CN107833149B - Power grid development period division method and system based on multiple discrimination indexes - Google Patents

Power grid development period division method and system based on multiple discrimination indexes Download PDF

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CN107833149B
CN107833149B CN201711001710.6A CN201711001710A CN107833149B CN 107833149 B CN107833149 B CN 107833149B CN 201711001710 A CN201711001710 A CN 201711001710A CN 107833149 B CN107833149 B CN 107833149B
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CN107833149A (en
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韩丰
李晖
彭冬
薛雅玮
张鹏飞
龙望成
赵朗
李金超
李金颖
侍剑峰
李树林
徐谦
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State Grid Corp of China SGCC
State Grid Zhejiang Electric Power Co Ltd
North China Electric Power University
State Grid Economic and Technological Research Institute
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State Grid Zhejiang Electric Power Co Ltd
North China Electric Power University
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Abstract

The invention relates to a multi-discriminant-index-based power grid development period division method and a multi-discriminant-index-based power grid development period division system, which are characterized by comprising the following steps of: 1) acquiring power grid original data containing a judgment index, wherein the power grid original data comprises historical data of the judgment index of the power consumption per person, the power generation per person, the power consumption per person and the power generation amount of renewable energy resources in a certain country; 2) processing the original data of the power grid by adopting a principal component analysis method to obtain a power grid development index; 3) fitting a power grid development index by adopting a curve; 4) the development process of the power grid development index is divided into different development periods through the geometrical characteristics of the curve. The invention can ensure higher safety and economy of the power grid, can make up for the defects of quantitative division of the power grid development period among countries, and provides a reference basis for the development planning and the power grid investment of the power grid.

Description

Power grid development period division method and system based on multiple discrimination indexes
Technical Field
The invention relates to a method and a system for dividing a power grid development period, in particular to a method and a system for dividing a power grid development period based on multiple discriminant indexes.
Background
As a fundamental industry of national economy, the development of the electric power industry in China also enters a new growth period. By 2013, the total electricity generation amount in China reaches 5207 hundred million kilowatt hours, the electricity generation amount is increased by 9.2 percent on the same scale, the electricity consumption amount per person is 3596 kilowatt hours, the electricity consumption amount is increased by 8.7 percent compared with the electricity consumption amount per year, and the electricity consumption amount per year exceeds the average level in the world. From the world, the electricity consumption of developed countries is slowly increased from 1990 s, gradually approaches or approaches to saturation, particularly after 2000 years, the economic development level tends to be stable, the electricity consumption is more slowly increased, and even the electricity consumption of some developed countries is reduced. Therefore, the power demand of a country cannot keep increasing situation all the time, the power demand can be saturated or even reduced, and therefore the power grid serving as an electric energy carrier cannot keep a high-speed development state all the time, and the development of the power grid gradually tends to be saturated along with the tendency of the social and economic development to be stable and the basic perfection of the power grid infrastructure. Although the power grid development of each country is influenced by the special economy, society and environment of the country, the power grid development of each country still follows the basic power grid development law, so that the process of the power grid development of each country is necessarily researched, the universal power grid development law is longitudinally combed and extracted, the basic development period to be experienced by the power grid development and the characteristics in the development period are determined, and the reference is provided for the development of the power grid of China.
The existing power grid development period division method basically focuses on qualitative analysis, power grid development is roughly divided into several periods mainly through the development stage of a power grid technology and the connectivity of a regional power grid, and the development rule of the power grid cannot be clearly depicted. Although the dividing method in the prior art also divides the development period of the power grid by adopting a quantitative analysis method, the existing dividing method only considers one index related to the development of the power grid, and cannot completely describe the development level of the power grid.
Disclosure of Invention
In view of the above problems, the present invention aims to provide a method and a system for dividing a power grid development period based on multiple criteria, which can not only ensure higher safety and economy of the power grid, but also make up for the deficiency in quantitative division of the power grid development period among countries, and provide a reference basis for power grid development planning and power grid investment.
In order to achieve the purpose, the invention adopts the following technical scheme: a power grid development period division method based on multiple discriminant indexes is characterized by comprising the following steps:
1) acquiring power grid original data containing a judgment index, wherein the power grid original data comprises historical data of per-capita electricity consumption, per-capita electricity generation, per-capita life electricity consumption and per-capita renewable energy generation of a certain country as the judgment index;
2) processing the original data of the power grid by adopting a principal component analysis method to obtain a power grid development index;
3) fitting a power grid development index by adopting a curve;
4) the development process of the power grid development index is divided into different development periods through the geometrical characteristics of the curve.
Further, the obtained power grid original data are expressed by adopting a matrix:
X＝(xij)m×n＝(X1,X2,…,Xm)
in the formula, the matrix X is composed of m values of index in n years, XijIndicating the value of the ith index at the jth year.
Further, the step 2) adopts a principal component analysis method to process the power grid original data, and the specific process of obtaining the power grid development index is as follows:
2.1) carrying out standardization processing on the power grid original data by adopting a Z-Score method, wherein the formula of the standardization processing of the Z-Score method is as follows:
Figure BDA0001443519270000021
in the formula (I), the compound is shown in the specification,
Figure BDA0001443519270000022
respectively is the mean value and the standard deviation of the ith index value;
the normalized index data matrix is: z ═ Zij)m×n＝(Z1,Z2,…,Zm) Satisfies the following conditions: e (Z)j) 0 and D (Z)j)＝1j＝1,2,…,m；
2.2) solving the matrix R of the decorrelation coefficients by adopting the standardized index data matrix to obtain (R)ij)m×mWherein r isijIndicating index ZiAnd ZjA coefficient of correlation between, wherein rijThe solving formula of (2) is as follows:
Figure BDA0001443519270000023
wherein, cov (Z)i,Zj) Is ZiAnd ZjThe covariance of (a);
2.3) solving the eigenvalue and the corresponding eigenvector of the correlation coefficient matrix R, and taking the eigenvector corresponding to all the eigenvalues obtained by the solution as a principal component coefficient;
since the vector X is non-zero, there is a det (R- λ E) of 0, i.e., a determinant
|R-λE|＝0(3)
Solving the formula (3) to obtain a matrix R to obtain all eigenvalues lambda, and calculating eigenvectors corresponding to the characteristic roots according to RX (X);
let R have k eigenvalues λ greater than 01≥λ2≥…≥λkMore than or equal to 0, and the characteristic vector corresponding to the characteristic values is A ═ a1,a2,…,ak) Considering A as a principal component coefficient;
the k principal components can be represented as follows:
Figure BDA0001443519270000031
wherein, yiDenotes the ith principal component, XiValue representing the i-th index
2.4) calculating each principal component yiThe contribution rate of the corresponding variance to the total variance;
Figure BDA0001443519270000032
the variance contribution rates of k principal components are gradually decreased, and then the cumulative variance contribution rate of the first t principal components is expressed as:
Figure BDA0001443519270000033
2.5) selecting the principal components meeting the conditions by adopting the set principal component selection standard, and calculating the power grid development index f by the principal component coefficient corresponding to the selected principal components according to the following calculation formula:
Figure BDA0001443519270000034
in the formula, k is the number of the principal components, and p is the number of the principal components meeting the selection condition of the principal component selection standard.
Further, the concrete process of fitting the power grid development index by using a curve in the step 3) is as follows:
3.1) determining the power grid development index fitting model as a Richards model, wherein the Richards model is expressed mathematically as follows:
Figure BDA0001443519270000035
wherein c is the limit value of the variable, and a is a parameter related to the initial value of the function; b is a growth rate parameter; d is a curve shape parameter;
3.2) determining Richards model parameters by adopting a nonlinear least square method as a curve fitting method;
3.3) substituting the calculated parameters of the Richards model into the Richards model to obtain a Richards curve of the power grid development index;
3.4) calculating the characteristic points of the Richards curve.
Further, the step 3.2) adopts an L-M method as a curve fitting method to determine the Richards model parameters.
Further, the specific process of calculating the characteristic points of the Richards curve in the step 3.4) is as follows:
characteristic points of the Richards curve include P'1、P′2And P'3Acceleration ofIn P'1Is at maximum of P'2Is zero, in P'3And (c) at a minimum, the three characteristic points are obtained by setting the second derivative and the third derivative of the Richards function to be zero, and the function values and the corresponding time points when the second derivative and the third derivative of the Richards function are zero:
Figure BDA0001443519270000041
Figure BDA0001443519270000042
in the formula, y1' and T1' is a feature point P1' and the corresponding time point, y2' and T2' is a feature point P2' and the corresponding time point, y3' and T3' is a feature point P3' and corresponding time point.
Further, the step 4) divides the development process of the power grid development index into different development periods through the geometric characteristics of the curve, and the specific division conditions are as follows: 0 to T at the initial development stage1', accelerated development period T1′～T2', deceleration development period T2′～T3' and the saturation development period T3′～+∞。
In order to achieve the purpose, the invention adopts the following technical scheme: a multi-discriminant-index-based power grid development period division system is characterized by comprising:
the data acquisition module is used for acquiring power grid original data containing a judgment index, wherein the power grid original data comprises historical data of the per-capita electricity consumption, the per-capita electricity generation, the per-capita electricity consumption and the per-capita renewable energy electricity generation of a certain country as the judgment index;
the data processing module is used for processing the original data of the power grid by adopting a principal component analysis method to obtain a power grid development index;
the curve fitting module is used for fitting the power grid development index by adopting a curve; and
the dividing module is used for dividing the development process of the power grid development index into different development periods through the geometric characteristics of the curve.
Due to the adoption of the technical scheme, the invention has the following advantages: 1. the invention divides the development period for the development of the power grid by a quantitative description method, so that the division of the development period is more definite and has higher operability, different strategic decisions can be made for different power grid development stages, the investment decision precision and efficiency can be improved, the problems of low asset utilization rate and the like caused by the constraint of economic development due to late investment or advanced investment can be avoided, and the invention has very obvious direct and indirect benefits. 2. According to the method, a plurality of indexes representing the power grid development level are combined into the power grid development index through principal component analysis, and the development period is divided for the power grid development according to the power grid development index, so that the defect of poor representativeness caused by dividing the power grid development period by depending on a single index is overcome. 3. According to the invention, the Richards curve is used as a fitting model, the excellent adaptability of the Richards curve ensures a good fitting effect, and the L-M method is used as a curve fitting method, so that the excellent optimizing performance and the faster convergence speed of the Richards curve ensure higher fitting precision. In conclusion, the method can ensure higher safety and economy of the power grid, can make up for the defects of quantitative division of the power grid development period among countries, and provides a reference basis for the development planning and the power grid investment of the power grid.
Drawings
FIG. 1 is a flow chart of a multi-discriminant-index-based power grid development period partitioning method of the present invention;
FIG. 2 is a Richards plot of the present invention;
fig. 3 is a Richards curve corresponding to the chinese grid development index of the present invention.
Detailed Description
The present invention is described in detail below with reference to the attached drawings. It is to be understood, however, that the drawings are provided solely for the purposes of promoting an understanding of the invention and that they are not to be construed as limiting the invention.
As shown in fig. 1, the method for dividing the power grid development period based on multiple discriminant indexes provided by the invention comprises the following steps:
1. acquiring power grid original data containing judgment indexes, wherein the power grid original data comprise historical data of the judgment indexes of the per-capita electricity consumption, the per-capita electricity generation, the per-capita electricity consumption and the per-capita renewable energy generation of a certain country, and the acquired power grid original data are expressed by adopting a matrix:
X＝(xij)m×n＝(X1,X2,…,Xm)
in the formula, the matrix X is composed of m values of index in n years, XijIndicating the value of the ith index at the jth year.
2. The method comprises the following steps of processing power grid original data by adopting a principal component analysis method to obtain a power grid development index, and specifically comprises the following steps:
2.1) carrying out standardization processing on the original data of the power grid to obtain a standardized index data matrix.
Since the raw data of the power grid have different orders of magnitude, they cannot be used directly for principal component analysis. Therefore, the power grid original data are subjected to standardization processing by adopting the Z-Score method, so that the order difference among the power grid original data is eliminated, and the processed data contain all information of the power grid original data. Wherein, the formula of the Z-Score method standardization treatment is as follows:
Figure BDA0001443519270000061
in the formula (I), the compound is shown in the specification,
Figure BDA0001443519270000062
respectively, the mean and standard deviation of the ith index value.
The normalized index data matrix is: z ═ Zij)m×n＝(Z1,Z2,…,Zm) Satisfies the following conditions: e (Z)j) 0 and D (Z)j)＝1(j＝1,2,…,m)。
2.2) adopting the standardized index data matrix to solve the correlation coefficient matrix.
Calculating a correlation coefficient matrix R ═ (R) of the normalization index data matrix Zij)m×mWherein r isijIndicating index ZiAnd ZjA coefficient of correlation between, wherein rijThe solving formula of (2) is as follows:
Figure BDA0001443519270000063
wherein, cov (Z)i,Zj) Is ZiAnd ZjThe covariance of (a). Due to, D (Z)j) 1, the correlation coefficient matrix is equal to the covariance matrix. Due to E (Z)j) When 0, the correlation coefficient matrix can be expressed as follows:
Figure BDA0001443519270000064
2.3) solving the eigenvalue and the corresponding eigenvector of the correlation coefficient matrix R, and taking the eigenvector corresponding to all the eigenvalues obtained by the solution as the principal component coefficient.
For an m × m order matrix R, if there is a number λ and an m-dimensional non-zero vector X such that RX ═ λ X, the number λ is called the eigenvalue of the square matrix R, and the non-zero vector X is the eigenvector of the square matrix R to which λ corresponds. Since the vector X is non-zero, there is a det (R- λ E) of 0, i.e., a determinant
|R-λE|＝0 (4)
Solving the formula (4) can obtain all eigenvalues λ of the matrix R, and then the eigenvector X corresponding to the eigen root can be calculated according to RX ═ λ X.
Let R have k eigenvalues λ greater than 01≥λ2≥…≥λkMore than or equal to 0, and the characteristic vector corresponding to the characteristic values is A ═ a1,a2,…,ak) In the present invention, A is regarded as a principal component coefficient.
The k principal components can be represented as follows:
Figure BDA0001443519270000065
wherein, yiDenotes the ith principal component, XiThe value of the ith index is expressed in a matrix form:
Y＝ATX (6)
2.4) calculating the contribution rate of the variance corresponding to each principal component to the total variance.
Since the principal components are independent of each other, and the ith principal component yiCorresponding characteristic value lambdaiIs the variance of the principal component, then principal component yiThe corresponding variance contribution to the total variance is expressed as:
Figure BDA0001443519270000071
variance contribution rate wiMain component y is reactediAnd (4) utilization rate of the original data information of the power grid.
The variance contribution rates of k principal components are gradually decreased, and then the cumulative variance contribution rate of the first t principal components is expressed as:
Figure BDA0001443519270000072
and 2.5) selecting the principal components meeting the conditions by adopting the set principal component selection standard, and calculating the power grid development index according to the principal component coefficients corresponding to the selected principal components.
4 indexes for measuring the power grid development level are represented by k main components, and no correlation exists among the main components, so that multiple collinearity of original data is avoided. When the power grid development index is calculated, the first p principal components with the cumulative variance contribution rate exceeding 85% can be selected, and then the calculation formula of the power grid development index f is calculated by the principal components with the cumulative variance contribution rate exceeding 85% is as follows:
Figure BDA0001443519270000073
the power grid development index f obtained at the moment is time series data and has most of information of the original data of the power grid, so that the development level of the power grid can be represented more comprehensively.
3. And fitting a power grid development index by using a Richards curve, wherein the following concrete steps are adopted:
3.1) determining the power grid development index fitting model as Richards model
The initial increment of the power grid development index f is small, but gradually enters a rapid growth period with the time, then the speed increase is gradually slowed down again, and finally the power grid development index is stabilized on a total amount, and the development process is similar to an elongated S-shaped curve. The types of S-shaped curves are more, and a Logistic curve, a Verhulstt curve, a Bertalanffy curve, a Richards curve and the like are commonly used, wherein the Richards curve has the advantage that other curves are difficult to compare, namely the Richards curve can be converted into other S-shaped curves through changing curve shape parameters, and the advantage enables the description range of the variety increase to be wider and the description capacity to be stronger. Therefore, the Richards model is adopted as a fitting model of the power grid development index. The mathematical expression of the Richards model is as follows:
Figure BDA0001443519270000074
wherein c is the limit value of the variable, and a is a parameter related to the initial value of the function; b is a growth rate parameter; d is a curve shape parameter. The Richards function is plotted as an S-shaped curve with c as the asymptote.
3.2) determining Richards model parameters.
Since the Richards model is a curve, the invention adopts a nonlinear least square method as a curve fitting method. In the conventional nonlinear least square method, the L-M method (Levenberg-Marquardt) has the advantages of a gradient method and a Newton method and has higher convergence rate, so that the L-M method is adopted as a parameter calculation method of the Richards model, the parameter calculation can be obtained by adopting the conventional Matlab programming calculation, and the description is omitted.
3.3) substituting the calculated parameters of the Richards model into the Richards model to obtain a Richards curve of the power grid development index.
3.4) calculating the characteristic points of the Richards curve.
The Richards curve can divide the development period by the variable described by different growth accelerations, and the different growth accelerations can pass through 3 characteristic points (P'1、P′2、P′3) Is distinguished, wherein the acceleration of the Richards curve is P'1Is at maximum of P'2Is zero, in P'3Is smallest. These 3 feature points can be derived by the second and third derivatives of the Richards function being zero.
The function values and corresponding time points when the second and third derivatives of the Richards function are zero are given below:
Figure BDA0001443519270000081
Figure BDA0001443519270000082
in the formula, y1' and T1' is a feature point P1' and the corresponding time point, y2' and T2' is a feature point P2' and the corresponding time point, y3' and T3' is a feature point P3' and corresponding time point.
4. The development process of the power grid development index is divided into different development periods through the geometrical characteristics of the Richards curve.
The Richards curve quantitatively represents the staged development process of the power grid development index, the power grid development index undergoes a slow-fast-slow-saturated development process, and the development process corresponds to the specific growth speed and curvature of the Richards curve, so that the development period can be divided for the development process of the power grid development index through the geometric characteristics of the Richards curve, and the development level of a national power grid is further clarified. The invention relates to a function corresponding to the zero point of the second derivative of the Richards functionThe value is used as the critical point (P) of the exponential growth of the power grid development2') the increasing acceleration of the power grid development index at the characteristic point is 0, and the increasing speed of the power grid development index is fastest at the moment; the invention takes the function values corresponding to the third derivative zero point of the Richards function as the accelerating points (P) of the power grid development exponential growth respectively1') and maturity point (P)3') at an acceleration point (P)1') the acceleration of the power grid development index reaches the maximum value, and the increase of the acceleration of the power grid development index is maximum at the moment; at the point of maturity (P)3') the acceleration of the power grid development index reaches the minimum value, and the reduction amplitude of the acceleration of the power grid development index is maximum at the moment. Correspondingly, according to the development track and the characteristic points of the power grid development index, the development process of the power grid development index can be divided into four development periods, namely an initial development period, an accelerated development period, a decelerated development period and a saturated development period. The detailed divisions of each development period are as follows:
initial development period (0-T)1'): the grid development index exhibits accelerated development during this period, but due to the low initial volume, the grid development index increases less than during other development periods. The development speed of the power grid is increased continuously in the period, and the increase of the speed is increased gradually.
Accelerated development period (T)1′～T2'): the grid development index still exhibits an accelerated increase during this period, but the increase in speed gradually decreases until the increase drops to 0. Due to the accumulation effect of early development, the development speed of the power grid is the fastest in the period, but the increase of the development speed is gradually reduced.
Deceleration development period (T)2′～T3'): the power grid development index still presents a growth situation in the period, but because the growth acceleration is smaller than 0, the growth speed of the power grid development index is continuously reduced, and the reduction range is continuously enlarged, and the growth situation at the moment is the deceleration growth of the continuous reduction of the growth speed. The power grid development speed in the period is reduced compared with the accelerated development period, but the speed is still increased rapidly.
Period of saturation development (T)3' - + ∞): the power grid development index still shows increasing trend in the periodThe potential, and the decreasing magnitude of the acceleration rate also gradually decreases, but the acceleration rate in this period is small due to the cumulative effect of the early deceleration, and also continuously decreases until the acceleration rate will be 0. The power grid in this period has a slow development speed and basically has the characteristics of a mature power grid.
In summary, the power grid can show different development characteristics in different development stages. In the initial development period, the scale of the power grid is small and the construction is slow, the speed increasing of the transformation capacity and the length of the power transmission line is low, and accordingly the investment requirement of the power grid is low. After the power grid enters an accelerated development period, the scale of the power grid is rapidly expanded, the transformation capacity and the length of a power transmission line are rapidly increased, and correspondingly, the investment requirement of the power grid is also rapidly increased. In the deceleration development stage, the power grid has a large scale, the scale of the power grid is continuously increased, but the speed increase is slowed down, at this time, the transformation capacity of the power grid and the speed increase of the power transmission line also start to decrease, but the fast speed increase is still kept, at this time, the investment requirement of the power grid is still high, and because the power grid has a large scale, the cost consumed in the aspects of power grid operation and maintenance is also increased. When the power grid enters a saturation stage, although the scale of the power grid is still expanded, the expansion speed of the power grid is reduced, the speed increase of the transformation capacity and the length of the power transmission line is gradually reduced, the investment of the power grid crosses a peak value at the moment, the investment of the power grid is reduced year by year and is finally stabilized at a smaller value, and the operation and maintenance cost of the power grid reaches the highest level and continues to increase. Therefore, the change of the power grid investment requirement is closely related to the development stage of the power grid, and the current development stage of the power grid is clear, so that a power grid enterprise can determine a proper power grid investment scale, the power grid can moderately advance the development of national economy, and the social service can be better realized. In addition, different power grid planning, construction, operation, maintenance and management tasks are carried out at different development stages of the power grid, and the power grid enterprise can timely adjust work emphasis and grasp work direction by grasping the development stage of the power grid. Therefore, the determination of the development stage and stage characteristics of the power grid is of great significance for ensuring the sustainable development of the power grid in China.
The invention also provides a power grid development period division system based on multiple discriminant indexes, which comprises:
the data acquisition module is used for acquiring power grid original data containing a judgment index, wherein the power grid original data comprises historical data of the per-capita electricity consumption, the per-capita electricity generation, the per-capita electricity consumption and the per-capita renewable energy electricity generation of a certain country as the judgment index;
the data processing module is used for processing the original data of the power grid by adopting a principal component analysis method to obtain a power grid development index;
the curve fitting module is used for fitting the power grid development index by adopting a curve; and
the dividing module is used for dividing the development process of the power grid development index into different development periods through the geometric characteristics of the curve. The specific process of the multi-discriminant-index-based power grid development period division method is described in detail below by using a specific embodiment, and the embodiment of the invention selects a Chinese power grid as a research object to divide the power grid development period.
In the embodiment, the average power consumption, the average power generation amount, the average domestic power consumption and the average renewable energy power generation amount of China in 1960-2014 are selected to form a power grid original data matrix X ═ (X ═ X)ij)4×44＝(X1,X2,X3,X4)。
Firstly, carrying out standardization processing on a power grid original data matrix X by adopting a Z-Score method to obtain a standardization index data matrix Z ═ (Z)ij)4×44＝(Z1,Z2,Z3,Z4)。
And then calculating a correlation coefficient matrix R of the standardized index data matrix Z, and solving the eigenvalue and the eigenvector of R. The correlation coefficient matrix R has 4 eigenvalues through calculation, so that R has 4 principal components, but the variance contribution rate w of the first principal component corresponding to the first eigenvalue1The method reaches 94.21%, and the principal component selection standard higher than 85% is adopted, so that the embodiment selects the first principal component to represent the original data of the power grid, and the coefficient of the principal component corresponding to the first principal component is as followsTable 1 below shows:
TABLE 1 coefficient of principal component
Figure BDA0001443519270000101
Figure BDA0001443519270000111
The power grid development index f in china obtained according to the formula (9) is shown in the following table 2:
TABLE 2 Power grid development index
Year of year 1971 1972 1973 1974 1975 1976 1977 1978 1979
f 234.64 251.87 269.33 264.17 304.25 311.81 339.31 388.08 420.24
Year of year 1980 1981 1982 1983 1984 1985 1986 1987 1988
f 424.26 428.65 445.86 468.73 499.28 538.12 582.66 636.40 688.07
Year of year 1989 1990 1991 1992 1993 1994 1995 1996 1997
f 726.33 759.57 822.46 908.09 994.37 1083.01 155.94 1218.81 1279.19
Year of year 1998 1999 2000 2001 2002 2003 2004 2005 2006
f 1304.41 1378.69 1496.28 1630.27 1808.84 2078.25 2386.76 2681.74 3068.79
Year of year 2007 2008 2009 2010 2011 2012 2013 2014
f 3501.09 3666.20 3916.34 4384.88 4936.22 5155.67 5604.66 5767.04
After the power grid development index of China is obtained, a Richards curve is fitted by using the power grid development index, an L-M algorithm is used in a fitting method, and the specific fitting process is completed by Matlab programming. The goodness of fit R of the Richards model to the data is shown through the fitting result20.9891, indicating that the Richards model fits well to the data. In addition, the limit value c of the function is 10044, the initial parameter a is 8.2899, the growth rate b is 0.1759, and the curve shape parameter d is 1.7834, so that a Richards model of the Chinese power grid development index can be obtained, and a corresponding Richards curve can be drawn. Richards curve fitted by Chinese grid development index is shown asAs shown in fig. 3. According to the obtained Richards model parameters, by combining the formula (11-12), the characteristic points for dividing the development period of the Chinese power grid can be obtained, and the characteristic points and the occurrence time thereof are shown in the following table 3:
TABLE 3 respective characteristic points and appearance times thereof
Characteristic point P′1 P′2 P′3
y' 2904.4 5657.2 8347.8
T' 2005 2014 2023
As can be seen from table 3, the power grid development in china was in the initial development period before 2005; the power grid development in China during the year 2005-2014 is in an accelerated development period; in the period of 2014-2023, the power grid development in China is in a deceleration development period; after 2023, the grid development in china was in a period of saturated development.
In conclusion, the invention combines a plurality of characteristic indexes representing the development level of the power grid into the power grid development index by adopting principal component analysis, so that the power grid development index can represent the development level of a national power grid better than a single characteristic index; according to the method, the Richards curve is used as a model for power grid development index fitting, an L-M algorithm is used as a model fitting method, good fitting goodness can be obtained, and the fitted model can well reflect the development level and the development trend of the power grid.
The above embodiments are only used for illustrating the present invention, and the implementation steps of the method and the like can be changed, and all equivalent changes and modifications based on the technical scheme of the present invention should not be excluded from the protection scope of the present invention.

Claims (6)

1. A power grid development period division method based on multiple discriminant indexes is characterized by comprising the following steps:
1) acquiring power grid original data containing a judgment index, wherein the power grid original data comprises historical data of the per-capita electricity consumption, the per-capita electricity generation, the per-capita electricity consumption and the per-capita renewable energy generation of a certain country as the judgment index, and the acquired power grid original data is expressed by adopting a matrix:
X＝(xij)m×n＝(X1,X2,…,Xm)
in the formula, the matrix X is composed of m values of index in n years, XijRepresents the value of the ith index in the jth year;
2) the method comprises the following steps of processing power grid original data by adopting a principal component analysis method to obtain a power grid development index, wherein the specific process comprises the following steps:
2.1) carrying out standardization processing on the power grid original data by adopting a Z-Score method, wherein the formula of the standardization processing of the Z-Score method is as follows:
Figure FDA0003280066640000011
in the formula (I), the compound is shown in the specification,
Figure FDA0003280066640000012
respectively the mean value of the ith index valueAnd standard deviation;
the normalized index data matrix is: z ═ Zij)m×n＝(Z1,Z2,…,Zm) Satisfies the following conditions: e (Z)j) 0 and D (Z)j)＝1 j＝1,2,…,m；
2.2) solving the matrix R of the decorrelation coefficients by adopting the standardized index data matrix to obtain (R)ij)m×mWherein r isijIndicating index ZiAnd ZjA coefficient of correlation between, wherein rijThe solving formula of (2) is as follows:
Figure FDA0003280066640000013
wherein, cov (Z)i,Zj) Is ZiAnd ZjThe covariance of (a);
2.3) solving the eigenvalue and the corresponding eigenvector of the correlation coefficient matrix R, and taking the eigenvector corresponding to all the eigenvalues obtained by the solution as a principal component coefficient;
since the vector X is non-zero, there is a det (R- λ E) of 0, i.e., a determinant
|R-λE|＝0 (3)
Solving the formula (3) to obtain all eigenvalues λ of the matrix R, and then calculating eigenvectors corresponding to the characteristic roots according to RX ═ λ X;
let R have k eigenvalues λ greater than 01≥λ2≥…≥λkMore than or equal to 0, and the characteristic vector corresponding to the characteristic values is A ═ a1,a2,…,ak) Considering A as a principal component coefficient;
the k principal components can be represented as follows:
Figure FDA0003280066640000021
wherein, yiDenotes the ith principal component, XiValue representing the i-th index
2.4) calculating each principal component yiThe contribution rate of the corresponding variance to the total variance;
Figure FDA0003280066640000022
the variance contribution rates of k principal components are gradually decreased, and then the cumulative variance contribution rate of the first t principal components is expressed as:
Figure FDA0003280066640000023
2.5) selecting the principal components meeting the conditions by adopting the set principal component selection standard, and calculating the power grid development index f by the principal component coefficient corresponding to the selected principal components according to the following calculation formula:
Figure FDA0003280066640000024
in the formula, k is the number of the main components, and p is the number of the main components meeting the selection condition of the main component selection standard;
3) fitting a power grid development index by adopting a curve;
4) the development process of the power grid development index is divided into different development periods through the geometrical characteristics of the curve.
2. The method for dividing the power grid development period based on multiple discriminant indexes as set forth in claim 1, wherein the specific process of curve fitting the power grid development index in the step 3) is as follows:
3.1) determining the power grid development index fitting model as a Richards model, wherein the Richards model is expressed mathematically as follows:
Figure FDA0003280066640000025
wherein c is the limit value of the variable, and a is a parameter related to the initial value of the function; b is a growth rate parameter; d is a curve shape parameter;
3.2) determining Richards model parameters by adopting a nonlinear least square method as a curve fitting method;
3.3) substituting the calculated parameters of the Richards model into the Richards model to obtain a Richards curve of the power grid development index;
3.4) calculating the characteristic points of the Richards curve.
3. The multi-discriminant-indicator-based power grid development period division method according to claim 2, wherein in the step 3.2), an L-M method is adopted as a curve fitting method to determine Richards model parameters.
4. The method for dividing the power grid development period based on multiple discriminant indexes as claimed in claim 2, wherein the specific process of calculating the characteristic points of the Richards curve in the step 3.4) is as follows:
the characteristic points of the Richards curve include P1'、P2' and P3' acceleration at P1' maximum at P2' is zero at P3At' minimum, the three characteristic points are obtained by the second derivative and the third derivative of the Richards function being zero, and the function values and corresponding time points when the second derivative and the third derivative of the Richards function are zero:
Figure FDA0003280066640000031
Figure FDA0003280066640000032
in the formula, y1' and T1' is a feature point P1' and the corresponding time point, y2' and T2' is a feature point P2' and the corresponding time point, y3' and T3' is a feature point P3' ofNumerical values and corresponding time points.
5. The method for dividing the power grid development period based on multiple discriminant indexes as claimed in claim 4, wherein the specific division of the step 4) into different development periods by the geometric characteristics of the curve is as follows: 0 to T at the initial development stage1', accelerated development period T1′～T2', deceleration development period T2′～T3' and the saturation development period T3′～+∞。
6. A multi-discriminant-index-based power grid development period division system is characterized by comprising:
the data acquisition module is used for acquiring power grid original data containing a judgment index, wherein the power grid original data comprises historical data of the per-capita electricity consumption, the per-capita electricity generation, the per-capita electricity consumption and the per-capita renewable energy generation of a certain country as the judgment index, and the acquired power grid original data is expressed by adopting a matrix:
X＝(xij)m×n＝(X1,X2,…,Xm)
in the formula, the matrix X is composed of m values of index in n years, XijRepresents the value of the ith index in the jth year;
a data processing module for processing the power grid original data by adopting a principal component analysis method to obtain a power grid development index, wherein the processing process is
The method comprises the following steps of processing power grid original data by adopting a principal component analysis method to obtain a power grid development index, wherein the specific process comprises the following steps:
the Z-Score method is adopted to carry out standardization processing on the power grid original data, and the formula of the standardization processing of the Z-Score method is as follows:
Figure FDA0003280066640000041
in the formula (I), the compound is shown in the specification,
Figure FDA0003280066640000042
respectively is the mean value and the standard deviation of the ith index value;
the normalized index data matrix is: z ═ Zij)m×n＝(Z1,Z2,…,Zm) Satisfies the following conditions: e (Z)j) 0 and D (Z)j)＝1 j＝1,2,…,m；
Using the normalized index data matrix to solve the matrix R ═ R (R)ij)m×mWherein r isijIndicating index ZiAnd ZjA coefficient of correlation between, wherein rijThe solving formula of (2) is as follows:
Figure FDA0003280066640000043
wherein, cov (Z)i,Zj) Is ZiAnd ZjThe covariance of (a);
solving the eigenvalue and the corresponding eigenvector of the correlation coefficient matrix R, and taking the eigenvector corresponding to all the eigenvalues obtained by the solution as a principal component coefficient;
since the vector X is non-zero, there is a det (R- λ E) of 0, i.e., a determinant
|R-λE|＝0 (3)
Solving the formula (3) to obtain all eigenvalues λ of the matrix R, and then calculating eigenvectors corresponding to the characteristic roots according to RX ═ λ X;
let R have k eigenvalues λ greater than 01≥λ2≥…≥λkMore than or equal to 0, and the characteristic vector corresponding to the characteristic values is A ═ a1,a2,…,ak) Considering A as a principal component coefficient;
the k principal components can be represented as follows:
Figure FDA0003280066640000044
wherein, yiDenotes the ith principal component, XiValue representing the i-th index
Calculating each principal component yiThe contribution rate of the corresponding variance to the total variance;
Figure FDA0003280066640000051
the variance contribution rates of k principal components are gradually decreased, and then the cumulative variance contribution rate of the first t principal components is expressed as:
Figure FDA0003280066640000052
selecting principal components meeting the conditions by adopting a set principal component selection standard, and calculating a calculation formula of the power grid development index f by using principal component coefficients corresponding to the selected principal components as follows:
Figure FDA0003280066640000053
in the formula, k is the number of the main components, and p is the number of the main components meeting the selection condition of the main component selection standard;
the curve fitting module is used for fitting the power grid development index by adopting a curve; and
the dividing module is used for dividing the development process of the power grid development index into different development periods through the geometric characteristics of the curve.
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