CN115099448A - A Short-Term Load Forecasting Method Based on VMD-Prophet - Google Patents

Abstract

The invention discloses a short-term load prediction method based on VMD-Prophet, which can be used to improve the accuracy of short-term power load prediction. The method includes: on the basis of the Prophet prediction model, introducing VMD decomposition, using the prepared data set, and dividing it into a training set and a test set, the training set is used for model training, and the test set is used to evaluate the accuracy of the final model; Input the decomposed subsequences into the Prophet prediction model for prediction, and then accumulate the prediction results of each subsequence to obtain the final prediction result; then use the two indicators of mean absolute value percent error and root mean square error to predict the results. Finally, the load of the next day is predicted, and the same evaluation index is used. The experimental results show that the prediction results of other LSTM, SARIMA and Prophet models that do not decompose the input signal by VMD are not as good as VMD‑ The Prophet prediction model proves the advantages of the present invention in short-term load prediction, and can improve the accuracy of short-term load prediction.

Description

A Short-Term Load Forecasting Method Based on VMD-Prophet

Technical field:

The invention relates to the field of power load forecasting, and proposes a short-term load forecasting method based on VMD-Prophet, which is suitable for short-term load forecasting and improving forecasting effect.

Background technique:

Under the background of my country's rapid economic development, the prediction of power load has become an important and arduous task. High-precision short-term load forecasting is of great significance for the dispatching management department of the power system to formulate efficient and economical power generation plans, reasonably arrange unit output, ensure the safety and stability of the power system, improve economic benefits, and reduce unnecessary energy consumption. At the same time, with the development of smart grid, high-precision load forecasting has become an increasingly urgent need.

The VMD-Prophet prediction model decomposes the input original load sequence into subsequences with better regularity. Compared with empirical mode decomposition and wavelet decomposition, VMD can restore the original signal better and has better noise robustness . Compared with traditional time series forecasting methods, Prophet, a time series forecasting framework, has better flexibility, easily adapts to the seasonality of multiple seasons, and makes different assumptions about trends through analysis. The measured values do not have to be equally spaced, and there is no need to interpolate missing values, and the fitting speed is faster. Combining the two in short-term load forecasting can effectively improve the accuracy of load forecasting.

Invention content:

In order to solve the above problems, the present invention proposes a short-term load prediction method based on VMD-Prophet.

A short-term load forecasting method based on VMD-Prophet, characterized in that it comprises the following steps:

S1: Before bringing the original load sequence into the Prophet model for prediction, perform Variational Mode Decomposition (VMD) on it to obtain subsequences with better regularity;

S2: Using VMD decomposition, the fluctuating signal can be decomposed into sub-signals of eigenmode functions of K different frequency bands. The specific process is as follows:

When using VMD for K-order decomposition, it can be regarded as the following constrained variational problem, as shown in equation (1):

为模态函数u_k对应中心频率ω_k的指数项，j为虚数。where f(t) is the undecomposed main signal, {u _k }={u ₁ ,...,u _k } and {ω _k }={ω ₁ ,...,ω _k } represent the set of K-order modes and Center frequency. δ(t) is the Dirac distribution, * means convolution,

is the exponential term of the modal function _uk corresponding to the center frequency ω _k , and j is an imaginary number.

The augmented Lagrangian function is introduced to solve the optimal solution of the above-mentioned constrained variational problem, as shown in equation (2):

In the formula: α is the quadratic penalty factor, which is used to reduce the interference of Gaussian noise; λ is the Lagrange multiplier. The optimal solution and augmented Lagrangian function of the above constrained variational problem are solved using the alternate direction method of multipliers.

The final update process of VMD is as follows, as shown in equations (3)-(5):

分别为f(t)、

和λⁿ(t)的傅里叶变换；τ为更新参数；n为迭代参数。in the formula

are f(t),

and λ ⁿ (t) Fourier transform; τ is the update parameter; n is the iteration parameter.

For a given discrimination accuracy ε>0, if the following relationship is satisfied, as shown in equation (6), the VMD converges and the update is stopped.

S3: Bring the decomposed load subsequences into the Prophet prediction model for prediction, and finally accumulate the prediction results of each subsequence to obtain the final prediction result;

S4: The prediction results are evaluated using the mean absolute percentage error (MAPE) and the root mean square error (RMSE), as shown in the following formula (7) and formula (8):

In the formula: x _predicted is the load prediction result, and x _real is the real load value.

S5: VMD algorithm parameters are respectively set as: initial center frequency ω=0, convergence criterion e=10 ^-7 , quadratic penalty factor and decomposition order are finally set to α=2000, K=3 after repeated experiments.

S6: Based on the Anaconda platform, the programming language is Python, create a virtual environment with Python version 3.7, and complete the construction of the VMD-Prophet prediction model in Spyder;

S7: Implement the prediction of each load subsequence by the VMD-Prophet prediction model through Python programming in Spyder;

S8: Test the effect of the VMD-Prophet forecasting model on load forecasting in Spyder.

Further, the VMD algorithm described in S2 decomposes the original load sequence into subsequences with better regularity, and at the same time extracts some trend components or noise components that affect the prediction results existing in the prediction process separately, reducing the trend component or the noise component. The influence of noise components on the overall forecast of short-term power load.

Further, the Prophet prediction model described in S3 has good flexibility, can easily adapt to the seasonality of multiple seasons, and make different assumptions about the trend through analysis; in addition, the measured values do not need to be equally spaced, and no interpolation is required. Missing values, and the fitting speed is faster.

Further, for the evaluation index described in S4, the prediction result is evaluated by the mean absolute value percentage error and the root mean square error, and the prediction result is quantified.

Further, the VMD-Prophet load prediction model described in S6 can be implemented in Spyder through Python programming in the virtual environment created by the Anaconda platform, and directly decompose and predict the load sequence.

As mentioned above, a short-term load forecasting method based on VMD-Prophet provided by the present invention has the following effects:

1. First divide the prepared data into a training set and a test set. The training set is used for model training, and the test set is used to evaluate the accuracy of the final model. Then, based on the Prophet prediction model, VMD decomposition is introduced to decompose the original load. The sequence is decomposed into subsequences with better regularity, and the influence of trend component or noise component on the overall short-term power load forecast is reduced, and the decomposed subsequences are respectively input into the Prophet prediction model for prediction;

2. Compared with other models used for load forecasting, LSTM, SARIMA, and Prophet without VMD decomposition of the input signal, it is proved that the VMD-Prophet model has the best prediction effect.

The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

Description of drawings:

Fig. 1 is the prediction flow chart of a kind of short-term load prediction method based on VMD-Prophet of the present invention;

Fig. 2 is the load VMD decomposition result diagram of a kind of short-term load forecasting method based on VMD-Prophet of the present invention;

FIG. 3 is a comparison diagram of the original data of a short-term load forecasting method based on VMD-Prophet of the present invention, and each model prediction curve of LSTM, SARIMA, Prophet and VMD-Prophet.

FIG. 4 is a short-term load forecasting method based on VMD-Prophet of the present invention and the accuracy results of each model for load forecasting for a future day.

Detailed ways:

Refer to Figures 1-4. The specific steps of a VMD-Prophet-based short-term load forecasting method of the present invention are as follows:

1. a short-term load forecasting method based on VMD-Prophet, is characterized in that, comprises the steps:

S1: Before bringing the original load sequence into the Prophet model for prediction, perform Variational Mode Decomposition (VMD) on it to obtain subsequences with better regularity;

S2: Using VMD decomposition, the fluctuating signal can be decomposed into sub-signals of eigenmode functions of K different frequency bands. The specific process is as follows:

When using VMD for K-order decomposition, it can be regarded as the following constrained variational problem, as shown in equation (1):

为模态函数u_k对应中心频率ω_k的指数项，j为虚数。where f(t) is the undecomposed main signal, {u _k }={u ₁ ,...,u _k } and {ω _k }={ω ₁ ,...,ω _k } represent the set of K-order modes and Center frequency. δ(t) is the Dirac distribution, * means convolution,

is the exponential term of the modal function _uk corresponding to the center frequency ω _k , and j is an imaginary number.

The augmented Lagrangian function is introduced to solve the optimal solution of the above-mentioned constrained variational problem, as shown in equation (2):

In the formula: α is the quadratic penalty factor, which is used to reduce the interference of Gaussian noise; λ is the Lagrange multiplier. The optimal solution and augmented Lagrangian function of the above constrained variational problem are solved using the alternate direction method of multipliers.

The final update process of VMD is as follows, as shown in equations (3)-(5):

分别为f(t)、

和λⁿ(t)的傅里叶变换；τ为更新参数；n为迭代参数。in the formula

are f(t),

and λ ⁿ (t) Fourier transform; τ is the update parameter; n is the iteration parameter.

For a given discrimination accuracy ε>0, if the following relationship is satisfied, as shown in equation (6), the VMD converges and the update is stopped.

S3: Bring the decomposed load subsequences into the Prophet prediction model for prediction, and finally accumulate the prediction results of each subsequence to obtain the final prediction result;

S4: The prediction results are evaluated using the mean absolute percentage error (MAPE) and the root mean square error (RMSE), as shown in the following formula (7) and formula (8):

In the formula: x _predicted is the load prediction result, and x _real is the real load value.

S5: VMD algorithm parameters are respectively set as: initial center frequency ω=0, convergence criterion e=10 ^-7 , quadratic penalty factor and decomposition order are finally set to α=2000, K=3 after repeated experiments.

S6: Based on the Anaconda platform, the programming language is Python, create a virtual environment with Python version 3.7, and complete the construction of the VMD-Prophet prediction model in Spyder;

S7: Implement the prediction of each load subsequence by the VMD-Prophet prediction model through Python programming in Spyder;

S8: Test the effect of the VMD-Prophet forecasting model on load forecasting in Spyder.

2. a kind of short-term load forecasting method based on VMD-Prophet according to claim 1, is characterized in that: VMD algorithm decomposes original load sequence into the subsequence with better regularity, simultaneously some influences that exist in the forecasting process The trend component or noise component of the forecast result is extracted separately to reduce the influence of the trend component or noise component on the overall forecast of short-term power load.

3. a kind of short-term load forecasting method based on VMD-Prophet according to claim 1, is characterized in that: Prophet forecasting model has better flexibility, can easily adapt to the seasonality of multiple seasons, and by analyzing the trend Different assumptions are made; in addition, the measurements do not have to be equally spaced, there is no need to interpolate missing values, and the fit is faster.

4. a kind of short-term load forecasting method based on VMD-Prophet according to claim 1, it is characterized in that: with mean absolute value percent error and root mean square error to evaluate the forecast result, can better show forecast effect .

5. a kind of short-term load forecasting method based on VMD-Prophet according to claim 1, is characterized in that: VMD-Prophet load forecasting model, can in the virtual environment that Anaconda platform creates, realizes in Spyder through Python programming , directly decompose and forecast the load sequence, and its forecasting process is shown in Figure 1.

The prediction process of the VMD-Prophet model can be implemented through Python programming in the virtual environment created by the Anaconda platform, and can be directly used for load prediction to improve the accuracy of load prediction.

The VMD-Prophet model introduces VMD decomposition on the basis of the Prophet prediction model. The decomposition result is shown in Figure 2. The decomposed subsequences are respectively input into the Prophet prediction model for prediction, and then the prediction results are accumulated; then The prediction results were evaluated using two indicators, the mean absolute percentage error and the root mean square error.

Using the prepared data set, it is divided into training set and test set, the training set is used for model training, and the test set is used to evaluate the accuracy of the final model; The input signal is compared with the Prophet decomposed by VMD. The comparison curve between the original data and the predicted value of each model is shown in Figure 3, and the results of the prediction accuracy of each model are shown in Figure 4.

Claims (5)

1. A short-term load prediction method based on VMD-Prophet is characterized by comprising the following steps:

s1: before the original load sequence is brought into a Prophet model for prediction, performing Variational Modal Decomposition (VMD) on the original load sequence to obtain a subsequence with better regularity;

s2: the VMD decomposition is used to decompose the fluctuating signal into K eigenmode function sub-signals of different frequency bands, and the specific process is as follows:

when the VMD is used for K-order decomposition, the problem can be regarded as the following constraint variation problem, as shown in formula (1):

wherein f (t) is the undecomposed main signal, { u _k }＝{u ₁ ,…,u _k And { omega } and _k }＝{ω ₁ ,…,ω _k represents the set of K-order modes and the center frequency, respectively. δ (t) is a dirac distribution, representing a convolution,

as a function of mode u _k Corresponding to center frequency omega _k J is an imaginary number.

Introducing an augmented Lagrange function, and solving an optimal solution of the constraint variation problem, wherein the optimal solution is shown as a formula (2):

in the formula: alpha is a secondary penalty factor used for reducing the interference of Gaussian noise; λ is the lagrange multiplier. And solving the optimal solution of the constraint variation problem and the augmented Lagrangian function by using a multiplier alternating direction method.

The final VMD update process is as follows, as shown in equations (3) to (5):

in the formula

Respectively f (t),

And λ ⁿ (t) Fourier transform; tau is an updating parameter; and n is an iteration parameter.

If the predetermined discrimination accuracy ε > 0 satisfies the following relationship, as shown in equation (6), the VMD converges and the update is stopped.

S3: respectively bringing the decomposed load subsequences into a Prophet prediction model for prediction, and finally accumulating the prediction results of each subsequence to obtain a final prediction result;

s4: and (3) evaluating the prediction result by using two indexes of a mean absolute value percent error (MAPE) and a Root Mean Square Error (RMSE), wherein the indexes are specifically shown in the following formula (7) and formula (8):

in the formula: x is the number of _predicted As a result of load prediction, x _real The load is the real value.

S5: the VMD algorithm parameters are respectively set as: initial center frequency ω is 0 and convergence criterion e is 10 ^-7 After repeated experiments, the secondary penalty factor and the resolution order are finally set to be alpha equal to 2000 and K equal to 3.

S6: based on an Anaconda platform, the programming language is Python, a virtual environment with a Python version of 3.7 is created, and the building of a VMD-Prophet prediction model is completed in a Spyder;

s7: the prediction of the VMD-Prophet prediction model for each load subsequence is realized in Spyder through Python programming;

s8: the effect of the VMD-Prophet predictive model on load prediction was tested in Spyder.

2. The VMD-Prophet-based short-term load prediction method according to claim 1, wherein: the VMD algorithm decomposes the original load sequence into subsequences with better regularity, and simultaneously extracts trend components or noise components which influence the prediction result and exist in the prediction process independently, so that the influence of the trend components or the noise components on the short-term power load overall prediction is reduced.

3. The VMD-Prophet-based short-term load prediction method according to claim 1, wherein: the Prophet prediction model has better flexibility, can easily adapt to the seasonality of a plurality of seasons, and makes different assumptions on the trend through analysis; in addition, the measured values do not need to be distributed at equal intervals, interpolation missing values are not needed, and the fitting speed is high.

4. The VMD-Prophet-based short-term load prediction method according to claim 1, wherein: the prediction result is evaluated by the average absolute value percentage error and the root mean square error, so that the prediction effect can be better shown.

5. The VMD-Prophet-based short-term load prediction method according to claim 1, wherein: the VMD-Prophet load prediction model can be realized in a virtual environment created by an Anaconda platform through Python programming in a Spyder, and the decomposition and prediction of a load sequence are directly carried out.

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