CN110380444B - Capacity planning method for distributed wind power orderly access to power grid under multiple scenes based on variable structure Copula - Google Patents
Capacity planning method for distributed wind power orderly access to power grid under multiple scenes based on variable structure Copula Download PDFInfo
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Abstract
The invention discloses a capacity planning method for distributed wind power orderly access to a power grid under multiple scenes based on variable structure Copula, which comprises the following steps: (1) forecasting regional load and distributed wind power output; (2) performing correlation analysis between variables according to the predicted values, and establishing an optimal variable structure Copula model; (3) obtaining typical scenes by utilizing K-means clustering division, and obtaining each scene split point; (4) and establishing a system optimization scheduling model containing distributed wind power for capacity planning. The variable structure Copula model established by the invention has high accuracy in describing the complex correlation among variables, and can be used for independently analyzing the edge distribution of each random variable and the correlation structure among the variables; the tail correlation among variables can be accurately described; and the most suitable Copula model can be provided for the description of the correlation of different stages according to the different structural characteristics of the variables; the method can accurately describe the correlation between the load and the distributed wind power, and realize reliable distributed wind power capacity planning.
Description
Technical Field
The invention belongs to the field of power grid planning, and particularly relates to a capacity planning method for orderly accessing distributed wind power to a power grid under multiple scenes based on variable structure Copula.
Background
At present, with the popularization and application of wind power generation, the access of distributed wind power to a low-voltage-level power grid becomes an important way for ensuring the safety of a power system and solving the environmental problems in China, and the distributed wind power is also an important form for the access of wind power to the power grid. The distributed access of the wind power refers to a wind power project which is close to a load center, a local power grid consumes the distributed wind power accessed nearby, and the power does not need to be transmitted in a long distance and large scale. The distributed wind power can directly provide electric energy for the terminal user, and the operation efficiency of the system is improved; the optimal configuration of electric energy resources can be promoted, and the electric energy is efficiently and flexibly used; the regulation is effectively carried out during the peak time or the valley time of the electricity consumption. In addition, the advantages of improving the pollution-free and renewable energy utilization efficiency and reducing the investment cost of the distributed wind power project enable the distributed wind power to be connected into a power grid form to become a main development direction. The deep research on the planning of the distributed wind power capacity can effectively realize the local consumption of wind power, greatly improve the utilization rate of wind power output, and solve the problems of reducing the phenomenon of wind abandonment and improving the income of related industries of wind power.
The load fluctuates along with time, the wind power output has the characteristics of discontinuity and randomness, and the research on the correlation between the distributed wind power output and the load plays a key role in obtaining reasonable wind power capacity planning. The existing methods for analyzing the correlation among the multivariate variables mainly comprise Nataf inverse transformation, time shifting technology and a correlation coefficient matrix method, but the correlation characteristics or the correlation matrix among the random variables must be determined firstly. In addition, in the existing power grid planning research, a constant load model is mostly established, the mutual independence between wind power and load is assumed, the influence of the correlation between the wind power and the load is not considered, and actually, the wind power and the load are not independent variables, and the influence is not negligible to the economic operation scheduling of the power grid. In addition, in the current research, a single Copula function is mostly used for modeling and fitting the load and the wind power correlation, and the randomness, the volatility and the time sequence of the wind power and the load are not considered, so that the model description is inaccurate.
Because the correlation among variables is relatively complex and has no obvious characteristics, the method and the model are possibly poor in fitting effect, therefore, the correlation between loads and wind power at each time interval is researched by using the variable structure Copula on the time interval basis, the capacity planning of the distributed wind power orderly connected to the power grid is carried out, and a more accurate planning result can be obtained.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the defects of the prior art, the invention provides a capacity planning method for orderly accessing distributed wind power into a power grid under multiple scenes based on variable structure Copula, which is based on the time-sharing research on load and wind power correlation by the variable structure Copula, and simultaneously establishes an electric power system optimization model under a typical scene by taking the maximum environmental guarantee brought to the society by the investment operation cost of a distributed wind power plant, the minimum line loss cost of an electric power system and the maximum supplementary function of the wind power plant, so that the problem of distributed wind power capacity planning is solved on the basis of ensuring the safe and stable operation of the system, the wind power utilization rate is improved, and the investment income of related industries is maximized.
The technical scheme is as follows: in order to realize the purpose of the invention, the technical scheme adopted by the invention is as follows: a capacity planning method for orderly accessing distributed wind power to a power grid under multiple scenes based on variable structure Copula comprises the following steps:
(1) establishing an ARMA model to predict regional loads and distributed wind power output;
(2) performing correlation analysis between variables according to the predicted values, and establishing an optimal variable structure Copula model;
(3) obtaining typical scenes by utilizing K-means clustering division, and obtaining load and distributed wind power values of each scene, namely quantiles;
(4) and establishing a system optimization scheduling model containing distributed wind power to carry out capacity planning on each scene sub-site.
Further, the step (1) comprises the following steps:
(1-1) establishing an ARMA model to predict regional load and wind power output data;
(1-2) converting the centralized wind power capacity, wherein the formula is as follows:
the centralized wind power installation is the sum of rated power of the wind power generator set, 397.3MW is taken, the distributed wind power installation is the maximum value of the specified planning distributed wind power capacity, 50MW is taken, the centralized wind power output predicted value is a predicted result obtained by inputting original wind power data into an ARMA model, and the distributed wind power output predicted value in the formula is a result obtained by converting the centralized wind power output predicted value into capacity, namely the result is obtained.
Further, in step (11), the ARMA model is:
Yt＝β0+β1Yt-1+β2Yt-2+…+βpYt-p+εt+α1εt-1+α2εt-2+…+αqεt-q
wherein, YtFor time series of wind power of load or dispersion type, Yt-pIs the time sequence of the p-th time point before the current time point t, beta is a correlation coefficient, epsilontIs a predicted error term, epsilont-qThe method is characterized in that the method is an error term of a qth time point before a current time point t, alpha is a correlation coefficient and represents the dependence of a prediction error term in different periods, p is an autoregressive process order, and q is a moving average process order. The model is then scaled by calculating the AIC index of the ARMA (p, q) model, as follows:
wherein σ2And (3) for predicting the variance of an error term, N is the number of historical data, p and q are the orders of an ARMA (p, q) model, calculating AIC values under a plurality of groups of p and q one by one from a low order, and selecting the corresponding p and q values as the optimal ARMA (p, q) model when the AIC value is minimum. According to the method, time sequences formed by regional loads and centralized wind power output are respectively used as original data, the original data are input into an ARMA model to solve orders p and q, and historical data are input into the model to predict loads and centralized wind power output data at future time points.
Further, in step (2), the model building includes the following steps:
(2-1) dividing periods by months or quarters;
(2-2) determining the edge probability distribution function of the load and the distributed wind power in each time interval;
(2-3) respectively establishing each basic Copula model based on the edge probability distribution function of the load and the distributed wind power: calculating various Copula function parameters according to a maximum likelihood estimation method by normal Copula, t-Copula, Clayton Copula, Gumbel Copula and Frank Copula, and drawing a density function graph and a distribution function graph;
(2-4) defining a target Copula function, calculating each parameter of the target Copula and evaluating each model in (2-3) according to the judgment index; the evaluation indexes comprise Pearson coefficients, Kendall coefficients, Spearman coefficients and Euclidean square distances between each Copula model and the empirical Copula;
(2-5) comparing the estimation results of the Copula parameters, and selecting the model with the maximum number of parameters closest to the target Copula parameter value as the optimal model.
Further, in step (3), the step of dividing the typical scene is as follows:
(3-1) discretizing the obtained Copula model in each time period to obtain n discrete points, and randomly selecting k data points from the n discrete points as initial condensation central points;
(3-2) comparing the distances between other objects except the aggregation center and each aggregation center, classifying the object with the closest distance as the class, and updating the cluster;
(3-3) calculating the clustering center, namely the mean value, of each obtained new cluster, and updating the clustering center;
(3-4) circulating the steps (3-2) to (3-3) until the set circulation times are reached;
and (3-5) obtaining the actual load and the distributed wind power quantile points by inverting the edge probability distribution function.
Further, after dividing into k scenes, inputting the load of each scene and the actual split point of the distributed wind power into an optimization model, and respectively carrying out distributed wind power capacity planning on each scene, wherein the step (4) comprises the following steps:
(4-1) performing optimization modeling on the power system in a typical scene, wherein the investment and operation cost and the environmental protection benefit of a distributed wind power plant and the line loss cost of the power system are taken as objective functions, and the function expression is as follows:
F＝min(f1+f2)
f1for the investment and operation cost and the environmental protection benefit of the distributed wind power plant, the expression is as follows:
wherein, PDWGRepresenting planned decentralized wind power capacity, CwtRepresenting the initial investment cost of a decentralized wind farm, CsrRepresents the environmental benefit per unit volume, r0And T represents the discount rate, and T represents the operation age of the distributed wind power plant.
f2For the line loss cost of the power system, the expression is as follows:
wherein N is the number of system nodes, Δ UijIs the voltage difference between system node i and node j, ZijIs the impedance value, C, of branch ijdjRepresents the unit cost of line loss and δ represents the power factor.
(4-2) the constraint conditions are set to include power flow constraint, generator active and reactive power output constraint, wind power capacity constraint, voltage constraint and phase angle constraint, and the specific function expression is as follows:
PGimin≤PGi≤PGimax
QGimin≤QGi≤QGimax
0≤PDWG≤PDWGmax
Uimin≤Ui≤Uimax
|θi-θj|≤|θi-θj|max
wherein N is the number of system nodes, PGi、QGiFor active and reactive power of the generator set, PGimin,PGimaxFor the upper and lower limit values of the active power output, Q, of the generatorGimin,QGimaxFor the upper and lower limit values of reactive power output, P, of the generatorDi，QDiFor testing the active and inactive values, P, of the node load in the systemDWGFor planned decentralized wind power capacity, Ui,UjIs the system node voltage, Uimin,UimaxIs the upper and lower limit of the system voltage, Gij,BijFor conductance, susceptance, theta, of branch i-jijIs the phase angle difference between node i and node j, PDWGmaxFor a defined upper limit of the capacity of the decentralized windi，θjThe voltage phase angles of the node i and the node j, respectively, and PDGWmax＝50MVA，Uimin＝0.9,Uimax1.05 (per unit value), upper limit of phase angle difference | θ between node i and node ji-θj|max5, according to the optimization model objective function and constraintsAnd (4) setting conditions, and solving each scene to plan the distributed wind power capacity.
Has the advantages that: compared with the prior art, the technical scheme of the invention has the following beneficial technical effects:
1. the variable structure Copula model can independently analyze the edge distribution of each random variable and the correlation structure among the variables without determining the correlation characteristics or correlation matrix among the random variables in advance;
2. the tail correlation among the variables can be accurately described, the complex correlation among the variables can be better reflected, and the method is unique compared with other correlation researches;
3. the most suitable Copula model can be provided for the description of the correlation at different stages according to the structural characteristics of the variables, the change of the correlation structure between the variables can be captured more flexibly, and the model fitting effect is better. In practical application, the method can accurately describe the correlation between the load and the distributed wind power, and realize reliable distributed wind power capacity planning.
Drawings
FIG. 1: a distributed wind power capacity planning flow chart based on variable structure Copula;
FIG. 2: a modified IEEE30 node test system;
FIG. 3: distributed wind power core distribution estimation and experience distribution images;
FIG. 4: load kernel distribution estimation and empirical distribution images;
FIG. 5: a binary frequency histogram of distributed wind power and load;
FIG. 6: a Gaussian-Copula density function graph and a distribution function graph;
FIG. 7: a t-Copula density function graph and a distribution function graph;
FIG. 8: Gumbel-Copula density function graph and distribution function graph;
FIG. 9: Frank-Copula density function graph and distribution function graph;
FIG. 10: a Clayton-Copula density function graph and a distribution function graph;
FIG. 11: empirical Copula distribution function plots.
Detailed Description
The technical solution of the present invention is further described below with reference to the accompanying drawings and examples.
Fig. 1 shows a flow of a distributed wind power capacity planning method based on variable structure Copula, where the method includes the following steps:
step 1: and predicting the regional load and the distributed wind power output.
The forecasting method comprises the following steps of firstly, establishing an ARMA model to forecast regional load and wind power output data, wherein the ARMA model is as follows:
Yt＝β0+β1Yt-1+β2Yt-2+…+βpYt-p+εt+α1εt-1+α2εt-2+…+αqεt-q
wherein, YtFor time series of wind power of load or dispersion type, Yt-pIs a time sequence before p predictions, beta is a correlation coefficient, epsilontIs a random variable sequence, epsilont-qThe method is characterized in that the method is an error term before q times of prediction, alpha is a correlation coefficient and reflects the dependence of the prediction error term in different periods, p is an autoregressive process order, and q is a moving average process order. The AIC index of ARMA (p, q) model is calculated for model order determination, and the formula is as follows:
wherein σ2And (3) for predicting the variance of an error term, N is the number of historical data, p and q are the orders of an ARMA (p, q) model, calculating AIC values under a plurality of groups of p and q one by one from a low order, and selecting the corresponding p and q values as the optimal ARMA (p, q) model when the AIC value is minimum. According to the method, time sequences formed by regional loads and centralized wind power output are respectively used as original data, the original data are input into an ARMA model to solve orders p and q, and historical data are input into the model to predict loads and centralized wind power output data at future time points.
Secondly, centralized wind power capacity reduction is performed. The conversion formula is as follows,
the centralized wind power installation is the sum of rated power of the wind generating set, 397.3MW is taken, the distributed wind power installation is the maximum value of the specified planning distributed wind power capacity, 50MW is taken, the centralized wind power output predicted value is the predicted result obtained by inputting the original wind power data into an ARMA model, and the distributed wind power output predicted value in the formula is the result of the centralized wind power output predicted value converted by the capacity, namely the result is obtained:
step 2: and performing correlation analysis among variables according to the predicted values, and establishing an optimal variable structure Copula model.
Which comprises the following steps: dividing time intervals according to months and quarters; drawing a binary frequency histogram in each time period, wherein the obtained extreme value correlation relationship among variables is not obvious, namely no obvious thick tail characteristic exists; respectively establishing five basic Copula models, and determining the edge probability distribution function of the load and the distributed wind power in each time period; according to a maximum likelihood estimation method, calculating various Copula model parameters, namely evaluation indexes including Pearson coefficients, Kendall coefficients, Spearman coefficients and Euclidean square distances, based on the edge probability distribution functions of loads and distributed wind power, and obtaining a density function diagram and a distribution function diagram. Among them, there are five types of basic Copula; normal Copula function, t-Copula function, Clayton Copula function, Gumbel Copula function, Frank Copula function; to select the optimal Copula, an empirical Copula function is defined, and the specific formula is as follows:
wherein x and y are load and distributed wind power samples, F (x)i)、G(yi) Empirical distribution function I of x and y, respectively[·]For an indicative function, u and v are both 0-1 distribution, n is the number of samples, and F (x) is satisfiedi)≤u，
F(xi)≥u，
And calculating each parameter of the experience Copula, namely a judgment index, selecting the optimal model with the closest parameter in the time period according to the proximity degree of each Copula function judgment index and each parameter of the experience Copula.
And step 3: and (4) obtaining typical scenes by utilizing K-means clustering division, and obtaining each scene quantile.
The typical scene division based on the K-means clustering comprises the following steps: firstly, discretizing a Copula model in each time period to obtain n discrete points, and randomly selecting k data points from the n discrete points as initial condensation center points; secondly, classifying the other objects except the condensation points according to the comparison result of the distances between the objects and each condensation center, namely updating the clusters; thirdly, calculating the clustering center, namely the mean value, of each obtained new cluster; fourthly, the second step to the third step are cycled until the set cycle number is reached; and fifthly, obtaining the actual load and the distributed wind power quantile through inversion of the probability distribution function.
And 4, step 4: and establishing a system optimization scheduling model containing distributed wind power for capacity planning.
After dividing into k scenes, inputting the original quantile points of each scene into an optimization model, and respectively carrying out distributed wind power capacity planning on each scene. Wherein, the step of establishing the optimization model comprises the following steps:
step 4.1: the optimization modeling of the power system under a typical scene takes the investment and operation cost and the environmental protection income of a distributed wind power plant and the line loss cost of the power system as objective functions, and the function expression is as follows:
F＝min(f1+f2)
f1for the investment and operation cost and the environmental protection benefit of the distributed wind power plant, the expression is as follows:
wherein, PDWGRepresenting planned decentralized wind power capacity, CwtRepresenting the initial investment cost of a decentralized wind farm, CsrRepresents the environmental benefit per unit volume, r0Expressing the discount rate, and T expressing the operation age of the distributed wind power plant;
f2for the line loss cost of the power system, the expression is as follows:
wherein N is the number of system nodes Delta UijIs the voltage difference between two nodes of the system, ZijIs the impedance value, C, of branch ijdjRepresents the unit cost of line loss and δ represents the power factor.
Step 4.2: the constraint conditions are set and comprise power flow constraint, generator active and reactive power output constraint, wind power capacity constraint, voltage constraint and phase angle constraint, and the specific function expression is as follows:
voltage constraint and phase angle constraint, and the specific function expression is as follows:
PGimin≤PGi≤PGimax
QGimin≤QGi≤QGimax
0≤PDWG≤PDWGmax
Uimin≤Ui≤Uimax
|θi-θj|≤|θi-θj|max
wherein N is the number of system nodes, PGi、QGiBeing a generator setActive and reactive power, PGimin,PGimaxFor the active power output limit, Q, of the generatorGimin,QGimaxFor the upper and lower limit values of reactive power output, P, of the generatorDi，QDiFor testing the active or passive value of the node load in the systemDWGFor planned decentralized wind power capacity, Ui,UjIs the system node voltage, Uimin,UimaxIs the upper and lower limit of the system voltage, Gij,BijFor conductance, susceptance, theta, of branch i-jijIs the phase angle difference between node i and node j, PDWGmaxFor a defined upper limit of the capacity of the decentralized windi，θjThe voltage phase angles of the node i and the node j, respectively, and PDGWmax＝50MVA，Uimin＝0.9,Uimax1.05 (per unit value), upper limit of phase angle difference | θ between node i and node ji-θj|maxAnd 5, solving each scene according to the setting of an objective function and a constraint condition of the optimization model to plan the distributed wind power capacity.
As shown in fig. 2, a modified IEEE30 node test system verifies a capacity planning optimization scheduling model of a distributed wind power ordered access power grid under multiple scenes based on a variable structure Copula.
In a specific embodiment, the data sample is the local centralized wind power output and load condition from 2017 th in 1 month to 2018 th in 1 month and 7 days in a certain area in Jiangsu province, and the sampling interval is five minutes.
Step 1: firstly, 108649 group data in 2017 are input into an ARMA model for short-term prediction to obtain 2019 related data. The steps p, q in the model are identified and the AIC criterion is used until a suitable model is determined, by looping through the steps starting from the lower order. The results of the model scaling are given in the following table:
TABLE 1 results of model scaling
Then, the following equation is used:
the centralized wind power installation is the sum of rated power of the wind generating set, 397.3MW is taken, the distributed wind power installation is the maximum value of the specified planning distributed wind power capacity, 50MW is taken, the centralized wind power output predicted value is a predicted result obtained by inputting original wind power data into an ARMA model, and the distributed wind power output predicted value in the formula is a result obtained by converting the centralized wind power output predicted value into capacity, namely the result is obtained.
Step 2: and determining the cumulative distribution function of the load and the distributed wind power by adopting a nonparametric estimation method, and drawing an empirical distribution function and a kernel distribution estimation curve. As shown in fig. 3 and 4, the empirical distribution function is used as a description standard of the actual distribution function, and by comparing the difference between the function diagrams, the result of the non-parametric estimation substantially coincides with the empirical distribution function, the difference is very small, and the estimation accuracy is high.
Particular embodiments choose to study in monthly time intervals, i.e., divided into 12 sub-intervals. And sequentially selecting a Copula function corresponding to the thick tail characteristic according to the thick tail characteristic of the data and a Copula evaluation index, and selecting a Pearson coefficient, a Kendall coefficient, a Spearman coefficient and a Euclidean square distance as the evaluation index selected by the Copula in the embodiment. And estimating the judgment indexes by using a maximum likelihood estimation method, and selecting the Copula which is closest to the empirical Copula parameters as the optimal Copula. The Copula selection of the monthly distributed wind power and the load is specifically explained below, and the same reason is applied in other months. According to the actual data of January, a binary frequency histogram (U) of the distributed wind power and the load is madei,Vi) (i ═ 1, 2.., n), as in fig. 5.
The binary frequency histogram can be used as an estimate of the combined density function of the distributed wind power and load (Copula density function). Since the obvious thick tail characteristic cannot be directly observed, each basic Copula model needs to be established and parameter estimation needs to be carried out on each Copula.
Fig. 6-10 show the Copula model density function graph and distribution function graph of the january load and the distributed wind power. As the characteristics of the distributed wind power output and load correlation data are fuzzy, calculating the Copula model parameters and evaluating the model quality by adopting a maximum likelihood estimation method as shown in Table 2.
TABLE 2 monthly Copula models and empirical Copula parameters
From the above table, it is summarized that the t-Copula model is closest to the empirical Copula in terms of Rho, Kendall, Spearman correlation coefficients, and the euclidean square distance, although not the smallest, is also very close to the empirical Copula. Namely, the t-Copula function model can better fit the correlation between the disperse wind power and the load in january.
Fig. 11 is a diagram of empirical Copula distribution function, and it can be seen that there is a region with a turn, but the distribution function curves of fig. 6 to 10 do not. This indicates that in this patch area, the above five basic Copula distributions do not fit the U and V correlations well, but fit well in other parts.
And step 3: and converting the inaccuracy of the distributed wind power and the load into a deterministic model by using a scene generation method based on K-means clustering.
Based on the Copula model obtained in each time period, 8000 random discrete points are generated by the model in a discrete mode, considering the correlation between the distributed wind power and the load, 8000 generated random discrete point samples are two-dimensional, namely 8000 multiplied by 2-dimensional sample data are obtained. Because the sample data is divided into 12 time intervals, 12 groups of 8000 × 2 dimensional sample data are obtained and spliced into one 96000 × 2 dimensional sample data. Selecting the number of the typical scenes as 6, selecting discrete points 16000,32000,48000,64000,80000,96000 as initial condensation points in 96000 × 2-dimensional sample data, and performing K-means clustering.
And calculating the distance from other single discrete points to each type of condensation point, selecting the minimum distance, sequentially dividing the sample points into the 6 types, and updating the central position of each type. The above steps are repeated until the specified cycle number of 100 is reached. And calculating the proportion of the number of random discrete sample samples in each class to the total number of samples, i.e. the probability P of each sceneL. And finally, converting the obtained 6 scene quantiles into scene quantiles of actual distributed wind power and loads through an inverse function of the probability distribution function. The results are given in the following table:
table 3 load and distributed wind power output quantile points and probabilities in typical scenes
From the results, it is known that each typical scene has a similar occurrence rate, which explains the rationality of dividing the initial point set into 6 typical scenes.
And 4, step 4: after dividing into 6 scenes, inputting the original quantile points of each scene into an optimization model, and respectively carrying out distributed wind power capacity planning on each scene. The optimization model comprises the steps of setting an objective function and constraint conditions, wherein the constraint conditions comprise nonlinear power flow equality constraint and inequality constraint, and solving the constrained nonlinear optimization model by setting an upper limit ub and a lower limit lb vector of a variable, a nonlinear inequality constraint c (x) and an equality constraint ceq (x) in a nolcon parameter by using an fmecon function, wherein c (x) is less than or equal to 0, and ceq (x) is equal to 0.
As shown in fig. 2, the distributed wind power is installed in node 13, and the load is installed in node 14. And obtaining the optimal solution of the target function of each scene under the constraint condition through an fmincon function, wherein the result comprises the distributed wind power capacity planning and the optimal value of the target function under each scene as shown in the following table:
table 4 distributed wind power output and objective function value for each scene
| Scene | Probability of | And the distributed wind power output is p.u. | Value of objective function ($) |
| 1 | 0.1834 | 0.5414 | 192600 |
| 2 | 0.1525 | 0.2205 | 1575.00 |
| 3 | 0.1566 | 0.2136 | 1555.92 |
| 4 | 0.1179 | 0.1221 | 1313.06 |
| 5 | 0.1388 | 0.5000 | 2291.19 |
| 6 | 0.1808 | 0.5422 | 190835 |
And finally, the distributed capacity planning takes the probability of each scene as a weight, namely:
PDWG＝0.5414*PL(1)+0.2205*PL(2)+0.2136*PL(3)+0.1221*PL(4)+0.5*PL(5)+0.5422*PL(6) 0.3481(p.u.), the final decentralized wind farm capacity plan is 34.81MVA since the reference capacity set by the system is 100 MVA.
In conclusion, a variable structure Copula model is established for the variables with different structural characteristics in different time periods, the change of the related structure between the variables can be captured more flexibly, the model has a better fitting effect compared with other single models, and reliable distributed wind power capacity planning can be realized more accurately.
The above is the preferred embodiment of the present invention, and the method is not limited to the test system of IEEE30 node, and other test systems are also applicable.
Claims (1)
1. A capacity planning method for orderly accessing distributed wind power to a power grid under multiple scenes based on variable structure Copula is characterized by comprising the following steps:
(1) the method for establishing the ARMA model to predict the regional load and the distributed wind power output comprises the following steps:
(1-1) establishing an ARMA model to predict regional load and wind power output data;
(1-2) converting the centralized wind power capacity, wherein the formula is as follows:
the system comprises a centralized wind power installation unit, a distributed wind power installation unit, an ARMA (autoregressive moving average) model and a distributed wind power installation unit, wherein the centralized wind power installation unit is the sum of rated power of a wind generating set, the distributed wind power installation unit is the maximum value of the capacity of the distributed wind power which is specified to be planned, the centralized wind power output predicted value is a predicted result obtained by inputting original wind power data into the ARMA model, and the distributed wind power output predicted value is a result obtained by converting the capacity of the centralized wind power output predicted value, namely the result is obtained;
in the step (1-1), the ARMA model is as follows:
Yt＝β0+β1Yt-1+β2Yt-2+···+βpYt-p+εt+α1εt-1+α2εt-2+···+αqεt-q
wherein, YtFor time series of wind power of load or dispersion type, Yt-pIs the time sequence of the p-th time point before the current time point t, beta is a correlation coefficient, epsilontIs an error term of the prediction of the current time point t, epsilont-qThe method comprises the steps that an error term of a qth time point before a current time point t is obtained, alpha is a correlation coefficient and represents the dependence relationship of a prediction error term in different periods, p is an autoregressive process order, q is a moving average process order, and then the AIC index of an ARMA (p, q) model is calculated to be a model order, wherein the formula is as follows:
wherein σ2The variance of the prediction error term is shown, and N is the number of historical data; presetting ranges of p and q, calculating AIC values under a plurality of groups of p and q one by one from a low order, and selecting the corresponding p and q values as an optimal ARMA (p, q) model when the AIC value is minimum;
(1-3) respectively taking time sequences formed by regional loads and centralized wind power output as original data, inputting an ARMA model to solve the orders p and q corresponding to the optimal model, and inputting historical data into the model to predict the loads at future time points and the centralized wind power output data;
(2) performing correlation analysis between variables according to the predicted values, and establishing an optimal variable structure Copula model; the method for establishing the optimal variable structure Copula model comprises the following steps:
(2-1) dividing periods by months or quarters;
(2-2) determining the edge probability distribution function of the load and the distributed wind power in each time interval;
(2-3) respectively establishing each basic Copula model based on the edge probability distribution function of the load and the distributed wind power: calculating various Copula function parameters according to a maximum likelihood estimation method by normal Copula, t-Copula, Clayton Copula, Gumbel Copula and Frank Copula, and drawing a density function graph and a distribution function graph;
(2-4) defining a target Copula function, calculating each parameter of the target Copula and evaluating each model in (2-3) according to the judgment index; the evaluation indexes comprise Pearson coefficients, Kendall coefficients, Spearman coefficients and Euclidean square distances between the Copula models and the target Copula;
(2-5) comparing the estimation results of the Copula parameters, and selecting the model with the most number of parameters closest to the target Copula parameter value as the optimal model;
(3) obtaining typical scenes by utilizing K-means clustering division, and obtaining load and distributed wind power values of each scene, namely quantiles; in the step (3), the typical scene division step is as follows:
(3-1) discretizing the obtained Copula model in each time period to obtain n discrete points, and randomly selecting k data points from the n discrete points as initial condensation central points;
(3-2) comparing the distances between other objects except the aggregation center and each aggregation center, classifying the object with the closest distance as the class, and updating the cluster;
(3-3) calculating the clustering center, namely the mean value, of each obtained new cluster, and updating the clustering center;
(3-4) circulating the steps (3-2) to (3-3) until the set circulation times are reached;
(3-5) obtaining actual load and distributed wind power sub-sites by inverting the edge probability distribution function;
(4) the method for capacity planning of each scene sub-site by establishing a system optimization scheduling model containing distributed wind power comprises the following steps:
(4-1) performing optimization modeling on the power system in a typical scene, wherein the investment and operation cost and the environmental protection benefit of a distributed wind power plant and the line loss cost of the power system are taken as objective functions, and the function expression is as follows:
F＝min(f1+f2)
f1for the investment and operation cost and the environmental protection benefit of the distributed wind power plant, the expression is as follows:
wherein, PDWGRepresenting planned decentralized wind power capacity, CwtRepresenting the initial investment cost of a decentralized wind farm, CsrEnvironmental benefit, r, expressed in unit volume0Expressing the discount rate, and T expressing the operation age of the distributed wind power plant;
f2for the line loss cost of the power system, the expression is as follows:
wherein N is the number of system nodes, Δ UijIs the voltage difference between system node i and node j, ZijIs the impedance value, C, of branch ijdjThe unit cost of the line loss is shown, and delta represents a power factor;
(4-2) the constraint conditions are set to include power flow constraint, generator active and reactive power output constraint, wind power capacity constraint, voltage constraint and phase angle constraint, and the specific function expression is as follows:
PGimin≤PGi≤PGimax
QGimin≤QGi≤QGimax
0≤PDWG≤PDWGmax
Uimin≤Ui≤Uimax
|θi-θj|≤|θi-θj|max
wherein N is the number of system nodes, PGi、QGiFor active and reactive power of the generator set, PGimin,PGimaxFor the upper and lower limit values of the active power output, Q, of the generatorGimin,QGimaxFor the upper and lower limit values of reactive power output, P, of the generatorDi，QDiFor testing the active and inactive values, P, of the node load in the systemDWGFor planned decentralized wind power capacity, Ui,UjIs the system node voltage, Uimin,UimaxIs the upper and lower limit of the system voltage, Gij,BijFor conductance, susceptance, theta, of branch i-jijIs the phase angle difference between node i and node j, PDWGmaxFor a defined upper limit of the capacity of the decentralized windi，θjAnd respectively solving the voltage phase angles of the node i and the node j according to the setting of the objective function and the constraint condition of the optimization model to plan the distributed wind power capacity.
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