Novel transient voltage stability assessment method

Abstract

The invention discloses a novel transient voltage stability evaluation method, which comprises the following steps of: extracting electrical quantity time sequence data of a load node, carrying out stability labeling to construct a transient voltage stability evaluation sample set, and replacing decision nodes in a multivariable decision tree with a support vector machine; and introducing a polynomial kernel function to construct a transient voltage stability evaluation model based on a multivariable decision tree, and extracting a trained decision tree rule path to form a transient voltage stability evaluation criterion set. According to the method, the transient voltage stability of the load node is rapidly evaluated, and the criterion rule set is generated.

Description

Technical Field

[0001] The invention belongs to the field of electric power technology, relates to a transient voltage stability assessment technology, and in particular to a novel transient voltage stability assessment method. Background Art

[0002] With the access of a high proportion of power electronic equipment and the gradual increase in the penetration rate of new energy sources, the scale of the power grid continues to expand, the operation mode becomes more complex and changeable, and the transient voltage stability problem of the new power system becomes more and more complicated. The transient voltage stability problem has obvious partition characteristics. Conventional machine learning evaluation models often only give the global transient voltage stability situation. Such results are relatively rough and the information of the evaluation results is limited. Therefore, more refined transient voltage stability evaluation models and criteria are needed.

[0003] In response to the above problems, a large number of scholars have conducted a series of studies and obtained corresponding solutions in the prior art. In the existing document 1 (patent number: CN202410185252.X), Zhu Lipeng, Huang Weizhi, Hou Jie and others proposed a transient voltage stability assessment method for power grids based on impedance information learning, in response to the problems of insufficient information learning of transient voltage instability mechanisms and low accuracy of machine learning assessment models in the prior art. That is, the load impedance time series trajectory and the Thevenin equivalent impedance time series trajectory are calculated through the electrical quantity time series trajectory of the key load nodes as the transient sample set and a convolutional neural network is constructed to perform transient voltage stability assessment. In the existing document 2 (patent number: CN202310357325.4), Li Li, Qin Changlong, Li Guang and others proposed a transient voltage assessment method for interconnected systems based on the Simpson formula, in response to the problem that the existing transient voltage analysis method is difficult to apply to large-scale interconnected systems. The method fully considers the cumulative effect of voltage drops and formulates a transient voltage stability index that does not depend on the parameters of the power grid model based on the Simpson formula.

[0004] Purpose of the Invention

[0005] The purpose of the present invention is to solve the problems of low accuracy and unclear judgment rules of existing transient voltage stability assessment technology. The present invention proposes a novel transient voltage stability assessment method, which has improved accuracy and a richer set of judgment criteria than the existing technology. Summary of the invention

[0006] According to a first aspect of the present application, a novel transient voltage stability assessment method is provided, which may include the following steps:

[0007] Step 1: Build the voltage collapse example of China Electric Power Research Institute on the PSD-BPA electromechanical transient simulation platform, and perform power flow calculation to obtain the initial operation results. Set a three-phase short circuit permanent fault with a fault duration of 5 cycles, perform N-1 and N-2 fault scans on the 500kV grid line, and obtain the expected fault set;

[0008] Step 2: Based on the batBPA batch processing program, input the power flow file, stability file and expected fault set file, perform stability calculation, export the result file, and obtain the initial data set;

[0009] Step 3: Extract the load node electrical quantity data in the initial data set to construct a transient voltage stability assessment data set, and label the transient voltage stability according to the transient voltage stability engineering criterion of the "Guidelines for Safety and Stability of Power Systems" to obtain a transient voltage stability assessment data set with node labels, and divide it into a training set and a test set in a ratio of 7:3;

[0010] Step 4: Use support vector machines to replace the internal nodes of the decision tree, build a multivariate decision tree model, introduce a polynomial kernel function to obtain an ascending-order multivariate decision tree model, input the transient voltage stability assessment training set containing node label information, train the transient voltage stability assessment model, save relevant hyperparameters, input the test set data to obtain the transient voltage stability assessment results, and use accuracy, precision, recall and F1 score to evaluate the model performance;

[0011] Step 5: Each path from the root node to the leaf node of the trained decision tree model can be regarded as a transient voltage stability assessment criterion, and the entire decision tree can be regarded as a rule set of transient voltage stability assessment criteria. Extract the decision functions of non-leaf nodes of the multivariate decision tree and the rule paths from the root node to each leaf node to generate a transient voltage stability assessment criterion set;

[0012] The fault set generation method described in step 1 is: perform N-1 and N-2 scans on the 500kV grid lines, N-1 means disconnecting one of the lines, and the other lines are operating normally. N-2 means disconnecting any two lines, and the other lines are operating normally. The constructed N-2 fault set is all sets of disconnecting any combination of two lines in all lines.

[0013] The electrical quantity data set in step 2 is: the initial data set constructed is the electrical quantity data of all nodes, and the electrical quantity data obtained by simulation calculation includes:

[0014] Node voltage U, node active power P, node reactive power Q, node load current I

[0015] Among them, the node load current is calculated from the other three electrical quantities:

[0016]

[0017] The transient voltage stability dataset X constructed in step 3 is a set of load node electrical quantities screened from the original dataset, including:

[0018] X=[UPQIY] (2)

[0019] Among them, U, P, Q, and I have the same structure and are electrical quantity time series data, and Y is the label value.

[0020]

[0021] According to the transient voltage stability engineering criterion of the "Guidelines for Power System Safety and Stability", if the node voltage can be restored to above 0.8pu within 10s, the voltage is stable and the label value is recorded as 1; if the node voltage cannot be restored to above 0.8pu within 10s, the voltage is unstable and the label value is recorded as 0. All nodes are labeled to form a transient voltage stability label value set Y, the size of Y is n×1, and n is the number of samples. The sampling interval of the data set is 0.3s from the next sampling point after the fault disappears.

[0022] The transient voltage stability assessment model constructed in step 4 includes:

[0023] The support vector machine is used to replace the classifier of the non-leaf node of the multivariate decision tree, and the optimal partitioning hyperplane is used to replace the partitioning method of the internal nodes of the original decision tree. All training samples are used as the input of the multivariate decision tree. First, the optimal hyperplane is trained at the root node. All training samples are divided into positive and negative classes according to the position relationship between the sample and the optimal hyperplane. Due to the existence of soft intervals, the positive and negative samples divided at this time are not pure positive and negative classes. Therefore, the two types of samples are trained again with the optimal hyperplane for partitioning, and the training decision tree is finally obtained. Its leaf nodes are the final decision results, thereby realizing transient voltage stability assessment. Among them, the classification hyperplane of the support vector machine as the decision node partitioning method is expressed as:

[0024]

[0025] The decision function is:

[0026]

[0027] The multivariate decision tree algorithm is implemented based on the classic classification and regression tree (CART). CART uses the Gini index to select the partition attribute. The purity of the current node sample set D can be measured by the Gini index:

[0028]

[0029] Among them, D is the current node sample set, |y| is the number of categories, p i is the proportion of samples of type i in the current sample set D. After the current node is further divided into two child nodes D1 and D2, the Gini index of the current node partitioning method (w, b) is:

[0030]

[0031] Therefore, the learning goal of CART is to select the partitioning method (w, b) that minimizes the Gini index after partitioning as the optimal partitioning.

[0032] Introduce polynomial kernel function in support vector machine:

[0033] K(x i ,x j )=(<x i ,x j >+1) 2 (9)

[0034] By performing polynomial combinations on the components of the input vector, a more complex feature expression is formed, that is, the original feature space is mapped to the quadratic polynomial feature space, so as to better divide the nonlinear separable data. The classification hyperplane is:

[0035]

[0036] The decision function is:

[0037]

[0038] According to the model evaluation results, the confusion matrix shown in Table 1 is constructed:

[0039] Table 1 Confusion matrix

[0040]

[0041] Model performance evaluation is performed using accuracy, precision, recall, and F1 score:

[0042] Accuracy:

[0043] The accuracy rate indicates the proportion of samples correctly classified by the model to the total number of samples, and is calculated as:

[0044]

[0045] Precision:

[0046] Precision indicates how many of the samples predicted by the model as positive are actually positive, and is calculated as:

[0047]

[0048] Recall:

[0049] Recall refers to the proportion of samples that the model can correctly predict as positive among all samples that are actually positive. It is calculated as:

[0050]

[0051] F1 score:

[0052] The F1 score is the harmonic mean of precision and recall, which combines the performance of both and is calculated as:

[0053]

[0054] The original data set is input into the transient voltage stability assessment model based on the multivariate decision tree to obtain the trained decision tree model, and the decision function of each non-leaf node is extracted:

[0055]

[0056] The transient voltage stability criterion set generated in step 5 is:

[0057] Each leaf node starts from the root node and forms a regular path after being judged by a series of decision nodes. A single path is represented as:

[0058] R1=sign(y1)∩sign(y2)∩...∩sign(y i ) (17)

[0059] i is the number of decision nodes on the path, sign is the sign function, and for the binary classification problem, the rule set of the entire decision tree can be expressed as:

[0060] {R1,...,R k |Node voltage stability}∩{R k+1 ,...,R j |Node voltage instability} (18)

[0061] Where j is the number of rules, the first k are stability criteria, and the last jk are instability criteria.

[0062] The beneficial effect of the present invention is that after being processed by the method, only four types of electrical quantity time series data of the load node are needed to realize transient voltage stability evaluation and generate a stability criterion set; it has certain significance for actual transient voltage stability evaluation. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 This is the wiring diagram for the example.

[0064] Figure 2 This is the SVM-MDT structure diagram.

[0065] Figure 3 This is the transient voltage stability assessment flow chart. DETAILED DESCRIPTION

[0066] The embodiments are described in detail below in conjunction with the accompanying drawings.

[0067] Step (1): Construct the voltage collapse example of China Electric Power Research Institute on the PSD-BPA electromechanical transient simulation platform, and perform power flow calculation to obtain the initial operation results. Set a three-phase short circuit permanent fault with a fault duration of 5 cycles, perform N-1 and N-2 fault scans on the 500kV grid line, and obtain the expected fault set. In this example, N-1 and N-2 scans are performed on the 500KV grid line. N-1 means disconnecting one of the lines, and the other lines operate normally. N-2 means disconnecting any two lines, and the other lines operate normally. The constructed N-2 fault set is all sets of disconnecting any combination of two lines in all lines.

[0068] Step (2): Figure 1 For the example wiring diagram, based on the batBPA batch processing program, input the power flow file, stability file and expected fault set file, perform stability calculation, export the result data, and obtain the initial data set. The constructed initial data set is the electrical quantity data of all nodes. The electrical quantity data obtained by simulation calculation includes:

[0069] Node voltage U, node active power P, node reactive power Q, node load current I

[0070] Among them, the node load current is calculated from the other three electrical quantities:

[0071]

[0072] Step (3): Extract the load node electrical quantity data in the initial data set to construct a transient voltage stability assessment data set, and perform transient voltage stability labeling according to the transient voltage stability engineering criterion of the "Guidelines for Safety and Stability of Power Systems", and obtain a transient voltage stability assessment data set with node labels, which is divided into a training set and a test set in a ratio of 7:3. The constructed transient voltage stability data set X is a set of load node electrical quantities selected from the original data set, including:

[0073] X=[UPQIY] (2)

[0074] Among them, U, P, Q, and I have the same structure and are electrical quantity time series data, and Y is the label value.

[0075]

[0076]

[0077] According to the transient voltage stability engineering criterion of the "Guidelines for Power System Safety and Stability", if the node voltage can be restored to above 0.8pu within 10s, the voltage is stable and the label value is recorded as 1; if the node voltage cannot be restored to above 0.8pu within 10s, the voltage is unstable and the label value is recorded as 0. All nodes are labeled to form a transient voltage stability label value set Y, the size of Y is n×1, and n is the number of samples. The sampling interval of the data set is 0.3s from the next sampling point after the fault disappears.

[0078] Step (4): Use support vector machines to replace the internal nodes of the decision tree, construct a multivariate decision tree model, use a polynomial kernel function to obtain an ascending-order multivariate decision tree model, input a transient voltage stability assessment data set containing node label information, and obtain a transient voltage stability assessment result. The constructed transient voltage stability assessment model includes:

[0079] The support vector machine is used to replace the classifier of the non-leaf node of the multivariate decision tree, and the optimal partitioning hyperplane is used to replace the partitioning method of the internal nodes of the original decision tree. All training samples are used as the input of the multivariate decision tree. First, the optimal hyperplane is trained at the root node. All training samples are divided into positive and negative classes according to the position relationship between the sample and the optimal hyperplane. Due to the existence of soft intervals, the positive and negative samples divided at this time are not pure positive and negative classes. Therefore, the two types of samples are trained again with the optimal hyperplane for partitioning, and the process is continuously recursive. Finally, a trained decision tree is obtained, and its leaf nodes are the final decision results, thereby realizing transient voltage stability assessment. Among them, the classification hyperplane of the support vector machine node is:

[0080]

[0081] The decision function is:

[0082]

[0083] The multivariate decision tree algorithm is implemented based on the classic classification and regression tree (CART). CART uses the Gini index to select the partition attribute. The purity of the current node sample set D can be measured by the Gini index:

[0084]

[0085] Among them, D is the current node sample set, |y| is the number of categories, p i is the proportion of samples of type i in the current sample set D. After the current node is further divided into two child nodes D1 and D2, the Gini index of the current node partitioning method (w, b) is:

[0086]

[0087] Therefore, the learning goal of CART is to select the partitioning method (w, b) that minimizes the Gini index after partitioning as the optimal partitioning.

[0088] Introduce polynomial kernel function in support vector machine:

[0089] K(x i ,x j )=(<x i ,x j >+1) 2 (9)

[0090] By performing polynomial combinations on the components of the input vector, a more complex feature expression is formed, that is, the original feature space is mapped to the quadratic polynomial feature space, so as to better divide the nonlinear separable data. The classification hyperplane is:

[0091]

[0092] The decision function is:

[0093]

[0094] According to the model evaluation results, the confusion matrix shown in Table 1 is constructed:

[0095] Table 1 Confusion matrix

[0096]

[0097]

[0098] Model performance evaluation is performed using accuracy, precision, recall, and F1 score:

[0099] Accuracy:

[0100] The accuracy rate indicates the proportion of samples correctly classified by the model to the total number of samples, and is calculated as:

[0101]

[0102] Precision:

[0103] Precision indicates how many of the samples predicted by the model as positive are actually positive, and is calculated as:

[0104]

[0105] Recall:

[0106] Recall refers to the proportion of samples that the model can correctly predict as positive among all samples that are actually positive. It is calculated as:

[0107]

[0108] F1 score:

[0109] The F1 score is the harmonic mean of precision and recall, which combines the performance of both and is calculated as:

[0110]

[0111] Step (5): Each path from the root node to the leaf node of the trained decision tree model can be regarded as a transient voltage stability assessment criterion, and the entire decision tree can be regarded as a rule set of transient voltage stability assessment criteria. The original data set is input into the transient voltage stability assessment model based on the multivariate decision tree to obtain the trained decision tree model, and the decision function of each non-leaf node is extracted:

[0112]

[0113] Each leaf node starts from the root node and forms a regular path after being judged by a series of decision nodes. A single path is represented as:

[0114] R1=sign(y1)∩sign(y2)∩...∩sign(y i ) (17)

[0115] i is the number of decision nodes on the path, sign is the sign function, and for the binary classification problem, the rule set of the entire decision tree can be expressed as:

[0116] {R1,...,R k |Node voltage stability}∩{R k+1 ,...,R j |Node voltage instability} (18)

[0117] Where j is the number of rules, the first k are stability criteria, and the last jk are instability criteria.

[0118] Example:

[0119] The embodiments used in the present invention are based on Figure 1 The voltage collapse standard calculation example of China Electric Power Research Institute shown in the figure is based on the PSD-BPA program for simulation calculation, Matlab2022b is used for data processing, and Python3.9 is used to implement the transient voltage stability assessment model. The SVM-MDT structure is as follows Figure 2As shown. A total of 16025 samples were obtained by simulation calculation, including 4992 unstable samples and 11033 stable samples. The sample data was divided into training set and test set in a ratio of 7:3. In order to illustrate the superiority of this method, the support vector machine model, the traditional single variable decision tree and the power current criterion were used for comparison. The support vector machine of the decision node of the multivariate decision tree adopts a linear kernel function, and the effect on the test set is as follows:

[0120] Table 2 Performance comparison of different methods

[0121]

[0122] Criteria set comparison:

[0123] SVM:

[0124] The hyperplane decision function is:

[0125]

[0126] The set of criteria is:

[0127] {F(x)>0, stable}∩{F(x)<0, unstable} (20)

[0128] CART-DT:

[0129] The decision function of non-leaf nodes is:

[0130] y=w T x+b (21)

[0131] Where w = [0, 0, 0, 1, ..., 0, 0], 1 corresponds to the maximum Gini index feature, b is the value of the feature, and each decision node corresponds to different w and b.

[0132] The path from the root node to the leaf node is:

[0133] R1=sign(y1)∩sign(y2)∩...∩sign(y i ) (twenty two)

[0134] The set of criteria is:

[0135] {R1,...,R k |Node voltage stability}∩{R k+1 ,...,R j |Node voltage instability} (23)

[0136] SVM-MDT:

[0137] The decision function of non-leaf nodes is:

[0138] y=wT x+b (24)

[0139] Where w is not 0, b is the value of the feature, and each decision node corresponds to different w and b.

[0140] The path from the root node to the leaf node is:

[0141] R1=sign(y1)∩sign(y2)∩...∩sign(y i ) (25)

[0142] The set of criteria is:

[0143] {R1,...,R k |Node voltage stability}∩{R k+1 ,...,R j |Node voltage instability} (26)

[0144] Table 3 Comparison of the number of criterion rules:

[0145]

[0146]

[0147] After introducing the polynomial kernel function, the effects of different sampling intervals are compared:

[0148] Table 4 Accuracy of linear kernel and polynomial kernel in different sampling intervals

[0149]

[0150] It can be seen that the method of the present invention has higher accuracy than the support vector machine and the traditional single variable decision tree algorithm and the power current criterion. By introducing the polynomial kernel function, the accuracy of transient voltage stability assessment in a shorter sampling interval after a fault is improved, and a transient voltage stability assessment criterion set can be extracted based on the trained multivariate decision tree.

[0151] The method of the present invention is not only applicable to the transient voltage stability assessment in the embodiment, but is also applicable to the transient voltage stability assessment of other AC systems or AC / DC hybrid systems.

[0152] Those skilled in the art should understand that the embodiments of the present invention are only to describe the preferred specific implementation methods of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed in the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A novel transient voltage stability assessment method, characterized in that: The following steps are involved: Step 1: Build the voltage collapse example of China Electric Power Research Institute on the PSD-BPA electromechanical transient simulation platform, perform power flow calculation to obtain the initial operation results; set a three-phase short circuit permanent fault with a fault duration of 5 cycles, perform N-1 and N-2 fault scans on the 500kV grid line, and obtain the expected fault set; Step 2: Based on the batBPA batch processing program, input the power flow file, stability file and expected fault set file, perform stability calculation, export the result file, and obtain the initial data set; Step 3: Extract the load node electrical quantity data in the initial data set to construct a transient voltage stability assessment data set, and label the transient voltage stability according to the transient voltage stability engineering criterion of the "Guidelines for Safety and Stability of Power Systems" to obtain a transient voltage stability assessment data set with node labels, and divide it into a training set and a test set in a ratio of 7:3; Step 4: Use support vector machines to replace the internal nodes of the decision tree, build a multivariate decision tree model, introduce a polynomial kernel function to obtain an ascending-order multivariate decision tree model, input the transient voltage stability assessment training set containing node label information, train the transient voltage stability assessment model, save relevant hyperparameters, input the test set data to obtain the transient voltage stability assessment results, and use accuracy, precision, recall and F1 score to evaluate the model performance; Step 5: Each path from the root node to the leaf node of the trained decision tree model can be regarded as a transient voltage stability assessment criterion, and the entire decision tree can be regarded as a rule set of transient voltage stability assessment criteria; extract the decision functions of non-leaf nodes of the multivariate decision tree and the rule paths from the root node to each leaf node to generate a transient voltage stability assessment criterion set.

2. The method according to claim 1, characterized in that: The fault set generation method described in step 1 is: N-1 and N-2 scans are performed on the 500KV grid lines. N-1 means disconnecting one of the lines while the other lines operate normally; N-2 means disconnecting any two lines while the other lines operate normally. The constructed N-2 fault set is the set of all lines that disconnect any combination of two lines.

3. The method according to claim 1, characterized in that: The initial data set constructed in step 2 is the electrical quantity data of all nodes. The electrical quantity data obtained by simulation calculation includes: Node voltage U, node active power P, node reactive power Q, node load current I, where the node load current is calculated from the other three electrical quantities:

4. The method according to claim 1, characterized in that: The transient voltage stability dataset X constructed in step 3 is a set of load node electrical quantities screened from the original dataset, including: X=[UPQIY] (2) Among them, U, P, Q, and I have the same structure and are electrical quantity time series data, and Y is the label value; According to the transient voltage stability engineering criterion of the "Guidelines for Safety and Stability of Power Systems", if the node voltage can recover to above 0.8pu within 10s, the voltage is stable and the label value is recorded as 1; if the node voltage cannot recover to above 0.8pu within 10s, the voltage is unstable and the label value is recorded as 0; all nodes are labeled to form a transient voltage stability label value set Y, the size of Y is n×1, n is the number of samples; the sampling interval of the data set is 0.3s from the next sampling point after the fault disappears.

5. The method according to claim 1, characterized in that: The transient voltage stability assessment model constructed in step 4 includes: The support vector machine is used to replace the classifier of the non-leaf node of the multivariate decision tree, and the optimal partitioning hyperplane is used to replace the partitioning method of the internal nodes of the original decision tree. All training samples are used as the input of the multivariate decision tree. First, the optimal hyperplane is trained at the root node. All training samples are divided into positive and negative classes according to the positional relationship between the samples and the optimal hyperplane. Due to the existence of soft intervals, the positive and negative samples divided at this time are not pure positive and negative classes. Therefore, the two types of samples are respectively trained again with the optimal hyperplane for partitioning, and the training decision tree is finally obtained. Its leaf nodes are the final decision results, thereby realizing transient voltage stability assessment; among them, the classification hyperplane of the support vector machine as the decision node partitioning method is expressed as: The decision function is: The multivariate decision tree algorithm is implemented based on the classic classification and regression tree (CART). CART uses the Gini index to select the partition attribute. The purity of the current node sample set D can be measured by the Gini index: Among them, D is the current node sample set, |y| is the number of categories, p i is the proportion of class i samples in the current sample set D; after the current node is further divided into two sub-nodes D1 and D2, the Gini index of the current node partitioning method (w, b) is: Therefore, the learning goal of CART is to select the partitioning method (w, b) that minimizes the Gini index after partitioning as the optimal partitioning; Introduce polynomial kernel function in support vector machine: K(x i ,x j )=(<x i ,x j >+1) 2 (9) By performing polynomial combinations on the components of the input vector, a more complex feature expression is formed, that is, the original feature space is mapped to the quadratic polynomial feature space, so as to better divide the nonlinear separable data. The classification hyperplane is: The decision function is: According to the model evaluation results, the confusion matrix shown in Table 1 is constructed: Table 1 Confusion matrix Model performance evaluation is performed using accuracy, precision, recall, and F1 score: Accuracy: The accuracy rate indicates the proportion of samples correctly classified by the model to the total number of samples, and is calculated as: Precision: Precision indicates how many of the samples predicted by the model as positive are actually positive, and is calculated as: Recall: Recall refers to the proportion of samples that the model can correctly predict as positive among all samples that are actually positive. It is calculated as: F1 score: The F1 score is the harmonic mean of precision and recall, which combines the performance of both and is calculated as:

6. The method according to claim 1, characterized in that Generation of transient voltage stability criteria set, including: The transient voltage stability assessment training set is input into the transient voltage stability assessment model based on the multivariate decision tree to obtain the trained decision tree model, and the decision function of each non-leaf node is extracted: Each leaf node starts from the root node and forms a regular path after being judged by a series of decision nodes. A single path is represented as: R1=sign(y1)∩sign(y2)∩...∩sign(y i ) (17) i is the number of decision nodes on the path, sign is the sign function, and for the binary classification problem, the rule set of the entire decision tree can be expressed as: {R1,...,R k |Node voltage stability}∩{R k+1 ,...,R j |Node voltage instability} (18) Where j is the number of rules, the first k are stability criteria, and the last jk are instability criteria.

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