CN110751342A - Power load time series prediction method based on MBG optimization - Google Patents

Power load time series prediction method based on MBG optimization Download PDF

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CN110751342A
CN110751342A CN201911037952.XA CN201911037952A CN110751342A CN 110751342 A CN110751342 A CN 110751342A CN 201911037952 A CN201911037952 A CN 201911037952A CN 110751342 A CN110751342 A CN 110751342A
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mbg
optimization
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power load
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周锋
陈俊东
朱培栋
于佳琪
郭文明
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Changsha University
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Abstract

The invention discloses a power load time sequence prediction method based on a small batch gradient descent optimization (MBG) algorithm. The method comprises the steps of firstly adopting a Combination (CM) model to model a power load time sequence, then adopting a small batch gradient descent optimization (MBG) algorithm to carry out online optimization on a parameter set of the CM model, and finally selecting a CM model order for carrying out online prediction on the power load time sequence according to a defined minimum information criterion. The method provided by the invention can effectively improve the real-time performance and accuracy of the power load time sequence prediction.

Description

Power load time series prediction method based on MBG optimization
Technical Field
The invention relates to the technical field of load time sequence prediction of a power system, in particular to a power load time sequence prediction method based on a small batch gradient descent optimization (MBG) algorithm.
Background
The method can be used for accurately predicting the power load, particularly predicting the power load in a short period, can be used for improving the influence of the load on a power system, and has important effects on making a more reasonable power generation plan for a power plant, reducing the cost, participating in power generation competition of a wind power plant and the like. The traditional short-term power load prediction models comprise an ARIMA model, a parametric regression model, a Kalman filtering model and the like. At present, with the rapid development of computer technology and the wide application of artificial intelligence technology in power systems, models such as neural networks, expert systems, support vector machines, etc. have also been applied to the prediction of power load time series. With the development of energy internet, the access of new energy and the enhancement of information between loads, the power grid puts higher requirements on the real-time performance and accuracy of data processing in load prediction, and how to solve the contradiction between the prediction real-time performance and accuracy of complex nonlinear models such as a neural network, an expert system, a support vector machine and the like is still a key scientific problem.
Previous studies have shown that a Combined (CM) model built by combining a neural network model and an autoregressive model can well integrate the advantages of the two. The established CM model can effectively avoid the problems of excessive nonlinear parameters, higher order and poorer real-time performance of the neural network caused by singly adopting the neural network model to optimize the power load time sequence, and can also effectively avoid the defect of weak nonlinear approximation capability caused by only adopting the autoregressive model. At present, parameter optimization methods for CM models include Levenberg-Marquardt methods, structured nonlinear optimization methods, variable projection algorithms and the like, but the methods are offline parameter optimization methods, and parameters of the models are fixed in an online prediction process, so that the accuracy and the real-time performance of the models are poor.
Disclosure of Invention
The invention aims to solve the technical problem of providing a power load time sequence prediction method based on a small batch gradient descent optimization (MBG) algorithm aiming at the defects of the prior art. According to the method, firstly, a Combined (CM) model is adopted to model a time sequence of the power load, then, an MBG algorithm is adopted to carry out online optimization on parameters of the CM model, and the method can remarkably improve the real-time performance and accuracy of the CM model on power load time prediction.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows: the MBG optimization-based power load time series prediction method comprises the following steps:
1) acquiring load data of a power system in real time to obtain power load time sequence data;
2) modeling the power load time series by adopting a CM model;
3) performing online optimization on the parameter set theta of the CM model designed in the step 2) by adopting a small batch gradient descent optimization (MBG) algorithm;
4) the minimum information criterion is used to select the order p and m of the optimal CM model.
In step 2), the CM model structure for modeling the power load time series is as follows:
Figure BDA0002252069870000021
wherein, ykIs the kth sample data of the electrical load ξkModeling error for the CM model; p and m are the order of the CM model; i | · | purple wind2Performing two-norm operation;
Figure BDA0002252069870000022
is a linear weight of the CM model, and n1＝0,1,...,p、n2＝0,1,...,m；
Figure BDA0002252069870000023
Is the center of the CM model, and n3＝1,...,m；wkIs the state vector of the CM model, and wk＝yk-1. By definition
Figure BDA0002252069870000024
Wherein: y isp,k＝[yk-1,yk-2,...,yk-p]T，And defines the parameter set θ ═ c to be optimized for the CM modelT,zT]TWherein c ═ c0,0,c1,0,...,cp,0,c0,1,c0,2,...,c0,m,c1,1,c1,2,...,c1,m,...,cp,1,cp,2,...,cp,m]T，z＝[z1,z2,...,zm]T(ii) a The CM model in step 2) can be finally transformed into yk＝μT(z,k)c+ξkIn the form of (1).
In step 3), a small batch gradient descent optimization (MBG) algorithm for optimizing the parameter set θ of the CM model in step 2) specifically includes the following steps:
(1) when k is 1, the MBG optimization algorithm is initialized. Selecting an initial value of a parameter set theta to be optimized
Figure BDA0002252069870000026
And vector
Figure BDA0002252069870000027
Andthe elements in the MBG optimization algorithm are set to be random quantities between 0 and 1, and the initial value of a convergence factor of the MBG optimization algorithm is set to be βθ,0Setting forgetting factor α of MBG optimization algorithm to be 0.92, setting termination error delta of MBG optimization algorithm to be 1 multiplied by 10-5。
(2) Real-time acquisition and storage of sampled data y of an electrical loadkUntil k is greater than or equal to l and l is greater than or equal to p>2. At this time, y is calculatedp,k＝[yk-1,yk-2,...,yk-p]T，Y(l,k)＝[yk,yk-1,...,yk-l+1]T。
(3) The MBG optimization algorithm waits for the optimization of the parameters from the k-1 step to the k step
Figure BDA0002252069870000029
The updating process is as follows: computing
Figure BDA00022520698700000210
Wherein wk＝yk-1(ii) a Computing
Figure BDA00022520698700000211
Wherein: y isp,k＝[yk-1,yk-2,...,yk-p]TAnd is and
Figure BDA0002252069870000031
calculating partial derivatives
Figure BDA0002252069870000032
Calculating an overall information vector of an algorithm
Figure BDA0002252069870000033
Stack matrix of calculation algorithm
Figure BDA0002252069870000034
And is
Figure BDA0002252069870000035
Computing
Figure BDA0002252069870000036
Calculating convergence factor of algorithm
Figure BDA0002252069870000037
And the forgetting factor α is equal to 0.92, and the model parameters at the moment are updated
Figure BDA0002252069870000038
(4) And judging whether the MBG optimization algorithm is terminated or continued to be optimized. Comparison
Figure BDA0002252069870000039
And
Figure BDA00022520698700000310
when in useIf so, k is k +1, and the Step goes to Step 3; otherwise, the MBG optimization process is ended, and a parameter N is defined to be k, and the MBG algorithm is optimized at the momentCM model parametersNamely, it is
In step4, the minimum information amount is defined as:
Figure BDA00022520698700000314
and (3) aiming at different CM model orders (p and m), the MBG optimization algorithm in the step 3) is repeatedly adopted to optimize the model parameters, and the minimum information quantity pi of the optimized CM model is calculated until a CM model order (p and m) which can enable the pi value to be minimum is found to be used as the optimal order of the CM model for online real-time prediction of the power load time sequence.
Compared with the prior art, the invention has the beneficial effects that: according to the invention, the CM model is adopted to model the power load time sequence, so that the problems of excessive neural network nonlinear parameters, higher order and poorer real-time performance caused by singly adopting the neural network model to optimize the power load time sequence are effectively avoided; meanwhile, the defect of weak nonlinear approximation capability caused by only adopting an autoregressive model is effectively avoided. According to the method, online optimization is performed on the parameters of the CM model by adopting an MBG optimization algorithm, so that the defect that the model parameters are fixed and unchanged in an online prediction process in an offline parameter optimization method is effectively overcome; meanwhile, compared with a random gradient descent optimization algorithm, the small-batch gradient descent optimization algorithm provided by the invention has higher precision.
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Fig. 1 is a schematic flow chart of a power load time series prediction method based on MBG optimization according to the present invention.
Detailed Description
The technical scheme of the invention is further explained by combining the attached figure 1 in the specification. With an active power time sequence of a certain mains power load as a specific embodiment, a flow diagram of the prediction method based on MBG optimization is shown in FIG. 1, and a specific implementation process of the technical scheme is as follows:
step 1: and collecting active power time sequence data of the power load between 15 days in the city by taking 8min as a sampling period, wherein the total number of the active power time sequence data is 2700 points, and the active power time sequence data is used for modeling the CM model in the step 2).
Step 2: the following CM model was used to model the power load time series:
Figure BDA0002252069870000041
in the above formula, ykIs the kth sample data of the electrical load ξkModeling error for the CM model; p and m are the order of the CM model; i | · | purple wind2Performing two-norm operation;
Figure BDA0002252069870000042
is a linear weight of the CM model, and n1＝0,1,...,p、n2＝0,1,...,m；
Figure BDA0002252069870000043
Is the center of the CM model, and n3＝1,...,m；wkIs the state vector of the CM model, and wk＝yk-1。
Definition of
Figure BDA0002252069870000044
Wherein: y isp,k＝[yk-1,yk-2,...,yk-p]T，
Figure BDA0002252069870000045
And is
Figure BDA0002252069870000046
Defining a parameter set θ ═ c to be optimized for the CM modelT,zT]TWherein c ═ c0,0,c1,0,...,cp,0,c0,1,c0,2,...,c0,m,c1,1,c1,2,...,c1,m,...,cp,1,cp,2,...,cp,m]T，z＝[z1,z2,...,zm]T. The CM model can eventually be transformed into a form with linear and non-linear parameter separations as follows:
yk＝μT(z,k)c+ξk(2)
and step 3: the specific calculation process of the small batch gradient descent optimization (MBG) algorithm for optimizing the parameter set theta of the CM model in the step 2) is as follows:
step 1: when k is 1, the MBG optimization algorithm is initialized. Selecting an initial value of a parameter set theta to be optimized
Figure BDA0002252069870000047
And vector
Figure BDA0002252069870000048
And
Figure BDA0002252069870000049
the elements in the MBG optimization algorithm are set to be random quantities between 0 and 1, and the initial value of a convergence factor of the MBG optimization algorithm is set to be βθ,0Setting forgetting factor α of MBG optimization algorithm to be 0.92, setting termination error delta of MBG optimization algorithm to be 1 multiplied by 10-5。
Step 2: real-time acquisition and storage of sampled data y of an electrical loadkUntil k is greater than or equal to l and l is greater than or equal to p>2. At this time, y is calculatedp,k＝[yk-1,yk-2,...,yk-p]T，Y(l,k)＝[yk,yk-1,...,yk-l+1]T。
Step 3: the MBG optimization algorithm waits for the optimization of the parameters from the k-1 step to the k step
Figure BDA00022520698700000410
The updating process is as follows: computing
Figure BDA0002252069870000051
Wherein wk＝yk-1(ii) a Computing
Figure BDA0002252069870000052
Wherein: y isp,k＝[yk-1,yk-2,...,yk-p]TAnd is and
Figure BDA0002252069870000053
calculating partial derivatives
Figure BDA0002252069870000054
Calculating an overall information vector of an algorithm
Figure BDA0002252069870000055
Stack matrix of calculation algorithm
Figure BDA0002252069870000056
And is
Figure BDA0002252069870000057
Computing
Figure BDA0002252069870000058
Calculating convergence factor of algorithmAnd the forgetting factor α is equal to 0.92, and the model parameters at the moment are updated
Figure BDA00022520698700000510
Step 4: and judging whether the MBG optimization algorithm is terminated or continued to be optimized. Comparison
Figure BDA00022520698700000511
And
Figure BDA00022520698700000512
when in useIf so, k is k +1, and the Step goes to Step 3; otherwise, the MBG optimization process is ended, and the parameter N is defined to be k, and then the CM model parameter optimized by the MBG algorithm is obtained at the moment
Figure BDA00022520698700000514
Namely, it is
Figure BDA00022520698700000515
And 4, step 4: the minimum information criterion is used to select the order p and m of the optimal CM model. The minimum amount of information defining the CM model is:
Figure BDA00022520698700000516
and (3) aiming at different CM model orders (p and m), the MBG optimization algorithm in the step 3) is repeatedly adopted to optimize the model parameters, and the minimum information quantity pi of the optimized CM model is calculated until a CM model order (p and m) which can enable the pi value to be minimum is found. The order of the CM model finally obtained in this specific embodiment is: (p-8 and m-3). The CM model (p 8 and m 3) is used to predict the time series of the active power of the utility power load online in real time.

Claims (5)

1. A power load time series prediction method based on MBG optimization is characterized by comprising the following steps:
1) acquiring load data of a power system in real time to obtain power load time sequence data;
2) modeling the power load time series by adopting a CM model;
3) performing online optimization on the parameter set theta of the CM model in the step 2) by adopting a small batch gradient descent optimization (MBG) algorithm;
4) the minimum information criterion is used to select the order p and m of the optimal CM model.
2. The MBG-optimization-based power load time series prediction method according to claim 1, wherein the CM model for modeling the power load time series in the step 2) has the following specific structure:
Figure FDA0002252069860000011
wherein, ykIs the kth sample data of the electrical load ξkModeling error for the CM model; p and m are the order of the CM model; i | · | purple wind2Performing two-norm operation;is a linear weight of the CM model, and n1＝0,1,...,p、n2＝0,1,...,m；Is the center of the CM model, and n3＝1,...,m；wkIs the state vector of the CM model, and wk＝yk-1。
3. The MBG-optimization-based power load time series prediction method according to claim 1, wherein in the step 2), the MBG-optimization-based power load time series prediction method is realized by defining
Figure FDA0002252069860000014
Wherein: y isp,k＝[yk-1,yk-2,...,yk-p]T，
Figure FDA0002252069860000015
And is
Figure FDA0002252069860000016
The CM model can be transformed into yk＝μT(z,k)c+ξkIn a form of (a), wherein: z is ═ z1,z2,...,zm]T，c＝[c0,0,c1,0,...,cp,0,c0,1,c0,2,...,c0,m,c1,1,c1,2,...,c1,m,...,cp,1,cp,2,...,cp,m]T。
4. The MBG-optimization-based power load time-series prediction method according to claim 1, wherein in step 3), a parameter set θ ═ c for the CM modelT,zT]TThe optimization method comprises the following steps of carrying out an optimized small batch gradient descent optimization (MBG) algorithm, wherein the specific optimization process comprises the following steps:
(1) when k is 1, the MBG optimization algorithm is initialized. Selecting an initial value of a parameter set theta to be optimized
Figure FDA0002252069860000017
And vector
Figure FDA0002252069860000018
And
Figure FDA0002252069860000019
the elements in the MBG optimization algorithm are set to be random quantities between 0 and 1, and the initial value of a convergence factor of the MBG optimization algorithm is set to be βθ,0Setting forgetting factor α of MBG optimization algorithm to be 0.92, setting termination error delta of MBG optimization algorithm to be 1 multiplied by 10-5。
(2) Real-time acquisition and storage of sampled data y of an electrical loadkUntil k is greater than or equal to l and l is greater than or equal to p>2. At this time, y is calculatedp,k＝[yk-1,yk-2,...,yk-p]T，Y(l,k)＝[yk,yk-1,...,yk-l+1]T。
(3) The MBG optimization algorithm waits for the optimization of the parameters from the k-1 step to the k step
Figure FDA0002252069860000021
The updating process is as follows: computing
Figure FDA0002252069860000022
Wherein wk＝yk-1(ii) a ComputingWherein: y isp,k＝[yk-1,yk-2,...,yk-p]TAnd is and
Figure FDA0002252069860000024
calculating partial derivativesCalculating an overall information vector of an algorithm
Figure FDA0002252069860000026
Stack matrix of calculation algorithm
Figure FDA0002252069860000027
And isComputing
Figure FDA0002252069860000029
Calculating convergence factor of algorithmAnd the forgetting factor α is equal to 0.92, and the model parameters at the moment are updated
Figure FDA00022520698600000211
(4) And judging whether the MBG optimization algorithm is terminated or continued to be optimized. Comparison
Figure FDA00022520698600000212
And
Figure FDA00022520698600000213
when in use
Figure FDA00022520698600000214
If so, k is k +1, and the Step goes to Step 3; otherwise, the MBG optimization process is ended, and the parameter N is defined to be k, and then the CM model parameter optimized by the MBG algorithm is obtained at the momentNamely, it is
Figure FDA00022520698600000216
5. The MBG-optimization-based power load time series prediction method according to claim 1, wherein in the step 4), the specific structure of the minimum information amount is as follows:
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