CN111400966A - Static voltage stability evaluation method of power system based on improved AdaBoost - Google Patents

Static voltage stability evaluation method of power system based on improved AdaBoost Download PDF

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CN111400966A
CN111400966A CN202010301886.9A CN202010301886A CN111400966A CN 111400966 A CN111400966 A CN 111400966A CN 202010301886 A CN202010301886 A CN 202010301886A CN 111400966 A CN111400966 A CN 111400966A
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刘颂凯
晏光辉
刘炼
陈浩
薛田良
张磊
叶婧
钟浩
鲍刚
李世春
杨苗
杨超
黎丽丽
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Abstract

A static voltage stability evaluation method of an electric power system based on improved AdaBoost comprises the following steps: constructing an initial data set containing power system operation variables and voltage stabilization safety classification labels; step 2: forming a high-efficiency data set; and step 3: on the basis of the high-efficiency data set, a voltage stability evaluation model of the power system is constructed by combining an improved AdaBoost algorithm, and the VSA model is trained and updated in an off-line mode by utilizing the high-efficiency data set; and 4, step 4: and performing online VSA on the power system by using a VSA model based on real-time measurement data collected by the synchronous phasor measurement unit. The method has strong generalization capability and high classification accuracy, can effectively avoid the occurrence of over-fitting phenomenon, and can perform reliable online safety evaluation on the power system.

Description

Static voltage stability evaluation method of power system based on improved AdaBoost
Technical Field
The invention relates to the field of static voltage stability evaluation of a power system, in particular to a static voltage stability evaluation method of the power system based on improved AdaBoost.
Background
Voltage Stability Assessment (VSA) is a method of preventing Voltage instability in the event of insufficient power system safety margin. With increasing loads and wide area interconnection of power grids, modern power systems operate increasingly close to system limits. Over the past few decades, severe power outage accidents related to voltage collapse have occurred more and more frequently. Therefore, there is a need for an effective tool for a safe and reliable VSA for power systems to reduce accident losses.
The key of the VSA is to determine the distance between the current voltage operating point and the voltage limit point, and there are many methods for calculating the voltage limit point, which are mainly classified into a method based on mechanism analysis and a method based on data driving. The method based on the mechanism analysis mainly comprises a direct method, a continuous power flow method, a nonlinear programming method and the like. Among them, the continuous power flow method is a very effective VSA method, which can reliably track the change of the steady-state operation of the power system with the load to obtain the voltage stability margin. However, the computation of the continuous power flow method is very time-consuming and difficult to meet the requirement of online safety assessment. Other methods based on mechanism analysis are mostly restricted by computing resource loss, and effective evaluation on the power system cannot be guaranteed.
With the development of Machine learning and the wide application of Phasor Measurement Units (PMUs), Decision Trees (DTs), Random Forest (RF), Support Vector Machines (SVMs), Extreme learning machines (E L M), and other data-driven methods are used for vsa of the power system, but with wide-area interconnection of modern power systems and a large amount of access of renewable energy, these data-driven methods also show problems of difficulty in processing mass data and insufficient estimation accuracy.
The patent document with the publication number of CN109378834A discloses a large-scale power grid voltage stability margin evaluation system based on maximum information correlation, which is characterized in that firstly, a power system large data set capable of approximately representing all the operation characteristics of the current power system is obtained based on PMU data or software simulation, on the basis, a feature set with the maximum correlation and the minimum redundancy with the voltage stability margin is constructed by using a maximum correlation and minimum redundancy algorithm for multiple times, MAT L AB is used for constructing a function expression of the relation between a selected variable and the voltage stability margin, real-time variable data obtained by the power system can directly estimate the voltage stability margin through the expression, and the result is fed back to a field dispatcher to make a decision in time.
Disclosure of Invention
In order to solve the problems, the invention provides an improved AdaBoost-based static voltage stability evaluation method for an electric power system. The method has strong generalization capability and high classification accuracy, can effectively avoid the occurrence of over-fitting phenomenon, and can perform reliable online safety evaluation on the power system.
In order to realize the purpose of the invention, the following technical scheme is adopted:
a static voltage stability evaluation method of an electric power system based on improved AdaBoost comprises the following steps:
step 1: solving a power flow based on simulation of historical operating data and an expected accident set of the power system, and constructing an initial data set containing operating variables and voltage stabilization safety classification labels of the power system;
step 2: preprocessing and selecting characteristics of the initial data set, selecting operation variables with high correlation degree with the voltage stabilization safety classification labels from a large number of operation variables as key characteristics, and combining the corresponding safety classification labels to form a high-efficiency data set;
and step 3: constructing a VSA (voltage stability Assessment) model by combining an improved AdaBoost algorithm based on the efficient data set, and performing offline training and updating on the VSA model by using the efficient data set;
and 4, step 4: and carrying out online VSA on the power system by utilizing the VSA model based on real-time measurement data collected by the PMU.
In the step 1, a P-V curve of the power system is solved by using a continuous power flow method, and a Voltage Stability Index (VSI) and a Voltage Stability safety classification label are constructed according to the P-V curve, as shown in the formulas (1) and (2):
Figure BDA0002454303500000021
Figure BDA0002454303500000022
in the formula: pmaxA load power that is a maximum power transmission point; piLoad power for the current operating point; VSIcThe voltage stability threshold is self-defined; label 1 represents steady state; label 0 indicates an unstable state.
Available vectors of samples in the initial dataset { x1,...,xnY represents wherein xi(i 1.., n) represents the operating variables of the power system in each sample; y represents the corresponding security class label. When a large number of samples are generated, the initial data set may use the matrix { X1,...,XnAnd Y represents.
In step 2, a large number of power system operating variables (such as voltage amplitude and phase angle of each node, active power output and reactive power output of a generator, and the like) in the initial data set are preprocessed, so that the value range of the power system operating variables is (0, 1) to reduce the calculation burden, and the preprocessing process is as shown in formula (3):
Figure BDA0002454303500000031
in the formula: x is the number ofiThe original value of a certain operation variable of the power system;
Figure BDA0002454303500000032
the operation variable is a value after pretreatment; x is the number ofminIs the minimum value of the running variable in the sample; x is the number ofmaxIs the maximum value of the operating variable in the sample.
Based on the preprocessed data set, utilizing a Distance Correlation Coefficient (DCC) to detect the correlation between various operation variables and voltage stabilization safety classification labels in the power system, sequencing the obtained DCC values in a descending order, and selecting the first z operation variables as key features to form a high-efficiency data set together with the corresponding safety classification labels.
DCC is shown in equation (4):
Figure BDA0002454303500000033
in the formula: x and y represent key features and corresponding security classification tags, respectively;
Figure BDA0002454303500000034
Figure BDA0002454303500000035
and
Figure BDA0002454303500000036
as shown in formulas (5) to (7), respectively:
Figure BDA0002454303500000037
Figure BDA0002454303500000038
Figure BDA0002454303500000039
computing by analogy
Figure BDA00024543035000000310
And
Figure BDA00024543035000000311
DCC has the following properties:
(1) when DCC is equal to 0, it means that the two variables are independent of each other;
(2) the larger the DCC, the stronger the correlation between the two variables.
In step 3, based on the feature-selected efficient dataset, a power system VSA model is constructed using the improved AdaBoost. And taking the key features as input and the voltage stabilization safety classification label as output to obtain the mapping relation between the key features and the safety classification label.
The principle of the AdaBoost algorithm is as follows:
(1) the efficient data set after preprocessing and feature selection is { X1,...,XnY, wherein XiRepresenting key features, and Y represents a voltage stabilization safety classification label;
(2) initializing training weights of the samples, performing iterative training, and generating a weak classifier corresponding to each feature in the samples;
(3) selecting a weak classifier with the minimum classification error from the determined weak classifiers during each training, and performing iterative training for M times to obtain M weak classifiers in total;
(4) and carrying out weighted integration on the M weak classifiers to form a strong classifier.
AdaBoost can judge whether the sample of each training is classified correctly, for the sample classified correctly, the weight of the sample is reduced, and for the sample classified incorrectly, the weight of the sample is increased. And determining the weight of each sample in the data set in the next iterative training based on the classification accuracy obtained in the last time. Therefore, the dynamic weight of the sample can be trained through each iteration, the classification focus is concentrated on the sample which is difficult to classify, and the higher classification accuracy is finally obtained.
In order to inhibit the occurrence of the overfitting phenomenon and process the training samples which are difficult to be classified, the method improves the weight updating mode, not only combines the error rate of stable samples and the error rate of unstable samples, but also inhibits the weight increase amplitude of the misclassified samples.
In consideration of the change of the operating conditions of the power system, the model after off-line training may not provide accurate and reliable evaluation results for the new operating conditions. At this time, the model needs to be updated, and the updating steps are as follows:
(1) if the new working condition generated by the change of the operating condition of the power system is contained in the offline data set, selecting a corresponding VSA model to evaluate the new working condition;
(2) if the operating conditions or topology changes of the power system are not contained in the offline data set, a new VSA model needs to be trained using the new data set.
In step 4, based on the real-time measurement data collected by the PMU, selecting corresponding key features, and performing online VSA on the power system by using the trained VSA model.
Compared with the prior art, the invention has the following beneficial effects:
(1) the high-dimensional data set is preprocessed and feature-selected, so that the dimensionality of the data is obviously reduced, irrelevant variables are eliminated, the required time for calculation is effectively reduced, and the VSA model provided by the text can meet the online VSA requirement of a modern power system;
(2) during VSA model training, continuously changing the sample learning weight according to the classification result of the weak classifier in the last iterative training, thereby improving the learning capability and generalization capability of the weak classifier;
(3) the weight updating is combined with the false detection rate of the stable sample and the unstable sample, so that the over-fitting phenomenon is effectively inhibited.
Drawings
The invention is further illustrated by the following examples in conjunction with the accompanying drawings:
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a VSA model in the present invention;
FIG. 3 is a power system P-V curve;
FIG. 4 shows the robustness test results of the VSA model in the IEEE30 node system according to the present invention;
FIG. 5 shows the robustness test results of the VSA model in the IEEE 50 system according to the present invention.
Detailed Description
An improved AdaBoost-based static voltage stability evaluation method for an electric power system is shown in fig. 1, and includes the following steps:
step 1: solving a power flow based on simulation of historical operating data and an expected accident set of the power system, and constructing an initial data set containing operating variables and voltage stabilization safety classification labels of the power system;
step 2: preprocessing and selecting characteristics of the initial data set, selecting operation variables with high correlation degree with the voltage stabilization safety classification labels from a large number of operation variables as key characteristics, and combining the corresponding safety classification labels to form a high-efficiency data set;
and step 3: constructing a power system VSA model by combining an improved AdaBoost algorithm based on the efficient data set, and performing offline training and updating on the VSA model by using the efficient data set as shown in FIG. 2;
and 4, step 4: and carrying out online VSA on the power system by utilizing the VSA model based on real-time measurement data collected by the PMU.
In step 1, a P-V curve of the power system is solved by using a continuous power flow method, as shown in FIG. 3, and a VSI and a voltage stabilization safety classification label are constructed according to the P-V curve, as shown in formulas (1) and (2):
Figure BDA0002454303500000061
Figure BDA0002454303500000062
in the formula: pmaxA load power that is a maximum power transmission point; piLoad power for the current operating point; VSIcThe voltage stability threshold is self-defined; label 1 represents steady state; label 0 indicates an unstable state.
Available vectors of samples in the initial dataset { x1,...,xnY represents wherein xi(i 1.., n) represents the operating variables of the power system in each sample; y represents the corresponding security class label. When a large number of samples are generated, the initial data set may use the matrix { X1,...,XnAnd Y represents.
In step 2, a large number of power system operating variables (such as voltage amplitude and phase angle of each node, active power output and reactive power output of a generator, and the like) in the initial data set are preprocessed, so that the value range of the power system operating variables is (0, 1) to reduce the calculation burden, and the preprocessing process is as shown in formula (3):
Figure BDA0002454303500000063
in the formula: x is the number ofiThe original value of a certain operation variable of the power system;
Figure BDA0002454303500000064
the operation variable is a value after pretreatment; x is the number ofminIs the minimum value of the running variable in the sample; x is the number ofmaxIs the maximum value of the operating variable in the sample.
Based on the preprocessed data set, the relevance of various operation variables and voltage stabilization safety classification labels in the power system is detected by using the DCC, the obtained DCC values are sorted in a descending order, the first z operation variables are selected as key features, and the key features and the corresponding safety classification labels form a high-efficiency data set.
DCC is shown in equation (4):
Figure BDA0002454303500000065
in the formula: x and y represent key features and corresponding security classification tags, respectively;
Figure BDA0002454303500000066
Figure BDA0002454303500000067
and
Figure BDA0002454303500000068
as shown in formulas (5) to (7), respectively:
Figure BDA0002454303500000069
Figure BDA0002454303500000071
Figure BDA0002454303500000072
computing by analogy
Figure BDA0002454303500000073
And
Figure BDA0002454303500000074
DCC has the following properties:
(1) when DCC is equal to 0, it means that the two variables are independent of each other;
(2) the larger the DCC, the stronger the correlation between the two variables.
In step 3, based on the feature-selected efficient dataset, a power system VSA model is constructed using the improved AdaBoost. And taking the key features as input and the voltage stabilization safety classification label as output to obtain the mapping relation between the key features and the safety classification label.
The principle of the AdaBoost algorithm is as follows:
(1) the efficient data set after preprocessing and feature selection is { X1,...,XnY, wherein XiRepresenting key features, and Y represents a voltage stabilization safety classification label;
(2) initializing training weight of a sample, performing iterative training, and generating a weak classifier h corresponding to each feature in the samplei(x) Weak classifier hi(x) As shown in equation (8):
Figure BDA0002454303500000075
in the formula: x is the number ofiThe ith characteristic value in the sample is taken; p is a radical ofi± 1, for changing the direction of the inequality; thetaiRepresenting the threshold of the ith weak classifier.
(3) Selecting a weak classifier h with the minimum classification error from the determined weak classifiers in each trainingtPerforming iterative training for M times to obtain M weak classifiers;
(4) the M weak classifiers are weighted and integrated to form a strong classifier, and the strong classifier is shown as a formula (9):
Figure BDA0002454303500000076
in the formula: m is the number of weak classifiers; a istIs a weak classifier htThe weight coefficient of (2).
AdaBoost can judge whether the sample of each training is classified correctly, for the sample classified correctly, the weight of the sample is reduced, and for the sample classified incorrectly, the weight of the sample is increased. And determining the weight of each sample in the data set in the next iterative training based on the classification accuracy obtained in the last time. Therefore, the dynamic weight of the sample can be trained through each iteration, the classification focus is concentrated on the sample which is difficult to classify, and the higher classification accuracy is finally obtained.
In order to inhibit the occurrence of the overfitting phenomenon and process the training samples which are difficult to be classified, the method improves the weight updating mode, not only combines the error rate of stable samples and the error rate of unstable samples, but also inhibits the weight increase amplitude of the misclassified samples. The improved weight update procedure is as follows:
(1) when the sample classification is correct, the classification weight of the sample is updated as shown in equation (10):
wt+1,j＝wt,jexp(-at) (10)
in the formula: a istIs a weak classifier htThe weight coefficient of (a); w is at,jTraining the weight of the sample j for the t iteration; w is at+1,jThe weight of the sample j in the t +1 th iterative training is given.
(2) When the sample is classified incorrectly, the weights of the samples are updated as follows:
error rate when stabilizing sample β1Positive real numbers greater than and tending to zero1The update of the weights of the wrongly-divided stable samples is shown in equation (11):
wt+1,j＝wt,jexp(at(1-β1)) (11)
error rate when unstable sample β2Positive real numbers greater than and tending to zero2The update of the weight of the erroneously divided unstable sample is shown in equation (12):
wt+1,j＝wt,jexp(at(1-β2)) (12)
in consideration of the change of the operating conditions of the power system, the model after off-line training may not provide accurate and reliable evaluation results for the new operating conditions. At this time, the model needs to be updated, and the updating steps are as follows:
(1) if the new working condition generated by the change of the operating condition of the power system is contained in the offline data set, selecting a corresponding VSA model to evaluate the new working condition;
(2) if the operating conditions or topology changes of the power system are not contained in the offline data set, a new VSA model needs to be trained using the new data set.
In step 4, based on the real-time measurement data collected by the PMU, selecting corresponding key features, and performing online VSA on the power system by using the trained VSA model.
Example (b):
the present invention was tested in an IEEE30 node system and an IEEE 50 machine system, respectively. Wherein the IEEE30 node system comprises 30 nodes, 6 generators and 41 transmission lines; the IEEE 50 system includes 50 generators, 145 buses, and 453 transmission lines. The simulation software adopts PSS/E to simulate three-phase short circuit faults, and the fault removal time is 1 second. 5000 samples were generated in the IEEE30 node system, and 8000 samples were generated in the IEEE 50 machine system. 80% of the samples generated by each system were used for training, and 20% were left for testing. All tests were performed on a computer equipped with an Intel Core i7 processor and 8GB memory.
Using the accuracy (A)cc) And F1Value to evaluate the model performance, F1Is the precision ratio (P)re) And recall rate (R)ec) Harmonic mean value of (1), of size PreAnd RecAnd (4) jointly determining. A. theccAnd F1As shown in formulas (13) to (16):
Figure BDA0002454303500000091
Figure BDA0002454303500000092
Figure BDA0002454303500000093
Figure BDA0002454303500000094
in the formula: t is11，T01，T10，T00The number of stable samples, the number of unstable samples, and the number of unstable samples are respectively determined as the number of stable samples, the number of unstable samples, and the number of unstable samples.
In order to verify the data processing speed and other various performances of the VSA model in the present invention, a series of performance tests were performed on the VSA model provided in the present invention in the IEEE30 node system and the IEEE 50 machine system, respectively, and the results of the VSA model performance tests are shown in table 1. As can be seen from Table 1, the VSA model provided by the invention has high data processing speed and evaluation accuracy, and can be used for carrying out safe and effective VSA on a modern power system.
TABLE 1VSA model Performance test results
Test system Training time Time of measurement Acc F1
IEEE30 node system 35.42 seconds 3.01 second 0.9784 0.9718
IEEE 50 machine system 73.37 seconds 6.28 seconds 0.9663 0.9605
Modern power systems are quite complex in structure and are changing from time to time. In order to verify the robustness of the VSA model provided by the present invention, the VSA model provided by the present invention is subjected to robustness tests in an IEEE30 node system and an IEEE 50 machine system, respectively, the system topology changes are shown in table 2, and the robustness test results of the VSA model are shown in fig. 4 and 5. As can be seen from fig. 4 and 5, the VSA model provided by the present invention has strong robustness in dealing with changes in the topology of the power system, and can meet the requirements of modern power system security evaluation.
TABLE 2
System topology change
Type of accident IEEE30 node system IEEE 50 machine system
N-1 Lines 2-6 are taken out of service Lines 90-92 are taken out of service
N-1 Lines 16-17 are taken out of operation Line 134 and 144 exit run
N-1 No. 3 generator quits operation No. 12 generator quits operation
N-2 No. 3 generator and 2-6 lines exit from operation Lines 90-92, 134 and 144 are taken out of service
N-2 No. 5 generator, lines 16-17 quit operation No. 12 generator, lines 90-92 exit operation
In order to further verify the superiority of the model proposed by the present invention, the same data were used to perform VSA on DT, RF, SVM, E L M, respectively, as shown in table 3, it can be seen from table 3 that the VSA model proposed by the present invention has higher accuracy compared to other models.
TABLE 3
VSA model and other model performance comparison results
Figure BDA0002454303500000111

Claims (9)

1. A static voltage stability evaluation method of an electric power system based on improved AdaBoost is characterized by comprising the following steps:
step 1: solving a power flow based on simulation of historical operating data and an expected accident set of the power system, and constructing an initial data set containing operating variables and voltage stabilization safety classification labels of the power system;
step 2: preprocessing and selecting characteristics of the initial data set, selecting operation variables with high correlation degree with the voltage stabilization safety classification labels from a large number of operation variables as key characteristics, and combining the corresponding safety classification labels to form a high-efficiency data set;
and step 3: constructing a Voltage Stability Assessment (VSA) model of the power system by combining an improved AdaBoost algorithm based on the efficient data set, and performing offline training and updating on the VSA model by using the efficient data set;
and 4, step 4: on the basis of real-time Measurement data collected by a Phasor Measurement Unit (PMU), online VSA is performed on the power system by using a VSA model.
2. The method for evaluating the static Voltage Stability of the power system based on the improved AdaBoost according to claim 1, wherein in step 1, a P-V curve of the power system is solved by using a continuous power flow method, and a Voltage Stability Index (VSI) and a Voltage Stability safety classification label are constructed according to the P-V curve, as shown in formulas (1) and (2):
Figure FDA0002454303490000011
Figure FDA0002454303490000012
in the formula: pmaxA load power that is a maximum power transmission point; piLoad power for the current operating point; VSIcThe voltage stability threshold is self-defined; label 1 represents steady state; label 0 indicates an unstable state.
3. The method for evaluating the static voltage stability of the power system based on the improved AdaBoost according to claim 1, wherein in step 2, a large number of power system operating variables (such as voltage amplitude and phase angle of each node, active power output and reactive power output of a generator, and the like) in the initial data set are preprocessed to make the value range of the power system operating variables (0, 1) so as to reduce the computational burden, and the preprocessing process is as shown in formula (3):
Figure FDA0002454303490000021
in the formula: x is the number ofiThe original value of a certain operation variable of the power system;
Figure FDA0002454303490000022
the operation variable is a value after pretreatment; x is the number ofminIs the minimum value of the running variable in the sample; x is the number ofmaxIs the maximum value of the operating variable in the sample.
4. The method as claimed in claim 3, wherein in step 2, based on the preprocessed data set, a Distance Correlation Coefficient (DCC) is used to detect correlations between various operating variables in the power system and voltage stabilization safety classification tags, and the obtained DCC values are sorted in a descending order, and the first z operating variables are selected as key features to form a high-efficiency data set together with the corresponding safety classification tags.
5. The method for evaluating the static voltage stability of the electric power system based on the improved AdaBoost according to claim 4, wherein in the step 2, DCC is as shown in formula (4):
Figure FDA0002454303490000023
in the formula: x and y represent key features and corresponding security classification tags, respectively;
Figure FDA0002454303490000024
Figure FDA0002454303490000025
and
Figure FDA0002454303490000026
as shown in formulas (5) to (7), respectively:
Figure FDA0002454303490000027
Figure FDA0002454303490000028
Figure FDA0002454303490000029
computing by analogy
Figure FDA00024543034900000210
And
Figure FDA00024543034900000211
6. the method for evaluating the static voltage stability of the power system based on the improved AdaBoost is characterized in that in step 3, based on the efficient data set selected through the features, an electric power system VSA model is constructed through the AdaBoost, the key features are used as input, the voltage stability safety classification labels are used as output, and the mapping relation between the key features and the safety classification labels is obtained.
7. The method as claimed in claim 1 or 6, wherein in step 3, the AdaBoost determines whether the samples trained each time are classified correctly, reduces the weight of the samples for correctly classified samples, increases the weight of the samples for incorrectly classified samples, determines the weight of each sample in a data set during next iterative training based on the classification accuracy obtained last time, and concentrates the classification focus on the samples difficult to classify by training the dynamic weight of the samples each time, so as to obtain a higher classification accuracy.
8. The method for evaluating the static voltage stability of the electric power system based on the improved AdaBoost as claimed in claim 7, wherein in step 3, in consideration of the change of the operating condition of the electric power system, the model after offline training may not provide an accurate and reliable evaluation result for the new operating condition, and at this time, the model needs to be updated, and the updating steps are as follows:
(1) if the new working condition generated by the change of the operating condition of the power system is contained in the offline data set, selecting a corresponding VSA model to evaluate the new working condition;
(2) if the operating conditions or topology changes of the power system are not contained in the offline data set, a new VSA model needs to be trained using the new data set.
9. A method for constructing a power system VSA model by utilizing an improved AdaBoost algorithm is characterized by comprising the following steps:
(1) initializing training weight of a sample, performing iterative training, and generating a weak classifier h corresponding to each feature in the samplei(x) Weak classifier hi(x) As shown in equation (8):
Figure FDA0002454303490000031
in the formula: x is the number ofiThe ith characteristic value in the sample is taken; p is a radical ofi± 1, for changing the direction of the inequality; thetaiA threshold representing the ith weak classifier;
(2) selecting a weak classifier h with the minimum classification error from the determined weak classifiers in each trainingtPerforming iterative training for M times to obtain M weak classifiers;
(3) the M weak classifiers are weighted and integrated to form a strong classifier, and the strong classifier is shown as a formula (9):
Figure FDA0002454303490000032
in the formula: m is the number of weak classifiers; a istIs a weak classifier htThe weight coefficient of (2).
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