Transient voltage stability constraint iterative solution method based on mechanism interpretation

Abstract

The invention discloses a transient voltage stability constraint iterative solution method based on mechanism explanation, which comprises the following steps of: establishing a transient voltage stability mechanism analysis framework combining qualitative analysis and quantitative analysis, identifying key factors influencing transient voltage stability through qualitative analysis, analyzing a response trend under a set condition, and calculating a transient voltage stability constraint iterative solution. Obtaining the range of the key characteristic value; local interpretation of the LIME is expanded to global interpretation, so that an interpretable analysis result of the LIME can be applied to an optimization problem; building an under-voltage load reduction model, and adding transient voltage stability constraint on the basis of the traditional load reduction model; building a constraint iteration solving algorithm based on sequential LIME to obtain an optimal load reduction scheme for guaranteeing the transient voltage stability of the system; and performing fault simulation on the traditional solution and the optimal solution considering the stability constraint, simulating the condition that the system operation is disturbed, and observing whether the transient voltage can be recovered to the standard level or not.

Description

Technical Field

[0001] The present invention relates to the technical field of interpretability analysis and optimization of transient voltage stability mechanisms of low-inertia power systems, and in particular to an iterative solution method for transient voltage stability constraints based on mechanism interpretation. Background Art

[0002] Energy is a key material resource to promote economic and social progress, and it is also one of the main sources of carbon emissions. On the basis of ensuring the security of energy supply, we should actively promote the replacement strategy of renewable energy and accelerate the establishment of a clean, low-carbon energy system that is both safe and efficient. Renewable energy such as wind power and solar power can effectively reduce the pollution caused by coal due to its clean and carbon-free characteristics. With the construction of new power systems and the continuous reform of the power system, my country's installed capacity in renewable energy such as wind power and solar power continues to increase, which not only promotes the clean and low-carbon transformation of energy, but also promotes the development of the power market and has achieved remarkable results.

[0003] However, the large-scale integration of renewable energy into the power grid will reduce the inertia of the power system. With the rapid increase in the access ratio of renewable energy and the load demand of the power system, the low inertia characteristics become more obvious, and the operating state of the system is getting closer and closer to the edge of voltage stability, which increases the risk of voltage instability. At the same time, the power system is currently facing more and more external interference and a decline in voltage regulation ability due to the high penetration rate of renewable energy. Therefore, exploring the interpretable analysis mechanism of transient voltage stability mechanism, and how to construct and solve the transient voltage stability constraints in the operation and dispatch of low-inertia power systems, has become an important research topic that needs to be solved urgently.

[0004] Common methods for transient voltage stability assessment include time-domain simulation, direct method, and machine learning methods. Although machine learning methods are becoming more and more popular and are often able to make accurate predictions and assessments, they lack interpretability and transparency to grid dispatchers, which limits their scope of application. Relevant reports point out that the application of machine learning in power systems is accompanied by risks related to model security and application security. Therefore, studying the mechanism of transient voltage stability and how to reveal the internal process behind the black box model has become an important research topic. Since transient voltage stability involves multiple factors and complex dynamic processes, and the mathematical motor model is a high-order nonlinear equation, this makes the analysis difficult.

[0005] As a new interpretable technology, the model-agnostic local interpreter (LIME) is expected to solve the above problems. So far, there are few studies that use LIME for interpretability analysis and apply the interpretation results. For example, the black-box model for wind power forecasting using LIME: Why should a model be trusted? (M. Yang, C. Xu, Y. Bai, M. Ma, and X. Su, "Investigating black-box model for wind power forecasting using local interpretable model-agnostic explanations algorithm: Why should a model be trusted?," CSEE J. Power Energy Syst., pp. 1–14, 2023. doi: 10.17775 / CSEEJPES.2021.07470.) uses the LIME method to study the black-box model for wind power forecasting, analyzes the importance of each feature in different scenarios, and compares it with prior knowledge. However, LIME only provides local explanations for a single sample, which hinders the overall understanding of the entire model output, and most applications of LIME focus on explaining prediction results, lacking research on how its interpretable results can guide operation optimization.

[0006] The transient voltage stability of the power system is a complex problem, which is related to its power flow, grid structure and dynamic characteristics of the power system. The constraint construction of the transient voltage stability optimization problem can be decomposed into two steps. The first step is to use LIME to quantify the boundary conditions of the key characteristics of transient voltage stability. The second step is to use the iterative solution idea to gradually expand the local interpretability to the global interpretability, and finally obtain the operating point that meets the transient voltage stability conditions. Based on the above ideas, the key factors affecting transient voltage stability are determined by exploring the transient voltage stability mechanism, and LIME is used to convert the impact of key factors on the transient voltage stability of the system into constraints. Finally, the operating point is iteratively solved to obtain the optimal solution considering the transient voltage stability optimization problem. Summary of the invention

[0007] The purpose of the present invention is to solve the above-mentioned defects in the prior art and provide a constrained iterative solution method suitable for transient voltage stability optimization problems. The constrained iterative solution method performs qualitative and quantitative analysis on the transient voltage stability mechanism, studies how the power grid flow, power grid structure and the dynamic characteristics of the power system affect the transient voltage stability, and how to use the interpretable results of LIME to apply to the constraint construction. Different from existing studies, the constrained iterative solution method can consider the improvement of transient voltage stability in ordinary optimization problems, and from the transient voltage stability interpretability mechanism, obtain the expression of transient voltage stability constraints, help improve the transient voltage stability of the system, and obtain a system with improved transient voltage stability compared to the initial result on the basis of satisfying the constraints of the initial model optimization problem, and can be widely used in various scenarios.

[0008] The present invention is achieved by at least one of the following technical solutions.

[0009] A transient voltage stability constraint iterative solution method based on mechanism interpretation includes the following steps:

[0010] S1. Build a transient voltage stability mechanism analysis framework that combines qualitative analysis with quantitative analysis, identify key factors affecting transient voltage stability through qualitative analysis, analyze the response trend under set conditions, and derive the range of key characteristic values;

[0011] S2. Extend the local interpretation of the model-agnostic local interpreter LIME to the global interpretation, so that the interpretable analysis results of the model-agnostic local interpreter LIME can be applied to optimization problems;

[0012] S3. Build an undervoltage load reduction model and add transient voltage stability constraints based on the traditional load reduction model;

[0013] S4. Build a constrained iterative solution algorithm based on the sequential agnostic model local interpreter LIME to solve the load reduction model considering transient voltage stability constraints, and obtain the optimal load reduction plan to ensure the transient voltage stability of the system.

[0014] S5. After obtaining the optimal load reduction plan to ensure the transient voltage stability of the system, fault simulation is performed on the traditional solution and the optimized solution considering the stability constraint to simulate the situation where the system operation encounters disturbances and observe whether the transient voltage can be restored to the standard level.

[0015] Furthermore, step S1 includes the following steps:

[0016] S1.1) Select transient voltage stability indicators to evaluate the stability of the system:

[0017] S1.2) Conduct qualitative analysis on transient voltage stability mechanism;

[0018] S1.3) Combined with the LIME interpreter, an analysis framework combining qualitative analysis and quantitative analysis is built. The key factors affecting transient voltage stability identified through qualitative analysis help understand the potential response trend of the system under specific conditions. The key influencing features selected from the qualitative analysis are used as input interpretable features for the construction of the agnostic model local interpreter LIME to obtain the local interpretation of the target sample to determine the ranking and specific value range of feature importance; the key nodes are identified from the feature value range obtained from the quantitative analysis, and the load safety thresholds of these nodes are determined to ensure the transient voltage stability and safety of the system.

[0019] Furthermore, the improved voltage recovery index IVRI is used to evaluate the severity of FIDVR:

[0020]

[0021]

[0022] Where N is the number of buses in the system, VSI i is the voltage deviation index of bus i, V i,0 is the voltage amplitude of bus i before the fault; V i,t is the voltage amplitude of bus i at time t after the disturbance; t c is the fault clearing time; T is the end time of the time domain simulation; is the reference voltage recovery curve of bus i; V i,max is the rated voltage amplitude of bus i; a is the curve recovery rate; the smaller the IVRI value, the better the performance of restoring transient voltage stability; in the case of voltage instability, the IVRI of the system is obtained by adding the IVRI of all buses. IVRI sets the voltage threshold to the voltage amplitude before the disturbance and deviates the voltage trajectory from the absolute value of the voltage threshold. The failure recovery rate is taken into account by multiplying the penalty factor associated with the recovery rate.

[0023] Furthermore, the qualitative analysis comprises the following steps:

[0024] Firstly, the experimental samples are generated by time domain simulation. By changing the fault location, fault duration, and active and reactive power requirements of the load nodes, different samples are generated for time domain simulation, and the IVRI value of each sample is calculated.

[0025] Then the load nodes are classified and the relationship between the load disturbance degree and IVRI value in the sample is statistically analyzed;

[0026] Then, the switch states are changed to construct different network topologies and the previous procedures are repeated to mark the key nodes of different network structures and analyze the impact of network structures on transient voltage stability and the distribution of key load nodes;

[0027] Finally, the renewable energy integration position is changed: renewable energy is randomly integrated at four key nodes, and the experimental steps are performed again to observe the impact of the renewable energy integration position on the system stability. Renewable energy includes wind energy and solar energy.

[0028] Further, step S2 includes the following steps:

[0029] Generate experimental samples using time domain simulation, select an initial sample, and use the model-agnostic local interpreter LIME for local interpretation to obtain the range of eigenvalues;

[0030] The next target sample is determined at the boundary of the eigenvalue range for the next local interpretation. Through multiple iterative processes of local interpretation of different samples, a series of accurate local interpretations and numerical ranges of different operating points are obtained to expand the local interpretation to the global interpretation.

[0031] Furthermore, the main objectives of traditional load shedding models are to minimize load shedding and balance power flow, including:

[0032] Defining ΔP Dj The amount of active power cut for each node, ΔQ Dj Indicates the reactive power reduction at each node, represents an n-dimensional real number set, each element is an n-dimensional vector, and the optimization variable is ΔP Dj and ΔQ Dj , ΔP Dj is related to ΔQ Dj proportional;

[0033] The objective function is to minimize the overall load reduction while ensuring that it meets the stability criteria and follows the network and power flow constraints. The objective function is defined as follows:

[0034]

[0035] Where N is the number of nodes in the system, P LS Indicates the total load reduction;

[0036] The active power P injected by each node j It is defined by the following formula:

[0037]

[0038] Where P Gjrepresents the active power generation of node j, P Dj represents the active load demand of node j, Represents the set of all nodes, the load reduction of active power needs to meet the following constraints:

[0039]

[0040] Furthermore, the formula of the traditional load reduction model P0 is as follows:

[0041] (P0)min P LS (19)

[0042] st(33)-(35)

[0043]

[0044]

[0045] P Gi represents the active power output of bus i, and Indicates the upper and lower limits of the active power output of the generator of bus i; Q Gi represents the reactive power output of bus i, and Indicates the upper and lower limits of the reactive power output of the generator of bus i; represents the set of nodes connected to the generator; P ij and Q ij They represent the active power flow and reactive power flow of the branch respectively. represents the upper limit of branch capacity, ε represents the set of first and last nodes of the branch; V i represents the voltage amplitude of node i, and Indicates the upper and lower limits of the node voltage amplitude; P j and Q j is the active power and reactive power injected into the node, V j is the voltage amplitude at node j, G ij and B ij is the conductance and susceptance of branch (i,j), θ ij represents the phase angle difference of branch (i, j); the objective function formula (7) minimizes the active power of load reduction, and the power generation is guaranteed by the generator capacity limit in the constraints (8)-(9). Constraint (10) is the power flow limit of each branch. Constraint (11) stipulates that the bus voltage amplitude must be within the voltage safety operation limit range, θ irepresents the voltage angle of bus i, π represents the phase angle range with a maximum of 180 degrees, and its value is restricted by constraint (12). Equations (13) and (14) represent the power flow calculation equations and active and reactive power balance equations on each bus.

[0046] Furthermore, the load reduction problem considering the improvement of transient voltage stability is expressed as the following model P1:

[0047] (P1)min P LS (27)

[0048] st(34)-(35),(37)-(43)

[0049]

[0050] Where P j Indicates the load active power of the key node, represents the set of key nodes, is the threshold value obtained based on the local interpretation of LIME. Constraint (16) ensures a higher probability of voltage recovery and stability after system faults.

[0051] Further, step S4, building a constrained iterative solver based on sequential model agnostic local interpreter LIME is an iterative algorithm based on sequential LIME to solve the load shedding problem considering the TVS mechanism, including:

[0052] First, the system data of the overload scenario is input, and the number of iterations is set to one. The traditional load reduction model P0 is executed without TVS constraints to establish the initial operating point, simulate the TVS after the fault, and use the LIME interpreter to obtain the local interpretation of the operating point;

[0053] According to the range of eigenvalues ​​obtained by LIME analysis, the value range of important features is selected by sorting the feature importance. For features that support system instability, the complement of their range is taken; for features that support system stability, their own range is obtained. If the condition is not met, ||P k -P k+1 ||2≤ε,P k represents the active power vector of each load node of the system obtained in the kth iteration, ε represents the minimum value in the mathematical limit, that is, the constraints based on the local interpretation are almost unchanged, and the process enters the next step;

[0054] In subsequent iterations, the model P1 with updated stability constraints is re-solved to obtain a new operating point that better meets the system stability goal; this iterative process continues, and each iteration gradually improves the load reduction strategy in combination with the latest understanding of system dynamics;

[0055] The iterative algorithm terminates when the iteration stop condition is met, indicating that the optimal solution has been found, and the final output includes the optimal load reduction solution and the updated stability constraints that ensure the TVS within the power system.

[0056] Furthermore, the random forest classification model is used as a proxy model for local samples of the model-agnostic local interpreter LIME:

[0057]

[0058] Where f is the complex model for transient voltage stability assessment, g is the proxy model of f, G is the alternative model used to explain the local linear relationship, k is a constant, and π x is the neighborhood distance of a single sample x to be explained, Ω(g) is the complexity of the surrogate model, and L is the process function of g approximating f in the local definition of x.

[0059] Compared with the existing technology, the present invention has the following beneficial effects:

[0060] 1. This paper proposes for the first time a method to extend the local interpretation of LIME to the global interpretation based on the sequential idea. By comprehensively considering the interpretable results of iterative operation points, the local interpretation is extended to the global interpretation, overcoming the challenge that the local interpretation cannot provide a complete perspective behind the model.

[0061] 2. This invention proposes for the first time a mechanism analysis framework combining qualitative and quantitative analysis of transient voltage stability, which provides prior knowledge and feature selection guidance for the construction of LIME's explanatory model, and can be cross-validated with LIME's feature importance ranking.

[0062] 3. The present invention applies the interpretable results of LIME to the construction of transient voltage stability constraints for the first time, and puts the feature importance ranking of LIME and the quantification results of the eigenvalues ​​into the traditional optimization problem for iterative solution, which can efficiently and quickly solve the optimization results of improving transient voltage stability.

[0063] 4. The present invention helps to improve the efficiency and reduce the complexity of the power grid in planning, analysis, optimization and control by providing intuitive and accurate constraint expressions, especially in the power grid optimization problem considering the improvement of transient voltage stability, showing broad application potential. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 It is a flow chart of the process steps of a transient voltage stability constraint iterative solution method based on mechanism explanation disclosed in an embodiment;

[0065] Figure 2The transient voltage stability constraint iterative solution flow chart combining qualitative analysis with quantitative analysis constructed in step S1 of the embodiment;

[0066] Figure 3 This is a schematic diagram of the calculation principle of transient voltage stability index;

[0067] Figure 4 Flowchart for solving an optimal load shedding solution and ensuring updated stability constraints for TVS in a power system. DETAILED DESCRIPTION

[0068] In order to enable those skilled in the art to better understand the scheme of the present invention, the present invention will be further described in detail below in conjunction with the accompanying drawings and specific implementation methods. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0069] Example

[0070] like Figure 1 As shown, this embodiment provides a transient voltage stability constraint iterative solution method based on mechanism explanation. Based on the optimization problem of undervoltage overload reduction, the load reduction problem is optimized to obtain a load reduction scheme with improved transient voltage stability. The constraint iterative solution method includes the following steps:

[0071] S1. Build a transient voltage stability mechanism analysis framework that combines qualitative analysis with quantitative analysis. Use qualitative analysis to identify key factors that affect transient voltage stability and help understand the response trend of the system under specific conditions. Then, use quantitative analysis to derive the range of key characteristic values.

[0072] S1.1) Select transient voltage stability indicators to evaluate the stability of the system:

[0073] Voltage instability is often caused by load dynamics attempting to recover power consumption that is greater than the capacity of the generation and combined transmission network. Long-term voltage stability involves slowly operating equipment while transient voltage stability involves the complex dynamics of load elements, including induction motors, which tend to recover the power they have consumed quickly. After a large disturbance, if the electrical torque cannot overcome the mechanical load torque, induction motors can decelerate or stop sharply due to a sudden drop in voltage, resulting in very large reactive currents that negatively affect the voltage amplitude. This can result in unacceptable voltage transient performance, such as delayed voltage recovery (FIDVR) or transient voltage collapse.

[0074] The evaluation of transient voltage stability mainly focuses on problems such as large transient voltage deviation, slow voltage recovery, and rapid voltage collapse after disturbance. Simple binary classification can distinguish between stable and unstable situations, but further quantitative analysis of the voltage recovery delay caused by the fault is required.

[0075] As an example, in order to quantitatively measure the short-term stability of voltage, an improved voltage recovery index (IVRI) is used to evaluate the severity of FIDVR. The voltage trajectory is as follows: Figure 3 shown.

[0076] The calculation of FIDVR severity using IVRI is expressed as follows:

[0077]

[0078] Where N is the number of buses in the system. i is the voltage deviation index of bus i, V i,0 is the voltage amplitude of bus i before the fault; V i,t is the voltage amplitude of bus i at time t after the disturbance; t c is the fault clearing time; T is the end time of the time domain simulation; is the reference voltage recovery curve of bus i; V i,max is the rated voltage amplitude of bus i; a is the curve recovery rate. Therefore, the smaller the IVRI value, the better the performance of restoring transient voltage stability. In the case of voltage instability, the IVRI value will be very large. The IVRI of the system is obtained by adding the IVRI of all buses. Compared with the traditional voltage recovery index, IVRI sets the voltage threshold to the voltage amplitude before the disturbance and deviates from the voltage trajectory by the absolute value of the voltage threshold. The fault recovery rate is taken into account by multiplying the penalty factor related to the recovery rate to make the difference between different voltage curves more obvious.

[0079] S1.2) Conduct qualitative analysis on transient voltage stability mechanism, corresponding to Figure 2 The framework diagram of qualitative analysis in Figure 2 shows the implementation of qualitative analysis through the following steps:

[0080] Firstly, the experimental samples are generated by time domain simulation. By changing the fault location, fault duration, and active and reactive power requirements of the load nodes, different samples are generated for time domain simulation, and the IVRI value of each sample is calculated.

[0081] Then, the load nodes are classified and the relationship between the load disturbance degree and IVRI value in the sample is statistically analyzed. Critical load nodes are nodes that significantly affect the system voltage stability. Small power disturbances may cause system voltage collapse. In contrast, ordinary load nodes have little impact on the transient voltage stability of the system.

[0082] Then, by changing the switch state to construct different network topologies and repeating the previous procedure, the key nodes of different network structures can be marked. The influence of network structure on transient voltage stability and the distribution of key load nodes can be studied.

[0083] Finally, the location of renewable energy integration is changed: renewable energy is randomly integrated at four key nodes, and the experimental steps are repeated to observe the impact of the location of renewable energy integration on system stability. Renewable energy includes wind energy and solar energy.

[0084] In a 33-node distribution network system, by changing the load disturbance degree, it can be observed that the IVRI value increases with the increase of active and reactive power of the load. In addition, the load level and the number of critical nodes significantly affect the transient voltage stability of the system. The qualitative analysis of the transient voltage stability mechanism will serve as the prior knowledge for the construction of the LIME interpreter and help to construct scientifically interpretable input features.

[0085] S1.3) Build a model-agnostic local explainer (LIME, Local Interpretable Model-AgnosticExplanations). The goal of local interpretability is to enable people to understand the decision process and machine learning model of each input sample. In contrast to global interpretability, the local interpretability of the model is oriented towards a single input sample, and is usually achieved by analyzing the contribution of each feature of the input sample to the final decision of the model. Local interpretability helps to explain a single prediction. LIME is a method that does not require adaptation to the original model and is widely used to quantify the contribution of each feature at a local sampling point.

[0086] LIME aims to explain the underlying logic of obtaining a prediction and identify factors that support and oppose the prediction. LIME is compatible with any supervised learning algorithm and is used to explain local linear relationships by building a highly transparent alternative model near a simple single sample. In this example, a random forest classification model is selected as a proxy model for local samples. LIME is as follows:

[0087]

[0088] Where f is the complex model for transient voltage stability assessment, g is the proxy model of f, and 2k 2 In this embodiment, it is set to 1. xis the neighborhood sample distance of a single sample x to be explained, that is, the distance between x and any other sample point x′ in the neighborhood. Ω(g) is the complexity of the proxy model, and the L function describes the process of g approximating f in the local definition of x, where Ω(g) must be low enough to be understood by humans.

[0089] S1.4) Combined with LIME for quantitative analysis, such as Figure 2 The framework of quantitative analysis in LIME is presented. The key factors affecting transient voltage stability identified by qualitative analysis help understand the potential response trend of the system under specific conditions. Then, the key influencing features selected from the qualitative analysis are used as input interpretable features for the construction of the LIME interpreter. Local interpretations of the target samples are obtained to determine the ranking and specific value range of feature importance. The ranking of feature importance can help dispatchers identify which features have the greatest impact on the transient voltage stability of the system. The feature value range derived from the quantitative analysis can identify key nodes and determine the load safety thresholds of these nodes to ensure the transient voltage stability and safety of the system. In addition, the feature importance ranking derived from LIME can be cross-validated with the results of qualitative analysis. This combination of qualitative and quantitative analysis not only refines the mechanistic explanation of transient voltage stability, but also enables it to be applied to real-world problems.

[0090] S2. Based on the idea of ​​sequentiality, the local explanation of LIME is extended to the global explanation, so that the interpretable analysis results of LIME can be applied to optimization problems. The local explanation provided by LIME for each sample can provide operators with a reference range of some feature values, but this local explanation is not enough to evaluate the entire model and cannot be directly applied to solve real-world problems. There is a sub-modulus selection method that provides a global understanding of the model by explaining a set of individual instances. This method is model-independent and supplements summary statistics. It selects a diverse and representative set of prediction samples to show operators a non-repetitive explanation that represents the global behavior of the model.

[0091] This method can help operators understand the entire model and determine its reliability. However, relying only on the results of global interpretation, the range of eigenvalues ​​is wider than that of local interpretation, and it can only provide one interpretation result when dealing with different operating points of the same model. Therefore, the present invention proposes a sequential interpretable analysis method that can produce more comprehensive results and can be better applied to practical problems.

[0092] First, an initial sample is selected from the experimental samples generated by the previous time-domain simulation, and LIME is used for local interpretation to obtain the range of eigenvalues. Then, the next target sample is determined at the boundary of the range for the next local interpretation. Through the iterative process of multiple local interpretations of different samples, a series of accurate local interpretations and numerical ranges of different operating points can be obtained, which extends the local interpretation to the global interpretation. This sequential analysis method is applied to solve the load reduction problem considering transient voltage stability constraints.

[0093] S3. Build an undervoltage load reduction model and add transient voltage stability constraints on the basis of the traditional load reduction model. The main goal of the traditional load reduction model is to minimize load reduction and balance power flow. In the distribution network, active power and reactive power are strongly coupled, so active load will significantly affect transient voltage stability. Define ΔP Dj The amount of active power cut for each node, ΔQ Dj Indicates the reactive power reduction at each node, ( represents an n-dimensional real number set, each element is an n-dimensional vector), and the optimization variable is ΔP Dj and ΔQ Dj Usually, ΔP Dj is related to ΔQ Dj The objective function is to minimize the overall load reduction while ensuring that it meets the stability criteria and obeys the network and power flow constraints. N is the number of nodes in the system. LS represents the total load reduction, and the objective function is defined as the following formula:

[0094]

[0095] In this embodiment, the active power P injected by each node is j It is defined by the following formula:

[0096]

[0097] Where P Gj represents the active power generation of node j and P Dj represents the active load demand of node j, Represents the set of all nodes. Active power load reduction needs to meet the following constraints:

[0098]

[0099] Therefore, the formula of the traditional load reduction model (P0) is as follows:

[0100] (P0)min P LS(36)

[0101] st(33)-(35)

[0102]

[0103] P Gi represents the active power output of bus i, and Indicates the upper and lower limits of the active power output of the generator of bus i; Q Gi represents the reactive power output of bus i, and Indicates the upper and lower limits of the reactive power output of the generator of bus i; represents the set of nodes connected to the generator; P ij and Q ij They represent the active power flow and reactive power flow of the branch respectively. represents the upper limit of branch capacity, ε represents the set of first and last nodes of the branch; V i represents the voltage amplitude of node i, and Indicates the upper and lower limits of the node voltage amplitude; P j and Q j is the active power and reactive power injected into the node, V j is the voltage amplitude at node j, G ij and B ij is the conductance and susceptance of branch (i,j), θ ij represents the phase angle difference of branch (i, j). The objective function formula (7) minimizes the active power of load reduction. The power generation is guaranteed by the generator capacity limit in the constraints (8)-(9). Constraint (10) is the power flow limit of each branch. Constraint (11) stipulates that the bus voltage amplitude must be within the voltage safety operating limit range. θ i represents the voltage angle of bus i, π represents the phase angle range up to 180 degrees, and its value is limited by constraint (12). Equations (13) and (14) represent the power flow calculation equations and active and reactive power balance equations on each bus.

[0104] Based on the transient voltage stability mechanism and the locally interpretable analysis results obtained from the LIME interpreter, the value range of the bus injection power with better transient voltage stability can be determined and integrated into the traditional load reduction problem as a constraint. By adopting this approach, the load reduction amount is optimized while considering the minimization objective and the improvement of transient voltage stability. The load reduction problem considering the improvement of transient voltage stability can be reformulated as the following model (P1):

[0105] (P1)min P LS(44)

[0106] st(34)-(35),(37)-(43)

[0107]

[0108] P j Indicates the load active power of the key node, and is the threshold size obtained based on the local interpretation of LIME, represents the set of critical nodes, and constraint (16) guarantees a higher probability of voltage recovery and stability after system faults.

[0109] S4. Build a constrained iterative solution framework based on the sequential LIME idea. The specific process is as follows: Figure 1 shown.

[0110] Although the LIME method is applicable to any model, it only provides local interpretation of individual samples. In the context of load shedding problem, the operating point parameters are dynamically changing. Therefore, only using LIME to analyze the initial operating point is not suitable for this problem. Therefore, this paper proposes an iterative algorithm based on sequential LIME to solve the load shedding problem considering the TVS mechanism.

[0111] Figure 1 The flowchart of the proposed iterative algorithm is shown. The schematic diagram in the figure outlines a systematic approach to optimize load shedding in a power system considering TVS constraints. The process begins by inputting system data of overload scenarios into the conventional load overload model and setting the number of iterations to one. Subsequently, the conventional load shedding model (P0) is executed without including TVS constraints to establish the initial operating point. After this, the post-fault TVS is simulated and the local interpretation of the operating point is obtained using the LIME interpreter.

[0112] The results of LIME analysis give the range of eigenvalues. The value ranges of important features are selected by sorting the feature importance. For features that support system instability, the complement of their ranges is taken; for features that support system stability, their own ranges are obtained. These value ranges are then aggregated and used to update the transient voltage stability constraints, thereby refining the stability requirements of the system. Then, if the condition ||P is not met k -P k+1 ||2≤ε,P kRepresents the active power vector of each load node in the system obtained in the kth iteration, ε represents the minimum value in the mathematical limit, that is, the constraints based on the local interpretation are almost unchanged, and the final stable constraints are obtained. Next, the final constraints are added to the traditional load overload model. In subsequent iterations, the model (P1) with updated stability constraints is re-solved to obtain a new operating point that better meets the system stability goal. This iterative process continues, and each iteration combines the latest understanding of system dynamics to gradually improve the load reduction strategy. When the iteration stop condition is met, the iterative algorithm terminates, indicating that the optimal solution has been found. The final output includes the optimal load reduction solution and the updated stability constraints to ensure TVS within the power system, such as Figure 4 shown.

[0113] S5. After obtaining the optimal load reduction scheme to ensure the transient voltage stability of the system, fault simulation is performed on the traditional solution and the optimized solution considering stability constraints to simulate the situation where the system operation encounters disturbances and observe whether the transient voltage can be restored to the standard level. The results show that the traditional load reduction system is very likely to be unable to guarantee that the transient voltage can be restored to the standard level after the disturbance, and there is a certain risk of transient voltage instability. This methodological procedure ensures the robustness and iterative enhancement of the load reduction strategy, which is based on the combination of machine learning interpretability and traditional power system analysis. The iterative nature of the process leads to the gradual refinement of the model, so as to form a more accurate and reliable strategy to maintain system stability in the face of emergencies.

[0114] The above embodiments are preferred implementation modes of the present invention, but the implementation modes of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications made without departing from the spirit and principles of the present invention shall be equivalent replacement methods and shall be included in the protection scope of the present invention.

Claims

1. A transient voltage stability constraint iterative solution method based on mechanism interpretation, characterized in that: The following steps are involved: S1. Build a transient voltage stability mechanism analysis framework that combines qualitative analysis with quantitative analysis, identify key factors affecting transient voltage stability through qualitative analysis, analyze the response trend under set conditions, and derive the range of key characteristic values; S2. Extend the local interpretation of the model-agnostic local interpreter LIME to the global interpretation, so that the interpretable analysis results of the model-agnostic local interpreter LIME can be applied to optimization problems; S3. Build an undervoltage load reduction model and add transient voltage stability constraints based on the traditional load reduction model; S4. Build a constrained iterative solution algorithm based on the sequential agnostic model local interpreter LIME to solve the load reduction model considering transient voltage stability constraints, and obtain the optimal load reduction plan to ensure the transient voltage stability of the system. S5. After obtaining the optimal load reduction plan to ensure the transient voltage stability of the system, fault simulation is performed on the traditional solution and the optimized solution considering the stability constraint to simulate the situation where the system operation encounters disturbances and observe whether the transient voltage can be restored to the standard level.

2. The transient voltage stability constraint iterative solution method based on mechanism interpretation according to claim 1 is characterized in that: Step S1 includes the following steps: S1.1) Select transient voltage stability indicators to evaluate the stability of the system: S1.2) Conduct qualitative analysis on transient voltage stability mechanism; S1.3) Combined with the LIME interpreter, an analysis framework combining qualitative analysis and quantitative analysis is built. The key factors affecting transient voltage stability identified through qualitative analysis help understand the potential response trend of the system under specific conditions. The key influencing features selected from the qualitative analysis are used as input interpretable features for the construction of the agnostic model local interpreter LIME to obtain the local interpretation of the target sample to determine the ranking and specific value range of feature importance; the key nodes are identified from the feature value range obtained from the quantitative analysis, and the load safety thresholds of these nodes are determined to ensure the transient voltage stability and safety of the system.

3. The transient voltage stability constraint iterative solution method based on mechanism interpretation according to claim 2 is characterized in that: The improved voltage recovery index IVRI is used to evaluate the severity of FIDVR: Where N is the number of buses in the system, VSI i is the voltage deviation index of bus i, V i,0 is the voltage amplitude of bus i before the fault; V i,t is the voltage amplitude of bus i at time t after the disturbance; t c is the fault clearing time; T is the end time of the time domain simulation; is the reference voltage recovery curve of bus i; V i,max is the rated voltage amplitude of bus i; a is the curve recovery rate; the smaller the IVRI value, the better the performance of restoring transient voltage stability; in the case of voltage instability, the IVRI of the system is obtained by adding the IVRI of all buses. IVRI sets the voltage threshold to the voltage amplitude before the disturbance and deviates the voltage trajectory from the absolute value of the voltage threshold. The failure recovery rate is taken into account by multiplying the penalty factor associated with the recovery rate.

4. The transient voltage stability constraint iterative solution method based on mechanism interpretation according to claim 2 is characterized in that: The qualitative analysis includes the following steps: Firstly, the experimental samples are generated by time domain simulation. By changing the fault location, fault duration, and active and reactive power requirements of the load nodes, different samples are generated for time domain simulation, and the IVRI value of each sample is calculated. Then the load nodes are classified and the relationship between the load disturbance degree and IVRI value in the sample is statistically analyzed; Then, the switch states are changed to construct different network topologies and the previous procedures are repeated to mark the key nodes of different network structures and analyze the impact of network structures on transient voltage stability and the distribution of key load nodes; Finally, the renewable energy integration position is changed: renewable energy is randomly integrated at four key nodes, and the experimental steps are performed again to observe the impact of the renewable energy integration position on the system stability. Renewable energy includes wind energy and solar energy.

5. The transient voltage stability constraint iterative solution method based on mechanism interpretation according to claim 1 is characterized in that: Step S2 includes the following steps: Generate experimental samples using time domain simulation, select an initial sample, and use the model-agnostic local interpreter LIME for local interpretation to obtain the range of eigenvalues; The next target sample is determined at the boundary of the eigenvalue range for the next local interpretation. Through multiple iterative processes of local interpretation of different samples, a series of accurate local interpretations and numerical ranges of different operating points are obtained to expand the local interpretation to the global interpretation.

6. The transient voltage stability constraint iterative solution method based on mechanism interpretation according to claim 2 is characterized in that: The main objectives of traditional load shedding models are to minimize load shedding and balance power flow, including: Defining ΔP Dj The amount of active power cut for each node, ΔQ Dj Indicates the reactive power reduction at each node, represents an n-dimensional real number set, each element is an n-dimensional vector, and the optimization variable is ΔP Dj and ΔQ Dj , ΔP Dj is related to ΔQ Dj proportional; The objective function is to minimize the overall load reduction while ensuring that it meets the stability criteria and follows the network and power flow constraints. The objective function is defined as follows: Where N is the number of nodes in the system, P LS Indicates the total load reduction; The active power P injected by each node j It is defined by the following formula: Where P Gj represents the active power generation of node j, P Dj represents the active load demand of node j, Represents the set of all nodes, the load reduction of active power needs to meet the following constraints:

7. The transient voltage stability constraint iterative solution method based on mechanism interpretation according to claim 6 is characterized in that: The formula of the traditional load reduction model P0 is as follows: (P0)min P LS (4) st(33)-(35) P Gi represents the active power output of bus i, and Indicates the upper and lower limits of the active power output of the generator of bus i; Q Gi represents the reactive power output of bus i, and Indicates the upper and lower limits of the reactive power output of the generator of bus i; represents the set of nodes connected to the generator; P ij and Q ij They represent the active power flow and reactive power flow of the branch respectively. represents the upper limit of branch capacity, ε represents the set of first and last nodes of the branch; V i Represents the voltage amplitude of node i, V i max and V i min Indicates the upper and lower limits of the node voltage amplitude; P j and Q j is the active power and reactive power injected into the node, V j is the voltage amplitude at node j, G ij and B ij is the conductance and susceptance of branch (i,j), θ ij represents the phase angle difference of branch (i, j); the objective function formula (7) minimizes the active power of load reduction, and the power generation is guaranteed by the generator capacity limit in the constraints (8)-(9). Constraint (10) is the power flow limit of each branch. Constraint (11) stipulates that the bus voltage amplitude must be within the voltage safety operation limit range, θ i represents the voltage angle of bus i, π represents the phase angle range with a maximum of 180 degrees, and its value is restricted by constraint (12). Equations (13) and (14) represent the power flow calculation equations and active and reactive power balance equations on each bus.

8. The transient voltage stability constraint iterative solution method based on mechanism interpretation according to claim 1 is characterized in that: The load reduction problem considering the improvement of transient voltage stability is expressed as the following model P1: (P1)min P LS (12) st(34)-(35),(37)-(43) Where P j Indicates the load active power of the key node, represents the set of key nodes, It is the threshold value obtained based on the local interpretation of LIME. Constraint (16) ensures a higher probability of voltage recovery and stability after system faults.

9. The transient voltage stability constraint iterative solution method based on mechanism interpretation according to claim 8 is characterized in that: In step S4, a constrained iterative solver based on a sequential agnostic model local interpreter LIME is constructed. The sequential LIME-based iterative algorithm is used to solve the load shedding problem considering the TVS mechanism, including: First, the system data of the overload scenario is input, and the number of iterations is set to one. The traditional load reduction model P0 is executed without TVS constraints to establish the initial operating point, simulate the TVS after the fault, and use the LIME interpreter to obtain the local interpretation of the operating point; According to the range of eigenvalues ​​obtained by LIME analysis, the value range of important features is selected by sorting the feature importance. For features that support system instability, the complement of their range is taken; for features that support system stability, their own range is obtained. If the condition is not met, ||P k -P k+1 ||2≤ε,P k represents the active power vector of each load node of the system obtained in the kth iteration, ε represents the minimum value in the mathematical limit, that is, the constraints based on the local interpretation are almost unchanged, and the process enters the next step; In subsequent iterations, the model P1 with updated stability constraints is re-solved to obtain a new operating point that better meets the system stability goal; this iterative process continues, and each iteration gradually improves the load reduction strategy in combination with the latest understanding of system dynamics; The iterative algorithm terminates when the iteration stop condition is met, indicating that the optimal solution has been found, and the final output includes the optimal load reduction solution and the updated stability constraints that ensure the TVS within the power system.

10. A transient voltage stability constraint iterative solution method based on mechanism interpretation according to any one of claims 1 to 9, characterized in that: The random forest classification model is used as a proxy model for local samples of the model-agnostic local interpreter LIME: Where f is the complex model for transient voltage stability assessment, g is the proxy model of f, G is the alternative model used to explain the local linear relationship, k is a constant, and π x is the neighborhood distance of a single sample x to be explained, Ω(g) is the complexity of the surrogate model, and L is the process function of g approximating f in the local definition of x.

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