Model prediction transient stability control method of VSC-PLL system in weak network environment

Abstract

The invention relates to the technical field of power electronic converter grid-connected control. The invention discloses a model prediction transient stability control method of a VSC-PLL system in a weak network environment. The model prediction transient stability control method is characterized by comprising the following steps: 1) constructing a dynamic model of the system: (1) constructing a physical model and a state equation; (2) discretizing the model; the core composition of the MPC optimization problem comprises (1) prediction model and time domain setting, (2) objective function design, (3) constraint condition set, and (3) rolling optimization and self-adaptive control mechanism: (1) real-time parameter updating, and (2) optimization solution and control execution. The method can realize on-line optimization of active / reactive current set values.

Description

Technical Field

[0001] This invention relates to the field of power electronic converter grid-connected control technology, specifically to a phase-locked loop (PLL) synchronous transient stability control method for voltage source converters (VSCs) connected to weak power grids based on model predictive control (MPC). Background Technology

[0002] Driven by the global energy transition and the "dual carbon" goal, the installed capacity of new energy power generation, represented by wind power and photovoltaics, has continued to climb. By the end of 2023, my country's installed capacity of new energy had exceeded 1.3 billion kilowatts, accounting for more than 50% of the total installed capacity. Against this backdrop, grid connection technology based on voltage source converters (VSCs) has become a core means of connecting new energy to the grid, especially in weak grid scenarios (such as grids in remote areas and offshore wind power grid-connected systems), where VSCs are widely used due to their flexible power regulation capabilities. However, weak grids typically exhibit a short-circuit ratio (SCR) of less than 2.5, a large equivalent impedance, and low system inertia, making VSC grid-connected systems highly susceptible to phase-locked loop (PLL) synchronization instability under large disturbances such as grid faults and power surges. Statistics show that approximately 37% of grid disconnection accidents involving new energy grid-connected systems in China during 2022-2023 were caused by PLL transient instability, seriously affecting the safe and stable operation of the power grid.

[0003] As a key component of VSC grid-connected control, the PLL's core function is to track the phase and frequency of the grid-connected voltage, providing a reference coordinate system for vector control. In the dq rotating coordinate system, the PLL's dynamic characteristics can be described as a second-order nonlinear system including phase angle error and integral elements. When a symmetrical fault occurs in the grid, the sudden drop in fault point voltage and changes in equivalent impedance disrupt the PLL's dynamic equilibrium, causing the phase angle tracking error to exceed the critical value, leading to system oscillations or even grid disconnection. Existing research indicates that the transient instability mechanism of the PLL under weak grid conditions differs fundamentally from that of traditional synchronous machines; its nonlinear characteristics are more pronounced, and its stability boundary is more complex due to the coupling effects of fault parameters, control parameters, and grid strength. Current research methods for transient stability of VSC-PLL systems have three main limitations: First, while the maximum estimated attraction domain (LEDA) construction method based on linear matrix inequalities (LMI) can quantify the stability boundary, it requires Taylor expansion of the nonlinear model containing trigonometric functions and determination of LEDA through iterative solution of matrix inequalities. Second, energy function-based analysis methods typically restrict the PLL phase angle to the range of (-π / 2, π / 2), resulting in excessively conservative LEDA and potentially leading to misjudgment of the feasible region for the current setpoint. Third, traditional dual-loop vector control strategies employ fixed-parameter PI regulation, which cannot adaptively adjust the control gain during weak network faults.

[0004] Transient stability control of VSC-PLL systems in weak network environments faces three major technical challenges: real-time stability boundary assessment of nonlinear models, adaptive adjustment of control parameters under dynamic changes in multiple parameters, and synergistic optimization of fault ride-through capability and transient stability. Existing technologies, due to high computational complexity, strong conservatism, or insufficient adaptability, cannot simultaneously meet the requirements of real-time performance and control accuracy in engineering. Therefore, a novel technical solution that balances stability analysis and dynamic control is urgently needed.

[0005] In the context of large-scale grid connection of new energy sources, when voltage source converters are connected to weak grids, large disturbances such as grid symmetrical faults can easily trigger synchronous transient instability of phase-locked loops (PLLs). Existing technologies, attraction domain analysis methods based on linear matrix inequalities (LMIs) suffer from high computational complexity and poor real-time performance, making them unsuitable for direct engineering applications. Traditional current control strategies lack dynamic awareness of transient stability boundaries, potentially causing current setpoints to exceed the system's stable range. Fixed-parameter PLL control cannot adapt to the time-varying characteristics of equivalent impedance and fault voltage under weak grid conditions, further reducing system stability margin. Summary of the Invention

[0006] The purpose of this invention is to provide a model predictive transient stability control method for a VSC-PLL system under weak network conditions, which can achieve online optimization of active / reactive current setpoints.

[0007] To achieve the above objectives, the technical solution adopted by this invention is a model predictive transient stability control method for a VSC-PLL system under weak network conditions, characterized by the following steps: 1) System Dynamic Model Construction (1) Physical model and state equation Topology: The VSC (Voltage Source Converter) is connected to the weak current grid through an LC filter. The fault point F is located between the grid connection point and the infinite power grid, with an equivalent impedance of... The voltage at the fault point is , The equivalent impedance at the fault point, The equivalent reactance at the fault point, The equivalent resistance at the fault point. It is the imaginary unit.

[0008] State-space description: Considering only the PLL dynamics, the second-order model of the system is: in: The phase angle of the PLL (phase-locked loop in weak grid conditions) is referenced to the phase angle of the infinite grid voltage. The integral voltage component is defined as follows: , The q-axis component of the grid connection point voltage; , The proportional / integral coefficient of the PLL ( , ); This represents the differential element in calculus.

[0009] , The active / reactive current settings to be optimized.

[0010] (2) Model discretization Discretization using a zero-order hold, sampling period The discretized state equation is: Introducing state vectors Control vector Then the discrete model can be expressed as: in, Indicates the sampling period. Represents discrete time. Represents the transpose of a matrix. Represents the state vector. Representing a discrete model, Indicates that the phase-locked loop is in The phase angle of the grid voltage is tracked in real time. Is Voltage at grid connection point at all times Axial components The integral term, Indicates in The phase angle of the grid voltage is tracked in real time. Indicates in Voltage at grid connection point at all times Axial components The integral term, Indicates that the phase-locked loop is in The rate of change of the grid voltage phase angle is tracked at all times. Indicates in Voltage at grid connection point at all times Axial components The rate of change of the integral term (the derivative in continuous time). Represents the control vector. The equivalent impedance at the fault point, Indicates the effective value of the voltage at the fault point. express Shaft current reference value, express Shaft current reference value, For terms containing nonlinear terms Discrete mapping function.

[0011] 2) Core Components of the MPC (Model Predictive Control) Optimization Problem (1) Prediction model and time domain setting Multi-step prediction: based on the current state Predicting the future The state trajectory of each cycle: in Predicting the time domain (Corresponding to a 1ms prediction length).

[0012] Controlling the Time Domain: Optimizing the Future Control quantity per cycle ( ,Pick Only the control input for the first cycle is executed; in, This represents the prediction time domain, used to predict the total number of steps to the future state. This represents the control time domain, used to optimize the control sequence length. Indicates the prediction step size index. Indicates the current sampling time. Indicates the control input variable, Represents state variables, The equivalent impedance at the fault point, Indicates the effective value of the voltage at the fault point. For terms containing nonlinear terms Discrete mapping function.

[0013] (2) Objective function design Multi-objective optimization framework: in: Describe the overall objective function. This represents the state tracking error term. This indicates the control input item.

[0014] State error term: The phase angle at the equilibrium point after the fault ( ), , These are weighting coefficients, emphasizing the priority of phase angle stability; Control smoothing term: , , Avoid sudden changes in current; in, Indicates the prediction time domain, Indicates control of the time domain, Indicates the prediction step size index. Indicates the current sampling time. , , , Weighting coefficients ( =8~15, =5~10, =0.3~1, =0.3~1), This represents the predicted PLL phase angle. This represents the predicted integral voltage. This indicates the PLL phase angle reference value. Equivalent reactance at the fault point express Shaft current reference value, express Shaft current reference value, Equivalent resistance at the fault point Indicates the effective value of the voltage at the fault point. express shaft current variation value express Changes in shaft current.

[0015] (3) Set of constraints Transient stability constraints: The safety threshold calibrated for the experiment (corresponding to a phase angle deviation of no more than 90° to avoid PLL lockout); Current limit constraint: This represents the maximum output current of the VSC. Fault parameter constraints: , This is the lower limit of voltage sag. This is the upper limit of the equivalent impedance of a weak network; in, This represents the predicted PLL phase angle. Indicates the prediction step size index. Indicates the current sampling time. This indicates the PLL phase angle reference value. This indicates the safe upper limit of the PLL phase angle deviation. Indicates the prediction time domain, Indicates control of the time domain, Indicates the effective value of the voltage at the fault point. This indicates the lower limit of voltage drop. The equivalent impedance at the fault point, Indicates the lower limit of the equivalent impedance. This indicates the upper limit of the equivalent impedance. express Shaft current reference value, express Shaft current reference value, This indicates the maximum output current of the voltage source converter.

[0016] 3) Rolling optimization and adaptive control mechanism (1) Real-time parameter update Fault characteristic acquisition: Real-time acquisition via voltage / current sensors: Fault point voltage (Based on the assumption of symmetrical faults, the effective values ​​of the three-phase voltages are taken.) Equivalent impedance , (Calculated by the changes in voltage and current before and after the fault:) ).

[0017] Weight adaptive adjustment: when When (serious malfunction), increase Up to 15, prioritize ensuring phase angle stability; when Time (minor fault), increase , Upgraded to version 1.0, optimizing current tracking performance; in, Indicates the effective value of the voltage at the fault point. Indicates the equivalent resistance at the fault point. Indicates the equivalent reactance at the fault point. The equivalent impedance at the fault point, This indicates the voltage change before and after the fault. This indicates the change in current before and after the fault.

[0018] (2) Optimize the solution and control the execution Convex optimization transformation: transforming nonlinear terms Perform a second-order Taylor expansion near the current equilibrium point: The problem is transformed into a convex quadratic programming problem, which can be solved quickly using the interior point method. Control output: Only the first control input of the optimized sequence is executed. The next cycle will restart the optimization based on the new state, forming a rolling control closed loop; in, This indicates the current discrete-time index, and the superscript "*" indicates the optimal solution. express The optimal control vector at time 1. express In the optimal control vector at time step Shaft current reference value, express In the optimal control vector at time step Shaft current reference value, Represents the transpose of a matrix. This represents the predicted PLL phase angle. This indicates the PLL phase angle reference value.

[0019] The inventive point of this invention: 1. Innovatively combining transient stability constraints with model predictive control, based on fault point voltage. Equivalent impedance By dynamically adjusting and optimizing the target in real time, the traditional method breaks through the dependence on fixed mathematical models and achieves the accuracy and adaptability of transient stability control.

[0020] 2. A nonlinear term approximation strategy based on Taylor expansion is designed to transform complex system models containing trigonometric functions into convex optimization problems that can be solved efficiently, with a single calculation time of <80μs, providing a mathematical basis for real-time control.

[0021] 3. Introduce a dynamic weighting coefficient adjustment mechanism to prioritize transient stability (stability domain expansion of 25%-40%) during severe faults, and take into account voltage support performance (reactive current tracking error <5%) during minor faults, thus resolving the contradiction between "stability and economy".

[0022] 4. Through collaborative design of "hardware architecture - software process - parameter calibration", engineering implementation is achieved, hardware costs are reduced by 20%-30%, equipment lifespan is extended by 10%-15%, and a complete solution is provided for the practical application of VSC-PLL system under weak network conditions.

[0023] The beneficial effects of this invention are 1. Significantly improved transient stability control capability: By using MPC rolling optimization to constrain the current setpoint within the transient stability domain, compared to traditional PID control, the system stability domain is expanded, phase angle deviation control accuracy is improved, and PLL lockout is effectively avoided. Dynamic updates of fault parameters (voltage drop depth, equivalent impedance) ensure compatibility with weak network environments with different short-circuit ratios (SCR=1.5-3.0), resulting in a significantly improved fault ride-through success rate.

[0024] 2. Breakthroughs in Real-Time Control and Computational Efficiency: Employing local linearization and convex optimization, the single-cycle computation time meets the 10kHz sampling frequency requirement, reducing control latency from 5-10 ms in the traditional LMI method to <1 ms, resulting in a 5-10 times improvement in real-time performance. Based on a DSP+FPGA architecture, it balances algorithm accuracy and engineering feasibility, making it suitable for industrial control scenarios.

[0025] 3. Intelligent and Adaptive Advantages of the Control Strategy: Through dynamic weight adjustment, phase angle stability is prioritized during severe faults, while current tracking performance is optimized during minor faults, achieving an adaptive balance between stability and performance, thus improving voltage support capability. No precise mathematical model is required; the system relies on experimentally calibrated phase angle safety thresholds and weighting coefficients, shortening on-site commissioning time and lowering the barrier to engineering applications.

[0026] 4. Engineering Application Value and Industry Promotion: Applicable to VSC grid connection scenarios for new energy sources such as wind power and photovoltaics, it enhances the grid's ability to absorb high proportions of renewable energy and reduces grid disconnection accidents caused by transient instability. Control smoothing terms avoid current surges, reduce switching losses of power devices such as IGBTs, extend equipment life, and lower maintenance costs. It provides a new industry technical standard reference for VSC control under weak grid conditions, fills the technical gap in transient stability constraints in existing fault ride-through control, and promotes the upgrading of power electronic converter control technology.

[0027] 5. This invention proposes a dynamic optimization strategy based on model predictive control. By constructing a predictive model incorporating PLL dynamics, transient stability constraints are transformed into an optimization problem solvable in real time, enabling online optimization of active / reactive current setpoints. This method aims to overcome the computational bottleneck of traditional analytical methods, improve the real-time performance and adaptability of transient stability control in VSC-PLL systems under weak grid faults, and provide a technical solution with both theoretical reliability and engineering practicality for fault ride-through control of renewable energy grid-connected systems. Attached Figure Description

[0028] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0029] Figure 1 This is a flowchart illustrating the specific implementation method of this invention.

[0030] Figure 2 This is a flowchart of the VSC-PLL system model prediction transient stability control under weak network conditions according to the present invention.

[0031] Figure 3 This is a comparison chart of the current tracking error.

[0032] Figure 4 This is a comparison chart of the stability domain range of this invention. Detailed Implementation

[0033] To transform the above technical solutions into practical engineering applications, the following details the specific implementation of the present invention, combining specific hardware architecture, software processes, and experimental verification scenarios. This includes the complete process of system initialization, real-time data processing, MPC optimization, and control execution. The effectiveness of the method is verified through typical fault conditions, providing clear operational guidance for practical applications.

[0034] The following section will detail the specific technical solutions from aspects such as system model construction, MPC optimization framework design, and rolling control implementation. The following are the hardware components: Controller: Adopts DSP+FPGA architecture, with DSP implementing MPC algorithm solution and FPGA handling high-speed sampling and pulse generation; Sampling module: includes voltage / current sensors, sampling frequency 10kHz, real-time acquisition of grid connection point voltage and VSC output current; Execution module: IGBT drive circuit, which generates PWM signal based on the optimized current setting value.

[0035] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0036] A model predictive transient stability control method for a VSC-PLL system under weak network conditions includes the following specific steps. Step S001: System Initialization and Core Parameter Calibration Before starting the VSC-PLL system in a weak network environment, complete the hardware platform setup and basic parameter configuration, specifically including: (1) Hardware architecture deployment: The controller adopts a "DSP+FPGA" architecture, with the DSP responsible for model prediction and optimization, and the FPGA handling high-speed data acquisition (sampling frequency). ) and PWM pulse generation (switching frequency) ).

[0037] Sensor configuration: Grid connection point voltage sensor (accuracy class 0.2), VSC (voltage source converter) output current sensor (accuracy class 0.1), and fault point voltage monitoring module are all connected to the controller through isolation conditioning circuit.

[0038] (2) Initialization of basic parameters: VSC Rated Parameters: Rated Power Rated voltage Maximum output current .

[0039] PLL control parameters: proportional coefficient Integral coefficient Initial phase angle reference .

[0040] MPC core parameters: prediction time domain (correspond ), control time domain Sampling period .in, Indicates the rated current. Indicates rated power. Indicates the rated voltage. Indicates the sampling frequency.

[0041] (3) Safety threshold calibration: The safety deviation threshold of PLL phase angle was determined through offline simulation and experiments. (Corresponding to approximately 85°, to avoid loss of lockout), lower limit of fault point voltage. Equivalent impedance range , Indicates the prediction step size index. It is an abbreviation for "per unit", which is a dimensionless method of representing relative values.

[0042] Step S002: System Dynamic Model Construction and Discretization Based on the physical characteristics of the VSC-PLL system under weak network conditions, a nonlinear model containing PLL dynamics is established and discretized. The steps are as follows: (1) Derivation of continuous-time state equations Define state vector ( For PLL phase angle, (Integral of the q-axis component of the grid connection point voltage), control vector (Active / Reactive Current Setpoints), then the system dynamic equation is: (1) in, , The equivalent resistance and reactance from the fault point to the grid connection point ( Equivalent resistance at the fault point (Equivalent reactance at the fault point) This is the effective value of the voltage at the fault point. Represents the state vector. Indicates the PLL phase angle. This represents the integral of the q-axis component of the grid connection point voltage. Represents the transpose of a matrix. This indicates that the grid connection point voltage is rotating synchronously. coordinate system Axial components, This indicates the phase angle of the phase-locked loop output. express Shaft current reference value, express Shaft current reference value, Represents the transpose of a matrix. This represents the PLL scaling factor. This represents the PLL integral coefficient.

[0043] (2) Model discretization: The continuous model is discretized using a zero-order hold (ZOH), and the discrete state equations are as follows: (2) Substituting into equation (1), we get: (3) (Note: , ) in, This indicates the current phase angle of the PLL. Indicates the current grid connection point voltage. Axial component integral value, This indicates the predicted PLL phase angle for the next moment. This indicates the predicted grid connection point voltage at the next moment. Axial component integral value, Indicates the sampling period. This represents the PLL scaling factor. Represents the PLL integral coefficient. Equivalent resistance at the fault point Equivalent reactance at the fault point Indicates the effective value of the voltage at the fault point. Indicates the current time Shaft current reference value, Indicates the current time Shaft current reference value, express The rate of change of the state variable over continuous time at any given moment.

[0044] Step S003: Real-time data acquisition and fault parameter identification During system operation, the power grid status and fault characteristics are collected in real time to provide input for MPC optimization. (1) Acquisition of state variables The three-phase voltage at the grid connection point is acquired via FPGA in each sampling cycle. , , With VSC output current , , The dq-axis components are obtained by Clark-Park transformation: , (4) in, This is the transformation matrix for a synchronous rotating coordinate system. express shaft voltage, express Shaft voltage.

[0045] Read the PLL output phase angle Calculate the integral term .

[0046] in, Indicates the PLL output phase angle. This represents the predicted grid connection point voltage at the previous moment. Axial component integral value, Indicates the sampling period. Indicates the current time Shaft voltage.

[0047] (2) Fault parameter estimation Fault point voltage : Acquired directly through a fault recording device, or estimated based on grid connection point voltage and current: (5) Equivalent impedance Identification using Recursive Least Squares (RLS): (6) in, , The gain matrix and forgetting factor are obtained from the RLS (Recursive Least Squares) method. , express The effective value of the voltage at the fault point at any given time. express time shaft voltage, express time shaft voltage, This represents the equivalent impedance from the fault point to the grid connection point. Indicates time Grid connection point current Axial components, Indicates time Grid connection point current Axial components, Indicates time Equivalent impedance from the fault point to the grid connection point Represents the imaginary unit. Indicates time RLS estimate of equivalent impedance Indicates time RLS estimate of equivalent impedance Indicates time The grid connection point current.

[0048] Step S004: Generation of Reference Trajectory and Control Target Based on the system's operating status and fault type, a reference trajectory for MPC optimization is generated: (1) Calculation of phase angle reference value The phase angle of the system's equilibrium point after the fault is: (7) in, , The current setpoint obtained from the previous cycle optimization. This indicates the PLL phase angle reference value. Indicates the equivalent reactance at the fault point. Indicates the equivalent resistance at the fault point. This indicates the effective value of the voltage at the fault point.

[0049] (2) Reactive current auxiliary target To support the voltage at the fault point, a lower limit for reactive current is set: (8) ( (Rated voltage) in, Indicates the equivalent reactance at the fault point. Indicates the effective value of the voltage at the fault point. Indicates the rated voltage. This indicates the lower limit of the reactive current reference.

[0050] Step S005: MPC Optimization Problem Construction Based on a discrete model and a reference trajectory, an optimization problem with multiple constraints is constructed: (1) State prediction Predicting the future based on equation (3) Step status: (9) in, For discretized state mapping function, The current measurement status is as follows. Indicates the prediction time domain, Indicates time-based Information prediction time The state vector, Indicates time-based Information, for The control quantity applied at any time, Indicates time-based Information, for The predicted value of the system state at any given time.

[0051] (2) Objective function design The objective function, which balances state tracking accuracy and control smoothness, is: (10) in: , State weights (prioritizing phase angle stability); , To control the weights (suppress sudden current changes); , Similarly ( right ).

[0052] in, Indicates the prediction step size index. Indicates the prediction time domain, Indicates control of the time domain, Indicates time-based Information, predictions The PLL phase angle state at time t. Indicates time-based Information, predicted timing Grid connection point voltage Axial component integral value, express Change in shaft current reference value express Change in shaft current reference value Indicates time The control vector.

[0053] (3) Setting constraints State constraints (phase angle stable boundary): (11) Control constraints (current limits): (12) (13) Fault parameter constraints: (14) in, Indicates time PLL phase angle reference value, This indicates the safe threshold for PLL phase angle deviation. Indicates the prediction time domain, Indicates control of the time domain, Indicates time of Shaft current reference value, Indicates time of Shaft current reference value, Represents time k Lower limit of shaft current reference value This indicates the maximum value of the VSC output current. Indicates the constraint conditions in the control time domain Each prediction step within must satisfy all arrive integers , This represents the lower limit of the equivalent impedance at the fault point. This represents the upper limit of the equivalent impedance at the fault point. This indicates the lower limit of the voltage at the fault point.

[0054] Step S006: Optimization Problem Solving and Control Variable Selection The MPC problem is solved using a convex optimization algorithm, and the steps are as follows: (1) Linearization of nonlinear terms For equation (3) exist Perform a second-order Taylor expansion at this point: (15) Transform it into an approximately linear model, making the objective function and constraints convex functions.

[0055] (2) Solving Quadratic Programming (QP) Transform the optimization problem into a standard QP (Queries Problem) form: (16) in, To optimize the variable vector, The coefficient matrix and vector are constructed based on equations (10)-(14). The interior-point method is used to solve the QP problem, achieving high iteration accuracy. Ensure solution time .

[0056] Selection of control variables: based on optimization results Extract the current setpoint for the first control cycle: (17) in, Represents the vector of optimization variables. Represents the coefficient matrix of the quadratic terms (by weights) (Dominant, ensuring positive definiteness) Represents the vector of coefficients of the first-order term (and the state deviation) , Related (the absolute value increases during a fault). Represents the coefficient matrix of the constraint inequality (mainly for) or ), Denotes the vector on the right side of the u-constraint inequality. Indicates based on Time information Shaft current reference value, Indicates based on Time information Shaft current reference value, Indicates based on Time information Shaft current reference value, Indicates based on Time information Shaft current reference value, This represents the first element of the optimal solution vector. This represents the second element of the optimal solution vector. Indicates time Optimal shaft current reference value Indicates time Optimal shaft current reference value Represents the transpose of a matrix. Indicates a time index.

[0057] Step S007: Control Execution and PWM Signal Generation (1) Current loop tracking control Current inner loop tracking is achieved using a PI controller: (18) in, express Shaft voltage reference value, express Shaft voltage reference value, , For the current loop PI parameters, Indicates time Grid connection point current Axial components, Indicates time Grid connection point current Axial components.

[0058] (2) PWM signal generation Will , The three-phase voltage reference is obtained by the Park-Clark inverse transform. , , The IGBT drive signal is generated by space vector pulse width modulation, and the switching period is consistent with the sampling period.

[0059] Step S008: Adaptive adjustment of weighting coefficients The objective function weights are dynamically adjusted based on the severity of the fault to enhance control adaptability. (1) Fault level classification: Define voltage drop coefficient Divided into: 1) Serious malfunction: ; 2) Moderate fault: ; 3) Minor fault: .

[0060] (2) Weight adjustment strategy: (19) in, This represents the voltage drop factor.

[0061] Step S009: Loop Execution and Post-Fault Recovery Rolling optimization loop: Steps S003-S008 are repeated in each sampling period to optimize the problem based on the latest state and parameter updates, thereby achieving closed-loop control of "acquisition-prediction-optimization-execution".

[0062] Fault clearing judgment: When After three consecutive cycles, the fault is determined to be cleared, and the system switches to normal operating mode. 1) The current setpoint reference is switched to power loop output ( , ) 2) The MPC weight is restored to the mild fault mode, and the phase angle stability weight is gradually reduced.

[0063] in, express Shaft current reference value, express Shaft current reference value, This indicates the active power command value. This indicates the reactive power command value.

[0064] Step S0010, Anomaly Protection and Fault Tolerance Handling of optimization failures: If the QP (Quadratic Programming) solution times out ( If no feasible solution is found, activate the backup control strategy: output the control quantity from the previous cycle and limit the rate of change of current. .

[0065] Sensor fault tolerance: When a sensor fails, the missing state is estimated using Kalman filtering based on data from other healthy sensors. (20) in, These are measurements taken by health sensors. For filter gain, For the observation matrix, Indicates time State estimates, Indicates time-based Information on time The predicted state value.

[0066] Through the above steps, this invention achieves real-time optimized control of the transient stability of the VSC-PLL system under weak network faults, taking into account both stability and control performance, and has strong engineering feasibility.

[0067] The various embodiments in this specification are described in a related manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, the system embodiments are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions of the method embodiments.

[0068] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention are included within the scope of protection of the present invention.

Claims

1. A model predictive transient stability control method for a VSC-PLL system under weak network conditions, characterized in that... Includes the following steps: 1) System Dynamic Model Construction (1) Physical model and state equation Topology: The VSC is connected to the weak current grid via an LC filter. The fault point F is located between the grid connection point and the infinite power grid, with an equivalent impedance of... The voltage at the fault point is , The equivalent impedance at the fault point, The equivalent reactance at the fault point, The equivalent resistance at the fault point. It is the imaginary unit; State-space description: Considering only the PLL dynamics, the second-order model of the system is: in: The phase angle of the PLL is referenced to the phase angle of the infinite mains voltage. The integral voltage component is defined as follows: , The q-axis component of the grid connection point voltage; , The proportional / integral coefficient of the PLL; Represents the differential element in calculus; , The active / reactive current setpoints to be optimized; (2) Model discretization Discretization using a zero-order hold, sampling period The discretized state equation is: Introducing state vectors Control vector Then the discrete model can be expressed as: in, Indicates the sampling period. Represents discrete time. Represents the transpose of a matrix. Represents the state vector. Representing a discrete model, Indicates that the phase-locked loop is in The phase angle of the grid voltage is tracked in real time. Is Voltage at grid connection point at all times Axial components The integral term, Indicates in The phase angle of the grid voltage is tracked in real time. Indicates in Voltage at grid connection point at all times Axial components The integral term, Indicates that the phase-locked loop is in The rate of change of the grid voltage phase angle is tracked at all times. Indicates in Voltage at grid connection point at all times Axial components The rate of change of the integral term (the derivative in continuous time). Represents the control vector. The equivalent impedance at the fault point, Indicates the effective value of the voltage at the fault point. express Shaft current reference value, express Shaft current reference value, For terms containing nonlinear terms Discrete mapping function; 2) Core Components of the MPC Optimization Problem (1) Prediction model and time domain setting Multi-step prediction: based on the current state Predicting the future The state trajectory of each cycle: in Predicting the time domain This corresponds to a 1ms prediction length; Controlling the Time Domain: Optimizing the Future Control quantity per cycle, ,Pick Only the control input for the first cycle is executed; in, This represents the prediction time domain, used to predict the total number of steps to the future state. This represents the control time domain, used to optimize the control sequence length. Indicates the prediction step size index. Indicates the current sampling time. Indicates the control input variable, Represents state variables, The equivalent impedance at the fault point, Indicates the effective value of the voltage at the fault point. For terms containing nonlinear terms Discrete mapping function; (2) Objective function design Multi-objective optimization framework: in: Describe the overall objective function. This represents the state tracking error term. Indicates the control input item; State error term: The phase angle at the equilibrium point after the fault ( ), , These are weighting coefficients, emphasizing the priority of phase angle stability; Control smoothing term: , , Avoid sudden changes in current; in, Indicates the prediction time domain, Indicates control of the time domain, Indicates the prediction step size index. Indicates the current sampling time. , , , These are the weighting coefficients. This represents the predicted PLL phase angle. This represents the predicted integral voltage. This indicates the PLL phase angle reference value. Equivalent reactance at the fault point express Shaft current reference value, express Shaft current reference value, Equivalent resistance at the fault point Indicates the effective value of the voltage at the fault point. express shaft current variation value express Shaft current variation; (3) Set of constraints Transient stability constraints: The safety threshold calibrated for the experiment (corresponding to a phase angle deviation of no more than 90° to avoid PLL lockout); Current limit constraint: This represents the maximum output current of the VSC. Fault parameter constraints: , This is the lower limit of voltage sag. This is the upper limit of the equivalent impedance of a weak network; in, This represents the predicted PLL phase angle. Indicates the prediction step size index. Indicates the current sampling time. This indicates the PLL phase angle reference value. This indicates the safe upper limit of the PLL phase angle deviation. Indicates the prediction time domain, Indicates control of the time domain, Indicates the effective value of the voltage at the fault point. This indicates the lower limit of voltage drop. The equivalent impedance at the fault point, Indicates the lower limit of the equivalent impedance. Indicates the upper limit of the equivalent impedance; express Shaft current reference value, express Shaft current reference value, This indicates the maximum output current of the voltage source converter; 3) Rolling optimization and adaptive control mechanism (1) Real-time parameter update Fault characteristic acquisition: Real-time acquisition via voltage / current sensors: Fault point voltage Based on the symmetrical fault assumption, the effective value of the three-phase voltage is taken; Equivalent impedance , Calculated by the changes in voltage and current before and after the fault: ; Weight adaptive adjustment: when At that time, a serious malfunction occurred, increasing the risk of serious damage. Up to 15, prioritize ensuring phase angle stability; when At times, minor faults increase , Upgraded to version 1.0, optimizing current tracking performance; in, Indicates the effective value of the voltage at the fault point. Indicates the equivalent resistance at the fault point. Indicates the equivalent reactance at the fault point. The equivalent impedance at the fault point, This indicates the voltage change before and after the fault. Indicates the change in current before and after the fault; (2) Optimize the solution and control the execution Convex optimization transformation: transforming nonlinear terms Perform a second-order Taylor expansion near the current equilibrium point: The problem is transformed into a convex quadratic programming problem, which can be solved quickly using the interior point method. Control output: Only the first control input of the optimized sequence is executed. The next cycle will restart the optimization based on the new state, forming a rolling control closed loop; in, This indicates the current discrete-time index, and the superscript "*" indicates the optimal solution. express The optimal control vector at time 1. express In the optimal control vector at time step Shaft current reference value, express In the optimal control vector at time step Shaft current reference value, Represents the transpose of a matrix. This represents the predicted PLL phase angle. This indicates the PLL phase angle reference value.

2. The model predictive transient stability control method for a VSC-PLL system under weak network conditions according to claim 1, characterized in that... In step 1): , .

3. The model predictive transient stability control method for a VSC-PLL system under weak network conditions according to claim 1, characterized in that... In step 2): =8~15, =5~10, =0.3~1, =0.3~1.

4. The model predictive transient stability control method for a VSC-PLL system under weak network conditions according to claim 1, characterized in that, Specifically, the steps include the following: Step S001: System Initialization and Core Parameter Calibration Before starting the VSC-PLL system in a weak network environment, complete the hardware platform setup and basic parameter configuration, specifically including: (1) Hardware architecture deployment: The controller adopts a "DSP+FPGA" architecture. The DSP is responsible for model prediction and optimization, while the FPGA handles high-speed data acquisition and PWM pulse generation, with a sampling frequency of [missing information]. Switching frequency ; Sensor configuration: The grid connection point voltage sensor, VSC output current sensor, and fault point voltage monitoring module are all connected to the controller through isolation conditioning circuits; (2) Initialization of basic parameters: VSC Rated Parameters: Rated Power Rated voltage Maximum output current ; PLL control parameters: proportional coefficient Integral coefficient Initial phase angle reference ; MPC core parameters: prediction time domain ,correspond Control Time Domain Sampling period ;in, Indicates the rated current. Indicates rated power. Indicates the rated voltage. Indicates the sampling frequency; (3) Safety threshold calibration: The safety deviation threshold of PLL phase angle was determined through offline simulation and experiments. This corresponds to approximately 85° to prevent loss of lockout; lower limit of fault point voltage. Equivalent impedance range , Indicates the prediction step size index; Step S002: System Dynamic Model Construction and Discretization Based on the physical characteristics of the VSC-PLL system under weak network conditions, a nonlinear model containing PLL dynamics is established and discretized. The steps are as follows: (1) Derivation of continuous-time state equations Define state vector , For PLL phase angle, Integrating the q-axis component of the grid connection point voltage, the control vector Given the active / reactive current setpoints, the system dynamic equations are: （1） in, , The equivalent resistance and reactance from the fault point to the grid connection point. This is the effective value of the voltage at the fault point. Represents the state vector. Indicates the PLL phase angle. This represents the integral of the q-axis component of the grid connection point voltage. Represents the transpose of a matrix. This indicates that the grid connection point voltage is rotating synchronously. coordinate system Axial components, This indicates the phase angle of the phase-locked loop output. express Shaft current reference value, express Shaft current reference value, Represents the transpose of a matrix. This represents the PLL scaling factor. Indicates the PLL integral coefficient; (2) Model discretization: The continuous model is discretized using a zero-order hold, and the discrete state equations are as follows: （2） Substituting into equation (1), we get: （3） Note: , ; in, This indicates the current phase angle of the PLL. Indicates the current grid connection point voltage. Axial component integral value, This indicates the predicted PLL phase angle for the next moment. This indicates the predicted grid connection point voltage at the next moment. Axial component integral value, Indicates the sampling period. This represents the PLL scaling factor. Represents the PLL integral coefficient. Equivalent resistance at the fault point Equivalent reactance at the fault point Indicates the effective value of the voltage at the fault point. Indicates the current time Shaft current reference value, Indicates the current time Shaft current reference value, express The rate of change of the state variable over continuous time at any given moment; Step S003: Real-time data acquisition and fault parameter identification During system operation, the power grid status and fault characteristics are collected in real time to provide input for MPC optimization. (1) Acquisition of state variables The three-phase voltage at the grid connection point is acquired via FPGA in each sampling cycle. , , With VSC output current , , The dq-axis components are obtained by Clark-Park transformation: , （4） in, This is the transformation matrix for a synchronous rotating coordinate system. express shaft voltage, express Shaft voltage; Read the PLL output phase angle Calculate the integral term ; in, Indicates the PLL output phase angle. This represents the predicted grid connection point voltage at the previous moment. Axial component integral value, Indicates the sampling period. Indicates the current time Shaft voltage; (2) Fault parameter estimation Fault point voltage : Acquired directly through a fault recording device, or estimated based on grid connection point voltage and current: （5） Equivalent impedance Identification using Recursive Least Squares (RLS): （6） in, , Here is the RLS gain matrix and the forgetting factor. , express The effective value of the voltage at the fault point at any given time. express time shaft voltage, express time shaft voltage, This represents the equivalent impedance from the fault point to the grid connection point. Indicates time Grid connection point current Axial components, Indicates time Grid connection point current Axial components, Indicates time Equivalent impedance from the fault point to the grid connection point Represents the imaginary unit. Indicates time RLS estimate of equivalent impedance Indicates time RLS estimate of equivalent impedance Indicates time The grid connection point current; Step S004: Generation of Reference Trajectory and Control Target Based on the system's operating status and fault type, a reference trajectory for MPC optimization is generated: (1) Calculation of phase angle reference value The phase angle of the system's equilibrium point after the fault is: （7） in, , The current setpoint obtained from the previous cycle optimization. This indicates the PLL phase angle reference value. Indicates the equivalent reactance at the fault point. Indicates the equivalent resistance at the fault point. Indicates the effective value of the voltage at the fault point; (2) Reactive current auxiliary target To support the voltage at the fault point, a lower limit for reactive current is set: （8） Rated voltage; in, Indicates the equivalent reactance at the fault point. Indicates the effective value of the voltage at the fault point. Indicates the rated voltage. Indicates the lower limit of reactive current reference; Step S005: MPC Optimization Problem Construction Based on a discrete model and a reference trajectory, an optimization problem with multiple constraints is constructed: (1) State prediction Predicting the future based on equation (3) Step status: （9） in, For discretized state mapping function, The current measurement status is as follows. Indicates the prediction time domain, Indicates time-based Information prediction time The state vector, Indicates time-based Information, for The control quantity applied at any time, Indicates time-based Information, for The predicted value of the system state at any given time; (2) Objective function design The objective function, which balances state tracking accuracy and control smoothness, is: （10） in: , As state weights, priority is given to ensuring phase angle stability; , To control the weights and suppress sudden current changes; , Similarly ( right ); in, Indicates the prediction step size index. Indicates the prediction time domain, Indicates control of the time domain, Indicates time-based Information, predictions The PLL phase angle state at time t. Indicates time-based Information, predicted timing Grid connection point voltage Axial component integral value, express Change in shaft current reference value express Change in shaft current reference value Indicates time The control vector; (3) Setting constraints State constraints (phase angle stable boundary): （11） Control constraints (current limits): （12） （13） Fault parameter constraints: （14） in, Indicates time PLL phase angle reference value, This indicates the safe threshold for PLL phase angle deviation. Indicates the prediction time domain, Indicates control of the time domain, Indicates time of Shaft current reference value, Indicates time of Shaft current reference value, Represents time k Lower limit of shaft current reference value This indicates the maximum value of the VSC output current. Indicates the constraint conditions in the control time domain Each prediction step within must satisfy all arrive integers , This represents the lower limit of the equivalent impedance at the fault point. This represents the upper limit of the equivalent impedance at the fault point. Indicates the lower limit of the fault point voltage; Step S006: Optimization Problem Solving and Control Variable Selection The MPC problem is solved using a convex optimization algorithm, and the steps are as follows: (1) Linearization of nonlinear terms For equation (3) exist Perform a second-order Taylor expansion at this point: （15） Transform it into an approximately linear model, making the objective function and constraints convex functions; (2) Solving Quadratic Programming (QP) Transform the optimization problem into a standard QP (Queries Problem) form: （16） in, To optimize the variable vector, The coefficient matrix and vector are constructed based on equations (10)-(14); the interior point method is used to solve the QP problem, and the iteration accuracy is [not specified]. Ensure solution time ; Selection of control variables: based on optimization results Extract the current setpoint for the first control cycle: （17） in, Represents the vector of optimization variables. Represents the coefficient matrix of the quadratic term. This represents the vector of coefficients for the first-order terms. This represents the coefficient matrix of the constraint inequality. Denotes the vector on the right side of the u-constraint inequality. Indicates based on Time information Shaft current reference value, Indicates based on Time information Shaft current reference value, Indicates based on Time information Shaft current reference value, Indicates based on Time information Shaft current reference value, This represents the first element of the optimal solution vector. This represents the second element of the optimal solution vector. Indicates time Optimal shaft current reference value Indicates time Optimal shaft current reference value Represents the transpose of a matrix. Indicates a time index; Step S007: Control Execution and PWM Signal Generation (1) Current loop tracking control Current inner loop tracking is achieved using a PI controller: （18） in, express Shaft voltage reference value, express Shaft voltage reference value, , For the current loop PI parameters, Indicates time Grid connection point current Axial components, Indicates time Grid connection point current Axial components; (2) PWM signal generation Will , The three-phase voltage reference is obtained by the Park-Clark inverse transform. , , The IGBT drive signal is generated by space vector pulse width modulation, and the switching period is consistent with the sampling period. Step S008: Adaptive adjustment of weighting coefficients The objective function weights are dynamically adjusted based on the severity of the fault to enhance control adaptability. (1) Fault level classification: Define voltage drop coefficient Divided into: 1) Serious malfunction: ; 2) Moderate fault: ; 3) Minor fault: ; (2) Weight adjustment strategy: （19） in, Indicates the voltage drop factor; Step S009: Loop Execution and Post-Fault Recovery Rolling optimization loop: Steps S003-S008 are repeated in each sampling period to optimize the problem based on the latest state and parameter updates, thereby achieving closed-loop control of "acquisition-prediction-optimization-execution"; Fault clearing judgment: When After three consecutive cycles, the fault is determined to be cleared, and the system switches to normal operating mode. 1) The current setpoint reference is switched to power loop output ( , ) 2) The MPC weight is restored to the mild fault mode, and the phase angle stability weight is gradually reduced; in, express Shaft current reference value, express Shaft current reference value, This indicates the active power command value. This indicates the reactive power command value; Step S0010: Anomaly Protection and Fault Tolerance Optimization failure handling: If the QP solution times out or there is no feasible solution, activate the backup control strategy: output the control quantity of the previous cycle and limit the rate of change of current. ; Sensor fault tolerance: When a sensor fails, the missing state is estimated using Kalman filtering based on data from other healthy sensors. （20） in, These are measurements taken by health sensors. For filter gain, For the observation matrix, Indicates time State estimates, Indicates time-based Information on time The predicted state value.

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