Power system output differential passivity-based observation method based on input-state trajectory

Abstract

The application discloses a power system output differential passivity measurement method based on input-state trajectory, which comprises the following steps: S1, input state trajectory data is acquired; S2, data normalization processing is performed; S3, a linear matrix inequality constraint is constructed; based on the normalized matrix in S2, the definition of output differential passivity is extended to the form of a matrix inequality constraint; and S4, an optimal output differential passivity index is solved. The power system output differential passivity measurement method based on input-state trajectory can further check the output differential passivity of the power system and calculate an optimal output differential passivity index under the condition that the internal parameters of equipment are not dependent, the equilibrium point is not known in advance and measurement noise exists, by means of the measured input state trajectory.

Description

Technical Field

[0001] This invention belongs to the field of power system stability analysis and control technology, specifically relating to a passive measurement method for the output differential of a power system based on input-state trajectories. Background Technology

[0002] With the popularization of new energy sources and DC transmission technology, a large number of power electronic devices with highly nonlinear and strongly coupled characteristics are connected to the power grid, making the dynamic characteristics of the system increasingly complex. Output differential passivity theory, as an analytical tool from the perspective of incremental energy, can map complex internal dynamics into port characteristics. Utilizing the stability principles of interconnected systems, it has become crucial for ensuring the safe grid connection of large-scale heterogeneous equipment. Especially in the research, design, testing, and analysis phases of power system equipment, researchers can obtain real-time state variables within the equipment. Unlike "black box" operation and maintenance scenarios that rely solely on port input and output information, fully utilizing this high-dimensional "input-state" data can more accurately capture the evolution of nonlinear dynamics within the system, providing direct evidence for locating the root causes of instability and optimizing control parameters.

[0003] Currently, there are two main technical approaches for output differential passivity analysis of power systems: First, the Jacobian matrix analysis method based on physical models. Its core idea is to use the system's Jacobian matrix and, through algebraic derivation, determine the incremental energy characteristics of the system in state space. Second, the passivity analysis method based on input-state trajectory. This method uses input-state trajectory data to establish linear matrix inequalities and then uses positive semidefinite optimization to determine whether the system satisfies conventional passivity.

[0004] However, the two existing technologies mainly face the following technical challenges: First, accurate physical models are difficult to obtain. Existing methods rely on detailed internal parameters and topology of the device. Due to the high-order nonlinearity and time-varying characteristics of heterogeneous devices, it is difficult to construct accurate mathematical models. Second, existing data-driven methods have limited metrics and cannot measure the output differential passivity. Existing methods based on "input-state" trajectories typically only measure the conventional passivity of the system and cannot characterize the incremental behavior of the system state between dynamic trajectories. Therefore, existing technologies cannot achieve the measurement of more general and refined output differential passivity, making it difficult to meet the needs of stability analysis for complex nonlinear systems. Summary of the Invention

[0005] The purpose of this invention is to provide a method for measuring the passive output differential property of a power system based on input-state trajectories. By measuring the input state trajectory, the passive output differential property of the power system can be further checked and the optimal passive output differential property index can be calculated without relying on internal equipment parameters, without needing to know the equilibrium point, and even with measurement noise.

[0006] The technical solution adopted in this invention is:

[0007] A passive measurement method for the output differential of a power system based on input-state trajectories is described below: S1. Acquire input state trajectory data: Acquire and process input-state trajectory data under non-ideal measurement environment, and construct input and state data matrix; S2. Data normalization processing: Mapping the input and state trajectory data to a dimensionless normalized space; S3. Construct linear matrix inequality constraints: Based on the normalized matrix in S2, extend the definition of the sourcelessness of the output differential to the form of matrix inequality constraints; S4. Solve for the optimal output differential passivity index: Construct an optimization model with the goal of maximizing the output differential passivity index, and solve for the index using the positive semidefinite optimization method.

[0008] The invention is further characterized by: Before processing S1, we first define the energy storage function of the discrete-time system as a quadratic form:

[0009] in, for The system state vector at time t. Let be the positive definite symmetric matrix to be solved, where ; According to the theory of output differential passivity, if the system is output differential passivity, then the change in its incremental storage function should be less than or equal to the incremental supply rate, using the following form of differential supply rate:

[0010] in, For system input, For system output, The output is a differential passivity index, the magnitude of which reflects the system's ability to suppress port disturbances; Therefore, the dissipation inequality that satisfies the output differential passivity condition can be expressed as:

[0011] That is, the increase in system energy should not exceed the incremental energy of the port input.

[0012] In S1, the non-ideal measurement environment specifically refers to the operating condition in which, due to the limitations of instrument transformer accuracy or environmental interference, the input status data collected at the port of the power system is superimposed with random measurement noise during actual operation.

[0013] The specific method for S1 is as follows: First, consider the following linear time-invariant system: (1) in, ;where the matrix A, B Unknown, matrix C Known; For a range of continuously acquired state and input data under a non-ideal measurement environment, the following matrix is ​​constructed: Assume the time window length for data collection is... The matrix is ​​constructed as follows: Current state matrix : ; Next-moment state matrix : ; Input data matrix : ; At this point, when the state data matrix is ​​known, it can be solved through a simple linear transformation. Obtain the output data matrix Output data matrix : ; The trajectory of the measured input and state needs to have sufficient information and must satisfy the following matrix rank condition: (2) in, The dimension of the system state variables. The dimension of the input variables. This represents the number of sampling points; Define the extended matrix ,like This indicates that the input signal stimulation within the current window is insufficient, and the dynamic information contained in the data is incomplete; if This indicates that the data meets the incentive conditions; Considering the non-ideal measurement environment under real-world conditions, namely measurement noise and system nonlinear characteristics in the actual power grid environment, a multi-cycle averaging method is used to extract input state trajectory data. The data points from this data are then extracted to meet the condition that the number of sampling points equals the rank of the extended matrix, and combined to form the input data matrix. State data matrix .

[0014] The multi-period averaging method refers to the method of superimposing and averaging multiple periodic data points by applying a periodic excitation signal and utilizing the periodicity of the system response to cancel random noise and extract the true steady-state data trajectory of the system that satisfies the rank condition.

[0015] The specific method for S2 is as follows: For the state and output data matrix after multi-period averaging in S1, calculate the Euclidean norm of each row of state variables and construct a diagonal scaling matrix. , , : (3) (4) (5) in and Representing the Euclidean norm of the time series of state components and output components; Define the normalized state trajectory and output trajectory and input trajectory The relationship between them is as follows: (6) (7) in, These are the normalized dimensionless state matrix, output matrix, and input matrix; This is the normalized equivalent observation matrix.

[0016] The specific method for S3 is as follows: Based on the normalized matrix above, the definition of the absence of source of output differential is extended to matrix form, and the intermediate variable matrix is ​​defined. : (8) in, , These are the normalized system state trajectory data matrices for the current and next time moments, respectively. ; The input trajectory sequence is normalized. , To output the differential passivity index; Furthermore, the necessary and sufficient condition for the system to satisfy the output differential passivity condition is the existence of a positive definite matrix. This makes the following linear matrix inequality hold: (9).

[0017] The specific method for S4 is as follows: Based on the linear matrix inequalities in S3, a method is constructed to maximize the output differential passivity index. The trace is the target, and it satisfies the positive definite symmetric matrix. The semidefinite programming convex optimization model is as follows:

[0018] (10)

[0019] Solving the above optimization model yields the optimal solution, which is the optimal output differential passive performance index in the normalized space. To ensure the convergence stability of the algorithm under noise interference, a numerical tolerance relaxation configuration is introduced, that is, the original feasibility tolerance, dual feasibility tolerance, and relative gap criterion of the solver are all relaxed to... Construct a relaxed constraint system; The optimal solution in the normalized space is obtained based on the above relaxed constraint system. Then, it needs to be mapped back to physical space to evaluate the actual output differential passivity of the system; according to the normalization transformation relation constructed in S2, the output differential passivity matrix in physical space is... It can be obtained from normalization Solution: (11) Finally, extract the matrix. The minimum value of the diagonal elements is taken as the final measurement index characterizing the physical dissipation properties of the system. : (12) at this time, This refers to the passive measurement index of the output differential of the power system under test under the current operating conditions.

[0020] The beneficial effects of this invention are: (1) The present invention is a power system output differential passivity measurement method based on input-state trajectory. First, the input state trajectory data is acquired and normalized. Based on the normalized matrix, the definition of output differential passivity is extended to the form of matrix inequality constraint. Finally, the optimal output differential passivity index is solved. This method is based entirely on the measured input-state trajectory to determine the output differential passivity of the system. It does not require knowledge of the specific physical parameters inside the equipment. The calculation method is simple and efficient. It transforms the complex system output differential passivity analysis into a linear matrix inequality constraint problem. (2) The passive measurement method of power system output differential based on input-state trajectory of the present invention can be applied to a variety of dynamic devices, has a good ability to suppress measurement noise, has a wider range of applications and stronger engineering practicality. Attached Figure Description

[0021] Figure 1 This is a schematic diagram illustrating the principle of extracting the input-state trajectory using the multi-cycle averaging method under non-ideal measurement conditions according to the present invention. Detailed Implementation

[0022] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0023] To ensure the successful implementation of this invention, the energy storage function of the discrete-time system is first defined as a quadratic form:

[0024] in, for The system state vector at time t. Let be the positive definite symmetric matrix to be solved, where ; According to the theory of output differential passivity, if the system is output differential passivity, then the change in its incremental storage function should be less than or equal to the incremental supply rate, using the following form of differential supply rate:

[0025] in, For system input, For system output, The output is a differential passivity index, the magnitude of which reflects the system's ability to suppress port disturbances; Therefore, the dissipation inequality that satisfies the output differential passivity condition can be expressed as:

[0026] That is, the increase in system energy should not exceed the incremental energy of the port input.

[0027] This invention relates to a passive measurement method for the output differential of a power system based on input-state trajectories. The specific method is as follows: S1. Acquire input state trajectory data: Acquire and process input-state trajectory data under non-ideal measurement environment, and construct input and state data matrix; Specifically, a non-ideal measurement environment refers to a situation in which, during actual operation of a power system, random measurement noise is superimposed on the input and output data collected at its ports due to limitations in the accuracy of instrument transformers or environmental interference.

[0028] The specific method for S1 is as follows: First, consider the following linear time-invariant system: (1) in, ;where the matrix A, B Unknown, matrix C Known; For a range of continuously acquired state and input data under a non-ideal measurement environment, the following matrix is ​​constructed: Assume the time window length for data collection is... The matrix is ​​constructed as follows: Current state matrix : ; Next-moment state matrix : ; Input data matrix : ; It should be noted that this invention only requires known input and state sequences. When the state data matrix is ​​known, it can be solved through a simple linear transformation. Obtain the output data matrix Output data matrix : ; The trajectory of the measured input and state in this invention needs to have sufficient information and must satisfy the following matrix rank condition: (2) in, The dimension of the system state variables. The dimension of the input variables. This represents the number of sampling points; Define the extended matrix ,like This indicates that the input signal stimulation within the current window is insufficient, and the dynamic information contained in the data is incomplete; if This indicates that the data meets the incentive conditions; Considering the non-ideal measurement environment under real-world conditions, namely measurement noise and system nonlinear characteristics in the actual power grid environment, this invention employs a multi-cycle averaging method to extract input state trajectory data, and extracts the amount of data from it such that the number of sampling points equals the rank of the extended matrix, combining them into an input data matrix. State data matrix .

[0029] Furthermore, the multi-period averaging method refers to the method of superimposing and averaging multiple periodic data points by utilizing the periodicity of the system response under the premise of applying a periodic excitation signal, thereby canceling random noise and extracting the true steady-state data trajectory of the system that satisfies the rank condition.

[0030] To visually illustrate the denoising effect of this method, we will use... Figure 1The following example uses a standard signal model for illustration. Figure 1 As shown, a unit sine function perturbed by 5% noise is set as the signal to be processed, where the dashed lines represent the trajectories of each period, and the solid lines represent the trajectories after multi-period averaging. This invention samples the data in the period after multi-period averaging. It should be noted that not all data points within that period are sampled at a step size; instead, the number of sampling points is selected to exactly satisfy the aforementioned extended matrix rank condition. Finally, the sequence is used for data normalization preprocessing in S2.

[0031] S2. Data Normalization Processing: Mapping the input and state trajectory data to a dimensionless normalized space; the specific method is as follows: For the state and output data matrix after multi-period averaging in S1, calculate the Euclidean norm of each row of state variables and construct a diagonal scaling matrix. , , : (3) (4) (5) in and Representing the Euclidean norm of the time series of state components and output components; At this point, the normalized state trajectory is defined. and output trajectory and input trajectory The relationship between them is as follows: (6) (7) in, These are the normalized dimensionless state matrix, output matrix, and input matrix; The normalized equivalent observation matrix represents the linear mapping relationship from the normalized state space to the output space.

[0032] S3. Constructing linear matrix inequality constraints: Based on the normalized matrix in S2, the definition of the absence of source of output differential is extended to the form of matrix inequality constraints. The specific method is as follows: Based on the normalized matrix described above, this invention extends the definition of the passivity of output differential to matrix form, defining the intermediate variable matrix. : (8) in, , These are the normalized system state trajectory data matrices for the current and next time moments, respectively. ; The input trajectory sequence is normalized. , To output the differential passivity index; Furthermore, the necessary and sufficient condition for the system to satisfy the output differential passivity condition is the existence of a positive definite matrix. This makes the following linear matrix inequality hold: (9).

[0033] It should be noted that the process of constructing the above linear matrix inequality constraints depends only on the data matrix. , , It does not involve any physical parameters of the internal mechanism of the device.

[0034] S4. Solving for the optimal output differential passivity index: Construct an optimization model with the objective of maximizing the output differential passivity index, and solve for the index using the positive semidefinite optimization method. The specific method is as follows: Based on the linear matrix inequality in S3, this invention transforms the identification of the system's output differential passivity into a positive semidefinite programming convex optimization problem, constructing a method to maximize the output differential passivity index. The trace is the target, and it satisfies the positive definite symmetric matrix. The semidefinite programming convex optimization model is as follows:

[0035] (10)

[0036] Solving the above optimization model yields the optimal solution, which is the optimal output differential passive performance index in the normalized space. To ensure the convergence stability of the algorithm under noise interference, a numerical tolerance relaxation configuration is introduced, that is, the original feasibility tolerance, dual feasibility tolerance, and relative gap criterion of the solver are all relaxed to... A relaxed constraint system is constructed; the objective function is allowed to float within a small range, thereby avoiding iteration interruption caused by data noise and ensuring the smooth calculation of the optimal solution.

[0037] The optimal solution in the normalized space is obtained based on the above relaxed constraint system. Then, it needs to be mapped back to physical space to evaluate the actual output differential passivity of the system; according to the normalization transformation relation constructed in S2, the output differential passivity matrix in physical space is... It can be obtained from normalization Solution: (11) Finally, extract the matrix. The minimum value of the diagonal elements is taken as the final measurement index characterizing the physical dissipation properties of the system. : (12) at this time, This refers to the passive measurement index of the output differential of the power system under test under the current operating conditions.

[0038] Example 1 In this embodiment, the node voltage phase angle and amplitude are selected as the system state, i.e. The active and reactive power outputs of the equipment are selected as the control inputs, i.e. In this embodiment, the output vector is consistent with the state vector, that is... .

[0039] Step 1: Input-State Trajectory Data Processing under Non-Ideal Measurement Environment Define the parameters related to the multi-period averaging method: , , , .in The period of the input signal, To meet the effective cutoff time set for the continuous incentive conditions, For the total measurement time, This is the sampling step size.

[0040] In the range of 0 to 200 s The system acquires raw input-state response data in a noisy environment over a period of time.

[0041] The 200 collected s The original data is according to The data is divided into 100 periodic data segments. An average is calculated along the periodic dimension of these 100 data segments to obtain a value between 0 and 2. s Single-cycle average trajectory data.

[0042] The single-period average trajectory data is truncated, retaining only the range of 0 to 1.6. s The data segment. By extracting the data sequence within this range, and assembling it into a state matrix according to the aforementioned data structure definition of this invention. The state matrix at the next time step and input data matrix Construct a combination matrix Calculate the rank of its matrix.

[0043] In this case, the calculation , which satisfies the rank condition.

[0044] Step 2: Perform normalization preprocessing on the extracted data. Based on the single-cycle truncated data matrix obtained in step 1, the row vector norms of the state and output are calculated respectively, and a diagonal scaling matrix is ​​constructed.

[0045] State scaling matrix Calculate the state matrix The Euclidean norm of each row is formed by taking its reciprocal. diagonal matrix .

[0046] Output scaling matrix Because this embodiment uses Output matrix With the state matrix The values ​​are the same. Calculate the reciprocal of its row norm and construct... diagonal matrix .

[0047] Input scaling matrix Construct using the row norm of the output matrix Input scaling matrix .

[0048] Using the scaling matrix described above, the original physical data is normalized and dimensionless mapped to obtain the normalized current state. Next moment state Input at the current time and the equivalent observation matrix in normalized space .

[0049] Step 3: Construct linear matrix inequality constraints Using the numerical matrix determined in step 1 Build intermediate items :

[0050] It should be noted that at this time All values ​​are known. Only matrices A linear function.

[0051] Based on this, the following specific linear matrix inequality constraints are established: Positive definiteness constraints:

[0052] Output differential passivity constraint: (13) At this point, the system of linear matrix inequalities based on the sampled data is complete.

[0053] Step 4: Output the differential passivity index based on the optimal solution of the semidefinite programming problem. This step, based on the linear matrix inequality constraints established in step 3, uses a positive semidefinite optimization algorithm to solve for the optimal output differential passivity index. To obtain the most compact output differential passivity index for the system within the current window, the output differential passivity analysis is transformed into the following convex optimization problem:

[0054] (14)

[0055] In this example, the MOSEK solver is used to solve the above problem. The solution accuracy tolerance is set to [value missing]. At this point, we obtain... .

[0056] At this point, the original space can be restored, and the calculation yields: (15) Finally, extract the matrix. The minimum value of the diagonal elements is taken as the final measurement index characterizing the physical dissipation properties of the system. : (16) at this time, This refers to the passive measurement index of the output differential of droop control under the current operating conditions.

[0057] To verify the accuracy of the data-driven method proposed in this invention, the above measurement results are compared with the theoretical true values ​​derived based on the physical model parameters. The system physical parameters are pre-set as inherent properties of the object under test and are used only to generate simulation data and provide a theoretical verification benchmark. The theoretical maximum under this operating condition... The value is obtained by taking the intersection of the lower bounds of the following two inequalities: (17) Based on the physical parameters set above, the theoretical output differential passivity index of the system is... The calculation is as follows: (18) The comparison shows that the measurement results obtained by the present invention under the condition of unknown model parameters are basically consistent with the theoretical true value, with a relative error of only 0.6%, which verifies the effectiveness of the method of the present invention.

[0058] Example 2 A passive measurement method for the output differential of a power system based on input-state trajectories is described below: S1. Acquire input state trajectory data: Acquire and process input-state trajectory data under non-ideal measurement environment, and construct input and state data matrix; In S1, the non-ideal measurement environment specifically refers to the operating condition in which, due to the limitations of instrument transformer accuracy or environmental interference, the input status data collected at the port of the power system is superimposed with random measurement noise during actual operation.

[0059] S2. Data normalization processing: Mapping the input and state trajectory data to a dimensionless normalized space; S3. Construct linear matrix inequality constraints: Based on the normalized matrix in S2, extend the definition of the sourcelessness of the output differential to the form of matrix inequality constraints; S4. Solve for the optimal output differential passivity index: Construct an optimization model with the goal of maximizing the output differential passivity index, and solve for the index using the positive semidefinite optimization method.

[0060] Example 3 The specific method for S1 is as follows: First, consider the following linear time-invariant system: (1) in, ;where the matrix A, B Unknown, matrix C Known; For a range of continuously acquired state and input data under a non-ideal measurement environment, the following matrix is ​​constructed: Assume the time window length for data collection is... The matrix is ​​constructed as follows: Current state matrix : ; Next-moment state matrix : ; Input data matrix : ; At this point, when the state data matrix is ​​known, it can be solved through a simple linear transformation. Obtain the output data matrix Output data matrix : ; The trajectory of the measured input and state needs to have sufficient information and must satisfy the following matrix rank condition: (2) in, The dimension of the system state variables. The dimension of the input variables. This represents the number of sampling points; Define the extended matrix ,like This indicates that the input signal stimulation within the current window is insufficient, and the dynamic information contained in the data is incomplete; if This indicates that the data meets the incentive conditions; Considering the non-ideal measurement environment under real-world conditions, namely measurement noise and system nonlinear characteristics in the actual power grid environment, a multi-cycle averaging method is used to extract input state trajectory data. The data points from this data are then extracted to meet the condition that the number of sampling points equals the rank of the extended matrix, and combined to form the input data matrix. State data matrix .

[0061] Among them, the multi-period averaging method refers to the method of superimposing and averaging multiple periodic data under the premise of applying a periodic excitation signal, taking advantage of the periodicity of the system response, thereby canceling random noise and extracting the true steady-state data trajectory of the system that satisfies the rank condition.

[0062] Example 4 The specific method for S2 is as follows: For the state and output data matrix after multi-period averaging in S1, calculate the Euclidean norm of each row of state variables and construct a diagonal scaling matrix. , , : (3) (4) (5) in and Representing the Euclidean norm of the time series of state components and output components; Define the normalized state trajectory and output trajectory and input trajectory The relationship between them is as follows: (6) (7) in, These are the normalized dimensionless state matrix, output matrix, and input matrix; This is the normalized equivalent observation matrix.

[0063] Example 5 The specific method for S3 is as follows: Based on the normalized matrix above, the definition of the absence of source of output differential is extended to matrix form, and the intermediate variable matrix is ​​defined. : (8) in, , These are the normalized system state trajectory data matrices for the current and next time moments, respectively. ; The input trajectory sequence is normalized. , To output the differential passivity index; Furthermore, the necessary and sufficient condition for the system to satisfy the output differential passivity condition is the existence of a positive definite matrix. This makes the following linear matrix inequality hold: (9).

[0064] Example 6 The specific method for S4 is as follows: Based on the linear matrix inequalities in S3, a method is constructed to maximize the output differential passivity index. The trace is the target, and it satisfies the positive definite symmetric matrix. The semidefinite programming convex optimization model is as follows:

[0065] (10)

[0066] Solving the above optimization model yields the optimal solution, which is the optimal output differential passive performance index in the normalized space. To ensure the convergence stability of the algorithm under noise interference, a numerical tolerance relaxation configuration is introduced, that is, the original feasibility tolerance, dual feasibility tolerance, and relative gap criterion of the solver are all relaxed to... Construct a relaxed constraint system; The optimal solution in the normalized space is obtained based on the above relaxed constraint system. Then, it needs to be mapped back to physical space to evaluate the actual output differential passivity of the system; according to the normalization transformation relation constructed in S2, the output differential passivity matrix in physical space is... It can be obtained from normalization Solution: (11) Finally, extract the matrix. The minimum value of the diagonal elements is taken as the final measurement index characterizing the physical dissipation properties of the system. : (12) at this time, This refers to the passive measurement index of the output differential of the power system under test under the current operating conditions.

Claims

1. A power system output differential passivity-based observation method based on input-state trajectory, characterized in that, The specific method is as follows: S1. Acquire input state trajectory data: Acquire and process input-state trajectory data under non-ideal measurement environment, and construct input and state data matrix; S2. Data normalization processing: Mapping the input and state trajectory data to a dimensionless normalized space; S3. Construct linear matrix inequality constraints: Based on the normalized matrix in S2, extend the definition of the sourcelessness of the output differential to the form of matrix inequality constraints; S4. Solve for the optimal output differential passivity index: Construct an optimization model with the goal of maximizing the output differential passivity index, and solve for the index using the positive semidefinite optimization method.

2. The power system output differential passivity-based observation method based on input-state trajectory according to claim 1, wherein, Before processing S1, we first define the energy storage function of the discrete-time system as a quadratic form: wherein is the system state vector at the time instant is a positive definite symmetric matrix to be solved, wherein ; According to the theory of output differential passivity, if the system is output differential passivity, then the change in its incremental storage function should be less than or equal to the incremental supply rate, using the following form of differential supply rate: in, For system input, For system output, The output is a differential passivity index, the magnitude of which reflects the system's ability to suppress port disturbances; Therefore, the dissipation inequality that satisfies the output differential passivity condition can be expressed as: That is, the increase in system energy should not exceed the incremental energy of the port input.

3. The passive measurement method for the output differential of a power system based on input-state trajectories according to claim 1, characterized in that, The non-ideal measurement environment in S1 specifically refers to the operating condition in which, due to the limitations of the accuracy of the current transformer or the influence of environmental interference, the input status data collected at the port of the power system is superimposed with random measurement noise during actual operation.

4. The passive measurement method for the output differential of a power system based on input-state trajectories according to claim 3, characterized in that, The specific method of S1 is as follows: First, consider the following linear time-invariant system: （1） in, ;where the matrix A, B Unknown, matrix C Known; For a range of continuously acquired state and input data under a non-ideal measurement environment, the following matrix is ​​constructed: Assume the time window length for data collection is... The matrix is ​​constructed as follows: Current state matrix : ; Next-moment state matrix : ; Input data matrix : ; At this point, when the state data matrix is ​​known, it can be solved through a simple linear transformation. Obtain the output data matrix Output data matrix : ; The trajectory of the measured input and state needs to have sufficient information and must satisfy the following matrix rank condition: （2） in, The dimension of the system state variables. The dimension of the input variables. This represents the number of sampling points; Define the extended matrix ,like This indicates that the input signal stimulation within the current window is insufficient, and the dynamic information contained in the data is incomplete; if This indicates that the data meets the incentive conditions; Considering the non-ideal measurement environment under real-world conditions, namely measurement noise and system nonlinear characteristics in the actual power grid environment, a multi-cycle averaging method is used to extract input state trajectory data. The data points from this data are then extracted to meet the condition that the number of sampling points equals the rank of the extended matrix, and combined to form the input data matrix. State data matrix .

5. The passive measurement method for the output differential of a power system based on input-state trajectories according to claim 4, characterized in that, The multi-period averaging method refers to the method of superimposing and averaging multiple periodic data points by utilizing the periodicity of the system response under the premise of applying a periodic excitation signal, thereby canceling random noise and extracting the true steady-state data trajectory of the system that satisfies the rank condition.

6. The passive measurement method for the output differential of a power system based on input-state trajectories according to claim 1, characterized in that, The specific method of S2 is as follows: For the state and output data matrix after multi-period averaging in S1, calculate the Euclidean norm of each row of state variables and construct a diagonal scaling matrix. , , : （3） （4） （5） in and Representing the Euclidean norm of the time series of state components and output components; Define the normalized state trajectory and output trajectory and input trajectory The relationship between them is as follows: （6） （7） in, These are the normalized dimensionless state matrix, output matrix, and input matrix; This is the normalized equivalent observation matrix.

7. The passive measurement method for the output differential of a power system based on input-state trajectories according to claim 1, characterized in that, The specific method of S3 is as follows: Based on the normalized matrix above, the definition of the absence of source of output differential is extended to matrix form, and the intermediate variable matrix is ​​defined. : （8） in, , These are the normalized system state trajectory data matrices for the current and next time moments, respectively. ; The input trajectory sequence is normalized. , To output the differential passivity index; Furthermore, the necessary and sufficient condition for the system to satisfy the output differential passivity condition is the existence of a positive definite matrix. This makes the following linear matrix inequality hold: （9）。 8. The passive measurement method for the output differential of a power system based on input-state trajectories according to claim 1, characterized in that, The specific method of S4 is as follows: Based on the linear matrix inequalities in S3, a method is constructed to maximize the output differential passivity index. The trace is the target, and it satisfies the positive definite symmetric matrix. The semidefinite programming convex optimization model is as follows: （10） Solving the above optimization model yields the optimal solution, which is the optimal output differential passive performance index in the normalized space. To ensure the convergence stability of the algorithm under noise interference, a numerical tolerance relaxation configuration is introduced, that is, the original feasibility tolerance, dual feasibility tolerance, and relative gap criterion of the solver are all relaxed to... Construct a relaxed constraint system; The optimal solution in the normalized space is obtained based on the above relaxed constraint system. Then, it needs to be mapped back to physical space to evaluate the actual output differential passivity of the system; according to the normalization transformation relation constructed in S2, the output differential passivity matrix in physical space is... It can be obtained from normalization Solution: （11） Finally, extract the matrix. The minimum value of the diagonal elements is taken as the final measurement index characterizing the physical dissipation properties of the system. : （12） at this time, This refers to the passive measurement index of the output differential of the power system under test under the current operating conditions.

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