CN116014724A - Active power distribution network gridding load prediction method - Google Patents
Active power distribution network gridding load prediction method Download PDFInfo
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Abstract
The invention discloses a method for predicting grid load of an active power distribution network, and relates to a method for predicting power consumption load of a power distribution network. A grid load prediction method for an active power distribution network comprises grid division of the power distribution network, load prediction of the power distribution network and net load prediction of the active power distribution network after distributed photovoltaic access. The meshing division of the power distribution network comprises the following steps: planning target determination, data acquisition, meshing, load prediction, network architecture determination and planning scheme evaluation. The power distribution network load prediction comprises grid load prediction based on BP neural network and grid load prediction based on support vector machine neural network.
Description
Technical Field
The invention discloses a method for predicting grid load of an active power distribution network, and relates to a method for predicting power consumption load of a power distribution network.
Background
The traditional power distribution network planning extends towards the power distribution network by taking the main network planning as a main direction, namely, a top-down mode is adopted, and a research object is generally the whole planning area. However, with the development of economy, the demand of social electricity consumption is gradually increased, the requirement of users on the electric energy quality is gradually increased, and the power distribution network is enlarged due to urban construction, so that a plurality of problems are exposed in the traditional planning mode. For example: the main network is taken as the main network, and the continuously increased electricity consumption requirement cannot be met in a top-down planning mode, so that the power supply reliability is reduced; the power supply range of the high-voltage transformer substation is fuzzy, and the phenomenon of repeated planning of a power distribution network, investment waste and the like exist. In summary, conventional power distribution planning methods cannot meet the requirements of socioeconomic development. It is necessary to provide a new solution to meet the actual social demands.
Disclosure of Invention
The invention provides the grid load prediction method for the active power distribution network, which can well realize the accurate prediction of the load of the power distribution network and has good economic value.
A grid load prediction method for an active power distribution network comprises grid division of the power distribution network, load prediction of the power distribution network and net load prediction of the active power distribution network after distributed photovoltaic access.
The meshing division of the power distribution network comprises the following steps: planning target determination, data acquisition, meshing, load prediction, network architecture determination and planning scheme evaluation.
The specific steps of grid division of the power distribution network are as follows:
first, a determination of a planning objective is made, including planning scope, planning reference year, horizontal year, and saturation year. Basic data of the planning area, including load types, load demand amounts and the like, are fully collected, and geographic features of the area are fully mastered. Grid division is carried out on the basis, and the grid division of the power distribution network is a core link of grid distribution planning and comprises three layers of division of a power supply area, a power supply grid and a power supply unit:
the power supply areas are divided based on the layout condition of the transformer substation, the construction current situation and future planning of the upper-layer main network are fully considered, and the urban administrative areas are divided.
The power supply grid is an important level for bearing the power supply area and the power supply unit, and is fully based on urban and rural future development planning and power grid construction planning in the dividing process, and meanwhile difficulty of line construction is considered. In addition, the power supply grid is required to ensure fineness, the range is not excessively large, and the standard wiring unit power supply area is generally corresponding to the power supply grid.
The power supply unit is the smallest hierarchy in gridding division, and in the dividing process, the actual demands and the load density of users are considered, and the loads of the same type are divided into the same unit as much as possible so as to be convenient for power supply. Meanwhile, the geographical boundaries of roads, rivers and the like are combined for division, so that local conditions are met. In rural power distribution network planning, a village and town is generally used as a power supply unit.
And after grid division, carrying out load prediction and determination of a network architecture planning scheme, carrying out power balance calculation according to a load prediction result, carrying out scheme evaluation from two aspects of feasibility and economy, and if the evaluation is unqualified, carrying out network architecture planning determination again.
The power distribution network load prediction comprises grid load prediction based on a BP neural network and grid load prediction based on a support vector machine neural network;
The method for predicting the grid load based on the BP neural network comprises the following steps:
the whole process is divided into two stages, load influence factor data of each grid is firstly used as input layer data, and BP neural network is utilized to obtain output data through certain nonlinear operation, namely, a forward propagation process; and then carrying out reverse correction weight and bias according to errors generated by the output value and the true value, thereby completing training of the network, and then calculating to obtain a load point prediction result.
(1) Network architecture and forward propagation process
The BP neural network structure is composed of an input layer, a hidden layer and an output layer, wherein the hidden layer is provided with one or more layers, and each layer can be provided with a plurality of neurons. The single neuron consists of three parts of connection weight, summation unit and nonlinear activation function, and the expression is as follows
Wherein x is j To input data, w kj B is the connection weight between the jth input data and the kth neuron k For the bias of the kth neuron, y k For the output of the kth neuron,
for the activation function, there are various types of activation functions, and tan sig function is selected as the activation function of the hidden layer, as shown in formula (2-2).
Substituting it into equation (2-1) yields the transfer function of a single hidden layer neuron as in equation (2-3).
Selecting purelin function as the activation function of the output layer, i.e
In summary, the output of a single neuron is determined by the weighted sum of the input data and the sum of the bias term, and then by the activation function. The process that input data sequentially passes through the hidden layer neuron and the output layer neuron to obtain output data is the forward propagation process.
(2) Reverse correction procedure
The output value obtained by forward propagation often has a certain error with the actual value, the error is reversely transmitted to the input layer by the output layer through the hidden layer, and the weights and the offsets of the hidden layer and the neurons of the output layer are adjusted in the process, so that the process of reducing the error is a reverse correction process.
Sample (x) k ,y k ) The output value of (2) is
The loss function is as shown in the formula (2-5).
Wherein n is the number of samples,
can be calculated by the formula (2-1). And iterating by using a gradient descent method, correcting the weight and the bias, and continuously reducing the loss function value until the requirement is met.
The principle of iteration by using the gradient descent method is shown as the formula (2-6).
Where a is the learning rate and L (w, b) is the loss function. According to the formula (2-6), w and b of the output layer and the hidden layer are sequentially adjusted, so that the purpose of minimizing the global loss function is achieved.
After the reverse correction, the corrected weight and offset value are used to input the load influence factor data instead of the prediction, forward transmission is carried out, and the obtained output value is the final prediction result.
(3) Program number determination
In the process of constructing the BP neural network prediction model, the number of nodes of an input layer and the number of nodes of an output layer are determined, and the number of nodes of an uncertain hidden layer is a key factor influencing the magnitude of errors of a prediction result. If the number of hidden layer nodes is too large, the network training is too slow and is easy to fall into local optimum; if too small, the network learning ability may be insufficient. In general, the determination method of the number of hidden layer nodes is as follows
Where h is the number of hidden layer nodes, m is the number of input layer nodes, n is the number of output layer nodes, and a is a constant between 0 and 10. After the value range of the number of the nodes is defined, the number of the hidden layer nodes can be determined by adopting a cross-validation method.
The grid load prediction method based on the support vector machine neural network comprises the following steps:
the support vector machine (Support Sector Machine, SVM) is a two-class model whose basic idea is to find a hyperplane to maximize the separation of the data points of the two classes of samples from the hyperplane. Support vector regression (Support Vactor Regression, SVR) is a branch of SVM, which is widely used in data prediction and the like due to its good fitting effect. Unlike SVM, SVR is the minimization of the distance of the sample data points from the hyperplane.
Let the sample training set be (x) i ,y i ) (i=1, 2, l), where l is the number of samples, x i For inputting data, the dimension is m, y i For output data, the dimension is n. The essence of using SVR for grid load prediction is to use a nonlinear mapping
Fitting to obtain a regression function f (x) so that f (x i )≈y i The fitting function thereof can be expressed as formula (2-7).
Wherein ω and b are regression coefficients, respectively representing an m-dimensional weight vector and a bias term. The regression coefficients can be found from the optimization problem in solution (2-8) according to the SVR principle.
The above formula is the principle of regression coefficient of epsilon-SVR solution, wherein C is penalty factor, epsilon is insensitive coefficient, and xi are calculated by the method i * Are all relaxation variables. In practical application, epsilon parameters are required to be determined empirically, in order to avoid difficult epsilon determination, a v-SVR model is selected for load prediction, and v parameters are introduced as follows
Solving by using a Lagrangian multiplier method to construct a Lagrangian function, namely formula (2-10).
Wherein alpha is i ,
d i ,/>
h is Lagrangian multiplier, both are greater than 0, according to Lagrangian multiplier principle, when
When the function existsMinimum, taking into account both the KKT conditions and the dual conditions, converts the problem into the form of formulas (2-11).
At this time, the regression function is converted into
Wherein K (x i X) is a kernel function, which has various forms, and a Gaussian kernel (RBF (Radial Basis Function) kernel) is used herein, which has the form of formula (2-13).
Wherein sigma is the width of the Gaussian kernel function, the action range of the kernel function is controlled, and optimization is needed.
Before training by using a support vector machine, parameters C, v and sigma are required to be optimized, so that the SVR fitting effect is best, a particle swarm algorithm is used for carrying out parameter iterative optimization by taking a minimum MSE as a target, and then a regression model is trained by using the optimized parameters, so that a point prediction result is obtained.
The active power distribution network net load prediction after the distributed photovoltaic access comprises active power distribution network gridding net load point prediction and active power distribution network gridding net load interval prediction;
the active power distribution network gridding net load point prediction method comprises the following steps:
the net load of a certain distribution grid is the difference between the grid load power and the distributed photovoltaic power generation power, and after the distributed photovoltaic output point prediction and the load point prediction are carried out, the net load point prediction value of the distribution grid can be obtained by taking the difference, wherein the prediction model adopts the PCA-GRNN model, the BP neural network and the support vector machine regression prediction model which are proposed in the foregoing.
At this time, two prediction models of grid load prediction are combined as a result to obtain a more accurate load prediction value.
(1) Combined load prediction model
After load prediction is performed by using BP neural network and support vector machine regression, two different results can be obtained, prediction errors are different, the two prediction results are combined by using a reciprocal variance method, and the final prediction result is obtained by calculating the weights of the two prediction models and carrying out weighted summation. So as to achieve the purposes of further reducing errors and improving prediction accuracy.
If there are m prediction models, each model has n prediction sample results, and P is used for ij Representing the prediction result of the jth sample in the ith prediction model, T j The weight of each prediction model, representing the true value of the jth sample, can be calculated by equations (2-15).
Wherein Q is i For the sum of variances of the ith predictive model result, i.e.
And then carrying out weighted summation on the prediction results, as shown in the formula (2-17).
Wherein the method comprises the steps of
As can be seen from the weighting process described above, the reciprocal variance method is essentially to assign a high weight to the small error model, so as to achieve the goal of reducing the overall error.
(2) Point predictive evaluation index
Average absolute percentage error (Mean Absolute Percentage Error, MAPE) and root mean square error (Root Mean Square Error, RMSE) are selected as the point prediction evaluation indexes. MAPE can intuitively represent the relative error between the predicted value and the actual value, and can be calculated by the formulas (2-18).
And RMSE can be calculated from the formulas (1-9) above.
The method for predicting the gridding net load section of the active power distribution network comprises the following steps:
the idea of net load interval prediction is consistent with point prediction, namely the difference value between a load prediction interval and a distributed photovoltaic output prediction interval under a certain confidence level. The method for predicting the distributed photovoltaic output interval based on PCA-GRNN-QR has been proposed, so that load interval prediction needs to be realized at present. Firstly, a fuzzy information granulating method is introduced, a fuzzy set is constructed to obtain the upper and lower boundaries of a section of a load history value under the confidence level, then the upper and lower boundaries are respectively predicted by utilizing the combination point prediction model provided by the prior art, so as to obtain a load prediction section, and then the load prediction section is differenced with a distributed photovoltaic output prediction section, and the fact that the load prediction upper boundary is differenced with the distributed photovoltaic output prediction lower boundary and the load prediction lower boundary is differenced with the distributed photovoltaic output prediction upper boundary is needed, so that a net load prediction section is obtained.
(1) Fuzzy information granulation
The fuzzy information granulation is to divide a whole body into a plurality of parts for research, wherein each part is an information particle, and the information granulation process can be divided into two stages of window division and blurring. The window division is to divide the original time sequence data into a plurality of subsequences according to a fixed time period, wherein each subsequence is an information granulating window; the key to blurring is to construct the fuzzy set. For a window X { X } 1 ,x 2 ,L,x N Establishing a fuzzy particle P, namely a fuzzy concept G which can reasonably describe X and takes X as a domainIf fuzzy particles P are used to replace fuzzy concept G, there is
P＝A(x) (2-19)
Where A is a membership function of G, and A (x) may be expressed as the membership of x to G. The nature of the blurring, i.e. determining membership functions, is herein applied with triangular blurring particles, i.e
Wherein X ε X, a, m, b represent the minimum, kernel and maximum values of the window time series, respectively. If the time sequence is arranged from small to large, the sequence is still X { X } 1 ,x 2 ,L,x N Then the kernel value m can be directly determined by equation (2-20).
The value of a is determined by
The value of b is thus determined
With [ a, b ] as the interval when the confidence level is 100%, all data of the window should lie within [ a, b ], i.e., all data of the window is not less than a and not more than b. In view of this, the values of a and b are further deduced below to simplify the calculation amount.
If m=x n Expanding Q (a) to obtain
Separating constants of left-hand terms of multiplier numbers, i.e.
As can be seen from the above equation, the smaller m-a, i.e., the closer a is to m, the larger Q (a) is, and considering that all the raw data of the window should be not smaller than a, a should take the minimum value of the raw data of the window.
Similarly, it can be deduced that b should take the maximum value of the window raw data.
After determining the membership function of each information grain, the historical upper and lower bound granulation data of the prediction interval is further determined according to the confidence level and the membership function. For an information grain, the function formula of determining the upper and lower boundaries of the interval under a certain confidence level by the membership function is as follows:
where CL is the confidence level, l and h are two points where membership is 1-CL, the bolded portion of the horizontal axis represents the entire interval where the confidence level is CL, and the principle is that [ a, b ] is the interval where the confidence level is 100%, and correspondingly, [ l, h ] is the interval where the confidence level is CL.
According to the method, historical boundary data of the interval can be obtained, and then the grid load interval prediction can be realized by utilizing a combined prediction method of the BP neural network and the SVR.
(2) Section prediction evaluation index
The prediction section coverage PICP and the average width PINAW are still used as evaluation indexes for section prediction.
(3) Example verification
The following performs an example verification on the payload section prediction model, and still uses an example of point prediction as an example to predict the payload at 7 to 17 days of 8 months 29. Taking 90% confidence level as an example, the PCA-GRNN-QR model is utilized to predict the distributed photovoltaic output interval.
And then, the load prediction interval and the distributed photovoltaic prediction interval are subjected to difference, namely, the upper limit of the load prediction interval is subtracted by the lower limit of the distributed photovoltaic prediction interval, and the lower limit of the load prediction interval is subtracted by the upper limit of the distributed photovoltaic prediction interval to obtain the prediction interval of the net load power.
And meanwhile, calculating to obtain the interval prediction evaluation index of the distributed photovoltaic power, the load power and the net load power.
Compared with the prior art, the invention has the following characteristics:
the grid division of the power distribution network is combined with planning of future urban and rural construction and actual demand of users on power supply, three-level division is further carried out, and the power distribution planning mode has important significance on aspects of power grid construction, economic development, realization of double-carbon targets and the like, and is specifically expressed as follows:
(1) The user requirements are met, and the power supply reliability is improved. The grid division of the power distribution network mainly uses user demands, and a bottom-up mode is adopted to fully ensure user power supply, so that the power supply of the power distribution network is more reliable.
(2) And the power supply is refined, and the scheduling flexibility is improved. The grid division of the power distribution network enables the power supply range of the transformer substation to be clearer, the power supply modes of each level to be finer, the power operation and maintenance management to be convenient, meanwhile, the control capability of power grid management staff to the power distribution network is improved, and the power resource scheduling is more flexible.
(3) And the urban power grid architecture is optimized, so that electric power construction is facilitated. In the project of grid division of the power distribution network, geographic characteristics and construction conditions of cities are fully considered, and power distribution network planning is optimized on the basis, so that repeated planning is avoided, power construction investment is reduced, and power construction workload is simplified.
(4) Energy saving and emission reduction, power assisting of carbon peak, carbon neutralization and target realization. On one hand, the grid power supply is adopted, so that the waste of power resources can be reduced on the basis of fully meeting the requirements of users; on the other hand, in the grid division process, distributed new energy power generation such as photovoltaic power generation, wind power generation and the like can be brought into the power distribution planning work, so that the new energy power generation permeability is improved to the maximum extent, and the power assisting double-carbon target is realized.
(5) Promote the development of the social and economic level. The meshing division can fully meet the power supply requirements of users with great contribution to economic development, such as industry, catering industry, tourism industry and the like, and ensure that the economic level is steadily improved; meanwhile, the requirements of urban and rural construction planning are considered, and the method conforms to the long-term development trend of society in the future.
Drawings
The invention will be further described with reference to the accompanying drawings
Fig. 1 is a schematic diagram of three power supply network layers of a power supply area, a power supply grid and a power supply unit of a grid division of a power distribution network in the invention.
Fig. 2 is a schematic flow chart of grid planning of a power distribution network in the present invention.
Fig. 3 is a schematic diagram of a grid load prediction process of the BP neural network in the present invention.
Fig. 4 is a schematic diagram of a process for predicting a grid-like net load point of an active power distribution network according to the present invention.
Fig. 5 is a prediction graph of the prediction result of the distributed photovoltaic output point in the present invention.
Fig. 6 is a prediction diagram of the load power point prediction result in the present invention.
FIG. 7 is a graph of the net load power point prediction result in the present invention.
Fig. 8 is a schematic diagram of a active power distribution network meshed payload section prediction flow in the present invention.
FIG. 9 is a graph of a membership function image determination interval boundary in the present invention.
FIG. 10 is a graph of the predicted interval of distributed photovoltaic output at 90% confidence level in the present invention.
FIG. 11 is a graph of load prediction intervals at 90% confidence level in the present invention.
FIG. 12 is a graph of the predicted intervals of the payload at 90% confidence level in the present invention.
Detailed Description
Referring to fig. 1-12, the method for predicting grid load of an active power distribution network comprises grid division of the power distribution network and power distribution network load prediction.
Further, the active power distribution network grid load prediction method further comprises the step of active power distribution network net load prediction after distributed photovoltaic access.
The grid division method of the power distribution network comprises the following steps:
referring to fig. 2, a general flow of grid planning of a power distribution network includes planning objective determination, data acquisition, grid partitioning, load prediction, determination of network architecture, and planning scheme evaluation.
As shown in fig. 1 and 2, the determination of the planning target is first performed, including the planning range, the planning reference year, the horizontal year, the saturation year, and the like. Basic data of the planning area, including load types, load demand amounts and the like, are fully collected, and geographic features of the area are fully mastered. Grid division is carried out on the basis, and the grid division of the power distribution network is a core link of grid distribution planning and comprises three layers of division of a power supply area, a power supply grid and a power supply unit:
(1) The power supply area is divided mainly based on the layout condition of the transformer substation, the construction current situation and future planning of the upper-layer main network are fully considered, and the urban administrative area is generally divided.
(2) The power supply grid is an important level for bearing the power supply area and the power supply unit, and is fully based on urban and rural future development planning and power grid construction planning in the dividing process, and meanwhile difficulty in line construction is considered. In addition, the power supply grid is required to ensure fineness, the range is not excessively large, and the standard wiring unit power supply area is generally corresponding to the power supply grid.
(3) The power supply unit is the smallest hierarchy in gridding division, and the actual demands and the load density of users are considered in the dividing process, and the loads of the same type are divided into the same unit as much as possible so as to be convenient for power supply. Meanwhile, the geographical boundaries of roads, rivers and the like are combined for division, so that local conditions are met. In rural power distribution network planning, a village and town is generally used as a power supply unit.
And after grid division, carrying out load prediction and determination of a network architecture planning scheme, carrying out power balance calculation according to a load prediction result, carrying out scheme evaluation from two aspects of feasibility and economy, and if the evaluation is unqualified, carrying out network architecture planning determination again.
Power distribution network load prediction
The gridding load prediction is an important link of gridding planning, and the load prediction result is an important basis for subsequent grid power balance calculation and grid division optimization. The traditional grid load prediction method comprises a load density method, a user-average distribution transformation capacity method and a large user-natural growth rate method, but the methods have the common problems that parameters required by prediction such as load density, natural growth rate and the like are difficult to determine, the determination process is too dependent on experience, the randomness of the load cannot be represented, and the prediction accuracy is poor. Therefore, the modern classical prediction algorithm BP neural network and a support vector machine are introduced in the section, and the load prediction of the power distribution network is performed according to a large amount of historical data, so that the prediction accuracy is improved.
Referring to fig. 3, the mesh load prediction method based on the BP neural network is as follows:
the whole process is divided into two stages, load influence factor data of each grid is firstly used as input layer data, and BP neural network is utilized to obtain output data through certain nonlinear operation, namely, a forward propagation process; and then carrying out reverse correction weight and bias according to errors generated by the output value and the true value, thereby completing training of the network, and then calculating to obtain a load point prediction result.
(1) Network architecture and forward propagation process
The BP neural network structure is composed of an input layer, a hidden layer and an output layer, wherein the hidden layer is provided with one or more layers, and each layer can be provided with a plurality of neurons. The single neuron consists of three parts of connection weight, summation unit and nonlinear activation function, and the expression is as follows
Wherein x is j To input data, w kj B is the connection weight between the jth input data and the kth neuron k For the bias of the kth neuron, y k For the output of the kth neuron,
for the activation function, there are various types of activation functions, and tan sig function is selected as the activation function of the hidden layer, as shown in formula (2-2).
Substituting it into equation (2-1) yields the transfer function of a single hidden layer neuron as in equation (2-3).
Selecting purelin function as the activation function of the output layer, i.e
In summary, the output of a single neuron is determined by the weighted sum of the input data and the sum of the bias term, and then by the activation function. The process that input data sequentially passes through the hidden layer neuron and the output layer neuron to obtain output data is the forward propagation process.
(2) Reverse correction procedure
The output value obtained by forward propagation often has a certain error with the actual value, the error is reversely transmitted to the input layer by the output layer through the hidden layer, and the weights and the offsets of the hidden layer and the neurons of the output layer are adjusted in the process, so that the process of reducing the error is a reverse correction process.
Sample (x) k ,y k ) The output value of (2) is
The loss function is as shown in the formula (2-5). />
Wherein n is the number of samples,
can be calculated by the formula (2-1). And iterating by using a gradient descent method, correcting the weight and the bias, and continuously reducing the loss function value until the requirement is met.
The principle of iteration by using the gradient descent method is shown as the formula (2-6).
Where a is the learning rate and L (w, b) is the loss function. According to the formula (2-6), w and b of the output layer and the hidden layer are sequentially adjusted, so that the purpose of minimizing the global loss function is achieved.
After the reverse correction, the corrected weight and offset value are used to input the load influence factor data instead of the prediction, forward transmission is carried out, and the obtained output value is the final prediction result.
(3) Program number determination
In the process of constructing the BP neural network prediction model, the number of nodes of an input layer and the number of nodes of an output layer are determined, and the number of nodes of an uncertain hidden layer is a key factor influencing the magnitude of errors of a prediction result. If the number of hidden layer nodes is too large, the network training is too slow and is easy to fall into local optimum; if too small, the network learning ability may be insufficient. In general, the determination method of the number of hidden layer nodes is as follows
Where h is the number of hidden layer nodes, m is the number of input layer nodes, n is the number of output layer nodes, and a is a constant between 0 and 10. After the value range of the number of the nodes is defined, the number of the hidden layer nodes can be determined by adopting a cross-validation method.
The grid load prediction method based on the support vector machine neural network comprises the following steps:
the support vector machine (Support Sector Machine, SVM) is a two-class model whose basic idea is to find a hyperplane to maximize the separation of the data points of the two classes of samples from the hyperplane. Support vector regression (Support Vactor Regression, SVR) is a branch of SVM, which is widely used in data prediction and the like due to its good fitting effect. Unlike SVM, SVR is the minimization of the distance of the sample data points from the hyperplane.
Let the sample training set be (x) i ,y i ) (i=1, 2, l), where l is the number of samples, x i For inputting data, the dimension is m, y i For output data, the dimension is n. The essence of using SVR for grid load prediction is to use a nonlinear mapping
Fitting to obtain a regression function f (x) so that f (x i )≈y i The fitting function thereof can be expressed as formula (2-7).
Wherein ω and b are regression coefficients, respectively representing an m-dimensional weight vector and a bias term. The regression coefficients can be found from the optimization problem in solution (2-8) according to the SVR principle.
The above formula is the principle of regression coefficient of epsilon-SVR solution, wherein C is penalty factor, epsilon is insensitive coefficient, and xi are calculated by the method i * Are all relaxation variables. In practical application, epsilon parameters are required to be determined empirically, in order to avoid difficult epsilon determination, a v-SVR model is selected for load prediction, and v parameters are introduced as follows
Solving by using a Lagrangian multiplier method to construct a Lagrangian function, namely formula (2-10).
Wherein alpha is i ,
d i ,/>
h is Lagrangian multiplier, both are greater than 0, according to Lagrangian multiplier principle, when
When the function has a minimum, the problem can be converted into the form of formula (2-11) by taking the KKT condition and the dual condition into consideration.
At this time, the regression function is converted into
Wherein K (x i X) is a kernel function, which has various forms, and a Gaussian kernel (RBF (Radial Basis Function) kernel) is used herein, which has the form of formula (2-13).
Wherein sigma is the width of the Gaussian kernel function, the action range of the kernel function is controlled, and optimization is needed.
Before training by using a support vector machine, parameters C, v and sigma are required to be optimized, so that the SVR fitting effect is best, a particle swarm algorithm is used for carrying out parameter iterative optimization by taking a minimum MSE as a target, and then a regression model is trained by using the optimized parameters, so that a point prediction result is obtained.
The active power distribution network net load prediction after distributed photovoltaic access comprises active power distribution network gridding net load point prediction and active power distribution network gridding net load interval prediction.
The active power distribution network gridding net load point prediction method comprises the following steps:
referring to fig. 4, the net load of a certain distribution grid is the difference between the grid load power and the distributed photovoltaic power generation power, and after the distributed photovoltaic output point prediction and the load point prediction are performed, the net load point prediction value of the distribution grid can be obtained by performing difference, wherein the prediction model adopts a PCA-GRNN model, a BP neural network and a support vector machine regression prediction model.
And combining the results of the two prediction models of the grid load prediction to obtain a more accurate load prediction value.
(1) Combined load prediction model
After load prediction is performed by using BP neural network and support vector machine regression, two different results can be obtained, prediction errors are different, the two prediction results are combined by using a reciprocal variance method, and the final prediction result is obtained by calculating the weights of the two prediction models and carrying out weighted summation. So as to achieve the purposes of further reducing errors and improving prediction accuracy.
If there are m prediction models, each model has n prediction sample results, and P is used for ij Representing the prediction result of the jth sample in the ith prediction model, T j The weight of each prediction model, representing the true value of the jth sample, can be calculated by equations (2-15).
Wherein Q is i For the sum of variances of the ith predictive model result, i.e.
And then carrying out weighted summation on the prediction results, as shown in the formula (2-17).
Wherein the method comprises the steps of
As can be seen from the weighting process described above, the reciprocal variance method is essentially to assign a high weight to the small error model, so as to achieve the goal of reducing the overall error.
(2) Point predictive evaluation index
Average absolute percentage error (Mean Absolute Percentage Error, MAPE) and root mean square error (Root Mean Square Error, RMSE) are selected as the point prediction evaluation indexes. MAPE can intuitively represent the relative error between the predicted value and the actual value, and can be calculated by the formulas (2-18).
(3) Example verification
In order to evaluate the effect of the point prediction model, an example verification is performed on the model using actual data of a certain place as an example. The practical distributed photovoltaic output and load power data of 2022, 8 months, 1 day to 8 months and 29 days are adopted as calculation examples, wherein the influence factors of the distributed photovoltaic output comprise nine indexes of air temperature, humidity, air pressure, precipitation, ground wind speed, wind direction, ground surface horizontal radiation, direct radiation and scattered radiation. And respectively carrying out point prediction of the distributed photovoltaic output and the load power of 29 days 7:00 to 17:00 by taking the data set of 8 months 1 to 28 months as a training set and the data of 8 months 29 days as a test set, and finally obtaining the net load power by difference.
Firstly, predicting distributed photovoltaic output power points, and in order to fully prove the necessity of dimension reduction, respectively predicting by using a PCA-GRNN model and a GRNN model, wherein the number K of folds of Kfold cross validation is 5, and the obtained optimal smoothness factors are 0.22 and 0.32 respectively, so that the prediction result of FIG. 5 is obtained.
Fig. 5 (a) shows a point prediction result diagram of the PCA-GRNN model, and (b) shows a point prediction result diagram of the GRNN model. It can be seen that both models can basically reflect the real fluctuation situation of the distributed photovoltaic output, while the PCA-GRNN model has larger error between 15 and 17, and the GRNN model has larger deviation between 11 and 15, and by comparison analysis, the result obtained by the prediction model after dimension reduction can be certainly more consistent with the real value situation.
And calculating prediction error evaluation indexes under two models, wherein the prediction error evaluation indexes are as follows:
table 2-1 evaluation index of distributed photovoltaic output prediction model
The smaller and better MAPE and RMSE are, the above calculation results can show that the PCA-GRNN model has better performance than the GRNN model, and it is notable that the prediction accuracy of the two models is not ideal, the reasons for analysis are possibly related to the distance deviation of a meteorological station and an in-field photovoltaic electric field of about 15 km and the measurement error of the distributed photovoltaic output per se, but the above results are enough to prove the necessity of performing dimension reduction operation.
And then, carrying out point prediction of load power, and predicting by using a BP neural network and a support vector machine regression combination prediction model. The BP neural network adopts Kfold cross verification to optimize the number of hidden layer nodes, and when K is 3, the optimal number of nodes is 4; the parameters of the support vector regression are optimized by a particle swarm algorithm to obtain the load power point prediction results with the values of C, v and sigma of 42.204, 0.382 and 60.735 respectively, and the obtained load power point prediction results are shown in fig. 6.
The weight distribution of the two models obtained by calculation is shown in Table 2-2.
TABLE 2-2 Combined prediction model prediction variance and weight distribution
| Model | Training set variance | Test set variance | Weight allocation |
| BP neural network | 13817.986 | 212.149 | 0.419 |
| Support vector machine | 9948.267 | 187.771 | 0.581 |
The results in Table 2-2 show that for the training set, the BP neural network prediction has a large error, so that the weight given is small; in contrast, the support vector machine has a smaller error and is therefore given a greater weight. For the test set, the prediction error of the BP neural network is far greater than that of the support vector machine, and the weight distribution calculated according to the variance of the training set is still applicable to the test set, which indicates that the weight distribution mode of the combined prediction model has no contingency and also proves that the distribution mode has certain rationality.
Meanwhile, the point prediction evaluation index of each model and the combined prediction model can be calculated:
TABLE 2-3 evaluation index of load prediction model
| Model | MAPE | RMSE |
| BP neural network | 8.094 | 4.392 |
| Support vector machine regression | 6.906 | 4.123 |
| Combined prediction model | 6.281 | 3.793 |
From the calculation results of the evaluation indexes, the results of the three models are ideal, and the indexes of the combined prediction model are smaller than those of the BP neural network and the regression of the support vector machine, so that the combined prediction result enables the predicted value to be more closely matched with the true value, the prediction precision is improved, and in conclusion, the combined prediction model based on the BP neural network and the regression of the support vector machine is good in precision, small in prediction error and applicable to load power point prediction. Then, the predicted power of the load point is differenced with the predicted power of the distributed photovoltaic output to obtain the predicted value of the net load power,
Referring to fig. 7, prediction errors at 7, 11 and 13 are large, and the other time point predictions substantially fit the true value, so that overall deviation of the predictions from the true value is not large. Meanwhile, the evaluation index of the calculated net load power point predicted value is as follows: the mean absolute percentage error of MAPE is 6.448%, the root mean square error of RMSE is 3.691, and according to the calculation result, the prediction error of the payload prediction model proposed herein can be considered to be smaller, and the prediction accuracy is good.
The method for predicting the gridding net load section of the active power distribution network comprises the following steps:
referring to fig. 8, the idea of net load interval prediction is consistent with point prediction, i.e., the difference between the load prediction interval and the distributed photovoltaic output prediction interval at a certain confidence level. The method for predicting the distributed photovoltaic output interval based on PCA-GRNN-QR has been proposed, so that load interval prediction needs to be realized at present. Firstly, a fuzzy information granulating method is introduced, a fuzzy set is constructed to obtain the upper and lower boundaries of a section of a load history value under the confidence level, then the upper and lower boundaries are respectively predicted by utilizing the combination point prediction model provided by the prior art, so as to obtain a load prediction section, and then the load prediction section is differenced with a distributed photovoltaic output prediction section, and the fact that the load prediction upper boundary is differenced with the distributed photovoltaic output prediction lower boundary and the load prediction lower boundary is differenced with the distributed photovoltaic output prediction upper boundary is needed, so that a net load prediction section is obtained.
(1) Fuzzy information granulation
The fuzzy information granulation is to divide a whole body into a plurality of parts for research, wherein each part is an information particle, and the information granulation process can be divided into two stages of window division and blurring. The window division is to divide the original time sequence data into a plurality of subsequences according to a fixed time period, wherein each subsequence is an information granulating window; the key to blurring is to construct the fuzzy set. For a window X { X } 1 ,x 2 ,L,x N Establishing a fuzzy particle P, namely a fuzzy concept G which can reasonably describe X, wherein G is a fuzzy set taking X as a discourse domain, and if the fuzzy particle P is used for replacing the fuzzy concept G, the fuzzy particle P is provided with
P＝A(x) (2-19)
Where A is a membership function of G, and A (x) may be expressed as the membership of x to G. The nature of the blurring, i.e. determining membership functions, is herein applied with triangular blurring particles, i.e
Wherein X ε X, a, m, b represent the minimum, kernel and maximum values of the window time series, respectively. If the time sequence is arranged from small to large, the sequence is still X { X } 1 ,x 2 ,L,x N Then the kernel value m can be directly determined by equation (2-20).
The value of a is determined by
The value of b is thus determined
With [ a, b ] as the interval when the confidence level is 100%, all data of the window should lie within [ a, b ], i.e., all data of the window is not less than a and not more than b. In view of this, the values of a and b are further deduced below to simplify the calculation amount.
If m=x n Expanding Q (a) to obtain
Separating constants of left-hand terms of multiplier numbers, i.e.
As can be seen from the above equation, the smaller m-a, i.e., the closer a is to m, the larger Q (a) is, and considering that all the raw data of the window should be not smaller than a, a should take the minimum value of the raw data of the window.
Similarly, it can be deduced that b should take the maximum value of the window raw data.
After determining the membership function of each information grain, the historical upper and lower bound granulation data of the prediction interval is further determined according to the confidence level and the membership function. For an information grain, an image of the upper and lower boundaries of the interval at a certain confidence level is determined from the membership function, see fig. 9.
In fig. 9, CL is a confidence level, l and h are two points at which membership is 1-CL, and the bolded portion on the horizontal axis represents the entire interval of the confidence level CL, which is based on the principle that [ a, b ] is an interval at which the confidence level is 100%, and correspondingly, [ l, h ] is an interval at which the confidence level is CL, which is calculated as in the formulas (2-26).
According to the method, historical boundary data of the interval can be obtained, and then the grid load interval prediction can be realized by utilizing a combined prediction method of the BP neural network and the SVR.
(2) Section prediction evaluation index
The prediction section coverage PICP and the average width PINAW are still used as evaluation indexes for section prediction.
(3) Example verification
The following performs an example verification on the payload section prediction model, and still uses an example of point prediction as an example to predict the payload at 7 to 17 days of 8 months 29. Taking 90% confidence level as an example, referring to fig. 10, a distributed photovoltaic output interval prediction is first performed using a PCA-GRNN-QR model.
It can be found that the true value of the distributed photovoltaic output lies almost entirely within the prediction interval. And predicting the load power by using a load section prediction model considering information granulation, taking every three hours as one information granule, and referring to fig. 11, so as to obtain a prediction result.
The load prediction interval is then differenced from the distributed photovoltaic prediction interval, i.e., the lower bound of the distributed photovoltaic prediction interval is subtracted from the upper bound of the load prediction interval, and referring to fig. 12, the upper bound of the distributed photovoltaic prediction interval is subtracted from the lower bound of the load prediction interval to obtain the prediction interval of the net load power.
Meanwhile, the interval prediction evaluation indexes of the distributed photovoltaic power, the load power and the net load power are calculated as follows:
table 2-4 section prediction model evaluation index
| Type(s) | PICP | PINAW |
| Distributed photovoltaic | 1.000 | 0.452 |
| Load of | 0.818 | 0.762 |
| Payload | 1.000 | 0.599 |
It can be seen that the true value of the distributed photovoltaic output, load or net load is basically located in the prediction interval, and the coverage condition of the prediction interval is better when the calculation result of the interval coverage rate is combined; but the prediction interval width of the distributed photovoltaic output, load and net load can be found to be wider, which is not ideal, and a certain error exists in the prediction result.
The reasons for error generation are analyzed, and the main reasons may be: 1) The measurement error effect of the distributed photovoltaic output measurement itself; 2) The distributed photovoltaic output prediction and the load prediction have certain errors; 3) The meteorological site has a distance deviation of 15 km from the field, etc.
However, under the influence of larger error factors, the model result can still achieve higher coverage rate, and meanwhile, the interval average width is not too bad, so that the meshing net load method containing the high-proportion distributed photovoltaic output, which is proposed herein, can be considered to have higher feasibility.
Claims (8)
1. A grid load prediction method for an active power distribution network is characterized by comprising the following steps of: the method comprises grid division of a power distribution network, load prediction of the power distribution network and net load prediction of the active power distribution network after distributed photovoltaic access.
2. The method for predicting grid load of active power distribution network according to claim 1, wherein: the meshing division of the power distribution network comprises the following steps: planning target determination, data acquisition, grid division, load prediction, network architecture determination and planning scheme evaluation;
the specific steps of grid division of the power distribution network are as follows:
firstly, determining a planning target, wherein the planning target comprises a planning range, a planning reference year, a horizontal year and a saturation year; basic data of the planning area including load types, load demand amounts and the like are fully collected, and geographic features of the area are fully mastered; grid division is carried out on the basis, and the grid division of the power distribution network is a core link of grid distribution planning and comprises three layers of division of a power supply area, a power supply grid and a power supply unit:
The power supply areas are divided based on the layout condition of the transformer substation, the construction current situation and future planning of an upper-layer main network are fully considered, and urban administrative areas are divided;
the power supply grid is an important level for bearing a power supply area and a power supply unit, and is fully based on urban and rural future development planning and power grid construction planning in the dividing process, and meanwhile, difficulty in line construction is considered; in addition, the power supply grid is required to ensure fineness, the range is not excessively large, and the standard wiring unit power supply area is generally corresponding to the power supply grid.
The power supply unit is the smallest hierarchy in gridding division, and in the dividing process, the actual demands and the load density of users are considered, and the loads of the same type are divided into the same unit as much as possible so as to supply power conveniently; meanwhile, the geographical boundaries of roads, rivers and the like are combined for division, so that local conditions are met, and a village and town is used as a power supply unit in rural power distribution network planning;
and after grid division, carrying out load prediction and determination of a network architecture planning scheme, carrying out power balance calculation according to a load prediction result, carrying out scheme evaluation from two aspects of feasibility and economy, and if the evaluation is unqualified, carrying out network architecture planning determination again.
3. The method for predicting grid load of active power distribution network according to claim 1, wherein: the power distribution network load prediction comprises grid load prediction based on BP neural network and grid load prediction based on support vector machine neural network.
4. A method for active power distribution network meshing load prediction according to claim 3, characterized by: the method for predicting the grid load based on the BP neural network comprises the following steps:
the whole process is divided into two stages, load influence factor data of each grid is firstly used as input layer data, and BP neural network is utilized to obtain output data through certain nonlinear operation, namely, a forward propagation process; then, reversely correcting the weight and biasing according to the error generated by the output value and the true value, so as to complete the training of the network, and then, calculating to obtain a load point prediction result;
(1) Network architecture and forward propagation process
The BP neural network structure consists of an input layer, a hidden layer and an output layer, wherein the hidden layer is provided with one or more layers, and each layer can be provided with a plurality of neurons; the single neuron consists of three parts of connection weight, summation unit and nonlinear activation function, and the expression is as follows
Wherein x is j To input data, w kj B is the connection weight between the jth input data and the kth neuron k For the bias of the kth neuron, y k For the output of the kth neuron,
for the activation function, the activation function is of various types, and tan sig function is selected as the activation function of the hidden layer, as shown in formula (2-2),
substituting the function into the formula (2-1) to obtain a transfer function of a single hidden layer neuron as shown in the formula (2-3);
selecting purelin function as the activation function of the output layer, i.e
In summary, the output of the single neuron is obtained by the weighted summation of the input data and the summation of the bias term, and then the activation function, and the input data sequentially passes through the hidden layer neuron and the output layer neuron to obtain the output data, namely the forward propagation process;
(2) Reverse correction procedure
The output value obtained by forward propagation often has a certain error with the actual value, the error is reversely transmitted to the input layer by the output layer through the hidden layer, and the weights and the biases of the hidden layer and the neurons of the output layer are adjusted in the process, so that the process of reducing the error is a reverse correction process;
sample (x) k ,y k ) The output value of (2) is
The loss function is as in equations (2-5),
wherein n is the number of samples, 
Can be calculated by the formula (2-1). Iterating by using a gradient descent method, correcting the weight and the bias, and continuously reducing the loss function value until the requirement is met;
the principle of iteration by using the gradient descent method is shown as formula (2-6),
where a is the learning rate and L (w, b) is the loss function. According to the formula (2-6), w and b of the output layer and the hidden layer are sequentially adjusted, so that the purpose of minimizing the global loss function is achieved;
after the reverse correction, the corrected weight and offset value are used to input the load influence factor data instead of the prediction, forward transmission is carried out, and the obtained output value is the final prediction result;
(3) Program number determination
In the process of constructing the BP neural network prediction model, the number of nodes of an input layer and the number of nodes of an output layer are determined, and the number of nodes of an uncertain hidden layer is a key factor influencing the magnitude of errors of a prediction result; if the number of hidden layer nodes is too large, the network training is too slow and is easy to fall into local optimum; if too small, the network learning ability is insufficient, and in general, the determination method of the number of hidden layer nodes is as follows
Wherein h is the number of hidden layer nodes, m is the number of input layer nodes, n is the number of output layer nodes, a is a constant between 0 and 10, and after the value range of the number of nodes is defined, the number of hidden layer nodes can be determined by adopting a cross verification method.
5. A method for active power distribution network meshing load prediction according to claim 3, characterized by: the grid load prediction method based on the support vector machine neural network comprises the following steps:
the support vector machine (Support Sector Machine, SVM) is a two-class model, the basic idea is to find a hyperplane, so that the distance between the data points of two types of samples and the hyperplane is the largest, the support vector regression (Support Vactor Regression, SVR) is a branch of the SVM, the SVR is widely applied in the aspects of data prediction and the like due to the good fitting effect, but is different from the SVM, and the SVR is to minimize the distance between the data points of the samples and the hyperplane;
let the sample training set be (x) i ,y i ) (i=1, 2, l), where l is the number of samples, x i For inputting data, the dimension is m, y i For outputtingData, the dimension of which is n; the essence of using SVR for grid load prediction is to use a nonlinear mapping
Fitting to obtain a regression function f (x) so that f (x i )≈y i The fitting function thereof can be expressed as formula (2-7);
wherein omega and b are regression coefficients respectively representing an m-dimensional weight vector and a bias term, and the regression coefficients can be obtained from the optimization problem in the solution formula (2-8) according to the SVR principle;
The above formula is the principle of regression coefficient of epsilon-SVR solution, wherein C is penalty factor, epsilon is insensitive coefficient, and xi and
all are relaxation variables; in practical application, epsilon parameters are required to be determined empirically, in order to avoid difficult epsilon determination, a v-SVR model is selected for load prediction, and v parameters are introduced as follows
Solving by using a Lagrangian multiplier method, and constructing a Lagrangian function (2-10);
wherein alpha is i ,
d i ,/>
h is Lagrangian multiplier, both are greater than 0, according to Lagrangian multiplier principle, when
When the function has a minimum value, the problem can be converted into the form of the formula (2-11) by considering the KKT condition and the dual condition;
at this time, the regression function is converted into
Wherein K (x i X) is a kernel function, which has various forms, and a Gaussian kernel (RBF (RadialBasis Function) kernel) is used herein, and has a form as shown in formulas (2-13);
wherein sigma is the width of the Gaussian kernel function, the action range of the kernel function is controlled, and optimization is needed;
before training by using a support vector machine, parameters C, v and sigma are required to be optimized, so that the SVR fitting effect is best, a particle swarm algorithm is used for carrying out parameter iterative optimization by taking a minimum MSE as a target, and then a regression model is trained by using the optimized parameters, so that a point prediction result is obtained.
6. The method for predicting grid load of active power distribution network according to claim 1, wherein: the active power distribution network net load prediction after distributed photovoltaic access comprises active power distribution network gridding net load point prediction and active power distribution network gridding net load interval prediction.
7. The method for predicting grid load of active power distribution network according to claim 6, wherein: the active power distribution network gridding net load point prediction method comprises the following steps:
the net load of a certain distribution grid is the difference between the grid load power and the distributed photovoltaic power generation power, and after the distributed photovoltaic output point prediction and the load point prediction are carried out, the net load point prediction value of the distribution grid can be obtained by taking the difference between the grid load power and the distributed photovoltaic output point prediction, wherein the prediction model adopts the PCA-GRNN model, the BP neural network and the support vector machine regression prediction model which are proposed in the foregoing;
at the moment, two prediction models of grid load prediction are combined as a result to obtain a more accurate load prediction value;
(1) Combined load prediction model
After load prediction is performed by using BP neural network and support vector machine regression, two different results can be obtained, prediction errors are different, the two prediction results are combined by using a reciprocal variance method, and the final prediction result is obtained by calculating the weights of the two prediction models and carrying out weighted summation. So as to achieve the purposes of further reducing errors and improving prediction accuracy;
If there are m prediction models, each model has n prediction sample results, and P is used for ij Representing the prediction result of the jth sample in the ith prediction model, T j Representing the true value of the j-th sample, the weights of the various predictive models may be calculated by equations (2-15),
wherein Q is i For the sum of variances of the ith predictive model result, i.e.
And then the prediction results are weighted and summed, as in equations (2-17),
wherein the method comprises the steps of
As can be seen from the weighting process, the reciprocal variance method is essentially to assign high weight to the small error model, so as to achieve the purpose of reducing overall error;
(2) Point predictive evaluation index
Selecting average absolute percentage error (Mean Absolute Percentage Error, MAPE) and root mean square error (Root Mean Square Error, RMSE) as point prediction evaluation indexes; MAPE can intuitively represent the relative error between the predicted value and the actual value, can be calculated by the formulas (2-18),
and RMSE can be calculated from the formulas (1-9) above.
8. The method for predicting grid load of active power distribution network according to claim 6, wherein: the method for predicting the gridding net load section of the active power distribution network comprises the following steps:
the idea of the net load section prediction is consistent with the point prediction, namely the difference value between the load prediction section and the distributed photovoltaic output prediction section under a certain confidence level, and the distributed photovoltaic output section prediction method based on PCA-GRNN-QR is provided, so that the load section prediction needs to be realized at present; firstly, a fuzzy information granulating method is introduced, a fuzzy set is constructed to obtain upper and lower boundaries of a section of a load history value under the confidence level, then the upper and lower boundaries are respectively predicted by utilizing a combination point prediction model provided by the prior art, so as to obtain a load prediction section, and then the load prediction section is differenced with a distributed photovoltaic output prediction section, and the fact that the load prediction upper boundary is differenced with a distributed photovoltaic output prediction lower boundary and the load prediction lower boundary is differenced with the distributed photovoltaic output prediction upper boundary is needed, so that a net load prediction section is obtained;
(1) Fuzzy information granulation
The fuzzy information granulation is to divide a whole body into a plurality of parts for research, wherein each part is an information particle, and the information granulation process can be divided into two stages of window division and blurring; the window division is to divide the original time sequence data into a plurality of subsequences according to a fixed time period, wherein each subsequence is an information granulating window; the key to blurring is to construct the fuzzy set. For a window X { X } 1 ,x 2 ,L,x N Establishing a fuzzy particle P, namely a fuzzy concept G which can reasonably describe X, wherein G is a fuzzy set taking X as a discourse domain, and if the fuzzy particle P is used for replacing the fuzzy concept G, the fuzzy particle P is provided with
P＝A(x) (2-19)
Wherein A is a membership function of G, A (x) can be expressed as a membership degree of x to G, the nature of blurring is to determine the membership function, triangular blurring particles are adopted herein, namely
Wherein X is X, a, m, b respectively represent the minimum value, the kernel value and the maximum value of the window time sequence; if the time sequence is arranged from small to large, the sequence is still X { X } 1 ,x 2 ,L,x N Core value m may be directly determined by equation (2-20);
the value of a is determined by
The value of b is thus determined
Taking [ a, b ] as an interval when the confidence level is 100%, all data of the window are positioned in [ a, b ], namely all data of the window are not less than a and not more than b; in view of this, the values of a and b are further deduced below to simplify the calculation amount.
If m=x n Expanding Q (a) to obtain
Separating constants of left-hand terms of multiplier numbers, i.e.
As can be seen from the above equation, the smaller m-a is, i.e. the closer a is to m, the larger Q (a) is, and considering that all the original data of the window should be not less than a, a should take the minimum value of the original data of the window;
similarly, the maximum value of the window original data to be taken by b can be obtained through deduction;
after determining the membership function of each information grain, further determining historical upper and lower bound granulation data of the prediction interval according to the confidence level and the membership function; for an information grain, the function formula of determining the upper and lower boundaries of the interval under a certain confidence level by the membership function is as follows:
wherein CL is a confidence level, l and h are two points when membership is 1-CL, and the bold part on the horizontal axis represents the whole interval of the confidence level CL, and the principle is that [ a, b ] is the interval when the confidence level is 100%, and correspondingly, [ l, h ] is the interval when the confidence level is CL;
according to the method, historical boundary data of the interval can be obtained, and then the grid load interval prediction can be realized by utilizing a combined prediction method of the BP neural network and the SVR;
(2) Section prediction evaluation index
The prediction section coverage PICP and the average width PINAW are still used as evaluation indexes for section prediction. The calculation is shown in the formulas (1-26) and (1-27);
(3) Example verification
Performing example verification on a net load section prediction model, predicting the net load in a specified time period by taking an example of point prediction as an example, and firstly performing distributed photovoltaic output section prediction by using a PCA-GRNN-QR model by taking a 90% confidence level as an example;
then, the load prediction interval and the distributed photovoltaic prediction interval are subjected to difference, namely, the lower limit of the distributed photovoltaic prediction interval is subtracted from the upper limit of the load prediction interval, and the upper limit of the distributed photovoltaic prediction interval is subtracted from the lower limit of the load prediction interval to obtain a prediction interval of net load power;
and meanwhile, calculating to obtain the interval prediction evaluation index of the distributed photovoltaic power, the load power and the net load power.
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| CN117674098A (en) * | 2023-11-29 | 2024-03-08 | 国网浙江省电力有限公司丽水供电公司 | Multi-element load space-time probability distribution prediction method and system for different permeability |
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