CN109390946A - A kind of optimum probability trend quick calculation method based on multi-parametric programming theory - Google Patents
A kind of optimum probability trend quick calculation method based on multi-parametric programming theory Download PDFInfo
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/04—Circuit arrangements for ac mains or ac distribution networks for connecting networks of the same frequency but supplied from different sources
- H02J3/06—Controlling transfer of power between connected networks; Controlling sharing of load between connected networks
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
- H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
Abstract
The invention discloses a kind of optimum probability trend quick calculation method based on multi-parametric programming theory, key steps are as follows: 1) be sampled to electric power networks, to extract sample data.2) according to conventional electric power generation unit operating cost and constraint, direct current Optimized model is established.3) theoretical based on multi-parametric programming, the parsing relationship 4 of optimal load flow result Yu renewable energy generation output power is calculated) according to renewable energy probability nature, extract k-th of renewable energy power generation machine output power sampleJudge renewable energy power generation machine output powerAffiliated critical region, and calculate optimal conventional electric power generation unit output powerI-th of critical region CRiMiddle optimal objective functionAnd Branch Power Flow5) convergence judgement, and count and export optimal load flow result.The present invention has flexible scalability, any to improve embeddable the mentioned quick calculation method of sampling algorithm, has further speeded up convergence rate.
Description
Technical field
The present invention relates to Economic Dispatch field, specifically a kind of optimum probability based on multi-parametric programming theory
Trend quick calculation method.
Background technique
Renewable energy power generation scale it is increasingly huge so that electric system uncertain factor increase sharply.Optimum probability tide
Stream can effectively consider that renewable energy uncertainty influences, therefore obtain answering extensively in Operation of Electric Systems optimization
With.Existing optimum probability trend method can be divided into simulation and analytic method.Typical generation of traditional Monte Carlo method as simulation
Table after the optimal load flow result by solving each sample, then by statistical obtains optimum probability power flow solutions.But to protect
Computational accuracy is demonstrate,proved, simulation need to carry out repeated optimization calculating to great amount of samples.It is existing for the disadvantage for overcoming calculation with imitation method time-consuming
Scholar proposes the analytic methods such as point estimations, Unscented transform method again.Point estimations and Unscented transform method only need to solve an other allusion quotation
Each rank statistical moment of description optimal load flow probability of outcome feature can be obtained in pattern sheet.But point estimations are difficult to obtain accurately
High Order Moment, no mark method of changing can not even obtain the information of three ranks and its higher order square.Therefore, existing optimum probability trend method
It is difficult to combine computational accuracy and calculates the time.
Summary of the invention
Present invention aim to address problems of the prior art.
To realize the present invention purpose and the technical solution adopted is that such, it is a kind of based on theoretical optimal of multi-parametric programming
Probabilistic Load Flow quick calculation method, mainly comprises the steps that
1) frequency in sampling threshold epsilon is set, and electric power networks are sampled, to extract sample data.The sample number
According to mainly including renewable energy generation output power PRWith power consumer load PD。
2) according to conventional electric power generation unit operating cost and constraint, direct current Optimized model is established.
Direct current Optimized model objective function is as follows:
In formula, PGFor conventional electric power generation unit output power.H (*) is conventional electric power generation unit operating cost function.To pass
System generating set minimum operating cost.
Direct current Optimized model constraint condition is respectively if formula (2) are to shown in formula (5), it may be assumed that
eGPG+eRPR=eDPD。 (2)
In formula, PRFor renewable energy generation output power.PDFor power consumer load.eG、eRAnd eDFor unit vector.
In formula,(*)WithIt is to represent lower and upper limit respectively.
In formula, PLineFor Branch Power Flow power.
PLine=PTDF × (MGPG+MRPR-MDPD)。 (5)
In formula, PTDF is power transmission distribution matrix.MG、MRAnd MDRespectively and PG、PRAnd PDRelevant node-branch closes
Join matrix.
3) theoretical based on multi-parametric programming, the solution of optimal load flow result Yu renewable energy generation output power is calculated
Analysis relationship.
Optimal load flow result is calculated and the key step of the parsing relationship of renewable energy generation output power is as follows:
3.1) decision variable x is set as conventional electric power generation unit output power PG, projecting parameter w is that renewable energy generation is defeated
Power P outR。
3.2) optimization aim is as follows:
In formula,For the generating set minimum operating cost of optimization.Matrix A, Matrix C and matrix D are for building
Vertical generating set trend Constraints of Equilibrium, generator capacity constrain and the certainty matrix of line transmission limit restraint.
3.3) the optimum segmentation equation of projecting parameter w is calculated.
Enabling K is the subscript of formula (6) constraint.Remember arbitrary constraint setFor AJ、CJAnd DJCorresponding submatrix, institute
Stating submatrix is the constraint for corresponding to lower label J in all constraints.
The hyperspace given for oneIfThe definition of its optimum segmentation is denoted as (γ (w), γc(w)),
That is:
In formula, w is projecting parameter.X is decision variable.x*It (w) is the optimal solution on critical region i.
3.4) critical region of projecting parameter w is calculated.
For given projecting parameterDefinitionFor (γ (w0),γc(w0)), then correspond to γ0Face
Boundary domain is as follows:
Wherein, i-th of critical region CRiKuhn tucker condition it is as follows:
In formula, JiFor in CRiIn operative constraint collection.For CRiIn correspond to operative constraint antithesis multiplier.▽xFor certainly
The gradient operator of plan variable x.
3.5) according to the critical region of projecting parameter w and optimum segmentation equation, critical region CR is obtainediIn optimal conventional electric generators
Group output powerWith renewable energy generation output power PRIn relationship, it may be assumed that
In formula, FxiAnd GxiFor in critical region CRiOn, by formula (9) obtained coefficient matrix.
3.6) formula (10) are substituted into objective function z=h (PG) in, obtain critical region CRiMiddle optimal objective function
That is:
Formula (10) are substituted into Branch Power FlowIn, obtain Branch Power FlowWith renewable energy machine
Group output power PRRelationship, it may be assumed that
Formula (10) are substituted into the inactivce constraints collection γ of formula (7)c(w) in, critical region CR is obtainediExpression formula, it may be assumed that
In formula, GiAnd HiIt is so required that be used to describe critical region CRiThe coefficient matrix of range.
Wherein, coefficient matrix GiWith coefficient matrix HiIt is as follows respectively:
In formula,WithRow submatrix respectively in matrix A and matrix G, corresponding to inactivce constraints collection.
In formula, DJcFor the row submatrix in matrix D, corresponding to inactivce constraints collection.
4) according to renewable energy probability nature, k-th of renewable energy power generation machine output power sample is extractedSentence
Disconnected renewable energy power generation machine output powerAffiliated critical region, and calculate optimal conventional electric power generation unit output powerI-th of critical region CRiMiddle optimal objective functionAnd Branch Power Flow
5) convergence judgement.
If sample number k >=ε stops sample calculation, and counts optimal load flow result.The optimal load flow result is mainly wrapped
Include conventional electric power generation unit output power PG, operating costBranch Power FlowMean value and standard deviation.If sample
Number k < ε, then enable k=k+1, and return step 3.
The solution have the advantages that unquestionable.A kind of quick side of calculating of probability optimal load flow proposed by the present invention
Method, on the basis of existing direct current Optimized model, theoretical by introducing multi-parametric programming, optimal load flow result is expressed as can be again
The analytical expression of raw energy output power.Further combined with Monte Carlo Analogue Method, the knot of optimum probability trend is directly obtained
Fruit, so that a large amount of repeated optimization be avoided to calculate.In addition, the present invention has flexible scalability: 1) any to improve sampling calculation
Embeddable the mentioned quick calculation method of method, further speeds up convergence rate；2) correlation of renewable energy and other are heavy
The uncertain feature wanted can also be considered by some conventional treatments in sampling.
Detailed description of the invention
Fig. 1 is method flow diagram.
Specific embodiment
Below with reference to embodiment, the invention will be further described, but should not be construed the above-mentioned subject area of the present invention only
It is limited to following embodiments.Without departing from the idea case in the present invention described above, according to ordinary skill knowledge and used
With means, various replacements and change are made, should all include within the scope of the present invention.
Embodiment 1:
Referring to Fig. 1, a kind of optimum probability trend quick calculation method based on multi-parametric programming theory mainly includes following
Step:
1) frequency in sampling threshold epsilon is set, and electric power networks are sampled, to extract sample data.The sample number
According to mainly including renewable energy generation output power PRWith power consumer load PD。
2) according to conventional electric power generation unit operating cost and constraint, direct current Optimized model is established.Conventional electric power generation unit is mainly
Refer to the generating set of traditional thermal power generation.
Direct current Optimized model objective function is as follows:
In formula, PGFor conventional electric power generation unit output power.h(PG) it is conventional electric power generation unit operating cost function.To pass
System generating set minimum operating cost.
Direct current Optimized model constraint condition is respectively if formula (2) are to shown in formula (5), it may be assumed that
eGPG+eRPR=eDPD。 (2)
In formula, PRFor renewable energy generation output power.PDFor power consumer load.eG、eRAnd eDFor unit vector.
In formula,(*)WithIt is to represent lower and upper limit respectively.PGFor conventional electric power generation unit output power lower limit.To pass
The system generating set output power upper limit.
In formula, PLineFor Branch Power Flow power.P LineFor the Branch Power Flow lower limit of the power.For the Branch Power Flow upper limit of the power.
PLine=PTDF × (MGPG+MRPR-MDPD)。 (5)
In formula, PTDF is power transmission distribution matrix.MG、MRAnd MDFor be respectively and PG、PRAnd PDRelevant node-branch
Incidence matrix.
3) theoretical based on multi-parametric programming, the solution of optimal load flow result Yu renewable energy generation output power is calculated
Analysis relationship, key step are as follows:
3.1) decision variable x is set as conventional electric power generation unit output power PG, projecting parameter w is that renewable energy generation is defeated
Power P outR。 For the renewable energy generation output power upper limit.
3.2) optimization aim is as follows:
In formula,For the generating set minimum operating cost of optimization.Matrix A, Matrix C and matrix D are for building
Vertical generating set trend Constraints of Equilibrium, generator capacity constrain and the certainty matrix of line transmission limit restraint.
3.3) the optimum segmentation equation of projecting parameter w is calculated.Enabling K is the subscript of formula (6) constraint.Remember arbitrary constraint setFor AJ、CJAnd DJCorresponding submatrix, the submatrix are the constraint for corresponding to lower label J in all constraints.
The hyperspace given for oneIfThe definition of its optimum segmentation is denoted as (γ (w), γc(w)),
That is:
In formula, w is projecting parameter.X is decision variable.x*It (w) is the optimal solution on critical region i.Matrix AJIt is matrix A
Submatrix, be by constraint set J represented by constraint.Matrix CJThe submatrix of Matrix C, be by constraint set J represented by constraint.
Matrix DJThe submatrix of matrix D, be by constraint set J represented by constraint.
3.4) critical region of projecting parameter w is calculated.
For given projecting parameterDefinitionFor (γ (w0),γc(w0)), then correspond to γ0Face
Boundary domain is as follows:
γ0For projecting parameter w0Optimum segmentation.
Wherein, i-th of critical region CRiKuhn tucker condition it is as follows:
In formula, JiFor in CRiIn operative constraint collection.For CRiIn correspond to operative constraint antithesis multiplier.For certainly
The gradient operator of plan variable x.It is the submatrix of matrix A, is by operative constraint collection JiRepresented constraint.It is matrix D
Submatrix is by operative constraint collection JiRepresented constraint.It is the submatrix of Matrix C, is by operative constraint collection JiIt is represented
Constraint.
3.5) according to the critical region of projecting parameter w and optimum segmentation equation, critical region CR is obtainediIn optimal conventional electric generators
Group output powerWith renewable energy generation output power PRIn relationship, it may be assumed that
In formula, FxiAnd GxiFor in critical region CRiOn, by formula (9) obtained coefficient matrix.
3.6) formula (10) are substituted into objective function z=h (PG) in, obtain critical region CRiMiddle optimal objective function
That is:
h(GxiPR+Fxi) it is with Gxi、PRAnd/or FxiFor the conventional electric power generation unit operating cost function of variable.
Formula (10) are substituted into Branch Power FlowIn, obtain Branch Power FlowWith renewable energy machine
Group output power PRRelationship, it may be assumed that
Formula (10) are substituted into the inactivce constraints collection γ of formula (7)c(w) in, critical region CR is obtainediExpression formula, it may be assumed that
In formula, GiAnd HiTo be obtained for describing critical region CRiThe coefficient matrix of range.
Wherein, coefficient matrix GiWith coefficient matrix HiIt is as follows respectively:
In formula,WithRow submatrix respectively in matrix A and matrix G, corresponding to inactivce constraints collection.
WithFormula (7) are seen respectively, refer to second formula of formula (7) with c subscript, and (7) second formula of formula are only to partially determining
Plan variable x works.
In formula,For the row submatrix in matrix D, corresponding to inactivce constraints collection.Formula (14) and formula (15) are will be public
Formula (10) is brought into obtained in formula (7).
4) according to renewable energy probability nature, k-th of renewable energy power generation machine output power sample is extractedSentence
Disconnected renewable energy power generation machine output powerAffiliated critical region, and calculate optimal conventional electric power generation unit output powerI-th of critical region CRiMiddle optimal objective functionAnd Branch Power Flow
5) convergence judgement.If sample number k >=ε stops sample calculation, and counts optimal load flow as a result, the optimal tide
Flowing result mainly includes conventional electric power generation unit output power PG, operating costBranch Power FlowMean value and mark
It is quasi- poor.If sample number k < ε, k=k+1, and return step 3 are enabled.
The present invention is based on direct current Optimized model, by multi-parametric programming by the operating cost and state in Optimized model
Variable is expressed as the function expression of renewable energy power generation unit output power；Further combined with Monte Carlo Analogue Method, solution
Analysis solves single optimal load flow calculated result.When renewable energy power generation unit output power changes, need to only be closed according to parsing
System, can be obtained accurate optimum probability power flow solutions by simple matrix operation.Whole process demand Xie Yici matrix is asked
Topic avoids multiplicating optimization and calculates the huge calculation amount of bring.
Embodiment 2:
The experiment of the optimum probability trend quick calculation method based on multi-parametric programming theory is verified, mainly includes following step
It is rapid:
1) 8 are accessed in 118 node system of IEEE, IEEE300 node system and Polish 2383 node systems respectively
Wind power plant amounts to 1600MW installed capacity.
2) by based on multi-parametric programming theory optimum probability trend quick calculation method and traditional Monte Carlo method it is (accurate
Solution), point estimations computational accuracy and calculate the time two in terms of compare.Sample frequency in sampling is 50000.118 section of IEEE
Dot system information is as shown in table 1 to table 3.IEEE300 node system information is as shown in table 4 and table 5.Polish 2383 node systems letter
Breath is as shown in table 6.
1 IEEE of table, 118 node system information I
2 IEEE of table, 118 node system information II
3 IEEE of table, 118 node system information III
4 IEEE of table, 300 node system information I
5 IEEE of table, 300 node system information II
Polish 2383 node system informations of table 6
Wherein, 118 node system information table 1 of IEEE is into mono- column Bus Type of table 3, and 1 indicates PQ node, and 2 indicate PV
Node, 3 indicate balance nodes.In Polish 2383 node systems, all wind speed all follow Two-parameter Weibull Distribution.Specific comparison
It is as follows:
2.1) computational accuracy.The mean value and standard deviation of operating cost result are as shown in table 1:
1 operating cost result of table compares and its error analysis
Note: "-" indicates that result can not obtain.
Optimum probability trend quick calculation method based on multi-parametric programming theory can get accurate operating cost result
Mean value and standard deviation.But mean value is obtained there are significant relative error based on point estimations, maximum relative error is reachable
53.38%.In Polish 2383 bus test systems, point estimations obtain the standard deviation of operating cost, this is because point estimation
The variance that method is calculated is negative value.
Similarly, for conventional electric power generation unit output power PG and Branch Power Flow PLine, it is poor also to will appear losing side.In addition,
The mean value of point estimations also has significant relative error, and maximum absolute error can reach 496MW and 606NW respectively.And based on more
The mean value and standard deviation of PG and PLine that the optimum probability trend quick calculation method of parametric programming theory obtains then are solved with accurate
It is completely the same.
2.2) time is calculated
Table 2 provides the calculating time comparison of three kinds of methods.It is compared with traditional Monte Carlo method, it is theoretical based on multi-parametric programming
Calculating time of optimum probability trend quick calculation method be greatly reduced.For example, in Polish 2383 bus test systems,
Traditional Monte Carlo method calculates 34 times of time about mentioned method.Although tP1 is about total the time required to multi-parametric programming analysis
The 24% of time ttol2 is calculated, but in most cases multi-parametric programming analysis only needs to execute once.This is because multi-parameter
Planning application is only and wind power plant position is related with installed capacity.Once wind power plant position and installed capacity determine, very long
In a period of time, they will not change.
Table 2 calculates time comparison
Note: ttol1The required time of sample is only solved comprising traditional Monte Carlo method.tp1For multi-parametric programming analysis time.
tp2The time of sample is solved for mentioned method.ttol2=tP1+tP2.ttol3The time of typical sample is only calculated comprising point estimations.
Claims (4)
1. a kind of optimum probability trend quick calculation method based on multi-parametric programming theory, which is characterized in that mainly include with
Lower step:
1) the frequency in sampling threshold epsilon is set, and electric power networks are sampled, to extract sample data；
2) direct current Optimized model is established；
3) theoretical based on multi-parametric programming, the parsing that optimal load flow result and renewable energy generation output power is calculated is closed
System.
4) according to renewable energy probability nature, k-th of renewable energy power generation machine output power sample is extractedJudgement can
Renewable source of energy generation machine output powerAffiliated critical region, and calculate optimal conventional electric power generation unit output power
I-th of critical region CRiMiddle optimal objective functionAnd Branch Power Flow
5) convergence judgement.
If sample number k >=ε, stop sample calculation, and counts and export optimal load flow result；The optimal load flow result is main
Including conventional electric power generation unit output power PG, operating costBranch Power FlowMean value and standard deviation；
If sample number k < ε, k=k+1, and return step 3 are enabled.
2. a kind of optimum probability trend quick calculation method based on multi-parametric programming theory according to claim 1,
Be characterized in that: the sample data mainly includes renewable energy generation output power PRWith power consumer load PD。
3. a kind of optimum probability trend quick calculation method based on multi-parametric programming theory according to claim 1 or 2,
It is characterized by: direct current Optimized model objective function is as follows:
In formula, PGFor conventional electric power generation unit output power；H (*) is conventional electric power generation unit operating cost function；For tradition hair
Motor group minimum operating cost；
Direct current Optimized model constraint condition is respectively if formula (2) are to shown in formula (5), it may be assumed that
eGPG+eRPR=eDPD； (2)
In formula, PRFor renewable energy generation output power；PDFor power consumer load；eG、eRAnd eDFor unit vector；
In formula,(*)WithRespectively represent lower and upper limit；
In formula, PLineFor Branch Power Flow power；
PLine=PTDF × (MGPG+MRPR-MDPD)； (5)
In formula, PTDF is power transmission distribution matrix；MG、MRAnd MDRespectively and PG、PRAnd PDRelevant node-branch is associated with square
Battle array.
4. a kind of optimum probability trend quick calculation method based on multi-parametric programming theory according to claim 1 or 3,
It is characterized by: the key step of the parsing relationship of optimal load flow result and renewable energy generation output power is calculated such as
Under:
1) decision variable x is set as conventional electric power generation unit output power PG, projecting parameter w is renewable energy generation output power
PR；
2) optimization aim is as follows:
In formula,For the generating set minimum operating cost of optimization；Matrix A, Matrix C and matrix D are to generate electricity for establishing
Unit trend Constraints of Equilibrium, generator capacity constrain and the certainty matrix of line transmission limit restraint；
3) the optimum segmentation equation of projecting parameter w is calculated；
Enabling K is the subscript of formula (6) constraint；Remember arbitrary constraint setFor AJ、CJAnd DJCorresponding submatrix, the submatrix
For the constraint for corresponding to lower label J in all constraints；
The hyperspace given for oneIfThe definition of its optimum segmentation is denoted as (γ (w), γc(w)), it may be assumed that
In formula, w is projecting parameter；X is decision variable；x*It (w) is the optimal solution on critical region i；
4) critical region of projecting parameter w is calculated；
For given projecting parameterDefinitionFor (γ (w0),γc(w0)), then correspond to γ0Critical region such as
Shown in lower:
Wherein, i-th of critical region CRiKuhn tucker condition it is as follows:
In formula, JiFor in CRiIn operative constraint collection；For CRiIn correspond to operative constraint antithesis multiplier；▽xFor decision change
Measure the gradient operator of x；
5) according to the critical region of projecting parameter w and optimum segmentation equation, critical region CR is obtainediIn the output of optimal conventional electric power generation unit
PowerWith renewable energy generation output power PRIn relationship, it may be assumed that
In formula, FxiAnd GxiFor in critical region CRiOn, by formula (9) obtained coefficient matrix；
6) formula (10) are substituted into objective function z=h (PG) in, obtain critical region CRiMiddle optimal objective functionThat is:
Formula (10) are substituted into Branch Power FlowIn, obtain Branch Power FlowIt is defeated with renewable energy generation
Power P outRRelationship, it may be assumed that
Formula (10) are substituted into the inactivce constraints collection γ of formula (7)c(w) in, critical region CR is obtainediExpression formula, it may be assumed that
In formula, GiAnd HiIt is so required that be used to describe critical region CRiThe coefficient matrix of range；
Wherein, coefficient matrix GiWith coefficient matrix HiIt is as follows respectively:
In formula,WithRow submatrix respectively in matrix A and matrix G, corresponding to inactivce constraints collection；
In formula,For the row submatrix in matrix D, corresponding to inactivce constraints collection.
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