CN111611741B - Time sequence wind speed simulation method and system based on finite state Markov sequence - Google Patents
Time sequence wind speed simulation method and system based on finite state Markov sequence Download PDFInfo
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Abstract
The invention provides a time sequence wind speed simulation method and a time sequence wind speed simulation system based on a finite state Markov sequence, wherein the method receives an original wind speed time sequence, and a polynomial normal transformation technology is utilized to transform the original wind speed time sequence into a time sequence obeying normal distribution; constructing a K-dimensional random vector by using a time sequence of which adjacent K moments obey normal distribution; the random vector obeys the multi-element normal distribution of the covariance matrix C; constructing a state transfer function according to the multi-element normal distribution; randomly sampling by using a state transfer function to obtain a Markov time sequence with a set time length; and transforming the Markov time sequence by using polynomial normal transformation to obtain a simulated wind speed time sequence. Based on this method, an analog system is also proposed. The invention establishes a time sequence model of wind speed in a continuous state space, and has higher simulation precision; the Markov random model of the wind speed time sequence is built in a normal space, the complexity of direct modeling is reduced, and modeling is more flexible and convenient.
Description
Technical Field
The invention belongs to the technical field of power systems and automation thereof, and particularly relates to a time sequence wind speed simulation method and system based on a finite state Markov sequence.
Background
Wind speed data is the basis for wind energy development and utilization. An accurate wind speed model is established and a key of wind speed simulation is developed. At present, a great deal of research is carried out on wind speed models at home and abroad, and a plurality of wind speed simulation methods are provided. At present, the wind speed time sequence simulation mainly comprises a time sequence model and a Markov model, the time sequence model needs more model parameters, so that the modeling is complex, the probability distribution is error, and the Markov process has higher precision because the probability distribution characteristic and the autocorrelation characteristic of a sample can be kept, so that the Markov model has more practical application value.
The wind speed is a physical process which is continuous in time and space, and can be statistically described as a random process with continuous time and continuous state, the current Markov model mainly adopts a discrete Markov chain to simulate the wind speed, the model discretizes the wind speed state, a discrete state probability matrix is established, the model precision depends on a discrete scale, but the high discretization can improve the model precision, but too many model parameters can be caused, and in most cases, the model precision is sacrificed in order to reduce the model complexity, so that the applicability is reduced. It can be seen that the existing wind speed time series simulation has the difficulty that the precision and the simplicity of the model are difficult to ensure simultaneously, and the bottleneck of the model constructs any type of state transfer function in a continuous state space.
Disclosure of Invention
The invention provides a time sequence wind speed simulation method and a time sequence wind speed simulation system based on a finite state Markov sequence, which are used for establishing a time sequence model of wind speed in a continuous state space and have higher simulation precision; the Markov random model of the wind speed time sequence is built in a normal space, the complexity of direct modeling is reduced, and modeling is more flexible and convenient.
In order to achieve the above object, the present invention proposes a time-series wind speed simulation method based on a finite state markov sequence, the method comprising the steps of:
s1: transforming the original wind speed time sequence into a time sequence obeying normal distribution by using a polynomial normal transformation technology;
s2: constructing a K-dimensional random vector by using a time sequence of which adjacent K moments obey normal distribution; the k-dimensional random vector obeys the multi-element normal distribution of the covariance matrix C; constructing a state transfer function according to the multi-element normal distribution;
s3: randomly sampling by using a state transfer function to obtain a Markov time sequence with a set time length;
s4: and transforming the Markov time sequence by using polynomial normal transformation to obtain a simulated wind speed time sequence.
Further, before step S1, the method further includes receiving a time sequence of the original wind speed.
Further, in step S1, the step of transforming the original wind speed time sequence into a time sequence compliant with a normal distribution by using a polynomial normal transformation technique is as follows:
s11: establishing an original wind speed time sequence W t Random variable Z t A polynomial functional relationship between; w (W) t ＝c 0 +c 1 Z t +c 2 Z t 2 +c 3 Z t 3 ；
wherein ,c0 ,c 1 ,c 2 ,c 3 Are all function model parameters; c 0 ＝μ v -σ v γ 3v /6,c 1 ＝σ v (33-3γ 4v )/24,c 2 ＝σ v γ 3v /6,c 3 ＝σ v (3γ 4v -3)/24；μ v Mathematical expectations for a random time sequence; sigma (sigma) v Standard deviation as random time series; gamma ray 3v A bias value which is a random time sequence; gamma ray 4v Kurtosis values that are random time series;
s12, utilizing the formula W t ＝c 0 +c 1 Z t +c 2 Z t 2 +c 3 Z t 3 Time-series W of original wind speed t Transforming into a time series Y subject to normal distribution t The method comprises the steps of carrying out a first treatment on the surface of the Wherein t=1, 2.
Further, the process of step S2 is as follows:
s21, constructing a k-dimensional random vector Y= (Y) by using a time sequence of adjacent k moments obeying normal distribution t-(k-1) ,...,Y t ,Y t+1 ) Then the k-dimensional random vector obeys a multivariate normal distribution with covariance matrix C:
s22: constructing random variable Y at t+1 time according to multi-element normal distribution t+1 Conditional probability distribution functions of (2); the conditional probability distribution function is a state transfer function;
the random variable Y t+1 The method comprises the following steps: wherein ,
further, the process of step S3 is as follows:
s31: randomly generating k-1 random numbers obeying normal distribution as initial values;
s32: bringing the k-1 initial values into the formulaCalculating the average value mu of the kth random variable;
s33: substituting μ into formulaObtaining a probability distribution function of a kth random variable, and randomly sampling to generate a kth moment wind speed random variable;
s34: repeating steps S32 to S33n times to obtain a Markov sequence X with length of n t (t＝1,2,....,n)。
Further, the process of step S4 is as follows: using formula W t ＝c 0 +c 1 Z t +c 2 Z t 2 +c 3 Z t 3 The normal distribution is distributed along with the time sequence W t (t=1, 2,) n) conversion to an analog wind speed time series V t (t＝1,2,....,n)。
The invention also provides a time sequence wind speed simulation system based on the finite state Markov sequence, which comprises a receiving module, a first transformation module, a solving module, a sampling module and a second transformation module;
the receiving module is used for receiving the original wind speed time sequence;
the first transformation module is used for transforming the original wind speed time sequence into a time sequence obeying normal distribution by using a polynomial normal transformation technology;
the acquisition module is used for constructing a K-dimensional random vector by utilizing a time sequence of which adjacent K moments obey normal distribution; the k-dimensional random vector obeys the multi-element normal distribution of the covariance matrix C; constructing a state transfer function according to the multi-element normal distribution;
the sampling module is used for randomly sampling by using a state transfer function to obtain a Markov time sequence with set time length;
the second transformation module is used for transforming the Markov time sequence into an analog wind speed time sequence by using polynomial normal transformation.
Further, the implementation process of the first transformation module is as follows:
establishing an original wind speed time sequence W t Random variable Z t A polynomial functional relationship between; w (W) t ＝c 0 +c 1 Z t +c 2 Z t 2 +c 3 Z t 3； wherein ,c0 ,c 1 ,c 2 ,c 3 Are all function model parameters; c 0 ＝μ v -σ v γ3v/6,c 1 ＝σ v (33-3γ 4v )/24,c 2 ＝σ v γ3v/6,C 3 ＝σ v (3γ 4v -3)/24；μ v Mathematical expectations for a random time sequence; sigma (sigma) v Standard deviation as random time series; gamma ray 3v A bias value which is a random time sequence; gamma ray 4v Kurtosis values that are random time series;
using formula W t ＝c 0 +c 1 Z t +c 2 Z t 2+c 3 Z t 3 Time-series W of original wind speed t Transforming into a time series Y subject to normal distribution t The method comprises the steps of carrying out a first treatment on the surface of the Wherein t=1, 2.
Further, the implementation process of the solving module is as follows: constructing a k-dimensional random vector y= (Y) using a time series of adjacent k moments subject to normal distribution t-(k-1) ,...,Y t ,Y t+1 ) Then the k-dimensional random vector obeys a multivariate normal distribution with covariance matrix C:
s22: constructing random variable Y at t+1 time according to multi-element normal distribution t+1 Conditional probability distribution functions of (2); the conditional probability distribution function is a state transfer function; the method comprises the steps of carrying out a first treatment on the surface of the
The random variable Y t+1 Is that wherein ,
further, the implementation process of the sampling module is as follows:
s31: randomly generating k-1 random numbers obeying normal distribution as initial values;
s32: bringing the k-1 initial values into the formulaCalculating the average value mu of the kth random variable;
s33: substituting μ into formulaObtaining a probability distribution function of a kth random variable, and randomly sampling to generate a kth moment wind speed random variable;
s34: repeating steps S32 to S33n times to obtain a Markov sequence X with length of n t (t＝1,2,....,n)。
The effects provided in the summary of the invention are merely effects of embodiments, not all effects of the invention, and one of the above technical solutions has the following advantages or beneficial effects:
the embodiment of the invention provides a time sequence wind speed simulation method and a time sequence wind speed simulation system based on a finite state Markov sequence, wherein after receiving an original wind speed time sequence, the method transforms the original wind speed time sequence into a time sequence obeying normal distribution by utilizing a polynomial normal transformation technology; constructing a K-dimensional random vector by using a time sequence of which adjacent K moments obey normal distribution; the k-dimensional random vector obeys the multi-element normal distribution of the covariance matrix C; constructing a state transfer function according to the multi-element normal distribution; randomly sampling by using a state transfer function to obtain a Markov time sequence with a set time length; and transforming the Markov time sequence by using polynomial normal transformation to obtain a simulated wind speed time sequence. The invention provides a time sequence wind speed simulation method based on a finite state Markov sequence, and also provides a time sequence wind speed simulation system based on the finite state Markov sequence. The method establishes a time sequence model of the wind speed in a continuous state space, accords with the physical change process of the actual wind speed, and has higher simulation precision; the Markov random model of the wind speed time sequence is built in a normal space, the complexity of direct modeling is reduced, and the modeling is more flexible and convenient, so that the method has good engineering application prospect.
Drawings
FIG. 1 is a flow chart of a time-series wind speed simulation method based on a finite state Markov sequence according to embodiment 1 of the present invention;
FIG. 2 is a schematic diagram showing 8760 hour wind speed time series of a certain region according to embodiment 1 of the present invention;
FIG. 3 shows a simulated wind speed frequency histogram based on the time-series wind speed simulation method based on finite state Markov sequence proposed in embodiment 1 of the present invention;
FIG. 4 shows a simulated wind speed autocorrelation function based on the finite state Markov sequence-based time-series wind speed simulation method proposed in embodiment 1 of the present invention;
fig. 5 shows a schematic diagram of a time-series wind speed simulation system based on a finite state markov sequence according to embodiment 1 of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Example 1
The invention provides a time sequence wind speed simulation method based on a finite state Markov sequence, as shown in FIG. 1, a flow chart of the time sequence wind speed simulation method based on the finite state Markov sequence is provided;
in step S101, the flow of processing is started.
In step S102, an original wind speed time series W is received t 。
In step S103, transforming the original wind speed time series into a time series compliant with a normal distribution using a polynomial normal transformation technique;
first, an original wind speed time sequence W is established t Random variable Z t A polynomial functional relationship between; w (W) t ＝c 0 +c 1 Z t +c 2 Z t 2 +c 3 Z t 3 ；
wherein ,c0 ,c 1 ,c 2 ,c 3 Are all function model parameters; c 0 ＝μ v -σvγ 3v /6,c 1 ＝σ v (33-3γ 4v )/24,c 2 ＝σ v γ 3v /6,c 3 ＝σ v (3γ 4v -3)/24；μ v Mathematical expectations for a random time sequence; sigma (sigma) v Standard deviation as random time series; gamma ray 3v A bias value which is a random time sequence; gamma ray 4v Kurtosis values that are random time series;
then utilize equation W t ＝c 0 +c 1 Z t +c 2 Z t 2 +c 3 Z t 3 Time-series W of original wind speed t Transforming into a time series Y subject to normal distribution t The method comprises the steps of carrying out a first treatment on the surface of the Wherein t=1, 2.
In step S104, a K-dimensional random vector is constructed using a time sequence in which K adjacent moments are subjected to normal distribution; the k-dimensional random vector obeys the multi-element normal distribution of the covariance matrix C; and constructing a state transfer function according to the multivariate normal distribution.
First, a k-dimensional random vector y= (Y) is constructed using a time series of adjacent k times subject to normal distribution t-(k-1) ,...,Y t ,Y t+1 ) Then the k-dimensional random vector obeys a multivariate normal distribution with covariance matrix C:
s22: constructing random variable Y at t+1 time according to multi-element normal distribution t+1 Conditional probability distribution functions of (2);the conditional probability distribution function is a state transfer function;
the random variable Y t+1 The method comprises the following steps: wherein ,
in step S105, random sampling is performed by using the state transfer function to obtain a markov time series with a set time length;
s31: randomly generating k-1 random numbers obeying normal distribution as initial values;
s32: bringing the k-1 initial values into the formulaCalculating the average value mu of the kth random variable;
s33: substituting μ into formulaObtaining a probability distribution function of a kth random variable, and randomly sampling to generate a kth moment wind speed random variable;
s34: repeating steps S32 to S33n times to obtain a Markov sequence X with length of n t (t＝1,2,....,n)。
In step S106: using formula W t ＝c 0 +c 1 Z t +c 2 Z t 2 +c 3 Z t 3 The normal distribution is distributed along with the time sequence W t (t=1, 2,) n) conversion to an analog wind speed time series V t (t＝1,2,....,n)。
In step S107, the flow ends.
A time series diagram of 8760 hours wind speed in a certain region is shown in fig. 2. Using time series sample data V of wind speed t (t=1, 2,) the polynomial transformation function relationship is found, 8760, and the settlement result is as follows:
using formula V t ＝c 0 +c 1 Z t +c 2 Z t 2 +c 3 Z t 3 Time series of wind speeds V t Conversion to a time series Z subject to normal distribution t The method comprises the steps of carrying out a first treatment on the surface of the Wherein t=1, 2..8760.
The state transfer function is obtained by using a normal distribution time sequence, a 2-order Markov sequence is set and adopted, and the settlement result is shown as follows:
random sampling by using state transfer function to obtain a normal distribution time sequence, assuming sampling time is 87600 time points (10 years) Z t (t＝1,2,....,87600)。
For normally distributed time series Z t (t=1, 2.,. 87600) according to the polynomial transformation function relationship V described above t ＝c 0 +c 1 Z t +c 2 Z t 2 +c 3 Z t 3 Can obtain wind speed time sequence V t (t=1, 2.,. 87600). FIG. 3 shows a simulated wind speed frequency histogram based on the time-series wind speed simulation method based on finite state Markov sequence proposed in embodiment 1 of the present invention; fig. 4 shows a simulated wind speed autocorrelation function based on the time-series wind speed simulation method based on the finite state markov sequence proposed in embodiment 1 of the present invention.
The invention also provides a time sequence wind speed simulation system based on the finite state Markov sequence, as shown in FIG. 5, the time sequence wind speed simulation system based on the finite state Markov sequence provided by the embodiment 1 of the invention comprises a receiving module, a first transformation module, a solving module, a sampling module and a second transformation module.
For receiving modulesReceiving the original wind speed time sequence W t 。
The first transformation module is used for transforming the original wind speed time sequence into a time sequence obeying normal distribution by using polynomial normal transformation technology.
The implementation process of the first transformation module is as follows: first, an original wind speed time sequence W is established t Random variable Z t A polynomial functional relationship between; w (W) t ＝c 0 +c 1 Z t +c 2 Z t 2 +c 3 Z t 3； wherein ,c0 ,c 1 ,c 2 ,c 3 Are all function model parameters; c 0 ＝γ v -σ v γ 3v /6,c 1 ＝σ v (33-3γ 4v )/24,c 2 ＝σ v γ 3v /6,c 3 ＝σ v (3γ 4v -3)/24；μ v Mathematical expectations for a random time sequence; sigma (sigma) v Standard deviation as random time series; gamma ray 3v A bias value which is a random time sequence; gamma ray 4v Kurtosis values that are random time series; then, using formula W t ＝c 0 +c 1 Z t +c 2 Z t 2 +c 3 Z t 3 Time-series W of original wind speed t Transforming into a time series Y subject to normal distribution t The method comprises the steps of carrying out a first treatment on the surface of the Wherein t=1, 2.
The solving module is used for constructing a K-dimensional random vector by utilizing a time sequence of adjacent K moments obeying normal distribution; the k-dimensional random vector obeys the multi-element normal distribution of the covariance matrix C; and constructing a state transfer function according to the multivariate normal distribution.
The implementation process of the solving module is as follows: first, a k-dimensional random vector y= (Y) is constructed using a time series of adjacent k times subject to normal distribution t-(k-1) ,...,Y t ,Y t+1 ) Then the k-dimensional random vector obeys a multivariate normal distribution with covariance matrix C:then, the time t+1 is constructed according to the multivariate normal distributionRandom variable Y of (2) t+1 Conditional probability distribution functions of (2); the conditional probability distribution function is a state transfer function;
random variable Y t+1 The method comprises the following steps: wherein ,
the sampling module is used for randomly sampling by using the state transfer function to obtain a Markov time sequence with set time length.
The concrete implementation process of the sampling module is as follows: randomly generating k-1 random numbers obeying normal distribution as initial values; bringing the k-1 initial values into the formulaCalculating the average value mu of the kth random variable; substituting μ into the formula +.>Obtaining a probability distribution function of a kth random variable, and randomly sampling to generate a kth moment wind speed random variable; repeating the process of obtaining the average value mu of the kth random variable and substituting mu into the probability distribution function of the kth random variable n times to obtain a Markov sequence X with the length of n t (t＝1,2,....,n)。
The second transformation module is used for transforming the Markov time sequence into an analog wind speed time sequence by using polynomial normal transformation, and using a formula W t ＝c 0 +c 1 Z t +c 2 Z t 2 +c 3 Z t 3 The normal distribution is distributed along with the time sequence W t (t=1, 2,) n) conversion to an analog wind speed time series V t (t＝1,2,....,n)。
The foregoing is merely illustrative and explanatory of the invention, as it is well within the scope of the invention as claimed, as it relates to various modifications, additions and substitutions for those skilled in the art, without departing from the inventive concept and without departing from the scope of the invention as defined in the accompanying claims.
Claims (8)
1. The time sequence wind speed simulation method based on the finite state Markov sequence is characterized by comprising the following steps of:
s1: transforming the original wind speed time sequence into a time sequence obeying normal distribution by using a polynomial normal transformation technology;
s2: constructing a k-dimensional random vector by using a time sequence of which adjacent k moments obey normal distribution; the k-dimensional random vector obeys the multi-element normal distribution of the covariance matrix C; constructing a state transfer function according to the multi-element normal distribution; the process of step S2 is:
s21, constructing a k-dimensional random vector Y= (Y) by using a time sequence of adjacent k moments obeying normal distribution t-(k-1) ,...,Y t ,Y t+1 ) Then the k-dimensional random vector obeys a multivariate normal distribution with covariance matrix C:
s22: constructing random variable Y at t+1 time according to multi-element normal distribution t+1 Conditional probability distribution functions of (2); the conditional probability distribution function is a state transfer function;
the random variable Y t+1 Is that wherein ,
s3: randomly sampling by using a state transfer function to obtain a Markov time sequence with a set time length;
s4: and transforming the Markov time sequence by using polynomial normal transformation to obtain a simulated wind speed time sequence.
2. The finite state markov sequence based time series wind speed simulation method of claim 1, further comprising receiving a raw wind speed time series prior to step S1.
3. The method for simulating time-series wind speed based on finite state markov sequence according to claim 1, wherein in step S1, the step of transforming the original wind speed time series into a time series compliant with a normal distribution by using a polynomial normal transformation technique is as follows:
s11: establishing an original wind speed time sequence W t Random variable Z t A polynomial functional relationship between; w (W) t ＝c 0 +c 1 Z t +c 2 Z t 2 +c 3 Z t 3； wherein ,c0 ,c 1 ,c 2 ,c 3 Are all function model parameters; c 0 ＝μ v -σ v γ 3v /6,c 1 ＝σ v (33-3γ 4v )/24,c 2 ＝σ v γ 3v /6,c 3 ＝σ v (3γ 4v -3)/24；μ v Mathematical expectations for a random time sequence; sigma (sigma) v Standard deviation as random time series; gamma ray 3v A bias value which is a random time sequence; gamma ray 4v Kurtosis values that are random time series;
s12, utilizing the formula W t ＝c 0 +c 1 Z t +c 2 Z t 2 +c 3 Z t 3 Time-series W of original wind speed t Transforming into a time series Y subject to normal distribution t The method comprises the steps of carrying out a first treatment on the surface of the Wherein t=1, 2.
4. A time-series wind speed simulation method based on finite state markov sequence according to claim 3, wherein the process of step S3 is:
s31: randomly generating k-1 random numbers obeying normal distribution as initial values;
s32: bringing the k-1 initial values into the formulaCalculating the average value mu of the kth random variable;
s33: substituting μ into formulaObtaining a probability distribution function of a kth random variable, and randomly sampling to generate a kth moment wind speed random variable;
s34: repeating steps S32 to S33n times to obtain a Markov sequence X with length of n t (t＝1,2,....,n)。
5. A time-series wind speed simulation method based on finite state markov sequence according to claim 3, wherein the process of step S4 is: using formula W t ＝c 0 +c 1 Z t +c 2 Z t 2 +c 3 Z t 3 The normal distribution is distributed along with the time sequence W t (t=1, 2,) n) conversion to an analog wind speed time series V t (t＝1,2,....,n)。
6. The time sequence wind speed simulation system based on the finite state Markov sequence is characterized by comprising a receiving module, a first transformation module, a solving module, a sampling module and a second transformation module;
the receiving module is used for receiving the original wind speed time sequence;
the first transformation module is used for transforming the original wind speed time sequence into a time sequence obeying normal distribution by using a polynomial normal transformation technology;
the acquisition module is used for constructing a k-dimensional random vector by utilizing a time sequence of which adjacent k moments obey normal distribution; the k-dimensional random vector obeys the multi-element normal distribution of the covariance matrix C; constructing a state transfer function according to the multi-element normal distribution; the obtaining moduleThe implementation process is as follows: constructing a k-dimensional random vector y= (Y) using a time series of adjacent k moments subject to normal distribution t-(k-1) ,...,Y t ,Y t+1 ) Then the k-dimensional random vector obeys a multivariate normal distribution with covariance matrix C:
constructing random variable Y at t+1 time according to multi-element normal distribution t+1 Conditional probability distribution functions of (2); the conditional probability distribution function is a state transfer function;
the random variable Y t+1 Is that wherein ,
the sampling module is used for randomly sampling by using a state transfer function to obtain a Markov time sequence with set time length;
the second transformation module is used for transforming the Markov time sequence into an analog wind speed time sequence by using polynomial normal transformation.
7. The finite state markov sequence based time series wind speed simulation system of claim 6 wherein the first transformation module is implemented as:
establishing an original wind speed time sequence W t Random variable Z t A polynomial functional relationship between; w (W) t ＝c 0 +c 1 Z t +c 2 Z t 2 +c 3 Z t 3； wherein ,c0 ,c 1 ,c 2 ,c 3 Are all function model parameters; c 0 ＝μ v -σ v γ 3v /6,c 1 ＝σ v (33-3γ 4v )/24,c 2 ＝σ v γ 3v /6,c 3 ＝σ v (3γ 4v -3)/24；μ v Mathematical expectations for a random time sequence; sigma (sigma) v Standard deviation as random time series; gamma ray 3v A bias value which is a random time sequence; gamma ray 4v Kurtosis values that are random time series;
using formula W t ＝c 0 +c 1 Z t +c 2 Z t 2 +c 3 Z t 3 Time-series W of original wind speed t Transforming into a time series Y subject to normal distribution t The method comprises the steps of carrying out a first treatment on the surface of the Wherein t=1, 2.
8. The finite state markov sequence based time series wind speed simulation system of claim 7 wherein the sampling module is implemented as:
s31: randomly generating k-1 random numbers obeying normal distribution as initial values;
s32: bringing the k-1 initial values into the formulaCalculating the average value mu of the kth random variable;
s33: substituting μ into formulaObtaining a probability distribution function of a kth random variable, and randomly sampling to generate a kth moment wind speed random variable;
s34: repeating steps S32 to S33n times to obtain a Markov sequence X with length of n t (t＝1,2,....,n)。
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