CN110350594A - A kind of Unit Commitment method based on the optimization of random robust - Google Patents
A kind of Unit Commitment method based on the optimization of random robust Download PDFInfo
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- CN110350594A CN110350594A CN201910519806.4A CN201910519806A CN110350594A CN 110350594 A CN110350594 A CN 110350594A CN 201910519806 A CN201910519806 A CN 201910519806A CN 110350594 A CN110350594 A CN 110350594A
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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
- H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
- H02J3/46—Controlling of the sharing of output between the generators, converters, or transformers
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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
- H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
- H02J3/46—Controlling of the sharing of output between the generators, converters, or transformers
- H02J3/48—Controlling the sharing of the in-phase component
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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]
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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
- H02J3/003—Load forecast, e.g. methods or systems for forecasting future load demand
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Abstract
The present invention relates to a kind of Unit Commitment methods based on the optimization of random robust, belong to technical field of power system operation control.This method initially sets up the Unit Commitment model being made of objective function and constraint condition；Constraint condition is converted, converts a nonlinear optimal problem for master mould；To the model solution after conversion, generator booting plan is obtained, and corresponding booting planning decision-making is carried out according to solving result and realizes Unit Combination.The present invention considers the fluctuation of renewable energy in electric system, reduces the cost of Corrective control, ensure that power system security, is suitably applied among the scenes such as the Unit Combination a few days ago of electric system.
Description
Technical field
The present invention relates to a kind of Unit Commitment methods based on the optimization of random robust, belong to Operation of Electric Systems
Control technology field.
Background technique
The Unit Combination of electric system has important directive function to Operation of Electric Systems, is responsible to define generating set
Booting plan, provides reference for subsequent generation schedule, real under the premise of meeting power load and guaranteeing power system security
Existing economical operation.
More and more wind power integration electric system in recent years, and the power output of wind-powered electricity generation has randomness, it is therefore desirable in electricity
It is introduced in the Unit Combination of Force system and considers probabilistic optimization algorithm.
Currently used Unit Combination method is mainly based upon the Unit Combination optimization of DC power flow, by solving one really
Qualitative MINLP model problem obtains unit booting plan, disadvantage is that can not consider new energy access electricity
System safety under Force system bring uncertainty, and do not account for the uncertainty of new energy.For example, Wang Beibei, Tang Nan,
Zhao Shengnan, Lin Kaiying, Wang Yan, Xiao Yong deliver " the random adjustable robust that demand response participates in wind electricity digestion mixes to be adjusted a few days ago
Spend model ", referring to Proceedings of the CSEE, 2017,37 (21): 6339-6346, wherein Unit Combination is divided into two times
Section, boots up the decision of plan, disadvantage is that not being able to achieve all the period of time using stochastic model and robust Model respectively
Stochastic model in conjunction with robust Model.
Summary of the invention
The purpose of the present invention is to propose to a kind of Unit Commitment methods based on the optimization of random robust, to overcome
There is the shortcoming of technology, the uncertainty of renewable energy is described using the probabilistic forecasting information of wind-powered electricity generation, it is non-thread by solving
Property optimization problem obtain Unit Combination scheme, the randomness bring safety problem of wind-powered electricity generation preferably in processing electric system.
Unit Commitment method proposed by the present invention based on the optimization of random robust, comprising the following steps:
(1) it is predicted, is obtained in each moment t power train using power of the Time series analysis method to electric system
The prediction power upper limit of wind-powered electricity generation at all nodes of systemPrediction power of the wind-powered electricity generation in t moment at i-th of node of electric system
The upper limit is denoted asWind-powered electricity generation is denoted as in the prediction power lower limit of t moment at i-th of nodeT=1,2 ... T, remember electric system
In each moment wind-powered electricity generation actual power be wt, wtFor a multidimensional uncertainty variable；
(2) establish the Unit Commitment model that optimizes based on random robust, detailed process the following steps are included:
(2-1) determines the objective function of Unit Commitment model: the target of Unit Commitment is assembly
This minimum, totle drilling cost include cost of electricity-generating, start and stop cost and abandonment punishment and subsequent Corrective control cost, in which:
The expression formula of cost of electricity-generating is as follows:
In above formula, GiIndicate that the cost of electricity-generating function of generator at i-th of node of electric system, T indicate the period of optimization
Number is known quantity,Indicate that generator is amount to be solved in the active power of t moment at i-th of node of electric system,
The electric system node set for indicating access generator is obtained from the on-position of all generators of electric system；
The cost of electricity-generating function of generator at i-th of nodeExpression formula it is as follows:
Wherein ai,bi,ciRepresent the cost of electricity-generating parameter of generator at i-th of node, ai,bi,ciBy power plant according to hair
Electric cost provides, and is known quantity；
The expression formula of start and stop cost is as follows:
In above formula,Indicate start and stop cost of the generator in t moment, expression formula at i-th of node are as follows:
Wherein,Indicate that for generator in the open state of t moment, 0 represents power generation organ at i-th of node of electric system
Machine, 1 represents generator booting,It is amount to be solved, max expression is maximized, SUiIt indicates to generate electricity at i-th of node of electric system
Machine starts primary cost, is known quantity, is provided by power plant according to the operating cost of generator, SDiIndicate electric system i-th
Generator closes primary cost at a node, is known quantity, is provided by power plant according to the operating cost of generator；
The expression formula of abandonment punishment is as follows:
In above formula,Respectively indicate wind-powered electricity generation at i-th of node of electric system t moment allow to contribute it is maximum
It is worth and allows minimum value of contributing,It is amount to be solved,Indicate the electric system node set of access wind-powered electricity generation,
It is acquired from the accessing position information of all wind-powered electricity generations of system, is known quantity；
The abandonment penalty of wind-powered electricity generation t moment at i-th of nodeExpression formula it is as follows:
Wherein, kiRepresent the abandonment penalty coefficient of wind-powered electricity generation at i-th of node, kiFor known quantity, by the scheduling control of electric system
Center processed provides, and general value is the positive number greater than zero,Wind-powered electricity generation at i-th of node is represented in the prediction power upper limit of t moment,For known quantity,The practical active power of wind-powered electricity generation t moment at i-th of node is represented, is a stochastic variable,It represents
The practical active power of wind-powered electricity generation t moment is at i-th of nodeProbability density function,For known quantity, by wind power plant
Probabilistic forecasting obtain；
The expression formula of Corrective control cost is as follows:
Wherein,This is made in the up-regulation control cost and down regulation for respectively representing generator at i-th of node；
The up-regulation of generator controls cost UR at i-th of nodeiExpression formula are as follows:
Wherein, giThe up-regulation cost coefficient for indicating generator at i-th of node, by power plant according to generator regulating power
It provides, is known quantity, αiThe Automatic Generation Control adjustment factor for indicating generator at i-th of node, by power plant according to power generation
Machine regulating power provides, and is known quantity,Indicate electric system in all wind-powered electricity generations t moment active power setting value summation,It is amount to be solved,Indicate that all wind-powered electricity generations allow minimum value summation of contributing in t moment,It is amount to be solved, utIt indicates
All wind-powered electricity generations are a stochastic variable, p (u in the practical active power summation of t momentt) all wind-powered electricity generations are represented in electric system in t
The practical active power summation at moment is the probability density function of ut, p (ut) it is known quantity, it is obtained by the probabilistic forecasting of wind power plant
It arrives；
This DR is made in the down regulation of generator at i-th of nodeiExpression formula are as follows:
Wherein, hiThe downward cost coefficient for indicating generator at i-th of node, by power plant according to generator regulating power
It provides, hiIt is known quantity,It indicates that all wind-powered electricity generations allow maximum value summation of contributing in t moment, is amount to be solved,It indicates
All wind-powered electricity generations t moment prediction active power upper limit summation,Pass through the institute to each moment t electric system in step (1)
There is the prediction power upper limit of wind-powered electricity generation at nodeSummation obtains；
(2-2) determines the constraint condition of Unit Commitment model, comprising:
The power constraint of (2-2-1) generator and wind-powered electricity generation:
Wherein,The active power setting value for indicating wind-powered electricity generation at i-th of node is amount to be solved, PGi,min,PGi,maxPoint
The minimum power and maximum power for not indicating generator at i-th of node, are known quantities, by power plant according to the power generation of generator
Ability provides；
The power balance equation of (2-2-2) electric system constrains:
Wherein,Indicate the electric system node set of access load,Indicate electric power at i-th of node of electric system
System load is known quantity in the active power of t moment, is provided by Power System Control Centers according to load prediction；
(2-2-3) forward direction branch power capacity-constrained and reversed branch power capacity-constrained:
Wherein,Number is L in electric system branch is respectively indicated relative to electric system node i and node j
Power is distributed transfer factor,To number sensitivity of the branch for being L relative to the active power of node i in electric system:
Wherein,Indicate the maximum allowable power for the branch that number is L,It is known quantity, by Power System Control Centers
It is provided according to the structural parameters of branch；
(3) objective function of above-mentioned steps (2) and constraint condition are constituted to the power system machine of a random robust optimization
Group built-up pattern, and the built-up pattern is rewritten into following mathematical form:
Ax≤b
Wherein,Representative is minimized x, and x indicates the open state of all generators, all power generations in electric system
The active power of machine, the set value of the power of all wind-powered electricity generations of electric system, all wind-powered electricity generations allow contribute minimum value and all wind-powered electricity generations
Maximum value composition vector, f (x) indicate Unit Combination objective function, write the constraint condition in above-mentioned steps (2) as square
Battle array inequality form, it is A that the left-hand side of the MATRIX INEQUALITIES, which is matrix corresponding with x, the right-hand side of the MATRIX INEQUALITIES
Constant matrices is b；
(4) sequential linearization method is utilized, the MATRIX INEQUALITIES of above-mentioned steps (3) is solved, obtains optimal solution, detailed process
It is as follows:
The objective function f (x) of Unit Combination is split into f by (4-1)1(x) and f2(x), wherein f1(x) in step (2-1)
Cost of electricity-generating and the sum of start and stop cost, f1It (x) is quadratic function, f2It (x) is the abandonment punishment and correction in step (2-1)
Control the sum of cost, f2It (x) is nonlinear function；
(4-2) uses MIQP appro ach, solves to obtain optimal solution x using following formula0:
Ax≤b
(4-3) uses MINLP model, solves to obtain optimal solution to be x using following formula1:
Ax≤b
Wherein,Indicate f2(x) function is in x0Derivative vector；
(4-4) sets an iteration allowable error ε, judges the calculated result of step (4-2) and step (4-3),
If abs (f (x1)-f(x0)) < ε, then determine x1For Unit Commitment optimal solution, stop iteration, if abs (f (x1)-f
(x0)) >=ε, then by x1Value replace x0, return step (4-3), wherein abs indicates to take absolute value；
(5) according to the open state value for corresponding to generator in the Unit Combination optimal solution of step (4), electric system is respectively sent out
Open state of the motor at each moment carries out value, formulates the booting plan of generator, completes the Unit Combination of electric system.
Unit Commitment method proposed by the present invention based on the optimization of random robust, its advantage is that:
Unit Commitment method based on the optimization of random robust of the invention, utilizes the probabilistic forecasting information of wind-powered electricity generation
The uncertainty of renewable energy is described, objective function uses stochastic model, and constraint condition uses robust Model, passes through solution
Nonlinear optimal problem obtains Unit Combination scheme, ensure that safety of the electric system under wind-powered electricity generation fluctuation by robust optimization
Property.Therefore the method for the present invention considers the fluctuation of renewable energy in electric system, reduces the cost of Corrective control, is suitble to answer
Among the scenes such as the Unit Combination a few days ago for electric system.
Specific embodiment
Unit Commitment method proposed by the present invention based on the optimization of random robust, comprising the following steps:
(1) it is predicted, is obtained in each moment t power train using power of the Time series analysis method to electric system
The prediction power upper limit of wind-powered electricity generation at all nodes of systemPre- measurement of power of the wind-powered electricity generation in t moment at i-th of node of electric system
The rate upper limit is denoted asWind-powered electricity generation is denoted as in the prediction power lower limit of t moment at i-th of nodeT=1,2 ... T, remember power train
The actual power of each moment wind-powered electricity generation is w in systemt, wtFor a multidimensional uncertainty variable；
(2) establish the Unit Commitment model that optimizes based on random robust, detailed process the following steps are included:
(2-1) determines the objective function of Unit Commitment model: the target of Unit Commitment is assembly
This minimum, totle drilling cost include cost of electricity-generating, start and stop cost and abandonment punishment and subsequent Corrective control cost, in which:
The expression formula of cost of electricity-generating is as follows:
In above formula, GiIndicate that the cost of electricity-generating function of generator at i-th of node of electric system, T indicate the period of optimization
Number is known quantity,Indicate that generator is amount to be solved in the active power of t moment at i-th of node of electric system,The electric system node set for indicating access generator is obtained from the on-position of all generators of electric system；
The cost of electricity-generating function of generator at i-th of nodeExpression formula it is as follows:
Wherein ai,bi,ciRepresent the cost of electricity-generating parameter of generator at i-th of node, ai,bi,ciBy power plant according to hair
Electric cost provides, and is known quantity；
The expression formula of start and stop cost is as follows:
In above formula,Indicate start and stop cost of the generator in t moment, expression formula at i-th of node are as follows:
Wherein,Indicate that for generator in the open state of t moment, 0 represents power generation organ at i-th of node of electric system
Machine, 1 represents generator booting,It is amount to be solved, max expression is maximized, SUiIt indicates to generate electricity at i-th of node of electric system
Machine starts primary cost, is known quantity, is provided by power plant according to the operating cost of generator, SDiIndicate electric system i-th
Generator closes primary cost at a node, is known quantity, is provided by power plant according to the operating cost of generator；
The expression formula of abandonment punishment is as follows:
In above formula,Respectively indicate wind-powered electricity generation at i-th of node of electric system t moment allow to contribute it is maximum
It is worth and allows minimum value of contributing,It is amount to be solved,Indicate the electric system node set of access wind-powered electricity generation,
It is acquired from the accessing position information of all wind-powered electricity generations of system, is known quantity；
The abandonment penalty of wind-powered electricity generation t moment at i-th of nodeExpression formula it is as follows:
Wherein, kiThe abandonment penalty coefficient of wind-powered electricity generation at i-th of node is represented,Wind-powered electricity generation is represented at i-th of node in t moment
The prediction power upper limit,For known quantity,The practical active power of wind-powered electricity generation t moment at i-th of node is represented, is one random
Variable,Represent the practical active power of wind-powered electricity generation t moment at i-th of node asProbability density function,For
The amount of knowing is obtained by the probabilistic forecasting of wind power plant；
The expression formula of Corrective control cost is as follows:
Wherein,This is made in the up-regulation control cost and down regulation for respectively representing generator at i-th of node；
The up-regulation of generator controls cost UR at i-th of nodeiExpression formula are as follows:
Wherein, giThe up-regulation cost coefficient for indicating generator at i-th of node, by power plant according to generator regulating power
It provides, is known quantity, αiThe Automatic Generation Control adjustment factor for indicating generator at i-th of node, by power plant according to power generation
Machine regulating power provides, and is known quantity,Indicate electric system in all wind-powered electricity generations t moment active power setting value summation,It is amount to be solved,Indicate that all wind-powered electricity generations are total in (i.e. the permission active power of the wind-powered electricity generation) minimum value that allows to contribute of t moment
With,It is amount to be solved, utIndicate that all wind-powered electricity generations are a stochastic variable, p (u in the practical active power summation of t momentt) generation
The probability density function that all wind-powered electricity generations are ut in the practical active power summation of t moment in table electric system, p (ut) it is known
Amount, is obtained by the probabilistic forecasting of wind power plant；
This DR is made in the down regulation of generator at i-th of nodeiExpression formula are as follows:
Wherein, hiThe downward cost coefficient for indicating generator at i-th of node, by power plant according to generator regulating power
It provides, hiIt is known quantity,It indicates that all wind-powered electricity generations allow maximum value summation of contributing in t moment, is amount to be solved,It indicates
All wind-powered electricity generations t moment prediction active power upper limit summation,Pass through the institute to each moment t electric system in step (1)
There is the prediction power upper limit of wind-powered electricity generation at nodeSummation obtains；
(2-2) determines the constraint condition of Unit Commitment model, comprising:
The power constraint of (2-2-1) generator and wind-powered electricity generation:
Wherein,The active power setting value for indicating wind-powered electricity generation at i-th of node is amount to be solved, PGi,min,PGi,maxPoint
The minimum power and maximum power for not indicating generator at i-th of node, are known quantities, by power plant according to the power generation of generator
Ability provides；
The power balance equation of (2-2-2) electric system constrains:
Wherein,Indicate the electric system node set of access load,Indicate electric power at i-th of node of electric system
System load is known quantity in the active power of t moment, is provided by Power System Control Centers according to load prediction；
(2-2-3) forward direction branch power capacity-constrained and reversed branch power capacity-constrained:
Wherein,Number is L in electric system branch is respectively indicated relative to electric system node i and node j
Power be distributed transfer factor,For in electric system number be L branch relative to node i active power it is sensitive
Degree:
Wherein,Indicate the maximum allowable power for the branch that number is L,It is known quantity, by Power System Control Centers
It is provided according to the structural parameters of branch；
(3) objective function of above-mentioned steps (2) and constraint condition are constituted to the power system machine of a random robust optimization
Group built-up pattern, and the built-up pattern is rewritten into following mathematical form:
Ax≤b
Wherein,Representative is minimized x, and x indicates the open state of all generators, all power generations in electric system
The active power of machine, the set value of the power of all wind-powered electricity generations of electric system, all wind-powered electricity generations allow contribute minimum value and all wind-powered electricity generations
Maximum value composition vector, f (x) indicate Unit Combination objective function, write the constraint condition in above-mentioned steps (2) as square
Battle array inequality form, it is A that the left-hand side of the MATRIX INEQUALITIES, which is matrix corresponding with x, the right-hand side of the MATRIX INEQUALITIES
Constant matrices is b；
(4) sequential linearization method is utilized, the MATRIX INEQUALITIES of above-mentioned steps (3) is solved, obtains optimal solution, detailed process
It is as follows:
The objective function f (x) of Unit Combination is split into f by (4-1)1(x) and f2(x), wherein f1(x) in step (2-1)
Cost of electricity-generating and the sum of start and stop cost, f1It (x) is quadratic function, f2It (x) is the abandonment punishment and correction in step (2-1)
Control the sum of cost, f2It (x) is nonlinear function；
(4-2) uses MIQP appro ach, solves to obtain optimal solution x using following formula0:
Ax≤b
(4-3) uses MINLP model, solves to obtain optimal solution to be x using following formula1:
Ax≤b
Wherein,Indicate f2(x) function is in x0Derivative vector；
(4-4) sets an iteration allowable error ε, judges the calculated result of step (4-2) and step (4-3),
If abs (f (x1)-f(x0)) < ε, then determine x1For Unit Commitment optimal solution, stop iteration, if abs (f (x1)-f
(x0)) >=ε, then by x1Value replace x0, return step (4-3), wherein abs indicates to take absolute value, one embodiment of the present of invention
In, the value of ε is 0.001；
(5) according to the open state value for corresponding to generator in the Unit Combination optimal solution of step (4), electric system is respectively sent out
Open state of the motor at each moment carries out value, formulates the booting plan of generator, completes the Unit Combination of electric system.
Claims (1)
1. a kind of Unit Commitment method based on the optimization of random robust, it is characterised in that this method includes following step
It is rapid:
(1) it is predicted, is obtained in each moment t electric system using power of the Time series analysis method to electric system
The prediction power upper limit of wind-powered electricity generation at all nodesWind-powered electricity generation is in the prediction power of t moment at i-th of node of electric system
Limit is denoted asWind-powered electricity generation is denoted as in the prediction power lower limit of t moment at i-th of nodeRemember electric system
In each moment wind-powered electricity generation actual power be wt, wtFor a multidimensional uncertainty variable；
(2) establish the Unit Commitment model that optimizes based on random robust, detailed process the following steps are included:
(2-1) determines the objective function of Unit Commitment model: the target of Unit Commitment be totle drilling cost most
Smallization, totle drilling cost include cost of electricity-generating, start and stop cost and abandonment punishment and subsequent Corrective control cost, in which:
The expression formula of cost of electricity-generating is as follows:
In above formula, GiIndicate that the cost of electricity-generating function of generator at i-th of node of electric system, T indicate the fixed number of optimization,
For known quantity,Indicate that generator is amount to be solved in the active power of t moment at i-th of node of electric system,It indicates
The electric system node set for accessing generator is obtained from the on-position of all generators of electric system；
The cost of electricity-generating function of generator at i-th of nodeExpression formula it is as follows:
Wherein ai,bi,ciRepresent the cost of electricity-generating parameter of generator at i-th of node, ai,bi,ciBy power plant according to power generation at
Originally it provides, is known quantity；
The expression formula of start and stop cost is as follows:
In above formula,Indicate start and stop cost of the generator in t moment, expression formula at i-th of node are as follows:
Wherein,Indicate that for generator in the open state of t moment, 0 represents generator shutdown, 1 generation at i-th of node of electric system
The booting of table generator,It is amount to be solved, max expression is maximized, SUiIndicate that generator opens at i-th of node of electric system
Primary cost is moved, is known quantity, is provided by power plant according to the operating cost of generator, SDiIndicate i-th of section of electric system
Generator closes primary cost at point, is known quantity, is provided by power plant according to the operating cost of generator；
The expression formula of abandonment punishment is as follows:
In above formula,Respectively indicate wind-powered electricity generation at i-th of node of electric system t moment allow to contribute maximum value and
Allow minimum value of contributing,It is amount to be solved,The electric system node set for indicating access wind-powered electricity generation, from being
Unite all wind-powered electricity generations accessing position information obtain, be known quantity；
The abandonment penalty of wind-powered electricity generation t moment at i-th of nodeExpression formula it is as follows:
Wherein, kiRepresent the abandonment penalty coefficient of wind-powered electricity generation at i-th of node, kiIt is known quantity, by the tune of Power System Control Centers
Degree system provides,Wind-powered electricity generation at i-th of node is represented in the prediction power upper limit of t moment,For known quantity,It represents i-th
The practical active power of wind-powered electricity generation t moment at node is a stochastic variable,Represent wind-powered electricity generation t moment at i-th of node
Practical active power isProbability density function,For known quantity, obtained by the probabilistic forecasting of wind power plant；
The expression formula of the Corrective control cost of generator is as follows at i-th of node:
Wherein,This is made in the up-regulation control cost and down regulation for respectively representing generator at i-th of node；
The up-regulation of generator controls cost UR at i-th of nodeiExpression formula are as follows:
Wherein, giThe up-regulation cost coefficient for indicating generator at i-th of node is provided by power plant according to generator regulating power,
It is known quantity, αiThe Automatic Generation Control adjustment factor for indicating generator at i-th of node is adjusted by power plant according to generator
Ability provides, and is known quantity,Indicate electric system in all wind-powered electricity generations t moment active power setting value summation,Be to
Solution amount,Indicate that all wind-powered electricity generations allow minimum value summation of contributing in t moment,It is amount to be solved, utIndicate all wind
Electricity is a stochastic variable, p (u in the practical active power summation of t momentt) all wind-powered electricity generations are represented in electric system in t moment
Practical active power summation is utProbability density function, p (ut) it is known quantity, it is obtained by the probabilistic forecasting of wind power plant；
This DR is made in the down regulation of generator at i-th of nodeiExpression formula are as follows:
Wherein, hiThe downward cost coefficient for indicating generator at i-th of node is provided by power plant according to generator regulating power,
hiIt is known quantity,It indicates that all wind-powered electricity generations allow maximum value summation of contributing in t moment, is amount to be solved,Indicate all wind
Electricity t moment prediction active power upper limit summation,Pass through all nodes to each moment t electric system in step (1)
Locate the prediction power upper limit of wind-powered electricity generationSummation obtains；
(2-2) determines the constraint condition of Unit Commitment model, comprising:
The power constraint of (2-2-1) generator and wind-powered electricity generation:
Wherein,The active power setting value for indicating wind-powered electricity generation at i-th of node is amount to be solved, PGi,min,PGi,maxTable respectively
The minimum power and maximum power for showing generator at i-th of node, are known quantities, by power plant according to the generating capacity of generator
It provides；
The power balance equation of (2-2-2) electric system constrains:
Wherein,Indicate the electric system node set of access load,Indicate electric system at i-th of node of electric system
It is supported on the active power of t moment, is known quantity, is provided by Power System Control Centers according to load prediction；
(2-2-3) forward direction branch power capacity-constrained and reversed branch power capacity-constrained:
Wherein,Respectively indicate the power of number is L in electric system branch relative to electric system node i and node j
Transfer factor is distributed,To number sensitivity of the branch for being L relative to the active power of node i in electric system:
Wherein,Indicate the maximum allowable power for the branch that number is L,Known quantity, by Power System Control Centers according to
The structural parameters of branch provide；
(3) objective function of above-mentioned steps (2) and constraint condition are constituted to the electric system unit group of a random robust optimization
Molding type, and the built-up pattern is rewritten into following mathematical form:
Ax≤b
Wherein,Representative is minimized x, and x indicates the open state of all generators in electric system, all generators
Active power, the set value of the power of all wind-powered electricity generations of electric system, all wind-powered electricity generations allow to contribute minimum value and all wind-powered electricity generations most
The vector of big value composition, f (x) indicate the objective function of Unit Combination, are write the constraint condition in above-mentioned steps (2) as matrix not
Equation form, it is A, the constant of the right-hand side of the MATRIX INEQUALITIES that the left-hand side of the MATRIX INEQUALITIES, which is matrix corresponding with x,
Matrix is b；
(4) sequential linearization method is utilized, the MATRIX INEQUALITIES of above-mentioned steps (3) is solved, obtains optimal solution, detailed process is such as
Under:
The objective function f (x) of Unit Combination is split into f by (4-1)1(x) and f2(x), wherein f1It (x) is the hair in step (2-1)
The sum of electric cost and start and stop cost, f1It (x) is quadratic function, f2(x) in step (2-1) abandonment punishment and Corrective control
The sum of cost, f2It (x) is nonlinear function；
(4-2) uses MIQP appro ach, solves to obtain optimal solution x using following formula0:
Ax≤b
(4-3) uses MINLP model, solves to obtain optimal solution to be x using following formula1:
Ax≤b
Wherein,Indicate f2(x) function is in x0Derivative vector；
(4-4) sets an iteration allowable error ε, judges the calculated result of step (4-2) and step (4-3), if abs
(f(x1)-f(x0)) < ε, then determine x1For Unit Commitment optimal solution, stop iteration, if abs (f (x1)-f(x0))≥
ε, then by x1Value replace x0, return step (4-3), wherein abs indicates to take absolute value；
(5) according to the open state value for corresponding to generator in the Unit Combination optimal solution of step (4), to each generator of electric system
Value is carried out in the open state at each moment, the booting plan of generator is formulated, completes the Unit Combination of electric system.
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| CN104935017A (en) * | 2015-05-19 | 2015-09-23 | 同济大学 | Wind turbine generating unit and thermal power generating unit combination method based on light robust optimization model |
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