CN117541291A - Electricity price prediction method and system based on EMD decomposition and SSA-SVM model - Google Patents
Electricity price prediction method and system based on EMD decomposition and SSA-SVM model Download PDFInfo
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Abstract
The invention discloses a power price prediction method and a system based on EMD decomposition and SSA-SVM model, which relate to the technical field of power price prediction and comprise the steps of obtaining original power price data and decomposing the power price data through an EMD algorithm; constructing an SSA-SVM model, and applying key parameters in the SSA optimized SVM model to predict to obtain a predicted value under each characteristic signal; and carrying out cumulative reconstruction on the predicted values to obtain a final predicted result. The invention can effectively process nonlinearity and non-stationarity, improve the electricity price prediction accuracy and better adapt to the real characteristics of electricity price data. The abnormal value and fluctuation in the electricity price data can be dealt with, the performance of the model is improved through parameter optimization, and the characteristics of the electricity price data are fitted better. The future electricity price trend and fluctuation can be predicted better, the utilization efficiency of energy resources is improved, and better economic benefit is realized.
Description
Technical Field
The invention relates to the technical field of electricity price prediction, in particular to an electricity price prediction method and system based on EMD decomposition and an SSA-SVM model.
Background
Based on artificial intelligence and data analysis techniques, a number of electricity price prediction models have been established. In view of the fact that a single model often has certain limitation and precision errors, the mixed electricity price prediction model is built by combining the characteristics of different algorithms to become a research hotspot.
Common hybrid prediction methods include a BP neural network (GA-BP) optimized by a genetic algorithm, an ARIMA (WT-ARIMA) decomposed by wavelet transformation, an LS-SVM (PSO-LSSVM) optimized by a particle swarm algorithm, an LSTM network (WPD-LSTM) decomposed by a wavelet packet, a hybrid Bayesian support vector machine method (BE-SVM), and the like.
The hybrid model has the defects when processing non-stationary and nonlinear time series change complicated electricity price data: GA-BP lacks generalization ability and may fall into local optimum, resulting in poor prediction performance; the WT-ARIMA nonlinear and non-stationarity processing characteristics are not adequately processed, and the prediction capability of the WT-ARIMA nonlinear and non-stationarity processing characteristics can be limited due to high computational complexity; although PSO-LSSVM can deal with the nonlinearity problem to a certain extent, LS-SVM still can not completely capture the intrinsic law of the electricity price data with high nonlinearity, so that the prediction performance is affected; the performance of the BE-SVM method depends on the selection of parameters to a great extent, the parameter tuning is difficult, the parameter tuning is sensitive to noise, and although the SVM has strong robustness, in the electricity price prediction, if the noise is large or outliers exist, the prediction performance of the BE-SVM can BE affected.
Disclosure of Invention
The invention is provided in view of the problems of the existing electricity price prediction method based on EMD decomposition and SSA-SVM model. By utilizing the advantages of EMD on nonlinear and non-stationary data processing, the implicit information of the electricity price sequence is fully mined, and the accuracy of electricity price prediction is improved by combining the characteristics of strong SSA adaptability and good SVM generalization performance. Accordingly, the present invention is directed to a method and system for predicting electricity prices based on EMD decomposition and SSA-SVM models.
In order to solve the technical problems, the invention provides the following technical scheme:
in a first aspect, an embodiment of the present invention provides an EMD decomposition and SSA-SVM model-based electricity price prediction method, which includes obtaining original electricity price data, dividing the original electricity price data into a training set and a test set, and decomposing the electricity price data through an empirical mode decomposition algorithm EMD; constructing an SSA-SVM model, optimizing key parameters in the SVM model by applying a sparrow search algorithm SSA, and inputting the decomposed electricity price data into the model for prediction to obtain a predicted value under each characteristic signal; and carrying out accumulation reconstruction on predicted values output by the model to obtain a final predicted result, and carrying out electricity price prediction based on EMD decomposition and an SSA-SVM model.
As a preferable embodiment of the electricity price prediction method based on the EMD decomposition and SSA-SVM model of the present invention, wherein: the EMD decomposition method specifically comprises determining all maximum and minimum points on the original electricity price data signal X (t), and constructing the signal by using cubic spline interpolationUpper envelope x of (2) max (t) and lower envelope x min (t); calculating the mean value of the envelopeThe correlation calculation formula is as follows:
solving an intermediate condition function h of the original signal according to the original signal and the envelope mean value 1 (t) the correlation calculation formula is as follows:
if h 1 (t) satisfying the IMF condition, obtaining a first feature component of the IMF; if h 1 And (t) if the IMF condition is not met, repeating the calculation until the IMF condition is met, and obtaining an IMF component, wherein the related formula is as follows:
IMF 1 (t)＝h 1 (t)
IMF is to 1 (t) stripping the residual component r from the signal 1 (t) the correlation calculation formula is as follows:
r 1 (t)＝x(t)-IMF 1 (t)
by r 1 And (t) is a signal to be processed, and the related calculation formula is as follows:
x(t)＝r 1 (t)
and obtaining a final decomposition result until the decomposition cannot be performed again, wherein a related calculation formula is as follows:
wherein x (t) is the original electricity price data signal, r n And (t) is a residual component, namely a signal to be processed after the final decomposition is completed.
As a preferable embodiment of the electricity price prediction method based on the EMD decomposition and SSA-SVM model of the present invention, wherein: the construction of the SSA-SVM model specifically comprises the steps of constructing the SVM model, selecting a kernel function of the model, and determining key parameters to be selected in the kernel function; optimizing the sparrow search algorithm SSA, and determining key parameters in the kernel function by using the optimized sparrow search algorithm; inputting the signals to be processed after EMD decomposition into a sparrow search algorithm to obtain a prediction parameter result, substituting the obtained prediction parameter result into an SVM model for training, and inputting the obtained signals to be processed into the model for prediction after model training is completed.
As a preferable embodiment of the electricity price prediction method based on the EMD decomposition and SSA-SVM model of the present invention, wherein: the SVM model specifically comprises the steps of adding a Lagrangian function, and obtaining a dual form of an original optimization problem according to optimal conditions, wherein the related expression is as follows:
the constraint conditions are as follows:
wherein x is i For input vector, y i For the output vector, l is the training sample, ε is the insensitive loss function, C is the penalty parameter, α i Is Lagrangian multiplier and alpha i Not less than 0; setting a nonlinear mapping value phi, mapping the training sample with a high-dimensional space, performing linear regression, and introducing a kernel function K (x, y) to realize nonlinear regression, wherein an optimization equation is converted into:
K(x,x i )＝exp(-||x-x i || 2 /2g 2 )
wherein x is i G is a prediction parameter for an input vector.
As a preferable embodiment of the electricity price prediction method based on the EMD decomposition and SSA-SVM model of the present invention, wherein: the key parameters comprise a prediction parameter g and a penalty parameter C in the kernel function, and the key parameters in the kernel function are determined by using an optimized sparrow search algorithm, and specifically comprise subsequences obtained by decomposing an original electricity price data sequence, and intrinsic mode IMF and residual components are used as prediction inputs; and carrying out normalization processing on each subsequence, wherein a correlation calculation formula is as follows:
wherein x 'is' i For the normalized result of the ith point of the subsequence, x i Electricity price x for the ith point of the subsequence max And x min Maximum and minimum values for electricity prices in the subsequence; determining the number of optimization parameters as 2, iterating times, initializing a sparrow population position vector, setting the number of sparrows, and setting the ratio of discoverers to early warning persons and an early warning threshold; calculating the fitness of each sparrow individual to obtain the current optimal position of the sparrow with high fitness value; judging whether a position updating condition is met, and if so, updating the position; if not, reserving the current position; judging whether the search stopping condition is met, if so, stopping optimizing to obtain an optimal solution.
As a preferable embodiment of the electricity price prediction method based on the EMD decomposition and SSA-SVM model of the present invention, wherein: the optimized sparrow searching algorithm specifically comprises an initialized population, iteration times, the proportion of discoverers to followers, and the corresponding expression is as follows:
wherein n is the number of sparrows, and d represents the dimension attached to individual sparrows; calculating individual fitness of sparrows, and the related expression is as follows:
wherein F is X The fitness value of each row of sparrow individuals is calculated; the discoverer with stronger searching capability, namely better fitness value, can obtain food preferentially in the searching process, and can obtain a larger foraging searching range than the follower as the explorer; the position update of the discoverer in the iterative process is as follows:
in the method, in the process of the invention,represents the position of the ith sparrow in the j dimension of iteration t times, and alpha represents (0, 1]Random number within range, T max Represents the maximum iteration number, R 2 ∈[0,1]Representing early warning value, ST epsilon [0,1]]Representing a security value, Q is a random number subject to normal distribution, L 1 Representing a matrix of 1×d columns, and all elements are 1; when R is 2 <In ST, the situation that natural enemies do not exist around sparrows is indicated, and the seeker performs global searching; if R2 is more than or equal to ST, part of sparrows are found to be predators, all sparrows take relevant actions, and the individual position is updated; updating follower position:
in the method, in the process of the invention,represents the optimal position, # of the producer in the j dimension at iteration (t+1)>Representing the worst position in the whole population at the t-th iteration; a represents a matrix in which each element is randomly allocated 1 or-1, and A + ＝A T (AA T ) -1 The method comprises the steps of carrying out a first treatment on the surface of the When i is more than n/2, indicating that the follower is in a very starving state, and controlling the value of the follower to accord with normal distribution by utilizing the product of a standard normal distribution random number and an exponential function taking natural logarithm as a base, namely acquiring more energy; when i is less than or equal to n/2, randomly finding a position near the current optimal position; updating the alerter location:
wherein, beta represents a step control coefficient subject to a normal distribution with a mean value of 0 and a variance of 1, and K represents [ -1,1]Random number of interval, f i Representing the fitness value of the current sparrow individual, f g Represents the current global best fitness value, f w Representing a current global worst fitness value, c being a constant; when the early warning sparrow is at the current optimal position, the sparrow can escape to the position nearby the sparrow, and if the current position of the sparrow is not the optimal position, the sparrow escapes to the position nearby the current optimal position.
As a preferable embodiment of the electricity price prediction method based on the EMD decomposition and SSA-SVM model of the present invention, wherein: the prediction results comprise modeling each subsequence respectively, repeating to obtain respective prediction results, and carrying out cumulative reconstruction on all the prediction results to obtain a final electricity price prediction result; in evaluating the model predictive performance, the evaluation index includes root mean square error, deviation error, decision coefficient, mean absolute percentage error, and nash coefficient.
In a second aspect, an embodiment of the present invention provides an electricity price prediction system based on an EMD decomposition and SSA-SVM model, comprising: the acquisition module is used for acquiring original electricity price data, dividing the original electricity price data into a training set and a testing set, and decomposing the electricity price data through an empirical mode decomposition algorithm (EMD); constructing a prediction module, constructing an SSA-SVM model, optimizing key parameters in the SVM model by applying a sparrow search algorithm SSA, and inputting decomposed electricity price data into the model for prediction to obtain a predicted value under each characteristic signal; and the output module is used for carrying out accumulated reconstruction on the predicted values output by the model to obtain a final predicted result and carrying out electricity price prediction based on the EMD decomposition and the SSA-SVM model.
In a third aspect, embodiments of the present invention provide a computer apparatus comprising a memory and a processor, the memory storing a computer program, wherein: the processor, when executing the computer program, implements any of the steps of the method described above.
In a fourth aspect, embodiments of the present invention provide a computer-readable storage medium having a computer program stored thereon, wherein: which when executed by a processor performs any of the steps of the method described above.
The invention has the beneficial effects that the original electricity price data is decomposed by using the EMD, so that nonlinearity and non-stationarity can be effectively processed, and the accuracy of electricity price prediction is improved. Each decomposed sub-sequence can be modeled according to its specific frequency component, so that the model is better adapted to the real characteristics of electricity price data. The high frequency noise component can be separated from the electricity price data, thereby reducing the interference of noise on prediction. This helps to improve the robustness of the model, making it more capable of coping with outliers and fluctuations in electricity price data. EMD decomposition allows processing of different frequency components separately, helping to extract important information in electricity price data. Analysis of the different components can reveal trends, seasonality and periodicity in the electricity price data, so that the model can better understand the cause of electricity price fluctuation. The sparrow search algorithm SSA is used for optimizing key parameters in the SVM model, and through parameter optimization, the performance of the model can be improved, and the characteristic of better fitting of electricity price data is ensured. The SSA-SVM model has higher flexibility and can adapt to different types of electricity price data. Whether market price, consumer electricity price or other electricity price data types, different situations can be adapted by parameter adjustment. By decomposing and accumulating the prediction results, the contributions of the different frequency components in the electricity price data can be better understood. The method is beneficial to time series analysis and can better predict future electricity price trend and fluctuation. The high-precision electricity price prediction provides powerful support for energy market participants, optimizes an electricity purchasing strategy, reasonably plans electricity consumption requirements and reduces cost. Through improving the accuracy of electricity price prediction, the electric power market participants can manage the cost more effectively, reduce unnecessary expenses, improve the utilization efficiency of energy resources and realize better economic benefit.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for the description of the embodiments will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art. Wherein:
FIG. 1 is a flow chart of a method of price prediction based on EMD decomposition and SSA-SVM models.
Fig. 2 is an EMD exploded flow chart.
Fig. 3 is a support vector regression block diagram.
Fig. 4 is a flow chart of a sparrow optimization algorithm.
Fig. 5 is a diagram of historical electricity price data.
FIG. 6 is a graph showing a comparison of the forecast of the price of electricity generated by each algorithm.
Fig. 7 is a comparison chart of retail electricity price predictions for each algorithm.
FIG. 8 is a graph showing the comparison of the prediction index of the wholesale electricity price of each algorithm.
Fig. 9 shows a comparison of retail electricity price prediction indexes of the algorithms.
FIG. 10 is a box plot of the predicted price of electricity for each algorithm.
Fig. 11 shows a box plot of retail price prediction errors for each algorithm.
Detailed Description
So that the manner in which the above recited objects, features and advantages of the present invention can be understood in detail, a more particular description of the invention, briefly summarized above, may be had by reference to the embodiments, some of which are illustrated in the appended drawings. All other embodiments, which can be made by one of ordinary skill in the art based on the embodiments of the present invention without making any inventive effort, shall fall within the scope of the present invention.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, but the present invention may be practiced in other ways other than those described herein, and persons skilled in the art will readily appreciate that the present invention is not limited to the specific embodiments disclosed below.
Further, reference herein to "one embodiment" or "an embodiment" means that a particular feature, structure, or characteristic can be included in at least one implementation of the invention. The appearances of the phrase "in one embodiment" in various places in the specification are not necessarily all referring to the same embodiment, nor are separate or alternative embodiments mutually exclusive of other embodiments.
Example 1
Referring to fig. 1, a first embodiment of the present invention provides a method for predicting electricity prices based on EMD decomposition and SSA-SVM model, including:
s1: the method comprises the steps of obtaining original electricity price data, dividing the original electricity price data into a training set and a testing set, and decomposing the electricity price data through an empirical mode decomposition algorithm (EMD);
in particular, EMD decomposition is carried out on electricity price data, and signals are decomposed into a plurality of Intrinsic Mode Functions (IMFs) and residual components (Res);
empirical Mode Decomposition (EMD) is a powerful tool for analyzing and processing nonlinear, non-stationary signals, which can decompose complex data signals into a series of fundamental, physically meaningful, oscillating eigen-components, also called eigenmode functions (Intrinsic Mode Functions, IMFs), each IMF being a constituent of the original signal, which together constitute the overall structure of the original signal. Each IMF has unique frequency characteristics, and these frequency characteristics are time-varying. This makes EMD well suited for processing signals that vary significantly on a time scale, such as power load signals and the power price signals to which the present invention relates, among many practical signals in the scientific research and engineering fields.
The EMD decomposition process is an iterative process in which IMFs with highest frequencies are sequentially extracted from the original signal and then subtracted from the original signal to obtain a new residual signal. This process is repeated until the residual signal is no longer decomposed or a preset stop condition is reached. Finally, each IMF, as well as the residual signal, may further use the Hilbert transform to obtain its instantaneous frequency and instantaneous amplitude over time. Thus, the main characteristics of the signals can be extracted, and the dynamic behaviors and the internal structures of the original signals can be understood and analyzed more deeply.
The implementation mode of the invention for decomposing the electricity price signal by using EMD is as follows:
determining all maximum and minimum points on the original electricity price signal X (t), and constructing an upper envelope curve X of the signal by using a cubic spline interpolation method max (t) and lower envelope x min (t)。
The envelope mean value can be calculated according to the upper envelope curve and the lower envelope curve
Solving an intermediate condition function h of the original signal according to the original signal and the envelope mean value 1 (t)：
If h 1 (t) satisfying the IMF condition, obtaining a first component of the IMF; if h 1 (t) not meeting the IMF condition, repeating the steps 1) -2) until the IMF condition is met, and obtaining an IMF component:
IMF 1 (t)＝h 1 (t)
IMF is to 1 (t) stripping the residual component r from the signal 1 (t)：
r 1 (t)＝x(t)-IMF 1 (t)
Then r is used 1 (t) is the signal to be processed:
x(t)＝r 1 (t)
repeating the steps 1) -7) until the decomposition cannot be carried out, and obtaining a final decomposition result:
s2: and constructing an SSA-SVM model, optimizing key parameters in the SVM model by applying a sparrow search algorithm SSA, and inputting the decomposed electricity price data into the model for prediction to obtain a predicted value under each characteristic signal.
Support vector regression, which is applied to regression problems by SVM, is a powerful regression model based on the interval maximization principle and the kernel method, and attempts to find a function so that the error between the predicted value and the true value does not exceed a preset threshold and at the same time the complexity of the model is minimized. The advantage of support vector regression is that it can efficiently cope with both linear and non-linear regression problems, which can map the original feature space into a higher dimensional space by introducing a kernel function, finding the optimal regression function in this new feature space. Compared with logistic regression and neural networks, the support vector machine provides a clearer and more powerful way when learning complex nonlinear equations.
In the SVM, the minimum value of the precision omega in the linear regression function is obtained, the norm of the minimized Euclidean space is adopted to convert into an optimization problem, and the constraint optimization problem is not easy to solve because the constraint optimization problem relates to a nonlinear optimization problem, and the dual form of the original optimization problem is obtained according to the optimal condition by introducing the Lagrangian function:
the constraint conditions are as follows:
wherein x is i For input vector, y i For the output vector, l is the training sample, ε is the insensitive loss function, C is the penalty parameter, α i Is Lagrangian multiplier and alpha i ≥0。
When the nonlinear regression problem is solved, the nonlinear mapping value phi needs to be set first, so that the training sample and the high-dimensional space can be mapped effectively and subjected to linear regression. Since the above solution can only be used for inner product calculation in high dimensional space, a kernel function K (x, y) can be introduced here instead of < phi (x), phi (x) > thus enabling nonlinear regression whose optimization equation can be transformed into:
the SVM selects different kernel functions to influence the advantages and disadvantages of the algorithm, and Radial Basis Function (RBF) is selected as the kernel function:
K(x,x i )＝exp(-||x-x i || 2 /2g 2 )
electricity prices are related to a number of factors (e.g., weather conditions, supply and demand relationships, coal prices, etc.), which tend to be non-linear. The RBF core can effectively solve the nonlinear problem, has certain robustness to some noise data, has good generalization capability when the parameter selection is proper, and can also show good prediction performance on unseen data. After the kernel function is determined, parameters g of the Radial Basis Function (RBF) and penalty parameters C are selected. The support vector regression structure is shown in figure 2.
Sparrow search algorithm (Sparrow SearchAlgorithm, SSA) is an intelligent optimization algorithm proposed in 2020. The design inspiration of the algorithm is derived from the foraging behavior and the predation prevention behavior of sparrows. During the sparrow's foraging process, the sparrow population can be divided into two roles, a "finder" and a "follower". The "finder" is responsible for finding food in the environment and providing the entire sparrow population with the foraging area and direction, while the "follower" relies on the "finder" to obtain food.
In SSA algorithm, the behavior of the two sparrows is modeled as two search strategies for finding the optimal solution in the solution space of the optimization problem. Meanwhile, an early warning mechanism is also introduced into the algorithm. In each iteration, a part of sparrow individuals are selected for early warning, and if the current solution is found to possibly cause the optimization process to be in local optimum or other adverse conditions, the sparrow individuals can choose to discard the current solution and search other areas of the solution space. This gives it good global optimization and adaptability. The specific implementation steps are as follows:
initializing population, iteration number, discoverer and follower ratio
Wherein: n is the number of sparrow populations and d represents the dimension attached to individual sparrows.
Calculating fitness
Wherein: f (F) X Fitness value for each sparrow individual
The discoverer with strong searching capability, namely good fitness value, can obtain food preferentially in the searching process. As a seeker, it can obtain a larger search range for foraging than a follower.
The position update of the discoverer in the iterative process is as follows:
wherein:represents the position of the ith sparrow in the j dimension of iteration t times, and alpha represents (0, 1]Random number within range, T max Represents the maximum iteration number, R 2 ∈[0,1]Representing early warning value, ST epsilon [0,1]]Representing a security value, Q is a random number subject to normal distribution, L 1 A matrix of 1×d columns is represented, and all elements are 1.
When R is 2 <In ST, this means that there are no natural enemies around, and the seeker can perform a global search. If R2. Gtoreq.ST means that some sparrows have found predators, all sparrows need to take relevant action.
Updating follower position:
in the method, in the process of the invention,represents the optimal position, # of the producer in the j dimension at iteration (t+1)>Representing the worst position in the whole population at the t-th iteration; a represents a matrix (1 row, d column) with 1 or-1 randomly assigned to each element, and A + ＝A T (AA T ) -1 。
When i is larger than n/2, the pursuer is in a very hungry state, and the product of a standard normal distribution random number and an exponential function taking natural logarithm as a base is utilized to control the value of the random number to accord with normal distribution, namely more energy is acquired. When i is less than or equal to n/2, the process can be interpreted as randomly finding a position near the current optimal position, and the variance of the optimal position of each dimension is smaller, and the value is more stable.
Updating the alerter location:
wherein: beta represents a step control coefficient subject to a normal distribution with a mean value of 0 and a variance of 1, K represents [ -1,1]Random number of interval, f i Representing the fitness value of the current sparrow individual, f g Represents the current global best fitness value, f w Representing the current global worst fitness value, c represents a constant, avoiding the denominator being set to zero.
When the early warning sparrow is at the current optimal position, the sparrow can escape to a position nearby the sparrow. If the position is not the optimal position, the vehicle escapes to the vicinity of the current optimal position.
Searching the optimal value of g and C by SSA, specifically,
the intrinsic mode IMF and a residual component IMF-Res obtained by decomposing the original electricity price sequence by EMD are used as subsequences of the intrinsic mode IMF and the residual component IMF-Res, and the subsequences are used as input of subsequent prediction.
Normalizing each subsequence, wherein the normalized value is between 0 and 1, and the calculation mode is that the data and the minimum value of the column are subjected to difference, and then the difference is divided by the extremely difference:
wherein: x's' i For the normalized result of the ith point of the subsequence, x i Electricity price x for the ith point of the subsequence max And x min Is the maximum and minimum of electricity prices in the subsequence.
And determining the number of optimization parameters as 2, iterating times, initializing a sparrow population position vector in a C, g empirical value range, setting the number of sparrow populations, the ratio of discoverers to early warning persons and the early warning threshold.
And calculating the fitness of each sparrow individual, and obtaining the current optimal position of the sparrow with high fitness value.
Judging whether a position updating condition is met, and if so, updating the position; if not, the current position is reserved.
Judging whether the search stopping condition is met, if so, stopping optimizing, and thus obtaining the optimal solution.
Substituting the obtained optimal parameter g and penalty parameter C into a support vector machine model for training.
Modeling each subsequence respectively, repeating to obtain respective prediction results, then carrying out cumulative reconstruction on all the prediction results to obtain a final electricity price prediction result, and judging the prediction results by calculating indexes such as RMSE, R2, MAE, MBE and the like.
Constructing an SVM model, selecting a kernel function of the model, and determining key parameters to be selected in the kernel function; optimizing the sparrow search algorithm SSA, and determining key parameters in the kernel function by using the optimized sparrow search algorithm; inputting the signals to be processed after EMD decomposition into a sparrow search algorithm to obtain a prediction parameter result, substituting the obtained prediction parameter result into an SVM model for training, and inputting the obtained signals to be processed into the model for prediction after model training is completed.
S3: and carrying out accumulation reconstruction on predicted values output by the model to obtain a final predicted result, and carrying out electricity price prediction based on EMD decomposition and an SSA-SVM model.
Further, the embodiment also provides an electricity price prediction system based on EMD decomposition and SSA-SVM model, comprising: the acquisition module is used for acquiring original electricity price data, dividing the original electricity price data into a training set and a testing set, and decomposing the electricity price data through an empirical mode decomposition algorithm (EMD); constructing a prediction module, constructing an SSA-SVM model, optimizing key parameters in the SVM model by applying a sparrow search algorithm SSA, and inputting decomposed electricity price data into the model for prediction to obtain a predicted value under each characteristic signal; and the output module is used for carrying out accumulated reconstruction on the predicted values output by the model to obtain a final predicted result and carrying out electricity price prediction based on the EMD decomposition and the SSA-SVM model.
The embodiment also provides a computer device, which is suitable for the situation of an electricity price prediction method based on EMD decomposition and SSA-SVM model, and comprises the following steps: a memory and a processor; the memory is used for storing computer executable instructions and the processor is used for executing the computer executable instructions to implement all or part of the steps of the method according to the embodiments of the present invention as set forth in the embodiments above.
The present embodiment also provides a storage medium having stored thereon a computer program which, when executed by a processor, performs the method of any of the alternative implementations of the above embodiments. The storage medium may be implemented by any type or combination of volatile or nonvolatile Memory devices, such as static random access Memory (Static Random Access Memory, SRAM), electrically erasable Programmable Read-Only Memory (Electrically Erasable Programmable Read-Only Memory, EEPROM), erasable Programmable Read-Only Memory (Erasable Programmable Read OnlyMemory, EPROM), programmable Read-Only Memory (PROM), read-Only Memory (ROM), magnetic Memory, flash Memory, magnetic disk, or optical disk.
The storage medium according to the present embodiment belongs to the same inventive concept as the data storage method according to the above embodiment, and technical details not described in detail in the present embodiment can be seen in the above embodiment, and the present embodiment has the same advantageous effects as the above embodiment.
From the above, the invention decomposes the original electricity price data by using the EMD, can effectively process nonlinearity and non-stationarity, improves electricity price prediction accuracy, can model according to specific frequency components, and is better suitable for the real characteristics of the electricity price data. The high-frequency noise component is separated from the electricity price data, so that the interference of noise on prediction is reduced. The method is beneficial to improving the robustness of the model and can be used for coping with abnormal values and fluctuation in electricity price data. Allowing different frequency components to be processed separately facilitates extraction of important information in electricity price data. Analysis of the different components can reveal trends, seasonality and periodicity in the electricity price data, so that the model can better understand the cause of electricity price fluctuation. Through parameter optimization, the performance of the model can be improved, and the characteristic of better fitting electricity price data is ensured. The contribution of different frequency components in the electricity price data can be better understood by decomposing and accumulating the prediction results through parameter adjustment to adapt to different situations. The method is beneficial to time series analysis and can better predict future electricity price trend and fluctuation. The high-precision electricity price prediction provides powerful support for energy market participants, optimizes an electricity purchasing strategy, reasonably plans electricity consumption requirements and reduces cost. Through improving the accuracy of electricity price prediction, the electric power market participants can manage the cost more effectively, reduce unnecessary expenses, improve the utilization efficiency of energy resources and realize better economic benefit.
Example 2
Referring to fig. 2 to 11, for a second embodiment of the present invention, an electricity price prediction method based on EMD decomposition and SSA-SVM model is provided, and in order to verify the beneficial effects of the present invention, scientific demonstration is performed through economic benefit calculation and simulation experiments.
Taking the wholesale electricity price and retail electricity price of the Guizhou electricity-saving market as examples, collecting historical electricity price data of 2021 month 1 to 2023 month 6, inputting external factors which influence electricity price, namely net surfing electricity quantity and coal price, as characteristic quantities to SVM, POS-SVM, EMD-SSA-SVM and the EMD-SSA-SVM prediction model for prediction comparison, and adopting root mean square error (RSME), mean square error (MAE), deviation error (MBE), mean Absolute Percentage Error (MAPE), decision coefficient (R2) and Nash coefficient (NSE) as evaluation indexes to compare the prediction results of the models in indexes, wherein the indexes are shown in the following table:
table 1 comparison of the wholesale Power price predictions for each model
From the prediction result of the wholesale electricity price, the EMD-SSA-SVM prediction model is smaller than the other three models on RMSE, MAE, MBE, MAPE, so that the sensitivity of the EMD-SSA-SVM prediction model to larger errors is the lowest, the average value of absolute values of the prediction errors and the prediction error percentage are the smallest, and the prediction accuracy is the highest.
Table 2 comparison of retail price forecast indicators for each model
From the retail price prediction results, the RMSE of the EMD-SVR and EMD-SSA-SVR is lowest, the average of the squares of the prediction errors of these two models is smallest, and they are less sensitive to large errors.
The EMD-SSA-SVR has the lowest MAE, the smallest average of absolute values of prediction errors, and the MBE value is closer to zero, which means that the deviation between the predicted value and the actual value is the smallest. MAPE is very close for all models, but the minimum MAPE for EMD-SSA-SVR indicates the minimum relative prediction error percentage and the highest prediction accuracy. Overall, the prediction results of the EMD-SSA-SVR are more accurate, which has better prediction performance. From the box diagram of the prediction error, the distance between the quartiles of the prediction error of the EMD-SSA-SVM is minimum, the distribution of the error is concentrated, and the stability is good. The median is closest to zero, so that the deviation of the error is smaller, and the prediction is more accurate. The method can effectively improve the prediction accuracy of electricity price.
From the above, the invention decomposes the original electricity price data by using the EMD, can effectively process nonlinearity and non-stationarity, improves electricity price prediction accuracy, can model according to specific frequency components, and is better suitable for the real characteristics of the electricity price data. The high-frequency noise component is separated from the electricity price data, so that the interference of noise on prediction is reduced. The method is beneficial to improving the robustness of the model and can be used for coping with abnormal values and fluctuation in electricity price data. Allowing different frequency components to be processed separately facilitates extraction of important information in electricity price data. Analysis of the different components can reveal trends, seasonality and periodicity in the electricity price data, so that the model can better understand the cause of electricity price fluctuation. Through parameter optimization, the performance of the model can be improved, and the characteristic of better fitting electricity price data is ensured. The contribution of different frequency components in the electricity price data can be better understood by decomposing and accumulating the prediction results through parameter adjustment to adapt to different situations. The method is beneficial to time series analysis and can better predict future electricity price trend and fluctuation. The high-precision electricity price prediction provides powerful support for energy market participants, optimizes an electricity purchasing strategy, reasonably plans electricity consumption requirements and reduces cost. Through improving the accuracy of electricity price prediction, the electric power market participants can manage the cost more effectively, reduce unnecessary expenses, improve the utilization efficiency of energy resources and realize better economic benefit.
It should be noted that the above embodiments are only for illustrating the technical solution of the present invention and not for limiting the same, and although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that the technical solution of the present invention may be modified or substituted without departing from the spirit and scope of the technical solution of the present invention, which is intended to be covered in the scope of the claims of the present invention.
Claims (10)
1. An electricity price prediction method based on EMD decomposition and SSA-SVM model is characterized in that: comprising the steps of (a) a step of,
the method comprises the steps of obtaining original electricity price data, dividing the original electricity price data into a training set and a testing set, and decomposing the electricity price data through an empirical mode decomposition algorithm (EMD);
constructing an SSA-SVM model, optimizing key parameters in the SVM model by applying a sparrow search algorithm SSA, and inputting the decomposed electricity price data into the model for prediction to obtain a predicted value under each characteristic signal;
and carrying out accumulation reconstruction on predicted values output by the model to obtain a final predicted result, and carrying out electricity price prediction based on EMD decomposition and an SSA-SVM model.
2. The EMD decomposition and SSA-SVM model-based electricity price prediction method of claim 1, wherein: the decomposition by the empirical mode decomposition algorithm EMD specifically includes,
determining all maximum and minimum points on the original electricity price data signal X (t), and constructing a letter by using cubic spline interpolationUpper envelope x of the number max (t) and lower envelope x min (t)；
Calculating the mean value of the envelopeThe correlation calculation formula is as follows:
solving an intermediate condition function h of the original signal according to the original signal and the envelope mean value 1 (t) the correlation calculation formula is as follows:
if h 1 (t) satisfying the IMF condition, obtaining a first feature component of the IMF;
if h 1 And (t) if the IMF condition is not met, repeating the calculation until the IMF condition is met, and obtaining an IMF component, wherein the related formula is as follows:
IMF 1 (t)＝h 1 (t)
IMF is to 1 (t) stripping the residual component r from the signal 1 (t) the correlation calculation formula is as follows:
r 1 (t)＝x(t)-IMF 1 (t)
by r 1 And (t) is a signal to be processed, and the related calculation formula is as follows:
x(t)＝r 1 (t)
and obtaining a final decomposition result until the decomposition cannot be performed again, wherein a related calculation formula is as follows:
wherein x (t) is the original electricity price data signal, r n (t) is the residual component, i.e. the signal to be processed after the final decomposition is completed。
3. The EMD decomposition and SSA-SVM model-based electricity price prediction method of claim 2, wherein: the construction of the SSA-SVM model specifically includes,
constructing an SVM model, selecting a kernel function of the model, and determining key parameters to be selected in the kernel function;
optimizing the sparrow search algorithm SSA, and determining key parameters in the kernel function by using the optimized sparrow search algorithm;
inputting the signals to be processed after EMD decomposition into a sparrow search algorithm to obtain a prediction parameter result, substituting the obtained prediction parameter result into an SVM model for training, and inputting the obtained signals to be processed into the model for prediction after model training is completed.
4. A method of price prediction based on EMD decomposition and SSA-SVM model as claimed in claim 3, wherein: the SVM model specifically includes,
adding a Lagrangian function, and obtaining a dual form of the original optimization problem according to the optimal condition, wherein the related expression is as follows:
the constraint conditions are as follows:
wherein x is i For input vector, y i For the output vector, l is the training sample, ε is the insensitive loss function, C is the penalty parameter, α i Is Lagrangian multiplier and alpha i ≥0；
Setting a nonlinear mapping value phi, mapping the training sample with a high-dimensional space, performing linear regression, and introducing a kernel function K (x, y) to realize nonlinear regression, wherein an optimization equation is converted into:
K(x,x i )＝exp(-||x-x i || 2 /2g 2 )
wherein x is i G is a prediction parameter for an input vector.
5. The EMD decomposition and SSA-SVM model-based electricity price prediction method of claim 4, wherein: the key parameters comprise a prediction parameter g and a punishment parameter C in the kernel function, the key parameters in the kernel function are determined by using an optimized sparrow search algorithm, and the key parameters comprise,
the subsequence obtained by decomposing the original electricity price data sequence is used as the input of prediction, and the intrinsic mode IMF and residual components are used as the input of prediction;
and carrying out normalization processing on each subsequence, wherein a correlation calculation formula is as follows:
wherein x 'is' i For the normalized result of the ith point of the subsequence, x i Electricity price x for the ith point of the subsequence max And x min Maximum and minimum values for electricity prices in the subsequence;
determining the number of optimization parameters as 2, iterating times, initializing a sparrow population position vector, setting the number of sparrows, and setting the ratio of discoverers to early warning persons and an early warning threshold;
calculating the fitness of each sparrow individual to obtain the current optimal position of the sparrow with high fitness value;
judging whether a position updating condition is met, and if so, updating the position; if not, reserving the current position;
judging whether the search stopping condition is met, if so, stopping optimizing to obtain an optimal solution.
6. The EMD decomposition and SSA-SVM model-based electricity price prediction method of claim 5, wherein: the optimized sparrow search algorithm specifically comprises,
initializing population, iteration times, ratio of discoverers to followers, and the corresponding expression is as follows:
wherein n is the number of sparrows, and d represents the dimension attached to individual sparrows;
calculating individual fitness of sparrows, and the related expression is as follows:
wherein F is X The fitness value of each row of sparrow individuals is calculated;
the discoverer with stronger searching capability, namely better fitness value, can obtain food preferentially in the searching process, and can obtain a larger foraging searching range than the follower as the explorer;
the position update of the discoverer in the iterative process is as follows:
in the method, in the process of the invention,represents the position of the ith sparrow in the j dimension of iteration t times, and alpha represents (0, 1]Random number within range, T max Represents the maximum iteration number, R 2 ∈[0,1]Representing early warning value, ST epsilon [0,1]]Representing a security value, Q is a random number subject to normal distribution, L 1 Representing a matrix of 1×d columns, and all elements are 1;
when R is 2 <In ST, the situation that natural enemies do not exist around sparrows is indicated, and the seeker performs global searching;
if R2 is more than or equal to ST, part of sparrows are found to be predators, all sparrows take relevant actions, and the individual position is updated;
updating follower position:
in the method, in the process of the invention,represents the optimal position, # of the producer in the j dimension at iteration (t+1)>Representing the worst position in the whole population at the t-th iteration; a represents a matrix in which each element is randomly allocated 1 or-1, and A + ＝A T (AA T ) -1 ；
When i is more than n/2, indicating that the follower is in a very starving state, and controlling the value of the follower to accord with normal distribution by utilizing the product of a standard normal distribution random number and an exponential function taking natural logarithm as a base, namely acquiring more energy; when i is less than or equal to n/2, randomly finding a position near the current optimal position;
updating the alerter location:
wherein, beta represents a step control coefficient subject to a normal distribution with a mean value of 0 and a variance of 1, and K represents [ -1,1]Random number of interval, f i Representing the current hempFitness value f of sparrow individual g Represents the current global best fitness value, f w Representing a current global worst fitness value, c being a constant;
when the early warning sparrow is at the current optimal position, the sparrow can escape to the position nearby the sparrow, and if the current position of the sparrow is not the optimal position, the sparrow escapes to the position nearby the current optimal position.
7. The EMD decomposition and SSA-SVM model-based electricity price prediction method of claim 6, wherein: the prediction results comprise modeling each subsequence respectively, repeating to obtain respective prediction results, and carrying out cumulative reconstruction on all the prediction results to obtain a final electricity price prediction result; in evaluating the model predictive performance, the evaluation index includes root mean square error, deviation error, decision coefficient, mean absolute percentage error, and nash coefficient.
8. An EMD decomposition and SSA-SVM model-based electricity price prediction system, based on the EMD decomposition and SSA-SVM model-based electricity price prediction method according to any one of claims 1 to 7, characterized in that: comprising the steps of (a) a step of,
the acquisition module is used for acquiring original electricity price data, dividing the original electricity price data into a training set and a testing set, and decomposing the electricity price data through an empirical mode decomposition algorithm (EMD);
constructing a prediction module, constructing an SSA-SVM model, optimizing key parameters in the SVM model by applying a sparrow search algorithm SSA, and inputting decomposed electricity price data into the model for prediction to obtain a predicted value under each characteristic signal;
and the output module is used for carrying out accumulated reconstruction on the predicted values output by the model to obtain a final predicted result and carrying out electricity price prediction based on the EMD decomposition and the SSA-SVM model.
9. A computer device comprising a memory and a processor, the memory storing a computer program, characterized in that: the processor, when executing the computer program, implements the steps of the EMD decomposition and SSA-SVM model-based electricity price prediction method of any one of claims 1 to 7.
10. A computer-readable storage medium having stored thereon a computer program, characterized by: the computer program, when executed by a processor, implements the steps of the EMD decomposition and SSA-SVM model-based electricity price prediction method of any of claims 1 to 7.
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