CN109242190A - Mid-long term load forecasting method and system based on BFGS-FA optimization fractional order gray model - Google Patents
Mid-long term load forecasting method and system based on BFGS-FA optimization fractional order gray model Download PDFInfo
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Abstract
The invention discloses a kind of Mid-long term load forecasting method and systems based on BFGS-FA optimization fractional order gray model, original integer rank gray model is replaced with fractional order gray model, it solves the problems, such as that new information preferentially uses, increases the freedom degree and flexibility ratio of model.Mid-long term load forecasting is carried out using fractional order grey forecasting model, the application range of gray prediction can be expanded, improve the anti-interference ability of gray model.The present invention seeks the optimal factor for taking fractional order grey forecasting model using the global convergence of BFGS-FA algorithm and the characteristic of super-linear convergence, and the accuracy of fractional order grey forecasting model can be improved.It is proved by Case Simulation, load prediction precision can be improved in the fractional order grey forecasting model based on BFGS-FA optimization, reaches better prediction effect.
Description
Technical field
The present invention relates to electric load analytical technologies, more particularly to a kind of BFGS-FA that is based on to optimize fractional order gray model
Mid-long term load forecasting method and system.
Background technique
Load forecast is to utilize currently known information (including historical information, status and the development trend in future),
The process that following load is judged.The precision of load prediction determines the cost of electricity-generating and confession of related power generation unit
Electric reliability.There is overload prediction meeting so that the cost of electricity-generating of power generation unit increases, underload prediction meeting occurs so that power supply is reliable
Property is affected.Since medium-term and long-term load is influenced by various uncertain factors, and the collection relatively short-term of related data,
Load prediction is more difficult, so the precision of prediction of general Mid-long term load forecasting is relatively poor.Traditional load forecasting method
Mainly there are electricity consumption unit consumption method, method of elasticity modulus, per capita household electricity consumption method, time series method, load density method, Grey System Method
Such as with some intelligent algorithms: neural network, support vector machine, deepness belief network.Wherein gray model due to its processing it is small
The characteristics of sample, poor information, has obtained extensive utilization in long term load forecasting in the power system.Many is proposed in recent years
The gray model of new model, including using extension, optimization and modified method, to reach better prediction effect.But
Optimized on the basis of traditional gray model cannot inherently solve input sample fluctuation it is larger when, prediction precision
The problem of reducing.
Summary of the invention
Present invention is primarily aimed at provide a kind of Mid-long Term Load based on BFGS-FA optimization fractional order gray model
Prediction technique and system, when being optimized on the basis of traditional gray model with solving the prior art, when the wave of input sample
When moving larger, the problem of precision of prediction can reduce.
The present invention is achieved through the following technical solutions:
A kind of Mid-long term load forecasting method based on BFGS-FA optimization fractional order gray model, comprising:
Step 1: the order r of the gray model of fractional order is arranged in initialization algorithm basic parameteri, give for calculating
The initial data X of gray prediction(0)=(x(0)(1),x(0)(2),L x(0)(n))；
Step 2: passing through order r respectivelyi, the predicted value of fractional order gray model is calculated, and calculate corresponding average opposite
Error f (ri)；
Step 3: calculating fitness function Fi；And utilize function FiDetermine the light intensity I of fireflyi；
Step 4: calculating riThe distance between Mij:
Update ri:
Step 5: calculating fitness function f (ri)；
Step 6: r is updated by BFGS algorithmi, calculate current fitness function f (ri), and calculate corresponding Fi *, obtain
Optimal value F outp *；
Step 7: more calculated function Fi *Value, if Fi *< Fp *, then ri=rp *；
Step 8: if Fp *(k)< Fp *(k+1), then Fp *(k)=Fp *(k+1), enable rp (k)=rp (k+1)；
Step 9: judging whether to meet algorithmic statement criterion, jump to step 10 if meeting, otherwise jump to step 3；
Step 10: passing through optimal factor rpThe predicted value for calculating fractional order gray model is exported as output valve.
Further, the step 2 includes:
Step 2-1: it calculates initial data and constitutes sequence X(0)RiRank Accumulating generation sequence
Step 2-2: rightFormation sequence as follows
Fractional order gray model is x(r-1)(k)+az(r)(k)=b, wherein
Step 2-3: it calculatesInverse accumulated generating sequence
Step 2-4: parameter matrix is solved as follows
Step 2-5: it determinesTime response formula；
Step 2-6: it calculates according to the following formulaThe analogue value:
Step 2-7: reduction finds out X according to the following formula(0)The analogue value
(k=2,3, L, n), wherein
Step 2-8: average relative error f (r is calculated according to the following formulai):
A kind of Mid-long term load forecasting system based on BFGS-FA optimization fractional order gray model, comprising:
Initialization module is used for initialization algorithm basic parameter, the order r of the gray model of fractional order is arrangedi, give and use
In the initial data X of the gray prediction of calculating(0)=(x(0)(1),x(0)(2),L x(0)(n))；
Fractional order Grey Model value computing module, for passing through order r respectivelyi, calculate fractional order gray model
Predicted value, and calculate corresponding average relative error f (ri)；
Firefly light intensity computing module, for calculating fitness function Fi；And utilize function FiDetermine firefly light intensity Ii；
Distance calculation module, for calculating riThe distance between Mij:
And update ri:
Fitness function computing module, for calculating fitness function f (ri)；
Optimal value computing module, for updating r by BFGS algorithmi, calculate current fitness function f (ri), and calculate
Corresponding Fi *, obtain optimal value Fp *；
Comparison module is used for more calculated function Fi *Value, if Fi *< Fp *, then ri=rp *；
Judgment module, in Fp *(k)< Fp *(k+1)When, enable Fp *(k)=Fp *(k+1), rp (k)=rp (k+1)；
Jump module meets algorithmic statement criterion for judging whether, jumps to output module if meeting, otherwise jumps
To firefly light intensity computing module；
Output module, for passing through optimal factor rpThe predicted value for calculating fractional order gray model is exported as output valve.
Further, the fractional order Grey Model value computing module includes:
Accumulating generation sequence computing module constitutes sequence X for calculating initial data(0)RiRank Accumulating generation sequence
Sequence generating module, for pairFormation sequence as follows
Fractional order gray model is x(r-1)(k)+az(r)(k)=b, wherein
Inverse accumulated generating sequence computing module, for calculatingInverse accumulated generating sequence
Parameter matrix solves module, for solving parameter matrix as follows
Time response formula determining module, for determiningTime response formula；
Analogue value computing module, for calculating according to the following formulaThe analogue value:
The analogue value restores computing module, finds out X for restoring according to the following formula(0)The analogue value
(k=2,3, L, n), wherein
Average relative error computing module, for calculating average relative error f (r according to the following formulai):
Compared with prior art, the Mid-long Term Load provided by the invention based on BFGS-FA optimization fractional order gray model
Prediction technique and system replace original integer rank gray model with fractional order gray model, solve new information and preferentially use
The problem of, increase the freedom degree and flexibility ratio of model.Mid-long term load forecasting is carried out using fractional order grey forecasting model, it can
To expand the application range of gray prediction, the anti-interference ability of gray model is improved.The present invention utilizes the overall situation of BFGS-FA algorithm
Convergence and the characteristic of super-linear convergence seek the optimal factor for taking fractional order grey forecasting model, and fractional order ash can be improved
The accuracy of color prediction model.It is proved by Case Simulation, the fractional order grey forecasting model based on BFGS-FA optimization can mention
High load capacity precision of prediction reaches better prediction effect.
Detailed description of the invention
Fig. 1 is the Mid-long term load forecasting provided in an embodiment of the present invention based on BFGS-FA optimization fractional order gray model
The flow diagram of method；
Fig. 2 is the Mid-long term load forecasting provided in an embodiment of the present invention based on BFGS-FA optimization fractional order gray model
The method flow schematic diagram of step S2 in method；
Fig. 3 is the Mid-long term load forecasting provided in an embodiment of the present invention based on BFGS-FA optimization fractional order gray model
The composition schematic diagram of system；
Fig. 4 is the Mid-long term load forecasting provided in an embodiment of the present invention based on BFGS-FA optimization fractional order gray model
The composition schematic diagram of system mid-score rank Grey Model value computing module.
Specific embodiment
To make the objectives, technical solutions, and advantages of the present invention clearer, below with reference to embodiment and attached drawing, to this
Invention is described in further detail.
Fractional order gray model has the irreplaceable advantage of integer rank gray model, in the same circumstances, fractional order ash
Color model has many advantages, such as that information is preferential compared with integer rank gray model, and disturbance circle is small, these advantages make fractional order grey
Model overcomes the shortcomings that integer rank gray model in load prediction, so that the result of prediction is than integer rank gray model
Accuracy be significantly improved.It can be seen that score exponent arithmetic(al) from the principle of fractional order grey forecasting model and be mainly reflected in number
According to preprocessing process in, the selection of order will affect the forecasting accuracy of fractional order gray model, therefore find optimal rank
Number is particularly significant.Since glowworm swarm algorithm FA has the ability of global optimizing, for other algorithms, sent out in the condition of convergence
Local optimum can be overcome the problems, such as when changing.But FA is slow in the later period convergence of optimization, and convergence precision is not high, to overcome FA's
Defect, using the preferable quasi-Newton method of numerical result, i.e. BFGS algorithm, by the algorithm use in FA iteration renewal process, with
Enhance its local optimal searching ability and convergence rate.
Fractional order grey forecasting model is established on the basis of fractional order Accumulating generation and fractional order inverse accumulated generating.It is logical
It crosses and the order of accumulated generating operator is adjusted, target sequence is generated according to the order of adjustment, to improve grey forecasting model
Fitting precision.
If original data sequence are as follows:
X(0)=(x(0)(1),x(0)(2),L,x(0)(n)), r ∈ R+, X(r)=(x(r)(1),x(r)(2),L,x(r)It (n)) is original
The cumulative ordered series of numbers of the r rank of beginning ordered series of numbers.
Fractional order gray model is x(r-1)(k)+az(r)(k)=b, in which:
Parameter vector in modelLeast Square Method can be used,
Wherein, Y, B are respectively
The differential equation of fractional order gray modelSolution are as follows:
Predicted value are as follows:
(k=2,3, L, n)
Wherein
Mid-long term load forecasting is carried out using fractional order grey forecasting model, the application range of gray prediction can be expanded,
Improve the anti-interference ability of gray model.And the seeking for order r value that focus on of fractional order grey forecasting model takes, r value is not
It is made a big difference with will lead to prediction result.The present invention utilizes the global convergence of BFGS-FA algorithm and superlinear convergence speed
The characteristic of degree seeks the optimal factor for taking fractional order grey forecasting model, and the accuracy of fractional order grey forecasting model can be improved.
The following are the specific implementation processes of technical solution of the present invention:
As shown in Figure 1, the Mid-long Term Load provided in an embodiment of the present invention based on BFGS-FA optimization fractional order gray model
Prediction technique, comprising:
Step S1: the order r of the gray model of fractional order is arranged in initialization algorithm basic parameteri, give for calculating
The initial data X of gray prediction(0)=(x(0)(1),x(0)(2),L x(0)(n))；
Step S2: pass through order r respectivelyi, the predicted value of fractional order gray model is calculated, and calculate corresponding average opposite
Error f (ri)；
Step S3: fitness function F is calculatedi；And utilize function FiDetermine the light intensity I of fireflyi；
Step S4: r is calculatediThe distance between Mij:
Update ri:
Step S5: fitness function f (r is calculatedi)；
Step S6: r is updated by BFGS algorithmi, calculate current fitness function f (ri), and calculate corresponding Fi *, obtain
Optimal value F outp *；
Step S7: more calculated function Fi *Value, if Fi *< Fp *, then ri=rp *；
Step S8: if Fp *(k)< Fp *(k+1), then Fp *(k)=Fp *(k+1), enable rp (k)=rp (k+1)；
Step S9: judging whether to meet algorithmic statement criterion, jumps to step S10 if meeting, otherwise jumps to step
S3；
Step S10: pass through optimal factor rpThe predicted value for calculating fractional order gray model is exported as output valve.
As shown in Fig. 2, the step S2 includes:
Step S2-1: it calculates initial data and constitutes sequence X(0)RiRank Accumulating generation sequence
Step S2-2: rightFormation sequence as follows
Fractional order gray model is x(r-1)(k)+az(r)(k)=b, wherein
Step S2-3: it calculatesInverse accumulated generating sequence
Step S2-4: parameter matrix is solved as follows
Step S2-5: it determinesTime response formula；
Step S2-6: it calculates according to the following formulaThe analogue value:
Step S2-7: reduction finds out X according to the following formula(0)The analogue value
(k=2,3, L, n), wherein
Step S2-8: average relative error f (r is calculated according to the following formulai):
Based on above-mentioned prediction technique, as shown in figure 3, the embodiment of the invention also provides one kind based on BFGS-FA optimization point
The Mid-long term load forecasting system of number rank gray model, comprising:
Initialization module 1 is used for initialization algorithm basic parameter, the order r of the gray model of fractional order is arrangedi, give
The initial data X of gray prediction for calculating(0)=(x(0)(1),x(0)(2),L x(0)(n))；
Fractional order Grey Model value computing module 2, for passing through order r respectivelyi, calculate fractional order gray model
Predicted value, and calculate corresponding average relative error f (ri)；
Firefly light intensity computing module 3, for calculating fitness function Fi；And utilize function FiDetermine firefly light intensity Ii；
Distance calculation module 4, for calculating riThe distance between Mij:
And update ri:
Fitness function computing module 5, for calculating fitness function f (ri)；
Optimal value computing module 6, for updating r by BFGS algorithmi, calculate current fitness function f (ri), and calculate
Corresponding F outi *, obtain optimal value Fp *；
Comparison module 7 is used for more calculated function Fi *Value, if Fi *< Fp *, then ri=rp *；
Judgment module 8, in Fp *(k)< Fp *(k+1)When, enable Fp *(k)=Fp *(k+1), rp (k)=rp (k+1)；
Jump module 9 meets algorithmic statement criterion for judging whether, jumps to output module 10 if meeting, on the contrary
Jump to firefly light intensity computing module 3；
Output module 10, for passing through optimal factor rpThe predicted value for calculating fractional order gray model is defeated as output valve
Out.
As shown in figure 4, the fractional order Grey Model value computing module 2 includes:
Accumulating generation sequence computing module 201 constitutes sequence X for calculating initial data(0)RiRank Accumulating generation sequence
Sequence generating module 202, for pairFormation sequence as follows
Fractional order gray model is x(r-1)(k)+az(r)(k)=b, wherein
Inverse accumulated generating sequence computing module 203, for calculatingInverse accumulated generating sequence
Parameter matrix solves module 204, for solving parameter matrix as follows
Time response formula determining module 205, for determiningTime response formula；
Analogue value computing module 206, for calculating according to the following formulaThe analogue value:
The analogue value restores computing module 207, finds out X for restoring according to the following formula(0)The analogue value
(k=2,3, L, n), wherein
Average relative error computing module 208, for calculating average relative error f (r according to the following formulai):
Above-mentioned forecasting system is corresponding with above-mentioned prediction technique, and each module in above-mentioned forecasting system is for executing above-mentioned prediction
Correspondence step in method, details are not described herein.
Above-described embodiment is only preferred embodiment, the protection scope being not intended to limit the invention, in spirit of the invention
With any modifications, equivalent replacements, and improvements made within principle etc., should all be included in the protection scope of the present invention.
Claims (4)
1. a kind of Mid-long term load forecasting method based on BFGS-FA optimization fractional order gray model characterized by comprising
Step 1: the order r of the gray model of fractional order is arranged in initialization algorithm basic parameteri, give pre- for the grey of calculating
The initial data X of survey(0)=(x(0)(1),x(0)(2),L x(0)(n))；
Step 2: passing through order r respectivelyi, the predicted value of fractional order gray model is calculated, and calculate corresponding average relative error f
(ri)；
Step 3: calculating fitness function Fi；And utilize function FiDetermine the light intensity I of fireflyi；
Step 4: calculating riThe distance between Mij:
Update ri:
Step 5: calculating fitness function f (ri)；
Step 6: r is updated by BFGS algorithmi, calculate current fitness function f (ri), and calculate corresponding Fi *, obtain optimal
Value Fp *；
Step 7: more calculated function Fi *Value, if Fi *< Fp *, then ri=rp *；
Step 8: if Fp *(k)< Fp *(k+1), then Fp *(k)=Fp *(k+1), enable rp (k)=rp (k+1)；
Step 9: judging whether to meet algorithmic statement criterion, jump to step 10 if meeting, otherwise jump to step 3；
Step 10: passing through optimal factor rpThe predicted value for calculating fractional order gray model is exported as output valve.
2. the Mid-long term load forecasting method as described in claim 1 based on BFGS-FA optimization fractional order gray model, special
Sign is that the step 2 includes:
Step 2-1: it calculates initial data and constitutes sequence X(0)RiRank Accumulating generation sequence
Step 2-2: rightFormation sequence as follows
Fractional order gray model is x(r-1)(k)+az(r)(k)=b, wherein
Step 2-3: it calculatesInverse accumulated generating sequence
Step 2-4: parameter matrix is solved as follows
Step 2-5: it determinesTime response formula；
Step 2-6: it calculates according to the following formulaThe analogue value:
Step 2-7: reduction finds out X according to the following formula(0)The analogue value
Wherein,
Step 2-8: average relative error f (r is calculated according to the following formulai):
3. a kind of Mid-long term load forecasting system based on BFGS-FA optimization fractional order gray model characterized by comprising
Initialization module is used for initialization algorithm basic parameter, the order r of the gray model of fractional order is arrangedi, give based on
The initial data X of the gray prediction of calculation(0)=(x(0)(1),x(0)(2),L x(0)(n))；
Fractional order Grey Model value computing module, for passing through order r respectivelyi, calculate the prediction of fractional order gray model
Value, and calculate corresponding average relative error f (ri)；
Firefly light intensity computing module, for calculating fitness function Fi；And utilize function FiDetermine firefly light intensity Ii；
Distance calculation module, for calculating riThe distance between Mij:
And update ri:
Fitness function computing module, for calculating fitness function f (ri)；
Optimal value computing module, for updating r by BFGS algorithmi, calculate current fitness function f (ri), and calculate correspondence
Fi *, obtain optimal value Fp *；
Comparison module is used for more calculated function Fi *Value, if Fi *< Fp *, then ri=rp *；
Judgment module, in Fp *(k)< Fp *(k+1)When, enable Fp *(k)=Fp *(k+1), rp (k)=rp (k+1)；
Jump module meets algorithmic statement criterion for judging whether, jumps to output module if meeting, otherwise jumps to firefly
Fireworm light intensity computing module；
Output module, for passing through optimal factor rpThe predicted value for calculating fractional order gray model is exported as output valve.
4. the Mid-long term load forecasting system as claimed in claim 3 based on BFGS-FA optimization fractional order gray model, special
Sign is that the fractional order Grey Model value computing module includes:
Accumulating generation sequence computing module constitutes sequence X for calculating initial data(0)RiRank Accumulating generation sequence
Sequence generating module, for pairFormation sequence as follows
Fractional order gray model is x(r-1)(k)+az(r)(k)=b, wherein
Inverse accumulated generating sequence computing module, for calculatingInverse accumulated generating sequence
Parameter matrix solves module, for solving parameter matrix as follows
Time response formula determining module, for determiningTime response formula；
Analogue value computing module, for calculating according to the following formulaThe analogue value:
The analogue value restores computing module, finds out X for restoring according to the following formula(0)The analogue value
Wherein,
Average relative error computing module, for calculating average relative error f (r according to the following formulai):
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111523736A (en) * | 2020-05-27 | 2020-08-11 | 南京晓庄学院 | Microgrid load prediction system based on cloud computing and machine learning |
| CN114048425A (en) * | 2021-11-17 | 2022-02-15 | 长春工业大学 | Modeling method of prediction model for representing driver intention |
| CN115660228A (en) * | 2022-12-14 | 2023-01-31 | 湖南能源大数据中心有限责任公司 | Power generation load prediction model training method, prediction method, device and storage medium |
-
2018
- 2018-09-19 CN CN201811096591.1A patent/CN109242190A/en active Pending
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111523736A (en) * | 2020-05-27 | 2020-08-11 | 南京晓庄学院 | Microgrid load prediction system based on cloud computing and machine learning |
| CN114048425A (en) * | 2021-11-17 | 2022-02-15 | 长春工业大学 | Modeling method of prediction model for representing driver intention |
| CN114048425B (en) * | 2021-11-17 | 2024-05-24 | 长春工业大学 | Modeling method of prediction model for representing intention of driver |
| CN115660228A (en) * | 2022-12-14 | 2023-01-31 | 湖南能源大数据中心有限责任公司 | Power generation load prediction model training method, prediction method, device and storage medium |
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Application publication date: 20190118 |