CN109684749B - Photovoltaic power station equivalent modeling method considering operating characteristics - Google Patents
Photovoltaic power station equivalent modeling method considering operating characteristics Download PDFInfo
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Abstract
The invention discloses a photovoltaic power station equivalent modeling method considering operating characteristics, which comprises the following steps: 1, extracting transient and steady state data of active response characteristics and reactive response characteristics of a photovoltaic power station as an initial variable matrix; 2, decomposing the initial variable matrix into a linear combination of a common factor and a special factor by using a factor analysis method to obtain a factor load matrix; calculating the evaluation value of the score of the common factor on all the photovoltaic power generation units, and using the evaluation value as a clustering index; 4, obtaining the similarity relation of the photovoltaic power generation units and clustering based on correlation analysis and hypothesis test; 5, judging the rationality of the clustering result by using a contour visualization method; and 6, calculating equivalent parameters of the photovoltaic power generation unit and equivalent impedance of the power collection system, and establishing an equivalent model of the photovoltaic power station. The method can effectively extract and quantify the operating characteristics of the photovoltaic power station under the three-phase short-circuit fault working condition, and is applied to equivalent modeling of the photovoltaic power station, so that the established model has higher precision in fitting the external output characteristics of the photovoltaic power station.
Description
Technical Field
The invention relates to the field of photovoltaic power station equivalent modeling methods, in particular to a photovoltaic power station equivalent modeling method based on factor analysis, correlation analysis, hypothesis testing and a contour visualization method.
Background
The maturity of the photovoltaic power generation technology promotes the large-scale development of photovoltaic power stations. The grid connection of a large photovoltaic power station has great influence on the dynamic characteristics of a power grid, and further has important influence on the safe and stable operation of the power grid, so that the modeling and simulation work of the photovoltaic power station is indispensable. The large photovoltaic power station is generally composed of dozens or even hundreds of photovoltaic power generation units, the detailed model data is huge, the structure is complex, the simulation speed is slow, the calculation amount is large, and a scheme for establishing a detailed model is not available. Therefore, the method has important practical significance for researching and establishing the equivalent model of the photovoltaic power station to replace a detailed model to be applied to simulation and analysis of actual engineering.
The research on equivalent modeling of the photovoltaic power station mainly focuses on the selection of clustering indexes and the selection of clustering methods.
The clustering index needs to be capable of representing information such as the operation condition, the fault disturbance and the network topology of the photovoltaic power generation unit. The input environmental parameter indexes of the photovoltaic power generation unit comprise atmospheric environmental factors such as illumination radiance, temperature and humidity and are direct factors influencing photovoltaic output fluctuation and difference, but the meteorological environment is complex and changeable, the uncertainty is too high when the meteorological environment is used as a clustering index, the data measurement is inaccurate, and the consideration on the operating characteristics of a photovoltaic inverter is lacked; the internal control parameter indexes of the photovoltaic inverter have great influence on the dynamic response characteristics of the photovoltaic power station, the differences among the photovoltaic power generation units are essentially reflected, the differences are used as clustering indexes, the equivalence precision is high, but the control parameters are not easy to obtain in actual engineering, a parameter identification method is often needed, and the equivalence difficulty is high; the operation characteristic indexes of the photovoltaic inverter comprise a voltage drop working condition, a protection circuit action, a low voltage ride through, a transient steady state operation working condition and the like, and the indexes are used for clustering, so that the physical significance is clear, and the high identifiability is achieved, but the operation characteristics are difficult to realize quantification and cannot be directly obtained to be used as clustering indexes; the external output characteristic index of the photovoltaic inverter is easy to obtain in actual engineering, the operating characteristic of the photovoltaic inverter can be represented, the external output characteristic index is used as a clustering index and is practical, the external output characteristic is usually a multi-dimensional time sequence index and contains redundant information, the selected variable has strong correlation and subjectivity, intrinsic essential information cannot be mined, and the operating characteristic of the photovoltaic inverter under a given operating condition is blurred.
Clustering methods can be generalized into two categories:
one is algorithm-based clustering. Clustering algorithms are various, such as a k-means algorithm based on partitioning, a Birch algorithm based on hierarchy, a DBSCAN algorithm based on density, a Sting algorithm based on grids and the like. These algorithms typically measure the characteristic distance between clustered data points in a multidimensional space to perform clustering. The clustering algorithm has high processing speed, but the clustering result is easily influenced by sensitive data such as data types, isolated data points, edge data points and the like due to the characteristic of no guidance classification, so that a global optimal solution cannot be obtained, and the accuracy of the clustering result is influenced.
And secondly, clustering based on characteristic information of the photovoltaic power generation units. For example, accurate clustering is achieved according to significant differences in operating characteristics of the photovoltaic inverters; analyzing the clustering characteristic of the transient and steady response curve, extracting the landmark demarcation points and realizing effective clustering; and measuring the similarity of the photovoltaic power generation units by using the clustering indexes to realize system clustering. The method does not need to depend on a complex algorithm, clustering is directly carried out according to the obvious characteristic difference between the photovoltaic power generation unit classes, the principle is simple, the calculation is convenient, but the characteristic information for direct clustering is often difficult to obtain or effectively quantize, and further research is needed.
Disclosure of Invention
In order to solve the problems, the invention provides a photovoltaic power station equivalent modeling method considering operating characteristics, so that the operating characteristics of a photovoltaic power station under a three-phase short-circuit fault working condition can be effectively extracted and quantified, and the method is applied to the photovoltaic power station equivalent modeling, so that a built model has higher precision in fitting the external output characteristics of the photovoltaic power station.
The technical scheme adopted by the invention for solving the technical problems is as follows:
the photovoltaic power station equivalent modeling method considering the operating characteristics is characterized by comprising the following steps of:
step 2.1, make the initial variable matrix record as
X i Represents the ith dimension initial variable and has: x i ＝[x i1 x i2 … x ij … x in ]，x ij J is more than or equal to 1 and less than or equal to n, i is more than or equal to 1 and less than or equal to p, n is the sample capacity, and p is the total number of dimensions;
establishing a factor analysis model by using the formula (1) for decomposing the jth sample x in the ith dimension initial variable ij ：
In the formula (1), f kj Represents the k-th common factor F k Score of factor on jth sample, and f kj ∈F k ，F k ＝[f k1 f k2 … f kj … f kn ]，F k ∈F，
Representing a common factor, wherein k is more than or equal to 1 and less than or equal to m, m is less than p, and m represents the number of the common factor; coefficient a ik Is the kth common factor F k Initial variable X of ith dimension i Factor load of (a) ik E.g. A, A represents the factor load matrix, and A = (a) ik ) p×m ，ε ij Is the ith dimension initial variable X i The specific factor of the j sample;
step 2.2, calculating the ith dimension initial variable X of the initial variable matrix X i And the t-dimensional initial variable X t Is related to it Thereby obtaining a correlation coefficient matrix R = (R) it ) p×p ，1≤t≤p；
Step 2.3, calculating an eigenvalue lambda and an eigenvector matrix U of the correlation coefficient matrix R, wherein the eigenvalue lambda has p solutions and is marked as lambda 1 ≥λ 2 ≥…≥λ t ≥…≥λ p ＞0，λ t The t-th characteristic root, U = (U), representing the correlation coefficient matrix R 1 ,u 2 ,…,u t ,…,u p )，u t The characteristic vector matrix U representing the correlation coefficient matrix R corresponds to the t-th characteristic root lambda t The t-th dimension of the feature vector, and u t ＝[u 1t u 2t … u it … u pt ] T ，u it An ith solution representing the t-dimensional feature vector;
step 2.4, obtaining the number m of the common factors by using the formula (2) and taking the number m as the number of the characteristic roots:
in the formula (2), δ represents a predetermined cumulative variance contribution ratio;
step 2.5, obtaining the kth common factor F by using the formula (3) k Initial variable X of ith dimension i Factor load of (a) ik To obtain a factor load matrix a:
step 3.1, performing maximum variance orthogonal rotation processing on the factor load matrix A to obtain a rotated factor load matrix A';
step 3.2, obtaining the evaluation value of the score of the m public factors on each sample by using the formula (4)
And is
Represents the score of the m common factors on the jth sample:
step 4.1, to the estimated value
Performing correlation analysis to obtain an estimated value>
Correlation coefficient matrix C = (C) hj ) n×n ，c hj Represents an evaluation value->
An h-th dimension vector>
And the jth dimension vector->
H is more than or equal to 1 and less than or equal to n;
step 4.2, according to the estimationValue of
Calculating to obtain the uncorrelated probability P (h, j) of the h photovoltaic power generation unit and the j photovoltaic power generation unit in the photovoltaic power station, and giving a hypothesis test level alpha;
if P (h, j) < alpha, the h photovoltaic power generation unit and the j photovoltaic power generation unit are obviously related; let the similar relationship between the h-th photovoltaic power generation unit and the j-th photovoltaic power generation unit be c hj * ＝c hj ；
If P (h, j) is larger than or equal to alpha, the h photovoltaic power generation unit and the j photovoltaic power generation unit are not related; let the similarity relation between the h photovoltaic power generation unit and the j photovoltaic power generation unit be c hj * =0; thereby obtaining a similarity relation matrix C of the photovoltaic power generation units * ＝(c hj * ) n×n ；
4.3, setting a strong correlation level theta, and setting a similarity relation matrix C of the photovoltaic power generation units * Clustering the photovoltaic power generation units, and if the similarity relation of the two photovoltaic power generation units is greater than a strong correlation level theta, clustering the two photovoltaic power generation units into one type; if the similarity relation of the two photovoltaic power generation units is smaller than the strong correlation level theta, the two photovoltaic power generation units are classified into different classes, and therefore clustering division of all photovoltaic power generation units in the photovoltaic power station is completed;
and 6, equating each type of photovoltaic power generation unit to be a photovoltaic power generation unit according to the clustering result of the photovoltaic power generation units, and calculating equivalent parameters of the photovoltaic power generation units and equivalent impedance of a power collection system so as to establish a photovoltaic power station equivalent model.
Compared with the prior art, the invention has the beneficial effects that:
1. the method uses factor analysis to perform dimensionality reduction processing on the initial variable, eliminates the correlation of the initial variable, fully excavates intrinsic essential information in data, quantifies the operation characteristic index of the photovoltaic inverter, and eliminates the subjectivity of the initial variable.
2. The invention takes objective data after factor analysis as a clustering index, measures the similarity relation between the photovoltaic power generation units by using correlation analysis and hypothesis test, realizes system clustering and saves the dependence on a clustering algorithm.
3. The invention utilizes a contour visualization method to visualize the clustering result. On the whole, the similarity relation of the photovoltaic power generation units is qualitatively analyzed, and the rationality of the clustering method can be effectively judged; on each factor dimension, the difference and the discrimination of each photovoltaic power generation unit on different operating characteristics are visually displayed, and the reasonability of a clustering result is conveniently analyzed and judged.
Drawings
FIG. 1 is a flow chart of a method for establishing an equivalent model of a photovoltaic power station according to the present invention;
FIG. 2 is a topological structure diagram of a photovoltaic power station in an embodiment of the present invention;
FIG. 3 is a diagram of the clustering effect of the profile visualization of the present invention;
FIG. 4 is a comparison simulation diagram of the active power of the photovoltaic power station equivalent model and the detailed model established in the invention;
FIG. 5 is a comparative simulation diagram of reactive power of the photovoltaic power station equivalent model and the detailed model established in the invention;
FIG. 6 is a comparative simulation diagram of the photovoltaic power station equivalent model and the detailed model output current established in the invention.
Detailed Description
In this embodiment, as shown in fig. 1, a photovoltaic power station equivalent modeling method considering an operation characteristic includes the following steps:
the operation characteristic change refers to the voltage drop, protection circuit action, low voltage ride through operation characteristic and the change process of the operation characteristic before and after the three-phase short circuit fault occurs in the photovoltaic power station. The active response characteristic and the reactive response characteristic can effectively represent the operation characteristic change of the photovoltaic power station, wherein the active response characteristic refers to the output active power P and the active current id of the photovoltaic power generation unit, and the reactive response characteristic refers to the output reactive power Q and the reactive current iq of the photovoltaic power generation unit. The transient steady state data refers to that 1 time point is selected in an initial steady state period, an index is marked as 1, 2 time points are selected in a transition period of action of a protection circuit after a fault starts, the index is marked as 2 and 3, 3 time points are selected in a transient steady state period after the fault starts, the index is marked as 4, 5 and 6, and data of 2 time points are selected after the fault is removed, and the index is marked as 7 and 8.
step 2.1, let the initial variable matrix be recorded as
X i Represents the ith dimension initial variable and has: x i ＝[x i1 x i2 … x ij … x in ]，x ij J is more than or equal to 1 and less than or equal to n, i is more than or equal to 1 and less than or equal to p, n is the sample capacity, and p is the total number of dimensions;
establishing a factor analysis model by using the formula (1) for decomposing the jth sample x in the ith dimension initial variable ij ：
In the formula (1), f kj Represents the k-th common factor F k The factor on the jth sample score, and f kj ∈F k ，F k ＝[f k1 f k2 … f kj … f kn ]，F k ∈F，
Representing a common factor, wherein k is more than or equal to 1 and less than or equal to m, m is less than p, and m represents the number of the common factor; coefficient a ik Is the k common factor F k Ith dimension initial variable X i Factor load of a ik E.g. A, A represents the factor load matrix, and A = (a) ik ) p×m ，ε ij Is the ith dimension initial variable X i The specific factor of the j sample;
step 2.2, calculating the ith dimension initial variable X of the initial variable matrix X i And the t-dimensional initial variable X t Is related to it Thereby obtaining a correlation coefficient matrix R = (R) it ) p×p ，1≤t≤p；
Step 2.3, calculating an eigenvalue lambda and an eigenvector matrix U of the correlation coefficient matrix R, wherein the eigenvalue lambda has p solutions and is marked as lambda 1 ≥λ 2 ≥…≥λ t ≥…≥λ p ＞0，λ t T-th characteristic root, U = (U), representing correlation coefficient matrix R 1 ,u 2 ,…,u t ,…,u p )，u t The characteristic vector matrix U representing the correlation coefficient matrix R corresponds to the t-th characteristic root lambda t The t-th dimension of the feature vector of (1), and u t ＝[u 1t u 2t … u it … u pt ] T ，u it An ith solution representing the t-dimensional feature vector;
step 2.4, obtaining the number m of the public factors by using the formula (2) and taking the number m as the number of the characteristic roots:
in the formula (2), δ represents a predetermined cumulative variance contribution ratio;
step 2.5, obtaining the kth common factor F by using the formula (3) k Initial variable X of ith dimension i Factor load of a ik To obtain a factor load matrix a:
step 3.1, performing maximum variance orthogonal rotation processing on the factor load matrix A to obtain a rotated factor load matrix A';
after the factor load matrix is rotated, each variable has larger load on only one common factor, namely, the load tends to +/-1, and the load on the rest common factors is smaller, namely, the load tends to 0. Factor load a ik Reflecting the relative importance of the ith dimension variable and the kth common factor, the greater the absolute value is, the higher the degree of closeness of the correlation is. Therefore, the relevant importance of the variables and the common factors can be judged according to the rotated factor load matrix, the common factors are named according to the operation characteristics of the photovoltaic power station represented by the variables, and the actual physical significance of the common factors is given.
Step 3.2, obtaining the score estimated value of m public factors on each sample by using the formula (4)
And is
F j * Represents the score of the m common factors on the jth sample:
step 4.1, to the estimated value
Performing correlation analysis to obtain estimated value/>
Correlation coefficient matrix C = (C) hj ) n×n ，c hj Represents an evaluation value->
Middle h-th dimension vector F h * And j-th dimension vector F j * H is more than or equal to 1 and less than or equal to n; />
Step 4.2, according to the estimated value
Calculating to obtain the uncorrelated probability P (h, j) of the h photovoltaic power generation unit and the j photovoltaic power generation unit in the photovoltaic power station, and giving a hypothesis test level alpha;
if P (h, j) < alpha, the h photovoltaic power generation unit and the j photovoltaic power generation unit are obviously related; let the similarity relation between the h photovoltaic power generation unit and the j photovoltaic power generation unit be c hj * ＝c hj ；
If P (h, j) is larger than or equal to alpha, the h photovoltaic power generation unit and the j photovoltaic power generation unit are not related; let the similarity relation between the h photovoltaic power generation unit and the j photovoltaic power generation unit be c hj * =0; thereby obtaining a similarity relation matrix C of the photovoltaic power generation units * ＝(c hj * ) n×n ；
4.3, setting a strong correlation level theta, and setting a similarity relation matrix C of the photovoltaic power generation units * Clustering the photovoltaic power generation units, and if the similarity relation of the two photovoltaic power generation units is greater than a strong correlation level theta, clustering the two photovoltaic power generation units into one type; if the similarity relation of the two photovoltaic power generation units is smaller than the strong correlation level theta, the two photovoltaic power generation units are classified into different classes, and therefore clustering division of all photovoltaic power generation units in the photovoltaic power station is completed;
in the invention, the outline visualization method means that each photovoltaic power generation unit in a photovoltaic power station can be regarded as a point in an m-dimensional space, and the coordinate value of each dimension is the factor score estimated value of the photovoltaic power generation unit of the dimension; taking m points on the abscissa of the two-dimensional plane, sequentially representing m public factors, sequentially connecting data points corresponding to each photovoltaic power generation unit to obtain a polygonal line, and drawing n polygonal lines by the n photovoltaic power generation units to form a contour diagram, wherein the ordinate corresponds to the estimated value of each public factor score.
And 6, equating each type of photovoltaic power generation unit to be a photovoltaic power generation unit according to the clustering result of the photovoltaic power generation units, and calculating the equivalent parameters of the photovoltaic power generation units and the equivalent impedance of the power collection system, so as to establish a photovoltaic power station equivalent model.
Obtaining equivalent parameters of the photovoltaic power generation units by adopting a capacity weighting method according to the number of the photovoltaic power generation units in the class;
the equivalent impedance of the current collection system comprises the equivalent impedance of a transformer and the equivalent impedance of a line, and the equivalent impedance of the transformer is obtained by connecting the impedance of each unit transformer in the class in parallel; if the equivalent photovoltaic power generation unit consists of s photovoltaic power generation units, the line equivalent impedance of the equivalent photovoltaic power generation unit is as follows:
in the formula (5), Z eq Equivalent impedance, Z, of the line for equivalent photovoltaic power generation units g The line impedance of the photovoltaic power generation unit g is more than or equal to 1 and less than or equal to s; p g For line impedance Z flowing through photovoltaic power generation unit g g Total power of P eq For line impedance Z flowing through equivalent photovoltaic power generation units eq The total power of (c).
Example (b):
1. and according to the topological structure and the model parameters of the photovoltaic power station, building a detailed photovoltaic power station model in DIgSILENT/PowerFactory software. The topological structure of the photovoltaic power station is shown in figure 2, and the model parameters are shown in table 1.
TABLE 1 model parameters
The detailed model consists of 40 photovoltaic power generation units and a power collection system, wherein the outlet voltage of each photovoltaic power generation unit is 400V, the photovoltaic power generation units are connected into a 35KV bus bar through unit transformers and power collection lines, and then the photovoltaic power generation units are boosted by main transformers and connected with a 220kV power grid through double-circuit lines. Setting a three-phase short-circuit fault to occur at the middle point of a double-circuit line of a grid-connected point of a photovoltaic power station, starting at the 1 st fault, clearing the 2 nd fault, analyzing the operation characteristic changes of the photovoltaic power station before and after the three-phase short-circuit fault process, namely the voltage drop, the protection circuit action and the low-voltage ride-through operation characteristic represented by active response and reactive response, according to the step 1, selecting a sampling time point, extracting the transient and steady state data of the active response characteristic and the reactive response characteristic of 40 photovoltaic power generation units as initial variables, wherein the dimensionality of the initial variables is 32, and rejecting 4 groups of 0 variables, namely rejecting Q 1 ，iq 1 ，iq 7 ，iq 8 After the four-dimensional variable, the initial variable dimension becomes 28.
2. Performing dimensionality reduction processing on the initial variable obtained in the step 1 according to the factor analysis in the step 2 to obtain a factor load matrix; the number of the common factors is determined to be 4 according to the requirement of the cumulative variance contribution rate.
3. Performing maximum orthogonal rotation on the factor load matrix according to the step 3 to obtain a rotated factor load matrix, wherein the result is shown in a table 2;
TABLE 2 rotated factor load matrix
And judging the relevant importance of each initial variable and the public factor according to the rotated factor load matrix, naming the public factor according to the operation characteristics of the photovoltaic power station represented by the variables, and giving the actual physical significance to the public factor. Wherein, the public factor 1 is positively correlated with the active power, the reactive power and the active current at the steady-state moment, and is named as a steady-state factor. The common factor 2 is in strong positive correlation with the active power and the active current at the transient moment and in strong negative correlation with the reactive power at the transient moment, and is named as a dropping factor. The public factor 3 is in strong positive correlation with the active power, the reactive power, the active current and the reactive current at the action moment of the protection circuit, and is named as a protection factor. The public factor 4 is in strong positive correlation with the reactive current at the transient time and is named as a low-penetration factor; and (4) calculating factor score estimated values of the 4 public factors on all the photovoltaic power generation units according to the method in the step (3) to serve as clustering indexes.
4. And (5) performing correlation analysis on the factor score estimated values according to the step (4) to obtain correlation coefficients, performing hypothesis test on the correlation coefficients to obtain the similarity relation of the photovoltaic power generation units, and obtaining the clustering result of the photovoltaic power generation units by using the similarity relation, wherein the clustering result is shown in a table 3.
TABLE 3 clustering results of photovoltaic power generation units
5. And (5) carrying out outline visualization on the clustering result according to the step (5), wherein the obtained result is shown in figure 3. The visual graph shows that the clustering effect of the photovoltaic power generation units is obvious, the similarity of the photovoltaic power generation units in the same class is high, the similarity difference of the photovoltaic power generation units in different classes is large, and the difference and the distinguishing degree of each photovoltaic power generation unit on different operating characteristics are visually shown.
6. According to the clustering result of the photovoltaic power generation unit obtained in the step 4, calculating equivalent parameters of the photovoltaic power generation unit and equivalent impedance of the power collection system according to the method in the step 6; and (3) establishing a photovoltaic power station equivalent model in DIgSILENT/PowerFactory software, and comparing the fitting effect of the output power external characteristics of the equivalent model and the detailed model, as shown in fig. 4, fig. 5 and fig. 6. The equivalent model and the detailed model have good fitting effect on the output active power, the output reactive power and the output current.
Claims (1)
1. A photovoltaic power station equivalent modeling method considering operation characteristics is characterized by comprising the following steps:
step 1, analyzing the operation characteristic changes of a photovoltaic power station before and after a three-phase short circuit fault process, and extracting transient and steady state data of active response characteristics and reactive response characteristics as an initial variable matrix;
step 2, decomposing the initial variable matrix into a linear combination of common factors and special factors by using a factor analysis method, thereby obtaining a factor load matrix A;
step 2.1, make the initial variable matrix record as
X i Represents the ith dimension initial variable and has: x i ＝[x i1 x i2 … x ij … x in ]，x ij J is more than or equal to 1 and less than or equal to n, i is more than or equal to 1 and less than or equal to p, n is the sample capacity, and p is the total number of dimensions;
establishing a factor analysis model by using the formula (1) for decomposing the jth sample x in the ith dimension initial variable ij ：
In the formula (1), f kj Represents the k-th common factor F k The factor on the jth sample score, and f kj ∈F k ，F k ＝[f k1 f k2 … f kj … f kn ]，F k ∈F，
Representing a common factor, wherein k is more than or equal to 1 and less than or equal to m, m is less than p, and m represents the number of the common factor; coefficient a ik Is the k common factor F k Initial variable X of ith dimension i Factor load of a ik E.g. A, A represents the factor load matrix, and A = (a) ik ) p×m ，ε ij Is the ith dimension initial variable X i The specific factor of the jth sample;
step 2.2, calculating the ith dimension initial variable X of the initial variable matrix X i And the t-dimensional initial variable X t Is related to coefficient r it Thereby obtaining a correlation coefficient matrix R = (R) it ) p×p ，1≤t≤p；
Step 2.3, calculating an eigenvalue lambda and an eigenvector matrix U of the correlation coefficient matrix R, wherein the eigenvalue lambda has p solutions and is marked as lambda 1 ≥λ 2 ≥…≥λ t ≥…≥λ p ＞0，λ t The t-th characteristic root, U = (U), representing the correlation coefficient matrix R 1 ,u 2 ,…,u t ,…,u p )，u t The characteristic vector matrix U representing the correlation coefficient matrix R corresponds to the t-th characteristic root lambda t The t-th dimension of the feature vector, and u t ＝[u 1t u 2t … u it … u pt ] T ，u it An ith solution representing the t-dimensional feature vector;
step 2.4, obtaining the number m of the public factors by using the formula (2) and taking the number m as the number of the characteristic roots:
in the formula (2), δ represents a predetermined cumulative variance contribution ratio;
step 2.5, obtaining the kth common factor F by using the formula (3) k Initial variable X of ith dimension i Factor load of a ik To obtain a factor load matrix a:
step 3, calculating the estimation value of the score of the common factor on all photovoltaic power generation units
And used as a clustering index;
step 3.1, performing maximum variance orthogonal rotation processing on the factor load matrix A to obtain a rotated factor load matrix A';
step 3.2, obtaining the evaluation value of the score of the m public factors on each sample by using the formula (4)
And is
F j * Represents the score of the m common factors on the jth sample:
step 4, obtaining the similarity relation of the photovoltaic power generation units and clustering based on correlation analysis and hypothesis test;
step 4.1, to the estimated value
Performing correlation analysis to obtain estimated value
Correlation coefficient matrix C = (C) hj ) n×n ，c hj Representing an estimated value
Vector F of h-th dimension h * And j-th dimension vector F j * H is more than or equal to 1 and less than or equal to n;
step 4.2, according to the estimated value
Calculating to obtain the uncorrelated probability P (h, j) of the h photovoltaic power generation unit and the j photovoltaic power generation unit in the photovoltaic power station, and giving a hypothesis test level alpha;
if P (h, j) < alpha, the h photovoltaic power generation unit and the j photovoltaic power generation unit are obviously related; let the similarity relation between the h photovoltaic power generation unit and the j photovoltaic power generation unit be c hj * ＝c hj ；
If P (h, j) is larger than or equal to alpha, the h photovoltaic power generation unit and the j photovoltaic power generation unit are not related; let the similarity relation between the h photovoltaic power generation unit and the j photovoltaic power generation unit be c hj * =0; thereby obtaining a similarity relation matrix C of the photovoltaic power generation units * ＝(c hj * ) n×n ；
4.3, setting a strong correlation level theta, and setting a similarity relation matrix C of the photovoltaic power generation units * Clustering the photovoltaic power generation units, and if the similarity relation of the two photovoltaic power generation units is greater than a strong correlation level theta, clustering the two photovoltaic power generation units into one type; if the similarity relation of the two photovoltaic power generation units is smaller than the strong correlation level theta, the two photovoltaic power generation units are classified into different classes, and therefore clustering division of all photovoltaic power generation units in the photovoltaic power station is completed;
step 5, carrying out visualization processing on the clustering result of the photovoltaic power generation unit by using a contour visualization method, and qualitatively analyzing the similarity relation of the photovoltaic power generation unit so as to judge the rationality of the clustering result;
and 6, equating each type of photovoltaic power generation unit to be a photovoltaic power generation unit according to the clustering result of the photovoltaic power generation units, and calculating equivalent parameters of the photovoltaic power generation units and equivalent impedance of a power collection system so as to establish a photovoltaic power station equivalent model.
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