CN107832259A - A kind of load forecasting method based on time series and Kalman filtering - Google Patents
A kind of load forecasting method based on time series and Kalman filtering Download PDFInfo
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Abstract
The invention discloses a kind of load forecasting method based on time series and Kalman filtering, methods described includes：Power system load data is carried out by tranquilization processing by first difference method；According to AIC criterion, access time series model；Data after tranquilization is handled substitute into the time series models of selection, obtain time series forecasting equation；Kalman filter equation is established, the Kalman filter equation of foundation is improved, obtains adaptive Kalman filter equation；Obtained time series forecasting equation is substituted into adaptive Kalman filter equation, obtains the power load forecasting module based on time series adaptive Kalman filter；Known Power system load data is substituted into power load forecasting module, obtains the load forecast data of subsequent time；Solve existing Methods of electric load forecasting and inaccurate technical problem be present, realize the technique effect for the precision for improving load forecast.
Description
Technical Field
The invention relates to the field of power load prediction, in particular to a load prediction method based on a time sequence and Kalman filtering.
Background
Providing users with high-quality, stable electrical energy is a major task of electrical power systems, and the premise for achieving this task is that electrical power is supplied to the system
The operation, scheduling and planning department must master the electricity usage rules and the variation trend of the users. The electric power marketization marks that monopoly is broken in each link of electric power production and supply, competition is introduced, optimal allocation of resources is realized, and social benefit and economic benefit are improved. Each enterprise in the electric power market must accurately grasp the market veins, understand the power demand, rule and change trend of users, and make reasonable marketing plan and development strategy to pursue the economic benefit of the enterprise. And the load prediction is a powerful tool for each enterprise to know the power demand, rule and change trend of the user.
The prediction method of the power grid load mainly comprises a continuous method, a time sequence method and a neural network method. Persistence methods are generally used as a reference for comparison with other predictive methods to evaluate the accuracy of a particular predictive method. The time series method requires less data, but the prediction accuracy is not high. The neural network method has high prediction precision, but has complex calculation and high requirement on data.
Disclosure of Invention
The invention provides a load prediction method based on a time sequence and Kalman filtering, solves the technical problems of inaccuracy or complex calculation of the conventional power load prediction method, and achieves the technical effects of improving the power load prediction precision and simple calculation.
In order to achieve the above object, the present application provides a power load prediction model optimization method, including:
carrying out stabilization processing on the power load data by a first-order difference method;
selecting a time sequence model according to an AIC criterion;
substituting the data after the stabilization treatment into the selected time series model to obtain a time series prediction equation;
establishing a Kalman filtering equation, and improving the established Kalman filtering equation to obtain a self-adaptive Kalman filtering equation;
substituting the obtained time series prediction equation into an adaptive Kalman filtering equation to obtain a power load prediction model based on time series-adaptive Kalman filtering; and substituting the known power load data into the power load prediction model to obtain power load prediction data at the next moment.
Further, the power load data is power load data of a past certain period.
Further, using difference operatorsPerforming stabilization treatment by using first-order difference transformation pair { Y t Obtaining after treatment:
{Y t is a discrete sequence of numbers, also called discrete time sequence, made up of a collection of time-varying quantities y (t), B being a delay operator, y t For the set of data at time t,the result is obtained after the difference is carried out on the data set at the time t;
after 1 st order difference of the formula (2-7), the following are obtained:
the above formula can be denoted ARIMA (p, d, q), where p is the autoregressive order of ARIMA; d is the difference number; q is the moving average order.
Further, according to the AIC criterion (minimum information criterion, which is a discrimination method for selecting a plurality of models), selecting a time series model specifically includes: and (3) calculating the value of AIC when p and q are different, and when the value of AIC is minimum, the obtained value of p and q is the optimal model order.
Further, the data subjected to the smoothing processing is substituted into the selected model, and an ARIMA (p, d, q) power load prediction equation based on the time series is obtained.
Further, establishing a kalman filtering equation specifically includes:
the discrete system is represented as
Wherein X (k) is an n-dimensional state vector at time k; z (k) is an m-dimensional observation vector at time k; w (k) is an n-dimensional noise vector at time k; v (k) is the m-dimensional measurement noise vector at time k; φ (k +1,k) is the state transition matrix from time k to time k + 1; Γ (k +1,k) is the excitation transfer matrix from time k to time k + 1; h (k + 1) is the prediction output matrix at time k + 1; x (k + 1) is an n-dimensional state vector at time k + 1; z (k + 1) is the m-dimensional observed phasor at time k + 1.
Further, the kalman filtering prediction recurrence equation is:
X'(k+1|k+1)＝φ(k+1,k)×X'(k|k)+K(k+1)×[Z(k+1)-H(k+1)×φ(k+1,k)×X'(k|k)]
K(k+1)＝P(k+1|k)×H T (k+1)×[H(k+1)×P(k+1|k)×H T (k+1)+R(k+1)]
P(k+1|k)＝φ(k+1,k)×P(k|k)×φ T (k+1,k)+Γ(k+1,k)×Q(k)×Γ T (k+1,k)
P(k+1|k+1)＝[I-K(k+1)×H(k+1)]×P(k+1|k)
wherein X' (k +1 calc + 1) is the value of the state estimate at time k + 1; x' (k | k) is a state estimation value at time k; k (K + 1) is the value of the Kalman gain matrix at time K + 1; z (k + 1) is an m-dimensional observation vector at the time of k + 1; p (k + 1|k) is the covariance matrix from time k to time k + 1; h T (k + 1) is the rank of the prediction output matrix at time k + 1; p (k +1 calving k)Is an error covariance matrix at the time of k + 1; r (k + 1) is a covariance matrix for v (k + 1); p (k | k) is the error covariance matrix at time k; phi is a T (k +1,k) is the transition rank of the state transition matrix from time k to time k + 1; gamma-shaped T (k +1,k) is the rank of the excitation transfer matrix from time k to time k + 1; q (k) is a covariance matrix for w (k); r (k) is a covariance matrix for v (k); i is an identity matrix;
further, the obtained Kalman filtering equation is improved, and the self-adaptive Kalman filtering equation is obtained. Introducing time-varying noise statistical estimation, and adopting the following biased estimation formula
G(k)＝[Γ T (k,k)×Γ(k,k)] -1 ×Γ T (k,k)
Q g (k+1)＝(1-z(k))×Q g (k)+z(k)×
{G(k)×[K(k+1)×ε(k+1)×ε T (k+1)×K T (k+1)+P(k+1|k+1)]×G T (k)}
R g (k+1)＝(1-z(k))×R g (k)+z(k)×[ε(k+1)×ε T (k+1)]
Wherein: Γ (k, k) is the excitation transfer matrix at time k; gamma-shaped T (k, k) is the rank of the excitation transfer matrix at time k; q g (k) Covariance matrix for w (k) at time k; ε (k + 1) is the deviation matrix at time k + 1; epsilon T (k + 1) is the rank of the deviation matrix at time k + 1; k T (k + 1) is the rank of the kalman gain matrix at time k + 1; r g (k) Is the covariance matrix for v (k) at time k. z (k + 1) is used for exponential weighting.
After the forgetting factors s are determined according to the 0-cloth s-woven fabric 1, the following steps are provided:
s 0 +s 1 +L+s k ＝(1-s k+1 )/(1-s)
to satisfy the weight coefficient sequence requirement, let:
z(k)＝(1-s)/(1-s k+1 )
at this point, every iteration of the Kalman filtering equation is performed, the calculated Q is used g (k+1)、R g (k + 1) instead of R (k) and Q (k) taking fixed values, the next iterative calculation is performed.
One or more technical solutions provided by the present application have at least the following technical effects or advantages:
according to the method, the time sequence method and the Kalman filtering method are combined, and the accuracy of the key factors influencing the prediction accuracy in the Kalman filtering prediction equation is improved, so that the method can reduce the errors of the accuracy of the respective prediction of the two prediction methods, and the technical effect of improving the accuracy of the power load prediction is realized.
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The accompanying drawings, which are included to provide a further understanding of the embodiments of the invention and are incorporated in and constitute a part of this application, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention;
fig. 1 is a schematic flow chart of a load prediction method based on time series and kalman filtering in the present application.
Detailed Description
The invention provides a load prediction method based on a time sequence and Kalman filtering, solves the technical problems of inaccuracy or complex calculation of the conventional power load prediction method, and achieves the technical effects of improving the power load prediction precision and simple calculation.
In order that the above objects, features and advantages of the present invention can be more clearly understood, a more particular description of the invention will be rendered by reference to the appended drawings. It should be noted that the embodiments and features of the embodiments of the present application may be combined with each other without conflicting with each other.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, however, the present invention may be practiced in other ways than those specifically described and thus the scope of the present invention is not limited by the specific embodiments disclosed below.
Referring to fig. 1, the present application provides a power load prediction model optimization method based on time series-adaptive kalman filtering, including the following steps:
s1, selecting power load data of a past certain period;
s2, carrying out stabilization processing on the data obtained in the step S1 through first-order difference;
by difference operatorsAnd carrying out stabilization treatment. Using a first order differential transform pair Y t Can be obtained after treatment
After the equation (1) is subjected to step difference, the obtained product can be obtained
The above equation can be written as ARIMA (p, d, q), where p is the autoregressive order of ARIMA; d is the difference number; q is the moving average order.
S3, selecting a proper time sequence model according to an AIC criterion;
calculating the value of AIC when p and q are different, and when the value of AIC is minimum, the obtained value of p and q is the optimal model order;
and S4, substituting the data obtained in the step S2 and subjected to the stabilization treatment into the model selected in the step S3 to obtain a time series prediction equation as follows:
ARIMA(p,d,q) (3)
s5, establishing a Kalman filtering equation;
a general discrete system can be represented as:
x (k) is an n-dimensional state vector at time k; z (k) is an m-dimensional observation vector at time k; w (k) is an n-dimensional noise vector at time k; v (k) is the m-dimensional measurement noise vector at time k; φ (k +1,k) is the state transition matrix from time k to time k + 1; Γ (k +1,k) is the excitation transfer matrix from time k to time k + 1; h (k + 1) is the prediction output matrix at time k + 1; x (k + 1) is an n-dimensional state vector at time k + 1; z (k + 1) is the m-dimensional observed phasor at time k + 1.
The Kalman filtering prediction recurrence equation is as follows:
X'(k+1|k+1)＝φ(k+1,k)×X'(k|k)+K(k+1)×[Z(k+1)-H(k+1)×φ(k+1,k)×X'(k|k)] (5)
K(k+1)＝P(k+1|k)×H T (k+1)×[H(k+1)×P(k+1|k)×H T (k+1)+R(k+1)] (6)
P(k+1|k)＝φ(k+1,k)×P(k|k)×φ T (k+1,k)+Γ(k+1,k)×Q(k)×Γ T (k+1,k) (7)
P(k+1|k+1)＝[I-K(k+1)×H(k+1)]×P(k+1|k) (8)
x' (k +1 calc + 1) is the value of the state estimate at time k + 1; x' (k | k) is a state estimation value at time k; k (K + 1) is the value of the Kalman gain matrix at time K + 1; z (k + 1) is an m-dimensional observation vector at the time of k + 1; p (k + 1|k) is the covariance matrix from time k to time k + 1; h T (k + 1) is the rank of the prediction output matrix at time k + 1; p (k +1 caldus k + 1) is an error covariance matrix at the moment of k + 1; r (k + 1) is a covariance matrix for v (k + 1); p (k | k) is the error covariance matrix at time k; phi is a T (k +1,k) is the rank of the state transition matrix from time k to time k + 1; gamma-shaped T (k +1,k) is the rank of the excitation transfer matrix from time k to time k + 1; q (k) is a covariance matrix for w (k); r (k) is a covariance matrix for v (k); i is an identity matrix;
and S6, improving the Kalman filtering equation obtained in the step S5 to obtain the self-adaptive Kalman filtering equation. A time-varying noise statistical estimate is introduced. The following biased estimation equation is used:
G(k)＝[Γ T (k,k)×Γ(k,k)] -1 ×Γ T (k,k) (9)
Q g (k+1)＝(1-z(k))×Q g (k)+z(k)×{G(k)×[K(k+1)×ε(k+1)×ε T (k+1)×K T (k+1)+P(k+1|k+1)]×G T (k)} (10)
R g (k+1)＝(1-z(k))×R g (k)+z(k)×[ε(k+1)×ε T (k+1)] (11)
Γ (k, k) is the excitation transfer matrix at time k; gamma-shaped T (k, k) is the rank of the excitation transfer matrix at time k; q g (k) Covariance matrix for w (k) at time k; ε (k + 1) is the deviation matrix at time k + 1; epsilon T (k + 1) is the rank of the deviation matrix at time k + 1; k T (k + 1) is the rank of the k +1 moment Kalman gain matrix; r g (k) Is the covariance matrix for v (k) at time k. z (k), z (k + 1) are used for exponential weighting.
After determining forgetting factors s according to 0-cloth s-woven fabric
s 0 +s 1 +L+s k ＝(1-s k+1 )/(1-s) (12)
To satisfy the requirement of the weight coefficient sequence, can make
z(k)＝(1-s)/(1-s k+1 ) (13)
The forgetting factor s can be generally 0.95 or 0.99;
so far, every iteration of the Kalman filter equation is performed by using Q obtained by calculation g (k+1)、R g (k + 1) replacing R (k) and Q (k) with fixed values, and then performing the next iterative computation;
s7, substituting the time series prediction model obtained in the step S2 into the adaptive Kalman filtering equation obtained in the step S6;
s8, power load prediction is carried out;
while preferred embodiments of the present invention have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. Therefore, it is intended that the appended claims be interpreted as including the preferred embodiment and all changes and modifications that fall within the scope of the invention.
It will be apparent to those skilled in the art that various changes and modifications may be made in the present invention without departing from the spirit and scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.
Claims (8)
1. A load prediction method based on a time series and Kalman filtering is characterized by comprising the following steps:
carrying out stabilization processing on the power load data by a first-order difference method;
selecting a time sequence model according to an AIC criterion;
substituting the data after the stabilization treatment into the selected time series model to obtain a time series prediction equation;
establishing a Kalman filtering equation, and improving the established Kalman filtering equation to obtain a self-adaptive Kalman filtering equation;
substituting the obtained time series prediction equation into an adaptive Kalman filtering equation to obtain a power load prediction model based on time series-adaptive Kalman filtering; and substituting the known power load data into the power load prediction model to obtain power load prediction data at the next moment.
2. The method of claim 1, wherein the power load data is power load data of a past time period.
3. The time series and kalman filter based load prediction method according to claim 1, characterized in that the smoothing process is performed with a difference operator =1-B, the { Y } pair being made with a first order difference transform t Obtaining after treatment:
▽y t ＝(1-B)y t ＝y t -y t-1 (1)
{Y t is a discrete sequence of numbers, also called discrete time sequence, made up of a collection of time-varying quantities y (t), B being a delay operator, y t Set of data for time t, # y t The result is obtained after the difference is carried out on the data set at the time t;
after d-order differentiation of equation (1), we obtain:
▽ d y t ＝(1-B) d y t (2)
equation (2) is denoted ARIMA (p, d, q), where p is the autoregressive order of ARIMA; d is the difference number; q is the moving average order.
4. The load prediction method based on time series and kalman filtering according to claim 3, wherein selecting the time series model specifically includes, according to the AIC criterion: and (3) calculating the value of AIC when p and q are different, and when the value of AIC is minimum, the obtained values of p and q are the optimal model order.
5. The time series and kalman filter based load prediction method according to claim 4, characterized in that the smoothed data is substituted into the selected model to obtain the time series based power load prediction equation ARIMA (p, d, q).
6. The power load prediction model optimization method according to claim 1, wherein the establishing of the kalman filter equation specifically comprises:
the discrete system is represented as
Wherein X (k) is an n-dimensional state vector at time k; z (k) is an m-dimensional observation vector at time k; w (k) is an n-dimensional noise vector at time k; v (k) is the m-dimensional measurement noise vector at time k; φ (k +1,k) is the state transition matrix from time k to time k + 1; Γ (k +1,k) is the excitation transfer matrix from time k to time k + 1; h (k + 1) is the prediction output matrix at time k + 1; x (k + 1) is an n-dimensional state vector at time k + 1; z (k + 1) is the m-dimensional observed phasor at time k + 1.
7. The time series and Kalman filter based load prediction method according to claim 6, characterized in that Kalman filter prediction recursion equation is:
X'(k+1|k+1)＝φ(k+1,k)×X'(k|k)+K(k+1)×[Z(k+1)-H(k+1)×φ(k+1,k)×X'(k|k)]
(4)
K(k+1)＝P(k+1|k)×H T (k+1)×[H(k+1)×P(k+1|k)×H T (k+1)+R(k+1)]
(5)
P(k+1|k)＝φ(k+1,k)×P(k|k)×φ T (k+1,k)+Γ(k+1,k)×Q(k)×Γ T (k+1,k)
(6)
P(k+1|k+1)＝[I-K(k+1)×H(k+1)]×P(k+1|k)(7)
wherein X' (k +1 calc + 1) is the value of the state estimate at time k + 1; x' (k | k) is a state estimation value at time k; k (K + 1) is the value of the Kalman gain matrix at time K + 1; z (k + 1) is an m-dimensional observation vector at the time of k + 1; p (k + 1|k) is the covariance matrix from time k to time k + 1; h T (k + 1) is the rank of the prediction output matrix at time k + 1; p (k +1 caldus k + 1) is an error covariance matrix at the moment of k + 1; r (k + 1) is a covariance matrix for v (k + 1); p (k | k) is the error covariance matrix at time k; phi is a T (k +1,k) is the transition rank of the state transition matrix from time k to time k + 1; gamma-shaped T (k +1,k) is the rank of the excitation transfer matrix from time k to time k + 1; q (k) is a covariance matrix for w (k); r (k) is a covariance matrix for v (k); i is the identity matrix.
8. The time series and kalman filter based load prediction method according to claim 7, characterized in that: improving the obtained Kalman filtering equation to obtain a self-adaptive Kalman filtering equation, so that a time-varying noise statistical estimation is introduced, and the following biased estimation formula is adopted:
G(k)＝[Γ T (k,k)×Γ(k,k)] -1 ×Γ T (k,k) (8)
Q g (k+1)＝(1-z(k))×Q g (k)+z(k)×
{G(k)×[K(k+1)×ε(k+1)×ε T (k+1)×K T (k+1)+P(k+1|k+1)]×G T (k)} (9)
R g (k+1)＝(1-z(k))×R g (k)+z(k)×[ε(k+1)×ε T (k+1)] (10)
wherein: Γ (k, k) is the excitation transfer matrix at time k; gamma-shaped T (k, k) is the rank of the excitation transfer matrix at time k; q g (k) Covariance matrix for w (k) at time k; ε (k + 1) is the deviation matrix at time k + 1; epsilon T (k + 1) is the rank of the deviation matrix at time k + 1; k T (k + 1) is the rank of the k +1 moment Kalman gain matrix; r g (k) Is the covariance matrix for v (k) at time k; z (k + 1) is used for exponential weighting;
after the forgetting factors s are determined according to the 0-cloth s-woven fabric 1, the following steps are provided:
s 0 +s 1 +L+s k ＝(1-s k+1 )/(1-s) (11)
to satisfy the weight coefficient sequence requirement, let:
z(k)＝(1-s)/(1-s k+1 ) (12)
so far, every iteration of the Kalman filter equation is performed by using Q obtained by calculation g (k+1)、R g (k + 1) instead of R (k) and Q (k) which take fixed values, the next iterative calculation is performed.
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| CN113391287B (en) * | 2021-06-10 | 2023-09-01 | 哈尔滨工业大学 | High-frequency ground wave radar sea state data fusion method based on time sequence |
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