Regional photovoltaic power direct interval prediction method based on graph convolutional neural network

Abstract

The invention discloses a regional photovoltaic power direct interval prediction method based on a graph convolutional neural network. The method comprises the following steps: firstly, introducing a conditional value-at-risk method and an augmented Lagrangian multiplier method, and converting an interval prediction optimization problem of opportunity constraints into an optimization problem containing linear inequality constraints; secondly, taking a covariance matrix of forecast irradiance of different geographic positions in the region as an adjacent matrix, and constructing a graph convolutional neural network taking weather forecast characteristics of multiple geographic positions as input; finally, by means of a ReLU activation function, it is ensured that output of the deep learning model based on the graph convolutional neural network meets linear inequality constraints, and training of the deep learning model is achieved through stochastic gradient descent by taking an optimization target of an optimization problem as a loss function. According to the method, rich meteorological information in a region is considered, a deep learning model is constructed to directly output an accurate and reliable photovoltaic power prediction interval, and efficient quantification of regional photovoltaic power prediction uncertainty is realized.

Description

Technical Field

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

[0002] With the rapid development of the new energy industry, photovoltaic power generation, as an important clean energy, has seen its penetration rate in the power system increase year by year. Affected by complex external weather conditions, distributed photovoltaic power generation has shown strong volatility and intermittency. Its strong uncertainty has posed a huge challenge to the economic and safe operation of the power system under high-proportion distributed photovoltaic access, and has further restricted the efficient absorption of photovoltaics.

[0003] Photovoltaic power forecasting can provide future photovoltaic output information and 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 under 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 in the region, so as to provide reliable data support for regional power system operation decision-making and analysis, and power and electricity balance.

[0004] Due to the chaotic characteristics of the meteorological environment, it is difficult to avoid prediction errors in the deterministic prediction method of regional photovoltaic power. In order to quantify the uncertainty of photovoltaic power prediction, the probabilistic prediction of photovoltaic power came into being. The probabilistic prediction method provides rich probabilistic information of future photovoltaic power generation in the form of intervals, quantiles, probability density functions, etc. Among them, the interval prediction method can provide the upper and lower limits of the photovoltaic power prediction interval under a given confidence level. The interval prediction method can be divided into indirect method and direct method. The former indirectly obtains the prediction interval based on the prediction probability distribution or quantile, and the latter establishes a prediction model to directly output the prediction interval. In the past, direct interval prediction methods were mostly based on machine learning models such as extreme learning machines to establish opportunity constrained optimization problems and solve the interval prediction model parameters. However, the limited nonlinear fitting ability of machine learning models limits the application of such methods in scenarios that require processing complex data, such as the day-ahead regional photovoltaic power prediction that requires considering massive meteorological information. Summary of the invention

[0005] In view of the limitations of existing photovoltaic power prediction methods, the purpose of the present invention is to provide a regional photovoltaic power direct interval prediction method based on graph convolutional neural network, which is based on graph convolutional neural network, fully considers the regional meteorological resources and the correlation of meteorological information in different geographical locations in the region, and introduces conditional risk value and augmented Lagrange multiplier method to transform the opportunity-constrained interval prediction optimization problem into an optimization problem with linear inequality constraints, and finally realizes the training of deep learning model through 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, broadens the application scenarios of direct interval prediction methods, and realizes efficient quantification of regional photovoltaic power prediction uncertainty.

[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, the method relies on a deep learning model based on a graph convolutional neural network, and the method for constructing a deep learning model based on a graph convolutional neural network includes the following steps:

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

[0009] Step 2: Calculate the weather forecast irradiance covariance matrix of multiple different geographical locations in the region as the graph convolutional neural network adjacency matrix. On this basis, construct a graph convolutional neural network with weather forecast features of 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, transform the optimization problem containing 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 weather 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 graph convolutional neural network to obtain a trained deep learning model based on graph convolutional neural network.

[0012] The conditional risk value and Lagrange multipliers are introduced into the direct prediction method of regional photovoltaic power of the present invention, the chance constrained optimization problem is converted into an optimization problem constrained by linear inequality, and the traditional optimizer-based solution is improved into 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, y is the measured value of the regional photovoltaic power, Indicates the probability of an event. In the constructed optimization problem, the optimization goal is to minimize the width of the prediction interval. The first constraint is the prediction interval reliability constraint, that is, it is necessary to ensure 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 is less than or equal to the upper limit of the prediction interval.

[0017] Furthermore, in step 1, the method of introducing conditional risk value to tighten the feasible domain of the opportunity 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 at the confidence level α, and CVaRα (z) is the value of the random variable z that exceeds VaR α (z) is the expected value of part 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 From the definition of (z), we know that VaR α (z)≤0 An optimal solution for Now assume that τ t *≤0; and:

[0028]

[0029] In the above formula, the first term on the right side of the equation 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 target of the chance-constrained optimization problem by 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 meteorological forecast irradiance covariance matrix of multiple different geographical locations in 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] Suppose 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 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] Wherein, 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 tth 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 measured value and the measured 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] Definition and solution of CVaR α The loss function of the optimization problem of (z) is

[0067]

[0068] The data set based on the meteorological forecast characteristics of multiple geographical locations and the measured data of regional photovoltaic power uses a parameter optimization algorithm based on stochastic gradient descent to solve the optimization problem with the model parameters as the 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 model based on graph convolutional neural network λ 0 , σ 0 , model learning rate η, penalty factor growth coefficient ρ, maximum training round N epoch , the 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 a deep learning model based on a 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 for 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 adjacency matrix of the graph convolutional neural network, and introduces 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 linear 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 a deep learning stochastic gradient descent algorithm is proposed, 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, it provides rich and reliable probabilistic information support for the economic and safe operation of regional power systems under a high proportion of distributed photovoltaic penetration. BRIEF DESCRIPTION OF THE DRAWINGS

[0084] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the prior art descriptions are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention, and for ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[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 structural diagram of a deep learning model based on a graph convolutional neural network designed for direct interval prediction in the present invention;

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

[0088] Figure 4 A covariance matrix heat map of the 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 implementation manner provided by the present invention; DETAILED DESCRIPTION

[0090] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are 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 creative work are 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, y is the measured value of the regional photovoltaic power, Indicates the probability of an event. In the constructed optimization problem, the optimization goal is to minimize the width of the prediction interval. The first constraint is the prediction interval reliability constraint, that is, it is necessary to ensure 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 is less than or equal to the upper limit of the prediction interval.

[0095] Next, the conditional risk value is introduced to tighten the feasible domain of the opportunity 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 at the confidence level α, and CVaR α (z) is the value of the random variable z that exceeds VaR α (z) is the expected value of part 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 From the definition of (z), we know that VaR α (z)≤0 An optimal solution for Now assume that τ t *≤0; and:

[0106]

[0107] In the above formula, the first term on the right side of the equation 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 in 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 in 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 ith and jth 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] Suppose 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, and 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; 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 respectively expressed as:

[0134]

[0135] l=g(x,ωα)

[0136] s=g(x,ω s )

[0137] τ=g(x,ω τ )

[0138] Wherein, 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 tth 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 measured value and the measured value minus the upper limit of the prediction interval in the tth sample.

[0145] Step 4: Based on a data set containing weather forecast features of multiple geographical locations and measured data of regional photovoltaic power (as a training data set), 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] Definition and solution of CVaR α The loss function of the optimization problem of (z) is

[0148]

[0149] The data set based on the meteorological forecast characteristics of multiple geographical locations and the measured data of regional photovoltaic power uses a parameter optimization algorithm based on stochastic gradient descent to solve the optimization problem with the model parameters as the 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 model based on graph convolutional neural network λ 0 , σ 0 , model learning rate η, penalty factor growth coefficient ρ, maximum training round N epoch , the 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 a deep learning model based on a 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 as follows: the new weather forecast information x in different geographical locations is used 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 forecasting. The time resolution of the time series is 15 minutes. The data contains weather forecast information and regional total photovoltaic power generation in different geographical locations in the region. The relative distribution of geographical locations corresponding to the weather information is as follows: Figure 3 As shown, the latitude and longitude values ​​in the figure have been processed. Figure 4 The covariance matrix of 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, otherwise it takes the value 0.

[0167] Table 1 Performance comparison of interval prediction methods

[0168]

[0169] Among them, the average coverage error (ACE) is the empirical coverage error (ECP) minus the nominal coverage error (NCP), which reflects the reliability of the prediction interval and can measure 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 calculation method of empirical coverage, average coverage error, and average interval width is 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 a higher reliability and a narrower interval width, which shows the superiority of the method.

[0174] Figure 5This 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 wide 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 the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. Such 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 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 photovoltaic power interval prediction as a chance-constrained optimization problem, introduce the conditional value at risk to tighten the feasible domain of the chance-constrained optimization problem, and transfer the chance constraint to the optimization objective of the chance-constrained optimization problem through the augmented Lagrange multiplier method, so as to reconstruct the chance-constrained optimization problem into an optimization problem with linear inequality constraints; Step 2: Calculate the weather forecast irradiance covariance matrix of multiple different geographical locations in the region as the graph convolutional neural network adjacency matrix. On this basis, construct a graph convolutional neural network with 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, transform the optimization problem containing 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 data set containing weather 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 graph convolutional neural network to obtain a trained deep learning model based on graph convolutional neural network.

2. According to claim 1, the method for direct interval prediction of regional photovoltaic power based on graph convolutional neural network is characterized in that: In step 1, the photovoltaic power interval prediction model is modeled as a chance constrained optimization problem, which is specifically expressed as: in, is the expected function, u and l are the upper and lower limits of the photovoltaic power prediction interval, y is the measured value of the regional photovoltaic power, represents the probability of an event occurring, and β is the significance level.

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: In step 1, the method of introducing conditional risk value to tighten the feasible domain of the opportunity constrained optimization problem is as follows: 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: z=max(ly,yu) At this time there are: Now we introduce the value at risk VaR and conditional value at risk CVaR under the confidence level α=100(1-β)%: Where f(z) is the probability density function of z; VaR α (z) means the quantile of the random variable z at the confidence level α, and CVaR α (z) is the value of the random variable z that exceeds VaR α (z) is the expected value of part CVaR α (z) is a convex function of z, which is obtained by the following formula: in, τ is the optimization variable when obtaining CVaR; 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 From the definition of (z), we know that VaR α (z)≤0 An optimal solution for Now assume that τ t *≤0; and: In the above formula, the first term on the right side of the equation is always non-negative, so: At this time, the chance-constrained optimization problem is transformed into:

4. The method for direct interval prediction of regional photovoltaic power based on graph convolutional neural network according to claim 3 is characterized in that: In step 1, the chance constraint is transferred to the optimization target of the chance constraint optimization problem by the augmented Lagrange multiplier method, and the chance constraint optimization problem is reconstructed into an optimization problem containing linear inequality constraints by first introducing an auxiliary variable s to reconstruct the transformed chance constraint optimization problem into: The reconstructed optimization problem is transformed into an optimization problem with inequality constraints by using the augmented Lagrange multiplier method: in, λ is the Lagrange multiplier and σ is the penalty factor.

5. 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 meteorological forecast irradiance covariance matrix for multiple different geographical locations in the region described in step 2 is as follows: 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.

6. 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 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 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: l＝a l u=a l +ReLU(a u ) s=ReLU(a s ) τ=-ReLU(a τ ) At this time, the model output u, l, s, τ satisfies the following linear inequality constraints: s≥0 l≤u τ≤0 The optimization problem with linear inequality constraints is transformed into an optimization problem with model parameters as optimization variables, specifically: u, l, s, τ are output by the deep learning model based on graph convolutional neural network, so u, l, s, τ are respectively expressed as: s=g(x,ω) s ) τ=g(x,ω) τ ) Wherein, g(·) represents the deep learning model based on graph convolutional neural network, 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; Then the optimization problem with model parameters as optimization variables is specifically: in, 7. The method for direct interval prediction of regional photovoltaic power based on graph convolutional neural network according to claim 6 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, T is the total number of historical samples, x t is the weather forecast information of different geographical locations of the tth 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 measured value and the measured value minus the upper limit of the prediction interval in the tth sample.

8. The method for direct interval prediction of regional photovoltaic power based on graph convolutional neural network according to claim 7 is characterized in that: In step 4, 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 ; Definition and solution of CVaR α The loss function of the optimization problem of (z) is The data set based on the meteorological forecast characteristics of multiple geographical locations and the measured data of regional photovoltaic power uses a parameter optimization algorithm based on stochastic gradient descent to solve the optimization problem with the model parameters as the 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 λ 0 , σ 0 , model learning rate η, penalty factor growth coefficient ρ, maximum training round N epoch , the total number of dataset batches N batch ; Step (2): Set the initial training round k = 1; Step (3): Set the initial batch j=1; Step (4): Calculate L CVaR The parameter ω corresponding to the auxiliary variable τ τ Gradient L CVaR And update the parameters: Step (5): Calculate L DL Gradient of the parameter ω of a deep learning model based on a graph convolutional neural network L DL And update ω: 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: s k+1 ←rs k 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.

9. 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 meteorological forecast information x in 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 .

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