Black-start path evaluation method based on multi-level indexes and fuzzy comprehensive evaluation

Abstract

The invention relates to a black-start path evaluation method based on multi-level indexes and fuzzy comprehensive evaluation, and belongs to the technical field of power system evaluation. According to the method, a multi-level index system including multiple dimensions such as safety margin, transient stability and unit recovery capability is constructed, index data of a to-be-evaluated path is normalized, subjective and objective weights are calculated in combination with an analytic hierarchy process and an entropy weight method, a membership matrix and a comprehensive evaluation vector are constructed by using a fuzzy comprehensive evaluation method, and the evaluation precision of the to-be-evaluated path is improved. And sorting optimization of a plurality of black-start paths is realized. According to the method, the problems of incomplete index coverage, flat structure, incapability of effectively processing uncertainty information and the like in an existing evaluation mode are solved, and the comprehensiveness, scientificity and reliability of an evaluation result are improved.

Description

Technical Field

[0001] This invention belongs to the field of power system evaluation technology and relates to a black-start path evaluation method based on multi-level indicators and fuzzy comprehensive evaluation. Background Technology

[0002] With the continuous expansion of power system scale and the increasing complexity of network structures, the security and stability of power systems face increasingly severe challenges. Following sudden events such as extreme weather, natural disasters, or major faults, the entire power grid may experience a complete blackout. In such cases, black start mechanisms are essential for system self-recovery. Black start refers to the crucial technical step of gradually establishing power supply capacity and restoring grid operation by relying on self-starting generating units when external power is completely lost. The rational selection and evaluation of black start paths are of great significance for improving system recovery efficiency, reducing outage time, and ensuring system safety.

[0003] Existing evaluation methods for black-start paths are mainly based on single-level indicator systems, which suffer from incomplete coverage of technical dimensions, a flat evaluation structure, and a lack of scalability. Firstly, single-level indicators typically select only certain typical indicators for quantitative analysis, making it difficult to comprehensively reflect the path's overall performance in terms of safety, stability, and operability. For example, in safety assessments, some methods only consider single factors such as generator self-excitation or no-load line overvoltage, failing to cover highly interconnected influencing factors such as main transformer overvoltage and excitation inrush current, which may lead to distorted evaluation results.

[0004] Secondly, traditional evaluation systems lack hierarchical decomposition in their structure, making it difficult to effectively integrate multi-dimensional and multi-indicator evaluation data, thus limiting the scientific nature of path ranking. Simultaneously, with the evolution of power grid operation characteristics and the increasing demands of evaluation, the number of evaluation indicators continues to grow. Directly incorporating new indicators into the original system can easily lead to an overabundance of indicators and blurred logical relationships between them, thereby affecting the efficiency and stability of the system evaluation.

[0005] Existing methods also have significant shortcomings in handling information uncertainty. Some studies employ fuzzy data envelopment analysis (Fuzzy DEA) for efficiency evaluation, but this method primarily focuses on boundary analysis of decision-making units, making it difficult to provide specific ranking criteria and limiting its ability to model fuzzy characteristics. Additionally, some studies combine fuzzy techniques with the analytic hierarchy process, but the weight determination process relies excessively on expert subjective judgment, lacking objective data support, which affects the objectivity and consistency of the evaluation results.

[0006] Therefore, there is an urgent need for a novel black-start path evaluation method that combines systematicity, scientific rigor, and robustness, in order to more rationally construct an evaluation index system, accurately handle fuzzy information, and achieve effective ranking and optimization of multiple alternatives. Summary of the Invention

[0007] In view of this, the purpose of this invention is to provide a black start path evaluation method based on multi-level indicators and fuzzy comprehensive evaluation, so as to provide a more reliable and practical decision-making basis for the selection of black start paths in power systems.

[0008] To achieve the above objectives, the present invention provides the following technical solution:

[0009] A black-start path evaluation method based on multi-level indicators and fuzzy comprehensive evaluation includes the following steps:

[0010] S1: Establish a comprehensive evaluation index system for black start paths, and normalize the original index data of the paths to be evaluated to construct a standardized evaluation matrix.

[0011] S2: Construct a judgment matrix using the analytic hierarchy process (AHP) to determine the subjective weights of the evaluation indicators;

[0012] S3: Use the entropy weight method to calculate the entropy value and difference coefficient of the indicators, and determine the objective weight of the evaluation indicators;

[0013] S4: Determine the comprehensive weight of the evaluation indicators based on their subjective and objective weights;

[0014] S5: Determine the set of evaluation factors and comments for the path to be evaluated, and construct the membership matrix of the evaluation indicators;

[0015] S6: Combine the membership matrix of the evaluation indicators with the comprehensive weight to calculate the fuzzy comprehensive evaluation vector of the path to be evaluated, and complete the ranking and optimization of the black start path.

[0016] Furthermore, the comprehensive evaluation index system for the black start path described in S1 includes multiple primary indicators, and each primary indicator further includes multiple secondary indicators.

[0017] The primary indicators include: recovery path safety margin, system transient stability, and unit recovery capability;

[0018] The secondary indicators corresponding to the recovery path safety margin include: generator self-excitation safety margin, no-load main transformer overvoltage, no-load main transformer excitation inrush current, and no-load line overvoltage;

[0019] The generator self-excitation safety margin is expressed as follows:

[0020]

[0021] Among them, W N Indicates the rated capacity of the generator; Q C This represents the line charging power after taking into account the effects of high-voltage and low-voltage shunt reactors; X d* This represents the per-unit value of the generator's equivalent synchronous reactance based on the generator's rated capacity. The generator's equivalent synchronous reactance is the sum of the generator's direct-axis synchronous reactance and the leakage reactance of the step-up transformer.

[0022] The overvoltage of the air-charged main transformer is expressed as follows:

[0023]

[0024] Among them, v i,k This represents the instantaneous maximum phase voltage obtained from simulation based on the sampling result of the k-th switch closing time when the i-th transformer is on the no-load black start path; v i,ul This represents the overvoltage limit that should not be exceeded as specified in the "Code for Design of Overvoltage Protection and Insulation Coordination of AC Electrical Installations" for the i-th transformer on the black-start path.

[0025] The inrush current of the empty-charge main transformer excitation is expressed as:

[0026]

[0027] Among them, i i,k This represents the peak value of the inrush current obtained from the simulation based on the sampling result of the k-th switch closing time when the i-th transformer is in the no-load black start path; i i,rated This represents the rated current of the i-th transformer.

[0028] The overvoltage of the empty charging line is expressed as follows:

[0029]

[0030] Among them, v i This represents the statistical overvoltage relative to ground at the end of the i-th line in the no-load black start path; v i,ul This represents the overvoltage limit that should not be exceeded as specified in the "Code for Design of Overvoltage Protection and Insulation Coordination of AC Electrical Installations" for the i-th line on the black-start path.

[0031] The secondary indicators corresponding to the transient stability of the system include: the maximum starting power of a single auxiliary machine, the voltage impact of auxiliary machine activation on the system, and the frequency impact of auxiliary machine activation on the system.

[0032] The maximum starting power of a single auxiliary machine refers to the maximum power required to start a single auxiliary machine in the plant load of the unit being started. Since the power support that the system can provide is limited in the early stage of recovery, the smaller the maximum starting power of a single auxiliary machine, the better.

[0033] The voltage surge to the system caused by the activation of the auxiliary equipment is expressed as follows:

[0034]

[0035] Among them, v i This represents the voltage at the voltage detection point during the i-th simulation step; v o This indicates the steady-state voltage at the voltage detection point before the auxiliary equipment is put into operation.

[0036] The frequency impact on the system caused by the activation of the auxiliary equipment is expressed as follows:

[0037]

[0038] Among them, f n Indicates the system's rated frequency; f i This represents the system frequency at the i-th simulation step.

[0039] The secondary indicators corresponding to the unit's recovery capability include: number of switching operations, unit startup status, unit capacity, and unit ramp-up rate;

[0040] The number of switching operations refers to the number of times the black starter provides starting power to the unit being started through the charging path. Due to differences in line length and voltage level, the difficulty of operation varies for each power supply path. Therefore, the number of switching operations through the black starter path is used as the evaluation standard. The smaller the number of switching operations, the less time is required for the black starter to provide starting power to the unit being started through the lines, plant busbars, and transformers.

[0041] The unit startup status refers to the division of the unit into five categories based on the critical range of turbine cylinder temperature: extremely cold, cold, warm, hot, and extremely hot. The lower the cylinder temperature, the longer the startup time, and the higher the cylinder temperature, the faster the startup response. The above five states are quantified by values ​​of 1, 3, 5, 7, and 9 in sequence. The larger the value, the higher the unit cylinder temperature and the shorter the startup time.

[0042] The unit capacity refers to the maximum active power output that a single unit can provide during normal operation; the larger the capacity of the unit being started, the more power support it can provide for the subsequent grid reconfiguration phase, which is conducive to speeding up the recovery process and shortening the recovery time.

[0043] The unit ramp rate refers to the maximum rate of change of active power per unit time during the operation of the unit. A unit with a large ramp rate can provide more electrical energy to the system in the same amount of time after startup.

[0044] The normalization of the original indicator data of the path to be evaluated and the construction of a standardized evaluation matrix are specifically as follows: the evaluation indicators are divided into cost-type indicators and benefit-type indicators. The cost-type indicators include: generator self-excitation safety margin, no-load main transformer overvoltage, no-load main transformer inrush current, and no-load line overvoltage under the recovery path safety margin; maximum starting power of a single auxiliary machine, voltage impact of auxiliary machine on the system, and frequency impact of auxiliary machine on the system under the system transient stability; and number of switching operations under the unit recovery capability. The benefit-type indicators include: unit starting status, unit capacity, and unit ramp rate under the unit recovery capability.

[0045] When the evaluation metric is a cost-based metric, inverse normalization is used:

[0046]

[0047] When the evaluation indicator is a benefit-type indicator, positive normalization is used:

[0048]

[0049] Where, x ij This represents the j-th indicator under the i-th black-start path. They are respectively referred to as index x j The maximum and minimum values ​​among all black boot paths;

[0050] A standardized evaluation matrix X is constructed based on the normalized evaluation indicators:

[0051]

[0052] Furthermore, the subjective weights of the evaluation indicators determined by the analytic hierarchy process (AHP) as described in S2 include the following sub-steps:

[0053] S21: The black start path is taken as the target layer, the first-level indicators of the comprehensive evaluation index system of the black start path are taken as the criterion layer, and the second-level indicators are taken as the indicator layer; the importance of the indicators is compared using the 1-9 scale method, and a judgment matrix is ​​constructed.

[0054] S22: Calculate the largest eigenvalue λ of the judgment matrix. max and the corresponding eigenvectors ω = [ω1, ω2, ..., ω n ] T The eigenvectors are then normalized. The normalized eigenvectors are the subjective weights of each evaluation indicator, and their calculation formulas are as follows:

[0055]

[0056] S23: Calculate the consistency index:

[0057]

[0058] Obtain the random consistency index RI from Table 1;

[0059] Table 1. Parameters of Random Consistency Index

[0060] Matrix order n 1 2 3 4 5 6 RI 0 0 0.58 0.90 1.12 1.24

[0061] Calculate the consistency ratio (CR):

[0062]

[0063] If CR < 0.1, the judgment matrix passes the consistency test; if CR ≥ 0.1, the scale of the judgment matrix is ​​adjusted, and S21 to S23 are repeated until CR < 0.1.

[0064] Furthermore, the objective weights for determining the evaluation indicators as described in S3 are specifically as follows:

[0065] Calculate the normalized index value The proportion of this indicator:

[0066]

[0067] Then, calculate the index x. j Entropy value:

[0068]

[0069] Calculation index x j Coefficient of difference g j :

[0070] g j =1-e j

[0071] The greater the difference between the indicators, the lower the entropy value and the greater the objective weight. This is achieved by considering the difference coefficients g of all indicators. j After normalization, the objective weight of the j-th indicator is obtained as follows:

[0072]

[0073] Furthermore, the determination of the evaluation factor set and comment set of the path to be evaluated, as described in S5, and the construction of the membership matrix of the evaluation indicators include the following steps:

[0074] S51: Taking the black start path of the target power system to be evaluated as the object to be evaluated, the established evaluation index system is the set of evaluation factors, and the evaluation comment set is set as V={v1,v2,v3,v4}, corresponding to the evaluation level {excellent, good, qualified, poor}.

[0075] S52: Calculate the membership degree of the secondary index to the comment set using the Gaussian membership function:

[0076]

[0077] Where, r ij (v k ) represents the j-th metric under the i-th black start path relative to the comment v. k Membership degree; σ jk This indicates that the j-th indicator is relative to the comment v. k The central value of the Gaussian function; k jk This indicates that the j-th indicator is relative to the comment v. k The standard deviation of the Gaussian function; from this, the membership matrix of the secondary index of the i-th black-start path can be obtained as:

[0078]

[0079] S53: Based on the comprehensive weight and membership matrix of the secondary indicators, the membership degree of the primary indicators to the comment set is calculated by the weighted average operator.

[0080] Furthermore, the specific optimization of the black-start path ranking described in S6 is as follows: based on the membership matrix and comprehensive weight of the primary indicators, the fuzzy comprehensive evaluation vector B of the black-start path is calculated. i =[b i1 ,b i2 ,b i3 ,b i4 The calculation formula is as follows:

[0081]

[0082] Among them, b ik Let ω' represent the membership degree of the i-th black-start path with respect to the k-th comment; j This represents the overall weight of the j-th primary indicator; to ensure that the sum of all membership degrees is 1, for B... i Normalization is performed to obtain the normalized fuzzy comprehensive evaluation vector. The calculation formula is as follows:

[0083]

[0084] based on The following two methods can be used to comprehensively sort the black boot paths:

[0085] (1) Press The "Excellent" membership degree is sorted in descending order. If the membership degree is the same, the membership degree of the secondary evaluations such as "Good" and "Medium" is compared in turn.

[0086] (2) Assign quantitative scores to the comment set V = {v1, v2, v3, v4}. Calculate the black start path score Press Z i Sort in descending order.

[0087] The beneficial effects of this invention are as follows: This invention overcomes the problems of existing technologies, such as a single evaluation system, flat structure, lack of systematicity, and inability to effectively handle information ambiguity. By constructing a multi-level indicator system containing multiple primary and secondary indicators, it can comprehensively reflect the overall performance of black-start paths in multiple dimensions, including safety, transient stability, and unit recovery capability, avoiding the one-sidedness of the evaluation process. The introduction of a weight determination mechanism combining the analytic hierarchy process (AHP) and entropy weighting method takes into account both subjective experience and objective data, improving the rationality and scientific nature of weight allocation. The use of fuzzy comprehensive evaluation to process multi-dimensional indicator information effectively solves the uncertainty and ambiguity problems in the evaluation process, realizes the relative superiority and inferiority ranking among multiple schemes, and enhances the discriminative power and decision-making reference value of path evaluation. This method is applicable to power systems of different scales and structures, providing a more feasible and reliable decision-making basis for the optimal selection of black-start paths in practical engineering.

[0088] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0089] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein:

[0090] Figure 1 This is a flowchart of the present invention. Detailed Implementation

[0091] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0092] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0093] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "front," and "rear" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0094] like Figure 1 As shown, a black-start path evaluation method based on multi-level indicators and fuzzy comprehensive evaluation includes the following steps:

[0095] (1) Establish a comprehensive evaluation index system for black start paths, and normalize the original index data of the paths to be evaluated to construct a standardized evaluation matrix.

[0096] The comprehensive evaluation index system for the black start path described in step (1) includes multiple primary indicators, and each primary indicator further includes multiple secondary indicators;

[0097] The primary indicators include: recovery path safety margin, system transient stability, and unit recovery capability;

[0098] The secondary indicators corresponding to the recovery path safety margin include: generator self-excitation safety margin, no-load main transformer overvoltage, no-load main transformer excitation inrush current, and no-load line overvoltage;

[0099] The generator self-excitation safety margin is expressed as follows:

[0100]

[0101] Among them, W N Indicates the rated capacity of the generator; Q C This represents the line charging power after taking into account the effects of high-voltage and low-voltage shunt reactors; X d* This represents the per-unit value of the generator's equivalent synchronous reactance based on the generator's rated capacity. The generator's equivalent synchronous reactance is the sum of the generator's direct-axis synchronous reactance and the leakage reactance of the step-up transformer.

[0102] The overvoltage of the air-charged main transformer is expressed as follows:

[0103]

[0104] Among them, v i,k This represents the instantaneous maximum phase voltage obtained from simulation based on the sampling result of the k-th switch closing time when the i-th transformer is on the no-load black start path; v i,ul This represents the overvoltage limit that should not be exceeded as specified in the "Code for Design of Overvoltage Protection and Insulation Coordination of AC Electrical Installations" for the i-th transformer on the black-start path.

[0105] The inrush current of the empty-charge main transformer excitation is expressed as:

[0106]

[0107] Among them, i i,k This represents the peak value of the inrush current obtained from the simulation based on the sampling result of the k-th switch closing time when the i-th transformer is in the no-load black start path; i i,rated This represents the rated current of the i-th transformer.

[0108] The overvoltage of the empty charging line is expressed as follows:

[0109]

[0110] Among them, v i This represents the statistical overvoltage relative to ground at the end of the i-th line in the no-load black start path; v i,ul This represents the overvoltage limit that should not be exceeded as specified in the "Code for Design of Overvoltage Protection and Insulation Coordination of AC Electrical Installations" for the i-th line on the black-start path.

[0111] The secondary indicators corresponding to the transient stability of the system include: the maximum starting power of a single auxiliary machine, the voltage impact of auxiliary machine activation on the system, and the frequency impact of auxiliary machine activation on the system.

[0112] The maximum starting power of a single auxiliary machine refers to the maximum power required to start a single auxiliary machine in the plant load of the unit being started. Since the power support that the system can provide is limited in the early stage of recovery, the smaller the maximum starting power of a single auxiliary machine, the better.

[0113] The voltage surge to the system caused by the activation of the auxiliary equipment is expressed as follows:

[0114]

[0115] Among them, v i This represents the voltage at the voltage detection point during the i-th simulation step; v oThis indicates the steady-state voltage at the voltage detection point before the auxiliary equipment is put into operation.

[0116] The frequency impact on the system caused by the activation of the auxiliary equipment is expressed as follows:

[0117]

[0118] Among them, f n Indicates the system's rated frequency; f i This represents the system frequency at the i-th simulation step.

[0119] The secondary indicators corresponding to the unit's recovery capability include: number of switching operations, unit startup status, unit capacity, and unit ramp-up rate;

[0120] The number of switching operations refers to the number of times the black starter provides starting power to the unit being started through the charging path. Due to differences in line length and voltage level, the difficulty of operation varies for each power supply path. Therefore, the number of switching operations through the black starter path is used as the evaluation standard. The smaller the number of switching operations, the less time is required for the black starter to provide starting power to the unit being started through the lines, plant busbars, and transformers.

[0121] The unit startup status refers to the division of the unit into five categories based on the critical range of turbine cylinder temperature: extremely cold, cold, warm, hot, and extremely hot. The lower the cylinder temperature, the longer the startup time, and the higher the cylinder temperature, the faster the startup response. The above five states are quantified by values ​​of 1, 3, 5, 7, and 9 in sequence. The larger the value, the higher the unit cylinder temperature and the shorter the startup time.

[0122] The unit capacity refers to the maximum active power output that a single unit can provide during normal operation; the larger the capacity of the unit being started, the more power support it can provide for the subsequent grid reconfiguration phase, which is conducive to speeding up the recovery process and shortening the recovery time.

[0123] The unit ramp rate refers to the maximum rate of change of active power per unit time during the operation of the unit. A unit with a large ramp rate can provide more electrical energy to the system in the same amount of time after startup.

[0124] The normalization process for the original indicator data of the path to be evaluated is specifically as follows: the evaluation indicators are divided into cost-type indicators and benefit-type indicators. The cost-type indicators include: generator self-excitation safety margin, no-load main transformer overvoltage, no-load main transformer inrush current, and no-load line overvoltage under the recovery path safety margin; maximum starting power of a single auxiliary machine, voltage impact of auxiliary machine activation on the system, and frequency impact of auxiliary machine activation on the system under the system transient stability; and number of switching operations under the unit recovery capability. The benefit-type indicators include: unit startup status, unit capacity, and unit ramp rate under the unit recovery capability.

[0125] When the evaluation metric is a cost-based metric, inverse normalization is used:

[0126]

[0127] When the evaluation indicator is a benefit-type indicator, positive normalization is used:

[0128]

[0129] Where, x ij This represents the j-th indicator under the i-th black-start path. They are respectively referred to as indicators x j The maximum and minimum values ​​among all black boot paths;

[0130] A standardized evaluation matrix X is constructed based on the normalized evaluation indicators:

[0131]

[0132] (2) Construct a judgment matrix using the analytic hierarchy process (AHP) to determine the subjective weights of the evaluation indicators;

[0133] The sub-steps for constructing a judgment matrix using the analytic hierarchy process (AHP) to determine the subjective weights of evaluation indicators are as follows:

[0134] (2.1) The black start path is taken as the target layer, the first-level indicators of the comprehensive evaluation index system of the black start path are taken as the criterion layer, and the second-level indicators are taken as the indicator layer; the importance of the indicators is compared by the 1-9 scale method, and a judgment matrix is ​​constructed.

[0135] (2.2) Calculate the largest eigenvalue λ of the judgment matrix max and the corresponding eigenvectors ω = [ω1, ω2, ..., ω n ] T The eigenvectors are then normalized. The normalized eigenvectors are the subjective weights of each evaluation indicator, and their calculation formulas are as follows:

[0136]

[0137] (2.3) Calculate the consistency index:

[0138]

[0139] Obtain the random consistency index RI from Table 1;

[0140] Table 1. Parameters of Random Consistency Index

[0141] Matrix order n 1 2 3 4 5 6 RI 0 0 0.58 0.90 1.12 1.24

[0142] Calculate the consistency ratio (CR):

[0143]

[0144] If CR < 0.1, the judgment matrix passes the consistency test; if CR ≥ 0.1, the scale of the judgment matrix is ​​adjusted, and steps (2.1) to (2.3) are repeated until CR < 0.1.

[0145] (3) The entropy weight method is used to calculate the entropy value and difference coefficient of the indicators to determine the objective weight of the evaluation indicators;

[0146] The entropy weight method is used to calculate the entropy value and difference coefficient of the indicators, and the objective weight of the evaluation indicators is determined as follows:

[0147] Calculate the normalized index value The proportion of this indicator:

[0148]

[0149] Then, calculate the index x. j Entropy value:

[0150]

[0151] Calculation index x j Coefficient of difference g j :

[0152] g j =1-e j (14)

[0153] The greater the difference between the indicators, the lower the entropy value and the greater the objective weight. This is achieved by considering the difference coefficients g of all indicators. j After normalization, the objective weight of the j-th indicator is obtained as follows:

[0154]

[0155] (4) Determine the comprehensive weight of the evaluation indicators based on the subjective and objective weights of the evaluation indicators;

[0156] Based on the subjective weights of the primary and secondary indicators obtained by the analytic hierarchy process (AHP) and the corresponding objective weights obtained by the entropy weight method, the comprehensive weights of the primary and secondary indicators are determined by a combined weighting method.

[0157]

[0158] (5) Determine the set of evaluation factors and the set of comments for the path to be evaluated, and construct the membership matrix of the evaluation indicators;

[0159] The sub-steps for determining the set of evaluation factors and comments for the path to be evaluated, and constructing the membership matrix of the evaluation indicators, are as follows:

[0160] (5.1) Taking the black start path of the target power system to be evaluated as the object to be evaluated, the established evaluation index system is the evaluation factor set, and the evaluation comment set is set as V={v1,v2,v3,v4}, corresponding to the evaluation level {excellent, good, qualified, poor}.

[0161] (5.2) Calculate the membership degree of the secondary index to the comment set using the Gaussian membership function:

[0162]

[0163] Where, r ij (v k ) represents the j-th metric under the i-th black start path relative to the comment v. k Membership degree; σ jk This indicates that the j-th indicator is relative to the comment v. k The central value of the Gaussian function; k jk This indicates that the j-th indicator is relative to the comment v. k The standard deviation of the Gaussian function; from this, the membership matrix of the secondary index of the i-th black-start path can be obtained as:

[0164]

[0165] (5.3) Based on the comprehensive weight and membership matrix of the secondary indicators, the membership degree of the primary indicators to the comment set is calculated by the weighted average operator.

[0166] (6) Calculate the fuzzy comprehensive evaluation vector of the path to be evaluated by combining the membership matrix of the evaluation indicators and the comprehensive weight, and complete the ranking and optimization of the black start path.

[0167] By combining the membership matrix of the evaluation indicators with the comprehensive weights, the fuzzy comprehensive evaluation vector of the path to be evaluated is calculated, and the ranking and optimization of the black-start path is completed as follows:

[0168] Based on the membership matrix and comprehensive weights of the primary indicators, the fuzzy comprehensive evaluation vector B of the black-start path is calculated. i =[b i1 ,b i2 ,b i3 ,b i4 ]:

[0169]

[0170] Among them, b ik Let ω' represent the membership degree of the i-th black-start path with respect to the k-th comment; j This represents the overall weight of the j-th primary indicator; to ensure that the sum of all membership degrees is 1, for B... i Normalization is performed to obtain the normalized fuzzy comprehensive evaluation vector.

[0171]

[0172] based on The following two methods can be used to comprehensively sort the black boot paths:

[0173] (1) Press The "Excellent" membership degree is sorted in descending order. If the membership degree is the same, the membership degree of the secondary evaluations such as "Good" and "Medium" is compared in turn.

[0174] (2) Assign quantitative scores to the comment set V = {v1, v2, v3, v4}. Calculate the black start path score Press Z i Sort in descending order.

[0175] The following example, using a black start path of a power grid in a certain region, will further illustrate this method.

[0176] Table 2 shows the evaluation index data of black start path of a power grid in a certain region.

[0177] Table 2 Evaluation Index System and Original Parameter Values ​​for Black Start Path

[0178]

[0179] (1) Obtain the data in Table 2, and normalize the evaluation index data to obtain the standardized evaluation matrix X:

[0180]

[0181] (2) Calculate the subjective weights of the evaluation indicators based on the analytic hierarchy process; take the black start path as the target layer, the first-level indicators of the comprehensive evaluation indicator system of the black start path as the criterion layer, and the second-level indicators as the indicator layer.

[0182] Construct the judgment matrix M of the target layer-criteria layer:

[0183]

[0184] The largest eigenvalue λ of the judgment matrix is ​​calculated. max =3.036 eigenvector ω=[0.577,0.408,0.289] T After normalizing the feature vectors, the subjective weights of the recovery path safety margin, system transient stability, and unit recovery capability are 0.546, 0.273, and 0.181, respectively.

[0185] Perform consistency checks on the judgment matrix:

[0186]

[0187] The result shows that CR = 0.031 < 0.1, thus passing the consistency test.

[0188] Similarly, construct the judgment matrix of the criterion layer-indicator layer. Assuming that the importance of the secondary indicators under each primary indicator is the same, the subjective weights of the secondary indicators are calculated to be 0.137, 0.09, and 0.045, respectively.

[0189] (3) The objective weights of the evaluation indicators were calculated using the entropy weight method based on the standardized evaluation matrix X. The calculation results are shown in Table 3.

[0190] Table 3 Calculation Results of Objective Weights for Evaluation Indicators

[0191]

[0192]

[0193] (4) Calculate the comprehensive weight of the evaluation indicators based on the subjective and objective weights of the evaluation indicators;

[0194] (5) Based on the standardized evaluation matrix X, the membership matrices of the primary and secondary indicators are calculated using Gaussian membership functions. The central value σ selected for the comment set is... jk With standard deviation k jk As shown in Table 4.

[0195] Table 4 Characteristic parameters of the comment set

[0196] Comments Level <![CDATA[Central value σ jk > <![CDATA[Standard deviation k jk > excellent 0.90 0.10 good 0.65 0.13 qualified 0.35 0.13 Poor 0.10 0.10

[0197] Therefore, the membership matrix of the secondary indicators in Scheme 1 can be calculated as follows:

[0198]

[0199] Its membership matrix for the primary indicators is as follows:

[0200]

[0201] Similarly, the membership matrices of the evaluation indicators in Scheme 2 and Scheme 3 are calculated.

[0202] (6) Calculate the fuzzy comprehensive evaluation vector of the black start path.

[0203]

[0204] If according to Sort the "excellent" membership degrees in descending order, and the sorting result is:

[0205] If we assign quantitative scores to the comment set V = {v1, v2, v3, v4} The overall scores for each option are 81.08, 71.87, and 78.75, respectively, resulting in the following ranking:

[0206] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A black-start path evaluation method based on multi-level indicators and fuzzy comprehensive evaluation, characterized in that: Includes the following steps: S1: Establish a comprehensive evaluation index system for black start paths, and normalize the original index data of the paths to be evaluated to construct a standardized evaluation matrix. S2: Construct a judgment matrix using the analytic hierarchy process (AHP) to determine the subjective weights of the evaluation indicators; S3: Use the entropy weight method to calculate the entropy value and difference coefficient of the indicators, and determine the objective weight of the evaluation indicators; S4: Determine the comprehensive weight of the evaluation indicators based on their subjective and objective weights; S5: Determine the set of evaluation factors and comments for the path to be evaluated, and construct the membership matrix of the evaluation indicators; S6: Combine the membership matrix of the evaluation indicators with the comprehensive weight to calculate the fuzzy comprehensive evaluation vector of the path to be evaluated, and complete the ranking and optimization of the black start path.

2. The black-start path evaluation method based on multi-level indicators and fuzzy comprehensive evaluation according to claim 1, characterized in that: In S1, the evaluation index system includes multiple primary indicators, and each primary indicator has multiple secondary indicators. The primary indicators include recovery path safety margin, system transient stability, and unit recovery capability.

3. The black-start path evaluation method based on multi-level indicators and fuzzy comprehensive evaluation according to claim 2, characterized in that: The secondary indicators corresponding to the recovery path safety margin include generator self-excitation safety margin, no-load main transformer overvoltage, no-load main transformer excitation inrush current, and no-load line overvoltage. The secondary indicators corresponding to the system transient stability include maximum starting power of a single auxiliary machine, voltage impact of auxiliary machine activation on the system, and frequency impact of auxiliary machine activation on the system. The secondary indicators corresponding to the unit recovery capability include number of switching operations, unit startup status, unit capacity, and unit ramp-up rate.

4. The black-start path evaluation method based on multi-level indicators and fuzzy comprehensive evaluation according to claim 1, characterized in that: The normalization process includes inverse normalization for cost-related indicators and forward normalization for benefit-related indicators, and constructing a standardized evaluation matrix based on the normalization results.

5. The black-start path evaluation method based on multi-level indicators and fuzzy comprehensive evaluation according to claim 1, characterized in that: In S2, constructing the judgment matrix using the analytic hierarchy process specifically includes: S21: Using the black start path as the target layer, the first-level indicators as the criterion layer, and the second-level indicators as the indicator layer, a judgment matrix is ​​constructed using the 1 to 9 scale method. S22: Calculate the largest eigenvalue and its eigenvector of the judgment matrix and normalize them to obtain the subjective weights; S23: Calculate the consistency ratio. If the consistency test is passed, retain the judgment matrix; otherwise, adjust the matrix and recalculate.

6. The black-start path evaluation method based on multi-level indicators and fuzzy comprehensive evaluation according to claim 1, characterized in that: In S3, determining the objective weights using the entropy weight method includes: (1) Calculate the weight of each indicator value under this indicator; (2) Calculate the entropy value of the index based on the proportion; (3) Calculate the difference coefficient based on the entropy value and normalize it to obtain the objective weight.

7. The black-start path evaluation method based on multi-level indicators and fuzzy comprehensive evaluation according to claim 1, characterized in that: In S5, constructing the membership matrix includes: S51: Set the evaluation factor set and the comment set. The comment set includes excellent, good, satisfactory and poor. S52: Use Gaussian membership functions to calculate the membership degree of the secondary indicators relative to each comment; S53: Calculate the membership degree of the primary indicator to the comment set by combining the comprehensive weight of the secondary indicators.

8. The black-start path evaluation method based on multi-level indicators and fuzzy comprehensive evaluation according to claim 1, characterized in that: In step S6, calculating the fuzzy comprehensive evaluation vector includes: (1) Calculate the fuzzy comprehensive evaluation vector of the path to be evaluated by combining the membership degree and comprehensive weight of each comment of the first-level indicator. (2) Normalize the fuzzy comprehensive evaluation vector so that the sum of all membership degrees is 1; (3) Sort in descending order based on the membership degree of the comments or sort by calculating the path score after assigning values ​​to the comments.

9. The black-start path evaluation method based on multi-level indicators and fuzzy comprehensive evaluation according to claim 1, characterized in that: The formula for calculating the self-excitation safety margin of the generator is as follows: Among them, S r Q represents the rated capacity of the generator. c X represents the line charging power after taking into account the effects of high-voltage and low-voltage parallel reactors. eq This represents the per-unit value of the generator's equivalent synchronous reactance.

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