A load uncertainty oriented VSC-HVDC DC capacitor and control collaborative design method

Abstract

The application relates to a VSC-HVDC direct-current capacitor and control collaborative design method facing load uncertainty, and belongs to the technical field of power electronics and direct-current transmission. The VSC-HVDC direct-current capacitor and control collaborative design method facing load uncertainty comprises the following steps: S1, configuring a state feedback control structure with direct-current voltage integral compensation; S2, establishing a state space model of a VSC-HVDC system; S3, constructing a robust stability criterion containing a direct-current capacitor and control parameters; and S4, realizing a direct-current capacitor and control collaborative design algorithm. The application linearizes modeling of the system under different load conditions, and uniformly represents the obtained model in the form of containing load-related uncertain parameters, so that the stability determination directly covers the influence of the equilibrium point drift caused by load change, thereby avoiding the problems that when the system deviates from the rated design equilibrium point, the direct-current capacitor design result and the stability conclusion based on the fixed equilibrium point are invalid.

Description

Technical Field

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

[0002] VSC-HVDC systems are widely used in scenarios such as long-distance, high-capacity power transmission and load center power supply. In these systems, the DC side plays a crucial role in power balancing and energy buffering, and its dynamic characteristics directly affect the system's operational stability under varying load conditions. With the increasing proportion of renewable energy integration, DC power exhibits uncertainties and time-varying characteristics, making system operating conditions more complex and placing higher demands on the coordination of DC side parameter design and control strategies. Against this backdrop, how to rationally design key DC side parameters under uncertain load conditions and coordinate with the dynamic adjustment capabilities of the control system to improve system stability and operational adaptability has become a pressing research issue in the VSC-HVDC field.

[0003] Existing technologies have conducted relatively systematic research on the stability analysis and selection of DC capacitor parameters for VSC-HVDC systems. Related studies typically consider the DC capacitor as one of the important parameters affecting the system's dynamic characteristics. Under the system's rated operating conditions or given operating conditions, mathematical models are established based on the corresponding operating equilibrium point to analyze the system's small-signal stability, oscillation characteristics, and dynamic response, and to explore the influence of the DC capacitor value on the system's stability margin. In terms of parameter design, existing methods mostly start from the single parameter of the DC capacitor, combining it with a predetermined converter station control structure to analyze and select the capacitor capacity. Furthermore, in the stability analysis and parameter design process, the relevant models generally assume that the system operates near a fixed and known equilibrium point, and considers changes in load power by equivalently analyzing them as independent conditions under different operating conditions, thus providing a theoretical basis for the selection of DC capacitor parameters.

[0004] Existing technologies for the quantitative design of DC capacitors have two shortcomings. First, existing technologies typically design based solely on a single parameter of the DC capacitor, failing to fully consider the dynamic adjustment capabilities of the converter station's control system, thus limiting design flexibility and room for improvement. Second, existing stability analysis and parameter design methods are mostly based on models established under fixed and known equilibrium point conditions. However, in actual operation, load power exhibits uncertainty and time-varying characteristics, and the operating equilibrium point of the VSC-HVDC system changes with load conditions. When the system deviates from the assumed equilibrium point during design, the parameter design and stability conclusions derived from a fixed equilibrium point may no longer be applicable. Summary of the Invention

[0005] The purpose of this invention is to provide a simple and rationally designed co-design method for VSC-HVDC DC capacitors and control oriented towards 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 and control co-design method for load uncertainty includes the following steps: S1: Configure a state feedback control structure with DC voltage integral compensation; S2: Establish the state-space model of the VSC-HVDC system; S3: Construct a robust stability criterion that includes DC capacitance and control parameters; S4: Implement a collaborative design algorithm for DC capacitors and control.

[0007] As a further optimization of the present invention, S1 specifically includes: A state feedback term is introduced from the input point of the outer loop of the DC voltage, and an integral term is set for the error between the DC voltage reference value and the actual value to eliminate steady-state deviation, forming a state feedback structure with DC voltage integral compensation. Its control law is expressed as: ; in, For system state variables, For state feedback gain, This is the DC voltage integral adjustment coefficient. For differential operators, and These are the reference value and the actual value of the DC voltage, respectively.

[0008] As a further optimization of the present invention, S2 specifically includes: S21: Establish a complete state-space model of the VSC-HVDC system. The model includes the electromagnetic transient dynamics of the AC side, DC side and AC-DC coupling relationship in the main circuit, as well as the control system dynamics of the sending and receiving converter stations, in order to characterize the dynamic characteristics of the system under different operating conditions. S22: Based on the above nonlinear model, the system's operating equilibrium point under different load levels is linearized, a linearized state-space model containing load-related uncertain parameters is constructed, and the system's Jacobian matrix is ​​expressed as a parameter-dependent form with interval uncertainties, thereby reflecting the impact of load changes on the system's dynamic characteristics.

[0009] As a further optimization of the present invention, S3 specifically includes: Based on the established model, a robust stability criterion containing DC capacitance and state feedback gain is constructed according to the Lyapunov theory of linear time-invariant systems. This criterion is then transformed into a finite number of solvable LMI (Linear Matrix Inequality) constraints to determine the stability of the system within a given load uncertainty interval.

[0010] As a further optimization of the present invention, S4 specifically includes: S41: Apply constraints to the state feedback gain of the design to limit the amplification effect of the original nonlinear effect of the system after the state feedback loop is introduced, thereby ensuring the effectiveness of the linearized model. S42: Construct a collaborative design algorithm using the logic of the binary search method. Start with any selected capacitance range, as long as the range contains any capacitance value that simultaneously satisfies the above stability criterion and gain constraint. Then, substitute the midpoint of the capacitance range into these two constraints. If the conditions are met, update the upper bound of the capacitance range to the midpoint; otherwise, update the lower bound of the capacitance range to the midpoint, thus obtaining a new, narrowed capacitance range. Repeat this process until the capacitance range is narrowed to the set tolerance. The upper bound of the latest capacitance range is the DC capacitor design result, and a state feedback gain design result is output, thereby realizing the collaborative design of DC capacitor and control.

[0011] The beneficial effects of this invention are as follows: 1. This invention introduces a state feedback control structure with DC voltage integral compensation and performs collaborative design of DC capacitor parameters and control parameters under load uncertainty. Under the premise of meeting system stability requirements, this invention achieves a further reasonable reduction in the DC capacitor capacity of the VSC-HVDC system, thereby solving the key problem of the difficulty in determining the DC capacitor capacity and the limited design space under load uncertainty.

[0012] 2. This invention, by introducing state feedback control into the outer loop of the DC voltage, eliminates the reliance on DC capacitor parameters for dynamic regulation of the system. This allows the system to participate in stability regulation through the control loop under load variations, thereby reducing dependence on DC capacitor capacity. Furthermore, by introducing a DC voltage error integral term into the state feedback control, it effectively compensates for steady-state DC voltage deviations that may be introduced by state feedback, ensuring that the DC voltage can stably converge to its reference value. By constructing a robust stability criterion that simultaneously includes DC capacitor parameters and control parameters, the stability of the system within a given load uncertainty range can be uniformly determined. Finally, by implementing a collaborative design algorithm based on the above criterion and gain constraints, the DC capacitor capacity and state feedback gain can be jointly determined within the same design framework, resulting in a DC capacitor design that meets stability requirements and corresponding control parameters. Attached Figure Description

[0013] Figure 1 A flowchart of a VSC-HVDC DC capacitor and control co-design method for load uncertainty in one embodiment of the present invention; Figure 2 This is a schematic diagram of the main circuit of a two-level VSC-HVDC system with two terminals in one embodiment of the present invention; Figure 3 This is a schematic diagram of the DC voltage control strategy of the sending-end converter station in one embodiment of the present invention; Figure 4 This is a schematic diagram of the AC voltage control strategy of the receiving-end converter station in one embodiment of the present invention; Figure 5 The waveform diagram is a simulation test of the DC capacitor of the VSC-HVDC system in one embodiment of the present invention. Detailed Implementation

[0014] 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.

[0015] Example 1: As Figure 1 As shown, a VSC-HVDC DC capacitor and control co-design method for load uncertainty includes: S1. Configure a state feedback control structure with DC voltage integral compensation; Specifically, in this embodiment, the control structure is extended in the DC voltage outer loop control. For example... Figure 3 As shown in the state feedback section, a state feedback control structure with DC voltage integral compensation is configured in the outer loop of the DC voltage. A state feedback term is introduced from the input point of the outer loop of the DC voltage, thereby introducing adjustable control parameters and providing control degrees of freedom for subsequent co-design of the DC capacitor and control. Simultaneously, considering that state feedback control will cause steady-state deviation of the DC voltage, an integral term of the DC voltage error is introduced at the same input point as compensation to ensure that the DC voltage converges to the reference value. Therefore, the control law of the proposed state feedback control with DC voltage integral compensation can be expressed as: in, For system state variables; The state feedback gain matrix; The DC voltage integral regulation coefficient is a definite parameter, and its value should follow certain rules. In terms of dynamic stability, since this integrator is located before the outer-loop PI controller, its integration speed should be slower than the latter. It must be less than the integral coefficient of the DC voltage outer loop PI controller; It is a differential operator; and These are the reference value and the actual value of the DC voltage, respectively.

[0016] S2. Establish the state-space model of the VSC-HVDC system; Specifically, the VSC-HVDC system model generally comprises two parts: the main circuit and the control system. The DC transmission network is connected to the grid and the load through sending-end and receiving-end converter stations, respectively. The implementation example studies the electromagnetic dynamics of the system, thus enabling consideration of the coordinated design of DC capacitance and control. For the main circuit, based on... Figure 2 The reference directions of voltage and current, Kirchhoff's laws, and the law of conservation of energy, as defined in the standard, can be used to establish the main circuit model. 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.

[0017] 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: 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 .

[0018] 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. This is the voltage of the DC capacitor at the receiving end.

[0019] 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: 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. It is the source of system uncertainty and can be an interval. any value in, where .

[0020] The control system of a VSC-HVDC converter 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 employed 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 This achieves 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. For example... 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... and The six state variables have the following state equations: in, These are the d-axis outputs of the outer loop and the d and q-axis outputs of the inner loop, respectively: 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 in the sending-end control system, respectively.

[0021] 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, frequency control has no dynamic characteristics. Therefore, Figure 4 Although the control structure shown only demonstrates the control of the PCC voltage amplitude, it can illustrate 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: in, These are the d-axis and q-axis outputs of the outer loop and the inner loop, respectively, as follows: 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 in the receiving-end control system, respectively.

[0022] definition These are the state variable vectors for the sending and receiving ends, respectively: Define state variable vector Input variable vector and nonlinear functions They are respectively: in, It includes all the state variables of the VSC-HVDC system; It includes all nonlinear terms.

[0023] Based on the model and vector definitions of the above modules, 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 21×21 real matrices. It is a 21×2 real matrix. It is a 21×4 real matrix. It is a 21×1 real matrix, representing the design parameters, DC capacitors, etc. The influence range, the steady linear part and the variable linear part of the system, the location of the nonlinear terms, the control input matrix and the state feedback input matrix; It is a diagonal matrix, and the diagonal elements of its 4th and 14th rows are... All other diagonal elements are 1.

[0024] nonlinear functions It involves 10 state variables, in the following order: The steady-state values ​​of these variables appear in the Jacobian matrix, thus affecting its Hurwitz stability, i.e., the local asymptotic stability of the VSC-HVDC system. For ease of explanation, these steady-state values ​​affecting the size of the Jacobian matrix elements are grouped into the following vector: In this context, the superscript 'e' of each element represents the steady-state value of each state variable.

[0025] 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: in, It is a 21-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 21-dimensional square matrix, where the element in the i-th row and j-th column is 1, and all other elements are zero.

[0026] 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. and state feedback gain Therefore, the Jacobian matrix... It will be subject to uncertain variables (Depend on and Composition and design parameters and The combined effects. Therefore, despite and It may cause system instability, but with proper design and It enables the system to be stable under all possible combinations.

[0027] S3. Construct a robust stability criterion that includes DC capacitance and control parameters; Specifically, define the equivalent load resistance. The range of variation is the following set of intervals. : 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 of the matrix that affects the Jacobian matrix will also change. An example study investigates the stability of all possible equilibrium points of the VSC-HVDC and defines... The range of variation is the following set of polyhedra. : 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. Let the composite uncertainty (a vector of uncertain variables) be... ) lies in the set of polyhedra defined below Inside: 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.

[0028] Given a DC capacitor C, there exists a state feedback gain K such that for any capacitor located in the set... within , If all values ​​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. sum matrix Given a DC capacitance Under the condition that the following set of matrix inequalities is satisfied: Due to the existence of decision variables and The coupling between these factors makes the robust stability criterion of the matrix inequality non-convex and difficult to compute. The embodiment employs a variable transformation method to obtain an equivalent, easily tractable LMI condition. For positive definite matrices... Define matrix and Then there is Substitute these substitution variables into the matrix inequality above, and multiply both sides of the inequality by the matrix on the left and right. We can obtain equivalent expressions regarding the variables. and The LMI condition is: Although the robust stability criterion for LMI successfully transforms non-convex conditions into convex constraints, the number of constraints remains infinite, and computational feasibility issues persist. It is necessary to completely resolve these feasibility issues and improve computational efficiency by reducing the number of LMIs. Therefore, this embodiment leverages the characteristic that the robust stability criterion is essentially an uncertain semidefinite programming problem, and that the constraints on the uncertain variables are interval constraints, transforming it into a computationally feasible solvable condition involving only two LMI constraints and 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: in, There is only one non-zero term with a value of 1, and its position and Then according to To determine.

[0029] According to the relevant theories of uncertain semidefinite programming, if the matrix variables are as follows... and 16 scalar variables Two LMI conditions ( If LMIA is true, then the robust stability criterion with an infinite number of LMI constraints is true: in, ; , , .

[0030] S4. Implement a collaborative design algorithm for DC capacitors and control; Specifically, the state feedback gain of the design Constraints are imposed to limit the potential amplification of the original nonlinear effects of the system after the introduction of state feedback, thereby ensuring the effectiveness of the linearized model. To this end, the embodiment utilizes a matrix... The inverse definition of the ellipsoid set as follows: When the system state trajectory Entering the ellipsoid set Let's assume this moment is the initial state, and record the time. .exist When, if the following two relationships with matrix variables are true, and LMI conditions ( If LMIB is established, then and Established: in, and Satisfying the robust stability criterion LMIA; It is the identity matrix; It is a constant.

[0031] State feedback gain constraint LMIB has and Two parameters; changing these two parameters adjusts the gain. The constraint strength. According to Schul's complement lemma, equation The LMI to the left of LMIB is equivalent to .when Increase, then Rayleigh quotient Decrease, according to Rayleigh's theorem, the matrix The eigenvalues ​​decrease, thus... It will decrease; in addition, when Decrease, then It will decrease. Therefore, we can conclude that it will increase. and decrease This can enhance the conditions. LMIB for gain The constraint effect. To determine a suitable value, the embodiment assumes the equilibrium point under rated load conditions. The linearization error within a ±1% neighborhood is sufficiently small. Based on this assumption, and The values ​​are respectively and Clearly, the value is not unique; this result is just one example.

[0032] Simultaneous robust stability conditions LMIA and gain constraints LMIB can be used to construct the following convex feasibility problem ( CVX): , Utilizing convex feasibility problems CVX, an implementation example, proposes a DC capacitor and control co-design algorithm based on the bisection method. First, a capacitance range is randomly selected, provided that the 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 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. This process can be summarized as the following DC capacitor and control co-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. Design results of state feedback gain The main process is as follows: A1. Calculate the midpoint of the tolerance range. ; A2, Order Solving the convex feasibility problem 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. and ; algorithm ALG only involves calculations and algebraic operations related to convex optimization problems, and is a feasible co-design method for VSC-HVDC DC capacitors and control in the face of load uncertainties.

[0033] This invention addresses the challenge of further reducing the DC capacitance of VSC-HVDC systems under uncertain load conditions by proposing a collaborative design method that combines DC capacitance parameter design with control strategy design. Unlike existing approaches that primarily focus on designing based on a single DC capacitance parameter, this invention introduces a state feedback control structure with integral compensation into the DC voltage outer loop. This allows the system's dynamic characteristics to be influenced by both DC capacitance and control parameters simultaneously, introducing new degrees of control freedom at the system parameter design level. Furthermore, compared to existing methods that typically rely on a fixed and known equilibrium point for stability analysis and parameter design, this invention eliminates the assumption of a single operating equilibrium point during modeling and stability analysis. Addressing the reality that load power uncertainty causes the system's operating equilibrium point to vary with operating conditions, this invention linearizes the system model under different load conditions and uniformly represents the resulting model in a form that includes load-related uncertain parameters. This allows stability assessments to directly cover the equilibrium point drift caused by load changes, thus avoiding the invalidation of DC capacitance design results and stability conclusions based on a fixed equilibrium point when the system deviates from its rated design equilibrium point.

[0034] Example 2 To verify the effectiveness of the proposed co-design method for DC capacitor and control, this invention embodiment builds a simulation platform such as 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 variable range of the uncertain load resistance is set to [0.91, 10] pu (corresponding to the load power range [0.1, 1.1] pu). An algorithm is executed using the CVX tool in MATLAB. ALG yields a DC capacitor design result of approximately 160μF, or 0.5pu, and also provides the state feedback control gain design result. Figure 5 The simulation waveform of the VSC-HVDC system is shown when the DC capacitor is 0.5 pu. Figure 5 Two points are demonstrated: First, when the load resistance varies within the range [0.91, 10] pu, after each decrease in load resistance, the DC power of the VSC-HVDC system, configured with state feedback control with DC voltage integral compensation, can rise to a new steady state, and the DC voltage can return to its rated value. This indicates that the designed DC capacitor value and state feedback gain can make the system stable within the given load range, proving the correctness of the proposed DC capacitor and control co-design method. Second, with the same DC capacitor capacity, the system can remain stable within the designed load range when there is state feedback control. However, without state feedback, i.e., relying solely on the uninvolved dual closed-loop control, the DC power and DC voltage begin to diverge and the system becomes unstable starting from a load resistance decrease to 2 p.u. This shows that the DC capacitor and control co-design method can effectively reduce the DC capacitor capacity compared to the single-parameter design of the DC capacitor.

[0035] 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 scope of protection of the present invention.

Claims

1. A VSC-HVDC DC capacitor and control co-design method for load uncertainty, characterized in that: Includes the following steps: S1: Configure a state feedback control structure with DC voltage integral compensation; S2: Establish the state-space model of the VSC-HVDC system; S3: Construct a robust stability criterion that includes DC capacitance and control parameters; S4: Implement a collaborative design algorithm for DC capacitors and control.

2. The VSC-HVDC DC capacitor and control co-design method for load uncertainty as described in claim 1, characterized in that: S1 specifically includes: A state feedback term is introduced from the input point of the outer loop of the DC voltage, and an integral term is set for the error between the DC voltage reference value and the actual value to eliminate steady-state deviation, forming a state feedback structure with DC voltage integral compensation. Its control law is expressed as: ； in, For system state variables, For state feedback gain, This is the DC voltage integral adjustment coefficient. For differential operators, and These are the reference value and the actual value of the DC voltage, respectively.

3. The VSC-HVDC DC capacitor and control co-design method for load uncertainty as described in claim 1, characterized in that: S2 specifically includes: S21: Establish a complete nonlinear state-space model of the VSC-HVDC system. The model includes the electromagnetic transient dynamics of the AC side, DC side and AC-DC coupling relationship in the main circuit, as well as the control system dynamics of the sending and receiving converter stations, in order to characterize the dynamic characteristics of the system under different operating conditions. S22: Based on the above nonlinear state-space model, the system's operating equilibrium point under different load levels is linearized to construct a linearized state-space model containing load-related uncertain parameters. The system's Jacobian matrix is ​​expressed as a parameter-dependent form with interval uncertainties, thereby reflecting the impact of load changes on the system's dynamic characteristics.

4. The VSC-HVDC DC capacitor and control co-design method for load uncertainty as described in claim 1, characterized in that: S3 specifically includes: Based on the established model, a robust stability criterion containing DC capacitance and state feedback gain is constructed according to the Lyapunov theory of linear time-invariant systems. This criterion is then transformed into a finite number of solvable LMI constraints to determine the stability of the system within a given load uncertainty interval.

5. The VSC-HVDC DC capacitor and control co-design method for load uncertainty as described in claim 1, characterized in that: S4 specifically includes: S41: Apply constraints to the state feedback gain of the design to limit the amplification effect of the original nonlinear effect of the system after the state feedback loop is introduced, thereby ensuring the effectiveness of the linearized model. S42: Construct a collaborative design algorithm using the logic of the binary search method. Start with any selected capacitance range, as long as the range contains any capacitance value that simultaneously satisfies the above stability criterion and gain constraint. Then, substitute the midpoint of the capacitance range into these two constraints. If the conditions are met, update the upper bound of the capacitance range to the midpoint; otherwise, update the lower bound of the capacitance range to the midpoint, thus obtaining a new, narrowed capacitance range. Repeat this process until the capacitance range is narrowed to the set tolerance. The upper bound of the latest capacitance range is the DC capacitor design result, and a state feedback gain design result is output, thereby realizing the collaborative design of DC capacitor and control.

Images