CN114091766B - CEEMDAN-LSTM-based space load prediction method - Google Patents

CEEMDAN-LSTM-based space load prediction method Download PDF

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CN114091766B
CN114091766B CN202111409054.XA CN202111409054A CN114091766B CN 114091766 B CN114091766 B CN 114091766B CN 202111409054 A CN202111409054 A CN 202111409054A CN 114091766 B CN114091766 B CN 114091766B
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肖白
高文瑞
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Abstract

The invention relates to a space load prediction method based on CEEMDAN-LSTM, which is characterized by comprising the following steps: firstly, carrying out singular value detection and correction on the actual measurement load data of each I-type cell based on a 3 sigma criterion; secondly, decomposing the corrected I-type cell load data into a plurality of eigenvalue components with different frequencies and different amplitudes by using a self-adaptive noise complete set empirical mode decomposition (CEEMDAN) technology; then respectively constructing a long-short-term memory neural network (LSTM) model of each intrinsic mode component to predict; and finally, accumulating all eigenvalue component prediction results to obtain a spatial load prediction result based on the class I cells in the target year, and obtaining a spatial load prediction result based on the class II cells by using a spatial power load meshing technology on the basis. The method has the advantages of science, reasonability, high accuracy, strong applicability and good effect.

Description

CEEMDAN-LSTM-based space load prediction method
Technical Field
The invention relates to a spatial load prediction method in an electric power system, in particular to a spatial load prediction method based on adaptive noise complete set empirical mode decomposition (complementary ensemble empirical mode decomposition with adaptive noise, CEEMDAN) and long-term memory neural network (long-short term memory neural networks, LSTM).
Background
Spatial power load prediction is a prediction of the magnitude and distribution of future power loads in an area to be predicted, and is also called spatial load prediction. The space load prediction is the basis of urban power grid planning, and the result provides important basis for the site selection and volume determination of power equipment, the safe scheduling of a system and the economic operation, and only if the accuracy of the space load prediction is improved, the construction and the use of a transformer substation, a feeder line, switching equipment and the like can be more reasonably guided, so that the investment and the operation of a power grid are more reasonable and economical. With the gradual maturation of support technologies such as measurement, communication, information physical fusion and the like, data acquired from a power distribution network are increased in mass, and how to effectively utilize the data to improve the space power load prediction effect is a problem to be solved urgently at present, and the document report and the practical application of a space load prediction method based on CEEMDAN-LSTM are not yet seen.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and establish a CEEMDAN-LSTM-based space load prediction method which is scientific, reasonable, high in applicability, good in effect and high in accuracy.
The technical scheme adopted for achieving the purpose is that the space load prediction method based on CEEMDAN-LSTM is characterized by comprising the steps of determining reasonable maximum values of daily loads of each I-type cell by utilizing a 3 sigma criterion, respectively decomposing daily reasonable maximum value time sequences of historical loads of each I-type cell into a plurality of intrinsic mode components (intrinsic mode function, IMF) by adopting a CEEMDAN technology, respectively constructing a corresponding LSTM model for each IMF component obtained by decomposition, and predicting, wherein the method comprises the following specific contents:
1) Determining a reasonable maximum for daily load per class I cell using the 3σ criterion
And (3) sequentially carrying out singular value detection and correction on the actual measurement data of the historical loads of each I-type cell by using a 3 sigma criterion, thereby determining the reasonable maximum value of each daily load of each I-type cell, and the specific method is as follows:
the sample with s data is denoted as [ X ] 1 ,X 2 ,…,X s ]；
(1) First calculate the arithmetic mean of the whole sampleEach data X in the sample 1 ,X 2 …, xs corresponds to the residual error V 1 ,V 2 ,…,V s Calculated with equation (1) and equation (2):
where p=1, 2, …, s, s is the number of data in the sample; x is X p Is the p-th data in the sample; v (V) p Is the residual error of the p-th data in the sample;
(2) the standard deviation σ of the whole sample is then calculated using equation (3):
(3) residual error V of each data 1 ,V 2 ,…,V s Taking absolute value and comparing with 3 sigma in turn, V p Satisfying formula (4), then it is considered to be V p Corresponding X p Is singular data;
|V p |＞3σ (4)
2) Decomposing the daily reasonable maximum time sequence of each class I cell historical load into a plurality of IMF components by CEEMDAN technology
Decomposing the daily reasonable maximum time sequence of each class I cell historical load into a plurality of IMF components under different time scales by adopting a CEEMDAN algorithm;
the CEEMDAN is an improved algorithm based on an empirical mode decomposition algorithm, and the CEEMDAN algorithm is an adaptive white noise sequence added at each stage of data decomposition, can extract load sequence characteristic information on different time scales under the condition of reducing average times, and obtains a plurality of IMF components with reconstruction errors close to 0, thereby avoiding the occurrence of a modal aliasing phenomenon and solving the problem of large reconstruction errors of the aggregate empirical mode decomposition, and the specific contents are as follows:
definition Y j (. Cndot.) is the calculation operator of the j-th IMF component obtained by empirical mode decomposition; f (n) is the original load time series; beta is an adaptive coefficient; b l (n) represents white noise sequences with standard normal distribution added at the time of the first experiment; f (f) l (n) a load time sequence after standard normal distribution white noise is added for the first experiment;the k IMF component obtained in the first empirical mode decomposition; k=1, 2, …, K representing the number of IMF components generated after empirical mode decomposition; />An mth IMF component generated for CEEMDAN; m=1, 2, …, M represents the number of IMF components generated after CEEMDAN decomposition;
(1) d times of experiments are carried out on the original load time series f (n), d new load time series are respectively formed, and the calculation formula is shown as formula (5):
f l (n)＝f(n)+β 0 b l (n) (5)
wherein, l=1, 2, …, d, d is the number of experiments; beta 0 Is an initial adaptive coefficient;
(2) respectively performing empirical mode decomposition on each new load time sequence, extracting respective first IMF component, and calculating average value to obtain first IMF component of CEEMDANAnd a first residual component r 1 (n) the calculation formulas are formulas (6) and (7):
(3) for the residual component r 1 (n) d experiments are carried out to construct d new sequences r 1 (n)+β 1 Y 1 (b l (n)) performing empirical mode decomposition on each new sequence until a first IMF component is obtained, and averaging to obtain a second IMF component of CEEMDANThe calculation formula is formula (8):
wherein beta is 1 Is the second adaptive coefficient;
(4) for each of the remaining stages, calculating to obtain the e-th residual component r of CEEMDAN e (n) and (e+1th) IMF componentsThe calculation formulas are formula (9) and formula (10):
wherein e=2, 3, …, M; beta e The e+1th adaptive coefficient;
5 repeatedly executing the step (4) until the number of the obtained extreme points of the residual components is not more than two, stopping the algorithm after the empirical mode decomposition is not decomposed any more, and finally decomposing the original signal sequence f (n) into M IMF components and a final residual component R (n) by using the formula (11) when the number of IMF components generated by CEEMDAN decomposition is M after the algorithm is stopped:
3) Respectively constructing a corresponding LSTM model for each IMF component obtained by decomposition and predicting
(1) Selecting LSTM neural network as prediction model
The LSTM neural network is a special cyclic neural network, three gate structures and a memory unit are added on the basis of the cyclic neural network, the daily reasonable maximum time sequence of the historical load of each I-type cell is used as the basis, the IMF components obtained by decomposing each sequence are respectively built into respective LSTM neural network models, the maximum value of the daily load of all I-type cells in a target year is predicted, and then the annual load maximum value of all I-type cells is obtained;
an LSTM neural network consists of an input layer, an hidden layer and an output layer, wherein the hidden layer consists of a plurality of memory unit modules;
at time t, the input of one memory cell module is represented by the input vector x at time t t State c of memory cell at last moment t-1 And state h of hidden layer at last moment t-1 Three parts; outputting the state c of the memory unit from the time t State h of hidden layer at this time t Two parts are formed; the module contains three doors inside: forget gate, input gate and output gate; the forgetting door controls whether to forget the cell information of the memory unit at the previous moment with a certain probability; the input gate determines how much information input at the current moment is stored to the current unit state; the output gate determines the information that the current cell is ultimately to output. The calculation formula is shown as formula (12-15);
f t ＝Sig(W hf h t-1 +U xf x t +B f ) (12)
i t ＝Sig(W hi h t-1 +U xi x t +B i ) (13)
v t ＝Tanh(W hc h t-1 +U xc x t +B c ) (14)
o t ＝Sig(W ho h t-1 +U xo x t +B o ) (15)
wherein f t 、i t 、o t Output results of the forget gate, the input gate and the output gate respectively, v t Representing new information input to the cell, W hc 、U xc Respectively represent h t-1 、x t And v t Is connected with the weight matrix; w (W) hf 、W hi 、W ho Respectively a forgetting door, an input door and an output door corresponding to h t-1 Weight matrix of U xf 、U xi 、U xo For forgetting door, input door, output door corresponding to x t Weight matrix of B f 、B i 、B o Bias vectors of the forget gate, the input gate and the output gate respectively; b (B) c A bias vector for the new information; sig represents a sigmoid activation function, and the input can control the output to be [0, 1] after the input passes through the activation function]Between them; tanh is a hyperbolic tangent activation function that scales the output between (-1, 1);
external output information c of memory unit module at time t t 、h t The calculation formulas of (1) are (16) - (17):
c t ＝f t ⊙c t-1 +i t ⊙v t (16)
h t ＝o t ⊙Tanh(c t ) (17)
wherein: the sense of point multiplication, i.e. the multiplication of the corresponding elements in the matrix;
(2) determining superparameters of LSTM neural networks
When constructing an LSTM neural network prediction model, the following super parameters of the model need to be determined first: input layer dimension, input layer time step number, hidden layer neuron number and output layer neuron number;
the number of input layers, the number of input layer time steps and the number of output layer neurons are determined by the input and output data; the hidden layers and the quantity of the neurons of the hidden layers influence the training and predicting effects of the neural network, so that the learning capacity and the training complexity of the model are comprehensively considered, and the hidden layers and the quantity of the neurons of the hidden layers are reasonably selected;
(3) training LSTM neural networks
Training the LSTM neural network by adopting a back propagation algorithm along with time and combining the set super parameters; the specific training steps are as follows:
a. after training data is transmitted to a neural network through an input layer, a predicted value is obtained through forward calculation of an initial weight and a bias value of an LSTM neuron;
b. reversely calculating according to a set loss function formula to obtain an error term of each LSTM neural network neuron;
c. selecting a proper optimizer, and adjusting the weight and the bias value through an error term to minimize a loss function;
after the weight and the bias value are adjusted for a plurality of times, the predicted value gradually approaches the expected value, and then an effective predicted model is obtained.
The invention provides a space load prediction method, which is a space load prediction method based on CEEMDAN-LSTM, and is characterized in that firstly, the singular value detection and the processing are carried out on the actual measurement load data of each I-type cell based on 3 sigma criterion; secondly, decomposing the processed I-type cell load data into a plurality of IMF components with different frequencies and different amplitudes by using CEEMDAN technology; then respectively constructing respective LSTM models for each IMF component to predict; finally, accumulating all IMF component prediction results to obtain a spatial load prediction result based on class I cells in the target year, and obtaining a spatial load prediction result based on class II cells by using a spatial power load meshing technology on the basis; engineering examples show that the method has the advantages of being scientific and reasonable, high in accuracy, strong in applicability and good in effect.
Drawings
FIG. 1 is a basic schematic diagram of a CEEMDAN-LSTM based spatial load prediction method;
FIG. 2 is a block diagram of an LSTM neural network memory cell module;
FIG. 3 is a diagram of land information within a administrative area;
FIG. 4 is a schematic diagram of class I cells within a administrative area;
FIG. 5 is a graph of the time series of loading of class I cells named \29682, spring line and CEEMDAN decomposition results;
FIG. 6 is a graph of the reconstructed error results after CEEMDAN decomposition;
FIG. 7 is a graph showing error distribution of prediction results of various spatial load prediction methods based on class I cells;
FIG. 8 is a quasi-measured graph of class II cell load for a target year for an area to be predicted;
FIG. 9 is a graph of a class II cell load prediction result of a target year of a region to be predicted, which is obtained by using a linear regression method;
FIG. 10 is a graph of a class II cell load prediction result of a target year of a region to be predicted, which is obtained by using a gray theory method;
FIG. 11 is a graph of a class II cell load prediction result of a target year of a region to be predicted, which is obtained by using an exponential smoothing method;
FIG. 12 is a graph of class II cell load prediction results for a target year for a region to be predicted using the LSTM method;
FIG. 13 is a graph of a class II cell load prediction result of a target year of an area to be predicted, which is obtained by the method of the invention;
FIG. 14 is a graph showing error distribution of prediction results based on various spatial load prediction methods of class II cells.
Detailed Description
The invention is further illustrated below with reference to fig. 1-14 and examples.
The invention relates to a space load prediction method based on CEEMDAN-LSTM, which comprises the steps of utilizing 3 sigma criterion, also called Laida criterion, to determine reasonable maximum value of each daily load of each I-type cell, adopting CEEMDAN technique to decompose the daily reasonable maximum value time sequence of each I-type cell historical load into a plurality of IMF components, respectively constructing a corresponding LSTM model for each IMF component obtained by decomposition, and predicting, wherein the specific contents are as follows:
1) Determining a reasonable maximum for daily load per class I cell using the 3σ criterion
The quality of the data used in the spatial load prediction will directly influence the accuracy of the prediction result; the load time sequence of the class I cell has multiple burrs, the base load is small and the fluctuation is large, and in the data acquisition process, the acquired data can be subjected to singular data in the measuring, converting and transmitting links; the maximum value is adopted for prediction in the planning-oriented spatial load prediction, and the actual measurement maximum value of the I-type cells is directly used for spatial load prediction, so that the prediction accuracy is reduced because the maximum value is singular data; for this reason, the 3 sigma criterion is utilized to sequentially detect and correct singular values of the measured data of the historical loads of each I-type cell, so as to determine the reasonable maximum value of each daily load of each I-type cell, and the specific method is as follows:
the sample with s data is denoted as [ X ] 1 ,X 2 ,…,X s ]；
(1) First calculate the arithmetic mean of the whole sampleEach data X in the sample 1 ,X 2 …, xs corresponds to the residual error V 1 ,V 2 ,…,V s Calculated with equation (1) and equation (2):
where p=1, 2, …, s, s is the number of data in the sample; x is X p Is the first in the samplep data; v (V) p Is the residual error of the p-th data in the sample;
(2) the standard deviation σ of the whole sample is then calculated using equation (3):
(3) residual error V of each data 1 ,V 2 ,…,V s Taking absolute value and comparing with 3 sigma in turn, V p Satisfying formula (4), then it is considered to be V p Corresponding X p Is singular data;
|V p |＞3σ (4)
2) Decomposing the daily reasonable maximum time sequence of each class I cell historical load into a plurality of IMF components by CEEMDAN technology
The class I cell load time sequence has random fluctuation, and the characteristic can make the built prediction model difficult to realize accurate prediction of load; in order to reduce adverse effects of random fluctuation on a prediction result, the prediction performance of a model is improved, and a CEEMDAN algorithm is adopted to decompose a daily reasonable maximum time sequence of historical loads of each class I cell into a plurality of IMF components under different time scales;
CEEMDAN is an algorithm that improves on the basis of empirical mode decomposition algorithms; the empirical mode decomposition is an algorithm for analyzing nonlinear and nonstationary signal sequences, has similarities with the wavelet decomposition, but does not need to preset a basis function, so that the problem of lack of adaptability in the selection of the wavelet decomposition basis function is avoided by the empirical mode decomposition; according to the algorithm, a complex signal is decomposed into a plurality of IMF components according to the characteristics of the signal, each IMF component corresponds to a local characteristic of the complex signal under a certain time scale, and each IMF component has stronger stationarity and regularity compared with an original sequence, but modal aliasing exists in the decomposed IMF components;
aiming at the defects of an empirical mode decomposition algorithm, aggregate empirical mode decomposition is proposed, white noise with zero mean value and fixed variance is added into an original signal in each decomposition process, so that the problem of mode aliasing in an empirical mode decomposition result is effectively solved, but white noise which is normally distributed and introduced in the decomposition process remains, and the error after reconstruction is large; for this reason, torres M E et al propose a CEEMDAN algorithm, which adds an adaptive white noise sequence at each stage of data decomposition, can extract load sequence characteristic information on different time scales under reduced average times, and obtain a plurality of IMF components with reconstruction errors close to 0, so as to avoid the occurrence of modal aliasing phenomenon and solve the problem of large reconstruction error of ensemble empirical mode decomposition, and the specific contents are as follows:
definition Y j (. Cndot.) is the calculation operator of the j-th IMF component obtained by empirical mode decomposition; f (n) is the original load time series; beta is an adaptive coefficient; b l (n) represents white noise sequences with standard normal distribution added at the time of the first experiment; f (f) l (n) a load time sequence after standard normal distribution white noise is added for the first experiment;the k IMF component obtained in the first empirical mode decomposition; k=1, 2, …, K representing the number of IMF components generated after empirical mode decomposition; />An mth IMF component generated for CEEMDAN; m=1, 2, …, M represents the number of IMF components generated after CEEMDAN decomposition;
(1) d times of experiments are carried out on the original load time series f (n), d new load time series are respectively formed, and the calculation formula is shown as formula (5):
f l (n)＝f(n)+β 0 b l (n) (5)
wherein, l=1, 2, …, d, d is the number of experiments; beta 0 Is an initial adaptive coefficient;
(2) empirical mode decomposition is performed on each new load time sequence, and the respective first IMF component is extracted and calculatedThe average value of the first IMF component of CEEMDAN is obtainedAnd a first residual component r 1 (n) the calculation formulas are formulas (6) and (7):
(3) for the residual component r 1 (n) d experiments are carried out to construct d new sequences r 1 (n)+β 1 Y 1 (b l (n)) performing empirical mode decomposition on each new sequence until a first IMF component is obtained, and averaging to obtain a second IMF component of CEEMDANThe calculation formula is formula (8):
wherein beta is 1 Is the second adaptive coefficient;
(4) for each of the remaining stages, calculating to obtain the e-th residual component r of CEEMDAN e (n) and (e+1th) IMF componentsThe calculation formulas are formula (9) and formula (10):
wherein e=2, 3, …, M; beta e The e+1th adaptive coefficient;
(5) and (3) repeatedly executing the step (4) until the number of the obtained residual component extreme points is not more than two, and stopping the algorithm after the empirical mode decomposition is not decomposed any more. At the termination of the algorithm, the CEEMDAN decomposition produces M IMF components, and the original signal sequence f (n) is finally decomposed into M IMF components and a final residual component R (n), where formula (11):
3) Respectively constructing a corresponding LSTM model for each IMF component obtained by decomposition and predicting
(1) Selecting LSTM neural network as prediction model
When the prior I-type cell is used as an object for space load prediction, a traditional feedforward neural network is adopted to construct a prediction model, the information in the feedforward neural network is propagated forwards layer by layer, and no feedback of other information except gradient information exists in the propagation process, so that the feedforward neural network ignores the time sequence relevance of the load sequence data; the circulating neural network is a neural network with a memory function, the feedback structure contained in the circulating neural network enables the output at the current moment to be determined by the influence generated by the input at the current moment and the previous input, the LSTM neural network is a special circulating neural network, and three gate structures and a memory unit are added on the basis of the circulating neural network, so that the problems of gradient dispersion and gradient explosion possibly occurring in the training process of the circulating neural network are effectively relieved, and the convergence speed of a model is accelerated; the long-term memory capacity of the LSTM neural network helps the LSTM neural network to obtain a remarkable improvement of the prediction precision in the field of time sequence prediction, and is very suitable for processing and predicting important events with relatively long intervals and delays in the time sequence; based on the daily reasonable maximum time sequence of the historical load of each I-type cell, respectively constructing respective LSTM neural network models for IMF components obtained by decomposing each sequence, predicting the maximum value of each daily load of all I-type cells in a target year, and further obtaining the annual load maximum value of all I-type cells;
an LSTM neural network is composed of an input layer, an hidden layer and an output layer, wherein the hidden layer is composed of a plurality of memory unit modules, and the overall structure diagram is shown in figure 2;
at time t, the input of one memory cell module is represented by the input vector x at time t t State c of memory cell at last moment t-1 And state h of hidden layer at last moment t-1 Three parts; outputting the state c of the memory unit from the time t State h of hidden layer at this time t Two parts are formed; the module contains three doors inside: forget gate, input gate and output gate; the forgetting door controls whether to forget the cell information of the memory unit at the previous moment with a certain probability; the input gate determines how much information input at the current moment is stored to the current unit state; the output gate determines the information that the current cell is ultimately to output. The calculation formula is shown as formula (12-15);
f t ＝Sig(W hf h t-1 +U xf x t +B f ) (12)
i t ＝Sig(W hi h t-1 +U xi x t +B i ) (13)
v t ＝Tanh(W hc h t-1 +U xc x t +B c ) (14)
o t ＝Sig(W ho h t-1 +U xo x t +B o ) (15)
wherein f t 、i t 、o t Output results of the forget gate, the input gate and the output gate respectively, v t Representing new information input to the cell, W hc 、U xc Respectively represent h t-1 、x t And v t Is connected with (a)A weight matrix; w (W) hf 、W hi 、W ho Respectively a forgetting door, an input door and an output door corresponding to h t-1 Weight matrix of U xf 、U xi 、U xo For forgetting door, input door, output door corresponding to x t Weight matrix of B f 、B i 、B o Bias vectors of the forget gate, the input gate and the output gate respectively; b (B) c A bias vector for the new information; sig represents a sigmoid activation function, and the input can control the output to be [0, 1] after the input passes through the activation function]Between them; tanh is a hyperbolic tangent activation function that scales the output between (-1, 1);
external output information c of memory unit module at time t t 、h t The calculation formulas of (1) are (16) - (17):
c t ＝f t ⊙c t-1 +i t ⊙v t (16)
h t ＝o t ⊙Tanh(c t ) (17)
wherein: the sense of point multiplication, i.e. the multiplication of the corresponding elements in the matrix;
(2) determining superparameters of LSTM neural networks
Different from the weight and the bias value obtained by training the neural network, the super-parameters refer to parameters manually set before training the model, and the performance of the neural network is affected; when constructing an LSTM neural network prediction model, the following super parameters of the model need to be determined first: input layer dimension, input layer time step number, hidden layer neuron number and output layer neuron number;
the number of input layers, the number of input layer time steps and the number of output layer neurons are determined by the input and output data; the hidden layers and the quantity of the neurons of the hidden layers influence the training and predicting effects of the neural network, the quantity is small, the generalization of the trained model is poor, the quantity is too large, the model structure is more complex, and the overfitting phenomenon is caused; therefore, in practical application, the learning capacity and the training complexity of the model are comprehensively considered, and the hidden layers and the quantity of neurons thereof are reasonably selected;
training LSTM neural network
The training algorithms of LSTM neural networks are mainly two kinds: a real-time recursive learning algorithm and a back propagation over time algorithm; compared with a real-time recursion learning algorithm, the backward propagation algorithm has clear concept and higher calculation efficiency; therefore, the LSTM neural network is trained by adopting a backward propagation algorithm with time and combining with the set super-parameters; the specific training steps are as follows:
a. after training data is transmitted to a neural network through an input layer, a predicted value is obtained through forward calculation of an initial weight and a bias value of an LSTM neuron;
b. reversely calculating according to a set loss function formula to obtain an error term of each LSTM neural network neuron;
d. selecting a proper optimizer, and adjusting the weight and the bias value through an error term to minimize a loss function;
after the weight and the bias value are adjusted for a plurality of times, the predicted value gradually approaches the expected value, and then an effective predicted model is obtained. Referring to FIG. 1, the invention is a CEEMDAN-LSTM based spatial load prediction method, comprising the following steps:
1) Determining a reasonable maximum for daily load per class I cell using the 3σ criterion
Fig. 3 and fig. 4 are a land information diagram and a corresponding class I cell layer of an area to be measured, respectively, and the method for establishing the land information diagram and the class I cell layer is as follows: firstly, selecting a region to be predicted, wherein the geographic coordinate of the region is 43.77543-43.87488 degrees in North latitude and 126.47445-126.55759 degrees in east longitude. According to the collected regional planning scheme, firstly dividing the land type of the region to be predicted into the following 8 types: the method comprises the steps of marking areas of different types with different colors to obtain a land information layer, wherein the land information layer is used for civilian use, commercial use, cultural entertainment use, industrial use, administrative use, greening use, municipal facility use and special use; and establishing a class I cell layer corresponding to the 10kV feeder line according to the power supply range of the 10kV feeder line.
As can be seen from analysis of the measured historical load data of the class I cells, the sampling period of each 10kV feeder gateway table is 5 minutes, namely 288 load data values are generated in one day of each class I cell. The historical load data of each class I cell 2009-2012 is grouped into 288 groups, and the 3 sigma criterion is adopted to detect the singular data in sequence. For the detected single-point singular values, adopting the average value of the day to replace the single-point singular values; for the detected continuous singular values, the data of the time period before and after the time of the data and the data of the similar days are used for reasonable replacement. And extracting the maximum load value of each day in each modified class I cell load sequence to form respective daily reasonable maximum load time sequences.
2) Decomposing the daily reasonable maximum time sequence of each class I cell historical load into a plurality of IMF components by CEEMDAN technology
And decomposing the obtained daily reasonable maximum time sequence of the historical load of each class I cell by adopting CEEMDAN technology, wherein in the process, the self-adaptive coefficient, the maximum iteration number and the white noise adding number are required to be determined. The adaptive coefficient is set to 0.2, the maximum iteration number is set to 500, and the number of white noise addition is set to 100, based on the characteristics of the data itself, because the adaptive coefficient is set to 0.01 to 0.5 and the number of white noise addition and the maximum iteration number are too large.
FIG. 5 shows the class I cell loading sequence of a line and the CEEMDAN decomposition result. It can be seen that the sequence is decomposed into nine IMF components, arranged from high to low frequency, and one residual component, each with reduced random ripple. Among these components, the load characterizing the random fluctuation is expressed in the form of a high-frequency component, and a component having a zero-crossing rate of more than 0.01 is regarded as a high-frequency component, and a component having a zero-crossing rate of less than 0.01 is regarded as a low-frequency component. In fig. 5, IMF1-IMF7 are high frequency components, but the amplitudes of these components are low, and the prediction error appears very small in front of the global error; the IMF8, IMF9 and residual components which have relatively large influence on the prediction result are more regular and stable, so that the LSTM can exert strong nonlinear fitting capability.
The obtained IMF components and residual components are reconstructed and compared with the original sequence, and the obtained reconstruction error map is shown in fig. 6. As can be seen from fig. 6, the reconstruction error of the reconstructed load sequence is close to 0 and can be ignored.
3) Respectively constructing a corresponding LSTM model for each IMF component obtained by decomposition and predicting
When an LSTM prediction model is constructed for each IMF component, the first 70% of each IMF component is taken as a training set, the remaining 30% is taken as a test set, the loss function of the model adopts mean square error, the initial learning rate is set to be 0.05, the maximum iteration number is set to be 250, the internal parameters are optimized by using an adaptive moment estimation method, and finally, the super parameters of each model are determined as follows through multiple experiments: the dimension of the input layer is 1; the input layer time step number is 7; the number of neurons of the output layer is 1; the hidden layer number is a single layer, and the number of neurons in the layer is 16. And finally, predicting the test set of each IMF component by using the constructed LSTM model.
In addition, in order to improve the convergence rate and the prediction accuracy of the model, normalization and inverse normalization processing are required to be performed on the data, namely, the data is normalized to be a dimensionless value between [ -1,1], and after training and prediction are completed, the result is normalized to be inverse, so that a prediction result with an initial dimension is obtained.
In order to verify the accuracy of the CEEMDAN-LSTM prediction method, the prediction results of the method are compared with the prediction results of the linear regression method, the gray theory method, the exponential smoothing method and the LSTM method, respectively, table 1 is the obtained partial load prediction results of the class I cells, and table 2 is the total error of the load prediction results of the class I cells of each method.
TABLE 1 spatial load prediction results based on class I cells for a target year
TABLE 2 general prediction error for a target year based on class I cell load
As can be seen from Table 2, compared with the linear regression method, the gray theory method, the exponential smoothing method and the LSTM method, the average absolute error index of the SLF method based on CEEMDAN-LSTM provided by the invention is respectively reduced by 0.5524MW, 0.549MW, 0.3605MW and 0.245MW, and the average relative error index is respectively reduced by 21.53%, 22.26%, 15.69% and 6.4%.
In order to examine the error distribution of cells, statistics are performed on the number of cells in each relative error interval in the prediction result of each SLF method, and fig. 6 is a statistical result. As can be seen from FIG. 6, the relative error of 23 cells in the CEEMDAN-LSTM-based SLF results is less than 20%, which accounts for 79.3% of all 29 cells, which are respectively superior to 44.8%, 37.9%, 51.7% and 65.5% of the linear regression method, the gray theory method, the exponential smoothing method and the LSTM method.
In the power geographic information system, class II cells are generated according to an equal-size square grid with the side length of 0.3km, a space power load meshing technology is adopted, an SLF result based on class I cells is converted into an SLF result based on class II cells, and statistics is carried out on the proportion of the number of class II cells in each relative error interval to the total number of cells in the area to be predicted, as shown in fig. 7-14. Since the number of class II cells is numerous, only the specific case of the SLF results of a portion of the cells is given at length, as shown in Table 3. The average overall error in class II cell loading for the various SLF methods is shown in table 4.
TABLE 3 spatial load prediction results based on class II cells for the target year
TABLE 4 general prediction error for target years based on class II cell load
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As can be seen from Table 4, compared with the CEEMDAN-LSTM-based spatial load prediction method, the average absolute error index is respectively reduced by 0.0619MW, 0.0532MW, 0.0521MW and 0.0304MW, and the average relative error index is respectively reduced by 18.63%, 14.72%, 18.25% and 7.13% by adopting the linear regression method, the gray theory method, the exponential smoothing method and the LSTM method. In addition, as can be seen from fig. 14, the CEEMDAN-LSTM based spatial load prediction method has a relative prediction error of less than 40% for all class II cells, wherein 77% of the class II cells have a relative prediction error of less than 10% and are far higher than the other 4 spatial load prediction methods. Therefore, compared with other 4 methods, the spatial load prediction method based on CEEMDAN-LSTM provided by the invention can better realize spatial load prediction.
The particular embodiments used in the present invention have been described in detail with respect to the present invention, but are not limited to the embodiments, and any obvious modifications will be apparent to those skilled in the art from the teachings of the present invention, and are within the scope of the appended claims.

Claims (1)

1. A space load prediction method based on CEEMDAN-LSTM is characterized by comprising the steps of determining reasonable maximum values of daily loads of each class I cell by using 3 sigma criterion, respectively decomposing a daily reasonable maximum value time sequence of historical loads of each class I cell into a plurality of IMF components by using CEEMDAN technology, respectively constructing a corresponding LSTM model for each IMF component obtained by decomposition, and predicting, wherein the specific contents are as follows:
1) Determining a reasonable maximum for daily load per class I cell using the 3σ criterion
And (3) sequentially carrying out singular value detection and correction on the actual measurement data of the historical loads of each I-type cell by using a 3 sigma criterion, thereby determining the reasonable maximum value of each daily load of each I-type cell, and the specific method is as follows:
the sample with s data is denoted as [ X ] 1 ,X 2 ,…,X s ]；
(1) First calculate the arithmetic mean of the whole sampleEach data X in the sample 1 ,X 2 …, xs corresponds to the residual error V 1 ,V 2 ,…,V s Calculated with equation (1) and equation (2):
where p=1, 2, …, s, s is the number of data in the sample; x is X p Is the p-th data in the sample; v (V) p Is the residual error of the p-th data in the sample;
(2) the standard deviation σ of the whole sample is then calculated using equation (3):
(3) residual error V of each data 1 ,V 2 ,…,V s Taking absolute value and comparing with 3 sigma in turn, V p Satisfying formula (4), then it is considered to be V p Corresponding X p Is singular data;
|V p |＞3σ (4)
2) Decomposing the daily reasonable maximum time sequence of each class I cell historical load into a plurality of IMF components by CEEMDAN technology
Decomposing the daily reasonable maximum time sequence of each class I cell historical load into a plurality of IMF components under different time scales by adopting a CEEMDAN algorithm;
the CEEMDAN is an improved algorithm based on an empirical mode decomposition algorithm, and the CEEMDAN algorithm is an adaptive white noise sequence added at each stage of data decomposition, can extract load sequence characteristic information on different time scales under the condition of reducing average times, and obtains a plurality of IMF components with reconstruction errors close to 0, thereby avoiding the occurrence of a modal aliasing phenomenon and solving the problem of large reconstruction errors of the aggregate empirical mode decomposition, and the specific contents are as follows:
definition Y j (. Cndot.) is the calculation operator of the j-th IMF component obtained by empirical mode decomposition; f (n) is the original load time series; beta is an adaptive coefficient; b l (n) represents white noise sequences with standard normal distribution added at the time of the first experiment; f (f) l (n) a load time sequence after standard normal distribution white noise is added for the first experiment;the k IMF component obtained in the first empirical mode decomposition; k=1, 2, …, K representing the number of IMF components generated after empirical mode decomposition;an mth IMF component generated for CEEMDAN; m=1, 2, …, M represents the number of IMF components generated after CEEMDAN decomposition;
(1) d times of experiments are carried out on the original load time series f (n), d new load time series are respectively formed, and the calculation formula is shown as formula (5):
f l (n)＝f(n)+β 0 b l (n) (5)
wherein, l=1, 2, …, d, d is the number of experiments; beta 0 Is an initial adaptive coefficient;
(2) respectively performing empirical mode decomposition on each new load time sequence, extracting respective first IMF component, and calculating average value to obtain first IMF component of CEEMDANAnd a first residual component r 1 (n) the calculation formulas are formulas (6) and (7):
(3) for the residual component r 1 (n) d experiments are carried out to construct d new sequences r 1 (n)+β 1 Y 1 (b l (n)) performing empirical mode decomposition on each new sequence until a first IMF component is obtained, and averaging to obtain a second IMF component of CEEMDANThe calculation formula is formula (8):
wherein beta is 1 Is the second adaptive coefficient;
(4) for each of the remaining stages, calculating to obtain the e-th residual component r of CEEMDAN e (n) and (e+1th) IMF componentsThe calculation formulas are formula (9) and formula (10):
wherein e=2, 3, …, M; beta e The e+1th adaptive coefficient;
(5) repeatedly executing the step (4) until the number of the obtained extreme points of the residual components is not more than two, stopping the algorithm by decomposing the empirical mode decomposition, wherein the number of IMF components generated by CEEMDAN decomposition is M when the algorithm is stopped, and finally decomposing the original signal sequence f (n) into M IMF components and a final residual component R (n), wherein the formula is shown as the formula (11):
3) Respectively constructing a corresponding LSTM model for each IMF component obtained by decomposition and predicting
(1) Selecting LSTM neural network as prediction model
The LSTM neural network is a special cyclic neural network, three gate structures and a memory unit are added on the basis of the cyclic neural network, the daily reasonable maximum time sequence of the historical load of each I-type cell is used as the basis, the IMF components obtained by decomposing each sequence are respectively built into respective LSTM neural network models, the maximum value of the daily load of all I-type cells in a target year is predicted, and then the annual load maximum value of all I-type cells is obtained;
an LSTM neural network consists of an input layer, an hidden layer and an output layer, wherein the hidden layer consists of a plurality of memory unit modules;
at time t, the input of one memory cell module is represented by the input vector x at time t t State c of memory cell at last moment t-1 And state h of hidden layer at last moment t-1 Three parts; outputting the state c of the memory unit from the time t State h of hidden layer at this time t Two parts are formed; the module contains three doors inside: forget gate, input gate and output gate; the forgetting door controls whether to forget the cell information of the memory unit at the previous moment with a certain probability; conveying deviceEntry determines how much information input at the current moment is saved to the current unit state; the output gate determines the information to be finally output by the current unit, and the calculation formula of the output gate is shown in formulas (12-15);
f t ＝Sig(W hf h t-1 +U xf x t +B f ) (12)
i t ＝Sig(W hi h t-1 +U xi x t +B i ) (13)
v t ＝Tanh(W hc h t-1 +U xc x t +B c ) (14)
o t ＝Sig(W ho h t-1 +U xo x t +B o ) (15)
wherein f t 、i t 、o t Output results of the forget gate, the input gate and the output gate respectively, v t Representing new information input to the cell, W hc 、U xc Respectively represent h t-1 、x t And v t Is connected with the weight matrix; w (W) hf 、W hi 、W ho Respectively a forgetting door, an input door and an output door corresponding to h t-1 Weight matrix of U xf 、U xi 、U xo For forgetting door, input door, output door corresponding to x t Weight matrix of B f 、B i 、B o Bias vectors of the forget gate, the input gate and the output gate respectively; b (B) c A bias vector for the new information; sig represents a sigmoid activation function, and the input can control the output to be [0, 1] after the input passes through the activation function]Between them; tanh is a hyperbolic tangent activation function that scales the output between (-1, 1);
external output information c of memory unit module at time t t 、h t The calculation formulas of (1) are (16) - (17):
c t ＝f t ⊙c t-1 +i t ⊙v t (16)
h t ＝o t ⊙Tanh(c t ) (17)
wherein: the sense of point multiplication, i.e. the multiplication of the corresponding elements in the matrix;
(2) determining superparameters of LSTM neural networks
When constructing an LSTM neural network prediction model, the following super parameters of the model need to be determined first: input layer dimension, input layer time step number, hidden layer neuron number and output layer neuron number;
the number of input layers, the number of input layer time steps and the number of output layer neurons are determined by the input and output data; the hidden layers and the quantity of the neurons of the hidden layers influence the training and predicting effects of the neural network, so that the learning capacity and the training complexity of the model are comprehensively considered, and the hidden layers and the quantity of the neurons of the hidden layers are reasonably selected;
(3) training LSTM neural networks
Training the LSTM neural network by adopting a back propagation algorithm along with time and combining the set super parameters; the specific training steps are as follows:
a. after training data is transmitted to a neural network through an input layer, a predicted value is obtained through forward calculation of an initial weight and a bias value of an LSTM neuron;
b. reversely calculating according to a set loss function formula to obtain an error term of each LSTM neural network neuron;
c. selecting a proper optimizer, and adjusting the weight and the bias value through an error term to minimize a loss function;
after the weight and the bias value are adjusted for a plurality of times, the predicted value gradually approaches the expected value, and then an effective predicted model is obtained.
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