CN104751253B - Distribution power flow Forecasting Methodology based on B- spline Basis bottom developed curve cluster - Google Patents
Distribution power flow Forecasting Methodology based on B- spline Basis bottom developed curve cluster Download PDFInfo
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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Abstract
The invention discloses a kind of distribution power flow Forecasting Methodologies based on B- spline Basis bottom developed curve cluster, and load is predicted using clustering technique, and then the probability of line loss per unit and its generation is predicted by Load flow calculation；Using the curve clustering method being unfolded based on B- spline Basis bottom, considering curvilinear motion rate discussion curve clustering problem, be conducive to comprehensive extraction of Function feature.The present invention solves the difficulty of directly prediction line loss per unit non-linear hour prediction；Curve all-order derivative function is included in curve clustering algorithm, is conducive to comprehensive extraction of Function feature, is conducive to the accuracy of cluster when load fluctuation is larger；Line loss per unit is calculated by load prediction, line loss prediction is made to have theoretical foundation, has avoided the difficulty of nonlinear prediction；The concept of trend probability of happening is introduced, is a supporting role to weighing economy operation of power grid situation, evaluation electric network composition and rationally distributed property, rationally assigning traffic order etc..
Description
Technical field
The invention belongs to Calculating Network Theoretical Line Loss electric powder predictions more particularly to a kind of B- spline Basis bottom that is based on to be unfolded song
The distribution power flow Forecasting Methodology of line cluster.
Background technology
Electric power networks loss is the power attenuation that electric energy generates in transmission process, and line loss per unit is one of electric power enterprise
Important technology economic indicator and the important symbol for weighing electric power enterprise technical merit and management level.It is power grid to reduce line loss
With an important process of power supply enterprise and raising enterprise profit, the important means of energy-saving and emission-reduction.According to country, " resource is examined
Method is laid equal stress on saving, and saving is put in the first place " principles and policies, electric power enterprise for reduce line loss per unit, improve electricity usage efficiency
And economic benefit, a large amount of manpower, finance, material resources are put into, the gratifying achievement gone.But the line loss per unit in China in the world
Compared to still higher, electric energy loss can substantially account for the 27%~32% of generated energy for developed country.Theoretical line loss caluclation and prediction pair
In measurement economy operation of power grid situation, evaluation electric network composition and rationally distributed property, traffic order etc. is rationally assigned with important
Effect.
However, theory wire loss prediction at present is that line loss per unit is directly predicted by generator processing etc. mostly, it is this non-thread
Sexual intercourse is difficult accurately to find, and causes line loss per unit prediction inaccurate.The accuracy of dispatching of power netwoks is directly affected, influences the line of power grid
Damage administrative analysis and transformation.
Invention content
The purpose of the present invention is to provide a kind of distribution power flow prediction sides based on B- spline Basis bottom developed curve cluster
Method, it is intended to which it is directly to predict that line loss per unit accuracy rate is low, makes by generator processing etc. mostly to solve current theory wire loss prediction
It is inaccurate into line loss per unit prediction, the problem of directly affecting the accuracy of dispatching of power netwoks, influence grid line loss administrative analysis and transformation.
The invention is realized in this way a kind of curve clustering method trend Forecasting Methodology based on the expansion of B- spline Basis bottom
Including：
Extract daily load curve；
Burden with power curve is clustered with the curve clustering method being unfolded based on B- spline Basis bottom, idle curve
Cluster result then with corresponding burden with power curve identical；The all-order derivative function of curve is included in curve clustering algorithm,
It is more conducive to comprehensive extraction of load curve feature；Considering curvilinear motion rate discussion curve clustering problem, favorably
In comprehensive extraction of Function feature, be conducive to the accuracy of cluster when load fluctuation is larger；
It is predicted with grey relational grade, it is bent as the prediction on the same day to find out the maximum a kind of average value of the degree of association
Line；Line loss per unit is predicted by predicting load, the difficulty for solving directly prediction line loss per unit non-linear hour prediction.
Estimate the probability that trend occurs；The concept of trend probability of happening is introduced, to weighing economy operation of power grid situation, evaluation
Electric network composition and rationally distributed property are rationally assigned traffic order etc. and are a supporting role.
The extraction daily load curve is to extract day active and reactive load total under power distribution network each step-down transformer
Curve, as the sample of cluster, for predicting following curve；
It is described every type load curve is carried out cluster be with k-means clustering methods to per first quarter load curve and
Its derivative is clustered respectively；
The prediction load curve simultaneously carries out Load flow calculation and carries out node voltage calculating, branch with being pushed forward the method that rewinds
Current calculation, the active power and reactive power and load factor of each node calculate；Line loss per unit is obtained by Load flow calculation.
Description of the drawings
Fig. 1 is the distribution power flow prediction side provided in an embodiment of the present invention clustered based on B- spline Basis bottom developed curve
Method flow chart；
Fig. 2 is provided in an embodiment of the present invention to carry out cluster flow chart to every type load curve；
Fig. 3 is prediction load curve provided in an embodiment of the present invention and carries out Load flow calculation flow chart.
Specific embodiment
In order to make the purpose , technical scheme and advantage of the present invention be clearer, with reference to embodiments, to the present invention
It is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, it is not used to
Limit the present invention.
Below in conjunction with the accompanying drawings and specific embodiment is further described the application principle of the present invention.
A kind of curve clustering method trend Forecasting Methodology (see Fig. 1) based on the expansion of B- spline Basis bottom of the present invention, packet
Extraction daily load curve is included, every type load curve is clustered, predict load curve and carries out Load flow calculation and estimation trend
The probability of generation；
The extraction daily load curve is to extract day active and reactive load total under power distribution network each step-down transformer
Curve；
It is described every type load curve is clustered (see Fig. 2) be to per first quarter load curve and its derivative respectively into
Row cluster；
The prediction load curve simultaneously carries out Load flow calculation (see Fig. 3) and includes that node voltage calculates, branch current calculates,
The active power and reactive power and load factor of each node calculate.
A kind of curve clustering method trend Forecasting Methodology based on the expansion of B- spline Basis bottom of the embodiment of the present invention is specifically wrapped
Include following steps：
Step 1, total day active and reactive load curve, is temporally divided under extraction power distribution network each step-down transformer
Spring, summer, autumn, four groups of winter, if some loads lack load or burden without work curve, it is as follows to match reactive power formula：Q=P*tan σ,
The line taking road head end power factor if cos σ are unknown；The variation of daily load curve has certain periodicity；Such as：Same season
Interior daily load curve and the week type on the same day have stronger association, and the season typical day load curve of different year has very
High similitude；
Step 2 clusters burden with power curve with the curve clustering method being unfolded based on B- spline Basis bottom, nothing
Work(curve cluster result then with corresponding burden with power curve identical；The all-order derivative function of curve is included in curve cluster
Algorithm, this way are more conducive to comprehensive extraction of load curve feature；
It specifically includes：
The first step, it is assumed that known a certain load day curve is in the value X at certain momenti(tij) (for fluctuating larger load
Its discrete value is The more the better), ti=[ti1,ti2,ti3,...timi] it is independent variable t m in section D=[0,24]iIt is a from
The column vector that scatterplot is formed；It is further assumed that curve XiIt (t) can be by one group of basis function { φ in some set spacei1(t),φi2
(t), it ... } states, i.e.,
Discrete data is turned into continuous data in this way, the estimated value in the case of finite dimension isWherein
αi=αi1, αi2... αik]T；
To all load curve Xi(t) (i=1 2 ..., n) is stated, and basis function is established as using identical substrate
Equidistant Nodes B- spline Basis bottom；ThenWherein L=M+K, Bk,M(t) it represents k-th
Internal node quantity is the M rank B- batten basis functions of K；Wherein BM(t)=[B1,M(t),B2,M(t),...,BL,M(t)]T, αi
=[αi1,αi2,...αik]T；
Second step, the function distance that basis function is asked to state；Remember load curve Xi(t) and Xj(t) distance is d2(i,j),
According to L2The definition of norm has squared-distance
Because employing identical substrate has Xi(t)-Xj(t)=[αi-αj]TBM(t) then d2(i, j)=[αi-αj]TL[αi-
αj], wherein：
It is symmetrical matrix for L*L, whereinMake Chu Liesiji points to real symmetric matrix L
Solution, there is L=UTU, U are the appropriate upper triangular matrix of size；It enables：bi=U αi；
Then d2(i, j)=[bi-bj]T[bi-bj]；
Third walks, the derivative distance that basis function is asked to state；Distance reciprocal can distinguish curvilinear function variation degree
Difference increases the accuracy of cluster；According to de Boor C, researches show that the derivative of B- batten basis functions is：
Then the derivative function of Xi (t) is：
WhereinFor backward difference；Write above formula as matrix form X'i(t)=[D αi]TBM-1(t)；
Wherein BM-1(t)=[B1,M-1(t),...,BL-1,M-1(t)]TFor L-1 dimensional vectors；
For (L-1) * (L-2) rank matrix, then first derivative function range formula is：
WhereinDt is symmetrical matrix for (L-1) *'s (L-1)；Ibid to real symmetric matrix L(1)Make Chu Liesiji decomposition：It enablesThen derivative function range formula is rewritten as
4th step, such as to total burden with power curve X under a certain transformeri(t) it is clustered, with the above method
Data processing is carried out, obtains biWithBy biWithConjunction is written as a column vectorObtain sample set
{Yi, maximum value, minimum value and the average value of each component of all samples of training sample set respectively constitute vectorial Ymax、YminAndThe sample concentrated to training sample is normalized：To Yi' carried out using k-means algorithms
Cluster；The object function of cluster is：In formula：wiFor class RiCluster centre；J is compiled for sample
Number；yjColumn vector for above-mentioned generation；N is sample number；C is cluster centre number；ajiJudge whether j-th of sample belongs to i-th
Class；
Idle curve cluster result then with corresponding burden with power curve identical；
Step 3 is predicted with grey relational grade；Most of electric system can be provided including day in the several years
The load and the historical data accumulation of the meteorologic factors such as temperature, precipitation, humidity that type, every day, integral point was carved, can be accordingly
Carry out modeling analysis；Wherein day type can be divided into working day and nonworkdays, as the independent variable of prediction model, be modeled
Shi Qianzhe represents that the latter is represented with 0 with 1；And the order of magnitude of the absolute data of load and meteorologic factor is differed from 10~1000, meter
Measure unit also disunity, it is therefore necessary to which the sample of data is first normalized；
Normalized value=(factor value-factor minimum value)/(the factor maximum value-factor minimum value)；
When load curve is estimated, only the result of cluster and the relevant parameter of day to be predicted need to be utilized to predict the day of this day
Load curve；The day type of day to be predicted is known conditions, and the meteorologic factors such as temperature, precipitation, humidity can pass through meteorology
Department obtains, therefore can calculate the feature vector of day to be predicted and the degree of correlation of each class, finds out the class of degree of correlation maximum,
The daily load curve of day to be predicted is the average value for the daily load curve for being taken as such interior every day；
According to the obtained load value of prediction, the flow situations for being pushed forward the method for pushing back and calculating power distribution network are utilized；Equipped with m drop
Pressure transformer, load curve cluster is a under i-th of transformer in certain first quarteriClass then corresponds to the trend of different load situation
Situation hasKind；
Step 4, known to the place season of trend to be estimated, it is assumed that the daily load curve historical data of a certain load shares X
Curve has been divided into y classes by cluster, has had x in jth classjCurveThen estimate that j type loads occur general
Rate is Pj=xj/X；
Certain total load probability occurred under known i-th of transformer is Pi, then load correspond to trend generation probability be
The foregoing is merely illustrative of the preferred embodiments of the present invention, is not intended to limit the invention, all essences in the present invention
All any modification, equivalent and improvement made within refreshing and principle etc., should all be included in the protection scope of the present invention.
Claims (5)
1. a kind of distribution power flow Forecasting Methodology based on B- spline Basis bottom developed curve cluster, which is characterized in that this is based on
The distribution power flow Forecasting Methodology of B- spline Basis bottom developed curve cluster is bent with B- spline Basis bottom expansion training daily load
Line clusters training result；By predicting that daily load curve calculates distribution power flow, specifically include：
Burden with power curve is clustered with the curve clustering method being unfolded based on B- spline Basis bottom, idle curve cluster
As a result then with corresponding burden with power curve identical；The all-order derivative function of curve is included in curve clustering algorithm, every class is born
It is that per first quarter load curve and derivative are clustered respectively that lotus curve, which carries out cluster,；
It is predicted with grey relational grade, predict load curve and carries out Load flow calculation；Prediction load curve simultaneously carries out trend
Calculating includes node voltage calculating, branch current calculates, the active power and reactive power of each node and load factor meter
It calculates；
Introduce the concept of trend probability of happening, the probability that estimation trend occurs；
The place season of trend to be estimated is it is known that the daily load curve historical data of a certain load shares X curve, by poly-
Class has been divided into y classes, has x in jth classjCurveThen estimate that the probability that j type loads occur is Pj=xj/X；
Certain total load probability occurred under known i-th of transformer is Pi, then load correspond to trend generation probability be
2. the distribution power flow Forecasting Methodology as described in claim 1 based on B- spline Basis bottom developed curve cluster, feature
It is, needs to extract daily load curve before clustering load curve, extraction daily load curve is that extraction power distribution network is each
Active and reactive load curve of total day under a step-down transformer.
3. the distribution power flow Forecasting Methodology as claimed in claim 2 based on B- spline Basis bottom developed curve cluster, feature
It is, the method for extracting daily load curve includes：
Total day active and reactive load curve, is temporally divided into spring, summer, autumn, winter under each step-down transformer of extraction power distribution network
Four groups, some loads lack load or burden without work curve, then it is as follows to match reactive power formula：The unknown then line takings of Q=P*tan σ, cos σ
Road head end power factor.
4. the distribution power flow Forecasting Methodology as described in claim 1 based on B- spline Basis bottom developed curve cluster, feature
It is, burden with power curve is clustered with the curve clustering method being unfolded based on B- spline Basis bottom, idle curve cluster
As a result then with corresponding burden with power curve identical；The all-order derivative function of curve is included in curve clustering algorithm to specifically include：
The first step, it is known that a certain load day curve is in the value X at certain momenti(tij), ti=[ti1,ti2,ti3,...timi] it is from change
Measure t m in section D=[0,24]iThe column vector that a discrete point is formed；Curve Xi(t) by one group of substrate letter in some set space
Number { φi1(t),φi2(t), it ... } states, i.e.,
Discrete data is turned into continuous data, the estimated value in the case of finite dimension is：
Whereinαi=[αi1,αi2,...αik]T；To all load curve Xi(t) (i=1,
It 2 ..., n) is stated using identical substrate, and basis function is established as Equidistant Nodes B- spline Basis bottom；ThenWherein L=M+K, Bk,M(t) the M ranks that k-th of internal node quantity is K are represented
B- batten basis functions；Wherein BM(t)=[B1,M(t),B2,M(t),...,BL,M(t)]T, αi=[αi1,αi2,...αik]T；
Second step, the function distance that basis function is asked to state；Remember load curve Xi(t) and Xj(t) distance is d2(i, j), according to
L2The definition of norm has squared-distance
Because employing identical substrate has Xi(t)-Xj(t)=[αi-αj]TBM(t) then d2(i, j)=[αi-αj]TL[αi-αj],
Wherein：
It is symmetrical matrix for L*L, whereinChu Liesiji decomposition is made to real symmetric matrix L, there is L
=UTU, U are the appropriate upper triangular matrix of size；It enables：bi=U αi；
Then d2(i, j)=[bi-bj]T[bi-bj]；
Third walks, the derivative distance that basis function is asked to state；Distance reciprocal distinguishes the difference of curvilinear function variation degree, B- samples
The derivative of basis function is：
Then the derivative function of Xi (t) is：
Wherein ▽ αk=αk-αk-1For backward difference；Write above formula as matrix form X 'i(t)=[D αi]TBM-1(t)；
Wherein BM-1(t)=[B1,M-1(t),...,BL-1,M-1(t)]TFor L-1 dimensional vectors；
For (L-1) * (L-2) rank matrix, then first derivative function range formula is：
WhereinWhat it is for (L-1) * (L-1) is symmetrical matrix；Ibid to real symmetric matrix L(1)Make Chu Liesi
Base decomposes：L(1)=[U(1)]TU(1)It enablesThen derivative function range formula is rewritten as
4th step, to total burden with power curve X under a certain transformeri(t) it is clustered, carries out data processing, obtain bi
WithBy biWithConjunction is written as a column vectorObtain sample set { Yi, all samples of training sample set
Maximum value, minimum value and the average value of each component respectively constitute vectorial Ymax、YminAndTo training sample concentrate sample into
Row normalized：To Yi' clustered using k-means algorithms；The object function of cluster is：In formula：wiFor class RiCluster centre；J is sample number；yjColumn vector for generation；N
For sample number；C is cluster centre number；ajiJudge whether j-th of sample belongs to the i-th class；
Idle curve cluster result then corresponding burden with power curve identical.
5. the distribution power flow Forecasting Methodology as described in claim 1 based on B- spline Basis bottom developed curve cluster, feature
Be, predicted with grey relational grade, according in the several years of offer day type, every day integral point carve load and temperature
Degree, precipitation, the accumulation of the historical data of humidity meteorologic factor, carry out modeling analysis；
Day, type was divided into working day and nonworkdays, and as the independent variable of prediction model, the former is represented with 1 when being modeled, after
Person is represented with 0；And the order of magnitude of the absolute data of load and meteorologic factor is differed from 10~1000, first to the sample of data elder generation
It is normalized；
Normalized value=(factor value-factor minimum value)/(the factor maximum value-factor minimum value)；
According to the obtained load value of prediction, the flow situations for being pushed forward the method for pushing back and calculating power distribution network are utilized；There is m downconverter
Device, load curve cluster is a under i-th of transformer in certain first quarteriClass, the then flow situations for corresponding to different load situation haveKind.
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| CN111915195B (en) * | 2020-08-06 | 2023-12-01 | 南京审计大学 | Public power resource allocation method combining blockchain and big data |
| CN112651797B (en) * | 2020-12-18 | 2024-04-12 | 国网青海省电力公司 | Typical daily supply and demand ratio curve forming method based on clustering algorithm |
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