CN112564090B - MBLDA-based AC/DC system transient voltage stability monitoring method - Google Patents
MBLDA-based AC/DC system transient voltage stability monitoring method Download PDFInfo
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Abstract
The invention discloses an alternating current-direct current system transient voltage stability monitoring method based on MBLDA, which comprises the following steps: reading voltage simulation data of each node to simulate the measurement process of a PMU; integrating the node voltages, constructing a node voltage track cluster related to the voltages by using the track cluster, describing the transient voltage after the power system fails by using the physical attributes of the track cluster, and constructing an input feature set reflecting the voltage state of the power system; randomly distributing an input feature set into a training set and a testing set, determining an optimal projection matrix w of a fault sample through four voltage state samples MBLDA in the training set, finishing the construction of a classifier model, and inputting the feature set corresponding to the testing set into the trained MBLDA model; and monitoring the voltage stable state of the power system by using the optimal projection matrix w, and performing transient stability monitoring on other fault samples of the power system by using the monitoring process. The invention overcomes the defect of the transient voltage monitoring type after the fault of the existing high-proportion power electronic receiving end system.
Description
Technical Field
The invention relates to the field of transient voltage stability, in particular to an alternating current-direct current power system transient voltage stability monitoring method based on multi-class linear discriminant analysis (MBLDA).
Background
With the continuous increase of the scale of the alternating current-direct current interconnected power system in China, the large-scale transfer of the power flow caused by the phase change failure of the direct current power system after the large disturbance, the voltage of the receiving end power system is reduced, and the voltage stability problem of the alternating current receiving end power system is more severe due to the shortage of transmission power [1] . The large-scale new energy and flexible direct-current trans-regional power transmission access gradually replace part of synchronous machines of the original synchronous power grid, and a high-proportion power electronic receiving end power system is formed [2] Therefore, the transient voltage stability monitoring of the high-proportion power electronic receiving system has important significance for ensuring the safe and stable operation of the power system [3] 。
The transient voltage stability monitoring method for power system mainly includes time domain method [4] Energy function method [5] And pattern recognition method [6] . The time domain simulation method is characterized in that a full power system model is formed by topological relations among all dynamic elements, and the change curves of the state quantity and the generation quantity of the power system are gradually obtained by solving a differential equation in the transient process of the power system, so that the stable state of the power system is judged. The method is simple and visual, but in the face of a large-scale power system, the simulation calculation amount is large, the conclusion whether the power system is stable can be obtained only through simulation, and accurate information of the stability degree of the power system is difficult to obtain [7] (ii) a The energy function method mainly carries out stability judgment by constructing the Lyapunov function, can make up the defects of time domain simulation on the calculation efficiency, and has the advantages of stability margin and the like, but the method is easily limited by a power system model and has complex dynamic conditionsThe energy function in the characteristic power system may not exist, and the model universality is poor [8] (ii) a The pattern recognition method utilizes a big data mining method to establish a mapping relation between a fault sample and the stable state of the power system, and carries out transient stability monitoring on the power system through the mapping relation, has the advantages of high calculation speed, high monitoring accuracy, small influence by the scale of the power system and the like, and is widely applied to real-time monitoring of the power system [9] 。
At present, a pattern recognition method mainly develops research around feature construction and classifier model construction. The characteristic construction aspect is as follows: current feature types can be divided into timing features, discrete features, and aggregate features that incorporate a time dimension. Document [10] describes a feature learning method taking key local trajectory difference of a power system stability/instability case as a core on the basis of time sequence trajectory Shapelet (subsequence with strongest category resolution), and shows feasibility of construction taking time sequence variables as features. Document [11] shows that the transient stability of the power system can be predicted in a shorter time after the fault by applying the voltage amplitude than the power angle, so that more reliable transient stability monitoring is realized. Document [12] performs transient stability prediction by extracting disturbed generator terminal voltage trajectory cluster characteristics.
The classifier construction aspect: the classifier in the current pattern recognition method can be roughly divided into an artificial neural network, a decision tree and a support vector machine. Compared with other methods such as a neural network and the like, the support vector machine has the advantages of few required training samples, strong generalization capability and the like, so that the support vector machine is widely applied to the field of transient stability monitoring of power systems. However, in practice, most problems exist in many types. Under the influence of multi-loop direct current centralized feed-in and penetration of new energy high-proportion power electronic equipment, the transient voltage instability state of a receiving-end power grid is mainly three types: delayed voltage recovery phenomenon [18] Continuous low voltage phenomenon of power system [19] Voltage oscillation fluctuation of power system [20] . Therefore, the students propose a multi-classification algorithm, which mainly has one-to-one support vectorMachine for producing thin films [13] And one-to-many support vector machines [14] However, the SVM (support vector machine) has the defect of high computational complexity [15] 。
In recent years, the method based on linear discriminant analysis has the advantage of high precision in processing high-dimensional data, and is paid certain attention [16][17] . However, the linear discriminant analysis method needs to calculate a characteristic value problem, which seriously affects the model solving speed and reduces the calculation efficiency, so that the application of the method in the transient voltage monitoring of a high-proportion power electronic receiving end power system is limited to a certain extent. In addition, the existing research only analyzes a single voltage type after the fault of the power system by a time domain simulation method, and does not analyze and monitor various voltage types after the fault of a high-proportion power electronic receiving end system.
Therefore, each voltage type after receiving end power grid fault is monitored by a pattern recognition method, and a power system can quickly take corresponding improvement measures, so that the method has important practical significance for constructing a safe, efficient, clean and environment-friendly high-proportion power electronic system.
Reference to the literature
[1] Cai Zexiang, feng Lei, yang Huanhuan, and so on, the influence of the reactive dynamics of the high-voltage direct-current system on the transient voltage stability [ J ]. Proceedings of university of science in south china (nature science edition), 2017, 45 (04): 1-7.
[2] Mao Angu, ma Jing, kuai shengyu, and the like, an evolution mechanism of system transient stability and voltage stability after a high-proportion new energy replaces a conventional power supply [ J ]. China Motor engineering newspaper 2020, 40 (09): 2745-2756.
[3] Chen Bo, wang Liang, zhang Bing and the like, the problem of voltage stabilization of a receiving-end power grid under the background of high-proportion penetration of extra-high voltage alternating current and direct current hybrid new energy is discussed [ J ]. Shandong power technology 2020, 47 (06): 36-40.
[4] Wang Yajun, wang Bo, tang Fei, et al. Power system online transient stability assessment based on response trajectory and core vector machine [ J ]. Proceedings of motor engineering, 2014, 34 (19): 3178-3186.
[5] Yao Dequan, gu Hongjie, zhao Shuai power system transient stability assessment and margin prediction based on a composite neural network [ J ] power system automation, 2013, 37 (20): 41-46.
[6] Jiang Tao, wang Changjiang, chen Houge, et al power system transient stability assessment based on regularized projection twin support vector machine [ J.
[7] Paqiang, duwenjuan, wang Haifeng, analysis of small disturbance stability of AC/DC series-parallel power system reviews [ J ]. Report on China Motor engineering, 2018, 38 (10): 2829-2840+3134.
[8] Chen Houge, wang Changjiang, jiang Tao, and so on, port energy-based transient stability assessment for VSC-HVDC-containing AC/DC hybrid systems [ J ]. Proc. Electrotechnical Commission, 2018, 33 (03): 498-511.
[9] Yang Xiaonan, sun Bo, lang Yansheng extra-high voltage direct current blocking fault intelligent scheduling decision [ J ] based on deep learning, china power, 2020, 53 (06): 8-17.
[10] Zhu Lipeng, liu Chao, yellow river, et al, transient voltage stability assessment based on timing trajectory characteristics learning [ J ] grid technology, 2019, 43 (06): 1922-1931.
[11]Francisco R.Gomez，Athula D.Rajapakse.Support vector mchine based algorithm for post-fault transient stability status prediction using synchronized measurements[J].IEEE Transactions on Power Systems，2011，26(3):1474-1483.
[12] Ji Lu Yu, wu Junyong, zhou Yanzhen, et al, prediction of transient stability of power systems based on WAMS perturbed voltage trajectory cluster characteristics [ J ]. High voltage techniques, 2015, 41 (03): 807-814.
[13]Liu Y，Bi JW，Fan Z P.A method for multi-class sentiment classification based on an improved one-vs-one(OVO)strategy and the support vector machine(SVM) algorithm[J].Information Sciences，2017，394:38-52.
[14] Hong Cui, paiyze, guo Mou, et al, improve the method for identifying faults in power distribution networks of multi-class support vector machines [ J ]. Electronic measurement and instrumentation reports, 2019 (1): 7-15.
[15] Dai Yuanhang, chen Lei, zhang Weiling, et al. Power System transient stability assessment based on Multi-SVM integration [ J ]. Proc. Chinese Motor engineering, 2016, 36 (5): 1173-1180.
[16]DAI Yuanhang，CHEN Lei，ZHANG Weiling，et al.Power System Transient Stability Assessment Based on Multi-Support Vector Machines[J].Proceedings of the CSEE， 201636(5):1173-1180.
[17]HU Wei，SHEN Weining，ZHOU Hua，et al.Matrix Linear Discriminant Analysis.[J].Technometrics:a journal of statistics for the physical，chemical，and engineering sciences，2020，62(2).
[18]Cheong Hee Park，Gyeong-Hoon Lee.Comparison of incremental linear dimension reduction methods for streaming data[J].Pattern Recognition Letters，2020，135.
[19] Auxiliary intelligence Sun Wen, li Xiaoming dynamic voltage/reactive power sensitivity method for improving power grid voltage delay recovery [ J ] power system and its automatic chemical report 2016, 28 (10): 42-46+54.
[20] Li Dongdong, liang Zichao, zhou Yuqi. Receiving end system transient voltage stability evaluation of wind farm [ J ] power system protection and control, 2015, 43 (13): 8-14.
Disclosure of Invention
The invention provides an alternating current-direct current system transient voltage stability monitoring method based on MBLDA, which overcomes the defects of the transient voltage monitoring type after the fault of the existing high-proportion power electronic receiving system and the problem that the monitoring speed of a multi-classifier model on a large-scale power system is slow, has stronger universality and practicability, and is described in detail as follows:
an MBLDA-based alternating current and direct current system transient voltage stability monitoring method comprises the following steps:
simulating the fault of the power system by a PSD-BPA time domain simulation method, and simulating the measurement process of a PMU by reading voltage simulation data of each node;
integrating the node voltages, constructing a node voltage track cluster related to the voltage by using the track cluster, describing the transient voltage after the power system fault through the physical attribute of the track cluster, and constructing an input feature set reflecting the voltage state of the power system;
randomly distributing an input feature set into a training set and a testing set, determining an optimal projection matrix w of a fault sample through four voltage state samples MBLDA in the training set, finishing the construction of a classifier model, and inputting the feature set corresponding to the testing set into the trained MBLDA model;
and monitoring the voltage stable state of the power system by using the optimal projection matrix w, comparing the monitoring result with the time domain simulation result, completing the precision test of the classifier model, and performing transient stability monitoring on other fault samples of the power system by using the monitoring process when the precision meets the requirement.
The optimal projection matrix w is used for enabling the similarity of the voltage data after projection to be high, and enabling a pair of categories to be far away from each other.
Further, the expression of the optimal projection matrix w is as follows:
s.t.||w ij ||＝1
wherein, 1 is less than or equal to i<j is less than or equal to k, and k is the number of categories; max J is w when the maximum of equation J ij The value of (c). w is a ij Projection matrices of class i and j, c i Is the mean vector of the i-th sample, T is the transposed matrix, o is the number of samples, c j Is the mean vector of the jth sample, p and q are respectively the pth sample and the qth sample, N P Is a category matrix, x q For class q sample voltage data, c p The mean vector of the p-th type sample is obtained;
the above formula is equivalent to:
s.t.||w ij ||＝1
wherein S is ij ＝o(c i -c j )(c i -c j ) T ；
Formula (2) is rewritten as:
s.t.||w||＝1
wherein, a = (a) 1 ,…,a n ) T Is a non-zero vector; w is a projection matrix; a is an intra-class dispersion matrix;
max λ
s.t.Bw＝λAw,||w||＝1
wherein B = aa T The formula is a generalized eigenvalue problem, and the maximum generalized eigenvalue lambda epsilon R of B is solved, and the generalized eigenvector w epsilon R corresponding to A is solved n And R is a real number set.
The technical scheme provided by the invention has the beneficial effects that:
1. the method can quickly and effectively classify four states of voltage quick recovery, voltage delay recovery, continuous low voltage and voltage oscillation after the fault through the MBLDA model, and monitors the specific voltage state of a receiving end power grid after the fault of the power system, so that corresponding improvement measures are taken, and the method has important practical significance for constructing a safe, efficient, clean and environment-friendly high-proportion power electronic system;
2. the method considers a high-proportion power electronic receiving end power grid, and adds devices such as a fan, a photovoltaic device, a flexible device and a straight device, so that the method has strong universality;
3. according to the method, fault samples of the high-proportion power electronic receiving end system are classified and monitored through the MBLDA model, the calculation efficiency can be effectively improved, a large amount of calculation time is saved on the premise that the monitoring accuracy is guaranteed, and precious time is strived for regulation and control after the fault.
Drawings
FIG. 1 is a flow chart of a transient voltage stability monitoring method for an MBLDA-based AC/DC system;
FIG. 2 is a topology diagram of a modified IEEE-39 node power system;
FIG. 3 is a comparison graph of monitoring accuracy at different sampling cycles;
FIG. 4 is a transient voltage plot of 100% rated power;
FIG. 5 is a transient voltage plot of 110% rated power;
FIG. 6 is a transient voltage plot of 120% rated power;
FIG. 7 is a comparison graph of training times for multiple classifiers.
FIG. 8 is a comparison graph of classification time for multiple classifiers.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention are described in further detail below.
In order to improve the speed and the precision of monitoring the transient voltage stability state of the alternating-current and direct-current power grid and make up the deficiency of time domain simulation in the calculation efficiency, the embodiment of the invention provides an alternating-current and direct-current system transient voltage stability monitoring method based on the MBLDA on the basis of a voltage trajectory cluster theory and inter-class linear discriminant analysis.
Firstly, acquiring information of each voltage disturbed track cluster of a power system after a fault, defining 29 characteristic indexes by using the geometric attributes of the track cluster, and constructing a characteristic set closely related to the transient voltage stability of the power system; and secondly, replacing the eigenvalue problem solved in the linear discriminant analysis with the under-determined homogeneous equation set problem, and reducing the calculation complexity, thereby improving the solving speed of the multi-classifier model on the samples and improving the monitoring efficiency of four voltage fault states in the actual operation process of the large-scale power system. And finally, constructing a high-proportion power electronic system to monitor the transient voltage stability, and verifying the feasibility and effectiveness of the method.
Example 1
The embodiment of the invention provides an MBLDA-based method for monitoring the transient voltage stability of an alternating current and direct current power system, which comprises the following steps of:
101: simulating a power system fault by a PSD-BPA (power flow and transient stability program) time domain simulation method, generating a fault sample library, and simulating a measurement process of a PMU (Wide area measurement System) by reading voltage simulation data of each node;
102: integrating the acquired node voltages, constructing a node voltage track cluster related to the voltage by using track cluster definition, describing the transient voltage after the power system fault through the physical attribute of the track cluster, and constructing an input feature set reflecting the voltage state of the power system;
103: randomly distributing an input feature set into a training set and a testing set, determining an optimal projection matrix w of a fault sample through four voltage state samples MBLDA in the training set, finishing the construction of a classifier model, and inputting the feature set corresponding to the testing set into the trained MBLDA model;
104: the voltage stable state of the power system is monitored by utilizing the optimal projection matrix w, the monitoring result is compared with the time domain simulation result, the precision test of the classifier model is completed, when the precision meets the engineering requirement, the transient stability monitoring can be carried out on other fault samples of the power system by utilizing the monitoring process, and the safe operation of the power system is guaranteed.
In summary, in the embodiments of the present invention, through the steps 101 to 104, the computation complexity is reduced by using the voltage trajectory cluster theory and the inter-class linear discriminant analysis method, so that the solution efficiency of the multi-classifier model is improved, and the accurate and fast monitoring of the transient voltage stability of the ac/dc system is further realized.
Example 2
The scheme of example 1 is further described below in conjunction with the specific calculation formula, table 1, and described in detail below:
201: regarding voltage track clusters of all nodes in a system after a fault as a whole, 3 major 29 characteristic indexes are defined according to the geometric attributes of the track clusters as follows:
if the track cluster is expressed as { X i(j) And j =1,2 … n, wherein n is the number of sampling points, and m is the number of voltage tracks of each node in the power system.
1) Track cluster base attribute
Mass center line:
the dispersion of each track on the track cluster section relative to the mass center line is as follows:
the upper envelope line, the lower envelope line and the central line are respectively as follows:
{max(X j )}j＝1,2,....n (3)
{min(X j )}j＝1,2,....n (4)
2) Rate of change and curvature properties
Rate of change of trajectory:
where h is the time sampling interval.
Curvature of the trajectory:
the mass center line, the dispersion and the change rate and curvature of the envelope can be calculated by the formula (6) and the formula (7), the specific calculation steps are well known in the art, and the detailed description is omitted in the embodiment of the invention.
3) Acceleration properties
Centroid line instantaneous change acceleration:
wherein r is c(j) The acceleration characteristic of the other basic attribute characteristic can be defined by equation (8) as the trajectory of the rate of change of the centroid line.
An input feature set is constructed from the above-described sought trajectory cluster attributes, as shown in table 1.
TABLE 1 track Cluster feature quantity definition
The voltage of the power system after the fault is described through 29 characteristic attributes, the constructed input characteristic set can reflect the operation condition of the power system after the fault, the change situation of the voltage of each node of the power system in a plurality of Zhou Bohou after the fault is removed is effectively described, and the method has certain representativeness on the stable state of the power system. Then, a more accurate classifier model can be trained through the input feature set, and the transient stability monitoring is performed on the state of the power system.
202: linear Discriminant Analysis (LDA) is a classification method with supervised learning, which can effectively utilize the category information of original data to perform accurate feature extraction, and by seeking a projection transformation matrix, the method makes different voltage categories have high dissimilarity and the same voltage category has high similarity, thereby effectively solving the problem of multi-classification.
Suppose there is X = [ X1, X2, …, X i ]∈R o×p A matrix representing a sample set of voltage data, o being the number of samples and p being the dimension. k is the number of voltage classes and the class matrix is N i (1≤i≤k)。
The LDA aims to search a projection matrix w to ensure that the heterogeneous dissimilarity is high and the homogeneous similarity is high, and an expression formula is shown as a formula (9):
where T is the transposed matrix, c i And c is the mean vector of the ith sample and the whole sample, respectivelyThe following equation (10) yields:
defining an intra-class dispersion matrix S of a sample w Comprises the following steps:
define an inter-class divergence matrix S of samples b Comprises the following steps:
equation (9) can be simplified as:
by solving equation (13) for the generalized eigenvalues, we need to make the partial derivative of w to maximize J (w) and make its derivative equal to 0, we can obtain:
(w T S w w)S b w＝(w T S b w)S w w (14) is derived from formula (13) formula (14):
S b w＝λS w w (15)
wherein λ is J (w).
Finishing to obtain (15):
the maximized object J (w) corresponds to the matrix
And the projection matrix is the eigenvector corresponding to this eigenvalue. The closed-form solution of the projection matrix w is then pick->
The N-1 maximum generalized eigenvalues of the data sample are calculated, and then the category of the data sample is judged according to the obtained projection matrix, so that the problem of multi-classification is solved.
203: the problem of low calculation efficiency when transient stability monitoring is carried out on a large-scale power system can be solved by adopting multi-between-class linear discriminant analysis (MBLDA). The model is consistent with the central idea of LDA, and samples are projected to a matrix, so that the projection points of the voltage homogeneous samples are as close as possible, and the projection points of the voltage heterogeneous samples are as far away as possible.
The data after the projection of the same kind of samples should be as close as possible, and the data is realized by minimizing the denominator in the formula (9) in the LDA; the data after heterogeneous sample projection is as far away as possible, which is achieved by maximizing the denominator in equation (9) in LDA. However, the LDA only considers the average condition of data when analyzing heterogeneous sample data, and should consider the worst condition of data between heterogeneous samples, so modifying equation (9) can obtain:
wherein x is q For class q sample voltage data, c p Is the mean vector of class p samples, N p Is a category matrix.
The above equation is equivalent to the mixed integer min-max programming problem, as shown in equation (18):
the above problem can be relaxed as a distance metric learning problem, which is a typical SDP (semi-defined programming) problem, but the solution obtained by the relaxation may not be an optimal solution, and it takes long time to solve a high-dimensional SDP problem, reducing computational efficiency.
As can be seen from equation (18), the optimization problem is associated with each two categories, and several simplified sub-problems can be obtained by determining i and j in equation (18), so as to find k (k-1)/2 approximate solutions, and find the optimal solution.
204: based on the thought, the method for linear discriminant analysis (MBLDA) among multiple classes is provided, and an approximate projection matrix w is searched ij The similarity between the projected voltage data and the class is made high and a pair of classes (i-th and j-th classes) are far from each other as shown in the following formula:
wherein i is more than or equal to 1 and j is less than or equal to k, and k is the number of categories.
Equation (19) may be equivalent to:
wherein S is ij ＝o(c i -c j )(c i -c j ) T 。
The visible formula (20) can be rewritten as follows:
wherein, a = (a 1, …, a) n ) T Is a non-zero vector.
Equation (21) can be solved by equation (22).
Wherein B = aa T The formula (22) is a generalized eigenvalue problem, and the maximum generalized eigenvalue lambda epsilon R of B and the corresponding generalized eigenvector w epsilon R of A are solved n And R is a real number set.
In order to rapidly solve the generalized eigenvalue problem, the generalized eigenvalue problem can be converted into an underdetermined equation problem, so that the calculation efficiency is improved.
The characteristic values of B are obviously:
μ 1 ＝||a|| 2 ,μ 2 ＝...μ n ＝0 (23)
wherein, mu 1 ，μ 2 ...μ n Is the characteristic value of B.
The corresponding set of feature vectors is represented as:
wherein, a 1 ,a 2 ,...,a n Is a numerical solution of the feature vector.
Introducing diagonal matrix D and nonsingular matrix V, then
D＝diag(μ 1 ,μ 2 ,...,μ n ) (25)
V＝(v 1 ,v 2 ,...,v n ) (26)
Wherein v is 1 ,v 2 ,...,v n Are vectors.
From the formulas (25) and (26):
BV＝VD (27)
wherein
Equation (28) may be equivalent to:
wherein U is a vector set of B eigenvalues.
Assuming that w = Vb/| Vb | |, is substituted into equation (28), and is obtained from equations (28) (29):
λUAVb＝0 (30)
wherein, b = (b) 1 ,b 2 ,…b n ) T
The vector b is the solution of the underdetermined homogeneous equation of UAVb = 0.
The united type (26), (29) and (30) can be solved as follows:
i.e. the solution of equation (22) is:
therefore, a solution of a generalized characteristic value is obtained by solving the vector b of an underdetermined homogeneous equation, and a classified projection matrix is obtained, so that the category of the voltage sample data is judged.
In summary, the embodiment of the present invention implements the MBLDA-based ac/dc system transient voltage stability monitoring method through the above steps 201 to 204. On one hand, the transient voltage stable state of the alternating current-direct current system can be rapidly and effectively judged, on the other hand, the defects that the traditional method is easily limited by a power system model and poor in universality are overcome, and the method has the advantages of being high in calculation speed, high in monitoring accuracy, small in influence of system scale and the like.
Example 3
The feasibility of the solutions of examples 1 and 2 is verified below with reference to the specific examples, fig. 2, fig. 3, fig. 4, fig. 5, fig. 6, fig. 7, fig. 8 and tables 2, 3, 4 and 5, as described in detail below:
in the embodiment, the accuracy and the validity of the transient voltage stability monitoring method are verified through the modified IEEE-39 node power system, and the topology of the modified IEEE-39 node power system is shown in figure 5.
In order to verify the accuracy and feasibility of the method, power system simulation software PSD-BPA is used for simulating PMU measurement data of each node after the power system fails, simulation models of 0%, 20% and 50% power electronization degrees are constructed, and N-1 three-phase short-circuit fault time domain simulation is carried out. Generating fault samples under different scenes in batches, and enabling the load level of a power system and the output of a generator to fluctuate in equal proportion within the range of 80-120% of rated power; secondly, enabling the three-phase short-circuit faults to occur at the positions of 5%, 25%, 50%, 75% and 95% of the lines respectively; and simultaneously, the fault clearing time is set to be 0.1 s-0.4 s after the fault occurs, 3400 three-phase short-circuit fault samples are generated in batches, and a fault sample library is constructed.
1) Sample cycle analysis
After N-1 fault samples of the information after the power system fault are obtained, firstly, the node voltage after the fault is processed through track cluster definition, and therefore 29 feature construction is completed. And secondly, judging the type of the node voltage after the fault, thereby obtaining an output characteristic set reflecting the state change of the power system and the stable type. Finally training the MBLDA multi-classifier model and carrying out transient voltage stability monitoring
When the power electronic equipment is 50%, 3400 offline samples randomly constitute 3000 training sets and 400 testing sets, and the classification conditions are shown in table 2.
TABLE 2 sample composition
In table 2, the first category is rapid voltage recovery after a fault, and belongs to a stable phenomenon; the second type is a voltage delay recovery phenomenon; the third type is the sustained low voltage phenomenon; the fourth type is voltage oscillation instability.
In the monitoring process, along with the difference of the selected cycles, the dimensions of the constructed input feature set are different, and the mapping relation obtained by the classifier is also different, so that the accuracy of the multi-classifier model is also changed, as shown in fig. 5.
When data in 4s after fault removal is selected as original data for constructing an input feature set, the MBLDA multi-classification accuracy rate is only 93%. As the read data window gradually increases from 4s to 6s, the model monitoring accuracy also increases to 95.1%. The transient voltage stability state of the power system after the fault can be effectively reflected by the characteristic data set and the characteristic, and meanwhile, the sampling period and the accuracy of the characteristic sample are in a direct proportion relation, so that the monitoring capability of the MBLDA model on the transient voltage is enhanced along with the increase of the sampling window period of the power system.
To achieve higher accuracy, the window period for sampling should be increased. However, as the sampling window period increases, the time for constructing the feature set also increases correspondingly, so that the transient voltage stability of the power system at a future time cannot be quickly judged. And selecting a proper sampling cycle, and making a quick response to the state of the power system after the fault on the basis of ensuring the high precision of the classifier model so as to ensure the safe and stable operation of the power system.
2) Analysis of different power electronization degrees
Compared with the traditional alternating current power system, the power electronic equipment in the power electronic system has the function of fast adjustment, and each element in the power system is subjected to interaction influence, so that the action mechanism is more complex. When the power electronic equipment accounts for 0%, 20% and 50%, respectively, the output of the corresponding conventional generator is adjusted to keep the output of the balancing machine consistent, and the same 3400 offline sample types are shown in table 3.
TABLE 3 sample composition
As can be seen from table 3, as the proportion of the power electronic device increases, the interaction and interaction of the elements in the power system become more complex, and the influence on the voltage stability of the power grid becomes relatively large, so that the number of first-class stable samples in the samples decreases, the number of unstable samples increases, and the risk of transient voltage instability of the power system increases.
The transient voltage curve is shown in fig. 6 when the power system load level and the generator output are at 100% of rated power. When the power electronic equipment accounts for 0% and 20%, the voltage is recovered to be more than 0.8p.u within 1s after the fault, and the power electronic equipment is stable. When the power electronic equipment accounts for 50%, the bus voltage in the power system is recovered to 0.8p.u.s.only 1.46s after the fault, so that the voltage delay recovery phenomenon is caused. With the increase of the power electronization degree of the power system, the voltage of the alternating current node drops seriously during the fault, and the voltage recovery speed is slow after the fault is removed, so that the transient voltage is unstable. Longer periods of low voltage may cause the induction motor load to absorb more reactive power from the grid, thereby further delaying the time for the power system voltage to recover.
When the power system load level and generator output are at 110% of rated power, the transient voltage curve is shown in FIG. 7. When the power electronic equipment accounts for 0% and 20%, the voltage can be quickly recovered after the fault. When the power electronic equipment accounts for 50%, the continuous low-voltage phenomenon occurs in the fan and the photovoltaic grid-connected point after the receiving-end power system fails, and the motor is blocked after the failure is cut off for 1.5 s. If the phenomenon occurs in the power grid, the fan can be guaranteed not to be disconnected through low voltage ride through, but the active power output of the fan is greatly reduced in the low ride through period. With the increase of the proportion of the fan, the reactive power which needs to be absorbed by the fan after the fault is removed is increased, so that the voltage is continuously reduced to further hinder the voltage recovery of a power grid, the fan is possibly disconnected when the voltage is too low, and when the load proportion of a power system is higher, the power system is caused to generate power shortage, and the safe and stable operation of the power system is not facilitated.
The transient voltage curves are shown in fig. 8 when the power system load level and the generator output are at 120% of rated power. As the degree of electronization of power increases, the instability phenomenon becomes more and more severe. When the power electronic equipment accounts for 50%, the voltage of the power system oscillates, so that the power system is broken down.
As can be seen from table 4, in the power systems with different power electronization degrees, after the characteristics are constructed by using the information in 6s after the fault, the accuracy of the MBLDA can be maintained at more than 95%, and the voltage after the fault of the power system is determined, so that corresponding improvement measures are taken to ensure the safe operation of the power system.
TABLE 4 MBLDA accuracy comparison
As can be seen from table 4, in the power systems with different power electronization degrees, after the characteristics are constructed by using the information in 6s after the fault, the accuracy of the MBLDA can be maintained at more than 95%, and the voltage after the fault of the power system is determined, so that corresponding improvement measures are taken to ensure the safe operation of the power system.
3) Accuracy compared to conventional classifiers
After determining the time window range of the data information for constructing the input feature set, the MBLDA is compared with other conventional classifiers for monitoring accuracy.
And each classifier model adopts the same fault sample library, and data processing is carried out on the fault samples by utilizing a voltage track cluster theory to complete feature construction. The input feature set is randomly divided into 3000 training sets and 400 testing sets, each classifier adopts the same training set to train the model, and the same testing set is used for accuracy detection, and the sample classes are shown in table 1.
The selected traditional classifier model comprises a pair of one-top-one (OVO SVMs) [11], a pair of one-top-rest (OVR SVMs) [12], a Linear Discriminant Analysis (LDA) [14], a multi-class Linear Discriminant Analysis (MBLDA), and a time window set to 4 to 6S, as shown in Table 5.
TABLE 5 MBLDA vs. traditional classifier monitoring accuracy
As can be seen from the table, the multi-classification accuracy of MBLDA increases with the time window for reading information from features, and the classification accuracy under different time windows is substantially higher than that of the other three conventional multi-classifiers. When each model adopts information in 4s after fault removal to construct an input feature set, the MBLDA monitoring accuracy can reach 94.8 percent, the monitoring accuracy of other three multi-classifiers is 82.2 percent, 81.7 percent and 94.5 percent respectively, and the MBLDA is higher than that of other classifiers; when the selected fault is removed and the information is in 5s, the MBLDA monitoring accuracy is 95.0%, the monitoring accuracy of other multi-classifiers is 83.6%, 82.2% and 94.9%, and the monitoring accuracy of the MBLDA on the state of the power system is still higher than that of the other multi-classifiers; when the data of the power system in 6s after fault removal is monitored, the monitoring accuracy of the LSPTSVM is 95.1%, the monitoring accuracy of other multi-classifiers is 84.5%, 82.5% and 95.1%, wherein the MBLDA has the same monitoring accuracy as the LDA and still has the advantage in the aspect of precision compared with other multi-classifiers.
Through the analysis, in the aspect of monitoring precision, the MBLDA has certain advantages compared with other traditional multi-classifier models, can still bring higher transient voltage monitoring precision on the premise of meeting engineering requirements, can make accurate judgment when facing a fault threatening normal operation of the power electronic system, provides corresponding information for improving regulation and control of the power system, and ensures safe and stable operation of the power system.
4) Compared with the traditional multi-classifier, the calculation speed
Another advantage of the MBLDA model is that it can quickly react to the transient process of the power system, monitor the voltage stability of the power system, and compare the monitoring time with the monitoring time of the other four kinds of multi-classifiers as shown in fig. 7 and fig. 8.
As can be seen from fig. 7, the training rate of MBLDA is significantly higher than that of other multi-classifiers in different window periods, where the time window is 4s, the training time of three conventional multi-classifiers is 166s, 268s and 324s, respectively, and the training time of MBLDA is 65s; when data within 6s after the fault is removed is selected for training, compared with the multiple classifiers with calculation time of 188s, 308s and 387s respectively and the MBLDA calculation time of 72s, the larger the input sample data amount is, the greater the training time calculation efficiency advantage is. As can be seen from fig. 8, the classification efficiency of MBLDA is significantly higher than other multi-classifiers under different window periods.
By comparing training time and classification time for monitoring the same fault sample set by the MBLDA and each multi-classifier, the calculation complexity is reduced after the MBLDA model converts the solution characteristic value into the solution underdetermined secondary equation in the original projection space, so that the MBLDA model can quickly analyze and solve the input characteristic quantity and quickly monitor the fault state. The training time of the MBLDA is far shorter than that of other multi-classifier models, and the MBLDA has great advantage in computational efficiency, and the advantage becomes more obvious as the scale of data processed by the models increases. After the power electronic receiving end power system suffers from a fault, the fault state can be judged, so that the mode information of improvement measures is provided, and precious time is strived for subsequent protection actions and prevention and control measures.
In the embodiment of the present invention, except for the specific description of the model of each device, the model of other devices is not limited, as long as the device can perform the above functions.
Those skilled in the art will appreciate that the drawings are only schematic illustrations of preferred embodiments, and the above-described embodiments of the present invention are merely provided for description and do not represent the merits of the embodiments.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.
Claims (2)
1. An MBLDA-based alternating current and direct current system transient voltage stability monitoring method is characterized by comprising the following steps:
simulating the fault of the power system by a PSD-BPA time domain simulation method, and simulating the measurement process of a PMU by reading voltage simulation data of each node;
integrating the node voltages, constructing a node voltage track cluster related to the voltage by using the track cluster, describing the transient voltage after the power system fault through the physical attribute of the track cluster, and constructing an input feature set reflecting the voltage state of the power system;
randomly distributing an input feature set into a training set and a test set, determining an optimal projection matrix w of a fault sample through four voltage state samples MBLDA in the training set, finishing the construction of a classifier model, and inputting the feature set corresponding to the test set into the trained MBLDA model;
monitoring the voltage stable state of the power system by using the optimal projection matrix w, comparing the monitoring result with a time domain simulation result, completing the precision test of the classifier model, and performing transient stability monitoring on other fault samples of the power system by using the monitoring process when the precision meets the requirement;
the expression of the optimal projection matrix w is as follows:
wherein, 1 is less than or equal to i<j is less than or equal to k, and k is the number of categories; max J is w when the maximum of equation J ij Value of (a), w ij Projection matrices of class i and j, c i Is the mean vector of the i-th sample, T is the transposed matrix, o is the number of samples, c j Is the mean vector of the jth sample, p and q are respectively the pth sample and the qth sample, N P Is a category matrix, x q For class q sample voltage data, c p The mean vector of the p-th type sample is obtained;
the above formula is equivalent to:
wherein S is ij ＝o(c i -c j )(c i -c j ) T ；
Formula (2) is rewritten as:
wherein, a = (a) 1 ,…,a n ) T Is a non-zero vector; w is a projection matrix; a is an intra-class dispersion matrix;
wherein B = aa T The formula (4) is a generalized eigenvalue problem, and the maximum generalized eigenvalue lambda epsilon R of B and the generalized eigenvector w epsilon R corresponding to A are solved n And R is a real number set.
2. The MBLDA-based AC/DC system transient voltage stability monitoring method according to claim 1, wherein the optimal projection matrix w is used to make the projected voltage data have high inter-class similarity and a pair of classes, i.e. class i and class j, are far away from each other.
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