Flexible interconnection device parameter optimization method based on nonlinear numerical analysis

Abstract

The invention provides a flexible interconnection device parameter optimization method based on nonlinear numerical analysis, which comprises the following steps of: (1) constructing a nonlinear numerical analysis solution of a power angle of a port converter of a flexible interconnection device based on an improved multi-scale method; step (2), constructing a stability boundary of the key parameters of the port converter of the flexible interconnection device based on a transient stability criterion; and step (3), constructing an optimization model of the key parameters of the flexible interconnection device according to the power angle numerical equation of the port converter, and solving the optimization model. According to the flexible interconnection device parameter optimization method based on nonlinear numerical analysis, the dynamic mathematical model of the flexible interconnection device after large disturbance is constructed, the optimal control parameters are obtained, the system can still keep high stability when facing power grid fluctuation, and the overall performance of the flexible interconnection device is further enhanced.

Description

Technical Field

[0001] This invention relates to the field of power electronics technology, and more specifically to a method for optimizing the parameters of flexible interconnect devices based on nonlinear numerical analysis. Background Technology

[0002] Double-ended flexible interconnection devices not only achieve stable power transmission but also possess active support capabilities. They autonomously adjust active and reactive power output to maintain system balance when grid voltage and frequency fluctuate. Traditional flexible interconnection devices often employ grid-following control strategies or grid-based control strategies based on virtual synchronous machines to adapt to grid scenarios of varying intensities. When grid disturbances occur, the stability of the flexible interconnection device is crucial for system operation; therefore, designing the control parameters of the flexible interconnection device is an urgent problem to be solved.

[0003] Currently, the parameter design of flexible interconnection devices based on power electronic converters mainly relies on small-signal models. By establishing the full-order small-signal state-space equations of the flexible interconnection device, all oscillation modes of the system can be analyzed, and control parameters can be selected based on the distribution of oscillation modes. However, small-signal models cannot reflect the stability of flexible interconnection devices under large disturbance scenarios, and their parameters do not match the actual scenario. Secondly, the selection of control parameters is too dependent on experience and lacks theoretical support, making it impossible to select the optimal parameters. On the other hand, for large disturbances, stability analysis based on the Lyapunov energy function method or the equal area rule is usually used to infer the parameter boundaries. However, this method can only determine the parameter range of the flexible interconnection device and cannot optimize the control parameters. Therefore, this invention proposes a parameter optimization method for flexible interconnection devices based on nonlinear numerical analysis to solve the problem of optimal parameter selection under nonlinear scenarios with large disturbances. Summary of the Invention

[0004] Purpose of the invention: The purpose of this invention is to propose a parameter optimization method for flexible interconnection devices based on nonlinear numerical analysis. By constructing a dynamic mathematical model of the flexible interconnection device after large disturbances, the optimal control parameters are obtained, enabling the system to maintain high stability when facing power grid fluctuations, and further enhancing the overall performance of the flexible interconnection device.

[0005] This invention discloses a parameter optimization method for flexible interconnection devices based on nonlinear numerical analysis. Based on nonlinear numerical analysis theory, this method first derives the precise numerical solution for the phase-locked angle or virtual power angle of the output port of the flexible interconnection device after disturbance; secondly, it obtains the constraints on each key parameter of the flexible interconnection device according to transient stability criteria; finally, based on the constraints, a nonlinear parameter optimization model is constructed, and the optimal parameters of the flexible interconnection device are solved using an intelligent algorithm. This method overcomes the limitation of the traditional equal-area method, which can qualitatively analyze the impact of different parameters on transient synchronization stability but lacks theoretical guidance for quantitative analysis of different control parameters. It provides a theoretical basis for selecting the control parameters of the converters on both sides of the flexible interconnection device, thereby significantly improving the reliability and stability of the flexible interconnection device. By constructing a dynamic mathematical model of the flexible interconnection device after large disturbances and obtaining the optimal control parameters, this invention enables the system to maintain high stability when facing grid fluctuations, further enhancing the overall performance of the flexible interconnection device.

[0006] To achieve optimal parameter selection for flexible interconnected devices, this invention employs the following technical solution: First, based on an improved multi-scale method, the invention analytically analyzes the output power angle swing equation at the converter port of the flexible interconnected device, deriving the precise numerical solution for the phase-locked angle or virtual power angle at the output port of the flexible interconnected device after disturbance. Second, according to the transient stability criterion, the transient stability boundary values ​​of different parameters are quantitatively calculated, obtaining the constraints on each key parameter of the flexible interconnected device. Finally, based on the aforementioned nonlinear power angle equation, with the goal of minimizing its deviation, a nonlinear parameter optimization model is constructed, and the optimal parameters of the flexible interconnected device are solved using an intelligent algorithm. Specific implementation steps include:

[0007] Step (1): Based on the improved multi-scale method, construct the nonlinear numerical analytical solution of the power angle of the port converter of the flexible interconnection device;

[0008] Step (2): Based on the transient stability criterion, construct the stability boundary of the key parameters of the port converter of the flexible interconnection device;

[0009] Step (3): Based on the numerical equation of the power angle of the port converter, construct an optimization model for the key parameters of the flexible interconnection device and solve it.

[0010] Compared with the prior art, the present invention has the following significant advantages:

[0011] This invention overcomes the limitations of traditional equal-area methods, which can qualitatively analyze the impact of different parameters on transient synchronization stability but struggle to quantitatively analyze different control parameters, thus hindering quantitative parameter design and optimization. This invention utilizes nonlinear analytical solving techniques to accurately characterize the dynamic trajectory of the flexible interconnection device after disturbance, providing a basis for quantitative analysis and enabling precise parameter optimization. This invention constructs a dynamic mathematical model of the flexible interconnection device after a large disturbance, obtaining optimal control parameters that allow the system to maintain high stability in the face of grid fluctuations, further enhancing the overall performance of the flexible interconnection device. Attached Figure Description

[0012] Figure 1 This is a flowchart of a method for optimizing the parameters of a flexible interconnection device based on nonlinear numerical analysis, according to the present invention.

[0013] Figure 2 This is a diagram of the VSG control strategy for the flexible interconnect device port of this invention;

[0014] Figure 3 This is a time-domain trajectory diagram of the output power angle of the port converter of the present invention;

[0015] Figure 4 This is a power angle curve diagram of different D values ​​according to the present invention;

[0016] Figure 5 This is a power angle curve diagram of different J values ​​according to the present invention. Detailed Implementation

[0017] The following detailed description, with reference to the accompanying drawings, illustrates a specific implementation of the parameter optimization method for flexible interconnection devices based on nonlinear numerical analysis according to the present invention.

[0018] This invention first uses an improved multi-scale method to analytically analyze the output power angle swing equation at the converter port of a flexible interconnect device, deriving precise numerical solutions for the phase-locked angle or virtual power angle at the output port of the flexible interconnect device after disturbance. Second, based on transient stability criteria, it quantitatively calculates the transient stability boundary values ​​for different parameters, obtaining the constraints on each key parameter of the flexible interconnect device. Finally, based on the aforementioned nonlinear power angle equation, and with the goal of minimizing its deviation, a nonlinear parameter optimization model is constructed, and the optimal parameters of the flexible interconnect device are solved using an intelligent algorithm. The specific implementation steps are as follows, and the overall flowchart is shown below. Figure 1 As shown.

[0019] Step (1): Based on the improved multi-scale method, construct the nonlinear numerical analytical solution of the power angle of the port converter of the flexible interconnection device;

[0020] Step (2): Based on the transient stability criterion, construct the stability boundary of the key parameters of the port converter of the flexible interconnection device;

[0021] Step (3): Based on the numerical equation of the power angle of the port converter, construct an optimization model for the key parameters of the flexible interconnection device and solve it.

[0022] 1. Establishment of a nonlinear numerical analytical solution for the power angle of the port converter in a flexible interconnection device.

[0023] Flexible interconnection devices are power electronic devices composed of back-to-back voltage source converters. The structure of a double-ended flexible interconnection device is symmetrical; the left and right converters are completely equivalent in design and function, possessing the same mathematical model. Both converters operate using a network control strategy based on a virtual synchronous machine, such as... Figure 2 As shown, the angle difference between the output voltage angle of the port converter and the grid connection point voltage can be expressed as the following second-order nonlinear differential equation:

[0024]

[0025] In the above formula: D is the virtual damping of the flexible interconnection device port converter network control; J is the virtual inertia; P ref This is a reference value for active power; U g U is the rated voltage at the grid connection point, and U is the actual voltage of the port converter; X g Let be the connection impedance between the converter and the grid connection point; δ is the phase angle difference between the grid voltage and the port converter voltage. The stability of the flexible interconnection device under large disturbances depends on the stability of δ. Therefore, it is necessary to solve the numerical solution of δ of the port converter under large disturbances to determine and optimize the control parameters.

[0026] Since the above equation is a nonlinear second-order model, the initial stable equilibrium point of sinδ before the large power angle disturbance can be Taylor expanded as follows:

[0027]

[0028] In the formula, the initial stable equilibrium point δ0 is determined by the output active power of the port converter before the disturbance:

[0029]

[0030] Similarly, the new stable equilibrium point δ after a large disturbance s Determined by the following formula:

[0031]

[0032] In the above formula, U gf This is the final value of the grid connection point voltage after the disturbance. Substituting equation (2) and the disturbed voltage value into equation (1), we can write the standard nonlinear vibration equation as follows:

[0033]

[0034] The parameters in the formula are as follows:

[0035]

[0036] Since the above equation is a strongly nonlinear problem, the classical KBM method is not effective when applied directly. Therefore, this invention introduces a perturbation parameter ε, and writes equation (5) in the general form of a nonlinear differential equation:

[0037]

[0038] The parameters in the formula are:

[0039]

[0040] Furthermore, ω 2 At ω0 2 Expanding into a power series of ε, i.e., ω 2 =ω0 2 +εω1+ε 2 ω2+….., and introduce the transformation parameter α=(εω1) / (ω0) 2 +εω1), after transformation, equation (7) can be expressed as:

[0041]

[0042] The above equation is the weak nonlinear vibration equation containing a small parameter α. The values ​​of the other parameters are given in equation (8). Equation (9) can be approximated using the multi-scale analysis method:

[0043]

[0044] The above equation is the time-domain equation for the output power angle of the port converter of the flexible interconnection device under large disturbances. This equation can be used to determine the key parameters of the port converter of the flexible interconnection device—J, D, and U. gf P ref The range of values ​​for Xg was determined, and the above parameters were optimized.

[0045] 2. Construction of stability boundaries for key parameters of port converters in flexible interconnected devices

[0046] As can be seen from equation (10) above, when a large disturbance occurs in the grid connection voltage of the flexible interconnection device, the operating trajectory of the power angle δ of its port converter is determined by various parameters, that is, the operating stability is determined by the parameters. The analytical solution of the power angle δ generally includes the normal grid voltage U. g Grid voltage drop U gf Converter terminal voltage U, virtual damping parameter D, virtual inertia parameter J, active power reference value P ref Line inductance X gIn order to obtain the range of values ​​for each parameter, this invention constructs the constraint range of each parameter based on the system transient stability criterion.

[0047] The analytical expression for the power angle (10) can be simply expressed as:

[0048] δ(t)=f(U g U gf ,D,J,P ref ,U,X g ,t) (11)

[0049] In the above formula, the function f is the equation corresponding to equation (10). By differentiating the above formula, the time t when the work angle is at its maximum can be calculated. m and the maximum work angle value δ m According to the transient stability criterion δ m ≤π-δ s We can then obtain the following inequality:

[0050] f(U g U gf ,D,J,P ref ,U,X g , t m )≤π-δ s (12)

[0051] And δ s It's about U gf P ref The functions of Xg are shown in equation (4), then inequality (12) can be transformed into:

[0052] g(U g U gf ,D,J,P ref ,U,X g ,t m )≤0 (13)

[0053] g is the implicit function name, and δ in equation (12) is... s Use U gf P ref By substituting Xg and simplifying, we can obtain the function g.

[0054] The maximum or minimum value of a specific key parameter can be obtained from the above formula, as shown in the following formula:

[0055]

[0056] In the above formula, D min The minimum permissible virtual damping coefficient for the network control of port converters in flexible interconnected devices; J max The maximum allowed virtual inertia; P ref,maxThe reference value for the maximum permissible active power; U gf,min The minimum allowable drop voltage value; X g,max This represents the maximum allowable connection impedance.

[0057] The above calculations can be used to determine the transient stability boundaries of different key parameters of the port converter of the flexible interconnection device.

[0058] 3. Construction and Solution of Optimization Model for Key Parameters of Flexible Interconnected Devices

[0059] After the disturbance is cleared within the limit clearing time, the power angle of the port converter of the flexible interconnection device will recover to the initial state after a certain period of time (provided that the constraint of equation (14) is met). At this time, the running trajectory of the power angle is also determined by key parameters. The quality of the parameters determines the convergence time, oscillation amplitude, etc. of the power angle. In order to enable the converter to recover to the initial value quickly and smoothly after the fault is cleared, this project uses the area enclosed by the power angle and the time axis as the objective function, and uses equation (14) as the constraint condition to construct a parameter optimization model, such as Figure 3 As shown.

[0060] Taking the minimum integral of the deviation of the work angle after disturbance as the objective function and Equation (13) as the constraint, the following optimization model is constructed:

[0061]

[0062] In the formula: C is the objective function, and there are n flexible interconnection devices in the system. The above optimization model is a nonlinear and nonconvex model, and the analytical expression of the optimal value cannot be directly obtained. Therefore, this invention uses an intelligent algorithm to find the optimal value. The solution steps of the optimization model are as follows:

[0063] Step (31): Establish the nonlinear power angle equation of the port converter of the flexible interconnection device, and obtain the approximate analytical solution after disturbance through the improved multi-scale method;

[0064] Step (32): Based on the transient stability criterion, after the disturbance occurs, find the maximum power angle and the corresponding time that the system satisfies the limit stability condition, and determine the optimization range of the key system parameters based on the trajectory;

[0065] Step (33): Take the area enclosed by the power angle and time axis after disturbance as the objective function, and establish a parameter optimization model in combination with the nonlinear differential equation of the system, constraints, and key parameters;

[0066] Step (34): Input the power angle trajectory equation and key parameter range obtained in steps (31) and (32) into the genetic algorithm. The genetic algorithm automatically generates the initial parameter set and iterates repeatedly to find the optimal value of the key parameters of the system until the genetic algorithm finally outputs the optimal value of the key parameters of the system.

[0067] To verify the effectiveness of the aforementioned optimization of key transient parameters of the port converter, simulation verification was performed using Matlab / Simulink. The port converter control is as follows: Figure 2 As shown in Table 1, the initial parameters are used to perform simulation verification in MATLAB / Simulink, taking the flexible interconnect device integrated into a single-machine infinite bus system as an example.

[0068] Table 1 Simulation parameter settings

[0069]

[0070]

[0071] To ensure the grid voltage drops to the same level within 0.5 seconds, set the following parameters: P ref =25kW; L g =6mH;U gf =0.4U g List four typical working conditions, such as Figure 4 and Figure 5 As shown. Operating condition 1: D = 370 N·m·s / rad, J = 100 kg·m 2 Operating condition 2: D = 350 N·m·s / rad, J = 100 kg·m 2 Operating condition 3: D is 500 N·m·s / rad, J = 240 kg·m 2 Operating condition 4: D is 500 N·m·s / rad, J = 260 kg·m 2 .

[0072] Under operating conditions 1 and 2, calculate D. min The damping parameter is 361 N·m·s / rad. Under condition 1, the damping parameter is greater than the minimum damping parameter. Figure 4 It can be seen that the power angle converges after oscillation, and the system is transiently stable. In case 2, the damping parameter is less than the minimum damping parameter, and the power angle suddenly oscillates after a period of time, leading to transient instability of the system. The two cases verify the accuracy of the damping parameter boundary values.

[0073] Under operating conditions 3 and 4, J was calculated. max The value is 252 kg·m 2 The inertia parameter for operating condition 3 is less than the maximum inertia parameter. Figure 5 After oscillation, the intermediate power angle converges, and the system becomes transiently stable. In operating condition 4, the inertia parameter exceeds its maximum value, clearly indicating transient instability. These operating conditions verify the accuracy of the inertia parameter boundary values.

[0074] Finally, it should be noted that the above embodiments are merely illustrative of the technical solutions of the present invention and not intended to limit it. Those skilled in the art should understand that modifications or equivalent substitutions can be made to the specific embodiments of the present invention, but such modifications or alterations are all within the scope of protection of the pending claims.

Claims

1. A parameter optimization method for flexible interconnection devices based on nonlinear numerical analysis, characterized in that, The method for optimizing the parameters of the flexible interconnection device includes the following steps: Step (1): Based on the improved multi-scale method, construct the nonlinear numerical analytical solution of the power angle of the port converter of the flexible interconnection device; Step (2): Based on the transient stability criterion, construct the stability boundary of the key parameters of the port converter of the flexible interconnection device; Step (3): Based on the numerical equation of the power angle of the port converter, construct an optimization model for the key parameters of the flexible interconnection device and solve it.

2. The method for optimizing the parameters of a flexible interconnection device based on nonlinear numerical analysis according to claim 1, characterized in that, The nonlinear numerical analytical solution for the power angle of the port converter in the flexible interconnection device is established as follows: Flexible interconnection devices are power electronic devices composed of back-to-back voltage source converters. The structure of a double-ended flexible interconnection device is symmetrical; the left and right converters are completely equivalent in design and function, possessing the same mathematical model. Both converters operate under a grid control strategy based on a virtual synchronous machine. The angle difference between the output voltage angle of the port converter and the grid connection point voltage can be expressed as the following second-order nonlinear differential equation: In the above formula: D is the virtual damping of the flexible interconnection device port converter network control; J is the virtual inertia; P ref This is a reference value for active power; U g U is the rated voltage at the grid connection point, and U is the actual voltage of the port converter; X g This is the connection impedance between the converter and the grid connection point; δ is the phase angle difference between the grid voltage and the port converter voltage; the stability of the flexible interconnection device under large disturbances depends on the stability of δ. Therefore, it is necessary to solve the numerical solution of δ of the port converter under large disturbances in order to determine and optimize the control parameters. Since the above equation is a nonlinear second-order model, the initial stable equilibrium point of sinδ before the large power angle disturbance can be Taylor expanded as follows: In the formula, the initial stable equilibrium point δ0 is determined by the output active power of the port converter before the disturbance: Similarly, the new stable equilibrium point δ after a large disturbance s Determined by the following formula: In the above formula, U gf This is the final value of the grid connection point voltage after the disturbance. Substituting equation (2) and the disturbed voltage value into equation (1), we can write the standard nonlinear vibration equation as follows: The parameters in the formula are as follows: Since the above equation is a strongly nonlinear problem, the classical KBM method is not effective when applied directly. Therefore, this invention introduces a perturbation parameter ε, and writes equation (5) in the general form of a nonlinear differential equation: The parameters in the formula are: Furthermore, ω 2 At ω0 2 Expanding into a power series of ε, i.e., ω 2 =ω0 2 +εω1+ε 2 ω2+….., and introduce the transformation parameter α=(εω1) / (ω0) 2 +εω1), after transformation, equation (7) can be expressed as: The above equation is the weak nonlinear vibration equation containing a small parameter α. The values ​​of the other parameters are given in equation (8). Equation (9) can be approximated by multi-scale analysis: The above equation is the time-domain equation for the output power angle of the port converter of the flexible interconnection device under large disturbances. This equation can be used to determine the key parameters of the port converter of the flexible interconnection device—J, D, and U. gf P ref The range of values ​​for Xg was determined, and the above parameters were optimized.

3. The method for optimizing parameters of a flexible interconnection device based on nonlinear numerical analysis according to claim 2, characterized in that, The stability boundary construction of key parameters for the port converter of the flexible interconnect device is as follows: Based on the system transient stability criterion, the constraint range of each parameter is constructed; The analytical expression for the power angle (10) can be simply expressed as: δ(t)=f(U g ,U gf ,D,J,P ref ,U,X g ,t) (11) In the above formula, the function f is the equation corresponding to equation (10). By differentiating the above formula, the time t when the work angle is at its maximum can be calculated. m and the maximum work angle value δ m According to the transient stability criterion δ m ≤π-δ s We can then obtain the following inequality: f(U g ,U gf ,D,J,P ref ,U,X g ,t m )≤π-δ s (12) And δ s It's about U gf P ref The functions of Xg are shown in equation (4), then inequality (12) can be transformed into: g(U g ,U gf ,D,J,P ref ,U,X g ,t m )≤0 (13) g is the implicit function name, and δ in equation (12) is... s Use U gf P ref By substituting Xg and simplifying, we can obtain the function g; The maximum or minimum value of a specific key parameter can be obtained from the above formula, as shown in the following formula: In the above formula, D min The minimum permissible virtual damping coefficient for the network control of port converters in flexible interconnected devices; J max The maximum allowed virtual inertia; P ref,max The reference value for the maximum permissible active power; U gf,min The minimum allowable drop voltage value; X g,max This represents the maximum allowable connection impedance.

4. The method for optimizing the parameters of a flexible interconnection device based on nonlinear numerical analysis according to claim 3, characterized in that, The specific steps for constructing the optimization model for key parameters of flexible interconnected devices are as follows: Taking the minimum integral of the deviation of the work angle after disturbance as the objective function and Equation (13) as the constraint, the following optimization model is constructed: In the formula: C is the objective function, and there are n flexible interconnection devices in the system.

5. The method for optimizing parameters of a flexible interconnection device based on nonlinear numerical analysis according to claim 3, characterized in that, Equation (14) is an optimization model that is nonlinear and nonconvex, and the analytical expression for the optimal value cannot be obtained directly. Therefore, this invention uses an intelligent algorithm to find the optimal value. The solution steps are as follows: Step (31): Establish the nonlinear power angle equation of the port converter of the flexible interconnection device, and obtain the approximate analytical solution after disturbance through the improved multi-scale method; Step (32): Based on the transient stability criterion, after the disturbance occurs, find the maximum power angle and the corresponding time that the system satisfies the limit stability condition, and determine the optimization range of the key system parameters based on the trajectory; Step (33): Take the area enclosed by the power angle and time axis after disturbance as the objective function, and establish a parameter optimization model in combination with the nonlinear differential equation of the system, constraints, and key parameters; Step (34): Input the power angle trajectory equation and key parameter range obtained in steps (31) and (32) into the genetic algorithm. The genetic algorithm automatically generates the initial parameter set and iterates repeatedly to find the optimal value of the key parameters of the system until the genetic algorithm finally outputs the optimal value of the key parameters of the system.

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