CN107368927A - Electrical energy flow point cloth collaboration optimized calculation method based on target cascade analysis - Google Patents

Electrical energy flow point cloth collaboration optimized calculation method based on target cascade analysis Download PDF

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CN107368927A
CN107368927A CN201710645076.3A CN201710645076A CN107368927A CN 107368927 A CN107368927 A CN 107368927A CN 201710645076 A CN201710645076 A CN 201710645076A CN 107368927 A CN107368927 A CN 107368927A
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mrow
msubsup
msub
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natural gas
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文云峰
瞿小斌
叶晓斌
杨仑
叶希
赵荣臻
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Chongqing University
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Abstract

The present invention discloses a kind of electrical energy flow point cloth collaboration optimized calculation method based on target cascade analysis.First according to the connection feature of electrical interconnection system, coupling element model is analyzed, and is abstracted as corresponding coupling constraint, determines flow of power, natural gas flow shared variable, and on this basis, build the electrical energy Traffic Decomposition synergistic mechanism based on target cascade analysis；Further by electrical energy stream collaboration optimization problem split into higher level coordinate primal problem and subordinate optimize subproblem (including：Electric power optimization subproblem, natural gas optimization subproblem), the superior and the subordinate alternately solve successively, until convergence, realizes that the distributed coordination optimization of flow of power and natural gas flow calculates.

Description

Electric-gas power flow distribution formula collaboration optimized calculation method based on target cascade analysis
Technical field
The invention belongs to the flow-optimized calculating field of multipotency, it is therefore an objective to realize power system, natural gas system Distributed Autonomous, association Tuning.Optimized calculation method is cooperateed with more particularly to a kind of electric-gas power flow distribution formula based on target cascade analysis.
Background technology
As environmental protection pressure increase and technological progress, the low-carbon trend of global Energy Consumption are increasingly apparent.With fire coal/combustion Oil machine group is compared, and natural gas unit relative clean, more and more important position is occupied in world power primary energy supply system Put：At present, the Gas Generator Set of the U.S., Britain and Japan accounts for 40%, 34% and 29% all to install respectively；By 2013 End of the year China's fuel gas generation installed capacity is 43,090,000 kW, account for national generator installation total amount 3.5% (wherein coal accounts for 63%, water 22.5% is accounted for, remaining is nuclear power and new energy).Development natural gas power is China's adjustment " coal is solely big " energy consumption structure Realistic choice,《Prevention and control of air pollution action plan》Clear and definite restriction is proposed to coal electricity development.
Influenceed by the factor such as the U.S. " shale gas revolution ", the discovery of East Africa natural gas, global market for natural gas general layout has occurred Change, Gas Prices are on a declining curve, and then promote fuel gas generation fast-developing.Unconventional gas technology has been verified by China Exploitable deposit position is at the forefront in the world, and China takes further steps to deepen the reform to Gas Prices market at present, following natural Gas will have certain price competitiveness compared with other fuel.
Randomness and the large-scale grid connection of intermittent generation of electricity by new energy add need of the power system to flexible regulating units Ask.Gas Generator Set start and stop are ideal high-quality peaking power sources flexibly and with creep speed and the speed of response quickly, energy The new energy output uncertain problem faced in reply traffic control is enough in, or in peak of power consumption, renewable energy power generation energy Emergency service is ensured during power deficiency.
Efficiency of energy utilization, the drop for helping to lift integrated energy system are merged in power system with the height of natural gas system Low environment pollutes and improves financial cost, however, the interaction between flow of power and natural gas flow also will interconnect energy to electric-gas Safety, economy and the reliability service of source system propose new challenge.
Electric power and natural gas system are only supported typically by different operator managements between two systems in reality Low volume data is interacted, and this tune of global information of whole electric-gas interconnection energy resource system is obtained by electric-gas combined dispatching center The problems such as degree method existence information difficult interface, information leakage.These problems need the reality for flow of power and natural gas flow badly Decision-making feature --- multiagent autonomy decision-making, solved with distributed collaboration optimization means.
The content of the invention
The purpose of the present invention is to be directed to the problems of the prior art, there is provided a kind of electric-gas energy based on target cascade analysis Measure flow point cloth collaboration optimized calculation method.
In the method for the present invention, first according to the connection feature of electric-gas interacted system, coupling element model is analyzed, and will It is abstracted as corresponding coupling constraint, determines flow of power, natural gas flow shared variable, and on this basis, structure is based on target The electric-gas energy Traffic Decomposition synergistic mechanism of cascade analysis；Electric-gas energy stream collaboration optimization problem is further split into higher level association Adjust primal problem and subordinate optimization subproblem (including：Electric power optimization subproblem, natural gas optimization subproblem), the superior and the subordinate replace successively Solve, until convergence, realizes that the distributed coordination optimization of flow of power and natural gas flow calculates.The specific steps of methods described are such as Under：
1) determine shared variable, split coupling constraint, structure decomposition synergistic mechanism
Gas Generator Set is the coupling element for connecting power system and natural gas system, and its effect is to turn natural gas chemistry Turn to electric energy.Gas Generator Set model is often described with its secondary consumption characteristic：
In formula：aNG, bNG, cNGFor the consumption coefficient vector of Gas Generator Set, PNGFor electric system variables (vector), combustion is characterized Mechanism of qi group active power output, gd,NGFor natural gas system variable (vector), Gas Generator Set gas consumption is characterized.This constraint characterizes Power system, natural gas system coupled relation, reasonable shared variable is chosen, it is realize that electric-gas system connects to split coupling constraint Even basis, Gas Generator Set natural gas consumption is chosen here as shared variable.Increase a Gas Generator Set in power system Natural gas consumption variable fNG(vector), i.e.,：
And it is required that shared variable f in power systemNGWith shared variable g in natural gas systemd,NGMeet as formula (3) is consistent Sexual intercourse, split and prepare for electric-gas system model.
fNG=gd,NG (3)
Build the electric-gas energy Traffic Decomposition synergistic mechanism based on target cascade analysis：Between power system, natural gas system Changing into power system and natural gas system by centralized bulk information direct interaction pattern only needs same higher level Consultation Center to transmit The interactive mode of shared variable, it would be desirable to which the comformity relation formula (3) of satisfaction, which is converted into, to be iterated to calculate with the superior and the subordinate, gradually restrained Calculation realize.
Decompose synergistic mechanism as shown in Figure 1, concrete operations are as follows：
Analysis framework 1-1) is cascaded according to target electric-gas energy stream collaboration optimization problem is converted into multiple subordinates' optimization Problem and higher level coordinate and optimize primal problem；
1-2) each subordinate's optimization subproblem (electric power system optimization subproblem, natural gas system optimization subproblem) is independent certainly Control, optimization calculates, and realizes the decoupling of electric-gas interacted system (because being provided with shared variable, each subproblem is separate)；
1-3) higher level coordinates and optimizes primal problem and all shared variables is carried out with unified collaboration optimization so that shared variable tends to It is equal, and then meet comformity relation formula (3), realize subproblem collaboration optimization；
1-4) subordinate subproblem, higher level's primal problem alternately solve to result restrain successively, so as to draw with centralization collaboration Optimize consistent result.
2) electric-gas power flow distribution formula collaboration Optimization Modeling
2-1) electric power system optimization subproblem model
Object function is with the minimum target of power system overall running cost：
In formula：ρEFor the fuel price coefficient row vector of power system；FGminArranged for the minimum load consumption of generating set Vector；KGIt is segmented and gathers for generating set active power output；ΔPjFor generating set jth section active power output vector；M is generating set (including Gas Generator Set) piecewise linearity slope matrix；Electric power subproblem is handed down in higher level Consultation Center in being calculated for kth time Gas Generator Set natural gas consumption shared variable (vector),The Gas Generator Set of subordinate electric power subproblem in being calculated for kth time The shared variable (vector) of natural gas consumption；The multiplier coefficient of electric power subproblem is handed down to for higher level Consultation Center (vector).
Constraints includes power balance, Line Flow constraint, unit output constraint, the constraint of Gas Generator Set consumption：
|Tp·Pn| ＜ PFmax (6)
In formula：PiFor generating set output column vector P i-th of component, ELnFor n-th of node (every mother of power system Line can regard a node as) electric load；PminFor generating set active power output lower limit column vector；For generating set J section active power output upper limit column vectors；TpFor power transmission distribution coefficient matrix, PnFor node active injection column vector；PFmaxFor line The active upper limit column vector in road,With Δ PNG,jRespectively Gas Generator Set minimum consumption column vector and jth segmentation active power output row Vector；MNGFor Gas Generator Set piecewise linearity slope matrix.
Formula (5) is system active balance equation, formula (6) and the unit output expression formula that formula (7) is piece-wise linearization, formula (8) it is line transmission power limit, formula (9) is the Gas Generator Set consumption function of piece-wise linearization.
2-2) natural gas system optimization subproblem model
Object function is with the minimum target of natural gas system overall running cost：
In formula：ρGFor the cost coefficient row vector of source of the gas；gpFor gas source feed amount column vector；On in being calculated for kth time The shared variable of the Gas Generator Set natural gas consumption of natural gas subproblem is handed down in level Consultation Center,In being calculated for kth time The shared variable (vector) of the Gas Generator Set natural gas consumption of subordinate natural gas subproblem；For higher level Consultation Center It is handed down to the multiplier coefficient (vector) of natural gas subproblem.
Constraints is as follows：
A) source of the gas and load of natural gas system
Natural air-air source and natural gas gas load should meet to limit as follows respectively：
In formula：WithThe respectively bound (column vector) of natural air-air source gas injection rate；WithRespectively day The bound (column vector) of right gas load (including Gas Generator Set) gas consumption.
B) gas pipeline model
Gas pipeline both ends node pressure difference is the necessary condition of natural gas transmission, and natural gas flows to low pressure by high voltage nodes Node, it can be represented by Weymouth equations, i.e.,
fl 2=Cl 2(πu-πv) (13)
In formula：flTo pass through natural gas line l air-flow；ClFor Weymouth constants；πuAnd πvRespectively pipeline l connects The air pressure (square value) of two end nodes connect；Respectively u-th of natural gas node (multiple pipeline of natural gas system Tie point is referred to as a natural gas node) bound of place's pressure square value.
For Weymouth nonlinear equations (13), have a variety of piece-wise linearization technologies at present.Increment line is used herein Property modelling technique is to the nonlinear terms f in formula (13)l 2Make following linearization process：
δs+1≤ψs≤δsS=1,2 ..., S-1 (17)
0≤δs≤ 1s=1,2 ..., S (18)
In formula：S is segments；fl,sFor the minimum value of s section air-flows (for known quantity)；δsTo represent every section of proportion Continuous variable；ψsTo characterize the binary-state variable whether segmentation s chooses.Flow through pipeline l air-flow flCorresponding segmented line Property functional arrangement is shown in accompanying drawing 2.
C) compressor model
For the air pressure loss in compensation gas pipeline, it is necessary to improve the air pressure of part of nodes by compressor.Due to pressure General very little is lost in the natural gas of mechanism of qi itself, and only the air pressure no-load voltage ratio of compressor can be defined.Assuming that natural gas is from calming the anger The node u of machine connection flows to node v, then Egress node v pressure needs to meet：
πv≤Γ·πu (19)
In formula：Γ is the compressibility factor of compressor.
D) natural gas network incidence matrix
Natural gas network can be considered the digraph being made up of node and pipeline, compressor, can establish node-pipeline association square Battle array AN×L, node-compressor incidence matrix BN×C, node-source of the gas incidence matrix EN×YAnd node-load incidence matrix FN×D。 Wherein, N is natural gas number of network node, and L is pipe number, and C is compressor number of units, and Y is source of the gas number, and D is load number.
E) node supply equilibrium equation
To meet to supply equilibrium relation, each node of natural gas system need to meet equation below：
EN×Y·gp-FN×D·gl-AN×L·fL-BN×C·fC=0 (20)
In formula：fLFor natural gas line air-flow column vector；fCFor compressor secondary gas flow column vector.
2-3) higher level coordinates and optimizes primal problem model
Object function is with each minimum optimization aim of shared variable deviation：
Constraints only includes uniformity coordination constraint：
3) global convergence criterion updates with multiplier
The condition of convergence of the interconnection system distributed Cooperative Optimization Algorithm of electric-gas is：
ε is that deviation tolerates the upper limit in formula, and (23) formula is used for the natural gas consumption of Gas Generator Set for judging that higher level Consultation Center issues ValueThe Gas Generator Set natural gas consumption value being calculated with control centre of subordinateBetween it is inclined Whether difference meets required precision.
If in kth time iteration, above convergence conditions are unsatisfactory for or not exclusively met, then higher level control centre should basis The value of formula (24), (25) renewal multiplier coefficient, and by the multiplier coefficient after renewal be handed down to each control centre of subordinate carry out it is next Secondary iterative calculation：
In formula：μ is constant；α and β initial value typically takes less constant.
4) solution procedure
Higher level's coordinated scheduling center optimization problem and subordinate electric power optimization subproblem, natural gas optimization subproblem must replace Iterative calculation, by coordinating Gas Generator Set natural gas consumption, the optimal fortune of electric-gas interacted system is obtained to reach each subproblem of regulation and control The purpose of row cost.It is based on target cascade analysis framework that electric-gas energy stream Cooperative Optimization Algorithm step is as described below：
4-1) put iterations k=1.Each subproblem shared variable (Gas Generator Set natural gas consumption) With multiplier coefficientInitial value and deviation tolerance upper limit ε, and by these data distributings to corresponding Control centre of subordinate.
4-2) each control centre of subordinate calls Cplex optimization bag auxiliary to solve electric power subproblem, natural gas subproblem respectively, The operating cost minimum Optimized Operation scheme each constrained is met, and obtained shared variable value will be solvedOn issue higher level's coordinated scheduling center.
After 4-3) higher level control centre receives the shared variable data that all control centres of subordinate upload, Cplex is called Optimization bag auxiliary solves primal problem, and minimum optimization is carried out to shared variable deviation.
4-4) higher level's coordinated scheduling center checks condition of convergence formula (23), if meet simultaneously, terminates iterative process, required It is optimal solution to obtain result；Otherwise, multiplier coefficient is updated, and multiplier coefficient and shared variable are issued according to formula (24), (25) To each control centre of subordinate, k=k+1, and return to step 4-2 are put) solve again.
Solve flow chart and see accompanying drawing 3.
The solution have the advantages that unquestionable, this method only needs electricity, gas decision-maker to provide a small amount of shared variable Information, calculated by multiple electric power, natural gas alternating iteration, realize flow of power and natural gas flow Distributed Autonomous, cooperate with what is optimized Purpose.Effectively solve the problems such as difficult information exchange, information leakage, while in turn ensure that the reasonability and economy of optimum results Property.
Brief description of the drawings
Fig. 1 is that electric-gas power flow distribution formula cooperates with Optimization Framework figure.
Fig. 2 is natural gas line air-flow piecewise linearity schematic diagram.
Fig. 3 is to cascade analysis framework by electric-gas energy stream Cooperative Optimization Algorithm flow chart based on target.
Fig. 4 is IEEE118-GAS14 node electric-gas interacted system structure diagrams.In figure, S1, S2, S3 represent natural gas gas Source, C1, C2 represent compressor, coupling element Gas Generator Set set：G4、G5、G11、G21、G29、G36、G43、G45.
Fig. 5 is electric-gas interacted system total cost convergence curve.
Embodiment
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, all should be included within the scope of the present invention.
IEEE118-GAS14 node electric-gas interacted system structure diagrams as shown in Figure 4, based on target cascade analysis Electric-gas power flow distribution formula collaboration optimized calculation method comprise the following steps that：
1) shared variable and electric-gas system decoupling are determined
According to system network architecture, Gas Generator Set set is determined：G4, G5, G11, G21, G29, G36, G43, G45, specify The natural gas consumption of eight Gas Generator Sets is as shared variable；Variable f is set up in power systemG4、fG5、fG11、fG21、fG29、 fG36、fG43、fG45, and meeting that formula (2) consumption constrains, electric-gas system completes decoupling.
2) power system subproblem Optimized model is established
Power system subproblem Optimized model is established with the minimum target of IEEE118 power system overall running costs, constrained Condition includes power balance, DC line trend constraint, the unit output constraint of piece-wise linearization, the gas engine of piece-wise linearization Group consumption constraint.Wherein, generating set active power output segmentation uses typical 3 segmentation point-score.
The power system subproblem based on Cplex Optimization Solution devices, which is write, with Matlab platforms optimizes program.
3) natural gas system subproblem Optimized model is established
Natural gas system subproblem Optimized model is established with the minimum target of GAS14 natural gas system overall running costs, about Beam condition includes：Source of the gas and load, piecewise linearity gas pipeline model (segments takes 3 sections), the compressor mould of natural gas system Type (compressibility factor of compressor, value 2), node supply equilibrium equation.
The natural gas system subproblem based on Cplex Optimization Solution devices, which is write, with Matlab platforms optimizes program.
4) establish higher level and coordinate and optimize primal problem model
Higher level is established with each minimum optimization aim of shared variable deviation and coordinates and optimizes primal problem model, constraints is only wrapped Coordination constraint containing uniformity.
The higher level based on Cplex Optimization Solution devices, which is write, with Matlab platforms coordinates and optimizes primal problem calculation procedure.
5) distributed collaboration Optimization Solution
The parameter of table 1 and initial value are set
Step 1：Put iterations k=1.Each subproblem shared variable (Gas Generator Set natural gas consumption) and multiplier coefficientInitial value and deviation tolerance upper limit ε, and these are counted According to corresponding control centre of subordinate is handed down to, Initial Information is shown in Table 1.
Step 2：Cplex optimization bag auxiliary solution electric power subproblem, natural gas is called to ask respectively in each control centre of subordinate Topic, the operating cost minimum Optimized Operation scheme each constrained is met, and obtained shared variable value will be solvedOn issue higher level's coordinated scheduling center.
Step 3：After higher level control centre receives the shared variable data that all control centres of subordinate upload, call Cplex optimization bag auxiliary solves primal problem, and minimum optimization is carried out to shared variable deviation.
Step 4：Higher level's coordinated scheduling center checks condition of convergence formula (26), if meet simultaneously, terminates iterative process, institute It is optimal solution to try to achieve result；Otherwise, multiplier coefficient is updated according to formula (27), (28), and by under multiplier coefficient and shared variable Each control centre of subordinate is issued, puts k=k+1, and return to step 2 solves again.
6) result is shown
Here contrasted with the centralized computational methods of tradition, comparing result is as follows：
The electric-gas of table 2 interconnects energy resource system Cost Optimization Comparative result
Optimization method W/ dollars WE/ dollar WN/ dollar
Centralization 335680 255900 79779
ATC 335680 255900 79779
The interconnection energy resource system Gas Generator Set optimum results contrast of the electric-gas of table 3
From operating cost (total cost W, power system expense WE, natural gas system expense WN) aspect to the inventive method with Centralized approach method is contrasted, as table 2 compared for operating cost：The inventive method can obtain and centralized solution expense Consistent globally optimal solution；As table 3 compared for Gas Generator Set natural gas consumption and unit output：The inventive method can be obtained and collected The consistent unit output scheme of Chinese style.Fig. 5 depicts electric-gas interacted system aberration curve, and as iterations increases, system is inclined Stable downward trend is presented in difference, has good convergence.
In summary, the electric-gas power flow distribution formula computational methods proposed by the present invention based on target cascade analysis can have Effect reduces electricity, the Inter-System Information interactive quantity of gas two, ensures information private, while also can guarantee that the correctness of result of calculation and have Effect property.

Claims (1)

  1. A kind of 1. electric-gas power flow distribution formula collaboration optimized calculation method based on target cascade analysis, it is characterised in that including Following steps:
    1) determine the shared variable, split coupling constraint, structure decomposition synergistic mechanism：
    Gas Generator Set model is often described with its secondary consumption characteristic：
    <mrow> <msub> <mi>a</mi> <mrow> <mi>N</mi> <mi>G</mi> </mrow> </msub> <msubsup> <mi>P</mi> <mrow> <mi>N</mi> <mi>G</mi> </mrow> <mn>2</mn> </msubsup> <mo>+</mo> <msub> <mi>b</mi> <mrow> <mi>N</mi> <mi>G</mi> </mrow> </msub> <msub> <mi>P</mi> <mrow> <mi>N</mi> <mi>G</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>c</mi> <mrow> <mi>N</mi> <mi>G</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>g</mi> <mrow> <mi>d</mi> <mo>,</mo> <mi>N</mi> <mi>G</mi> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>
    In formula：aNG, bNG, cNGFor the consumption coefficient vector of Gas Generator Set, PNGFor electric system variables, gd,NGFor natural gas system Variable.
    Increase a Gas Generator Set natural gas consumption variable f in power systemNG, i.e.,：
    <mrow> <msub> <mi>a</mi> <mrow> <mi>N</mi> <mi>G</mi> </mrow> </msub> <msubsup> <mi>P</mi> <mrow> <mi>N</mi> <mi>G</mi> </mrow> <mn>2</mn> </msubsup> <mo>+</mo> <msub> <mi>b</mi> <mrow> <mi>N</mi> <mi>G</mi> </mrow> </msub> <msub> <mi>P</mi> <mrow> <mi>N</mi> <mi>G</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>c</mi> <mrow> <mi>N</mi> <mi>G</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>f</mi> <mrow> <mi>N</mi> <mi>G</mi> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>
    And it is required that shared variable f in power systemNGWith shared variable g in natural gas systemd,NGMeet that formula (3) uniformity such as is closed System, split and prepare for electric-gas system model.
    fNG=gd,NG (3)
    Build the electric-gas energy Traffic Decomposition synergistic mechanism based on target cascade analysis：By collecting between power system, natural gas system Chinese style bulk information direct interaction pattern, which changes into power system and natural gas system, only needs same higher level Consultation Center transmission shared The interactive mode of variable, it would be desirable to the comformity relation formula (3) of satisfaction be converted into iterated to calculate with the superior and the subordinate, gradually convergent meter Calculation mode is realized；It is as follows to decompose synergistic mechanism operation：
    Analysis framework 1-1) is cascaded according to target electric-gas energy stream collaboration optimization problem is converted into multiple subordinates' optimization subproblems Primal problem is coordinated and optimized with higher level；
    1-2) each subordinate's optimization subproblem self-government, optimization calculate, and realize the decoupling of electric-gas interacted system；
    1-3) higher level coordinates and optimizes primal problem and all shared variables is carried out with unified collaboration optimization so that shared variable tends to phase Deng, and then meet comformity relation formula (3), realize subproblem collaboration optimization；
    1-4) subordinate subproblem, higher level's primal problem alternately solve to result restrain successively, optimize so as to draw with centralization collaboration Consistent result.
    2) electric-gas power flow distribution formula collaboration Optimization Modeling：
    2-1) electric power system optimization subproblem model
    Object function is with the minimum target of power system overall running cost：
    <mrow> <mtable> <mtr> <mtd> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&amp;rho;</mi> <mi>E</mi> </msub> <mo>&amp;CenterDot;</mo> <mrow> <mo>(</mo> <msup> <mi>FG</mi> <mi>min</mi> </msup> <mo>+</mo> <munder> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>&amp;Element;</mo> <msub> <mi>K</mi> <mi>G</mi> </msub> </mrow> </munder> <msub> <mi>M</mi> <mi>j</mi> </msub> <msub> <mi>&amp;Delta;P</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msubsup> <mi>&amp;alpha;</mi> <mi>E</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>)</mo> </mrow> <mi>T</mi> </msup> <mrow> <mo>(</mo> <msubsup> <mover> <mi>f</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>N</mi> <mi>G</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>-</mo> <msubsup> <mi>f</mi> <mrow> <mi>N</mi> <mi>G</mi> </mrow> <mi>k</mi> </msubsup> <mo>)</mo> </mrow> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msubsup> <mi>&amp;beta;</mi> <mi>E</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>)</mo> </mrow> <mi>T</mi> </msup> <msup> <mrow> <mo>(</mo> <msubsup> <mover> <mi>f</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>N</mi> <mi>G</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>-</mo> <msubsup> <mi>f</mi> <mrow> <mi>N</mi> <mi>G</mi> </mrow> <mi>k</mi> </msubsup> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
    In formula：ρEFor the fuel price coefficient row vector of power system；FGminFor the minimum load consumption column vector of generating set； KGIt is segmented and gathers for generating set active power output；ΔPjFor generating set jth section active power output vector；M is generating set segmented line Property slope matrix；The Gas Generator Set natural gas consumption of electric power subproblem is handed down in higher level Consultation Center in being calculated for kth time Shared variable,The shared variable of the Gas Generator Set natural gas consumption of subordinate electric power subproblem in being calculated for kth time；The multiplier coefficient of electric power subproblem is handed down to for higher level Consultation Center.
    Constraints includes power balance, Line Flow constraint, unit output constraint, the constraint of Gas Generator Set consumption：
    <mrow> <munder> <mo>&amp;Sigma;</mo> <mi>i</mi> </munder> <msub> <mi>P</mi> <mi>i</mi> </msub> <mo>=</mo> <munder> <mo>&amp;Sigma;</mo> <mi>n</mi> </munder> <msub> <mi>EL</mi> <mi>n</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>
    |Tp·Pn| ＜ PFmax (6)
    <mrow> <mi>P</mi> <mo>=</mo> <msup> <mi>P</mi> <mi>min</mi> </msup> <mo>+</mo> <munder> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>&amp;Element;</mo> <msub> <mi>K</mi> <mi>G</mi> </msub> </mrow> </munder> <msub> <mi>&amp;Delta;P</mi> <mi>j</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <mn>0</mn> <mo>&amp;le;</mo> <msub> <mi>&amp;Delta;P</mi> <mi>j</mi> </msub> <mo>&amp;le;</mo> <msubsup> <mi>&amp;Delta;P</mi> <mi>j</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <msubsup> <mi>FG</mi> <mrow> <mi>N</mi> <mi>G</mi> </mrow> <mi>min</mi> </msubsup> <mo>+</mo> <munder> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>&amp;Element;</mo> <msub> <mi>K</mi> <mi>G</mi> </msub> </mrow> </munder> <msub> <mi>M</mi> <mrow> <mi>N</mi> <mi>G</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <msub> <mi>&amp;Delta;P</mi> <mrow> <mi>N</mi> <mi>G</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>f</mi> <mrow> <mi>N</mi> <mi>G</mi> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow>
    In formula：PiFor generating set output column vector P i-th of component, ELnFor n-th of node, (every bus of power system can Regard a node as) electric load；PminFor generating set active power output lower limit column vector；For generating set jth section Active power output upper limit column vector；TpFor power transmission distribution coefficient matrix, PnFor node active injection column vector；PFmaxFor circuit Active upper limit column vector,With Δ PNG,jRespectively Gas Generator Set minimum consumption column vector and jth segmentation active power output arrange to Amount；MNGFor Gas Generator Set piecewise linearity slope matrix.
    Formula (5) is system active balance equation, and formula (6) and the unit output expression formula that formula (7) is piece-wise linearization, formula (8) are Line transmission power limit, formula (9) are the Gas Generator Set consumption function of piece-wise linearization.
    2-2) natural gas system optimization subproblem model
    Object function is with the minimum target of natural gas system overall running cost：
    <mrow> <mtable> <mtr> <mtd> <mi>min</mi> </mtd> <mtd> <mrow> <msub> <mi>&amp;rho;</mi> <mi>G</mi> </msub> <mo>&amp;CenterDot;</mo> <msub> <mi>g</mi> <mi>p</mi> </msub> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msubsup> <mi>&amp;alpha;</mi> <mi>N</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>)</mo> </mrow> <mi>T</mi> </msup> <mrow> <mo>(</mo> <msubsup> <mover> <mi>g</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>d</mi> <mo>,</mo> <mi>N</mi> <mi>G</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>-</mo> <msubsup> <mi>g</mi> <mrow> <mi>d</mi> <mo>,</mo> <mi>N</mi> <mi>G</mi> </mrow> <mi>k</mi> </msubsup> <mo>)</mo> </mrow> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msubsup> <mi>&amp;beta;</mi> <mi>N</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>)</mo> </mrow> <mi>T</mi> </msup> <msup> <mrow> <mo>(</mo> <msubsup> <mover> <mi>g</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>d</mi> <mo>,</mo> <mi>N</mi> <mi>G</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>-</mo> <msubsup> <mi>g</mi> <mrow> <mi>d</mi> <mo>,</mo> <mi>N</mi> <mi>G</mi> </mrow> <mi>k</mi> </msubsup> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow>
    In formula：ρGFor the cost coefficient row vector of source of the gas；gpFor gas source feed amount column vector；Higher level assists in being calculated for kth time The shared variable of the Gas Generator Set natural gas consumption of natural gas subproblem is handed down at tune center,Subordinate in being calculated for kth time The shared variable of the Gas Generator Set natural gas consumption of natural gas subproblem；It is handed down to naturally for higher level Consultation Center The multiplier coefficient of gas subproblem.
    Constraints is as follows：
    A) source of the gas and load of natural gas system
    Natural air-air source and natural gas gas load should meet to limit as follows respectively：
    <mrow> <msubsup> <mi>g</mi> <mi>p</mi> <mi>min</mi> </msubsup> <mo>&amp;le;</mo> <msub> <mi>g</mi> <mi>p</mi> </msub> <mo>&amp;le;</mo> <msubsup> <mi>g</mi> <mi>p</mi> <mi>max</mi> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <msubsup> <mi>g</mi> <mi>d</mi> <mi>min</mi> </msubsup> <mo>&amp;le;</mo> <msub> <mi>g</mi> <mi>d</mi> </msub> <mo>&amp;le;</mo> <msubsup> <mi>g</mi> <mi>d</mi> <mi>max</mi> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>12</mn> <mo>)</mo> </mrow> </mrow>
    In formula：WithThe respectively bound (column vector) of natural air-air source gas injection rate；WithIt is respectively natural The bound (column vector) of gas load (including Gas Generator Set) gas consumption.
    B) gas pipeline model
    Gas pipeline both ends node pressure difference is the necessary condition of natural gas transmission, and natural gas flows to low pressure section by high voltage nodes Point, represented by Weymouth equations, i.e.,
    <mrow> <msubsup> <mi>f</mi> <mi>l</mi> <mn>2</mn> </msubsup> <mo>=</mo> <msubsup> <mi>C</mi> <mi>l</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <msub> <mi>&amp;pi;</mi> <mi>u</mi> </msub> <mo>-</mo> <msub> <mi>&amp;pi;</mi> <mi>v</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>13</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <msubsup> <mi>&amp;pi;</mi> <mi>u</mi> <mi>min</mi> </msubsup> <mo>&amp;le;</mo> <msub> <mi>&amp;pi;</mi> <mi>u</mi> </msub> <mo>&amp;le;</mo> <msubsup> <mi>&amp;pi;</mi> <mi>u</mi> <mi>max</mi> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>14</mn> <mo>)</mo> </mrow> </mrow>
    In formula：flTo pass through natural gas line l air-flow；ClFor Weymouth constants；πuAnd πvRespectively pipeline l connected two The air pressure (square value) of end node；Respectively u-th of natural gas node (multiple pipeline tie point of natural gas system A referred to as natural gas node) place's pressure square value bound.
    For Weymouth nonlinear equations (13), have a variety of piece-wise linearization technologies at present.Linearized herein using increment Modelling technique is to the nonlinear terms f in formula (13)l 2Make following linearization process：
    <mrow> <msubsup> <mi>f</mi> <mi>l</mi> <mn>2</mn> </msubsup> <mo>=</mo> <msubsup> <mi>f</mi> <mrow> <mi>l</mi> <mo>,</mo> <mn>1</mn> </mrow> <mn>2</mn> </msubsup> <mo>+</mo> <munder> <mo>&amp;Sigma;</mo> <mrow> <mi>k</mi> <mo>&amp;Element;</mo> <mi>K</mi> </mrow> </munder> <mrow> <mo>(</mo> <msubsup> <mi>f</mi> <mrow> <mi>l</mi> <mo>,</mo> <mi>s</mi> <mo>+</mo> <mn>1</mn> </mrow> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>f</mi> <mrow> <mi>l</mi> <mo>,</mo> <mi>s</mi> </mrow> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> <msub> <mi>&amp;delta;</mi> <mi>s</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>15</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <msub> <mi>f</mi> <mi>l</mi> </msub> <mo>=</mo> <msub> <mi>f</mi> <mrow> <mi>l</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>+</mo> <munder> <mo>&amp;Sigma;</mo> <mrow> <mi>s</mi> <mo>&amp;Element;</mo> <mi>S</mi> </mrow> </munder> <mrow> <mo>(</mo> <msub> <mi>f</mi> <mrow> <mi>l</mi> <mo>,</mo> <mi>s</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>f</mi> <mrow> <mi>l</mi> <mo>,</mo> <mi>s</mi> </mrow> </msub> <mo>)</mo> </mrow> <msub> <mi>&amp;delta;</mi> <mi>s</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>16</mn> <mo>)</mo> </mrow> </mrow>
    δs+1≤ψs≤δsS=1,2 ..., S-1 (17)
    0≤δs≤ 1s=1,2 ..., S (18)
    In formula：S is segments；fl,sFor the minimum value of s section air-flows (for known quantity)；δsTo represent the continuous of every section of proportion Variable；ψsTo characterize the binary-state variable whether segmentation s chooses.Flow through pipeline l air-flow flCorresponding piecewise linear function Figure is shown in accompanying drawing 2.
    C) compressor model
    For the air pressure loss in compensation gas pipeline, it is necessary to improve the air pressure of part of nodes by compressor.Due to compressor General very little is lost in the natural gas of itself, and only the air pressure no-load voltage ratio of compressor can be defined.Assuming that natural gas connects from compressor The node u connect flows to node v, then Egress node v pressure needs to meet：
    πv≤Γ·πu (19)
    In formula：Γ is the compressibility factor of compressor.
    D) natural gas network incidence matrix
    Natural gas network can be considered the digraph being made up of node and pipeline, compressor, can establish node-pipeline incidence matrix AN×L, node-compressor incidence matrix BN×C, node-source of the gas incidence matrix EN×YAnd node-load incidence matrix FN×D.Its In, N is natural gas number of network node, and L is pipe number, and C is compressor number of units, and Y is source of the gas number, and D is load number.
    E) node supply equilibrium equation
    To meet to supply equilibrium relation, each node of natural gas system need to meet equation below：
    EN×Y·gp-FN×D·gl-AN×L·fL-BN×C·fC=0 (20)
    In formula：fLFor natural gas line air-flow column vector；fCFor compressor secondary gas flow column vector.
    2-3) higher level coordinates and optimizes primal problem model
    Object function is with each minimum optimization aim of shared variable deviation：
    <mrow> <mi>min</mi> <mfenced open = "{" close = "}"> <mtable> <mtr> <mtd> <mrow> <msup> <mrow> <mo>(</mo> <msubsup> <mi>&amp;alpha;</mi> <mi>E</mi> <mi>k</mi> </msubsup> <mo>)</mo> </mrow> <mi>T</mi> </msup> <mrow> <mo>(</mo> <msubsup> <mover> <mi>f</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>N</mi> <mi>G</mi> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msubsup> <mi>f</mi> <mrow> <mi>N</mi> <mi>G</mi> </mrow> <mi>k</mi> </msubsup> <mo>)</mo> </mrow> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msubsup> <mi>&amp;alpha;</mi> <mi>N</mi> <mi>k</mi> </msubsup> <mo>)</mo> </mrow> <mi>T</mi> </msup> <mrow> <mo>(</mo> <msubsup> <mover> <mi>g</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>d</mi> <mo>,</mo> <mi>N</mi> <mi>G</mi> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msubsup> <mi>g</mi> <mrow> <mi>d</mi> <mo>,</mo> <mi>N</mi> <mi>G</mi> </mrow> <mi>k</mi> </msubsup> <mo>)</mo> </mrow> <mo>+</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <mrow> <mo>(</mo> <msubsup> <mi>&amp;beta;</mi> <mi>E</mi> <mi>k</mi> </msubsup> <mo>)</mo> </mrow> <mi>T</mi> </msup> <msup> <mrow> <mo>(</mo> <msubsup> <mover> <mi>f</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>N</mi> <mi>G</mi> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msubsup> <mi>f</mi> <mrow> <mi>N</mi> <mi>G</mi> </mrow> <mi>k</mi> </msubsup> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msubsup> <mi>&amp;beta;</mi> <mi>N</mi> <mi>k</mi> </msubsup> <mo>)</mo> </mrow> <mi>T</mi> </msup> <msup> <mrow> <mo>(</mo> <msubsup> <mover> <mi>g</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>d</mi> <mo>,</mo> <mi>N</mi> <mi>G</mi> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msubsup> <mi>g</mi> <mrow> <mi>d</mi> <mo>,</mo> <mi>N</mi> <mi>G</mi> </mrow> <mi>k</mi> </msubsup> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>21</mn> <mo>)</mo> </mrow> </mrow>
    Constraints only includes uniformity coordination constraint：
    <mrow> <mtable> <mtr> <mtd> <mrow> <mi>s</mi> <mo>.</mo> <mi>t</mi> <mo>.</mo> </mrow> </mtd> <mtd> <mrow> <msubsup> <mover> <mi>f</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>N</mi> <mi>G</mi> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msubsup> <mover> <mi>g</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>d</mi> <mo>,</mo> <mi>N</mi> <mi>G</mi> </mrow> <mi>k</mi> </msubsup> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>22</mn> <mo>)</mo> </mrow> </mrow>
    3) global convergence criterion updates with multiplier
    The condition of convergence of the interconnection system distributed Cooperative Optimization Algorithm of electric-gas is：
    <mrow> <mo>|</mo> <msubsup> <mover> <mi>f</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>N</mi> <mi>G</mi> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msubsup> <mi>f</mi> <mrow> <mi>N</mi> <mi>G</mi> </mrow> <mi>k</mi> </msubsup> <mo>|</mo> <mo>+</mo> <mo>|</mo> <msubsup> <mover> <mi>g</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>d</mi> <mo>,</mo> <mi>N</mi> <mi>G</mi> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msubsup> <mi>g</mi> <mrow> <mi>d</mi> <mo>,</mo> <mi>N</mi> <mi>G</mi> </mrow> <mi>k</mi> </msubsup> <mo>|</mo> <mo>&lt;</mo> <mi>&amp;epsiv;</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>23</mn> <mo>)</mo> </mrow> </mrow>
    ε is that deviation tolerates the upper limit in formula, and (23) formula is used to judge the Gas Generator Set natural gas consumption value that higher level Consultation Center issuesThe Gas Generator Set natural gas consumption value being calculated with control centre of subordinateBetween deviation be It is no to meet required precision.
    If in kth time iteration, above convergence conditions are unsatisfactory for or not exclusively met, then higher level control centre should be according to formula (24), the value of (25) renewal multiplier coefficient, and the multiplier coefficient after renewal is handed down to each control centre of subordinate and carried out next time Iterative calculation：
    <mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>&amp;alpha;</mi> <mi>E</mi> <mi>k</mi> </msubsup> <mo>=</mo> <msubsup> <mi>&amp;alpha;</mi> <mi>E</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>+</mo> <mn>2</mn> <msup> <mrow> <mo>(</mo> <msubsup> <mi>&amp;beta;</mi> <mi>E</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mrow> <mo>(</mo> <msubsup> <mover> <mi>f</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>N</mi> <mi>G</mi> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msubsup> <mi>f</mi> <mrow> <mi>N</mi> <mi>G</mi> </mrow> <mi>k</mi> </msubsup> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>&amp;alpha;</mi> <mi>N</mi> <mi>k</mi> </msubsup> <mo>=</mo> <msubsup> <mi>&amp;alpha;</mi> <mi>N</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>+</mo> <mn>2</mn> <msup> <mrow> <mo>(</mo> <msubsup> <mi>&amp;beta;</mi> <mi>N</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mrow> <mo>(</mo> <msubsup> <mover> <mi>g</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>d</mi> <mo>,</mo> <mi>N</mi> <mi>G</mi> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msubsup> <mi>g</mi> <mrow> <mi>d</mi> <mo>,</mo> <mi>N</mi> <mi>G</mi> </mrow> <mi>k</mi> </msubsup> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>24</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>&amp;beta;</mi> <mi>E</mi> <mi>k</mi> </msubsup> <mo>=</mo> <msubsup> <mi>&amp;mu;&amp;beta;</mi> <mi>E</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>&amp;beta;</mi> <mi>N</mi> <mi>k</mi> </msubsup> <mo>=</mo> <msubsup> <mi>&amp;mu;&amp;beta;</mi> <mi>N</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>25</mn> <mo>)</mo> </mrow> </mrow>
    In formula：μ is constant；α and β initial value typically takes less constant.
    4) solution procedure
    It is based on target cascade analysis framework that electric-gas energy stream Cooperative Optimization Algorithm step is as described below：
    4-1)：Put iterations k=1.Initial value and deviation the tolerance upper limit ε of each subproblem shared variable and multiplier coefficient, And give these data distributings to corresponding control centre of subordinate.
    4-2)：Each control centre of subordinate calls Cplex optimization bag auxiliary to solve electric power subproblem, natural gas subproblem respectively, obtains The operating cost minimum Optimized Operation scheme each constrained to satisfaction, and will solve and higher level association is issued in obtained shared variable value Adjust control centre.
    4-3)：After higher level control centre receives the shared variable data that all control centres of subordinate upload, Cplex optimizations are called Bag auxiliary solves primal problem, and minimum optimization is carried out to shared variable deviation.
    4-4)：Higher level's coordinated scheduling center checks condition of convergence formula (23), if meet simultaneously, terminates iterative process, is tried to achieve As a result it is optimal solution；Otherwise, multiplier coefficient is updated, and multiplier coefficient and shared variable are handed down to according to formula (24), (25) Each control centre of subordinate, puts k=k+1, and return to step 4-2) solve again.
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Cited By (12)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108448619A (en) * 2018-03-30 2018-08-24 东南大学 Meter and the alternating current-direct current microgrid Robust Scheduling method of uncontrollable generator power tracking
CN108875269A (en) * 2018-07-09 2018-11-23 重庆大学 A kind of multi-period energy flux computation method of electric-gas interacted system considering electric system multi-balancing machine and natural gas system slow motion step response
CN108964143A (en) * 2018-06-28 2018-12-07 重庆大学 A kind of natural gas network Static Equivalent model of electric-gas integrated energy system
CN109066695A (en) * 2018-09-29 2018-12-21 广东电网有限责任公司 A kind of electrical optimal energy flux computation method of two stages linearisation
CN109325679A (en) * 2018-09-11 2019-02-12 浙江大学 Consider that the integrated energy system of integration requirement response linearizes accidental scheduling method
CN109409705A (en) * 2018-10-11 2019-03-01 河海大学 A kind of Multiobjective Optimal Operation method of regional complex energy resource system
CN110489788A (en) * 2019-07-09 2019-11-22 广东工业大学 A kind of linkage operation method of electrical interconnection
CN110866773A (en) * 2019-09-29 2020-03-06 西安交通大学 Electric-gas combined market distributed clearing method based on alternative direction multiplier method
CN111769603A (en) * 2020-07-13 2020-10-13 国网天津市电力公司 Unit optimal scheduling method based on safety margin of electric-gas coupling system
CN111928294A (en) * 2020-08-06 2020-11-13 华能太原东山燃机热电有限责任公司 Method for apportioning thermoelectric cost of gas-steam combined cycle unit
CN112362096A (en) * 2020-10-26 2021-02-12 南方电网科学研究院有限责任公司 Method and device for monitoring running state of multi-energy flow, terminal equipment and storage medium
CN113098018A (en) * 2021-04-14 2021-07-09 湘潭大学 Multi-energy-flow calculation convergence adjustment method for electricity-gas region comprehensive energy system

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2002312537A (en) * 2001-04-17 2002-10-25 Tokyo Gas Co Ltd Environmentalism calculating device and recording medium
CN105119289A (en) * 2015-07-27 2015-12-02 华南理工大学 Multi-region power system completely distributed dynamic and economical dispatching method
CN106712035A (en) * 2017-03-29 2017-05-24 南方电网科学研究院有限责任公司 Electric system economical dispatching method
CN106874554A (en) * 2017-01-13 2017-06-20 重庆大学 A kind of improved method of natural gas system energy flux computation

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2002312537A (en) * 2001-04-17 2002-10-25 Tokyo Gas Co Ltd Environmentalism calculating device and recording medium
CN105119289A (en) * 2015-07-27 2015-12-02 华南理工大学 Multi-region power system completely distributed dynamic and economical dispatching method
CN106874554A (en) * 2017-01-13 2017-06-20 重庆大学 A kind of improved method of natural gas system energy flux computation
CN106712035A (en) * 2017-03-29 2017-05-24 南方电网科学研究院有限责任公司 Electric system economical dispatching method

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
AMIN KARGARIAN 等: "Distributed security-constrained unit commitment for large-scale power systems", 《2015 IEEE POWER & ENERGY SOCIETY GENERAL MEETING》 *
YAMIN WANG 等: "Distributed optimization approaches for emerging power systems operation: A review", 《ELECTRIC POWER SYSTEM RESEARCH》 *
瞿小斌 等: "基于串行和并行ADMM算法的电-气能量流分布式协同优化", 《电力系统自动化》 *

Cited By (20)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108448619A (en) * 2018-03-30 2018-08-24 东南大学 Meter and the alternating current-direct current microgrid Robust Scheduling method of uncontrollable generator power tracking
CN108448619B (en) * 2018-03-30 2021-04-30 东南大学溧阳研究院 AC/DC micro-grid robust scheduling method considering uncontrollable generator power tracking
CN108964143A (en) * 2018-06-28 2018-12-07 重庆大学 A kind of natural gas network Static Equivalent model of electric-gas integrated energy system
CN108875269A (en) * 2018-07-09 2018-11-23 重庆大学 A kind of multi-period energy flux computation method of electric-gas interacted system considering electric system multi-balancing machine and natural gas system slow motion step response
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CN109325679B (en) * 2018-09-11 2022-04-05 浙江大学 Linear random scheduling method of comprehensive energy system considering comprehensive demand response
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CN110866773A (en) * 2019-09-29 2020-03-06 西安交通大学 Electric-gas combined market distributed clearing method based on alternative direction multiplier method
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