CN111222700A - Day-ahead electricity price probability prediction method based on dynamic network quantile model - Google Patents

Abstract

The invention discloses a day-ahead electricity price probability prediction method based on a dynamic network quantile model, which is characterized by comprising the following steps: according to the incidence relation between different influence factors and the electricity price sequence, comprehensive influence factors are designed to carry out electricity price similar day selection, a dynamic network quantile electricity price prediction model is designed, and the nuclear density electricity price probability based on the dynamic network quantile electricity price prediction model is predicted, so that the prediction precision is high, and the running time can be greatly shortened; the model is little influenced by the related risk of price fluctuation and has strong tolerance to singular values. Has the advantages of scientific and reasonable structure, good applicability, good effect and the like.

Description

Day-ahead electricity price probability prediction method based on dynamic network quantile model

Technical Field

The invention relates to the field of intelligent power grids and power data analysis, in particular to a day-ahead electricity price probability prediction method based on a dynamic network quantile model.

Background

Since the emergence of competitive power markets, electricity price prediction (EPF) is becoming an essential important link in the investment decision making process of power selling companies. The current price of electricity is a reference price for energy trading decision, and is concerned about the direct influence on the income of the electricity selling company. With the rapid development of smart grids, a large amount of distributed renewable energy resources are connected into the power grid, and become an important component of a strong smart grid. However, the intermittency and uncertainty of renewable energy sources have a significant impact on price-oriented electricity markets, which will greatly reduce the accuracy of the day-ahead electricity price forecast. Therefore, the problem that the power selling company needs to overcome urgently is to find an accurate day-ahead power price prediction method. Early investigations indicated that for every 1% improvement in prediction error, the cost of operating electricity at 10 billion miles was increased. Therefore, how to further improve the day-ahead electricity price prediction accuracy in an open power market environment has very important practical significance for electricity selling companies.

The existing day-ahead electricity price prediction method mainly obtains predicted day electricity prices by inputting data of using historical day electricity prices into models such as an SVM (support vector machine), a BP (back propagation) neural network and the like, (1) because data sets related to the historical day electricity prices are directly input into different prediction models to predict the day-ahead electricity prices, day periodicity characteristics of the electricity prices are ignored, if data which are not consistent with the predicted day electricity price characteristics are input into the prediction models, not only is the calculated amount increased, but also the day-ahead electricity price prediction precision is reduced; (2) most of the research on the day-ahead electricity price prediction is not probability prediction but is focused on point prediction, so that certain limitation exists, the probability prediction can finely reflect the fluctuation range of electricity price change, and richer information is provided for decision makers and is more highly valued by academia and operators; (3) in the existing probability prediction model, a quantile regression neural network probability prediction model (QFNN) is widely applied to load and wind power probability prediction because the QFNN does not need prior distribution hypothesis and can provide stable prediction information, but the FNN needs to preset the number of network nodes, and the prediction precision of the model is reduced when the number of the network nodes is too large or too small. So far, no literature report and practical application of the day-ahead electricity price probability prediction method based on the dynamic network quantile model exist.

Disclosure of Invention

The invention aims to overcome the defects of the prior art and provide a day-ahead electricity price probability prediction method based on a dynamic network quantile model, which is scientific, reasonable, high in applicability and high in prediction precision.

The purpose of the invention is realized by the following technical scheme: a day-ahead electricity price probability prediction method based on a dynamic network quantile model is characterized by comprising the following steps:

1) designing comprehensive influence factors according to incidence relations between different influence factors and electricity price sequences to select electricity price on similar days

① weather factor similarity calculation

x_iThe sun weather particle characteristic vector is shown, wherein i is 1,2, the_i＝(x_i(1),...,x_i(n)), n is a factor number; and predict the daily eigenvector x₀＝(x₀(1),...,x₀(n)), calculating the sequence x according to the improved grey correlation₀And x_iSimilarity gamma_iIs represented by the formula (1),

wherein, T is the dimension of each prediction day and the index sequence of the influence factors of the historical solar meteorological phenomena,

representing a sequence of predicted weather factors x₀And historical solar weather factor sequence x_iFrom the minimum of the absolute difference of the ratios,

representing a sequence of predicted weather factors x₀And historical solar weather factor sequence x_iMaximum of absolute difference from absolute; rho is a resolution coefficient, and omega (t) represents a correlation coefficient of the influence factor index at the tth time and the ith meteorological influence factor

Weight of, meteorological particlesSimilarity is gamma_iThe process of ω (t) is:

first, define t₁And t₂Time-of-day priority concatenation matrix G ═ G (G)_t1t2)_T×TWherein

Represents t₁Time and t₂Comparing the importance degrees of the moments under certain influence factor conditions, and calculating the comparison result into an expression (2) according to the principle of the magnitude of the moments:

then G is equal to (G)_t1t2)_T×TConversion to fuzzy consistent matrix

Wherein b is_t1As shown in formula (3), b_t1t2As shown in the formula (4),

finally, the sum of the column terms is calculated and is expressed as formula (5):

② load and renewable energy power generation similarity calculation

Standardizing the load curve, and setting q_i,jWhen the load value at the j hour on the i day is 1,2, …, d, j is 1,2, …,24, the normalized load value is:

wherein the content of the first and second substances,

represents the average load value at the j-th hour,

the normalized historical daily load characteristic vector is y for the standard deviation of the electricity price at the jth hour_i＝(y_i(1),...,y_i(n)), n is the number of calculation times, and the predicted daily load feature vector is y₀＝(y₀(1),...,y₀(n)), calculating the sequence y using the DTW similarity coefficient formula₀And y_iIs calculated as formula (6):

wherein, gamma (y)_i(n),y₀(n)) represents the degree of similarity,

representing Euclidean distance of corresponding elements of two sequences in the cost matrix D, the closer the distance is, the gamma (y)_i(n),y₀(n)) the smaller; conversely, the greater the similarity, the greater the gamma (y)_i(n),y₀(n)) is denoted by q_iLet p in the same way_iGenerating capacity similarity of renewable energy sources;

③ date type similarity calculation

The electricity price fluctuation rule has a strong correlation with the week type and the interval days, the electricity price change has periodicity, and the closer the week type is, the more similar the fluctuation of the electricity price curve is; the closer the predicted day is to the historical day, the greater the electricity price similarity, and the week similarity epsilon_iSimilarity to similar days η_iThe calculation of (a) is formula (7) or formula (8);

ε_i＝1-|d(x_i)-d(x₀)| (7)

wherein d (x)₀) And d (x)_i) Respectively represent x₀And x_iMapped value, λIs a day-independent coefficient, and theta is a week-decline-independent coefficient; d is the number of days between the predicted day and the ith historical day; mod is a remainder function; int is a rounding operation; w₁、W₂The value is 7, and z is the lower limit of the similarity;

④ comprehensive impact factor calculation

Calculating a comprehensive influence factor by adopting a weighted addition method of similarity of all factors, wherein the calculation is as shown in formula (9):

ξ_i＝f₁r_i+f₂q_i+f₃p_i+f₄η_i+f₅ε_i(9)

wherein f is₁，f₂，f₃，f₄，f₅Respectively assigning the similarity weight coefficients of the day characteristic meteorological factor, the load, the renewable energy power generation amount, the week type and the similar day according to the action degrees of different influence factors, and enabling f to be the same₂>f₁>f₄>f₅>f₃,f₁₊f₂+f₃+f₄+f₅Determining the integrated impact factor ξ between the ith and predicted days at 1_iComparison ξ_iThe historical days with the comprehensive influence factors ranked in the first third are selected as similar days;

2) designing dynamic network quantile electricity price prediction (QGDFNN) model

① QGDFNN model input layer

The QGDFNN model is divided into four layers, namely an input layer, a membership Radial Basis Function (RBF) layer, a rule layer and an output layer, wherein the total number of input electricity price related variables in the input layer is n and is marked as X_i，i＝1,2,...,n；

② QGDFNN model membership RBF layer

In the subordinate RBF layer, there are u subordinate RBFs and each X_iIf the nodes are connected, the total number of the nodes is u multiplied by n, a Gaussian function is selected as a membership RBF, and the membership RBF is calculated as a formula (10):

wherein τ ∈ (0,1) is capable of generating different quantiles g₁(τ) is the membership RBF output result, c_ij(τ) represents an input variable X_iI 1,2, and n, j 1,2, mu, sigma_ijTo be subordinate to RBF width, let x_i(t) represents new input data, t 1,2,.. m, m ≦ n, which is compared to the boundary set φ_iMinimum euclidean distance ed between_i(j_n) When ed is_i(j_n)≥k_mfWhen, σ_ijThe formula (11) is adjusted:

at this time, the process of the present invention,

as a newly generated center of the Gaussian function, C_i-1,j、C_i+1,jIs the center of two Gaussian functions of the neighbors, k_mfThe value range is [0,0.5 ]]Is a system definable constant;

③ QGDFNN model rule layer

In the rule layer, new input sample data is set as (X)_i,P_i)，P_iIs the ith desired output, and the increase and decrease of the rule need to follow the principle: when (X)_i,P_i) If the epsilon-completeness of the fuzzy rule is not satisfied, a new rule needs to be added; when (X)_i,P_i) Output error e of_i>i_eWhen, new rules need to be considered for generation; and when the importance of the jth fuzzy rule ψ_j<K_errThen the jth rule is deleted, where e_i＝||P_i-y_i||，K_errIs a system tolerance error, y_iIs the output value of QGDFNN under the current structure, i_eIs a threshold value predefined according to the desired accuracy, and the variation process thereof is formula (12):

defining a deviation reduction rate matrix E ═ p (ρ ═ f)₁,ρ₂,...,ρ_u) J column ρ of E_j(n +1) deviation reduction rates corresponding to the jth rule, in g₂(τ) represents the output of the jth fuzzy rule, calculated as equation (13):

④ QGDFNN model output layer

In the output layer, the output result of the rule layer is weighted and summed to obtain an output result which is the formula (14):

wherein the result Y (τ | X) is output₁,X₂,...,X_n) The dependent variable Y is equal to (X) at the input variable₁,X₂,...,X_n) Corresponding quantile under the conditions, W_j(τ) is a quantile weight matrix of the jth fuzzy rule from the rule layer to the output layer, j being 1, 2.

Integrating QGDFNN model expressions into an expression (15) and an expression (16):

Q_Y(τ|X)＝f(X_i,c_ij(τ),W_j(τ)) (15)

wherein Q is_Y(τ | X) represents the τ conditional quantile for the dependent variable Y when the independent variable is X;

3) nuclear density electricity price probability prediction based on QGDFNN model

① QGDFNN model solution

Performing parameter estimation on the model, and performing parameter estimation on c in the model_ij(τ)、W_j(τ) the estimation problem is converted into the solution (17)

Wherein n is the number of samples, rho_τ(u) is a loss function defined as formula (18), and c is obtained by formula (17)_ij(τ) and W_j(τ) taking the optimal estimated value into equation (15) to obtain the conditional quantile of the corresponding variable,

② day-ahead electricity price probability generation based on KDE method

Inputting the data related to the similar day electricity prices into the model, wherein the data is specifically defined as: order to

Representing the d influence factor of the ith similar day in t embodiments, the QGDFNN model finally outputs the quantile of the condition of the predicted daily price of electricity, and the quantile is recorded as: z_i＝Q_yi(τ|x_i) However, to obtain the predicted daily probability price, it is necessary to estimate Z by a Kernel Density Estimation (KDE) method_iConverting into a predicted daily electricity price probability curve, simulating real probability distribution by fitting an observed value through a smooth peak function by a KDE method, and finally, fitting Z_iAs an input value of the kernel function, carrying out probability density prediction by selecting a proper bandwidth to obtain a probability density function of the day-ahead electricity price; and performing corresponding interval integral solution on the day-ahead power price probability density to obtain a day-ahead power price probability prediction curve, and assuming Z₁,Z₂,...,Z_nIs an independent same-distribution random sample, and the probability density function of a certain point is expressed by the formula (19):

wherein h is the bandwidth of the smoothing parameter which needs to be automatically started and set, n is the sample size, K (·) is regarded as a non-negative kernel function, an epanechnikov kernel function is selected, and the formula (20) is calculated:

wherein, I (·) is an indicative function, when the condition in the brackets is true, the value is 1, otherwise, the value is 0;

③ model evaluation index

For comprehensive evaluation of QGDFNN model performance, the evaluation index is formula (21) to formula (25):

(a) mean Absolute Percent Error (MAPE), used for error analysis of the prediction results, with smaller MAPE values being better, defined as equation (21):

wherein n represents the total number of days of the predicted electricity rate day, A_hAnd F_hRespectively representing the actual value and the predicted value of the electricity price at the h hour;

(b) relative Mean Square Error (RMSE) for reflecting the degree of deviation of the predicted value from the actual value, the smaller the RMSE value, the better, defined as equation (22):

(c) standard Deviation Error (SDE), which measures the risk associated with price volatility for a given time series, is defined by equation (23):

E_h＝F_h-A_h，

E_his the predicted electricity price error at the h-th hour,

is the average error of the prediction period, and the smaller the SDE value is, the price of the error of the predicted value is provedThe smaller the fluctuation influence is;

(d) the minimum information criterion (AIC), which balances the complexity of the estimated model and the goodness of the model fitting data, is defined as equation (24):

wherein k represents a model parameter, and the smaller the k value is, the more compact the representative model is; the larger the value of L, the more accurate the model is represented, SSE is the sum of squares error, which is used to measure the variation in the time series, and if all cases in the time series are the same, then SSE will be equal to 0, and SSE is defined as equation (25):

the day-ahead electricity price probability prediction method based on the dynamic network quantile model adopts the comprehensive influence factor designed according to the incidence relation between different influence factors and the electricity price sequence to select electricity price similar days, design the dynamic network quantile electricity price prediction (QGDFNN) model and predict the nuclear density electricity price probability based on the QGDFNN model, and compared with the prior art, the method has the advantages that: the QGDFNN model-based day-ahead electricity price probability prediction is carried out by using similar day data, the prediction precision is remarkably improved, and the operation time is greatly shortened; the method has high accuracy for predicting the day-ahead electricity price, and can also keep good accuracy for predicting the electricity price of a week in the future, so that the method is proved to have stability under the condition of a large sample; through model index comparison and evaluation, the SDE value of the QGDFNN model is far smaller than that of other models, which shows that the model is less influenced by the risk related to price fluctuation and has strong tolerance to singular values. It is scientific and reasonable, and has good applicability and effect.

Drawings

FIG. 1 is a flow chart of the method of the present invention;

FIG. 2 is a graph comparing the predicted results of example 1 using similar day data versus historical day data;

FIG. 3 is a graph comparing the predicted results of example 2 using similar day data versus historical day data;

FIG. 4 is a graph comparing the predicted results of example 3 using similar day data versus historical day data;

FIG. 5 is a graph comparing the predicted results of example 4 using similar day data versus historical day data;

FIG. 6 is a graph comparing SDE values of models;

FIG. 7 is a comparison graph of AIC values of models;

FIG. 8 is a graph of a prediction comparison using different prediction methods for example 1;

FIG. 9 is a graph of a prediction comparison using different prediction methods for example 2;

FIG. 10 is a graph of a prediction comparison using different prediction methods for example 3;

fig. 11 predicts a contrast map using a different prediction method for example 4.

Detailed Description

The method for predicting the day-ahead electricity price probability based on the dynamic network quantile model is described in detail below with reference to the accompanying drawings.

Referring to fig. 1, the method for predicting the day-ahead electricity price probability based on the dynamic network quantile model of the invention comprises the following steps:

1) designing comprehensive influence factors according to incidence relations between different influence factors and electricity price sequences to select electricity price on similar days

① weather factor similarity calculation

x_iThe sun weather particle characteristic vector is shown, wherein i is 1,2, the_i＝(x_i(1),...,x_i(n)), n is a factor number; and predict the daily eigenvector x₀＝(x₀(1),...,x₀(n)), calculating the sequence x according to the improved grey correlation₀And x_iSimilarity gamma_iIs represented by the formula (1),

wherein, T is the dimension of each prediction day and the index sequence of the influence factors of the historical solar meteorological phenomena,

representing a sequence of predicted weather factors x₀And historical solar weather factor sequence x_iFrom the minimum of the absolute difference of the ratios,

representing a sequence of predicted weather factors x₀And historical solar weather factor sequence x_iMaximum of absolute difference from absolute; rho is a resolution coefficient which is usually 0.5, and omega (t) represents a correlation coefficient of the influence factor index at the tth time and the ith meteorological influence factor

The meteorological particle similarity is gamma_iThe process of ω (t) is:

first, define t₁And t₂Time-of-day priority concatenation matrix G ═ G (G)_t1t2)_T×TWherein

Represents t₁Time and t₂Comparing the importance degrees of the moments under certain influence factor conditions, and calculating the comparison result into an expression (2) according to the principle of the magnitude of the moments:

then G is equal to (G)_t1t2)_T×TConversion to fuzzy consistent matrix

Wherein b is_t1As shown in formula (3), b_t1t2As shown in the formula (4),

finally, the sum of the column terms is calculated and is expressed as formula (5):

② load and renewable energy power generation similarity calculation

Standardizing the load curve, and setting q_i,jWhen the load value at the j hour on the i day is 1,2, …, d, j is 1,2, …,24, the normalized load value is:

wherein the content of the first and second substances,

represents the average load value at the j-th hour,

the normalized historical daily load characteristic vector is y for the standard deviation of the electricity price at the jth hour_i＝(y_i(1),...,y_i(n)), where n is 144 and the predicted daily load feature vector is y₀＝(y₀(1),...,y₀(n)), calculating the sequence y using the DTW similarity coefficient formula₀And y_iIs calculated as formula (6):

wherein, gamma (y)_i(n),y₀(n)) represents the degree of similarity,

representing Euclidean distance of corresponding elements of two sequences in the cost matrix D, the closer the distance is, the gamma (y)_i(n),y₀(n)) the smaller; conversely, the greater the similarity, the greater the gamma (y)_i(n),y₀(n)) is denoted by q_iLet p in the same way_iGenerating capacity similarity of renewable energy sources;

③ date type similarity calculation

The electricity price fluctuation rule has a strong correlation with the week type and the interval days, the electricity price change has periodicity, and the closer the week type is, the more similar the fluctuation of the electricity price curve is; the closer the predicted day is to the historical day, the greater the electricity price similarity, and the week similarity epsilon_iSimilarity to similar days η_iThe calculation of (a) is formula (7) or formula (8);

ε_i＝1-|d(x_i)-d(x₀)| (7)

in the formula (7), d (x)₀) And d (x)_i) Respectively represent x₀And x_iThe mapped value, in equation (8), is λ a day-independent coefficient and θ a cycle-decay-independent coefficient, where λ, θ ∈ [0.9,0.98 ]]Let λ be 0.93; d is the number of days between the predicted day and the ith historical day; mod is a remainder function; int is a rounding operation; w₁、W₂The value is 7, and z is the lower limit of the similarity;

④ comprehensive impact factor calculation

Calculating a comprehensive influence factor by adopting a weighted addition method of similarity of all factors, wherein the calculation is as shown in formula (9):

ξ_i＝f₁r_i+f₂q_i+f₃p_i+f₄η_i+f₅ε_i(9)

wherein f is₁，f₂，f₃，f₄，f₅Respectively assigning the similarity weight coefficients of the day characteristic meteorological factor, the load, the renewable energy power generation amount, the week type and the similar day according to the action degrees of different influence factors, and enabling f to be the same_2>f_1>f_4>f_5>f₃,f₁₊f₂+f₃+f₄+f₅Determining between the ith and predicted day 1Synthetic impact factor ξ_iComparison ξ_iThe historical days with the comprehensive influence factors ranked in the first third are selected as similar days;

2) designing dynamic network quantile electricity price prediction (QGDFNN) model

① QGDFNN model input layer

The QGDFNN model is divided into four layers, namely an input layer, a membership Radial Basis Function (RBF) layer, a rule layer and an output layer, wherein the total number of input electricity price related variables in the input layer is n and is marked as X_i，i＝1,2,...,n；

② QGDFNN model membership RBF layer

In the subordinate RBF layer, there are u subordinate RBFs and each X_iIf the nodes are connected, the total number of the nodes is u multiplied by n, a Gaussian function is selected as a membership RBF, and the membership RBF is calculated as a formula (10):

wherein τ ∈ (0,1) is capable of generating different quantiles g₁(τ) is the membership RBF output result, c_ij(τ) represents an input variable X_iI 1,2, and n, j 1,2, mu, sigma_ijTo be subordinate to RBF width, let x_i(t) represents new input data, t 1,2,.. m, m ≦ n, which is compared to the boundary set φ_iMinimum euclidean distance ed between_i(j_n) When ed is_i(j_n)≥k_mfWhen, σ_ijThe formula (11) is adjusted:

at this time, the process of the present invention,

as a newly generated center of the Gaussian function, C_i-1,j、C_i+1,jIs the center of two Gaussian functions of the neighbors, k_mfTaking 0.05;

③ QGDFNN model rule layer

In the rule layer, new input sample data is set as (X)_i,P_i)(P_iIs the ith desired output), the increase or decrease of the rule needs to follow the principle: when (X)_i,P_i) If the epsilon-completeness of the fuzzy rule is not satisfied, a new rule needs to be added; when (X)_i,P_i) Output error e of_i>i_eWhen, new rules need to be considered for generation; and when the importance of the jth fuzzy rule ψ_j<K_errThen the jth rule is deleted, where e_i＝||P_i-y_i||，K_errIs a system tolerance error, y_iIs the output value of QGDFNN under the current structure, i_eIs a threshold value predefined according to the desired accuracy, and the variation process thereof is formula (12):

defining a deviation reduction rate matrix E ═ p (ρ ═ f)₁,ρ₂,...,ρ_u) J column ρ of E_j(n +1) deviation reduction rates corresponding to the jth rule, in g₂(τ) represents the output of the jth fuzzy rule, calculated as equation (13):

④ QGDFNN model output layer

In the output layer, the output result of the rule layer is weighted and summed to obtain an output result which is the formula (14):

wherein the result Y (τ | X) is output₁,X₂,...,X_n) The dependent variable Y is equal to (X) at the input variable₁,X₂,...,X_n) Pair under the conditionNumber of fractions, W_j(τ)_j＝_1,2,...,_uA quantile weight matrix for the jth fuzzy rule between the rule layer and the output layer;

integrating QGDFNN model expressions into an expression (15) and an expression (16):

Q_Y(τ|X)＝f(X_i,c_ij(τ),W_j(τ)) (15)

wherein Q_Y(τ | X) represents the τ conditional quantile for the dependent variable Y when the independent variable is X;

3) nuclear density electricity price probability prediction based on QGDFNN model

① QGDFNN model solution

Performing parameter estimation on the model, and performing parameter estimation on c in the model_ij(τ)、W_j(τ) the estimation problem is converted into the solution (17)

Wherein n is the number of samples, rho_τ(u) is a loss function defined as formula (18), and c is obtained by formula (17)_ij(τ) and W_j(τ) taking the optimal estimated value into equation (15) to obtain the conditional quantile of the corresponding variable,

② day-ahead electricity price probability generation based on KDE method

Inputting the data related to the similar day electricity prices into the model, wherein the data is specifically defined as: order to

The d influence factor representing the l-th similar day is shown in table 1, the independent variables input by the specific model are shown in table 1, and the QGDFNN model finally outputs the quantile of the condition of the predicted daily electricity price, and the quantile is recorded as: z_i＝Q_yi(τ|x_i) However, to obtain the predicted daily probability price, it is necessary to estimate Z by a Kernel Density Estimation (KDE) method_iConverting into a predicted daily electricity price probability curve, simulating real probability distribution by fitting an observed value through a smooth peak function by a KDE method, and finally, fitting Z_iAs an input value of the kernel function, carrying out probability density prediction by selecting a proper bandwidth to obtain a probability density function of the day-ahead electricity price; and performing corresponding interval integral solution on the day-ahead power price probability density to obtain a day-ahead power price probability prediction curve, and assuming Z₁,Z₂,...,Z_nIs an independent same-distribution random sample, and the probability density function of a certain point is expressed by the formula (19):

wherein h is the bandwidth of the smoothing parameter which needs to be automatically started and set, n is the sample size, K (·) is regarded as a non-negative kernel function, an epanechnikov kernel function is selected, and the formula (20) is calculated:

wherein, I (·) is an indicative function, when the condition in the brackets is true, the value is 1, otherwise, the value is 0;

table 1 description of independent variables of examples on similar days

③ model evaluation index

For comprehensive evaluation of QGDFNN model performance, the evaluation indexes adopt formula (21) to formula (25):

(a) mean Absolute Percent Error (MAPE), used for error analysis of the prediction results, with smaller MAPE values being better, defined as equation (21):

whereinN represents the total number of days of the predicted electricity price day, A_hAnd F_hRespectively representing the actual value and the predicted value of the electricity price at the h hour;

(b) relative Mean Square Error (RMSE) for reflecting the degree of deviation of the predicted value from the actual value, the smaller the RMSE value, the better, defined as equation (22):

(c) standard Deviation Error (SDE), which measures the risk associated with price volatility for a given time series, is defined by equation (23):

E_his the predicted electricity price error at the h-th hour,

the average error of the prediction period is shown, and the smaller the SDE value is, the smaller the influence of price fluctuation on the error of the predicted value is proved to be;

(d) the minimum information criterion (AIC), which balances the complexity of the estimated model and the goodness of the model fitting data, is defined as equation (24):

wherein k represents a model parameter, and the smaller the k value is, the more compact the representative model is; the larger the value of L, the more accurate the model is represented, SSE is the sum of squares error, which is used to measure the variation in the time series, and if all cases in the time series are the same, then SSE will be equal to 0, and SSE is defined as equation (25):

in order to verify that the day-ahead electricity price probability prediction method based on the dynamic network quantile model provided by the invention can effectively improve the day-ahead electricity price prediction accuracy, the inventor respectively adopts the method provided by the invention to carry out experimental verification: 1) performing prediction comparison analysis on the same date by using the similar date data and the historical date data; 2) index evaluation is respectively carried out on the SVM, the BP neural network, the ELM model and the QGDFNN model; 3) the results of the prediction were analyzed by comparing 3 different prediction methods with the method of the present invention. Experimental data: relevant data from 2018, month 1 and year 1 to 2019, month 3 and month 1 in California of the United states are collected and collated, and a comprehensive prediction experiment data set is constructed (shown in Table 2). Wherein, the electricity price and the load data come from a United states PJM website (https:// www.pjm.com /); temperature, humidity, wind speed, solar intensity data from the United states Meteorological center website (https:// www.weather.gov /); coal power generation, hydraulic power generation, nuclear power generation, wind power generation, photovoltaic power generation, and operator sales power data come from the united states energy agency website (https:// www.eia.gov /).

TABLE 2 comprehensive prediction experiment data set

When the prediction embodiment is selected, similar day selection needs to be carried out on the prediction embodiment:

the prediction date is selected in consideration of the influence of seasonal factors and the type of date (holiday and weekday) on the prediction of the day-ahead electricity prices, and similar day search examples (and prediction examples of example analysis) are determined to be classified as in table 3.

TABLE 3 prediction dates of all examples

The comprehensive prediction experiment data set and the similar day search range in the table 3 are used for respectively carrying out assignment calculation on different embodiments, and f is enabled to be₁＝0.1,f₂＝0.4,f₃＝0.05,f₄＝0.3,f₅0.15. calculated ξ_i(i 1.., L) are ranked from large to small, if the maximum overall similarity factor (e.g., ξ)_i-1) Synthesize similar factors with a certain day (e.g. ξ)_i+1) If the difference is less than 0.0005, the two days are all considered to be predicted similar days. The results of similar days searched are shown in table 4.

TABLE 4 similar day selection results

The data sets of similar days selected in examples 1-4 of Table 3 were normalized. And inputting the QGDFNN model to obtain the electricity price predicted values on different quantiles corresponding to the prediction days. The invention selects the quantile range of 0.001 to 0.999 with the interval of 0.02. And then, the predicted hour power price quantile is used as an input variable of an epanechnikov kernel function, and the hour power price prediction probability density of the embodiment 1-4 is obtained by combining a kernel density estimation method. And finally, integrating the electricity price prediction probability density of the embodiment 1-4 in a corresponding interval to obtain an electricity price probability prediction curve.

The inventor respectively adopts the similar day data selected by the similar day selection method provided by the invention and the historical days to respectively carry out power price probability prediction results on the same date, and comparison indexes of the same date and different models and prediction results of different day-ahead power price prediction methods. FIG. 2 is a comparison of similar day data used with historical day data predictions for example 1, FIG. 3 is a comparison of similar day data used with historical day data predictions for example 2, FIG. 4 is a comparison of similar day data used with historical day data predictions for example 3, FIG. 5 is a comparison of similar day data used with historical day data predictions for example 4, FIG. 6 is a comparison of model SDE values, FIG. 7 is a comparison of model AIC values (MAPE vs. RMSE values are shown in Table 5), FIG. 8 is a comparison of predictions using different prediction methods for example 1, FIG. 9 is a comparison of predictions using different prediction methods for example 2, FIG. 10 is a comparison of predictions using different prediction methods for example 3, and FIG. 11 is a comparison of predictions using different prediction methods for example 4. As can be seen from fig. 2 to 5, the electricity price prediction accuracy is effectively improved by using the data selected by the similar day selection method of the invention to predict the electricity price. As can be seen from FIGS. 6 and 7, the performance of each aspect of the model is superior to that of the other three classical prediction models by using the model of the invention. As can be seen from fig. 8 to 11, the prediction accuracy is higher with the prediction method of the present invention than with other methods.

TABLE 5 comparison of the MAPE and RMSE of the models

The embodiments of the present invention are not exhaustive, and those skilled in the art will still fall within the scope of the present invention as claimed without simple duplication and modification by the inventive efforts.

Claims (1)

1. A day-ahead electricity price probability prediction method based on a dynamic network quantile model is characterized by comprising the following steps:

1) designing comprehensive influence factors according to incidence relations between different influence factors and electricity price sequences to select electricity price on similar days

① weather factor similarity calculation

x_iThe sun weather particle characteristic vector is shown, wherein i is 1,2, the_i＝(x_i(1),...,x_i(n)), n is a factor number; and predict the daily eigenvector x₀＝(x₀(1),...,x₀(n)), calculating the sequence x according to the improved grey correlation₀And x_iSimilarity gamma_iIs represented by the formula (1),

wherein, T is the dimension of each prediction day and the index sequence of the influence factors of the historical solar meteorological phenomena,

representing a sequence of predicted weather factors x₀And historical solar weather factor sequence x_iFrom the minimum of the absolute difference of the ratios,

representing a sequence of predicted weather factors x₀And historical solar weather factor sequence x_iMaximum of absolute difference from absolute; rho is a resolution coefficient, and omega (t) represents a correlation coefficient of the influence factor index at the tth time and the ith meteorological influence factor

The meteorological particle similarity is gamma_iThe process of ω (t) is:

first, define t₁And t₂Time-of-day priority concatenation matrix G ═ G (G)_t1t2)_T×TWherein

Represents t₁Time and t₂Comparing the importance degrees of the moments under certain influence factor conditions, and calculating the comparison result into an expression (2) according to the principle of the magnitude of the moments:

then G is equal to (G)_t1t2)_T×TConversion to fuzzy consistent matrix

Wherein b is_t1As shown in formula (3), b_t1t2As shown in the formula (4),

finally, the sum of the column terms is calculated and is expressed as formula (5):

② load and renewable energy power generation similarity calculation

Standardizing the load curve, and setting q_i,jWhen the load value at the j hour on the i day is 1,2, …, d, j is 1,2, …,24, the normalized load value is:

wherein the content of the first and second substances,

represents the average load value at the j-th hour,

the normalized historical daily load characteristic vector is y for the standard deviation of the electricity price at the jth hour_i＝(y_i(1),...,y_i(n)), n is the number of calculation times, and the predicted daily load feature vector is y₀＝(y₀(1),...,y₀(n)), calculating the sequence y using the DTW similarity coefficient formula₀And y_iIs calculated as formula (6):

wherein, gamma (y)_i(n),y₀(n)) represents the degree of similarity,

representing Euclidean distance of corresponding elements of two sequences in the cost matrix D, the closer the distance is, the gamma (y)_i(n),y₀(n)) the smaller; conversely, the greater the similarity, the greater the gamma (y)_i(n),y₀(n)) is denoted by q_iLet p in the same way_iGenerating capacity similarity of renewable energy sources;

③ date type similarity calculation

The electricity price fluctuation rule has a strong correlation with the week type and the interval days, the electricity price change has periodicity, and the closer the week type is, the more similar the fluctuation of the electricity price curve is; the closer the predicted day is to the historical day, the greater the electricity price similarity, and the week similarity epsilon_iSimilarity to similar days η_iThe calculation of (a) is formula (7) or formula (8);

ε_i＝1-|d(x_i)-d(x₀)| (7)

wherein d (x)₀) And d (x)_i) Respectively represent x₀And x_iIn the mapped value, lambda is a day-independent coefficient, and theta is a week-decay-independent coefficient; d is the number of days between the predicted day and the ith historical day; mod is a remainder function; int is a rounding operation; w₁、W₂The value is 7, and z is the lower limit of the similarity;

④ comprehensive impact factor calculation

Calculating a comprehensive influence factor by adopting a weighted addition method of similarity of all factors, wherein the calculation is as shown in formula (9):

ξ_i＝f₁r_i+f₂q_i+f₃p_i+f₄η_i+f₅ε_i(9)

wherein f is₁，f₂，f₃，f₄，f₅Respectively assigning the similarity weight coefficients of the day characteristic meteorological factor, the load, the renewable energy power generation amount, the week type and the similar day according to the action degrees of different influence factors, and enabling f to be the same_2>f_1>f_4>f_5>f₃,f₁₊f₂+f₃+f₄+f₅Determining the integrated impact factor ξ between the ith and predicted days at 1_iComparison ξ_iThe historical days with the comprehensive influence factors ranked in the first third are selected as similar days;

2) designing dynamic network quantile electricity price prediction (QGDFNN) model

① QGDFNN model input layer

The QGDFNN model is divided into four layers, namely an input layer, a membership Radial Basis Function (RBF) layer, a rule layer and an output layer, wherein the total number of input electricity price related variables in the input layer is n and is marked as X_i，i＝1,2,...,n；

② QGDFNN model membership RBF layer

In the subordinate RBF layer, there are u subordinate RBFs and each X_iIf the nodes are connected, the total number of the nodes is u multiplied by n, a Gaussian function is selected as a membership RBF, and the membership RBF is calculated as a formula (10):

wherein τ ∈ (0,1) is capable of generating different quantiles g₁(τ) is the membership RBF output result, c_ij(τ) represents an input variable X_iI 1,2, and n, j 1,2, mu, sigma_ijTo be subordinate to RBF width, let x_i(t) represents new input data, t 1,2,.. m, m ≦ n, which is compared to the boundary set φ_iMinimum euclidean distance ed between_i(j_n) When ed is_i(j_n)≥k_mfWhen, σ_ijThe formula (11) is adjusted:

at this time, the process of the present invention,

as a newly generated center of the Gaussian function, C_i-1,j、C_i+1,jIs the center of two Gaussian functions of the neighbors, k_mfThe value range is [0,0.5 ]]Is a system definable constant;

③ QGDFNN model rule layer

In the rule layer, new input sample data is set as (X)_i,P_i)，P_iIs the ith desired output, and the increase and decrease of the rule need to follow the principle: when (X)_i,P_i) If the epsilon-completeness of the fuzzy rule is not satisfied, a new rule needs to be added; when (X)_i,P_i) Output error e of_i>i_eWhen, new rules need to be considered for generation; and when the importance of the jth fuzzy rule ψ_j<K_errThen the jth rule is deleted, where e_i＝||P_i-y_i||，K_errIs a system tolerance error, y_iIs the output value of QGDFNN under the current structure, i_eIs a threshold value predefined according to the desired accuracy, and the variation process thereof is formula (12):

defining a deviation reduction rate matrix E ═ p (ρ ═ f)₁,ρ₂,...,ρ_u) J column ρ of E_j(n +1) deviation reduction rates corresponding to the jth rule, in g₂(τ) represents the output of the jth fuzzy rule, calculated as equation (13):

④ QGDFNN model output layer

In the output layer, the output result of the rule layer is weighted and summed to obtain an output result which is the formula (14):

wherein the result Y (τ | X) is output₁,X₂,...,X_n) The dependent variable Y is equal to (X) at the input variable₁,X₂,...,X_n) Corresponding quantile under the conditions, W_j(τ) is the jth ambiguity from the rule layer to the output layerA regular quantile weight matrix, j 1, 2.

Integrating QGDFNN model expressions into an expression (15) and an expression (16):

Q_Y(τ|X)＝f(X_i,c_ij(τ),W_j(τ)) (15)

wherein Q is_Y(τ | X) represents the τ conditional quantile for the dependent variable Y when the independent variable is X;

3) nuclear density electricity price probability prediction based on QGDFNN model

① QGDFNN model solution

Performing parameter estimation on the model, and performing parameter estimation on c in the model_ij(τ)、W_j(τ) the estimation problem is converted into the solution (17)

Wherein n is the number of samples, rho_τ(u) is a loss function defined as formula (18), and c is obtained by formula (17)_ij(τ) and W_j(τ) taking the optimal estimated value into equation (15) to obtain the conditional quantile of the corresponding variable,

② day-ahead electricity price probability generation based on KDE method

Inputting the data related to the similar day electricity prices into the model, wherein the data is specifically defined as: order to

Representing the d influence factor of the ith similar day in t embodiments, the QGDFNN model finally outputs the quantile of the condition of the predicted daily price of electricity, and the quantile is recorded as:Z_i＝Q_yi(τ|x_i) However, to obtain the predicted daily probability price, it is necessary to estimate Z by a Kernel Density Estimation (KDE) method_iConverting into a predicted daily electricity price probability curve, simulating real probability distribution by fitting an observed value through a smooth peak function by a KDE method, and finally, fitting Z_iAs an input value of the kernel function, carrying out probability density prediction by selecting a proper bandwidth to obtain a probability density function of the day-ahead electricity price; and performing corresponding interval integral solution on the day-ahead power price probability density to obtain a day-ahead power price probability prediction curve, and assuming Z₁,Z₂,...,Z_nIs an independent same-distribution random sample, and the probability density function of a certain point is expressed by the formula (19):

wherein h is the bandwidth of the smoothing parameter which needs to be automatically started and set, n is the sample size, K (·) is regarded as a non-negative kernel function, an epanechnikov kernel function is selected, and the formula (20) is calculated:

wherein, I (·) is an indicative function, when the condition in the brackets is true, the value is 1, otherwise, the value is 0;

③ model evaluation index

For comprehensive evaluation of QGDFNN model performance, the evaluation index is formula (21) to formula (25):

(a) mean Absolute Percent Error (MAPE), used for error analysis of the prediction results, with smaller MAPE values being better, defined as equation (21):

wherein n represents the total number of days of the predicted electricity rate day, A_hAnd F_hRespectively representing the actual value and the predicted value of the electricity price at the h hour;

(b) relative Mean Square Error (RMSE) for reflecting the degree of deviation of the predicted value from the actual value, the smaller the RMSE value, the better, defined as equation (22):

(c) standard Deviation Error (SDE), which measures the risk associated with price volatility for a given time series, is defined by equation (23):

E_h＝F_h-A_h，

E_his the predicted electricity price error at the h-th hour,

the average error of the prediction period is shown, and the smaller the SDE value is, the smaller the influence of price fluctuation on the error of the predicted value is proved to be;

(d) the minimum information criterion (AIC), which balances the complexity of the estimated model and the goodness of the model fitting data, is defined as equation (24):

wherein k represents a model parameter, and the smaller the k value is, the more compact the representative model is; the larger the value of L, the more accurate the model is represented, SSE is the sum of squares error, which is used to measure the variation in the time series, and if all cases in the time series are the same, then SSE will be equal to 0, and SSE is defined as equation (25):

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