VSC-HVDC direct current capacitor design method considering load uncertainty

Abstract

The invention relates to the technical field of power electronics and direct-current power transmission, in particular to a VSC-HVDC direct-current capacitor design method considering load uncertainty, which comprises the following steps of: 1, establishing a state space model; step 2, establishing a model containing uncertain variables; step 3, stability criterion; and step 4, direct current capacitor algorithm design: by introducing load uncertainty modeling, constructing a computable robust stability criterion and combining with a systematic parameter search method, the direct current capacitor design is expanded from a fixed operation point to a load change interval, and compared with the prior art, the direct current capacitor algorithm design method has the advantages that the design efficiency is improved, and the cost is reduced. The method has obvious advantages in the aspects of applicability, calculation feasibility and engineering guidance significance, the direct current capacitor design is expanded from a fixed operation point to a load change interval by introducing load uncertainty modeling, constructing a computable robust stability criterion and combining a systematic parameter search method, and compared with the prior art, the method has the advantages that the method is simple and convenient to operate, and the cost is low. The method has obvious advantages in the aspects of applicability, calculation feasibility and engineering guiding significance.

Description

Technical Field

[0001] This invention belongs to the field of power electronics and DC transmission technology, and specifically relates to a VSC-HVDC DC capacitor design method that considers load uncertainty. Background Technology

[0002] VSC-HVDC stands for Flexible DC Transmission, often abbreviated as Flexible DC. It is typically used to transmit power from remote power sources to load centers. In such transmission systems, variations in transmission power can affect the system's stability margin. DC capacitors act as buffers to suppress power disturbances. With proper design, for example, if the capacitance value exceeds a certain threshold, the system can still remain stable under given load conditions.

[0003] Existing technologies have conducted extensive research on the stability analysis of VSC-HVDC systems and the selection of DC capacitor parameters. However, there are still some shortcomings in the quantitative design of DC capacitors. First, existing stability analysis methods usually assume that the system's operating equilibrium point is fixed and known, and analyze the system's stability based on this equilibrium point. However, in actual power systems, the load power has uncertainty and time-varying characteristics. The actual operating equilibrium point of the VSC-HVDC system changes with the load conditions and is often difficult to obtain accurately in advance.

[0004] Under the above circumstances, the stability analysis results obtained based on the fixed equilibrium point assumption are difficult to directly guide the engineering design of DC capacitors. Secondly, although existing technologies have revealed the influence of DC capacitors on the dynamic stability of VSC-HVDC systems from an analytical perspective, related research is mostly limited to the analytical level and has not yet formed a method for systematically and quantitatively selecting DC capacitors under uncertain load conditions. Especially in application scenarios that require simultaneous consideration of system stability and engineering economy, there is still a lack of effective design basis and systematic technical solutions for how to reasonably determine the capacitance value of DC capacitors while meeting stability requirements. Summary of the Invention

[0005] The purpose of this invention is to provide a simple and rationally designed VSC-HVDC DC capacitor design method that considers load uncertainty in order to solve the above-mentioned problems.

[0006] The present invention achieves the above objectives through the following technical solutions: A VSC-HVDC DC capacitor design method considering load uncertainty includes the following steps: Step 1, establishing a state-space model; Step 2, establishing a model containing uncertain variables; Step 3, stability criterion; and Step 4, DC capacitor algorithm design. In step one above, the state-space model of the VSC-HVDC system is first established. In step two above, a linearized state-space model of the VSC-HVDC system containing uncertain variables is established. In step three above, a robust stability criterion is constructed based on robust optimization theory; In step four above, a DC capacitor design algorithm is constructed based on the bisection method.

[0007] Preferably, in step one, the method for establishing the state-space model includes: S1. Define the reference direction and establish a mathematical model of the main circuit of the two-level VSC-HVDC system. The main circuit includes three parts: the sending end, the DC side, and the receiving end. According to the modeling principle, the main circuit model includes three parts: the AC side, the DC side, and the AC / DC connection. S2. Based on the control structure diagram, establish the state space model of the VSC-HVDC system converter station control system. The station control system includes two parts: the sending end and the receiving end converter station control system. S3. Define the state variable vector and the input variable vector, and combine the state equations of the above models. Multiple state equations together form a state equation set to obtain the state space model of the VSC-HVDC system.

[0008] Preferably, for the AC side model, based on Kirchhoff's laws, a set of circuit equations is established in a three-phase stationary coordinate system, and then transformed to a synchronous rotating coordinate system using the Park transformation. For the DC side, the set of circuit equations established using Kirchhoff's laws is the required model. For the AC / DC connection model, the AC / DC connection equations are established using the law of conservation of energy.

[0009] Preferably, the station control system comprises two parts: a sending-end converter station control system and a receiving-end converter station control system. Regarding the selection of state variables, the basic controller used in the control system is a PI controller.

[0010] Preferably, in step two, the method includes: S1. Perform Taylor series expansion on the polynomials in the above state equation system, retain the first-order terms, and establish a small-signal model. S2. For the Jacobian matrix in the above small-signal model, filter out the uncertain variables. The uncertain variables are composed of parameters that reflect the load size and steady-state values ​​of state variables that affect the size of Jacobian matrix elements. The linearized state-space model of the system is represented as a Jacobian matrix form containing linear uncertain variables.

[0011] Preferably, in step three, the construction method includes: S1. Define the upper and lower bounds of the variation interval of the uncertain parameters in the Jacobian matrix, thereby obtaining the upper and lower bounds of the variation interval of the uncertain variable composed of the uncertain parameters. When the uncertain variable varies in a non-empty set, there are infinitely many different Jacobian matrices. According to the Lyapunov theory of linear time-invariant systems, if there exists a common Lyapunov matrix such that all Jacobian matrices satisfy their respective Lyapunov inequalities, then all Jacobian matrices are Hurwitz stable. Therefore, when the load varies within a given interval, the equilibrium point of the corresponding VSC-HVDC system is locally asymptotically stable, which is called robust stability. Based on this, a robust stability criterion with infinitely many LMI constraints can be constructed. S2. Since the robust stability criterion with an infinite number of LMI constraints is actually an uncertain semidefinite programming problem, and the constraints of the uncertain variables are interval constraints, the criterion can be equivalently transformed into a criterion with a finite number of LMI constraints that is independent of the number of uncertain variables, specifically a robust stability criterion with two LMI constraints.

[0012] Preferably, in step four, the purpose of designing the DC capacitor parameters is to obtain a smaller value that meets the stability requirements, and this parameter is reflected in the aforementioned robust stability criterion. Therefore, a binary search logic can be used to construct an algorithm for designing the DC capacitor. This includes starting with any selected capacitance range, provided that the range contains any capacitance value that makes the aforementioned criterion with two LMI constraints valid. Then, the midpoint of the capacitance range is substituted into the criterion. If the criterion is valid, the upper bound of the capacitance range is updated to the midpoint; otherwise, the lower bound of the capacitance range is updated to the midpoint, thus obtaining a smaller new capacitance range. First, a capacitance range is randomly selected, provided that the range contains an initial guess value that makes the problem solvable. Then, the problem is solved at the midpoint of the range. If a solution is found, the upper bound of the current range is replaced with the midpoint, and vice versa. This process is repeated until the capacitance range tolerance condition is met, and the upper bound of the latest capacitance range is the DC capacitor design result.

[0013] The beneficial effects of this invention are as follows: 1. Unlike existing technologies that typically conduct stability analysis based on a fixed equilibrium point under rated power conditions, this invention explicitly introduces load-related factors into the linearized model during the system modeling stage. By constructing a Jacobian matrix containing linear uncertainty, the impact of load changes on the system equilibrium point and dynamic characteristics can be uniformly incorporated into the analysis framework. This modeling method avoids dependence on a single, fixed operating point, enabling subsequent stability analysis and DC capacitor design to cover various operating scenarios where the load varies within a given range, which is more consistent with the uncertain and time-varying operating characteristics of loads in actual power systems.

[0014] 2. This invention introduces the concept of robust stability analysis, transforming load uncertainty into parameter interval constraints, and constructs a stability criterion for this type of uncertainty based on Lyapunov theory. For infinitely many stability constraint problems caused by continuous changes in uncertain parameters, this invention further utilizes the structural characteristic of uncertainty as interval constraints to equivalently transform the originally difficult-to-solve uncertain semidefinite programming problem into a criterion form containing only a finite number of linear matrix inequality constraints, thereby significantly reducing computational complexity and improving the feasibility of the method in engineering software environments.

[0015] 3. This invention uses DC capacitor parameters as design variables in the criterion and constructs a DC capacitor design algorithm by combining a binary search strategy. By progressively searching and judging whether the robust stability condition is met within a given parameter range, the range of DC capacitor values ​​that meet the stability requirements can be obtained, and the required capacitor design result can be further determined. This method has clear logic and simple implementation. It can provide a direct basis for the reasonable selection of DC capacitor parameters while ensuring system stability, and helps to avoid overly conservative parameter configurations in engineering applications.

[0016] 4. By introducing load uncertainty modeling, constructing a computable robust stability criterion, and combining it with a systematic parameter search method, this invention extends DC capacitor design from a fixed operating point to a range of load variations. Compared with existing technologies, it has significant advantages in terms of applicability, computational feasibility, and engineering guidance. Attached Figure Description

[0017] Figure 1 This is a flowchart of the method of the present invention; Figure 2 This is a schematic diagram of the main circuit of the VSC-HVDC system with two voltage levels at both ends according to the present invention; Figure 3 This is a schematic diagram of the DC voltage control strategy for the sending-end converter station of the present invention. Figure 4 This is a schematic diagram of the AC voltage control strategy for the receiving-end converter station of the present invention. Figure 5 This is a waveform diagram of the DC capacitor simulation test of the VSC-HVDC system of the present invention. Detailed Implementation

[0018] The present application will now be described in further detail with reference to the accompanying drawings. It should be noted that the following specific embodiments are only used to further illustrate the present application and should not be construed as limiting the scope of protection of the present application. Those skilled in the art can make some non-essential improvements and adjustments to the present application based on the above application content.

[0019] Example: Please refer to Figure 1 , Figure 2 , Figure 3 , Figure 4 and Figure 5 A design method for VSC-HVDC DC capacitors considering load uncertainty includes the following steps: Step 1, establishing a state-space model; Step 2, establishing a model with uncertain variables; Step 3, stability criteria; and Step 4, DC capacitor algorithm design. In step one above, the state-space model of the VSC-HVDC system is first established. Specifically, the VSC-HVDC system model generally includes two parts: the main circuit and the control system. The DC transmission network is connected to the power grid and the load through the sending-end converter station and the receiving-end converter station, respectively. The embodiment studies the electromagnetic dynamics of the system, thus enabling the consideration of DC capacitor design issues. For the main circuit, based on... Figure 2 Based on the reference directions of voltage and current defined in Kirchhoff's laws and the law of conservation of energy, a main circuit model can be established; for the control system, it can be based on... Figure 3 and Figure 4 A state-space model of the control system in a synchronous rotating coordinate system is directly established; the embodiment involves Park transformation, and the Park transformation matrix from the three-phase stationary coordinate system (abc) to the synchronous rotating coordinate system (dq0) is:

[0020] in, The electrical angle is d-axis (with a-axis as a reference). Convert three-phase AC quantities (including but not limited to voltage and current) into DC quantities in a synchronous rotating coordinate system with equal amplitude; The main circuit consists of three parts: the sending-end converter station, the DC line, and the receiving-end converter station. The sending-end converter station contains three state variables, namely the d-axis component of the AC inductor current in the dq coordinate system. and q-axis components and the voltage of the DC capacitor. The dynamic model for these three state variables is as follows:

[0021] in, , and These are the AC-side equivalent inductance, AC-side equivalent resistance, and DC capacitance of the sending-end converter station, respectively. and These are the d-axis and q-axis voltages of the sending-end power grid, respectively. and These are the d-axis and q-axis voltages at the output of the sending-end converter, respectively. This refers to the current in a DC transmission line. The angular frequency of the sending-end AC system; nonlinear terms include and ; The DC transmission line is modeled as a In the equivalent circuit model, the two capacitors are considered within the DC capacitors of the converters at both ends; the state variable of the DC transmission line model is the DC current. Its dynamic characteristics are: in, and These are the equivalent inductance and equivalent resistance of a DC transmission line, respectively. The voltage of the DC capacitor at the receiving end; An LC low-pass filter is used on the AC side of the receiving-end converter station to suppress high-order harmonics and improve power quality; the energy storage components of the receiving-end converter station include the inductance of the LC filter line. and capacitor and DC capacitor Therefore, the receiving-end converter station contains five state variables, which are the d-axis components of the filter inductor current in the dq coordinate system. and q-axis components The d-axis component of the voltage of the filter capacitor in the dq coordinate system and q-axis components and the voltage of the DC capacitor. The state equations for these five state variables are:

[0022] in, The equivalent resistance on the AC side of the receiving-end converter station; This is the equivalent load resistance; and These are the d-axis and q-axis voltages at the output of the receiving-end converter, respectively. The angular velocity of the synchronous rotating coordinate system in the AC voltage control system at the receiving end; nonlinear terms include and The load at the receiving end is modeled as a resistor. This is the source of system uncertainty, and may be an interval. any value in, where ; The control system of VSC-HVDC consists of two parts: a DC voltage control system at the sending end and an AC voltage control system at the receiving end; the DC voltage control strategy adopted by the sending-end converter is as follows: Figure 3 As shown, the DC voltage is adjusted through the inner and outer loop controllers on the d-axis. To reference value To balance the transmission of active power; to effectively utilize equipment capacity and reduce losses caused by reactive power transmission, the VSC-HVDC converter generally operates in unity power factor mode, and the reactive current is adjusted through the inner loop controller of the q-axis. To reference value To achieve the control objective of zero reactive power, the input of the PWM valve control loop of the two-level VSC is the d and q components of the voltage reference value at the VSC output, and the output is the d and q components of the actual voltage value. This loop is modeled as a first-order inertial loop with a time constant of one switching cycle. The gain is 1; such as Figure 3 As shown, if the outputs of the integrator and the inertial elements are selected as state variables, then the DC voltage control system at the sending end includes... Five state variables, their state equations are:

[0023] in, These are the d-axis outputs of the outer loop and the d and q-axis outputs of the inner loop, respectively:

[0024] in, These are the proportional and integral parameters of the outer loop PI controller of the sending-end control system, respectively. These are the proportional and integral parameters of the inner loop PI controller of the sending-end control system, respectively. The AC voltage control strategy adopted at the receiving end is as follows: Figure 4 As shown, a stable voltage is provided to the passive network load by controlling the PCC (point of common coupling) voltage; the PCC voltage serves as the phase reference for the receiving-end AC system, therefore its q-axis component reference value... It must be zero; it should be noted that, due to the angular frequency of the receiving-end AC system... ( Since the receiving frequency is given, the frequency control has no dynamic characteristics; therefore, Figure 4 Although the control structure shown only reflects the control of the PCC voltage amplitude, it demonstrates the dynamic characteristics of V / f control; selection Figure 4 If the outputs of the integrator and the inertial elements are used as state variables, then the receiving-end AC voltage control system includes... The six state variables have the following state equations:

[0025] in, These are the d-axis and q-axis outputs of the outer loop and the inner loop, respectively, as follows:

[0026] in, These are the proportional and integral parameters of the outer loop PI controller of the receiving-end control system, respectively. These are the proportional and integral parameters of the inner loop PI controller of the receiving-end control system, respectively. definition These are the state variable vectors for the sending and receiving ends, respectively:

[0027] Define state variable vector Input variable vector and nonlinear functions They are respectively:

[0028] in, It includes all the state variables of the VSC-HVDC system; It includes all nonlinear terms; Based on the above models and vector definitions, the overall state-space model of the VSC-HVDC system can be expressed as follows (including uncertain parameters): Nonlinear systems: Among them, matrix Both are 20×20 real number matrices. It is a 20×2 real matrix. It is a 20×4 real number matrix, representing the design parameters, DC capacitor, etc. The influence range, the steady linear part and the variable linear part of the system, the location of the nonlinear terms, and the control input matrix; It is a diagonal matrix, and the diagonal elements of its 4th and 14th rows are... All other diagonal elements are 1.

[0029] In step two above, a linearized state-space model of the VSC-HVDC system containing uncertain variables is established. Specifically, nonlinear functions It involves 10 state variables, in the following order: The steady-state values ​​of these variables will appear in the Jacobian matrix, thus affecting the Hurwitz stability of the matrix, i.e., the local asymptotic stability of the VSC-HVDC system. For ease of explanation, these steady-state values ​​that affect the size of the Jacobian matrix elements are grouped into the following vector. In this context, the superscript 'e' of each element indicates the steady-state value of each state variable; Let the equilibrium point of the system be a vector. and state With equilibrium point The difference is The dynamic characteristics of the VSC-HVDC system near the equilibrium point are approximated by the first-order term of its Taylor expansion, i.e., the small-signal model is:

[0030] in, It is a 20-dimensional Jacobian matrix; It contains all the uncertain variables in the Jacobian matrix, a total of 11, and Representing vectors The kth term; Uncertain variables The input matrix; Specifically: ; ; ; in, It is a 20-dimensional square matrix, where the element in the i-th row and j-th column is 1, and all other elements are zero; In the Jacobian matrix above, the unknown parameter is the equivalent load resistance. Steady-state values ​​of state variables related to the Jacobian matrix The design parameters are DC capacitors. It can be seen that the Jacobian matrix It will be subject to uncertain variables (Depend on and Composition and design parameters The combined effects; therefore, despite and It may cause system instability, but with proper design It enables the system to be stable under all possible combinations.

[0031] In step three above, a robust stability criterion is constructed based on robust optimization theory. Specifically, define the equivalent load resistance. The range of variation is the following set of intervals. :

[0032] in, These are the lower and upper bounds of the interval, respectively; When the equivalent load resistance In the set The equilibrium point of the system when the inner value is different It may also change accordingly. As The portion that affects the Jacobian matrix will also change; the example studies the stability of all possible equilibrium points of VSC-HVDC and defines... The range of variation is the following set of polyhedra. :

[0033] in, For vectors The i-th term; These are the lower and upper bounds of the interval, respectively; because and The constraints are all interval-based, therefore the composite uncertain variables... The constraint should also be an interval; suppose the composite uncertainty (vector of uncertain variables) ) lies in the set of polyhedra defined below Inside:

[0034] in, These are the lower and upper bounds of the interval, respectively, and these two boundaries are defined by... and The upper and lower bounds are determined; Given a DC capacitor C, for any location in the set within , If all are Hurwitz stable, then the VSC-HVDC system is said to be robustly stable; according to Lyapunov theory for linear time-invariant systems, For any set within A sufficient condition for all of them to possess Hurwitz stability is that there exists a common symmetric positive definite matrix P in a given DC capacitance. Under the following conditions, the LMIs must be met:

[0035] Since the robust stability criterion mentioned above contains an infinite number of LMI constraints, its direct solution would involve a considerable amount of computation. To improve the computational feasibility of the robust stability criterion, this embodiment utilizes the fact that the robust stability criterion is actually an uncertain semidefinite programming problem, and that the constraints on the uncertain variables are interval constraints, transforming it into a computationally feasible equivalent condition that involves only two LMI constraints and is independent of the number of uncertain variables. To achieve this goal, each matrix is ​​decomposed... It is in the form of the sum of multiple rank-1 matrices, and the rank-1 matrix is ​​represented by the right multiplication of column vectors by row vectors, specifically:

[0036] in, There is only one non-zero term with a value of 1, and its position and Then according to To determine; Based on the relevant theories of robust optimization for uncertain semidefinite programming, an equivalent condition for the robust stability criterion with an infinite number of LMI constraints is that there exists a matrix... and and 16 positive scalars It satisfies the following two linear matrix inequalities LMIs:

[0037] in, ; , , .

[0038] In step four above, a DC capacitor design algorithm is constructed based on the bisection method. Specifically, does it exist with respect to a given DC capacitance? Matching To satisfy the above The problem of LMIs can be expressed as the following convex feasibility problem. CVX: Utilizing convex feasibility problems CVX, in its implementation example, proposes a DC capacitor design algorithm based on the bisection method. First, a capacitance range is randomly selected, provided that this range contains an initial guess that allows the problem to be solved. Then, the problem is solved at the midpoint of this range. If a solution exists, the upper bound of the current range is replaced with the midpoint, and vice versa. This process is repeated until the capacitance range tolerance condition is met. This process can be summarized as a DC capacitor design algorithm. ALG: The algorithm's input parameters include the initial guess of the capacitance. Initial lower bound of the tolerance range and the initial upper bound and tolerance range The final output is the DC capacitor design result that meets the accuracy requirements. The main process is as follows: A1. Calculate the midpoint of the tolerance range. ; A2. Solving convex feasibility problems using convex optimization tools CVX; A3. If the problem is feasible, then update the upper bound of the current interval to... Otherwise, adjust the lower bound to... ; A4. Repeat steps A1 to A3 until... and output the results. ; algorithm ALG only involves calculations and algebraic operations related to convex optimization problems, and is a feasible design method for VSC-HVDC DC capacitors that takes into account load uncertainties.

[0039] It should be noted that this invention presents a VSC-HVDC DC capacitor design method that considers load uncertainty. To verify the correctness of the proposed DC capacitor design method, a simulation platform was built on MATLAB / Simulink. Figures 2 to 4 The simulation model of the described VSC-HVDC system has a DC side rated parameter of 20kV / 10MW and an AC side rated voltage of 10kV; the variation range of the uncertain load is assumed to be [0.6, 1.1]. The algorithm is executed using the CVX tool in MATLAB. ALG yielded a DC capacitor design result of approximately 1190μF, or 3.74 pu. Figure 5 The simulation waveform of the VSC-HVDC system is shown when the DC capacitor is 3.74 pu; (The rest of the text appears to be a fragment and requires further context for accurate translation.) Figure 5 As can be seen, when the load resistance varies within the range [0.91, 1.67] pu (corresponding to the set load power range [0.6, 1.1] pu), the DC power can rise to a new steady state each time the load resistance decreases, and the DC voltage can also return to the rated value. This indicates that the designed DC capacitor value can make the system stable within the given load range, proving the effectiveness of the DC capacitor design method proposed in this invention.

[0040] The embodiments described above are merely examples of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the protection scope of the present invention.

Claims

1. A VSC-HVDC DC capacitor design method considering load uncertainty, comprising: Step 1, establishing a state-space model; Step 2, establishing a model containing uncertain variables; Step 3, stability criterion; Step 4, DC capacitor algorithm design; characterized in that: In step one above, the state-space model of the VSC-HVDC system is first established. In step two above, a linearized state-space model of the VSC-HVDC system containing uncertain variables is established. In step three above, a robust stability criterion is constructed based on robust optimization theory; In step four above, a DC capacitor design algorithm is constructed based on the bisection method.

2. The VSC-HVDC DC capacitor design method considering load uncertainty according to claim 1, characterized in that: In step one, the method for establishing the state-space model includes: S1. Define the reference direction and establish a mathematical model of the main circuit of the two-level VSC-HVDC system. The main circuit includes three parts: the sending end, the DC side, and the receiving end. According to the modeling principle, the main circuit model includes three parts: the AC side, the DC side, and the AC / DC connection. S2. Based on the control structure diagram, establish the state space model of the VSC-HVDC system converter station control system. The station control system includes two parts: the sending end and the receiving end converter station control system. S3. Define the state variable vector and the input variable vector, and combine the state equations of the above models. Multiple state equations together form a state equation set to obtain the state space model of the VSC-HVDC system.

3. The VSC-HVDC DC capacitor design method considering load uncertainty according to claim 2, characterized in that: For the AC side model, based on Kirchhoff's laws, a set of circuit equations is established in the three-phase stationary coordinate system, and then transformed to the synchronous rotating coordinate system using the Park transformation. For the DC side, the set of circuit equations established using Kirchhoff's laws is the required model. For the AC / DC connection model, the AC / DC connection equations are established using the law of conservation of energy.

4. The VSC-HVDC DC capacitor design method considering load uncertainty according to claim 2, characterized in that: The station control system consists of two parts: the sending end and the receiving end converter station control system. In terms of the selection of state variables, the basic controller used in the control system is a PI controller.

5. The VSC-HVDC DC capacitor design method considering load uncertainty according to claim 2, characterized in that: In step two, the method includes: S1. Perform Taylor series expansion on the polynomials in the above state equation system, retain the first-order terms, and establish a small-signal model. S2. For the Jacobian matrix in the above small-signal model, filter out the uncertain variables. The uncertain variables are composed of parameters that reflect the load size and steady-state values ​​of state variables that affect the size of Jacobian matrix elements. The linearized state-space model of the system is represented as a Jacobian matrix form containing linear uncertain variables.

6. The VSC-HVDC DC capacitor design method considering load uncertainty according to claim 1, characterized in that: In step three, the construction method includes: S1. Define the upper and lower bounds of the variation interval of the uncertain parameters in the Jacobian matrix, thereby obtaining the upper and lower bounds of the variation interval of the uncertain variable composed of the uncertain parameters. When the uncertain variable varies in a non-empty set, there are infinitely many different Jacobian matrices. According to the Lyapunov theory of linear time-invariant systems, if there exists a common Lyapunov matrix such that all Jacobian matrices satisfy their respective Lyapunov inequalities, then all Jacobian matrices are Hurwitz stable. Therefore, when the load varies within a given interval, the equilibrium point of the corresponding VSC-HVDC system is locally asymptotically stable, which is called robust stability. Based on this, a robust stability criterion with infinitely many LMI constraints can be constructed. S2. Since the robust stability criterion with an infinite number of LMI constraints is actually an uncertain semidefinite programming problem, and the constraints of the uncertain variables are interval constraints, the criterion can be equivalently transformed into a criterion with a finite number of LMI constraints that is independent of the number of uncertain variables, specifically a robust stability criterion with two LMI constraints.

7. The VSC-HVDC DC capacitor design method considering load uncertainty according to claim 6, characterized in that: In step four, the purpose of DC capacitor parameter design is to obtain a smaller value that meets the stability requirements, and this parameter is reflected in the robust stability criterion mentioned above. Therefore, a binary search logic can be used to construct an algorithm for designing the DC capacitor. This includes starting with any selected capacitance range, as long as the range contains any capacitance value that makes the criterion with two LMI constraints valid. Then, the midpoint of the capacitance range is substituted into the criterion. If the criterion is valid, the upper bound of the capacitance range is updated to the midpoint; otherwise, the lower bound is updated to the midpoint, resulting in a smaller new capacitance range. First, a capacitance range is randomly selected, as long as it contains an initial guess that allows the problem to be solved. Then, the problem is solved at the midpoint of the range. If a solution is found, the upper bound of the current range is replaced with the midpoint, and vice versa. This process is repeated until the capacitance range tolerance condition is met, and the upper bound of the latest capacitance range is the DC capacitor design result.

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