CN104008433A  Method for predicting mediumandlongterm power loads on basis of Bayes dynamic model  Google Patents
Method for predicting mediumandlongterm power loads on basis of Bayes dynamic model Download PDFInfo
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 CN104008433A CN104008433A CN201410242690.1A CN201410242690A CN104008433A CN 104008433 A CN104008433 A CN 104008433A CN 201410242690 A CN201410242690 A CN 201410242690A CN 104008433 A CN104008433 A CN 104008433A
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Abstract
The invention discloses a method for predicting mediumandlongterm power loads on basis of a Bayes dynamic model. According to the internal change rule of mediumandlongterm power load data, the Bayes dynamic model with polynomial regression and index structures is built; according to the Bayes theory, the power load value of the next year is obtained in real time in a statistical interference mode according to prior information and test samples, and dynamic recursion prediction of the mediumandlongterm power loads in small sample capacity is achieved. The number of sample data required by the method is small, and the change rule of current power loads can be tracked in real time by means of model monitoring and subjective interference, so that a power load prediction result is more reliable, and an effective way is provided for improvement on mediumandlongterm power load prediction precision.
Description
Technical field
The present invention relates to Methods of electric load forecasting field, be specially a kind of longmedium term power load forecasting method based on Bayesian Dynamic.
Background technology
Electric Power Network Planning is directly connected to socioeconomic development and energy resource supply, longmedium term power load forecasting is the basis of formulating Electric Power Network Planning, and its accuracy directly has influence on rationality, energy resources supply and balance, the power industry economy of Electricity Investment, network topology.
Midlong term load forecasting is to take historical data as basis, sets up effective forecast model, seeks its variation tendency and the rule of development, predict future payload.Electric load development and change rule complexity is various, affected by the uncertain factor of Various Complex, load prediction is very difficult very accurately, its theoretical research is just taken much count of always, load forecasting method is varied, common are method of elasticity modulus, regression analysis, trend extrapolation, Grey Theory Forecast method etc.Affected by the multiple uncertain factors such as socioeconomic development trend, climate change, the difficulty of prediction and the complicacy of model have been increased, for concrete network load data, to select appropriate forecast model, adopt if desired several mathematical model modelings simultaneously, comparative analysis, so that selection appropriate model, obtain and approach historical law, model that precision of prediction is high most.
Fastdeveloping Bayesian forecasting theory is to infer that according to prior imformation and sample information obtaining posterior information carries out modeling, has following distinguishing feature in recent years:
Bayesian model is a kind of dynamic model, and it regards conditional probability distribution as prediction distribution, and dopester can obtain prediction distribution according to prior imformation, and uses Bayes' theorem to try to achieve posteriority distribution, and constantly prior imformation is revised;
Bayes method utilizes prior imformation and sample information to forecast.Therefore, while obtaining fresh information in forecasting process (standard volume of inserting as interval etc.), as long as regard the forecast information in this moment as obtain priori, and and sample information combination now, just can revise original forecasting model, not only convenient but also quick, and then the timevarying characteristics of tracking sequence in time;
Bayesian Dynamic has various structures, as seaconal model, regression model, multinomial model, noise model etc., and these models can also be combined and be represented a complex sequence by superposition principle, so Bayes Modeling and Prediction does not have stationarity restriction to data, be applicable to very much the error random series Modeling and Prediction of kinetic measurement nonstationary;
Because Bayesian schools regards probability as the trusting degree of people to something or other as, rather than the stability of frequency, so the approval of some subjectivities also can be described as form of probability, and these are all the subjective prior imformations of relevant research object.During Bayesian forecasting, can not only utilize objective data message, can also utilize the subjective prior imformation of the platform reason that dopester itself can provide to intervene and correction model.In this case, dopester just can process the abnormal conditions that some can expect, for unforeseeable emergency case, can process by the sequential method for supervising of Bei Shisi.This will make Bayesian forecasting result more reliable, improve forecast precision.
Fastdeveloping Bayesian forecasting theory is applied in longmedium term power load forecasting in recent years.In order to overcome traditional combination forecasting method, do not take explicitly into account the uncertainty of model, document [open big. the prediction of Bayesian model average combined and applied research [J] based on EM. modern commerce and trade industry, 2010], in, application Bayesian model average combined Forecasting Methodology is accurately estimated the weight of Single model.Use support vector machine to carry out Combined Method of Midlong Term Load Forecast, but support vector machine is to nuclear parameter, the selected possibility that exists of regularization parameter, document [Niu Dongxiao, Lv Haitao, Zhang Yun's cloud. the Middlelong Electric Power Load Forecast of least square method supporting vector machine [J] under Bayesian frame. North China Electric Power University's journal, 2008,35 (6): 6266] the longmedium term power load forecasting model of application based on LSSVM under Bayesian frame, the parameter that has provided support vector machine algorithm for estimating is selected and method of adjustment.
Whether Spatial Load Forecasting model validity depends on the division of grade under the piece of space region to be predicted correct to a great extent, [inscription on pottery is refined for document, open particle, Pan Hong etc. the Spatial Load Forecasting based on bilateral Bayes's classification [J]. Proceedings of the CSEE, 2007] adopt the Doublelevel Bayesian Classification model based on sample data to carry out Spatial Load Forecasting, improved the correctness to sample classification.Document [Hu Yunsheng, Zheng Jiming. the load forecast based on principal component analysis and genetic neural network [J]. control theory and application, 2008,27 (8): 13] for longmedium term power load forecasting, be subject to the factors such as economy, population, weather, policy, it is all taken into account to the input as forecast model, adopt the method for principal component analysis that the input of network is simplified, select Bayes's normalization method to carry out training network, the training speed that has improved network has also improved the precision of prediction.
When utilizing additive method prediction, introduce bayes method and carry out auxiliary parameter estimation, cluster or do the prediction of some parts, the bayes method that utilizes yet there are no in complete meaning carries out the correlative study of longmedium term power load forecasting.
Summary of the invention
The object of this invention is to provide a kind of longmedium term power load forecasting method based on Bayesian Dynamic, to realize the realtime estimate of the Midlong Term Load under small sample capacity.
In order to achieve the above object, the technical solution adopted in the present invention is:
Longmedium term power load forecasting method based on Bayesian Dynamic, is characterized in that: comprise the following steps:
(1) set up Bayes's exponential polynomials regression model of Power system load data:
Most long Electric Power Load data have the feature that approaches exponential relationship, can consider that Bayes's exponential polynomials regression model of setting up Power system load data realizes Midlong term load forecasting.Electric load model based on Bayesian Dynamic Prediction is generally comprised of observation equation and state equation, and the polynomial expression that is generally no more than second order just can provide the matching of good localized variation trend, and binomial Exponential Regression Model can be expressed as:
Observation equation: (logE)
_{i}=F
_{i} ^{t}θ
_{i}+ v
_{i}v
_{i}～N (0, V
_{i}),
State equation: θ
_{i}=G θ
_{i1}+ ω
_{i}ω
_{i}～N (0, W
_{i}),
In formula, E is electric load value, (logE)
_{i}electric load time series, θ
_{i}=(a
_{i}, b
_{i}, c
_{i})
^{t}for i state parameter vector constantly, F
_{i}=(1, t, t
^{2})
^{t}i dynamic regression matrix constantly,
$G=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]$ For statetransition matrix, ν
_{i}and ω
_{i}be respectively mutually independently observational error and state error variable, and ω
_{n}, ω
_{l}and ν
_{n}, ν
_{l}(n ≠ l) is separate;
(2) determine the prior imformation of associated arguments:
While adopting Bayesian Dynamic prediction recursion, need the prior imformation of known associated arguments, and generally, the prior imformation of parameter is difficult to obtain, and therefore adopts asemantic reference analysis method to determine the prior imformation of associated arguments;
In analyzing without information reference, suppose observational error ν
_{i}(0, V), V is unknown parameter to Normal Distribution N, state equation error ω
_{i}meeting average is 0, and variance is W
_{i}t distribute, in abovementioned electric load model, have 3 state parameter a, b, c and 1 observational variance V, totally 4 unknown parameters, therefore can determine θ according to 4 of initial acquisition Power system load datas
_{i}with the initial information of V, due to the observation data adopting when determining initial information very little, can not estimate or detect any variation of parameter, so can establish W
_{i}=0 (i=1,2,3,4);
If D
_{i}represent the i moment and the set of all effective informations constantly in the past thereof, D
_{i}(i=0) be the set of i=0 initial information, by initial apriority, θ
_{1}with V without D under information condition
_{0}condition joint probability distribution be proportional to the V reciprocal of variance
^{1}:
P(θ
_{1},VD
_{0})∝V
^{1}??V>0
According to Bayesian formula and Power system load data point y
_{1}, y
_{2}, y
_{3}, y
_{4}can recursion obtain posteriority joint probability distribution P (θ
_{4}, VD
_{4}), and then obtain θ
_{4} D
_{4}and V
^{1} D
_{4}condition marginal distribution P (θ
_{4} D
_{4}) and P (V
^{1} D
_{4}), during recursion, need first define following each amount:
H
_{i}＝(G
^{1})
^{T}K
_{i1}G
^{1}
h
_{i}＝(G
^{1})
^{T}k
_{i1}
K
_{i}＝H
_{i}+F
_{i}F
_{i} ^{T}
k
_{i}＝h
_{i}+F
_{i}y
_{i}
Wherein, r
_{i}=r
_{i1}+ 1
λ
_{i}＝δ
_{i1}
δ
_{i}＝λ
_{i}+y
_{i} ^{2}
Here, H
_{i}, h
_{i}, λ
_{i}, r
_{i}, δ
_{i}, K
_{i}, k
_{i}be all the intermediate variable for initial information recursion, recursion initial value is H
_{1}=0, h
_{1}=0, λ
_{1}=0, r
_{0}=0.
Through deriving, obtain θ
_{i}, associating priori, the posteriority of V (i=1,2,3,4) are respectively:
According to abovementioned derivation, obtain P (θ
_{4}, VD
_{4}) after, just can obtain θ
_{4} D
_{4}and V
^{1} D
_{4}posteriority distribute:
(θ
_{i}D
_{i})～T[M
_{i},C
_{i}]
(V
^{1}D
_{i})～Γ[n
_{i}/2,d
_{i}/2]
State variable θ
_{i}posteriority conditional probability to obey average be M
_{i}, variance is C
_{i}t distribute, V
^{1}it is n that posteriority conditional probability is obeyed average
_{i}/ 2, variance is d
_{i}/ 2 Γ distributes.Wherein,
${M}_{i}={{K}_{i}}^{1}{k}_{i},{C}_{i}={S}_{i}{K}_{i}^{1},{S}_{i}={d}_{i}/{n}_{i},{n}_{i}={r}_{i}3,{d}_{i}={\mathrm{\δ}}_{i}{k}_{i}^{T}{M}_{i},$ Try to achieve θ
_{4} D
_{4}and V
^{1} D
_{4}condition marginal distribution after, just using this as initial information, model is revised;
(3) recursion correction and the prediction of Power system load data:
If initial information is:
ω
_{i}～T[0,W
_{i}]
(θ
_{i1}D
_{i1})～T[M
_{i1},C
_{i1}]
(θ
_{i}D
_{i1})～T[A
_{i},R
_{i}],A
_{i}＝GM
_{i1},R
_{i}＝GC
_{i1}G
^{T}+W
_{i}
(V
^{1}D
_{i1})～Γ(n
_{i1}/2,d
_{i1}/2),S
_{i1}＝d
_{i1}/n
_{i1}
In formula, A
_{i}, R
_{i}state variable θ
_{i}the average of prior distribution and variance; S
_{i}it is the point estimation of V.
Observed reading y
_{i}a step forward prediction distribution obey average f
_{i}, variance Q
_{i}t distribute:
(y
_{i}D
_{i1})～T[f
_{i},Q
_{i}],f
_{i}＝F
_{i} ^{T}A
_{i},Q
_{i}＝F
_{i} ^{T}R
_{i}F
_{i}+S
_{i1}
Recursion correction relation:
(θ
_{i}D
_{i})～T[M
_{i},C
_{i}],(V
^{1}D
_{i})～Γ[n
_{i}/2,d
_{i}/2],
M
_{i}＝A
_{i}+B
_{i}e
_{i}
C
_{i}＝(S
_{i}/S
_{i1})[R
_{i}B
_{i}F
_{i} ^{T}Q
_{i}]
Wherein, e
_{i}=y
_{i}f
_{i}for predicated error, B
_{i}=R
_{i}f
_{i}/ Q
_{i}for correction factor matrix.
K walks prediction distribution forward: to k>0,
(θ
_{i+k}D
_{i})～T[A
_{i}(k),R
_{i}(k)]
(y
_{i+k}D
_{i})～T[f
_{i}(k),Q
_{i}(k)]
A
_{i}(k)＝GA
_{i}(k1)
R
_{i}(k)＝GR
_{i}(k1)G
^{T}+W
_{i}
Wherein,
${f}_{i}\left(k\right)={F}_{i++k}^{T}{A}_{i}(k1)$
Initial value is A
_{i}(0)=M
_{i}, R
_{i}(0)=C
_{i},
The predicted value E of electric load
_{i}for y
_{i}prediction average f
_{i}exponential function:
To Comprehensive analysis load, prediction has practical value in the present invention, for load prediction in Electric Power Network Planning provides effective analytical calculation instrument, further promotes the accuracy of predicting under small sample capacity, has good development prospect.
The present invention is directed to one group of electric load measured data, set up dynamic linear builtup pattern, according to bayesian theory, by prior imformation with measure sample, the electric load value of statistical inference next year in real time, realizes the dynamic stepwise predict of long Electric Power Load.The method, according to the inherent Changing Pattern of long Electric Power Load data, has been set up the Bayesian Dynamic with polynomial regression and construction of indexes, has solved the shortcoming of the single model prediction of long Electric Power Load.The sample data that the method requires is less, and can be by the form of Model Monitoring and Subjective Intervention, follow the tracks of in real time the Changing Pattern of current electric load, this will make load forecast result more reliable, for improving longmedium term power load forecasting precision, provide an effective way.
Accompanying drawing explanation
Fig. 1 is Bayesian forecasting recursive algorithm figure in step of the present invention (4).
Embodiment
(1) set up Bayes's exponential polynomials regression model of Power system load data:
Electric load model based on Bayesian Dynamic Prediction is generally comprised of observation equation and state equation, and its binomial Exponential Regression Model can be expressed as:
Observation equation: (logE)
_{i}=F
_{i} ^{t}θ
_{i}+ v
_{i}v
_{i}～N (0, V
_{i}),
State equation: θ
_{i}=G θ
_{i1}+ ω
_{i}ω
_{i}～N (0, W
_{i}),
In formula, E is electric load value, (logE)
_{i}electric load time series, θ
_{i}=(a
_{i}, b
_{i}, c
_{i})
^{t}for i state parameter vector constantly, F
_{i}=(1, t, t
^{2})
^{t}i dynamic regression matrix constantly,
$G=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]$ For statetransition matrix, ν
_{i}and ω
_{i}be respectively mutually independently observational error and state error variable, and ω
_{n}, ω
_{l}and ν
_{n}, ν
_{l}(n ≠ l) is separate;
(2) determine the prior imformation of associated arguments:
While adopting Bayesian Dynamic prediction recursion, need the prior imformation of known associated arguments, and generally, the prior imformation of parameter is difficult to obtain, and therefore adopts asemantic reference analysis method to determine the prior imformation of associated arguments;
In analyzing without information reference, suppose observational error ν
_{i}(0, V), V is unknown parameter to Normal Distribution N, state equation error ω
_{i}meeting average is 0, and variance is W
_{i}t distribute, in abovementioned electric load model, have 3 state parameter a, b, c and 1 observational variance V, totally 4 unknown parameters, therefore can determine θ according to 4 of initial acquisition Power system load datas
_{i}with the initial information of V, due to the observation data adopting when determining initial information very little, can not estimate or detect any variation of parameter, so can establish W
_{i}=0 (i=1,2,3,4);
If D
_{i}represent the i moment and the set of all effective informations constantly in the past thereof, D
_{i}(i=0) be the set of i=0 initial information, by initial apriority, θ
_{1}with V without D under information condition
_{0}condition joint probability distribution be proportional to the V reciprocal of variance
^{1}:
P(θ
_{1},VD
_{0})∝V
^{1}??V>0
According to Bayesian formula and Power system load data point y
_{1}, y
_{2}, y
_{3}, y
_{4}can recursion obtain posteriority joint probability distribution P (θ
_{4}, VD
_{4}), and then obtain θ
_{4} D
_{4}and V
^{1} D
_{4}condition marginal distribution P (θ
_{4} D
_{4}) and P (V
^{1} D
_{4}), during recursion, need first define following each amount:
H
_{i}＝(G
^{1})
^{T}K
_{i1}G
^{1}
h
_{i}＝(G
^{1})
^{T}k
_{i1}
K
_{i}＝H
_{i}+F
_{i}F
_{i} ^{T}
k
_{i}＝h
_{i}+F
_{i}y
_{i}
Wherein, r
_{i}=r
_{i1}+ 1
λ
_{i}＝δ
_{i1}
δ
_{i}＝λ
_{i}+y
_{i} ^{2}
Here, H
_{i}, h
_{i}, λ
_{i}, r
_{i}, δ
_{i}, K
_{i}, k
_{i}be all the intermediate variable for initial information recursion, recursion initial value is H
_{1}=0, h
_{1}=0, λ
_{1}=0, r
_{0}=0.
Through deriving, obtain θ
_{i}, associating priori, the posteriority of V (i=1,2,3,4) are respectively:
According to abovementioned derivation, obtain P (θ
_{4}, VD
_{4}) after, just can obtain θ
_{4} D
_{4}and V
^{1} D
_{4}posteriority distribute:
(θ
_{i}D
_{i})～T[M
_{i},C
_{i}]
(V
^{1} D
_{i})～Γ [n
_{i}/ 2, d
_{i}/ 2] state variable θ
_{i}posteriority conditional probability to obey average be M
_{i}, variance is C
_{i}t distribute, V
^{1}it is n that posteriority conditional probability is obeyed average
_{i}/ 2, variance is d
_{i}/ 2 Γ distributes.Wherein,
${M}_{i}={{K}_{i}}^{1}{k}_{i},{C}_{i}={S}_{i}{K}_{i}^{1},{S}_{i}={d}_{i}/{n}_{i},{n}_{i}={r}_{i}3,{d}_{i}={\mathrm{\δ}}_{i}{k}_{i}^{T}{M}_{i},$ Try to achieve θ
_{4} D
_{4}and V
^{1} D
_{4}condition marginal distribution after, just using this as initial information, model is revised;
(3) recursion correction and the prediction of Power system load data:
The recursion correction of electric load and the basic ideas of prediction are as shown in Figure 1:
If initial information is:
ω
_{i}～T[0,W
_{i}]
(θ
_{i1}D
_{i1})～T[M
_{i1},C
_{i1}]
(θ
_{i}D
_{i1})～T[A
_{i},R
_{i}],A
_{i}＝GM
_{i1},R
_{i}＝GC
_{i1}G
^{T}+W
_{i}
(V
^{1}D
_{i1})～Γ(n
_{i1}/2,d
_{i1}/2),S
_{i1}＝d
_{i1}/n
_{i1}
In formula, A
_{i}, R
_{i}state variable θ
_{i}the average of prior distribution and variance; S
_{i}it is the point estimation of V.
Observed reading y
_{i}a step forward prediction distribution obey average f
_{i}, variance Q
_{i}t distribute:
(y
_{i}D
_{i1})～T[f
_{i},Q
_{i}],f
_{i}＝F
_{i} ^{T}A
_{i},Q
_{i}＝F
_{i} ^{T}R
_{i}F
_{i}+S
_{i1}
Recursion correction relation:
(θ
_{i}D
_{i})～T[M
_{i},C
_{i}],(V
^{1}Di)～Γ[n
_{i}/2,d
_{i}/2],
M
_{i}＝A
_{i}+B
_{i}e
_{i}
C
_{i}＝(S
_{i}/S
_{i1})[R
_{i}B
_{i}F
_{i} ^{T}Q
_{i}]
Wherein, e
_{i}=y
_{i}f
_{i}for predicated error, B
_{i}=R
_{i}f
_{i}/ Q
_{i}for correction factor matrix.
K walks prediction distribution forward: to k>0,
(θ
_{i+k}D
_{i})～T[A
_{i}(k),R
_{i}(k)]
(y
_{i+k}D
_{i})～T[f
_{i}(k),Q
_{i}(k)]
A
_{i}(k)＝GA
_{i}(k1)
R
_{i}(k)＝GR
_{i}(k1)G
^{T}+W
_{i}
Wherein,
${f}_{i}\left(k\right)={F}_{i++k}^{T}{A}_{i}(k1)$
Initial value is A
_{i}(0)=M
_{i}, R
_{i}(0)=C
_{i},
The predicted value E of electric load
_{i}for y
_{i}prediction average f
_{i}exponential function:
Specific embodiment:
In order to verify the validity of the Methods of electric load forecasting based on Bayesian Dynamic, the total electricity consumption of a certain area several years has been carried out to modeling and forecasting, and contrasted with at present conventional improved grey model model prediction result.Original Power system load data, Bayesian Dynamic and improved grey model model prediction result (unit: comparison hundred million kilowatt hours) is in Table 1.
Table 1 Bayesian Dynamic and improved grey model model prediction result (unit: hundred million kilowatt hours)
Time  Original Power system load data  Improved grey model model prediction result  Bayesian Dynamic predicts the outcome 
1  0.4754  0.4754  0.47544 
2  0.6058  0.41692  0.58608 
3  0.6103  0.46933  0.63791 
4  0.6063  0.53012  0.59241 
5  0.6098  0.60075  0.51313 
6  0.4898  0.32414  0.53936 
7  0.5183  0.40558  0.39319 
8  0.6152  0.50231  0.4271 
9  0.6963  0.61706  0.57183 
10  0.9880  1.1722  0.72989 
11  1.1878  1.3498  1.1495 
12  1.5672  1.5575  1.5646 
13  2.2420  1.8005  2.1743 
By relatively finding, in this example, the Methods of electric load forecasting precision of prediction based on Bayesian Dynamic is high, effective, feasible effective.
Claims (1)
1. the longmedium term power load forecasting method based on Bayesian Dynamic, is characterized in that: comprise the following steps:
(1) set up Bayes's exponential polynomials regression model of Power system load data:
Most long Electric Power Load data have the feature that approaches exponential relationship, can consider that Bayes's exponential polynomials regression model of setting up Power system load data realizes Midlong term load forecasting.Electric load model based on Bayesian Dynamic Prediction is generally comprised of observation equation and state equation, and the polynomial expression that is generally no more than second order just can provide the matching of good localized variation trend, and binomial Exponential Regression Model can be expressed as:
Observation equation: (logE)
_{i}=F
_{i} ^{t}θ
_{i}+ v
_{i}v
_{i}～N (0, V
_{i}),
State equation: θ
_{i}=G θ
_{i1}+ ω
_{i}ω
_{i}～N (0, W
_{i}),
In formula, E is electric load value, (logE)
_{i}electric load time series, θ
_{i}=(a
_{i}, b
_{i}, c
_{i})
^{t}for i state parameter vector constantly, F
_{i}=(1, t, t
^{2})
^{t}i dynamic regression matrix constantly,
$G=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]$ For statetransition matrix, ν
_{i}and ω
_{i}be respectively mutually independently observational error and state error variable, and ω
_{n}, ω
_{l}and ν
_{n}, ν
_{l}(n ≠ l) is separate;
(2) determine the prior imformation of associated arguments:
While adopting Bayesian Dynamic prediction recursion, need the prior imformation of known associated arguments, and generally, the prior imformation of parameter is difficult to obtain, and therefore adopts asemantic reference analysis method to determine the prior imformation of associated arguments;
In analyzing without information reference, suppose observational error ν
_{i}(0, V), V is unknown parameter to Normal Distribution N, state equation error ω
_{i}meeting average is 0, and variance is W
_{i}t distribute, in abovementioned electric load model, have 3 state parameter a, b, c and 1 observational variance V, totally 4 unknown parameters, therefore can determine θ according to 4 of initial acquisition Power system load datas
_{i}with the initial information of V, due to the observation data adopting when determining initial information very little, can not estimate or detect any variation of parameter, so can establish W
_{i}=0 (i=1,2,3,4);
If D
_{i}represent the i moment and the set of all effective informations constantly in the past thereof, D
_{i}(i=0) be the set of i=0 initial information, by initial apriority, θ
_{1}with V without D under information condition
_{0}condition joint probability distribution be proportional to the V reciprocal of variance
^{1}:
P(θ
_{1},VD
_{0})∝V
^{1}??V>0
According to Bayesian formula and Power system load data point y
_{1}, y
_{2}, y
_{3}, y
_{4}can recursion obtain posteriority joint probability distribution P (θ
_{4}, VD
_{4}), and then obtain θ
_{4} D
_{4}and V
^{1} D
_{4}condition marginal distribution P (θ
_{4} D
_{4}) and P (V
^{1} D
_{4}), obtain P (θ
_{4}, VD
_{4}) after, just can obtain θ
_{4} D
_{4}and V
^{1} D
_{4}posteriority distribute:
(θ
_{i}D
_{i})～T[M
_{i},C
_{i}]
(V
^{1}D
_{i})～Γ[n
_{i}/2,d
_{i}/2]
State variable θ
_{i}posteriority conditional probability to obey average be M
_{i}, variance is C
_{i}t distribute, V
^{1}it is n that posteriority conditional probability is obeyed average
_{i}/ 2, variance is d
_{i}/ 2 Γ distributes.Try to achieve θ
_{4} D
_{4}and V
^{1} D
_{4}condition marginal distribution after, just using this as initial information, model is revised;
(3) recursion correction and the prediction of Power system load data:
If initial information is:
ω
_{i}～T[0,W
_{i}]
(θ
_{i1}D
_{i1})～T[M
_{i1},C
_{i1}]
(θ
_{i}D
_{i1})～T[A
_{i},R
_{i}],A
_{i}＝GM
_{i1},R
_{i}＝GC
_{i1}G
^{T}+W
_{i}
(V
^{1}D
_{i1})～Γ(n
_{i1}/2,d
_{i1}/2),S
_{i1}＝d
_{i1}/n
_{i1}
In formula, A
_{i}, R
_{i}state variable θ
_{i}the average of prior distribution and variance; S
_{i}it is the point estimation of V.
Observed reading y
_{i}a step forward prediction distribution obey average f
_{i}, variance Q
_{i}t distribute:
(y
_{i}D
_{i1})～T[f
_{i},Q
_{i}],f
_{i}＝F
_{i} ^{T}A
_{i},Q
_{i}＝F
_{i} ^{T}R
_{i}F
_{i}+S
_{i1}
Recursion correction relation:
(θ
_{i}D
_{i})～T[M
_{i},C
_{i}],(V
^{1}D
_{i})～Γ[n
_{i}/2,d
_{i}/2],
M
_{i}＝A
_{i}+B
_{i}e
_{i}
C
_{i}＝(S
_{i}/S
_{i1})[R
_{i}B
_{i}F
_{i} ^{T}Q
_{i}]
Wherein, e
_{i}=y
_{i}f
_{i}for predicated error, B
_{i}=R
_{i}f
_{i}/ Q
_{i}for correction factor matrix.
K walks prediction distribution forward: to k>0,
(θ
_{i+k}D
_{i})～T[A
_{i}(k),R
_{i}(k)]
(y
_{i+k}D
_{i})～T[f
_{i}(k),Q
_{i}(k)]
A
_{i}(k)＝GA
_{i}(k1)
R
_{i}(k)＝GR
_{i}(k1)G
^{T}+W
_{i}
Wherein,
${f}_{i}\left(k\right)={F}_{i++k}^{T}{A}_{i}(k1)$
Initial value is A
_{i}(0)=M
_{i}, R
_{i}(0)=C
_{i},
The predicted value E of electric load
_{i}for y
_{i}prediction average f
_{i}exponential function:
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Cited By (4)
Publication number  Priority date  Publication date  Assignee  Title 

CN104200283A (en) *  20140827  20141210  华北电力大学  Medium and long term power load forecasting method based on factormain attribute model 
CN104573881A (en) *  20150210  20150429  广东石油化工学院  Adaptive prediction method of residual service life of service equipment modeled based on degradation data 
CN105976069A (en) *  20160530  20160928  朱明增  Regionalismbased prediction system and method for shortterm power load of grid region at Guigang 
CN109270842A (en) *  20181025  20190125  浙江大学  A kind of district heating model predictive control system and method based on Bayesian network 

2014
 20140603 CN CN201410242690.1A patent/CN104008433A/en active Pending
NonPatent Citations (2)
Title 

吕林涛、李军怀、吕晖、宋昕、张杰: "贝叶斯动态模型及其预测算法在数据挖掘中的应用研究", 《计算机工程与应用》 * 
樊红东、胡昌华、丁力: "基于贝叶斯动态模型的某器件性能预测", 《电光与控制》 * 
Cited By (6)
Publication number  Priority date  Publication date  Assignee  Title 

CN104200283A (en) *  20140827  20141210  华北电力大学  Medium and long term power load forecasting method based on factormain attribute model 
CN104200283B (en) *  20140827  20170613  华北电力大学  A kind of longmedium term power load forecasting method based on factor primary attribute model 
CN104573881A (en) *  20150210  20150429  广东石油化工学院  Adaptive prediction method of residual service life of service equipment modeled based on degradation data 
CN104573881B (en) *  20150210  20180109  广东石油化工学院  A kind of military service equipment residual life adaptive forecasting method based on degraded data modeling 
CN105976069A (en) *  20160530  20160928  朱明增  Regionalismbased prediction system and method for shortterm power load of grid region at Guigang 
CN109270842A (en) *  20181025  20190125  浙江大学  A kind of district heating model predictive control system and method based on Bayesian network 
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