A direct interval prediction method for regional photovoltaic power based on graph convolutional neural network

Abstract

The present invention discloses a method for direct interval prediction of regional photovoltaic power based on a graph convolutional neural network. The method first introduces the conditional value at risk and the augmented Lagrange multiplier method to transform the chance-constrained interval prediction optimization problem into an optimization problem with linear inequality constraints; secondly, the covariance matrix of the forecast irradiance at different geographical locations in the region is used as the adjacency matrix to construct a graph convolutional neural network with meteorological forecast features of multiple geographical locations as input; finally, with the help of the ReLU activation function, the output of the deep learning model based on the graph convolutional neural network is guaranteed to meet the linear inequality constraints, and the optimization objective of the optimization problem is used as the loss function, and the deep learning model is trained by stochastic gradient descent. This method takes into account the rich meteorological information in the region, constructs a deep learning model to directly output accurate and reliable photovoltaic power prediction intervals, and realizes efficient quantification of regional photovoltaic power prediction uncertainty.

Description

Technical Field

[0001] The present invention relates to a method for direct interval prediction of regional photovoltaic power based on graph convolutional neural network, belonging to the field of new energy power prediction of power systems. Background Art

[0002] With the rapid development of the new energy industry, photovoltaic power generation, as a key clean energy source, has seen its penetration rate in the power system increase year by year. Affected by complex external weather conditions, distributed photovoltaic power generation exhibits significant volatility and intermittency. This high uncertainty poses significant challenges to the economic and secure operation of power systems with a high proportion of distributed photovoltaic power installed, further hindering the efficient absorption of photovoltaic power.

[0003] Photovoltaic power forecasting can provide future photovoltaic output information to support the economic and safe operation of the power system. However, most photovoltaic power forecasting research focuses on centralized photovoltaic power stations and cannot meet the complex operation requirements of regional power systems with a high proportion of distributed photovoltaic penetration. There is an urgent need for a regional photovoltaic power forecasting method that fully considers the meteorological resources and photovoltaic power generation characteristics within the region to provide reliable data support for regional power system operation decision-making and analysis, as well as power and electricity balance.

[0004] Due to the chaotic nature of the meteorological environment, deterministic regional photovoltaic power forecasting methods are difficult to avoid prediction errors. To quantify the uncertainty of photovoltaic power forecasting, probabilistic photovoltaic power forecasting has emerged. Probabilistic forecasting methods provide rich probabilistic information about future photovoltaic power generation in the form of intervals, quantiles, and probability density functions. Interval forecasting methods can provide upper and lower bounds of the photovoltaic power forecast interval for a given confidence level. Interval forecasting methods can be divided into indirect and direct methods. The former indirectly obtains the prediction interval based on the predicted probability distribution or quantiles, while the latter directly outputs the prediction interval by establishing a prediction model. Previous direct interval forecasting methods have mostly used machine learning models such as extreme learning machines to formulate chance-constrained optimization problems and solve the interval forecast model parameters. However, the limited nonlinear fitting capabilities of machine learning models restrict the application of such methods in scenarios requiring complex data processing, such as day-ahead regional photovoltaic power forecasting that requires considering massive amounts of meteorological information. Summary of the Invention

[0005] To address the limitations of existing photovoltaic power forecasting methods, the present invention provides a direct interval forecasting method for regional photovoltaic power based on a graph convolutional neural network. This method, based on a graph convolutional neural network, fully considers regional meteorological resources and the correlation of meteorological information at different locations within the region. It also introduces the conditional value at risk and augmented Lagrange multiplier method to transform the chance-constrained interval forecasting optimization problem into an optimization problem with linear inequality constraints. Finally, a deep learning model is trained using stochastic gradient descent. This method considers the rich meteorological information within a region, constructs a deep learning model to directly output accurate and reliable photovoltaic power forecast intervals, broadens the application scenarios of direct interval forecasting methods, and enables efficient quantification of uncertainty in regional photovoltaic power forecasts.

[0006] To achieve the above object, the present invention proposes the following technical solutions:

[0007] A method for direct interval prediction of regional photovoltaic power based on a graph convolutional neural network is provided. The method relies on a deep learning model based on a graph convolutional neural network. The method for constructing a deep learning model based on a graph convolutional neural network includes the following steps:

[0008] Step 1: Model the PV power interval prediction as a chance-constrained optimization problem. Introduce the conditional value at risk to tighten the feasible region of the chance-constrained optimization problem. Then, transfer the chance constraint to the optimization objective of the chance-constrained optimization problem through the augmented Lagrange multiplier method, and reconstruct the chance-constrained optimization problem into an optimization problem with linear inequality constraints.

[0009] Step 2: Calculate the weather forecast irradiance covariance matrix for multiple different geographical locations within the region and use it as the graph convolutional neural network adjacency matrix. Based on this, construct a graph convolutional neural network with weather forecast features for multiple geographical locations as input; the weather forecast information includes temperature, humidity, total irradiance, direct irradiance, etc.

[0010] Step 3: Design a deep learning model structure based on the graph convolutional neural network so that the model output satisfies the linear inequality constraints. Convert the optimization problem with the linear inequality constraints into an optimization problem with model parameters as optimization variables, and use the augmented Lagrangian function as the loss function of the deep learning model based on the graph convolutional neural network.

[0011] Step 4: Based on a data set containing meteorological forecast features of multiple geographical locations and regional photovoltaic power measured data, a parameter optimization algorithm based on stochastic gradient descent is used to solve the optimization problem with model parameters as optimization variables, thereby optimizing the parameters of the deep learning model based on the graph convolutional neural network to obtain a trained deep learning model based on the graph convolutional neural network.

[0012] The present invention introduces conditional value at risk and Lagrange multipliers into the direct regional photovoltaic power prediction method, transforming the chance-constrained optimization problem into a linear inequality-constrained optimization problem, and improving the traditional optimizer-based solution to deep learning model training, which greatly expands the application scenarios of the direct interval prediction method and efficiently quantifies the uncertainty of regional photovoltaic power prediction in the form of intervals.

[0013] The present invention is also applicable to other regional new energy power prediction scenarios.

[0014] Furthermore, in step 1, the photovoltaic power interval prediction model is modeled as a chance constrained optimization problem, which is specifically expressed as:

[0015]

[0016] in, is the expected function, u and l are the upper and lower limits of the photovoltaic power prediction interval, and y is the measured value of the regional photovoltaic power. represents the probability of an event occurring. In the constructed optimization problem, the optimization objective is to minimize the width of the prediction interval. The first constraint is the prediction interval reliability constraint, which ensures that the probability that the predicted interval covers the measured photovoltaic power is not less than the set confidence level α = 100(1-β)%, where β is the significance level. This constraint is also called the chance constraint. The second constraint requires that the lower limit of the prediction interval be less than or equal to the upper limit of the prediction interval.

[0017] Furthermore, in step 1, the method of introducing conditional value at risk to tighten the feasible region of the chance-constrained optimization problem is as follows:

[0018] The random variable z is recorded as the maximum value of the lower limit of the prediction interval minus the measured value ly and the measured value minus the upper limit of the prediction interval yu:

[0019] z=max(ly,yu)

[0020] At this time there are:

[0021]

[0022] Now we introduce the Value at Risk (VaR) and Conditional Value at Risk (CVaR) under the confidence level α = 100(1-β)%:

[0023]

[0024] Where f(z) is the probability density function of z; VaR α (z) means the quantile of the random variable z under the confidence level α, and CVaRα (z) is the value of the random variable z that exceeds VaR α The expected value of part (z) and CVaR α (z) is a convex function of z, which is obtained by the following formula:

[0025]

[0026] in, τ is the optimization variable when obtaining CVaR;

[0027] CVaR α When (z) takes the optimal value, the corresponding τ is denoted as τ*, and the value set of τ* is By CVaR α The definition of (z) shows that VaR α (z)≤0 is An optimal solution for Now assume that τ t *≤0; and:

[0028]

[0029] In the above formula, the first term on the right side is always non-negative, so:

[0030]

[0031] At this time, the chance-constrained optimization problem is transformed into:

[0032]

[0033] Furthermore, in step 1, the chance constraint is transferred to the optimization objective of the chance-constrained optimization problem by using the augmented Lagrange multiplier method, and the chance-constrained optimization problem is reconstructed into an optimization problem containing linear inequality constraints in the following manner:

[0034] First, the auxiliary variable s is introduced to reconstruct the transformed chance-constrained optimization problem as follows:

[0035]

[0036] The reconstructed optimization problem is transformed into an optimization problem with inequality constraints by using the augmented Lagrange multiplier method:

[0037]

[0038] in, λ is the Lagrange multiplier and σ is the penalty factor.

[0039] Furthermore, the calculation method of the weather forecast irradiance covariance matrix for multiple different geographical locations within the region described in step 2 is as follows:

[0040]

[0041] Among them, Σ ij is the element in the i-th row and j-th column of the covariance matrix Σ, X i and X j are the meteorological forecast irradiance variables for the i-th and j-th geographical locations, respectively.

[0042] Furthermore, in step 3, the structure of the deep learning model based on graph convolutional neural network is as follows:

[0043] Assume that the graph convolutional neural network is a nonlinear function g GCN (x,ω g ), where x is the weather forecast information for different geographical locations, ω g is the graph convolutional neural network parameter; let the output of the graph convolutional neural network be vector a=g GCN (x,ω g ) and a=[a u ,a l ,a s ,a τ ], where a u ,a l ,a s ,a τ are intermediate variables, corresponding to u, l, s, τ respectively; with the help of ReLU activation function, the upper and lower limits of the prediction interval u, l and auxiliary variables s, τ of the model output are expressed by the following formulas:

[0044] l=a l

[0045] u=a l +ReLU(a u )

[0046] s=ReLU(a s )

[0047] τ=-ReLU(a τ )

[0048] At this time, the model output u, l, s, τ satisfies the following linear inequality constraints:

[0049] s≥0

[0050] l≤u

[0051] τ≤0

[0052] The optimization problem with linear inequality constraints is transformed into an optimization problem with model parameters as optimization variables, specifically:

[0053] Because u, l, s, τ are output by the deep learning model based on the graph convolutional neural network, u, l, s, τ can be expressed as:

[0054]

[0055] l=g(x,ω α )

[0056] s=g(x,ω s )

[0057] τ=g(x,ω τ )

[0058] Where g(·) represents the deep learning model based on graph convolutional neural network, ω α ,ω s ,ω τ are the parameters in the deep learning model based on graph convolutional neural network corresponding to u, l, s, and τ respectively;

[0059] Then the optimization problem with model parameters as optimization variables is specifically:

[0060]

[0061] in,

[0062] Furthermore, in step 3, the loss function of the deep learning model based on graph convolutional neural network is specifically:

[0063]

[0064] in, L DL is the loss function of the deep learning model based on graph convolutional neural network, T is the total number of historical samples, x t is the weather forecast information of different geographical locations of the t-th sample, y t is the measured data of regional photovoltaic power for the tth sample, z t It is the maximum value of the lower limit of the prediction interval minus the observed value and the observed value minus the upper limit of the prediction interval in the tth sample.

[0065] Furthermore, in step 4, the solution of the optimization problem with the model parameters as optimization variables involves two levels of optimization problems: the first level is to solve CVaR(z), and the second level is to optimize L DL ;

[0066] Define and solve CVaR α The loss function of the optimization problem of (z) is

[0067]

[0068] Based on the dataset of meteorological forecast features and regional photovoltaic power measurement data of multiple geographical locations, a parameter optimization algorithm based on stochastic gradient descent is used to solve the optimization problem with model parameters as optimization variables, thereby optimizing the parameters of the deep learning model based on the graph convolutional neural network (all parameters of the deep learning model based on the graph convolutional neural network are denoted as ω) to obtain a trained deep learning model based on the graph convolutional neural network. The specific steps are as follows:

[0069] Step (1): Given a training dataset Initial parameters of deep learning models based on graph convolutional neural networks λ 0 ,σ 0 , model learning rate η, penalty factor growth coefficient ρ, maximum training round N epoch , total number of dataset batches N batch ;

[0070] Step (2): Set the initial training round k = 1;

[0071] Step (3): Set the initial batch j=1;

[0072] Step (4): Calculate L CVaR The parameter ω corresponding to the auxiliary variable τ τ Gradient And update the parameters:

[0073]

[0074] Step (5): Calculate L DL Gradient of the parameter ω of the deep learning model based on graph convolutional neural network And update ω:

[0075]

[0076] Step (6): Perform steps (4)-(5) on all sample batches, and then proceed to step (7);

[0077] Step (7): Update model parameters, Laplace operator, and penalty factor:

[0078]

[0079] σ k+1 ←ρσk

[0080] Step (8): Repeat steps (3)-(7) until the maximum number of rounds N is reached. epoch , end training and return model parameters You can get a trained deep learning model based on graph convolutional neural network.

[0081] Furthermore, the deep learning model based on graph convolutional neural network is used to obtain new weather forecast information x at different geographical locations. T+t ,t≥0 is used as the input of the trained deep learning model based on graph convolutional neural network to obtain the regional photovoltaic power interval prediction result u T+t 、l T+t .

[0082] The main advantages and effects of the present invention are as follows:

[0083] First, the present invention adopts a graph convolutional neural network to simultaneously process the weather forecast information of different geographical locations in the region, and uses the covariance matrix of the weather forecast irradiance at different geographical locations as the graph convolutional neural network adjacency matrix, introducing prior knowledge to improve the interpretability of the model; secondly, the present invention models the photovoltaic power interval prediction as a chance-constrained optimization problem, introduces the concept of conditional risk value, and uses the augmented Lagrange multiplier method to transform the original problem into a linearly constrained optimization problem; finally, by designing a deep learning model structure based on a graph convolutional neural network, the model output satisfies the linear inequality constraints, and then proposes a deep learning stochastic gradient descent algorithm, based on which efficient training of the deep learning direct interval prediction model can be achieved; the present invention expands the application scenarios of the direct interval prediction method, and by quantifying the uncertainty of regional photovoltaic power prediction, provides rich and reliable probabilistic information support for the economic and safe operation of regional power systems under high-proportion distributed photovoltaic penetration. BRIEF DESCRIPTION OF THE DRAWINGS

[0084] To more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. Those skilled in the art can also derive other drawings based on these drawings without inventive effort.

[0085] Figure 1 This is a flow chart of a method for constructing a deep learning model based on a graph convolutional neural network in the present invention;

[0086] Figure 2 A diagram showing the structure of a deep learning model based on a graph convolutional neural network for direct interval prediction designed for this invention;

[0087] Figure 3 A geographical distribution map of meteorological information according to a specific embodiment of the present invention;

[0088] Figure 4 A covariance matrix heat map of weather forecast irradiance according to a specific embodiment of the present invention;

[0089] Figure 5 A regional photovoltaic power interval prediction curve diagram in a specific embodiment provided by the present invention; DETAILED DESCRIPTION

[0090] To make the purpose, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts shall fall within the scope of protection of the present invention.

[0091] This embodiment provides a method for directly predicting regional photovoltaic power based on a graph convolutional neural network. The method relies on a deep learning model based on a graph convolutional neural network. The method for constructing a deep learning model based on a graph convolutional neural network is as follows: Figure 1 As shown, the following steps are included:

[0092] Step 1: First, the PV power interval prediction is modeled as a chance-constrained optimization problem, specifically:

[0093]

[0094] in, is the expected function, u and l are the upper and lower limits of the photovoltaic power prediction interval, and y is the measured value of the regional photovoltaic power. represents the probability of an event occurring. In the constructed optimization problem, the optimization objective is to minimize the width of the prediction interval. The first constraint is the prediction interval reliability constraint, which ensures that the probability that the predicted interval covers the measured photovoltaic power is not less than the set confidence level α = 100(1-β)%, where β is the significance level. This constraint is also called the chance constraint. The second constraint requires that the lower limit of the prediction interval be less than or equal to the upper limit of the prediction interval.

[0095] Next, the conditional value at risk is introduced to tighten the feasible domain of the chance-constrained optimization problem:

[0096] The random variable z is recorded as the maximum value of the lower limit of the prediction interval minus the measured value ly and the measured value minus the upper limit of the prediction interval yu:

[0097] z=max(ly,yu)

[0098] At this time there are:

[0099]

[0100] Now we introduce the value at risk VaR and conditional value at risk CVaR under the confidence level α = 100(1-β)%:

[0101]

[0102] Where f(z) is the probability density function of z; VaR α (z) means the quantile of the random variable z under the confidence level α, and CVaR α (z) is the value of the random variable z that exceeds VaR α The expected value of part (z) and CVaR α (z) is a convex function of z, which is obtained by the following formula:

[0103]

[0104] in, τ is the optimization variable when obtaining CVaR;

[0105] CVaR α When (z) takes the optimal value, the corresponding τ is denoted as τ*, and the value set of τ* is By CVaR α The definition of (z) shows that VaR α (z)≤0 is An optimal solution for Now assume that τ t *≤0; and:

[0106]

[0107] In the above formula, the first term on the right side is always non-negative, so:

[0108]

[0109] At this time, the chance-constrained optimization problem is transformed into:

[0110]

[0111] Finally, the chance constraint is transferred to the optimization objective of the chance-constrained optimization problem by using the augmented Lagrange multiplier method, and the chance-constrained optimization problem is reconstructed into an optimization problem with linear inequality constraints:

[0112] First, the auxiliary variable s is introduced to reconstruct the transformed chance-constrained optimization problem as follows:

[0113]

[0114] The reconstructed optimization problem is transformed into an optimization problem with inequality constraints by using the augmented Lagrange multiplier method:

[0115]

[0116] in, λ is the Lagrange multiplier and σ is the penalty factor.

[0117] Step 2: Calculate the weather forecast irradiance covariance matrix for multiple different geographical locations within the region as the graph convolutional neural network adjacency matrix; the calculation method of the weather forecast irradiance covariance matrix for multiple different geographical locations within the region is as follows:

[0118]

[0119] Among them, Σ ij is the element in the i-th row and j-th column of the covariance matrix Σ, is the expected function, X i and X j are the weather forecast irradiance variables for the i-th and j-th geographical locations respectively; on this basis, a graph convolutional neural network is constructed with the weather forecast features of multiple geographical locations as input, where the weather forecast information includes temperature, humidity, total irradiance, direct irradiance, etc.

[0120] Step 3: Design a deep learning model structure based on the graph convolutional neural network so that the model output satisfies the linear inequality constraint. The designed deep learning model structure based on the graph convolutional neural network is as follows: Figure 2 As shown:

[0121] Assume that the graph convolutional neural network is a nonlinear function g GCN (x,ω g ) indicates that the graph convolutional neural network takes the weather forecast features x of multiple geographical locations as input, ω g is the graph convolutional neural network parameter, the output vector a of the graph convolutional neural network is g GCN (x,ω g ) and the vector a contains 4 elements, that is, a=[a u ,a l ,a s ,a τ ], where a u ,a l ,a s ,a τ are intermediate variables, corresponding to u, l, s, τ respectively; and then the elements in vector a are processed as follows with the help of ReLU activation function:

[0122] u=a l +m u

[0123] m u =ReLU(a u )

[0124] l=a l

[0125] s=m s

[0126] m s =ReLU(a s )

[0127] τ=-ReLU(a τ )

[0128] Among them, m u ,m s is the intermediate output, because So m u ,m s It is always a positive number. At this time, the model output u, l, s, τ satisfies the following linear inequality constraints:

[0129] s≥0

[0130] l≤u

[0131] τ≤0

[0132] Then, the optimization problem with linear inequality constraints is transformed into an optimization problem with model parameters as optimization variables:

[0133] Because u, l, s, τ are output by the deep learning model based on graph convolutional neural network, u, l, s, τ are expressed as:

[0134]

[0135] l=g(x,ωα)

[0136] s=g(x,ω s )

[0137] τ=g(x,ω τ )

[0138] Where g(·) represents the deep learning model based on graph convolutional neural network, ω α ,ω s ,ω τ are the parameters in the deep learning model based on graph convolutional neural network corresponding to u, l, s, and τ respectively;

[0139] Then the optimization problem with model parameters as optimization variables is specifically:

[0140]

[0141] in,

[0142] Finally, the augmented Lagrangian function is used as the loss function of the deep learning model based on graph convolutional neural network:

[0143]

[0144] in, L DL is the loss function value of the deep learning model based on graph convolutional neural network, T is the total number of historical samples, x t is the weather forecast information of different geographical locations of the t-th sample, y t is the measured data of regional photovoltaic power for the tth sample, z t It is the maximum value of the lower limit of the prediction interval minus the observed value and the observed value minus the upper limit of the prediction interval in the tth sample.

[0145] Step 4: Based on a dataset containing weather forecast features and regional photovoltaic power measurement data from multiple geographical locations (as a training dataset), a parameter optimization algorithm based on stochastic gradient descent is used to solve the optimization problem with model parameters as optimization variables, thereby optimizing the parameters of the deep learning model based on the graph convolutional neural network to obtain a trained deep learning model based on the graph convolutional neural network:

[0146] The solution of the optimization problem with model parameters as optimization variables involves two levels of optimization problems: the first level is to solve CVaR(z), and the second level is to optimize L DL ;

[0147] Define and solve CVaR α The loss function of the optimization problem of (z) is

[0148]

[0149] Based on the dataset of meteorological forecast features and regional photovoltaic power measurement data of multiple geographical locations, a parameter optimization algorithm based on stochastic gradient descent is used to solve the optimization problem with model parameters as optimization variables, thereby optimizing the parameters of the deep learning model based on the graph convolutional neural network (all parameters of the deep learning model based on the graph convolutional neural network are denoted as ω) to obtain a trained deep learning model based on the graph convolutional neural network. The specific steps are as follows:

[0150] Step (1): Given a training dataset Initial parameters of deep learning models based on graph convolutional neural networks λ 0 ,σ 0 , model learning rate η, penalty factor growth coefficient ρ, maximum training round N epoch , total number of dataset batches N batch ;

[0151] Step (2): Set the initial training round k = 1;

[0152] Step (3): Set the initial batch j=1;

[0153] Step (4): Calculate L CVaR The parameter ω corresponding to the auxiliary variable τ τ Gradient And update the parameters:

[0154]

[0155] Step (5): Calculate L DL Gradient of the parameter ω of the deep learning model based on graph convolutional neural network And update ω:

[0156]

[0157] Step (6): Perform steps (4)-(5) on all sample batches, and then proceed to step (7);

[0158] Step (7): Update model parameters, Laplace operator, and penalty factor:

[0159]

[0160] σ k+1 ←ρσ k

[0161] Step (8): Repeat steps (3)-(7) until the maximum number of rounds N is reached. epoch , end training and return model parameters You can get a trained deep learning model based on graph convolutional neural network.

[0162] The above-trained deep learning model based on graph convolutional neural network is used for prediction. The specific method is: using the new weather forecast information x at different geographical locations T+t , t≥0 as input, the regional photovoltaic power interval prediction result u can be obtained T+t 、l T+t .

[0163] The spring photovoltaic power generation power of a certain region of China is selected for day-ahead interval forecast. The time series has a time resolution of 15 minutes. The data contains weather forecast information and regional total photovoltaic power generation for different geographical locations in the region. The relative distribution of geographical locations corresponding to weather information is as follows: Figure 3 As shown, the latitude and longitude values ​​in the figure have been processed. Figure 4 is the covariance matrix of the meteorological forecast irradiance calculated for different geographical locations.

[0164] Table 1 shows the prediction interval performance indicators obtained by the method of the present invention and the comparative method, wherein the comparative method uses the Winkler score as the interval prediction loss function, and the Winkler score is calculated as follows:

[0165]

[0166] in, is an indicator function that takes the value 1 if the event in the brackets is true, and 0 otherwise.

[0167] Table 1 Performance comparison of interval prediction methods

[0168]

[0169] The average coverage error (ACE) is the empirical coverage error (ECP) minus the nominal coverage error (NCP). It reflects the reliability of the prediction interval and measures the statistical consistency between the prediction result and the observation result. Higher reliability means that the empirical coverage probability is closer to the nominal coverage. The average interval width (AW) measures the sharpness of the prediction interval. Under the premise of ensuring reliability, the narrower the prediction interval, the smaller the prediction uncertainty. The empirical coverage, average coverage error, and average interval width are calculated as follows:

[0170]

[0171] ACE=ECP-100(1-β)%

[0172]

[0173] It can be seen from Table 1 that under different prediction interval nominal coverage, compared with the comparison method, the prediction interval provided by the method of the present invention has higher reliability and narrower interval width, which shows the superiority of the method.

[0174] Figure 5The following is a graph showing the prediction curve of the photovoltaic power range in the spring region when the nominal confidence level is 90%. Since the photovoltaic power generation output is 0 at night, the graph only shows the predicted range and measured value of the photovoltaic power during the day. Figure 5 It can be seen that the prediction interval provided by the method of the present invention can effectively adapt to the fluctuation of photovoltaic power. It should be noted that in addition to photovoltaic power, this method is also applicable to the interval prediction of other energy sources and load time series, and has a wide range of applicability.

[0175] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements will not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A method for direct interval prediction of regional photovoltaic power based on graph convolutional neural network, characterized in that: The method relies on a deep learning model based on a graph convolutional neural network. The method for constructing a deep learning model based on a graph convolutional neural network includes the following steps: Step 1: Model the PV power interval prediction as a chance-constrained optimization problem. Introduce the conditional value at risk to tighten the feasible region of the chance-constrained optimization problem. Then, transfer the chance constraint to the optimization objective of the chance-constrained optimization problem through the augmented Lagrange multiplier method, and reconstruct the chance-constrained optimization problem into an optimization problem with linear inequality constraints. Step 2: Calculate the weather forecast irradiance covariance matrix for multiple different geographical locations within the region and use it as the graph convolutional neural network adjacency matrix. Based on this, construct a graph convolutional neural network with the weather forecast features of multiple geographical locations as input; Step 3: Design a deep learning model structure based on the graph convolutional neural network so that the model output satisfies the linear inequality constraints. Convert the optimization problem with the linear inequality constraints into an optimization problem with model parameters as optimization variables, and use the augmented Lagrangian function as the loss function of the deep learning model based on the graph convolutional neural network. Step 4: Based on a dataset containing meteorological forecast features and regional photovoltaic power measurement data for multiple geographical locations, a parameter optimization algorithm based on stochastic gradient descent is used to solve the optimization problem with the model parameters as optimization variables, thereby optimizing the parameters of the deep learning model based on the graph convolutional neural network to obtain a trained deep learning model based on the graph convolutional neural network; In step 1, the photovoltaic power interval prediction model is modeled as a chance constrained optimization problem, which is specifically expressed as follows: ， in, is the expected function, 、 are the upper and lower limits of the photovoltaic power prediction interval, is the measured value of regional photovoltaic power, represents the probability of an event occurring, is the significance level; The method of introducing conditional value at risk to tighten the feasible region of the chance-constrained optimization problem is as follows: Random variables The lower limit of the prediction interval minus the observed value and the observed value minus the upper limit of the prediction interval The maximum of the two: ， At this time there are: ， ， Now introduce confidence The value at risk VaR and conditional value at risk CVaR are: ， ， in, for The probability density function of The meaning of random variable In confidence The quantile below is a random variable Value exceeds The expected value of the part, and for The convex function of is obtained by the following formula: ， in, , To optimize the variables when obtaining CVaR; Will The corresponding optimal value Record ,remember The value set of ,Depend on The definition of for An optimal solution of , now assume ; and: ， In the above formula, the first term on the right side is always non-negative, so: ， At this point, the chance-constrained optimization problem is transformed into: 。 2. The method for direct interval prediction of regional photovoltaic power based on graph convolutional neural network according to claim 1 is characterized in that: In step 1, the chance constraint is transferred to the optimization objective of the chance-constrained optimization problem by using the augmented Lagrange multiplier method, and the chance-constrained optimization problem is reconstructed into an optimization problem containing linear inequality constraints in the following manner: First, introduce auxiliary variables The transformed chance-constrained optimization problem is reconstructed as: ， The reconstructed optimization problem is transformed into an optimization problem with inequality constraints by using the augmented Lagrange multiplier method: ， in, , is the Lagrange multiplier, is the penalty factor.

3. The method for direct interval prediction of regional photovoltaic power based on graph convolutional neural network according to claim 1 is characterized in that: The calculation method of the weather forecast irradiance covariance matrix for multiple different geographical locations within the region described in step 2 is as follows: ， in, is the covariance matrix No. Rank Elements of the column, and Respectively and The meteorological forecast irradiance variable for each geographical location.

4. The method for direct interval prediction of regional photovoltaic power based on graph convolutional neural network according to claim 2 is characterized in that: In step 3, the structure of the deep learning model based on graph convolutional neural network is as follows: Assume that the graph convolutional neural network is a nonlinear function Indicates that Weather forecast information for different geographical locations, is the graph convolutional neural network parameter; let the output of the graph convolutional neural network be vector and ,in are intermediate variables, corresponding to ; With the help of ReLU activation function, the upper and lower limits of the prediction interval output by the model are set 、 and auxiliary variables 、 It is expressed by the following formula: ， ， ， ， At this time, the model output The following linear inequality constraints are satisfied: ， The optimization problem with linear inequality constraints is transformed into an optimization problem with model parameters as optimization variables, specifically: Output from the deep learning model based on graph convolutional neural network, 、 、 、 Respectively expressed as: ， in, Represents the deep learning model based on graph convolutional neural network, They are The corresponding parameters in the deep learning model based on graph convolutional neural network; Then the optimization problem with model parameters as optimization variables is specifically: ， in, , .

5. The method for direct interval prediction of regional photovoltaic power based on graph convolutional neural network according to claim 4 is characterized in that: In step 3, the loss function of the deep learning model based on graph convolutional neural network is specifically: ， in, , , L DL is the loss function value of the deep learning model based on graph convolutional neural network, is the total number of historical samples, For the Weather forecast information of different geographical locations of samples, For the The measured data of regional photovoltaic power of samples, For the The maximum of the two values ​​in the sample, the lower bound of the prediction interval minus the observed value and the upper bound of the prediction interval minus the observed value.

6. The method for direct interval prediction of regional photovoltaic power based on graph convolutional neural network according to claim 5 is characterized in that: In step 4, the solution of the optimization problem with model parameters as optimization variables has two levels of optimization problems: the first level is to solve , the second layer is optimized ; Define the solution The loss function of the optimization problem is ， Based on the dataset containing meteorological forecast features of multiple geographical locations and regional photovoltaic power measurement data, a parameter optimization algorithm based on stochastic gradient descent is used to solve the optimization problem with model parameters as optimization variables, thereby optimizing the parameters of the deep learning model based on the graph convolutional neural network to obtain a trained deep learning model based on the graph convolutional neural network. The specific steps are as follows: Step (1): Given a training dataset , initial parameters of deep learning model based on graph convolutional neural network , , , model learning rate , Penalty factor growth coefficient , maximum number of training rounds , total number of dataset batches ; Step (2): Set the initial training round ; Step (3): Set up this initial batch ; Step (4): Calculation For auxiliary variables Corresponding parameters Gradient And update the parameters: ； Step (5): Calculation Parameters of deep learning models based on graph convolutional neural networks Gradient and update : ； Step (6): Perform steps (4)-(5) on all sample batches, and then proceed to step (7); Step (7): Update model parameters, Laplace operator, and penalty factor: ， ， ， Step (8): Repeat steps (3)-(7) until the maximum number of rounds is reached. , end training and return model parameters , you can get a trained deep learning model based on graph convolutional neural network.

7. The method for direct interval prediction of regional photovoltaic power based on graph convolutional neural network according to claim 1 is characterized in that: The deep learning model based on graph convolutional neural network is used to directly predict the regional photovoltaic power interval. The specific method is to use the new weather forecast information of different geographical locations As input, the regional photovoltaic power range prediction results can be obtained 、 .

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