signal and turn-off due to the forward current being less than the holding current. For the thyristor in the main circuit, S... th Characterizing the switching function of a thyristor, we have:

[0079] (1)

[0080] In the formula, S f and S i These represent whether the trigger signal has arrived and whether the forward current is less than the holding current, respectively, and can be expressed using a step function as follows:

[0081] (2)

[0082] In the formula, φ is the firing angle, φ is the synchronization phase, i is the forward current, and I is the forward current. hold To maintain the current; and the step function H(x) is expressed as:

[0083] .

[0084] In one embodiment, the discontinuous elements in the control loop are limiting and switching. For the limiting element (taking the output limiting of the constant current controller as an example) and the switching element (taking the low-voltage current limiting unit as an example) in the control loop, the following equations (3) and (4) are used to characterize their discontinuity:

[0085] (3)

[0086] (4)

[0087] In the formula, α in / min / max These represent the input / output lower limit / output upper limit of the firing angle of the constant current limiting circuit, respectively; u dc / min / max These represent the DC voltage input to the low-voltage current limiting unit, the lower limit of the DC voltage, and the upper limit of the DC voltage, respectively; I ord This is the output current command value; These represent the lower and upper limits of the output current command, respectively.

[0088] In one embodiment, a continuous approximation of the step function is achieved using a linear combination of hyperbolic tangent functions, and the accuracy of the approximation is adjusted using an approximation coefficient k. An adjustable coefficient k is defined, and it is noted that when x ≠ 0, ... Therefore, equation (5) can be used to approximate equations (2) to (4) while ensuring the continuity of the mathematical description:

[0089] (5)

[0090] Substituting the relevant parts of equations (2) to (4) as independent variables of the hyperbolic tangent function into equation (5), we obtain the corresponding continuous expression of the function.

[0091] In one embodiment, for the rectifier-side main circuit module, the following mathematical model of the differential equations between port voltage and current can be written based on the characteristics of the thyristor switch:

[0092] (6)

[0093] in , . The switching function of the upper (lower) bridge arm of phase j (i.e., S in the aforementioned embodiment) th (And process it using the continuous approximation method in step S2). For example, for the upper arm of phase A... Its expression is:

[0094] (7)

[0095] For the inverter-side main circuit module, the following mathematical model of the differential equations between port voltages and currents can be written based on the averaged sub-module dynamic process:

[0096] (8)

[0097] in This represents the sum of the capacitor voltages of the upper (lower) bridge arm submodules in phase j; the equivalent capacitance C eq The submodule capacitance value divided by the number of bridge arm submodules; equivalent inductance L eq =L t +0.5L arm L t For transformer inductance, L arm For bridge arm inductance; u nN Indicates the voltage difference between AC and DC neutral points; i j This represents the j-phase current at the common coupling point. This indicates the circulating current in phase j of the bridge arm; Indicates the differential mode voltage of the bridge arm; The modulation signal for the upper (lower) bridge arm of phase j.

[0098] In one embodiment, taking the rectifier-side constant current control loop as an example, the control loop includes a first-order inertial filter and a proportional-integral (PI) circuit. Therefore:

[0099] (9)

[0100] Where x 1,dc and x 2,dc For state variables; T m and G m i represents the time constant and proportional coefficient of the first-order inertial filter element; dc k is the DC current on the rectifier side. i I is the integral coefficient in the proportional-integral series; ord The current command value (i.e., I in the aforementioned embodiment) ord (And processed using the continuous approximation method in step S2). The firing angle α output by the control system, after processing in step S2, is written as:

[0101] (10)

[0102] Where k p This refers to the proportional coefficient in the proportional-integral circuit. The AC / DC side network main circuit module consists of inductors, capacitors, and resistors, and its differential equations can be directly written.

[0103] In one embodiment, combining the modules yields a nonlinear mathematical model of a hybrid DC transmission system that considers discontinuous characteristics, written in the following form:

[0104] (11)

[0105] Where x is the system state variable, i.e., the differential on the left side of equations (6)-(9), and N is the total number of system state variables; It is a nonlinear vector field. For example, i in equation (6) a As the first state variable x1 in equation (11), f1(x) is written as:

[0106] (12)

[0107] All the variables appearing on the right side of equation (12) are related to other state variables (such as equation (9) in the control system module).

[0108] Through the above steps, a highly accurate nonlinear mathematical model of the hybrid DC transmission system can be effectively established, accurately characterizing the system's periodic time-varying processes and switching, limiting, and transposition processes, laying a solid foundation for stability and bifurcation analysis.

[0109] The above data and process can be used for simulation verification:

[0110] Build such in PSCAD / EMTDC Figure 2 The simplified simulation model of a real hybrid DC transmission system shown has a rated power of 1250MW. The LCC on the rectifier side adopts constant current control and considers the role of the low-voltage current limiting unit. The MMC on the inverter side adopts constant voltage / constant reactive power outer loop and inner loop vector current control and is equipped with circulating current suppression control.

[0111] Taking the DC current command value of the rectifier side constant current controller as an example, which drops sharply from 1 pu to 0.5 pu in 2 seconds, Figure 3 and Figure 4 The simulation results of PSCAD / EMTDC in this scenario and the solution results of the mathematical model proposed in this patent in MATLAB are presented respectively. Figure 3 Provide the waveforms of AC current, DC current, and DC voltage on the rectifier side; Figure 4 The waveforms of AC current, DC current, and DC voltage on the inverter side are given. It is evident that the solution results of the nonlinear mathematical model of the hybrid DC transmission system proposed in this patent are highly consistent with the simulation results.

[0112] Based on the same inventive concept, this application also provides a device for establishing a nonlinear mathematical model of a hybrid DC transmission system considering discontinuous characteristics, for implementing the aforementioned method for establishing a nonlinear mathematical model of a hybrid DC transmission system considering discontinuous characteristics. The solution provided by this system is similar to the solution described in the above method. Therefore, the specific limitations in the embodiments of the device for establishing a nonlinear mathematical model of a hybrid DC transmission system considering discontinuous characteristics provided below can be found in the limitations of the method for establishing a nonlinear mathematical model of a hybrid DC transmission system considering discontinuous characteristics described above, and will not be repeated here.

[0113] Please see Figure 5 The present invention also provides a device for establishing a nonlinear mathematical model of a hybrid DC transmission system considering discontinuous characteristics, comprising:

[0114] The first processing module is used to represent the dynamic process of discontinuous links in the main circuit and control circuit of the hybrid DC transmission system using step functions;

[0115] The second processing module is used to approximate the step function as a continuous function by using a linear combination of hyperbolic tangent functions to obtain a continuous function expression.

[0116] The third processing module is used to obtain the modular nonlinear differential equations of the rectifier side, inverter side and AC / DC side networks, and to replace the discontinuous dynamic parts involved in the modular nonlinear differential equations with corresponding continuous functional expressions.

[0117] The model building module is used to interconnect the various modules according to the input-output relationship to obtain a complete nonlinear mathematical model of the hybrid DC transmission system that takes into account discontinuous characteristics.

[0118] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is merely an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the system can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiments can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit. Furthermore, the specific names of the functional units and modules are only for easy differentiation and are not intended to limit the scope of protection of this application. The specific working process of the units and modules in the above system can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0119] Reference Figure 6 The present invention also provides a computer device, including: a memory and a processor, and a computer program stored in the memory. When the computer program is executed on the processor, it implements the method for establishing a nonlinear mathematical model of a hybrid DC transmission system considering discontinuous characteristics as described in any of the above methods.

[0120] The computer device may be a desktop computer, laptop, handheld computer, or cloud server, etc. This computer device may include, but is not limited to, a processor and memory. Those skilled in the art will understand that... Figure 6 The examples of computer devices are merely examples and do not constitute a limitation on computer devices. They may include more or fewer components than shown in the illustration, or combinations of certain components, or different components. For example, they may also include input / output devices, network access devices, etc.

[0121] The processor referred to can be a Central Processing Unit (CPU), but it can also be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor can be a microprocessor or any conventional processor.

[0122] In some embodiments, the memory may be an internal storage unit of the computer device, such as a hard drive or RAM. In other embodiments, the memory may be an external storage device of the computer device, such as a plug-in hard drive, Smart Media Card (SMC), Secure Digital (SD) card, or Flash Card. Furthermore, the memory may include both internal and external storage units of the computer device. The memory is used to store the operating system, applications, bootloader, data, and other programs, such as the program code of the computer program. The memory can also be used to temporarily store data that has been output or will be output.

[0123] This invention also provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the method for establishing a nonlinear mathematical model of a hybrid DC transmission system considering discontinuous characteristics as described in any of the above methods.

[0124] In this embodiment, if the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include at least: any entity or device capable of carrying computer program code to a photographing device / terminal device, a recording medium, a computer memory, a read-only memory (ROM), a random access memory (RAM), an electrical carrier signal, a telecommunication signal, and a software distribution medium. Examples include USB flash drives, portable hard drives, magnetic disks, or optical disks. In some jurisdictions, according to legislation and patent practice, computer-readable media cannot be electrical carrier signals or telecommunication signals.

[0125] In the above embodiments, the descriptions of each embodiment have different focuses. For parts that are not described in detail or recorded in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0126] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0127] In the embodiments disclosed in this application, it should be understood that the disclosed devices / terminal equipment and methods can be implemented in other ways. For example, the device / terminal equipment embodiments described above are merely illustrative. For instance, the division of modules or units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the displayed or discussed mutual coupling or direct coupling or communication connection may be through some interfaces; the indirect coupling or communication connection between devices or units may be electrical, mechanical, or other forms.

[0128] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. 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. Such 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 method for establishing a nonlinear mathematical model of a hybrid DC transmission system considering discontinuous characteristics, characterized in that, Includes the following steps: The dynamic process of discontinuous links in the main circuit and control circuit of a hybrid DC transmission system is represented by a step function; The step function is approximated as a continuous function by using a linear combination of hyperbolic tangent functions to obtain a continuous expression of the function. Obtain the modular nonlinear differential equations of the rectifier side, inverter side and AC / DC side networks, and replace the discontinuous dynamic parts involved in the modular nonlinear differential equations with the corresponding function expressions expressed continuously. By interconnecting the modules according to their input-output relationships, a complete nonlinear mathematical model of the hybrid DC transmission system considering discontinuous characteristics is obtained.

2. The method for establishing a nonlinear mathematical model of a hybrid DC transmission system considering discontinuous characteristics according to claim 1, characterized in that, The discontinuities in the main circuit are thyristors. The dynamic processes of these discontinuities in the main circuit of the hybrid DC transmission system are represented using step functions, including: Using S th Characterizing the switching function of a thyristor, we have: In the formula, S f and S i These represent whether the trigger signal has arrived and whether the forward current is less than the holding current, respectively, and can be expressed using a step function as follows: In the formula, φ is the firing angle, φ is the synchronization phase, i is the forward current, and I is the forward current. hold To maintain the current; and the step function H(x) is expressed as: 。 3. The method for establishing a nonlinear mathematical model of a hybrid DC transmission system considering discontinuous characteristics according to claim 1, characterized in that, The discontinuous elements in the control loop are the limiting element and the switching element. The dynamic process of the discontinuous elements in the control loop of the hybrid DC transmission system is represented by a step function, including: The discontinuities of the limiting stage and the switching stage are characterized by the following formulas: In the formula, α in / min / max These represent the input / output lower limit / output upper limit of the firing angle of the constant current limiting circuit, respectively; u dc / min / max These represent the DC voltage input to the low-voltage current limiting unit, the lower limit of the DC voltage, and the upper limit of the DC voltage, respectively; I ord This is the output current command value; Let H(x) represent the lower and upper limits of the output current command, respectively; and let the step function H(x) be expressed as: 。 4. The method for establishing a nonlinear mathematical model of a hybrid DC transmission system considering discontinuous characteristics according to claim 2 or 3, characterized in that, The step function is approximated as a continuous function using a linear combination of hyperbolic tangent functions, as follows: In the formula, h(x) is a linear combination of hyperbolic tangent functions, tanh is a hyperbolic tangent function, and k is an adjustable coefficient.

5. The method for establishing a nonlinear mathematical model of a hybrid DC transmission system considering discontinuous characteristics according to claim 1, characterized in that, For the rectifier-side main circuit module, the discontinuous dynamic parts involved in the modular nonlinear differential equation are replaced with the corresponding continuously expressed functional expressions, including: Based on the characteristics of the thyristor switch, the mathematical model of the differential equation between the port voltage and current of the rectifier-side main circuit module is determined as follows: In the formula, L t For transformer inductance, i a / b / c For phases A, B, and C, , , and These are the switching functions for the upper and lower bridge arms of phase j, respectively. The bridge arm switching function, after being approximated by the hyperbolic tangent function, is used to replace the original bridge arm switching function. and Thus, a new differential equation mathematical model of the rectifier-side main circuit module is obtained.

6. The method for establishing a nonlinear mathematical model of a hybrid DC transmission system considering discontinuous characteristics according to claim 1, characterized in that, For the rectifier-side constant current control loop, the discontinuous dynamic parts involved in the modular nonlinear differential equation are replaced by the corresponding continuously expressed functional expression, including: The mathematical model of the differential equations for the control loop is determined as follows: In the formula, x 1,dc and x 2,dc T is a state variable. m and G m Let i be the time constant and proportional coefficient of the first-order inertial filter element. dc k is the DC current on the rectifier side. i I is the integral coefficient in the proportional-integral system. ord This is the current command value; The current command value that is approximated by a linear combination of the hyperbolic tangent function is used to replace the original current command value I. ord ; The firing angle α is determined based on the current command value through continuous approximation, and then continuously approximated as follows: In the formula, α in / min / max Let h(x) represent the input / output lower limit and output upper limit of the constant current limiting circuit, respectively. h(x) is a linear combination of hyperbolic tangent functions, and k... p This is the proportional coefficient in the proportional-integral process.

7. The method for establishing a nonlinear mathematical model of a hybrid DC transmission system considering discontinuous characteristics according to claim 1, characterized in that, The expression for the complete hybrid DC transmission system's nonlinear mathematical model is as follows: In the formula, x is the system state variable, that is, the differential component in the modular nonlinear differential equation, and N is the total number of system state variables; It is a nonlinear vector field.

8. A device for establishing a nonlinear mathematical model of a hybrid DC transmission system considering discontinuous characteristics, characterized in that, include: The first processing module is used to represent the dynamic process of discontinuous links in the main circuit and control circuit of the hybrid DC transmission system using step functions; The second processing module is used to perform a continuous approximation of the step function using a linear combination of hyperbolic tangent functions to obtain a continuous function expression. The third processing module is used to obtain the modular nonlinear differential equations of the rectifier side, inverter side and AC / DC side network, and to replace the discontinuous dynamic parts involved in the modular nonlinear differential equations with the corresponding function expressions expressed in continuous form. The model building module is used to interconnect the various modules according to the input-output relationship to obtain a complete nonlinear mathematical model of the hybrid DC transmission system that takes into account discontinuous characteristics.

9. A computer device, characterized in that, The device includes a processor and a memory: The memory is used to store computer programs and send the instructions of the computer programs to the processor; The processor executes the method for establishing a nonlinear mathematical model of a hybrid DC transmission system considering discontinuous characteristics as described in any one of claims 1-7, according to the instructions of the computer program.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the method for establishing a nonlinear mathematical model of a hybrid DC transmission system considering discontinuous characteristics as described in any one of claims 1-7.

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