A stability determination method and system of a new energy base automatic voltage control closed-loop system

Abstract

This invention discloses a stability determination method and system for an automatic voltage control closed-loop system in a new energy base. The method includes: acquiring system parameters of the automatic voltage control closed-loop system; establishing a discrete state update model including the current cycle control command and the previous cycle control command; constructing augmented state variables and establishing a unified closed-loop discrete mapping relationship considering control laws and limiting constraints; dividing the state space into an unsaturated subspace and a saturated subspace according to whether the control command touches the limiting constraint, and establishing corresponding piecewise discrete mapping relationships; constructing a linear matrix inequality stability criterion for the unsaturated subspace under the condition that the voltage-reactive power characteristics satisfy the bounded incremental sector, and transforming it into a semi-positive definite programming problem to obtain the stability determination result. This invention can accurately characterize the dynamic behavior of the AVC closed loop in a new energy base under the combined effects of sample-and-hold, time delay, and limiting, and realize the analysis and determination of the system's stability state and oscillation mode.

Description

Technical Field

[0001] This invention belongs to the field of power system and its automation technology, specifically relating to a stability determination method and system for an automatic voltage control closed-loop system in a new energy base. Background Technology

[0002] With the large-scale centralized development of new energy sources such as wind power and photovoltaics, new energy bases have become an important component of new power systems. To ensure voltage quality and operational safety of the collection and transmission system, it is usually necessary to coordinate various reactive power / voltage regulation resources, such as static var generators (SVG), synchronous condensers, parallel capacitors / reactors, and on-load tap changers, through an Automatic Voltage Control (AVC) system to achieve the goal of hierarchical and zonal voltage regulation with local balance. The AVC system of a new energy base generally consists of a master station and substations. The master station generates reactive power and voltage regulation commands based on operating conditions and sends them to the substations. The substations then drive the continuous / discrete adjustable reactive power devices within the station to perform control, thus forming a closed-loop control link of measurement, calculation, command, execution, and verification.

[0003] In the prior art, Chinese patent application CN118432112A discloses an active voltage support control method, device, and system for new energy power plants. This method employs different control parameters based on the system voltage range: steady-state voltage reactive power control parameters in the steady-state range and optimized control parameters in the rapid voltage support range, thereby achieving rapid voltage regulation of the new energy power plant. The key to this solution lies in the switching of control strategies and parameter configuration under different voltage ranges, which can improve the active voltage support capability of the power plant.

[0004] Chinese patent application CN116111598A discloses a frequency-voltage coordinated control method based on MPC. This method combines the dynamic equations of the power grid frequency and voltage to form a frequency-voltage coordinated model, which is then transformed into an incremental form of a discrete-time system state-space model. Model predictive control is then used for coordinated control. This scheme focuses on the coordinated control and predictive optimization of frequency and voltage, and can improve the dynamic adjustment capability of the power grid after disturbances to a certain extent.

[0005] Chinese patent application CN109361242A discloses an automatic voltage control method for photovoltaic (PV) power generation. Through bidirectional interaction between the AVC master station and the PV power plant's AVC substation, it calculates the global reactive power optimization of the PV power plant, achieving automatic voltage control in the PV power generation aggregation area. This scheme primarily addresses hierarchical voltage control and global reactive power optimization allocation in the PV power plant aggregation area, and can adapt to the automatic voltage control requirements under large-scale PV power generation grid connection conditions.

[0006] However, the existing technologies still have the following shortcomings: First, most existing solutions focus on control strategy design, parameter switching, or global reactive power optimization allocation, without establishing a unified discrete dynamic model of sampled data for the AVC master-slave closed-loop system of the new energy base. This makes it difficult to accurately characterize the impact of the master station control commands being sampled and issued periodically, the zero-order hold between adjacent control cycles, and the equivalent delays introduced by communication and computation delays on the closed-loop dynamic behavior. Second, existing solutions do not fully consider the limiting characteristics of continuously adjustable reactive power device control commands under equipment capacity constraints, thus making it difficult to describe the piecewise discrete dynamic characteristics formed by the switching between unsaturated and saturated states of the closed-loop system under limiting action. Third, existing solutions generally lack stability criteria that match the aforementioned sampling, delay, and limiting coupling characteristics, making it impossible to effectively analyze and determine the stability state and oscillation mode of the AVC closed-loop system under different parameter configurations and operating conditions.

[0007] In the actual operation of the AVC system in the new energy base, AVC commands are issued according to the master station control cycle and remain unchanged between adjacent control cycles. However, there are communication and execution delays between the completion of command calculation by the master station and its execution by the substation, resulting in an equivalent time delay. Furthermore, the control commands for continuously adjustable reactive power resources are also limited by device capacity and operating boundaries, requiring upper and lower limit constraints. The coupling of these multiple factors—control cycle, zero-order hold, equivalent time delay, and amplitude limiting constraints—may lead to a decrease in system convergence speed and regulation accuracy, and even trigger sustained oscillations, severely impacting voltage regulation performance and system operational safety.

[0008] Therefore, it is necessary to propose a new technical solution that can establish a sampling data model for the automatic voltage control closed-loop system of new energy bases, taking into account sample-and-hold, equivalent time delay, first-order input memory, and amplitude limiting constraints. This model can construct a piecewise closed-loop discrete mapping relationship corresponding to the unsaturated / saturated subspaces, and establish a calculable stability criterion under the condition that the voltage-reactive power nonlinear mapping satisfies the bounded incremental sector condition. This will enable effective analysis and determination of the stability state and oscillation mode of the AVC closed-loop system of new energy bases, improving the accuracy of system modeling and analysis and its engineering application value. Summary of the Invention

[0009] The purpose of this invention is to address the common problems in existing automatic voltage control technologies for new energy bases, such as insufficient characterization of the master-slave closed-loop dynamic process, difficulty in uniformly representing the coupling effect of sample-and-hold and equivalent time delay, difficulty in describing the piecewise dynamic characteristics caused by control command limiting, and lack of calculable stability determination methods. This invention provides a stability determination method and system for the closed-loop system of automatic voltage control in new energy bases. This method can establish a closed-loop sampled data model that considers the zero-order hold characteristics, equivalent time delay, and limiting constraints of the master station control commands within the control cycle. This model accurately reflects the dynamic behavior of the AVC system in the new energy base and enables the analysis and determination of the system's stable state and oscillation mode, thereby improving the accuracy of dynamic analysis and the engineering application value of the automatic voltage control system in new energy bases.

[0010] To achieve the above objectives, the present invention adopts the following technical solution: a method for determining the stability of an automatic voltage control closed-loop system in a new energy base, comprising the following steps: Step S1: Obtain the system parameters of the automatic voltage control closed-loop system. The system parameters include the master station control cycle, equivalent time delay, dynamic parameters of continuously adjustable reactive power resources, control command limit value, and nonlinear mapping characteristics between voltage and reactive power. Step S2: Based on the system parameters, establish a continuous-time state model of continuously adjustable reactive power resources, and combine the zero-order hold characteristic of the master station control command in the master station control cycle and the equivalent time delay to discretize the continuous-time state model to obtain a discrete state update model that simultaneously contains the current cycle control command and the previous cycle control command. Step S3: Based on the discrete state update model, construct an augmented state variable that includes reactive resource state variables and control commands from the previous cycle, and combine the nonlinear mapping characteristics between voltage and reactive power, the preset control law and the control command amplitude limit constraint to establish a unified closed-loop discrete mapping relationship. Step S4: Based on the triggering state of the control command limiting constraint, divide the state space corresponding to the closed-loop discrete mapping relationship to obtain unsaturated subspaces and saturated subspaces, and establish the piecewise discrete mapping relationship corresponding to each subspace. Step S5: When the nonlinear mapping characteristics between voltage and reactive power satisfy the preset incremental sector bounded condition, construct a linear matrix inequality stability criterion for the unsaturated subspace, and transform the linear matrix inequality stability criterion into a semi-positive definite programming problem for solution to obtain the stability determination result of the automatic voltage control closed-loop system.

[0011] Furthermore, the establishment of a continuous-time state model for continuously adjustable reactive power resources specifically includes: Based on the dynamic characteristics of continuously adjustable reactive power resources, the internal state of the reactive power resources is selected as the state variable, and the control commands issued by the master station are selected as the input variable. A continuous-time state-space model is established, which is expressed by the formula: in, This represents the state variable of continuously adjustable reactive power resources. Indicates control commands, The state matrix, For the input matrix, Represents state variables Regarding time The first derivative; Based on the control structure of the continuously adjustable reactive power resource and in combination with the dynamic characteristics of the device, the parameters of the state matrix A and the input matrix B are determined.

[0012] Furthermore, the discretization of the continuous-time state model to obtain a discrete state update model that simultaneously includes the current cycle control command and the previous cycle control command specifically includes: Within each master station control cycle, the holding characteristics of the control command are described using the zero-order hold method, so that the control command remains unchanged within each control cycle. Based on the equivalent delay, each control cycle is divided into a time interval affected by the control command of the previous cycle and a time interval affected by the control command of the current cycle. Under the zero-order preservation property and equivalent time delay constraints, the continuous-time state model is discretized to obtain a discrete-time state update model, which is expressed by the following formula: in, Indicates the first Each control cycle refers to the state variables of the current control cycle. Indicates the first The state variables corresponding to each control cycle Indicates the first Control commands for each control cycle Indicates the first Each control cycle is the control command of the previous control cycle. The discrete state transition matrix, This is the control command action matrix for the current cycle. This is the matrix representing the action of the control commands from the previous cycle; The discrete state transition matrix and the aforementioned action matrix and They are determined in the following ways: in, This represents the state matrix in a continuous-time state model. This represents the input matrix in a continuous-time state model. Indicates the main station control cycle. Indicates the equivalent delay. Let represent the integral variable, and the equivalent time delay satisfies: .

[0013] Furthermore, based on the discrete state update model, constructing an augmented state variable that includes reactive resource state variables and the control command from the previous cycle specifically includes: The augmented state variable is represented as: in, Indicates the first Augmented state variables for each control cycle This represents the state variables of the current control cycle. Indicates the control command from the previous control cycle; Based on the discrete state update model, the update relationship of the augmented state variables is expressed as follows: in, Indicates the first Augmented state variables for each control cycle This represents the augmented state transition matrix. Represents the control input matrix; The augmented state transition matrix and control input matrix They are represented as follows: in, These represent the discrete state transition matrix, the current cycle control command action matrix, and the previous cycle control command action matrix, respectively. Represents the identity matrix.

[0014] Furthermore, the establishment of a unified closed-loop discrete mapping relationship by combining the nonlinear mapping characteristics between voltage and reactive power, the preset control law, and the control command amplitude limiting constraint specifically includes: Based on the nonlinear mapping characteristic between voltage and reactive power, the output relationship is established as follows: in, Indicates the first Voltage measurement value for each control cycle This represents a nonlinear mapping function between voltage and reactive power. Indicates operating condition parameters; Based on the aforementioned output relationship and combined with the preset control law, the control command is obtained, expressed as: in, Indicates the first Control commands for each control cycle This represents the feedforward control variable. The feedback parameter matrix represents the control law. Indicates the voltage reference value; Applying a limiting constraint to the control command yields the actual control command, expressed as: in, This indicates the control command after amplitude limiting. This represents the limiting operator, used to impose upper and lower limit constraints on control commands; Substituting the actual control command into the update relation of the augmented state variables, the closed-loop state update relation is obtained, expressed as: in, This represents the augmented state transition matrix. Represents the control input matrix; The closed-loop state update relationship is written as a unified closed-loop discrete mapping relationship, expressed as: in, This represents the closed-loop discrete mapping function composed of the nonlinear mapping function, the control law, and the amplitude limiting constraint.

[0015] Furthermore, the step of dividing the state space corresponding to the closed-loop discrete mapping relationship according to the triggering state of the control command limiting constraint to obtain unsaturated subspaces and saturated subspaces, and establishing piecewise discrete mapping relationships corresponding to each subspace, specifically includes: augmented state variables value space Based on whether the actual control commands of each control channel reach the upper and lower limits, an unsaturated subspace that does not trigger amplitude limiting is obtained. and several saturated subspaces that trigger amplitude limiting , represented as: in, This indicates the number of control channels for continuously adjustable reactive power resources; For each state subspace Define the corresponding piecewise closed-loop discrete mapping relationship: in, In the state subspace Below, by augmented state variables Voltage-reactive nonlinear mapping function Control Law and limiting operator Together they form a closed-loop discrete mapping function; For unsaturated subspaces The closed-loop discrete mapping relationship maintains a linear form: in, For the augmented state transition matrix, To augment the control input matrix, Represents the state selection matrix. Represents the bias vector; For saturated subspace The closed-loop discrete mapping relationship adjusts the control command through the amplitude limiting operator, thereby forming a segmented switching discrete mapping structure: Furthermore, the construction of a linear matrix inequality stability criterion for the unsaturated subspace, under the condition that the nonlinear mapping characteristic between voltage and reactive power satisfies the preset incremental sector bounded condition, specifically includes: For unsaturated subspaces Set the voltage-reactive nonlinear mapping function The incremental sector is bounded, that is: Or equivalently represented as: in, This represents the increment of the augmented state variable from the steady state. This is a steady-state augmented state; This represents the increment of the output voltage from the steady state. Choose a matrix for the state; and The parameter matrix for the bounded conditions of incremental sectors is determined by local linearization of power flow calculation, identification of historical operating data, or estimation of the upper and lower bounds of the power flow Jacobian matrix. Under the condition that the incremental sector is bounded, a stability criterion in the form of a linear matrix inequality is constructed, expressed as: in, For unsaturated subspace The closed-loop state matrix; For unsaturated subspace The closed-loop input matrix; It is a symmetric positive definite matrix; is the contraction factor, representing the rate of contraction of the augmented state variable trajectory; If a symmetric positive definite matrix exists and contractile factor If ∈[0,1), then the system is in the unsaturated subspace. The condition that the trajectory of the augmented state variable converges to a stable operating state is satisfied, thus constituting a stability criterion for characterizing the convergence characteristics of the trajectory of the augmented state variable.

[0016] Furthermore, the process of transforming the linear matrix inequality stability criterion into a semi-positive definite programming problem for solution, to obtain the stability determination result of the automatic voltage control closed-loop system, specifically includes: The stability criterion is transformed into a semidefinite programming problem, expressed as: in, It is a symmetric positive definite matrix used to determine the convergence of the trajectory of the augmented state variable; It is a contraction factor; These are the optimization variables for a semidefinite programming problem. It is the identity matrix; These are the non-triggered amplitude-limiting subspaces. The closed-loop state matrix and the closed-loop input matrix; Choose a matrix for the state; and The parameter matrix represents the bounded conditions for incremental sectors; The semidefinite programming problem is solved by a convex optimization solver. When a feasible solution exists for the semidefinite programming problem, the automatic voltage control closed-loop system is determined to satisfy the stability criterion in the unsaturated subspace, and the system is determined to converge and have a unique equilibrium point. When no feasible solution exists for the semidefinite programming problem, the stability criterion cannot provide sufficient guarantee under the current parameter conditions.

[0017] Another aspect of the present invention provides a stability determination system for an automatic voltage control closed-loop system in a new energy base, comprising: The parameter acquisition module is used to acquire the system parameters of the automatic voltage control closed-loop system. The system parameters include the master station control cycle, equivalent time delay, dynamic parameters of continuously adjustable reactive power resources, control command limit value, and nonlinear mapping characteristics between voltage and reactive power. The sampling data modeling module is used to establish a continuous-time state model of continuously adjustable reactive power resources based on the system parameters, and to discretize the continuous-time state model by combining the zero-order hold characteristic of the master station control command in the master station control cycle and the equivalent time delay, so as to obtain a discrete state update model that simultaneously contains the control command of the current cycle and the control command of the previous cycle. The augmented modeling module is used to construct an augmented state variable that includes reactive resource state variables and control commands from the previous cycle, based on the discrete state update model. The closed-loop mapping construction module is used to establish a unified closed-loop discrete mapping relationship by combining the nonlinear mapping characteristics between voltage and reactive power, preset control law and control command amplitude limit constraint. The segmented mapping module is used to divide the state space corresponding to the closed-loop discrete mapping relationship according to the triggering state of the control command limiting constraint, to obtain unsaturated subspaces and saturated subspaces, and to establish the segmented discrete mapping relationship corresponding to each subspace. The stability determination module is used to construct a linear matrix inequality stability criterion for the unsaturated subspace when the nonlinear mapping characteristics between voltage and reactive power meet the preset incremental sector bounded condition, and to transform the linear matrix inequality stability criterion into a semi-positive definite programming problem for solution, so as to obtain the stability determination result of the automatic voltage control closed-loop system.

[0018] Furthermore, the stability determination module is also used for: When a feasible solution exists for the semidefinite programming problem, it is determined that the automatic voltage control closed-loop system satisfies the contraction condition in the unsaturated subspace, and based on this, it is determined that the system converges and the equilibrium point is unique. When no feasible solution exists for the semidefinite programming problem, it is determined that the stability criterion cannot provide sufficient guarantees under the current parameter conditions.

[0019] Compared with the prior art, the present invention has the following advantages: (1) This invention establishes a sampling data model for the automatic voltage control closed-loop system of new energy base, taking into account the zero-order hold characteristics of the master station control command, equivalent time delay and amplitude limiting constraint. This model can more accurately characterize the dynamic behavior of the master station-substation closed-loop system under discrete control conditions and improve the model's description accuracy of the actual operation process.

[0020] (2) By constructing augmented state variables and establishing a piecewise discrete mapping relationship between unsaturated and saturated subspaces, this invention can effectively characterize the piecewise dynamic characteristics of continuously adjustable reactive power resources under the control command limiting effect, thereby improving the understanding of the mechanism of the closed-loop dynamic process of AVC in new energy bases.

[0021] (3) Under the condition that the voltage-reactive nonlinear mapping satisfies the bounded incremental sector, the present invention constructs a linear matrix inequality stability criterion and transforms it into a semi-positive definite programming problem for solution, thereby realizing the analysis and determination of the stability state and oscillation mode of the automatic voltage control closed-loop system of the new energy base, improving the accuracy of system dynamic analysis and engineering application value. Attached Figure Description

[0022] Figure 1 Flowchart of a sampling data modeling and stability determination method for an automatic voltage control closed-loop system in a new energy base; Figure 2 A schematic diagram of the closed-loop architecture for automatic voltage control in a new energy base. Figure 3 This is a schematic diagram of the system sampling and delay. Figure 4 A schematic diagram of augmented state space partitioning and piecewise mapping; Figure 5 Here is the topology diagram of the example system; Figure 6 This is a comparison chart of the time-domain simulation and dynamic model calculation results for the example system; Figure 7 A structural block diagram of a sampling data modeling and stability determination system for an automatic voltage control closed-loop system in a new energy base. Detailed Implementation

[0023] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only for explaining the present invention and are not intended to limit the scope of protection of the present invention. Unless otherwise specified, the various embodiments of the present invention and the technical features thereof can be combined with each other. For those skilled in the art, equivalent substitutions, simple transformations, or modifications made to the technical solution of the present invention without departing from the concept of the present invention should all fall within the scope of protection of the present invention.

[0024] Example 1: In one embodiment, such as Figures 1 to 4 As shown, this invention provides a sampling data modeling and stability determination method for an automatic voltage control closed-loop system in a new energy base. This method is applicable to the dynamic modeling and stability analysis of a master-slave closed-loop system for automatic voltage control in a new energy base. The method comprehensively considers the periodic sampling and zero-order hold characteristics of the master station control commands, the equivalent time delay introduced by the communication and computation links between the master and slave stations, the dynamic response characteristics of continuously adjustable reactive power resources, and the amplitude limiting constraints of the control commands. This establishes a closed-loop sampling data model that reflects the actual engineering operation characteristics, and further enables the analysis and determination of the system's stability state and oscillation patterns.

[0025] This embodiment discloses a method for determining the stability of an automatic voltage control closed-loop system in a new energy base, such as... Figure 1 As shown, it includes the following steps: Step S1: Obtain the system parameters of the automatic voltage control closed-loop system. The system parameters include the master station control cycle, equivalent time delay, dynamic parameters of continuously adjustable reactive power resources, control command limit value, and nonlinear mapping characteristics between voltage and reactive power.

[0026] In this embodiment, for Figure 2 The automatic voltage control closed-loop system of the new energy base, as shown, first obtains the system parameters of the automatic voltage control closed-loop system. These system parameters include: master station control cycle, equivalent time delay, dynamic parameters of continuously adjustable reactive power resources, control command limit values, and voltage-reactive power nonlinear mapping characteristics. Specifically, the master station control cycle represents the time interval between the automatic voltage control master station sampling, calculating, and issuing control commands to the system operating status at a fixed period; the equivalent time delay represents the comprehensive delay time between the start of the current cycle and the actual effect of the control command on the substation side or the continuously adjustable reactive power resource side, which can be obtained by combining the master station calculation time, communication transmission time, substation execution delay, and related processing delays; the dynamic parameters of continuously adjustable reactive power resources are used to characterize the dynamic response characteristics of SVG, grid-type reactive power support devices, or other continuously adjustable reactive power devices; the control command limit values ​​include the upper and lower limits allowed by each control channel; and the voltage-reactive power nonlinear mapping characteristics are used to characterize the nonlinear relationship between voltage changes and reactive power regulation near the system operating point.

[0027] In practical applications, the aforementioned system parameters can be obtained through device controller parameters, system debugging records, historical operating data, offline simulation model parameters, field test results, or scheduling-side configuration files. This invention does not limit the method of parameter acquisition, as long as the parameters required for subsequent sampling data modeling and stability determination can be obtained.

[0028] Step S2: Based on the system parameters, establish a continuous-time state model of continuously adjustable reactive power resources, and combine the zero-order hold characteristic of the master station control command within the master station control cycle and the equivalent time delay to discretize the continuous-time state model to obtain a discrete state update model that simultaneously includes the current cycle control command and the previous cycle control command.

[0029] After acquiring the system parameters, based on the dynamic characteristics of continuously adjustable reactive power resources, the internal state of the reactive power resources is selected as the state variable, and the control commands issued by the master station are selected as the input variable. A continuous-time state-space model is established, expressed by the formula: in, This represents the state variable of continuously adjustable reactive power resources. Indicates control commands, The state matrix, For the input matrix, Represents state variables Regarding time The first derivative; Based on the control structure of the continuously adjustable reactive power resource and in combination with the dynamic characteristics of the device, the parameters of the state matrix A and the input matrix B are determined.

[0030] like Figure 3 As shown, since the master station control commands are executed according to the control cycle... T s The commands are issued discretely and remain unchanged between adjacent control cycles; therefore, the master station control commands adopt a zero-order hold form. That is, at time Control commands issued Throughout the entire time period The internal time remains constant. Simultaneously, the equivalent time delay is considered. τ The existence of control means that within a control cycle, the evolution of the system state is usually influenced by both the control commands of the previous cycle and the control commands of the current cycle. Specifically, in the first time interval of the control cycle, the system is still subject to the control commands of the previous cycle; in the second time interval of the control cycle, the control commands of the current cycle begin to take effect.

[0031] Based on this, under the zero-order preservation characteristic and equivalent time delay constraint, the continuous-time state model is discretized to obtain a discrete-time state update model, which is expressed by the following formula: in, Indicates the first Each control cycle refers to the state variables of the current control cycle. Indicates the first The state variables corresponding to each control cycle Indicates the first Control commands for each control cycle Indicates the first Each control cycle is the control command of the previous control cycle. The discrete state transition matrix, This is the control command action matrix for the current cycle. This is the matrix representing the action of the control commands from the previous cycle; The discrete state transition matrix and the aforementioned action matrix and They are determined in the following ways: in, This represents the state matrix in a continuous-time state model. This represents the input matrix in a continuous-time state model. Indicates the main station control cycle. Indicates the equivalent delay. Let represent the integral variable, and the equivalent time delay satisfies: .

[0032] The discrete state update equation also includes the current cycle control input. and the control input of the previous cycle This fully characterizes the first-order input memory effect introduced by the coupling of sample-and-hold and equivalent time delay, providing a mathematical foundation for subsequent augmented state construction and closed-loop discrete mapping.

[0033] Step S3: Based on the discrete state update model, construct an augmented state variable that includes reactive resource state variables and control commands from the previous cycle, and combine the nonlinear mapping characteristics between voltage and reactive power, the preset control law, and the control command amplitude limit constraint to establish a unified closed-loop discrete mapping relationship.

[0034] Because the discrete state update model simultaneously contains the current cycle control command. and the control command of the previous cycle This indicates that the system state is not only related to the current input, but also possesses a first-order input memory characteristic introduced by the input of the previous cycle. To uniformly describe this characteristic, an augmented state vector is further constructed in this embodiment, represented as: in, Indicates the first Augmented state variables for each control cycle This represents the state variables of the current control cycle. Indicates the control command from the previous control cycle; Based on the discrete state update model, the update relationship of the augmented state variables is expressed as follows: in, Indicates the first Augmented state variables for each control cycle This represents the augmented state transition matrix. Represents the control input matrix; The augmented state transition matrix and control input matrix They are represented as follows: in, These represent the discrete state transition matrix, the current cycle control command action matrix, and the previous cycle control command action matrix, respectively. Represents the identity matrix.

[0035] Furthermore, based on the nonlinear mapping characteristics between voltage and reactive power, an output relationship is established, expressed as: in, Indicates the first Voltage measurement value for each control cycle This represents a nonlinear mapping function between voltage and reactive power. The operating condition parameters are represented; the voltage-reactive nonlinear mapping does not need to be solved in explicit form, but only the voltage-reactive Jacobian matrix under various operating conditions needs to be obtained for subsequent incremental sector bounded conditions.

[0036] Based on the aforementioned output relationship and combined with the preset control law, the control command is obtained, expressed as: in, Indicates the first Control commands for each control cycle This represents the feedforward control variable. The feedback parameter matrix represents the control law. Indicates the voltage reference value; Applying a limiting constraint to the control command yields the actual control command, expressed as: in, This indicates the control command after amplitude limiting. This represents the limiting operator, used to impose upper and lower limit constraints on control commands; Substituting the actual control command into the update relation of the augmented state variables, the closed-loop state update relation is obtained, expressed as: in, This represents the augmented state transition matrix. Represents the control input matrix; The closed-loop state update relationship is written as a unified closed-loop discrete mapping relationship, expressed as: in, The closed-loop discrete mapping function, composed of the nonlinear mapping function, control law, and amplitude limiting constraint, fully describes the dynamic behavior of the AVC system under the combined effects of sample-and-hold, equivalent time delay, and command amplitude limiting.

[0037] Step S4: Based on the triggering state of the control command limiting constraint, divide the state space corresponding to the closed-loop discrete mapping relationship to obtain unsaturated subspaces and saturated subspaces, and establish the segmented discrete mapping relationship corresponding to each subspace.

[0038] augmented state variables value space Based on whether the actual control commands of each control channel reach the upper and lower limits, an unsaturated subspace that does not trigger amplitude limiting is obtained. and several saturated subspaces that trigger amplitude limiting , represented as: in, This indicates the number of control channels for continuously adjustable reactive power resources.

[0039] Without loss of generality, this embodiment assumes n =3, take the state variable z The last three dimensions, namely the reactive power command u Then the space can be regarded as a cube, such as Figure 4 As shown, the unsaturated subspace is the center of the cube, and the saturated subspace consists of the cube's faces, edges, and vertices. A cube has 6 faces, 12 edges, and 8 vertices, totaling 26, which is roughly equivalent to the total number of saturated subspaces. To facilitate the visualization of the system trajectory within the unsaturated subspace, Figure 4 It also demonstrates a dimensionality reduction mapping method that can clearly show the system dynamics evolution process in a three-dimensional subspace in a two-dimensional plane.

[0040] For each state subspace Define the corresponding piecewise closed-loop discrete mapping relationship: in, In the state subspace Below, by augmented state variables Voltage-reactive nonlinear mapping function Control Law and limiting operator The closed-loop discrete mapping function is formed by these factors. The above equation shows that the amplitude limiting constraint causes the closed-loop discrete dynamics to exhibit a piecewise (switching) structure; the trajectory's crossing of the subspace boundary will lead to different mappings. Switching For unsaturated subspaces The closed-loop discrete mapping relationship maintains a linear form: in, For the augmented state transition matrix, To augment the control input matrix, Represents the state selection matrix. Let represent the bias vector. The above equation shows that the closed-loop system in the unsaturated subspace It exhibits a discrete Lur'e-type structure.

[0041] For saturated subspace The closed-loop discrete mapping relationship adjusts the control command through the amplitude limiting operator, thereby forming a segmented switching discrete mapping structure: By constructing the state space and segmented mapping as described above, the closed-loop dynamic switching behavior caused by the control command limiting can be characterized more accurately: for the unsaturated subspace, since the output of each control channel does not reach the limiting, the closed-loop system maintains the mapping form under the original control law; for the saturated subspace, since the output of some control channels is truncated by the limiting operator, the mapping relationship of the closed-loop system changes accordingly.

[0042] Step S5: When the nonlinear mapping characteristics between voltage and reactive power satisfy the preset incremental sector bounded condition, construct a linear matrix inequality stability criterion for the unsaturated subspace, and transform the linear matrix inequality stability criterion into a semi-positive definite programming problem for solution to obtain the stability determination result of the automatic voltage control closed-loop system.

[0043] After completing the above sampling data system modeling, in order to analyze and determine the stability state and oscillation mode of the automatic voltage control closed-loop system, a stability criterion is further constructed in this embodiment.

[0044] For unsaturated subspaces Set the voltage-reactive nonlinear mapping function The incremental sector is bounded, that is: Or equivalently represented as: in, This represents the increment of the augmented state variable from the steady state. This is a steady-state augmented state; This represents the increment of the output voltage from the steady state. Choose a matrix for the state; and The parameter matrix for the bounded conditions of incremental sectors is determined by local linearization of power flow calculation, identification of historical operating data, or estimation of the upper and lower bounds of the power flow Jacobian matrix. Under the condition that the incremental sector is bounded, a stability criterion in the form of a linear matrix inequality is constructed, expressed as: in, For unsaturated subspace The closed-loop state matrix; For unsaturated subspace The closed-loop input matrix; It is a symmetric positive definite matrix; is the contraction factor, representing the rate of contraction of the augmented state variable trajectory; If a symmetric positive definite matrix exists and contractile factor If ∈[0,1), then the system is in the unsaturated subspace. The condition that the trajectory of the augmented state variable converges to a stable operating state is satisfied, thus constituting a stability criterion for characterizing the convergence characteristics of the trajectory of the augmented state variable.

[0045] Furthermore, the stability criterion is transformed into a semidefinite programming problem, expressed as: in, It is a symmetric positive definite matrix used to determine the convergence of the trajectory of the augmented state variable; It is a contraction factor; These are the optimization variables for a semidefinite programming problem. It is the identity matrix; These are the non-triggered amplitude-limiting subspaces. The closed-loop state matrix and the closed-loop input matrix; Choose a matrix for the state; and The parameter matrix represents the bounded conditions for incremental sectors; The semidefinite programming problem is solved by a convex optimization solver. When a feasible solution exists for the semidefinite programming problem, the automatic voltage control closed-loop system is determined to satisfy the stability criterion in the unsaturated subspace, and the system is determined to converge and have a unique equilibrium point. When no feasible solution exists for the semidefinite programming problem, the stability criterion cannot provide sufficient guarantee under the current parameter conditions.

[0046] Example 2: In one embodiment, the method of the present invention is verified by a numerical simulation based on a computational example system. A simulation system is constructed based on data from a data collection system of a certain new energy base. Figure 5The topology of the 3-machine, 6-node example system is shown in Table 1. The parameters of the example system are shown in Table 1.

[0047] Table 1 Two scenarios were designed for the simulation system: Scenario 1: Feedback matrix K=diag([8,8,8]), PI coefficients of reactive power compensation equipment Kp=[0.1,0.1,0.1], Ki=[0.4,1.2,1.2]; Scenario 2: Feedback matrix K=diag([5,5,5]), PI coefficients of reactive power compensation equipment Kp=[0.1,0.1,0.1], Ki=[0.4,1.2,1.2].

[0048] For two scenarios, time-domain simulations were modeled and run for over 100 seconds in Matlab / Simulink. Simultaneously, based on the closed-loop discrete dynamics model established in steps 1-4, initial states identical to those in the time-domain simulation were set, and step-by-step calculations were performed. The calculation results were compared... Figure 6 As shown in the figure, the solid line represents the time-domain simulation waveform, and the dots represent the step-by-step calculation results of the discrete dynamics model. It can be seen that the solid line passes through the dots, indicating that the calculation results of the established model are almost equal to the values ​​of the simulation waveform at the sampling time. The results show that the sampling data model established by this invention can accurately characterize the dynamic state of the system at the sampling time.

[0049] Set the shrinkage rate η = 0.999, solve the positive semidefinite optimization problem in step 5 for scenarios 1 and 2 respectively, and then convert the results of the positive semidefinite optimization solution into the desired value. α Table 2 summarizes the stability characteristics represented by the value, stability criterion, and time-domain simulation results. As can be seen from the table, the stability of scenario 1... α <0, the criterion proposed in this invention determines that the system is unstable, and simulation results show that the system gradually diverges and eventually enters a constant-amplitude oscillation state; Scenario 2 α If the value is greater than 0, the stability criterion of this invention determines that the system is stable, and simulation results show that the system converges to a single point. The results demonstrate that the stability criterion constructed in this invention can effectively distinguish between stable and unstable operating states of the system under different scenarios.

[0050] Table 2 Example 3: In one embodiment, such as Figure 7As shown, the present invention also provides a sampling data modeling and stability determination system for implementing the above method. The system includes a parameter acquisition module, a sampling data modeling module, an augmentation modeling module, a closed-loop mapping construction module, a segmented mapping module, and a stability determination module. The parameter acquisition module is used to acquire the master station control cycle, equivalent time delay, dynamic parameters of continuously adjustable reactive power resources, control command limit value, and voltage-reactive power nonlinear mapping characteristics of the automatic voltage control closed-loop system. The sampling data modeling module is used to establish a continuous-time state model and perform discretization processing to obtain a discrete state update model containing the control command of the current cycle and the control command of the previous cycle. The augmented modeling module is used to construct augmented state variables containing state variables and the control command of the previous cycle. The closed-loop mapping construction module is used to establish a unified closed-loop discrete mapping relationship by combining the voltage-reactive power nonlinear mapping characteristics, control law, and limit constraint. The piecewise mapping module is used to divide the unsaturated subspace and saturated subspace according to the control command limit state and establish the piecewise discrete mapping relationship corresponding to each subspace. The stability determination module is used to construct a linear matrix inequality stability criterion and transform it into a semidefinite programming problem for solution to output the stability determination result.

[0051] The above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for determining the stability of an automatic voltage control closed-loop system in a new energy base, characterized in that, Includes the following steps: Step S1: Obtain the system parameters of the automatic voltage control closed-loop system. The system parameters include the master station control cycle, equivalent time delay, dynamic parameters of continuously adjustable reactive power resources, control command limit value, and nonlinear mapping characteristics between voltage and reactive power. Step S2: Based on the system parameters, establish a continuous-time state model of continuously adjustable reactive power resources, and combine the zero-order hold characteristic of the master station control command in the master station control cycle and the equivalent time delay to discretize the continuous-time state model to obtain a discrete state update model that simultaneously contains the current cycle control command and the previous cycle control command. Step S3: Based on the discrete state update model, construct an augmented state variable that includes reactive resource state variables and control commands from the previous cycle, and combine the nonlinear mapping characteristics between voltage and reactive power, the preset control law and the control command amplitude limit constraint to establish a unified closed-loop discrete mapping relationship. Step S4: Based on the triggering state of the control command limiting constraint, divide the state space corresponding to the closed-loop discrete mapping relationship to obtain unsaturated subspaces and saturated subspaces, and establish the piecewise discrete mapping relationship corresponding to each subspace. Step S5: When the nonlinear mapping characteristics between voltage and reactive power satisfy the preset incremental sector bounded condition, construct a linear matrix inequality stability criterion for the unsaturated subspace, and transform the linear matrix inequality stability criterion into a semi-positive definite programming problem for solution to obtain the stability determination result of the automatic voltage control closed-loop system.

2. The stability determination method according to claim 1, characterized in that, The establishment of a continuous-time state model for continuously adjustable reactive power resources specifically includes: Based on the dynamic characteristics of continuously adjustable reactive power resources, the internal state of the reactive power resources is selected as the state variable, and the control commands issued by the master station are selected as the input variable. A continuous-time state-space model is established, which is expressed by the formula: in, This represents the state variable of continuously adjustable reactive power resources. Indicates control commands. The state matrix, For the input matrix, Represents state variables Regarding time The first derivative; Based on the control structure of the continuously adjustable reactive power resource and in combination with the dynamic characteristics of the device, the parameters of the state matrix A and the input matrix B are determined.

3. The stability determination method according to claim 1, characterized in that, The discretization of the continuous-time state model to obtain a discrete state update model that simultaneously includes the current cycle control command and the previous cycle control command specifically includes: Within each master station control cycle, the holding characteristics of the control command are described using the zero-order hold method, so that the control command remains unchanged within each control cycle. Based on the equivalent delay, each control cycle is divided into a time interval affected by the control command of the previous cycle and a time interval affected by the control command of the current cycle. Under the zero-order preservation property and equivalent time delay constraints, the continuous-time state model is discretized to obtain a discrete-time state update model, which is expressed by the following formula: in, Indicates the first Each control cycle refers to the state variables of the current control cycle. Indicates the first The state variables corresponding to each control cycle Indicates the first Control commands for each control cycle Indicates the first Each control cycle is the control command from the previous control cycle. The discrete state transition matrix, This is the control command action matrix for the current cycle. This is the matrix representing the action of the control commands from the previous cycle; The discrete state transition matrix and the aforementioned action matrix and They are determined in the following ways: in, This represents the state matrix in a continuous-time state model. This represents the input matrix in a continuous-time state model. Indicates the main station control cycle. Indicates the equivalent delay. Let represent the integral variable, and the equivalent time delay satisfies: .

4. The stability determination method according to claim 1, characterized in that, Based on the discrete state update model, an augmented state variable is constructed that includes reactive resource state variables and control commands from the previous cycle, specifically including: The augmented state variable is represented as: in, Indicates the first Augmented state variables for each control cycle This represents the state variables of the current control cycle. Indicates the control command from the previous control cycle; Based on the discrete state update model, the update relationship of the augmented state variables is expressed as follows: in, Indicates the first Augmented state variables for each control cycle This represents the augmented state transition matrix. Represents the control input matrix; The augmented state transition matrix and control input matrix They are represented as follows: in, These represent the discrete state transition matrix, the current cycle control command action matrix, and the previous cycle control command action matrix, respectively. Represents the identity matrix.

5. The stability determination method according to claim 1, characterized in that, The establishment of a unified closed-loop discrete mapping relationship, combining the nonlinear mapping characteristics between voltage and reactive power, a preset control law, and control command amplitude constraints, specifically includes: Based on the nonlinear mapping characteristic between voltage and reactive power, the output relationship is established as follows: in, Indicates the first Voltage measurement value for each control cycle This represents a nonlinear mapping function between voltage and reactive power. Indicates operating condition parameters; Based on the aforementioned output relationship and combined with the preset control law, the control command is obtained, expressed as: in, Indicates the first Control commands for each control cycle This represents the feedforward control quantity. The feedback parameter matrix represents the control law. Indicates the voltage reference value; Applying a limiting constraint to the control command yields the actual control command, expressed as: in, This indicates the control command after amplitude limiting. This represents the limiting operator, used to impose upper and lower limit constraints on control commands; Substituting the actual control command into the update relation of the augmented state variables, the closed-loop state update relation is obtained, expressed as: in, This represents the augmented state transition matrix. Represents the control input matrix; The closed-loop state update relationship is written as a unified closed-loop discrete mapping relationship, expressed as: in, This represents the closed-loop discrete mapping function composed of the nonlinear mapping function, the control law, and the amplitude limiting constraint.

6. The stability determination method according to claim 1, characterized in that, The step of dividing the state space corresponding to the closed-loop discrete mapping relationship according to the triggering state of the control command limiting constraint to obtain unsaturated subspaces and saturated subspaces, and establishing piecewise discrete mapping relationships corresponding to each subspace, specifically includes: augmented state variables value space Based on whether the actual control commands of each control channel reach the upper and lower limits, an unsaturated subspace that does not trigger amplitude limiting is obtained. and several saturated subspaces that trigger amplitude limiting , is represented as: in, This indicates the number of control channels for continuously adjustable reactive power resources; For each state subspace Define the corresponding piecewise closed-loop discrete mapping relationship: in, In the state subspace Below, by augmented state variables Voltage-reactive nonlinear mapping function Control Law and limiting operator Together they form a closed-loop discrete mapping function; For unsaturated subspaces The closed-loop discrete mapping relationship maintains a linear form: in, For the augmented state transition matrix, To augment the control input matrix, Represents the state selection matrix. Represents the bias vector; For saturated subspace The closed-loop discrete mapping relationship adjusts the control command through the amplitude limiting operator, thereby forming a segmented switching discrete mapping structure: 。 7. The stability determination method according to claim 1, characterized in that, When the nonlinear mapping characteristic between voltage and reactive power satisfies the preset incremental sector bounded condition, a stability criterion for linear matrix inequalities is constructed for the unsaturated subspace, specifically including: For unsaturated subspaces Set the voltage-reactive nonlinear mapping function The incremental sector is bounded, that is: Or equivalently represented as: in, This represents the increment of the augmented state variable from the steady state. This is a steady-state augmented state; This represents the increment of the output voltage from the steady state. Choose a matrix for the state; and The parameter matrix for the bounded conditions of incremental sectors is determined by local linearization of power flow calculation, identification of historical operating data, or estimation of the upper and lower bounds of the power flow Jacobian matrix. Under the condition that the incremental sector is bounded, a stability criterion in the form of a linear matrix inequality is constructed, expressed as: in, For unsaturated subspace The closed-loop state matrix; For unsaturated subspace The closed-loop input matrix; It is a symmetric positive definite matrix; is the contraction factor, representing the rate of contraction of the augmented state variable trajectory; If a symmetric positive definite matrix exists and contractile factor If ∈[0,1), then the system is in the unsaturated subspace. The condition that the trajectory of the augmented state variable converges to a stable operating state is satisfied, thus constituting a stability criterion for characterizing the convergence characteristics of the trajectory of the augmented state variable.

8. The stability determination method according to claim 1, characterized in that, The process of transforming the linear matrix inequality stability criterion into a semi-positive definite programming problem for solution, to obtain the stability determination result of the automatic voltage control closed-loop system, specifically includes: The stability criterion is transformed into a semidefinite programming problem, expressed as: in, It is a symmetric positive definite matrix used to determine the convergence of the trajectory of the augmented state variable; It is a contraction factor; These are the optimization variables for a semidefinite programming problem. It is the identity matrix; These are the non-triggered amplitude-limiting subspaces. The closed-loop state matrix and the closed-loop input matrix; Choose a matrix for the state; and The parameter matrix represents the bounded conditions for the incremental sector. The semidefinite programming problem is solved by a convex optimization solver. When a feasible solution exists for the semidefinite programming problem, the automatic voltage control closed-loop system is determined to satisfy the stability criterion in the unsaturated subspace, and the system is determined to converge and have a unique equilibrium point. When no feasible solution exists for the semidefinite programming problem, the stability criterion cannot provide sufficient guarantee under the current parameter conditions.

9. A stability determination system for an automatic voltage control closed-loop system in a new energy base, characterized in that, include: The parameter acquisition module is used to acquire the system parameters of the automatic voltage control closed-loop system. The system parameters include the master station control cycle, equivalent time delay, dynamic parameters of continuously adjustable reactive power resources, control command limit value, and nonlinear mapping characteristics between voltage and reactive power. The sampling data modeling module is used to establish a continuous-time state model of continuously adjustable reactive power resources based on the system parameters, and to discretize the continuous-time state model by combining the zero-order hold characteristic of the master station control command in the master station control cycle and the equivalent time delay, so as to obtain a discrete state update model that simultaneously contains the control command of the current cycle and the control command of the previous cycle. The augmented modeling module is used to construct an augmented state variable that includes reactive resource state variables and control commands from the previous cycle, based on the discrete state update model. The closed-loop mapping construction module is used to establish a unified closed-loop discrete mapping relationship by combining the nonlinear mapping characteristics between voltage and reactive power, preset control law and control command amplitude limit constraint. The segmented mapping module is used to divide the state space corresponding to the closed-loop discrete mapping relationship according to the triggering state of the control command limiting constraint, to obtain unsaturated subspaces and saturated subspaces, and to establish the segmented discrete mapping relationship corresponding to each subspace. The stability determination module is used to construct a linear matrix inequality stability criterion for the unsaturated subspace when the nonlinear mapping characteristics between voltage and reactive power meet the preset incremental sector bounded condition, and to transform the linear matrix inequality stability criterion into a semi-positive definite programming problem for solution, so as to obtain the stability determination result of the automatic voltage control closed-loop system.

10. The stability determination system for the automatic voltage control closed-loop system of the new energy base according to claim 9, characterized in that, The stability determination module is also used for: When a feasible solution exists for the semidefinite programming problem, it is determined that the automatic voltage control closed-loop system satisfies the contraction condition in the unsaturated subspace, and based on this, it is determined that the system converges and the equilibrium point is unique. When no feasible solution exists for the semidefinite programming problem, it is determined that the stability criterion cannot provide sufficient guarantees under the current parameter conditions.

Images