CN107330568A - Energy storage, distributed power source and the power distribution network coordinated planning method decoupled based on Benders - Google Patents
Energy storage, distributed power source and the power distribution network coordinated planning method decoupled based on Benders Download PDFInfo
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Abstract
The invention discloses the energy storage decoupled based on Benders, distributed power source and power distribution network coordinated planning method, setting up meter and energy storage, on the basis of the power distribution network coordinated planning model of distributed power source, thought is decoupled according to Benders, it is primal problem and subproblem by model decomposition, and subproblem is decomposed again, formed and decompose subproblem and relaxation subproblem, solve and decompose the value that subproblem obtains subproblem continuous variable, solve the value that relaxation subproblem obtains subproblem discrete variable, and form effective cut set and feed back to primal problem, by iterative, obtain taking into account primal problem and the total optimization solution of subproblem.The present invention decompose with decomposing again to the mixed integer nonlinear optimization problem comprising a large amount of integer variables and continuous variable, reduce problem scale, solve and the problem of multistage, the Large-scale programming of multivariable are difficult to solve is considered in distribution network planning, coordinated planning is carried out with rack reconstruct for energy storage, distributing rationally for distributed power source simultaneously, Efficient Solution is realized.
Description
Technical field
The present invention relates to the energy storage decoupled based on Benders, distributed power source and power distribution network coordinated planning method, belong to and match somebody with somebody
Electric Power Network Planning technical field.
Background technology
With the change and the development of new energy technology of energy resource structure, power system is also faced with structural adjustment, closely
Nian Lai, country has put into effect a series of development of support on policy new energy power generation technologies, and distributed power source, energy storage connect in power distribution network
Enter ratio to gradually step up, cause distribution net work structure to be changed.How the access digit of the equipment such as distributed power source, energy storage is directed to
Put and carry out decision-making with capacity, as a new study hotspot in distribution network planning.
Due to the presence of Kirchhoff's law in trend constraint, distribution network planning problem is typically a MIXED INTEGER non-thread
Property planning problem, and the problem non-convex, it is a big difficult point in optimization process how it solve, most of research at present
The quadratic constraints for taking the method for piece-wise linearization to form Kirchhoff's law simplifies, and this will cause constraints, determine
The increase of plan variable, reduces solving precision.Some documents by non-convex, nonlinear constraints slacking in model be second order cone about
Beam, former problem is converted into the convex optimization problem of the constraint containing cone, and solving precision is improved while variable number is reduced.
Conventional electrical distribution network planning stroke is planned mainly for the construction scheme of rack and transformer station, as distributed energy is set
Standby access, distribution network planning model becomes more complicated, it is necessary to consider to many factors, current many researchs
It is determined that grid structure on the basis of consider the addressing constant volume scheme of distributed power source or energy storage, only for distributed power source and
Distributing rationally for energy storage is planned, is not combined it with distribution network planning, it is considered to which problem is not comprehensive enough.In distribution network planning
In drawing, it should integrate and examine line construction, rack reconstruct and the construction of the equipment such as distributed power source, energy storage, set up coordinated planning mould
Type, can just obtain the programme of more science.
In existing literature, the research for power distribution network coordinated planning model all rests on model construction aspect substantially, for
Object function and all kinds of constraintss are discussed, and the research in terms of algorithm is less.Research on model solution method is main
It is improved and applies for all kinds of intelligent algorithm, including genetic algorithm, particle cluster algorithm etc., but these intelligent algorithms are being asked
Global convergence is difficult to ensure that during solution distribution network planning problem, and the difference between current optimum results and globally optimal solution can not be weighed
Away from not as numerical method on performance is solved.But a big problem is faced with using numerical method direct solution：Line is considered simultaneously
The programme of the factors such as road, transformer station, energy storage, distributed power source will include a large amount of discrete variables and continuous variable, every kind of
All comprising a large amount of constraints under the method for operation, direct solution will expend for a long time, and be difficult to reach final convergence, not have still at present
Document conducts a research for this problem.
The basic ideas of conventional Benders decomposition algorithms are：It is primal problem and subproblem, primal problem processing by PROBLEM DECOMPOSITION
Discrete variable, subproblem processing continuous variable, subproblem forms cut set and acts on primal problem, and current this algorithm is in the machine of solution
Applied in group combinatorial problem.But in meter and energy storage, the distribution network planning problem of distributed power source, subproblem is one
It is individual while comprising discrete variable and the problem of continuous variable, it is impossible to directly form cut set, it is necessary to further processing.
The content of the invention
The technical problems to be solved by the invention are：Energy storage, distributed power source and the distribution decoupled based on Benders is provided
Professional etiquette is entered in net coordinated planning method, the construction for the equipment such as a certain local distribution network and its supporting energy storage, distributed power source
Draw；It is determined that on the basis of meter and energy storage, the power distribution network coordinated planning model of distributed power source, it is proposed that one kind is improved
Benders algorithms, make the solution efficiency of model be greatly improved.
The present invention uses following technical scheme to solve above-mentioned technical problem：
Energy storage, distributed power source and the power distribution network coordinated planning method decoupled based on Benders, is comprised the following steps：
Step 1, power distribution network information is initialized, based on second order cone optimization, the distribution of meter and energy storage and distributed power source is set up
Net coordinated planning model, the model is with construction in project period and runs the minimum optimization aim of totle drilling cost, the constraint bar of the model
Part includes building constraint, operation constraint, network topology constraint, element volume constraint and second order cone constraint, and by the model table
It is shown as schematic style；
Step 2, decoupled based on Benders, be a primal problem and multiple subproblems by above-mentioned model decomposition, and to examination in chief
Topic is solved, and the optimum results of subproblem are embodied by way of introducing auxiliary variable and cut set constraint, project period are obtained each
The distribution network construction scheme in stage, when solving primal problem for the first time, it is believed that auxiliary variable is 0 and does not consider cutting for subproblem formation
Collection；
Step 3, multiple Run-time scenarios are considered in each stage, each subproblem is directed to the distribution under a kind of Run-time scenario
Running State is optimized, for each subproblem, is carried out integrated solution, is obtained the value of subproblem discrete variable；
Step 4, each subproblem is decomposed, obtains decomposing subproblem and relaxation subproblem, and decompose subproblem only
The explicit continuous variable included in subproblem, solves and decomposes subproblem, obtain the value and optimum results of subproblem continuous variable,
And form subproblem cut set；
Step 5, the optimum results of subproblem and subproblem cut set are separately added into the object function and constraint bar of subproblem
Part, and be continuous variable by the discrete variable relaxation in subproblem, relaxation subproblem is set up, relaxation subproblem is solved, is led
Problem cut set, return to step 2 solves the primal problem containing cut set, obtains the optimum results of primal problem, whether judge the optimum results
Convergence requirement is met, program results is exported if meeting, otherwise into next iteration.
As a preferred embodiment of the present invention, the model is expressed as schematic style described in step 1, it is specific as follows：
Wherein, r, s, t are the coefficient sets in object function, αuThe variable related to process of construction is represented,Represent
The discrete variable related to running status,Represent the continuous variable in operation constraint, Iu、Mu、Au、bu、 It is the coefficient sets in constraint, u ∈
U、y∈Y、T ∈ T represent respectively the planning stage, the year in each planning stage, it is annual in chosen according to 4 season
Typical scene, the hour in typical day, subscript T represents transposition.
As a preferred embodiment of the present invention, the model of primal problem is as follows described in step 2：
Wherein, t is the coefficient sets in object function, αuRepresent the variable related to process of construction, zy,uRepresent subproblem
The lower limit of object function, Au、bu、Iu、Mu、It is the coefficient sets in constraint, u ∈ U, y
∈Y、T ∈ T represent respectively the planning stage, the year in each planning stage, it is annual in the typical case that is chosen according to 4 season
Scene, the hour in typical day, TYAnnual time span is represented,It is pair that loose subproblem produces
Even coefficient, It is to decompose the antithesis coefficient that subproblem produces, subscript T represents transposition.
As a preferred embodiment of the present invention, the model of subproblem is as follows described in step 3：
Wherein, s, t are the coefficient sets in object function,The discrete variable related to running status is represented,
The continuous variable in operation constraint is represented,The optimal value of the variable related to process of construction is represented,Iu、Mu、Be constraint in coefficient sets, u ∈ U,
y∈Y、T ∈ T represent respectively the planning stage, the year in each planning stage, it is annual in the allusion quotation chosen according to 4 season
Type scene, the hour in typical day, TYAnnual time span is represented, subscript T represents transposition.
As a preferred embodiment of the present invention, the model that subproblem is decomposed described in step 4 is as follows：
Wherein,The minimum value of decomposition subproblem object function is represented, t is the coefficient sets in object function,Table
Show the continuous variable in operation constraint,Mu、 It is to be in constraining
Manifold is closed,The optimal value of the variable related to process of construction is represented,Become by discrete in the subproblem tried to achieve in step 4
The optimal value of amount,Be decompose subproblem produce antithesis coefficient, u ∈ U, y ∈ Y,T ∈ T distinguish
Represent the planning stage, the year in each planning stage, it is annual in the typical scene, small in typical day chosen according to 4 season
When, subscript T represents transposition.
As a preferred embodiment of the present invention, the model of relaxation subproblem is as follows described in step 5：
Wherein, s is the coefficient sets in object function,The discrete variable related to running status is represented,Represent
The minimum value of subproblem object function is decomposed,Iu、Mu、It is about
Coefficient sets in beam,The optimal value of the variable related to process of construction is represented,It is that loose subproblem produces
Antithesis coefficient,Be decompose subproblem produce antithesis coefficient, u ∈ U, y ∈ Y,T points of t ∈
Not Biao Shi the planning stage, the year in each planning stage, it is annual in chosen according to 4 season typical scene, in typical day
Hour, subscript T represents transposition.
The present invention uses above technical scheme compared with prior art, with following technique effect：
1st, the present invention establishes meter and energy storage, the power distribution network coordinated planning model of distributed power source, to be built in project period
With operation the minimum optimization aim of totle drilling cost, for the equipment such as a certain local distribution network and its supporting energy storage, distributed power source
Construction carry out multistage programming, determine rack extension, the side of distributing rationally of transformer substation construction and energy storage and distributed power source
Case.
2nd, the present invention is on the basis of model is set up, and the thought decoupled according to Benders builds model decomposition for optimization
The subproblem of the primal problem of scheme and optimization running status, and further being decomposed to subproblem, formed decompose subproblem and
Relaxation subproblem.Value and subproblem cut set that subproblem obtains subproblem continuous variable are decomposed by solving, is added them into
In subproblem, and it is continuous variable by the discrete variable relaxation of subproblem, obtains the subproblem that relaxes.Relaxation subproblem is solved to obtain
The value of subproblem discrete variable, and form effective cut set and feed back to primal problem, by iterative, finally give and take into account examination in chief
Topic and the total optimization solution of subproblem.
3rd, the present invention is decomposed to the mixed integer nonlinear optimization problem comprising a large amount of integer variables and continuous variable
With decomposing again, problem scale is reduced, solves and considers that multistage, the Large-scale programming of multivariable are difficult to ask in distribution network planning
The problem of solution, solution efficiency is set to have obtained large increase.
Brief description of the drawings
Fig. 1 is the flow of energy storage, distributed power source and power distribution network coordinated planning method that the present invention is decoupled based on Benders
Figure.
Embodiment
Embodiments of the present invention are described below in detail, the example of the embodiment is shown in the drawings.Below by
The embodiment being described with reference to the drawings is exemplary, is only used for explaining the present invention, and is not construed as limiting the claims.
The present invention proposes a kind of energy storage, distributed power source and power distribution network coordinated planning method decoupled based on Benders, first
Meter and energy storage, the power distribution network coordinated planning model of distributed power source are first set up, and is second order cone by restriction of current relaxation in model
Constraint, makes model be converted into the convex optimization constrained comprising second order cone by the MIXED INTEGER non-convex nonlinear optimal problem for being difficult to solve
Problem.It is optimized construction scheme by PROBLEM DECOMPOSITION on the basis of model is set up, it is proposed that one kind improves Benders algorithms
The subproblem of primal problem and optimization running status, because subproblem is simultaneously comprising discrete variable and continuous variable, it is difficult to be formed with
Cut set is imitated, therefore subproblem is further decomposed, is formed and decomposes subproblem and relaxation subproblem.Subproblem is decomposed for son
Continuous variable in problem is solved, and is formed cut set and acted on loose subproblem；Relaxation subproblem by subproblem from
It is continuous variable to dissipate variable relaxation, and solution, which is free of the subproblem of discrete variable and forms cut set, feeds back to primal problem.By iteration
Solve, finally give the total optimization solution for taking into account primal problem and subproblem.
As shown in figure 1, describing the implementing procedure of planing method proposed by the present invention：Inputting the number of power distribution network to be planned
According on the basis of being initialized to parameter, solution does not consider the primal problem of subproblem optimized variable and cut set, and is changing every time
In generation, starts the preceding upper bound to global optimization target and sets.The solution of subproblem includes three steps：Subproblem is entered first
Row integrated solution；Then the discrete variable value fixed in subproblem, sets up the only decomposition subproblem comprising continuous variable and solves,
Produce subproblem cut set；Subproblem cut set is finally added to the constraints of subproblem, the discrete variable in subproblem is relaxed
For continuous variable, set up relaxation subproblem and solve, produce primal problem cut set.After the solution of subproblem is completed, by primal problem
Cut set adds primal problem constraints and solved, and obtains the lower bound of global optimization target, when optimum results meet convergence requirement
When, you can obtain final power distribution network planning scheme.Specifically include following steps：
Step 10) Initial System Information, including distribution net work structure, payload, equipment construction expense etc., based on second order
Cone optimization, sets up the power distribution network coordinated planning model of meter and energy storage and distributed power source, model is with system synthesis sheet in project period
Minimum optimization aim, comprising the constraint in terms of construction, operation, element volume, network topology, and is expressed as outline by model
Form；
Step 20) based on Benders decouplings, it is a primal problem and multiple subproblems by model decomposition, first to examination in chief
Topic is solved, and is obtained in the power grid construction scheme in each stage, primal problem by way of introducing auxiliary variable and cut set constraint
The optimum results of subproblem are embodied, in first solve, it is believed that auxiliary variable is 0 and does not consider the cut set that subproblem is formed；
Step 30) multiple Run-time scenarios are considered in each construction period, each subproblem, which is directed under a kind of scene, is
System running status is optimized, because subproblem includes discrete variable and continuous variable, it is impossible to form effective cut set, it is therefore desirable to
It is further processed, for each subproblem, integrated solution is carried out first, the initial value of discrete variable is obtained；
Step 40) subproblem is further decomposed, formed and decompose subproblem and relaxation subproblem, decompose subproblem only explicit
Comprising the continuous variable in subproblem, solve and decompose subproblem, obtain the value of subproblem continuous variable, and form subproblem cutting
Collection；
Step 50) optimum results and subproblem cut set that decompose subproblem are separately added into the object function peace treaty of subproblem
Beam condition, and be continuous variable by the discrete variable relaxation in subproblem, relaxation subproblem is set up, relaxation subproblem, production is solved
Raw primal problem cut set, return to step 20), the primal problem containing cut set is solved, and judge whether optimum results meet convergence requirement,
Then output result is met, otherwise into next iteration.
Step 10) in, meter and energy storage and distributed power source power distribution network coordinated planning model is with the whole network construction and runs into
This minimum optimization aim, in constraints, by second order cone relaxation by Optimized model by the nonlinear MIXED INTEGER of non-convex
Optimization problem is converted into the convex optimization problem constrained comprising second order cone, and the thought based on virtual power sets up anti-isolated island constraint,
Guarantee system has correct topological structure, described below.
The object function of model considers construction cost and operating cost, with the minimum optimization aim of totle drilling cost, it is considered to
To project period comprising multiple stages, it is necessary to which with discount rate by all cost-exchanges to current time, capital recovery system is incorporated herein
Number and two parameters of present factor.
For any appliance yet to be built, it is believed that the annual single-candidate of its lifetime undertakes construction cost, returned first using capital
Receive coefficient and construction cost is converted to each year for arriving lifetime.Capital recovery factor is an economics concept, i.e., a certain amount of goods
Coin present worth, calculates following each issue of payment or the single-candidate currency collected by multiple profit, can be formulated as：
Wherein, τ is capital recovery factor, and γ is inflation rate, and LT is equipment life.
After annual cost calculation is come out, in addition it is also necessary to by annual cost reduction to current, present factor is incorporated herein：
Wherein, μu,yFor present factor, u and y represent current generation and current year respectively.
On this basis, objective function is as follows：
The totle drilling cost of project period includes construction cost, cost of electricity-generating, maintenance cost and charge for cutting and used, and latter three are referred to as fortune
Row cost, is defined by formula (4) to (7) respectively.Here U stage will be divided into project period, each stage includes Y, every year again
It is divided into Λ season, TYRepresent annual time span.Construction scheme is relevant with number of stages, and different phase has different construction
Construction scheme in scheme, but same stage is certain；Operating scheme then changes with the change of load level, for one
Choose a typical day each season in year to represent the method for operation in the season, planned, obtained for these typical days
Operating cost under different running situations, and collectively constitute using them the object function of model.
Segment angle target implication being related in model is listed below at this：
The footmark implication of table 1
In addition, Ω*The set on * is represented, * can be replaced by symbols such as the feeder line in upper table, load, nodes here,
Ω.jRepresent the line set being connected with node j, Ωs,ex、Ωf,exRepresent already present transformer station and feeder line set, Ωs,cd、
Ωf,cdExpression transformer station yet to be built and feeder line set.
Formula (4) calculates circuit, transformer station, transformer, distributed power source, energy storage and SVG construction cost sum.
In formula：--- transformer station, transformer, SVG construction cost；
--- circuit unit length, distributed power source unit capacity construction cost；
--- the unit capacity cost and specific work of energy-storage system (Energy Storage System, ESS)
Rate cost；
δij,a,u、σi,u、ρi,b,u、ψi,u--- 0-1 variables, determine circuit, transformer station, transformer, conventional distribution
Whether formula power supply, wind distribution formula power supply, SVG build；
CBi,u、--- continuous variable, represent some node ESS installed capacitys, power；
lij--- circuit ij length；
--- distributed power source rated capacity.
Formula (5) represents cost of electricity-generating, including from the expense and the generating expense of distributed power source of transformer station's power purchase, this is punished
Cloth power supply considers two kinds of the conventional distributed power source and wind distribution formula power supply generated electricity using traditional energy.
In formula：--- from transformer station's power purchase expense；
--- the conventional, cost of electricity-generating of wind distribution formula power supply；
--- transformer station's active power；
--- the conventional, apparent energy of wind distribution formula power supply.
Formula (6) represents line upkeep expense, to prevent line inactive from putting into operation.
In formula：--- circuit annual maintenance expense；
--- 0-1 variables, represent whether circuit ij puts into operation from top to end；
--- 0-1 variables, represent whether circuit ij puts into operation from end to top.
Formula (7) calculates cutting load power and abandons wind power, realizes the combination of economy and reliability.
In formula：--- removal of load rejection penalty is with abandoning wind rejection penalty；
--- removal of load power is with abandoning wind power.
The constraints of model includes building constraint, operation constraint, network topology constraint, element volume constraint and second order cone
Constraint.
Building constraint is used to determining the construction scheme in each stage, including circuit, transformer station and transformer, distributed power source,
Energy storage, SVG etc. building time and quantity, for every kind of equipment, a type construction can only be selected in a certain place, and
The equipment that a previous stage builds up can only be at most built in all stages, will be existed in next stage.
In formula：--- the transformer upper limit that transformer station i can be installed；
--- the conventional, rated capacity of wind distribution formula power supply；
--- the maximum carrying capacity of the stage node i；
ξ --- distributed power source permeability level；
οi,u--- 0-1 variables, decide whether to build energy storage in some node；
--- continuous variable, determine some node ESS power；
--- certain node ESS installations are maximum, minimum power；
CBi,u--- continuous variable, determine the ESS installed capacitys of some node；
CBMax、CBMin--- certain node ESS installations are maximum, minimum installed capacity；
--- system ESS maximum installed capacitys；
--- capacitor module installs the number upper limit.
Wherein formula (8)-(9) represent the construction constraint of circuit；Formula (10)-(13) represent the constraint of transformer station and transformer,
Transformer station extends or could install transformer after newly-built, in order to prevent the empty node of line end connection, if to build or reinforce
Certain circuit, its connected transformer station must build；Access quantity, capacity and distribution of formula (14)-(16) to distributed power source
Formula power supply permeability is made that limitation；Formula (17)-(21) are the constraint related to energy storage, power, the capacity all Ying Yun of energy storage
Perhaps in the range of bound, and half of the instantaneous power no more than stored energy capacitance size of setting energy storage, it is total that energy storage is installed
Capacity should be less than the maximum capacity of system permission；Formula (22)-(23) are SVG constraint, and it is built sum and permitted no more than system
Perhaps the upper limit.
Operation constraint is used to determine the system running state under each scene, for following all formula, there is u ∈ ΩU、y
∈ΩY、h∈ΩT, current stage, time, season and time are represented respectively.
In formula：--- connecting node i and node j circuit are designated as circuit ij, this symbol table timberline road ij's has
Work(power, the circuit puts into operation from i ends to j ends；
--- circuit ij active power, the circuit puts into operation from j ends to i ends；
--- square of circuit ij current amplitudes, the circuit puts into operation from i ends to j ends；
--- the apparent energy of two class distributed power sources；
--- the power factor of two class distributed power sources and load；
--- the charge-discharge electric power of node i energy storage；
--- the active power that transformer station sends；
--- current loads level；
--- circuit resistance per unit length；
--- circuit ij reactive power, the circuit puts into operation from top to end；
--- circuit ij reactive power, the circuit puts into operation from end to top；
--- the reactive power that transformer station sends；
--- SVG reactive powers；
--- circuit unit length reactance；
--- square of node i voltage magnitude；
--- square of circuit ij current amplitudes, the circuit puts into operation from j ends to i ends；
--- the existing transformer station's rated capacity being connected with node i；
--- the rated capacity of transformer；
χ --- system minimum wind power utilization；
uwi--- wind-powered electricity generation active volume ratio；
--- circuit rated capacity；
--- energy storage current capacities；
ηch、ηdis--- the efficiency for charge-discharge of energy storage.
Wherein formula (23), (24) represent that the active reactive Constraints of Equilibrium of node, i.e. node inject active reactive power respectively
With equal to output active reactive power, wherein injecting power include circuit injecting power and accessed by the node transformer station, point
Cloth power supply is exerted oneself, and injects the idle transformer station accessed including circuit injecting power and by the node, distributed power source, SVG hairs
What is gone out is idle.
For the circuit put into operation, the difference of circuit top voltage and terminal voltage should be equal to line voltage distribution loss, such as formula (26)
It is shown, equality constraint is split as two inequality constraints (27) and (28) herein, and a very big arithmetic number H is introduced, use
Carry out control voltage Constraints of Equilibrium, it is met when circuit ij puts into operation, inequality right-hand member is equal to 0, and formula (27), (28) and (26) are imitated
Really identical, when circuit ij does not put into operation, inequality right-hand member is equal to H, and formula (27), (28) are changed intoConstraint is lost
Effect.
Formula (29)-(30) are transformer station's power constraint, and the quadratic sum of transformer station's active and reactive power should be less than transformer station's volume
Square of constant volume；Formula (31) constrains for wind distribution formula power, for the consideration to grid stability, the grid-connected need of blower fan
Will its exert oneself and reach certain level, therefore wind distribution formula power supply is exerted oneself and should meet wind-powered electricity generation minimum access and require；Formula (32)-(33)
Constrained for line power, the active power and reactive power for flowing through circuit all should be less than circuit rated capacity, to be applicable constraint
In all circuits, the power for the circuit that ensures not put into operation using variable that whether circuit puts into operation is represented is zero；Formula (34)-(35) are
Energy storage is constrained, according to the discharge and recharge rule of energy storage, if the initial value of daily energy storage storage energy is the half of its capacity, other periods
Meet energy storage discharge and recharge equilibrium equation.
Here the second order cone relaxation of restriction of current is provided, in formula (24)-(28), line current can use formula (36) table
Show：
Wherein,The active and reactive power of circuit is represented respectively, and this is constrained to non-convex, non-linear shape
Formula, is solved for problem is converted into MIXED INTEGER Second-order cone programming problem, and constraint relaxation is constrained into formula for second order cone
(37)。
On network topology constraint, in power distribution network, it should ensure that network has radial topological structure first, secondly, also
It should prevent that sub-load is only powered by DG after DG accesses, so as to depart from major network formation isolated island.
Introduce the running status variable of circuitWithRunning status should be consistent with line construction situation.
Radial topological structure is substantially a kind of tree construction, according to the characteristics of power distribution network, and power transformation tiny node can only conduct
Father node, power flows out from transformer station, and in the absence of its node of power flow direction, load bus needs injecting power to ensure
Electric energy is supplied, other node one and only one father nodes of putting into operation.
Wherein, Sli,uNow access node i load capacity is represented, the process of construction scheme and operating scheme is being considered
In, it is required for introducing anti-isolated island constraint, on the one hand needs to prevent power supply is isolated from putting into operation, on the other hand need to prevent load from departing from master
Net, the concept of virtual power is introduced for this, a virtual power system is built, including the void of transformer station, load and circuit
Intend power.
Anti- isolated island constraint in process of construction is discussed first here, for transformer station, it is believed that each transformer station, which has, to be more than
Zero injecting powerIn the absence of the node of transformer stationIt is zero.
Defining virtual load isAlso the virtual power demand of the node is represented, load is not zero or existed distributed electrical
Source, the node of energy storage accessFor 1, other node virtual loads are 0.
To flow through circuit ij virtual power, the power-balance with exporting is injected according to node, formula (43) is set up.
Virtual power bound is constrained as shown in formula (44) to (46).
When above-mentioned constraint is all met, it is ensured that the spoke that the power distribution network currently run is not zero by one or more loads
Penetrate shape network to constitute, have in each network and only one of which transformer station powers, isolated island generation is not had.
Similarly, in planning operation scheme, it is also desirable to anti-isolated island constraint is met, wherein (41) to (44) constraint type is not
Become, but variable therein needs the virtual power variable that is changed under the running status, at the same in the constraint of circuit virtual power with
The circuit state that puts into operation substitutes setup state, will (45), (46) be rewritten as (47), (48).
This external system should also meet the constraint that some limit working range, including node voltage bound, line current are about
Beam, distributed power source, energy storage and SVG capacity-constrained, cutting load power and abandon wind power constraint.
In formula：--- upper voltage limit；
V --- lower voltage limit；
--- line voltage grade；
--- SVG maximum sizes.
Wherein formula (49) constrains for node voltage；Formula (50) constrains for line current；Formula (51)-(52) are conventional distributed
The capacity-constrained of power supply and wind distribution formula power supply；Formula (53)-(55) are the limitation of energy storage installation power and capacity；Formula (56) table
Show that cutting load power should be no more than load capacity；Formula (57) represents that wind distribution formula power supply capacity should be no more than by abandoning wind power；Formula
(58) it is SVG capacity-constraineds.
For the ease of description Benders decoupling methods, the schematic style of model is provided here：
Wherein, αuRepresent the variable related to process of construction, including discrete variable δij,a,u,σi,u,ρi,b,u,
ψi,u, they represent the quantity of the decision whether built and construction, and continuous variable CBi,u、Represent energy storage capacity and
Power；Represent that the discrete variable related to running status, i.e. circuit put into operation variable Represent operation about
Continuous variable in beam, including
All variables in DSEP models can be classified as this three class.Based on model decomposition
Problem and subproblem, primal problem are Construction Problems, with variable αuCorrelation, subproblem is operation problem, with variablePhase
Close.
Iu、Mu、Au、bu、 For
Coefficient sets in constraint, rT、sT、tTFor the coefficient sets in object function, u ∈ U, y ∈ Y,T ∈ T represent rule respectively
The stage of drawing, the year in each planning stage, it is annual in chosen according to 4 season typical scene, the hour in typical day, subscript
T represents transposition.
There is following corresponding relation between outline model and master mould：(60) correspondence constraint (38) is constrained, (61) generation is constrained
Table constraint (31), (34), (42), (46), (51)-(55), (57), constraint (62) include constraint (27), (28), (32), (33),
(47), (48), (50), constrain (63) and include constraint (8)-(23), constrain (64) and represent constraint (39), (40), constraint (65) etc.
Imitate in constraint (24), (25), (29), (30), (35), (37), (41), (43), (45), (49), (56), (58).Due to equation
Constraint can be equivalent to two inequality constraints, therefore all be expressed in inequality form.
Step 20) in, the primal problem (MP) that Benders is decomposed is Construction Problems, only includes the variable α of construction periodu, no
The explicit variable for including subproblem, subproblem is fed back its optimum results by way of introducing auxiliary variable and forming cut set
To principal function.
In MP object function,Represent feeder line, transformer station, transformer, distributed power source, storage
The built by separate periods expense of energy and SVG, ICy,uEmbody and see formula (4).Variable zy,uThe lower limit of subproblem object function is represented,
Formula (68) is the Benders cut sets of subfunction formation, and the optimum results of subproblem are fed back to primal problem by them jointly.
Step 30) in, the subproblem (SP) that Benders is decomposed is operation problem, includes discrete variableWith continuous variable1 year in each subproblem correspondence project period, it was divided into Λ season by 1 year, a typical case is chosen from each season
Day represents the running status in the season, calculates under the state operating cost of system and various quarters expense is summed, you can obtain
The operating cost of this year.In known primal problem optimal valueOn the premise of, set up subproblem model：
SP with the minimum object function of operating cost under a certain Run-time scenario, whereinIt is related to the circuit situation that puts into operation,
Line upkeep expense is represented,Relevant with power, including power purchase expense and rejection penalty, expression is shown in (5)-(7),
Active reactive power, node voltage, Line Flow, the circuit that solution subproblem can obtain transformer station and DG under the state put into operation
Situation, energy storage state etc. run variable.
Because SP is simultaneously comprising discrete variable and continuous variable, it is impossible to directly form cut set, therefore also need to carry out it
Further processing.Integrated solution is carried out firstly the need of to SP.In view of being interrupted when each typical case's day includes 24 after meter and energy storage
Face, problem scale is larger, and problem is carried out at this to simplify processing：For each year in project period, ignore the selection of typical day
And the coupling between energy storage time section, take the running status of peak load point to represent the running status of this year, problem is converted
For single phase optimization problem, now problem solving gets up to be relatively easy to, and carries out integrated solution to it, obtains discrete variable's
Value, is designated as
Step 40) in, the Benders subproblems decomposed are decomposed again, obtained decomposition subproblem (DSP) is by SP
Discrete variable be considered as known constant setContinuous variable is now only included in problemIt can produce and effectively cut
Collection.
Wherein,It is DSP antithesis coefficient, cut set can be formed according to solving result, step is acted on
50) the relaxation subproblem RSP proposed in.
Formula (79) generally goes through simple equivalent deformation, is written as formula (80), and its antithesis coefficient is
Step 50) in, relaxation subproblem (RSP) is by auxiliary variableObject function peace treaty is separately added into cut set (80)
Beam condition, and by the discrete variable in subproblemRelaxation is continuous variable.
Formula (80)
Wherein,It is RSP antithesis coefficient, solves RSP, the constraint that can be formed in new cut set, i.e. MP
(68) it, is added to primal problem, then primal problem is solved, you can the lower bound of the solution of former problem is obtained, it is upper that contrast is solved
Gap between lower bound, the output result if convergence requirement is met, otherwise into next iteration.
The technological thought of above example only to illustrate the invention, it is impossible to which protection scope of the present invention is limited with this, it is every
According to technological thought proposed by the present invention, any change done on the basis of technical scheme each falls within the scope of the present invention
Within.
Claims (6)
1. the energy storage, distributed power source and the power distribution network coordinated planning method that are decoupled based on Benders, it is characterised in that including such as
Lower step：
Step 1, power distribution network information is initialized, based on second order cone optimization, the power distribution network association of meter and energy storage and distributed power source is set up
Plan model is adjusted, the model is with construction in project period and runs the minimum optimization aim of totle drilling cost, the constraints bag of the model
Construction constraint, operation constraint, network topology constraint, element volume constraint and second order cone constraint are included, and the model is expressed as
Schematic style；
Step 2, decoupled based on Benders, be a primal problem and multiple subproblems by above-mentioned model decomposition, and primal problem is entered
Row is solved, and the optimum results of subproblem are embodied by way of introducing auxiliary variable and cut set constraint, project period in each stage is obtained
Distribution network construction scheme, for the first time solve primal problem when, it is believed that auxiliary variable be 0 and do not consider subproblem formed cut set；
Step 3, multiple Run-time scenarios are considered in each stage, each subproblem is directed to the power distribution network fortune under a kind of Run-time scenario
Row state is optimized, for each subproblem, is carried out integrated solution, is obtained the value of subproblem discrete variable；
Step 4, each subproblem is decomposed, obtains decomposing subproblem and relaxation subproblem, and it is only explicit to decompose subproblem
Comprising the continuous variable in subproblem, solve and decompose subproblem, obtain the value and optimum results of subproblem continuous variable, and shape
Into subproblem cut set；
Step 5, the optimum results of subproblem and subproblem cut set are separately added into the object function and constraints of subproblem, and
It is continuous variable by the discrete variable relaxation in subproblem, sets up relaxation subproblem, solves relaxation subproblem, obtain primal problem and cut
Collection, return to step 2 solves the primal problem containing cut set, obtains the optimum results of primal problem, judge whether the optimum results meet receipts
The requirement of holding back property, exports program results, otherwise into next iteration if meeting.
2. the energy storage, distributed power source and the power distribution network coordinated planning method that are decoupled according to claim 1 based on Benders,
Characterized in that, the model is expressed as schematic style described in step 1, it is specific as follows：
<mrow>
<msub>
<mi>A</mi>
<mi>u</mi>
</msub>
<munder>
<mo>&Sigma;</mo>
<mrow>
<mi>u</mi>
<mo>&Element;</mo>
<mi>U</mi>
</mrow>
</munder>
<msub>
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<mi>u</mi>
</msub>
<mo>&le;</mo>
<msub>
<mi>b</mi>
<mi>u</mi>
</msub>
</mrow>
Wherein, r, s, t are the coefficient sets in object function, αuThe variable related to process of construction is represented,Represent and fortune
The related discrete variable of row state,Represent the continuous variable in operation constraint, Iu、Mu、Au、bu、 It is the coefficient sets in constraint, u ∈
U、y∈Y、T ∈ T represent respectively the planning stage, the year in each planning stage, it is annual in chosen according to 4 season
Typical scene, the hour in typical day, subscript T represents transposition.
3. the energy storage, distributed power source and the power distribution network coordinated planning method that are decoupled according to claim 1 based on Benders,
Characterized in that, the model of primal problem described in step 2 is as follows：
<mfenced open = "" close = "">
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<mtd>
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<mi>n</mi>
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<mo>&Sigma;</mo>
<mrow>
<mi>u</mi>
<mo>&Element;</mo>
<mi>U</mi>
</mrow>
</munder>
<mo>&lsqb;</mo>
<msup>
<mi>r</mi>
<mi>T</mi>
</msup>
<msub>
<mi>&alpha;</mi>
<mi>u</mi>
</msub>
<mo>+</mo>
<munder>
<mi>&Sigma;</mi>
<mrow>
<mi>y</mi>
<mo>&Element;</mo>
<mi>Y</mi>
</mrow>
</munder>
<msub>
<mi>z</mi>
<mrow>
<mi>y</mi>
<mo>,</mo>
<mi>u</mi>
</mrow>
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</mrow>
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</mtable>
</mfenced>
1
<mrow>
<msub>
<mi>A</mi>
<mi>u</mi>
</msub>
<munder>
<mo>&Sigma;</mo>
<mrow>
<mi>u</mi>
<mo>&Element;</mo>
<mi>U</mi>
</mrow>
</munder>
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<mi>u</mi>
</msub>
<mo>&le;</mo>
<msub>
<mi>b</mi>
<mi>u</mi>
</msub>
</mrow>
Wherein, t is the coefficient sets in object function, αuRepresent the variable related to process of construction, zy,uRepresent subproblem target
The lower limit of function, Au、bu、Iu、Mu、Be constraint in coefficient sets, u ∈ U, y ∈ Y,T ∈ T represent respectively the planning stage, the year in each planning stage, it is annual in the typical field chosen according to 4 season
Scape, the hour in typical day, TYAnnual time span is represented,It is the antithesis that loose subproblem produces
Coefficient, It is to decompose the antithesis coefficient that subproblem produces, subscript T represents transposition.
4. the energy storage, distributed power source and the power distribution network coordinated planning method that are decoupled according to claim 1 based on Benders,
Characterized in that, the model of subproblem described in step 3 is as follows：
Wherein, s, t are the coefficient sets in object function,The discrete variable related to running status is represented,Represent
Continuous variable in operation constraint,The optimal value of the variable related to process of construction is represented,Iu、Mu、Be constraint in coefficient sets, u ∈ U,
y∈Y、T ∈ T represent respectively the planning stage, the year in each planning stage, it is annual in the allusion quotation chosen according to 4 season
Type scene, the hour in typical day, TYAnnual time span is represented, subscript T represents transposition.
5. the energy storage, distributed power source and the power distribution network coordinated planning method that are decoupled according to claim 1 based on Benders,
Characterized in that, the model that subproblem is decomposed described in step 4 is as follows：
Wherein,The minimum value of decomposition subproblem object function is represented, t is the coefficient sets in object function,Represent fortune
Continuous variable in row constraint,Mu、 It is the coefficient set in constraint
Close,The optimal value of the variable related to process of construction is represented,By discrete variable in the subproblem tried to achieve in step 4
Optimal value,Be decompose subproblem produce antithesis coefficient, u ∈ U, y ∈ Y,T ∈ T are represented respectively
Planning stage, the year in each planning stage, it is annual in chosen according to 4 season typical scene, the hour in typical day, on
Mark T represents transposition.
6. the energy storage, distributed power source and the power distribution network coordinated planning method that are decoupled according to claim 1 based on Benders,
Characterized in that, the model of relaxation subproblem is as follows described in step 5：
Wherein, s is the coefficient sets in object function,The discrete variable related to running status is represented,Represent to decompose
The minimum value of subproblem object function,Iu、Mu、In being constraint
Coefficient sets,The optimal value of the variable related to process of construction is represented,It is pair that loose subproblem produces
Even coefficient,Be decompose subproblem produce antithesis coefficient, u ∈ U, y ∈ Y,T ∈ T distinguish table
Show the planning stage, the year in each planning stage, it is annual in chosen according to 4 season typical scene, the hour in typical day,
Subscript T represents transposition.
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Application publication date: 20171107 |