Method for calculating parameters of multi-dc voltage control converter station of flexible dc power grid

Abstract

The application provides a flexible DC power grid multi-DC voltage control converter station parameter analysis calculation method, comprising: constructing a whole mathematical model of the flexible DC power grid; constructing a system simplified equivalent model based on the whole mathematical model of the flexible DC power grid; constructing a per-unit analysis calculation model based on the system simplified equivalent model; determining initial controller parameters of each converter station of the flexible DC power grid based on the per-unit analysis calculation model; performing stability checking on each control converter station based on the initial controller parameters of each converter station of the flexible DC power grid, and judging whether a single DC voltage control converter station can meet the system stability requirement; if yes, taking the initial controller parameters of the converter station of the flexible DC power grid as the controller parameters of the multi-DC voltage control converter station. The method can enable the multi-terminal flexible DC system to realize the expected adjustment time, small overshoot and good damping characteristic under the multi-DC voltage control condition.

Description

Technical Field

[0001] This application relates to the fields of power system automation and flexible DC transmission technology, and in particular to a method for analytical calculation of parameters of multiple DC voltage control converter stations in flexible DC power grids. Background Technology

[0002] In recent years, with the maturity and engineering application of Modular Multilevel Converter (MMC) technology, flexible DC transmission systems have been widely used in fields such as new energy grid connection, offshore wind power transmission, urban power grid interconnection, and inter-regional power transmission, accelerating the application of flexible DC projects. In multi-terminal flexible DC power grid transmission systems, DC voltage is a crucial factor in maintaining system power balance and stable operation. When an imbalance occurs between the input and output power of the DC system, the unbalanced power is first absorbed or released by energy storage elements on the DC side, manifesting as an increase or decrease in DC voltage. Therefore, DC voltage reflects the power balance state of the DC system. To maintain DC voltage stability, converter stations that perform DC voltage control or participate in DC voltage regulation typically achieve stable DC voltage control by adjusting the power exchange with the DC network.

[0003] Currently, the mainstream control methods for flexible DC transmission systems include single-point master-slave control, droop control, and voltage margin control. Single-point master-slave control is suitable for simple systems, while the latter two are suitable for more complex systems. Single-point master-slave control, with its simplicity and precise control performance, has become the mainstream strategy in current engineering applications. Its disadvantage is that after the DC voltage control station (master station) is taken out of operation, voltage control must be transferred to other stations to maintain continuous system operation, and the master station is prone to overcurrent problems. The latter two strategies can achieve redundant control by adjusting the power injected into the DC network or the operating mode according to the DC voltage magnitude. Although this improves operational reliability, it cannot achieve precise control of the DC voltage and power of the converter station. With the increasing interconnectivity of regional flexible DC transmission systems in the future, the traditional single-voltage control station mode is no longer sufficient to meet the reliability, redundancy, and dynamic performance requirements of large-scale DC transmission systems. Therefore, to improve system operational reliability, setting up multiple DC voltage control stations in different areas to jointly participate in DC voltage regulation has become an important development direction.

[0004] Current research on DC voltage controller parameter design mostly focuses on the parameter tuning of a single converter station controller, primarily employing empirical tuning methods, root locus methods, frequency response analysis methods, and state-space matrix-based modeling methods. Existing technologies suffer from the following shortcomings: 1) They only focus on the design of the outer-loop controller parameters of a single DC voltage station, neglecting the impact of connected systems on the station; 2) They only consider the stability perspective when providing parameter selection ranges, without considering the dynamic response characteristics of the system; 3) They only provide calculation methods for a single DC voltage controller, without providing a general calculation formula for parameters of multi-point DC voltage controllers. Summary of the Invention

[0005] This application provides an analytical calculation method for parameters of multiple DC voltage-controlled converter stations in flexible DC power grids. To solve the above-mentioned technical problems, this application adopts the following technical method: This application provides an analytical calculation method for parameters of multiple DC voltage-controlled converter stations in flexible DC power grids, including: Constructing an overall mathematical model of the flexible DC power grid; Based on the overall mathematical model of the flexible DC power grid, a simplified equivalent model of the system is constructed. Based on the simplified equivalent model of the system, an analytical calculation model for per-unit values ​​is constructed. Based on the per-unit value analytical calculation model, the initial controller parameters of each converter station of the flexible DC power grid are determined. Based on the initial controller parameters of each converter station in the flexible DC grid, the stability of each control converter station is checked, and it is determined whether a single DC voltage control converter station can meet the system stability requirements. If so, the initial controller parameters of each converter station in the flexible DC grid will be used as the controller parameters of the multi-DC voltage control converter station.

[0006] Optionally, the step of constructing a simplified equivalent model of the system based on the overall mathematical model of the flexible DC power grid includes: Based on the overall mathematical model of the flexible DC power grid, a linearized model of the flexible DC power grid based on the average value model is constructed. Based on the overall linearized model of the flexible DC power grid based on the average value model, a simplified equivalent model of the system is constructed.

[0007] Optionally, the step of constructing a per-unit value analytical calculation model based on the simplified equivalent model of the system includes: Based on the simplified equivalent model of the system, an overall analytical calculation model of the nominal value control system is constructed. Based on the overall analytical calculation model of the named value control system, a per-unit value analytical calculation model is constructed.

[0008] Optionally, the steps for constructing the overall mathematical model of the flexible DC power grid specifically include: The average value modeling method is used to establish the AC side voltage equation, the arm current equation, the DC side voltage equation, and the power balance equation, respectively. Based on the coupling relationship between the above equations, the model of each MMC converter station is constructed. A dual closed-loop control structure with an outer voltage loop and an inner current loop is adopted. The phase angle of the synchronous rotating coordinate system is obtained through a phase-locked loop, and the Park transformation is used to construct the AC side and control system model of the converter station. Based on the topology of the flexible DC power grid, a DC transmission line model is constructed; The mathematical models of each MMC converter station, the AC side and control system model of the converter station, and the DC transmission line model are coupled in a unified manner according to the network topology to form an overall mathematical model of the flexible DC power grid.

[0009] Optionally, the step of constructing a linearized overall model of the flexible DC power grid based on the overall mathematical model of the flexible DC power grid includes: For each MMC converter station model in the overall mathematical model of the flexible DC power grid, the switching state of the submodule is ignored, and the average value model of the DC side of the MMC is constructed based on the power balance relationship between the AC side and DC side of the MMC, the capacitor equation of the submodule, and the relationship between the resistance and inductance of the bridge arm. Taking the steady-state operation of the system as the linearized operating point, each state variable of the MMC DC side average value model is expressed as the sum of steady-state value and small disturbance quantity, and second-order and higher-order small disturbance terms are ignored to form multiple MMC converter station average value small signal models. Based on the topology of the flexible DC grid, the average small-signal model of the multiple MMC converter stations, the DC transmission line model, and the AC side and control system model of the converter stations are uniformly coupled according to the node connection relationship. Combined with the DC network node voltage equation and line dynamic equation, an overall linearized model of the flexible DC grid based on the average model is constructed.

[0010] Optionally, the construction of a simplified equivalent model of the system based on the overall linearized model of the flexible DC power grid based on the average value model includes: The multiple power control converter stations in the overall linearization model of the flexible DC power grid based on the average value model are uniformly equivalent to power control current sources; The multiple DC voltage-controlled converter stations in the overall linearization model of the flexible DC grid based on the average value model are uniformly equivalent to DC voltage-controlled current sources; The energy storage component in the overall linearization model of the flexible DC power grid based on the average value model is uniformly equivalent to the system's equivalent capacitance; Based on the power-controlled current source, the DC voltage-controlled current source, and the system equivalent capacitance, a simplified equivalent model of the system is constructed.

[0011] Optionally, the step of constructing a comprehensive analytical calculation model for the nominal value control system based on the simplified equivalent model of the system includes: The multiple power control stations and multiple DC voltage control stations in the simplified equivalent model of the system are uniformly equivalent to a common DC network. The dynamic equilibrium relationship of the system is established based on Kirchhoff's current law, and the dynamic equation of DC voltage of the flexible DC grid is obtained. Substitute the control relationships of each DC voltage control station into the dynamic equation of DC voltage in the flexible DC grid to construct an overall analytical calculation model of the nominal value control system.

[0012] Optionally, the step of constructing a per-unit value analytical calculation model based on the overall analytical calculation model of the named value control system includes: The overall analytical calculation model of the named value control system is processed by per-unit value to construct a per-unit value analytical calculation model.

[0013] Optionally, when the determination result of whether each DC voltage control converter station can meet the system stability requirements is negative, the following steps are included: Calculate the power injection coefficient; Determine whether to use a per-unit value system; If so, the power injection coefficient is substituted into the per-unit analytical calculation model to recalculate the controller parameters of each converter station in the flexible DC power grid; If not, the power injection coefficient is substituted into the overall analytical calculation model of the nominal value control system, and the controller parameters of each converter station of the flexible DC grid are recalculated. The above calculation process is repeated until a judgment result is obtained that a single DC voltage-controlled converter station can meet the system stability requirements.

[0014] This application has the following beneficial effects: The method proposed in this application enables multi-terminal flexible DC systems to achieve the expected settling time, small overshoot, and good damping characteristics under multiple DC voltage control conditions. Attached Figure Description

[0015] Figure 1 A flowchart illustrating the analytical calculation method for parameters of a flexible DC grid multi-DC voltage control converter station provided in an embodiment of this application; Figure 2 A diagram of the main circuit and control system of the converter station provided in the embodiments of this application; Figure 3 A small-signal model diagram of the average value of a single MMC converter station provided in the embodiments of this application; Figure 4 A diagram of the overall linearized model of the flexible DC power grid based on the average value model provided in this application embodiment; Figure 5 A simplified equivalent model diagram of the system provided in the embodiments of this application; Figure 6 This is a diagram illustrating the overall analytical calculation model of the named value control system provided in this application embodiment; Figure 7 A diagram illustrating the per-unit value analytical calculation model provided in this application embodiment; Figure 8 A flowchart illustrating the control parameter design optimization diagram provided in the embodiments of this application; Figure 9 Simulation results of two DC voltage controllers with different expected adjustment times provided for embodiments of this application; Figure 9 (a) shows the simulation results of two DC voltage controllers when the expected adjustment time is 0.2s and the smoothing reactor is 0mH; Figure 9 (b) shows the simulation results of two DC voltage controllers with a desired settling time of 0.2s and a smoothing reactor of 200mH; Figure 9 (c) shows the simulation results of two DC voltage controllers when the expected settling time is 0.3s and the smoothing reactor is 0mH; Figure 9 (d) shows the simulation results of two DC voltage controllers with an expected adjustment time of 0.3s and a smoothing reactor of 200mH. Detailed Implementation

[0016] To facilitate understanding by those skilled in the art, the present application will be further described below in conjunction with embodiments and accompanying drawings. The content mentioned in the embodiments is not intended to limit the present application.

[0017] To solve the above technical problems, such as Figure 1 As shown, this application proposes an analytical calculation method for parameters of multiple DC voltage-controlled converter stations in flexible DC power grids, including: Step S101: Construct an overall mathematical model of the flexible DC power grid; This embodiment extends the main circuit of a single converter station to a flexible DC grid. The system mainly consists of multiple MMC converter stations, an AC system, and DC transmission lines. Multiple converter stations perform DC voltage control, while the remaining converter stations employ constant power control. All converter stations are interconnected via DC transmission lines to form a multi-terminal flexible DC grid. The overall mathematical model construction process for the aforementioned flexible DC grid is as follows: First, a mathematical model of a single converter station is established based on the MMC main circuit structure. Using the average value modeling method, the AC side voltage equation, bridge arm current equation, DC side voltage equation, and power balance equation are established respectively. Based on the coupling relationship between these equations, models of each MMC converter station are constructed. The converter station control system adopts a dual closed-loop control structure with an outer voltage loop and an inner current loop. The phase angle of the synchronous rotating coordinate system is obtained through a phase-locked loop, and the AC side and control system models of the converter station are constructed using Park transformation. Figure 2 The control structure allows for the establishment of mathematical models for MMC converter stations. After modeling a single MMC converter station, a DC transmission line model is established based on the flexible DC grid topology. Finally, the mathematical models of each MMC converter station, the AC side and control system models of the converter stations, and the DC transmission line models are coupled together according to the network topology to form a unified mathematical model of the flexible DC grid. Figure 2 .

[0018] Figure 2 middle, , For alternating voltage and current, , For the resistance and inductance of the transformer, For smoothing reactors, , , , For the voltage and current along the d-axis and q-axis, This is the DC voltage reference value. This is a power reference value. , The current is the tracking current in the inner loop PI control of the dq coordinate system. , The reference voltage for the MMC AC output voltage dq modulation.

[0019] Step S102: Based on the overall mathematical model of the flexible DC power grid, construct a simplified equivalent model of the system; Based on the established overall mathematical model of the flexible DC power grid, in order to obtain a small-signal model suitable for analytical calculation of controller parameters, this embodiment processes the MMC and its DC side using an average value modeling method. Specifically: First, for each MMC converter station model in the overall mathematical model of the flexible DC power grid, the switching states of submodules are ignored. Based on the power balance relationship between the AC and DC sides of the MMC, the capacitance equations of the submodules, and the voltage drop relationship between the arm resistance and inductance, an average value model of the DC side of the MMC is constructed. Then, taking the steady-state operation of the system as the linearized operating point, each state variable is expressed as the sum of the steady-state value and small disturbances, ignoring second-order and higher-order small disturbance terms, forming multiple average value small-signal models of the MMC converter stations, such as... Figure 3As shown. During the linearization process, its linearized model based on the average value model can be obtained, as shown in equation (1): (1) In the formula, For converter station capacitors, This is the steady-state value of the DC-side voltage. This refers to the power output from the DC side. and These are the DC-side resistor and inductor, respectively. It is the change in capacitor voltage at the converter station. This represents the change in DC-side voltage. This is the rate of change of DC-side output power. This is the rate of change of DC-side current.

[0020] After obtaining the average small-signal model of a single MMC converter station, based on the flexible DC grid topology, the average small-signal models of multiple MMC converter stations, the DC transmission line model, and the AC side and control system models of the converter stations are uniformly coupled according to the node connection relationship. Combined with the DC network node voltage equations and line dynamic equations, an overall linearized model of the flexible DC grid based on the average model is established, such as... Figure 4 As shown.

[0021] Figure 4 middle, (i=1, 2, 3, 4) represents the i-th Disturbance to the active power reference value of each converter station Indicates the first Disturbance of reactive power reference value of each converter station Indicates the first Disturbance to the DC voltage reference value of each converter station No. Actual voltage disturbance at the DC port of each converter station. No. The actual current disturbance injected into or flowing out of the DC port of the converter station.

[0022] The overall linearization model comprehensively considers the dynamic coupling relationship between multiple DC voltage-controlled converter stations formed through the DC network. It integrates the control systems of each converter station, the DC network, and the AC system into a unified state-space model, establishing the dynamic relationship between system state variables, control inputs, and output variables. Based on this model, the impact of controller parameter changes on system dynamic response and DC voltage stability can be further analyzed, and a unified linearized mathematical foundation can be provided for subsequent simplified equivalent modeling of the system and analytical calculation of controller parameters.

[0023] Based on the aforementioned established linearized model of the flexible DC power grid based on the average value model, to facilitate the analytical calculation of controller parameters, a dynamic equivalent processing is performed on the multi-terminal flexible DC power grid transmission system, and a simplified equivalent model of the system is constructed. Its equivalent structure is as follows: Figure 5 As shown.

[0024] Figure 5 middle, The equivalent current of the converter station for power control. The equivalent regulating current of the DC voltage-controlled converter station. For the common DC bus voltage, This is the equivalent capacitance.

[0025] The equivalent process is as follows: First, the system is classified according to the converter station control method. Converter stations operating under active power control are primarily responsible for system power transmission. During controller parameter analysis, multiple power-controlled converter stations are uniformly represented as power-controlled current sources. This is used to represent the total current injected into or absorbed by the system into the DC network.

[0026] Converter stations operating under DC voltage control are responsible for maintaining stable DC voltage in the system. To reflect the dynamic characteristics of multiple DC voltage-controlled converter stations jointly participating in DC voltage regulation, these multiple DC voltage-controlled converter stations are uniformly equivalent to DC voltage-controlled current sources. This is used to describe the system's ability to regulate the voltage of the common DC bus.

[0027] Furthermore, the energy storage component in the flexible DC grid is uniformly equivalent. Since the capacitance of each MMC converter station submodule and the distributed capacitance of the DC line jointly determine the DC-side energy storage characteristics of the system, the equivalent capacitance of each converter station and the distributed capacitance of the DC line are uniformly converted into the equivalent capacitance of the system. The system's equivalent capacitance comprehensively reflects the overall energy storage capacity of the flexible DC grid, and its expression is: (2) In the formula, This is the equivalent capacitance. T The number of converter stations. B This refers to the number of transmission lines. c This represents the capacitance per unit length of the line. For the first The length of each line; the former in this formula represents the equivalent capacitance of all converter stations, and the latter represents the equivalent capacitance of all lines. This is the capacitance value of a single converter station.

[0028] Subsequently, multiple converter stations were connected together via a common DC bus, using the common DC bus voltage. As the only state variable of the system, the dynamic equations for the common DC bus are established based on Kirchhoff's current law: (3) In the formula, The equivalent current of the converter station for power control. The equivalent regulating current of the DC voltage-controlled converter station. This is the common DC bus voltage.

[0029] As can be seen from equation (3), the change in the common DC bus voltage is determined by the difference between the injected current of the power-controlled converter station and the regulating current of the DC voltage-controlled converter station. When the system power changes, the DC voltage-controlled converter station adjusts the output current to restore the DC voltage to the set value, thereby maintaining the stable operation of the flexible DC grid.

[0030] Through the above equivalent processing, the original multi-terminal flexible DC grid model is simplified into a low-order dynamic model consisting of the system equivalent capacitance, the common DC bus voltage, the power control equivalent current, and the DC voltage control equivalent current, such as... Figure 5 As shown in the figure, this model retains the main dynamic characteristics and DC voltage control characteristics of the flexible DC grid, while significantly reducing the system model order, providing a unified mathematical foundation for the subsequent establishment of a global analytical calculation model and a per-unit analytical calculation model for the nominal control system.

[0031] Step S103: Based on the simplified equivalent model of the system, construct an analytical calculation model for per-unit values; After completing the system simplification and equivalence, according to Figure 5 The established simplified equivalent model of the system unifies multiple power control stations and multiple DC voltage control stations into a common DC network. Based on Kirchhoff's current law, the dynamic equilibrium relationship of the system is established, yielding the dynamic equation of the DC voltage of the flexible DC grid. Furthermore, the control relationships of each DC voltage control station are substituted into the dynamic equation of the DC voltage of the flexible DC grid to establish a global analytical calculation model of the nominal value control system, such as... Figure 6 As shown.

[0032] Figure 6 middle, Indicates the first Disturbance of active power reference value of each power control station This is a disturbance to the DC bus voltage reference value. This represents actual DC bus disturbance. The rated voltage of the DC system. For the first The steady-state DC current of each converter station Let represent the equivalent transfer function of the j-th voltage control station from DC voltage deviation to active power change.

[0033] according to Figure 6 Each DC voltage control station participates in DC voltage regulation, and its dynamic process satisfies the established mathematical relationship.

[0034] (4) In the formula, s is the Laplace operator. The damping term generated by proportional control. For the recovery term generated by integral control, This is the rated voltage of the DC system; For the first The rated voltage of the AC side of each converter station.

[0035] By rearranging the closed-loop characteristic equations of the system, an analytical relationship between the system's dynamic performance and the controller parameters can be established, yielding mathematical expressions for the system's natural frequency, damping ratio, and controller parameters: (5) Considering the differences in capacity among different DC voltage control stations, this application introduces a converter station power injection coefficient to ensure that multiple control stations can coordinate their participation in DC voltage regulation: (6) The power injection coefficient is used to characterize the first The power allocation ratio of a DC voltage controlled converter station when multiple DC voltage controlled converter stations jointly undertake the task of DC power regulation of the system is determined, and the corresponding DC current regulation of each converter station is determined based on the power allocation relationship, and then participates in the analytical calculation of the PI controller parameters of each converter station.

[0036] Subsequently, a standard second-order system model is established based on the expected dynamic performance of the system. The natural frequency and damping ratio of the system are used as control targets. The mathematical expression (5) obtained from the closed-loop characteristic equation of the system is combined with the power injection coefficient of each DC voltage control converter station, i.e., formula (6), to obtain the analytical calculation formulas of the proportional coefficient and integral coefficient of the controller of each DC voltage control station as shown in the following formula: (7) In the above formula, and They represent the first The proportional and integral coefficients of the outer loop PI controller for the DC voltage control converter station; The system damping ratio is used to characterize the damping properties of the system's dynamic response. The system's natural angular frequency (or controller design bandwidth) is used to determine the system's dynamic response speed; The equivalent DC capacitance of the flexible DC grid is composed of the equivalent capacitance of each converter station and the distributed capacitance of the DC lines. This is the rated voltage of the DC system; For the first Rated voltage of the AC side of each converter station; For the first Power allocation coefficient of a DC voltage-controlled converter station For the first The power of each converter station.

[0037] Subsequently, in order to adapt to the per-unit control system commonly used in actual engineering, [the following was done]: Figure 6 The model is standardized and a per-unit model is established. Figure 7 The per-unit value analytical calculation model is shown.

[0038] Figure 7 middle, Indicates the first The rated power or power reference value of each converter station. This is the rated power of the first voltage control station. This indicates the rated power of the last converter station. Indicates the first The per-unit DC voltage control transfer function of a voltage control station.

[0039] Step S104: Based on the per-unit value analytical calculation model, determine the initial controller parameters of each converter station in the flexible DC power grid; in accordance with Figure 7 The per-unit value transformation relationship of the per-unit value analytical calculation model can be used to obtain the analytical calculation formula for controller parameters under the per-unit value control system.

[0040] (8) In equation (8), and They represent the first The proportional and integral coefficients of the outer loop PI controller for the DC voltage control converter station; The system damping ratio is used to characterize the damping properties of the system's dynamic response. The system's natural angular frequency (or controller design bandwidth) is used to determine the system's dynamic response speed; The equivalent DC capacitance of the flexible DC grid is composed of the equivalent capacitance of each converter station and the distributed capacitance of the DC lines. This is the rated voltage of the DC system; For the first Rated voltage of the AC side of each converter station; For the first Power allocation coefficient of a DC voltage-controlled converter station For the first The power of each converter station; Through the above analytical calculation process, the proportional coefficient and integral coefficient of each DC voltage control converter station can be directly calculated based on the system equivalent parameters, system bandwidth, damping ratio, and rated capacity of each converter station, thus realizing the transformation of controller parameters from empirical tuning to analytical calculation.

[0041] Step S105: Based on the initial controller parameters of each converter station in the flexible DC grid, perform stability verification on each control converter station and determine whether a single DC voltage control converter station can meet the system stability requirements; If so, the initial controller parameters of each converter station in the flexible DC grid will be used as the controller parameters of the multi-DC voltage control converter station.

[0042] After completing the analytical calculation of controller parameters, obtaining the initial controller parameters for each converter station of the flexible DC power grid, and clarifying the controller design constraints (including system damping ratio, settling time, and allowable bandwidth range, which are determined by the flexible DC power grid operating mode, converter station capacity, and control objectives), this embodiment further improves the stable operation capability of the flexible DC power grid according to... Figure 8 The process shown optimizes the existing controller parameters. Subsequently, based on the obtained proportional and integral coefficients of the controllers of each DC voltage control converter station, the stability of each control station is checked. If the DC voltage control station cannot meet the requirements for stable system operation, the parameter optimization process is initiated: the power injection coefficient is recalculated based on the converter station capacity, and it is determined whether to use the per-unit system calculation. If so, the power injection coefficient is substituted into the per-unit analytical calculation model (formula (7)) to recalculate the controller parameters of each converter station in the flexible DC grid; if not, the power injection coefficient is substituted into the overall analytical calculation model of the nominal value control system (formula (8)) to recalculate the controller parameters of each converter station in the flexible DC grid; the proportional and integral coefficients of the controllers of each control station are recalculated to complete the coordinated allocation of control tasks among multiple control stations. The above calculation process is repeated until the judgment result that a single DC voltage control converter station can meet the system stability requirements is obtained. After obtaining the updated controller parameters, a stability analysis was conducted on the entire flexible DC power grid. The controller design bandwidth was determined based on the system's lowest resonant frequency, ensuring that the controller's closed-loop bandwidth was lower than the system's lowest resonant frequency. Furthermore, the proportional and integral coefficients were optimized based on the system's damping characteristics. Ultimately, the controller parameters for the multi-DC voltage control converter station were obtained, simultaneously meeting the requirements for stability, dynamic response speed, and engineering applications, thus achieving the integration of controller parameter analytical calculation and optimization design.

[0043] Simulation verification To verify the correctness of the analytical calculation method for parameters of multiple DC voltage-controlled converter stations in the flexible DC grid proposed in this application, a seven-terminal flexible DC transmission system was constructed as the verification object. Two DC voltage-controlled converter stations were located in different areas, while the remaining converter stations adopted a constant power control mode. The number of converter station bridge arm sub-modules was 250. The main circuit parameters of the converter stations are shown in Table 1, the rated voltage of the DC system was 500kV, and the DC line parameters are shown in Table 2.

[0044] Table 1. Main circuit parameters of the converter station ; Table 2 Equivalent parameters of DC lines ; First, following the parameter analysis steps outlined in this application, the system damping ratio is set to 0.707, and the desired settling times are given as 0.2s and 0.3s, respectively. The proportional and integral coefficients of the two DC voltage control stations are calculated using the controller parameter analysis formula derived in this application. These are kpdc = 4.96 and kidc = 66.1, respectively. Subsequently, under stable system conditions, a 20kV step disturbance is applied to the DC voltage reference value, and the two DC voltage control stations are simultaneously activated for coordinated control. The verification results are as follows: Figure 9 As shown.

[0045] Depend on Figure 9 It can be seen that: 1) Under the two operating conditions with expected adjustment times of 0.2s and 0.3s, the DC voltage of each converter station can be stably converged to the new steady-state value; 2) When the two DC voltage control stations operate in coordination, the DC voltage response curve is smoother and the overshoot is significantly reduced; 3) The actual adjustment time is basically consistent with the preset expected adjustment time, indicating that the controller parameters obtained by analytical calculation in this application have high accuracy.

[0046] It can be seen that the method proposed in this application enables multi-terminal flexible DC systems to achieve the expected adjustment time, small overshoot, and good damping characteristics under two DC voltage control conditions, thereby verifying the correctness and engineering effectiveness of the method proposed in this application.

[0047] In summary, the method proposed in this application enables multi-terminal flexible DC systems to achieve the expected settling time, small overshoot, and good damping characteristics under multiple DC voltage control conditions.

[0048] In some embodiments, this application also provides a computer system including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps in the above-described method embodiments.

[0049] This application also provides a computer-readable storage medium for storing a computer program. This computer-readable storage medium can be applied to a computer device, and the computer program causes the computer device to execute the corresponding processes in the methods described above in the embodiments of this application; for brevity, further details are omitted here.

[0050] The above embodiments are preferred implementations of this application. In addition, this application can be implemented in other ways. Any obvious substitutions without departing from the concept of this technical solution are within the protection scope of this application.

[0051] To facilitate understanding by those skilled in the art of the improvements made by this application compared to the prior art, some of the accompanying drawings and descriptions have been simplified, and for clarity, some other elements have been omitted from this application. Those skilled in the art should realize that these omitted elements may also constitute the content of this application.

Claims

1. A method for analytical calculation of parameters of multiple DC voltage-controlled converter stations in flexible DC power grids, characterized in that, include: Constructing an overall mathematical model of the flexible DC power grid; Based on the overall mathematical model of the flexible DC power grid, a simplified equivalent model of the system is constructed. Based on the simplified equivalent model of the system, an analytical calculation model for per-unit values ​​is constructed. Based on the per-unit value analytical calculation model, the initial controller parameters of each converter station of the flexible DC power grid are determined. Based on the initial controller parameters of each converter station in the flexible DC grid, the stability of each control converter station is checked, and it is determined whether a single DC voltage control converter station can meet the system stability requirements. If so, the initial controller parameters of each converter station in the flexible DC grid will be used as the controller parameters of the multi-DC voltage control converter station.

2. The method according to claim 1, characterized in that, The simplified equivalent model of the system is constructed based on the overall mathematical model of the flexible DC power grid, including: Based on the overall mathematical model of the flexible DC power grid, a linearized model of the flexible DC power grid based on the average value model is constructed. Based on the overall linearized model of the flexible DC power grid based on the average value model, a simplified equivalent model of the system is constructed.

3. The method according to claim 2, characterized in that, The construction of a per-unit value analytical calculation model based on the simplified equivalent model of the system includes: Based on the simplified equivalent model of the system, an overall analytical calculation model of the nominal value control system is constructed. Based on the overall analytical calculation model of the named value control system, a per-unit value analytical calculation model is constructed.

4. The method according to claim 3, characterized in that, The specific steps for constructing the overall mathematical model of the flexible DC power grid include: The average value modeling method is used to establish the AC side voltage equation, the arm current equation, the DC side voltage equation, and the power balance equation, respectively. Based on the coupling relationship between the above equations, the model of each MMC converter station is constructed. A dual closed-loop control structure with an outer voltage loop and an inner current loop is adopted. The phase angle of the synchronous rotating coordinate system is obtained through a phase-locked loop, and the Park transformation is used to construct the AC side and control system model of the converter station. Based on the topology of the flexible DC power grid, a DC transmission line model is constructed; The mathematical models of each MMC converter station, the AC side and control system model of the converter station, and the DC transmission line model are coupled in a unified manner according to the network topology to form an overall mathematical model of the flexible DC power grid.

5. The method according to claim 4, characterized in that, The construction of a linearized overall model of the flexible DC power grid based on the average value model, based on the overall mathematical model of the flexible DC power grid, includes: For each MMC converter station model in the overall mathematical model of the flexible DC power grid, the switching state of the submodule is ignored, and the average value model of the DC side of the MMC is constructed based on the power balance relationship between the AC side and DC side of the MMC, the capacitor equation of the submodule, and the relationship between the resistance and inductance of the bridge arm. Taking the steady-state operation of the system as the linearized operating point, each state variable of the MMC DC side average value model is expressed as the sum of steady-state value and small disturbance quantity, and second-order and higher-order small disturbance terms are ignored to form multiple MMC converter station average value small signal models. Based on the topology of the flexible DC grid, the average small-signal model of the multiple MMC converter stations, the DC transmission line model, and the AC side and control system model of the converter stations are uniformly coupled according to the node connection relationship. Combined with the DC network node voltage equation and line dynamic equation, an overall linearized model of the flexible DC grid based on the average model is constructed.

6. The method according to claim 5, characterized in that, The simplified equivalent model of the system, based on the overall linearized model of the flexible DC power grid based on the average value model, is constructed, including: The multiple power control converter stations in the overall linearization model of the flexible DC power grid based on the average value model are uniformly equivalent to power control current sources; The multiple DC voltage-controlled converter stations in the overall linearization model of the flexible DC grid based on the average value model are uniformly equivalent to DC voltage-controlled current sources; The energy storage component in the overall linearization model of the flexible DC power grid based on the average value model is uniformly equivalent to the system's equivalent capacitance; Based on the power-controlled current source, the DC voltage-controlled current source, and the system equivalent capacitance, a simplified equivalent model of the system is constructed.

7. The method according to claim 6, characterized in that, The construction of a comprehensive analytical calculation model for the nominal value control system based on the simplified equivalent model of the system includes: The multiple power control stations and multiple DC voltage control stations in the simplified equivalent model of the system are uniformly equivalent to a common DC network. The dynamic equilibrium relationship of the system is established based on Kirchhoff's current law, and the dynamic equation of DC voltage of the flexible DC grid is obtained. Substitute the control relationships of each DC voltage control station into the dynamic equation of DC voltage in the flexible DC grid to construct an overall analytical calculation model of the nominal value control system.

8. The method according to claim 7, characterized in that, The construction of a per-unit value analytical calculation model based on the overall analytical calculation model of the named value control system includes: The overall analytical calculation model of the named value control system is processed by per-unit value to construct a per-unit value analytical calculation model.

9. The method according to claim 8, characterized in that, When the determination result of whether the single DC voltage control converter station can meet the system stability requirements is negative, the following steps are included: Calculate the power injection coefficient; Determine whether to use a per-unit value system; If so, the power injection coefficient is substituted into the per-unit analytical calculation model to recalculate the controller parameters of each converter station in the flexible DC power grid; If not, the power injection coefficient is substituted into the overall analytical calculation model of the nominal value control system, and the controller parameters of each converter station of the flexible DC grid are recalculated. The above calculation process is repeated until a judgment result is obtained that a single DC voltage-controlled converter station can meet the system stability requirements.

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