CN114004098B - Opportunity constraint considered maximum energy supply capacity evaluation method for electrical coupling system - Google Patents

Opportunity constraint considered maximum energy supply capacity evaluation method for electrical coupling system Download PDF

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CN114004098B
CN114004098B CN202111302009.4A CN202111302009A CN114004098B CN 114004098 B CN114004098 B CN 114004098B CN 202111302009 A CN202111302009 A CN 202111302009A CN 114004098 B CN114004098 B CN 114004098B
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CN114004098A (en
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孙琦润
吴志
顾伟
陆于平
郑舒
赵景涛
席旸旸
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Southeast University
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • H02J3/46—Controlling of the sharing of output between the generators, converters, or transformers
    • H02J3/466—Scheduling the operation of the generators, e.g. connecting or disconnecting generators to meet a given demand
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/04—Constraint-based CAD
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2113/00—Details relating to the application field
    • G06F2113/04—Power grid distribution networks
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/06—Power analysis or power optimisation
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2300/00—Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation
    • H02J2300/20—The dispersed energy generation being of renewable origin
    • H02J2300/28—The renewable source being wind energy
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2300/00—Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation
    • H02J2300/40—Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation wherein a plurality of decentralised, dispersed or local energy generation technologies are operated simultaneously
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
    • Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
    • Y04S10/00—Systems supporting electrical power generation, transmission or distribution
    • Y04S10/50—Systems or methods supporting the power network operation or management, involving a certain degree of interaction with the load-side end user applications

Abstract

The invention discloses an evaluation method for the maximum energy supply capacity of an electric coupling system in consideration of opportunity constraint, which comprises the steps of constructing an evaluation model for the maximum energy supply capacity of the electric coupling system in consideration of random wind energy output and opportunity constraint; secondly, converting the wind energy output joint opportunity constraint into an equivalent mixed integer linear constraint group by adopting a Boolean reconstruction method; then, converting the model into a mixed integer second-order cone programming model containing a penalty term by adopting a convex-concave method; and finally, decomposing the model into power grid and gas grid submodels for distributed iterative solution based on a target cascade analysis method. According to the method, the coupling relation of the power grid and the air network is fully considered, the influence of the output randomness of the fan is considered, and a maximum energy supply capacity evaluation model of the electric coupling system is established; the method is based on a target cascade decomposition method, decomposes the integral model into a power grid sub-model and a power grid sub-model for distributed independent solution, and meets the actual engineering requirements better.

Description

Opportunity constraint considered maximum energy supply capacity evaluation method for electrical coupling system
Technical Field
The invention relates to the technical field of comprehensive energy system optimization, in particular to an evaluation method for the maximum energy supply capacity of an electric coupling system considering opportunity constraint.
Background
With the continuous increase of installed capacity of the gas turbine and the development of an electric ventilation technology, the coupling degree of the power system and the natural gas system is continuously deepened, and the electric coupling system also effectively promotes the consumption of renewable energy sources. With the vigorous development of national economy, a user puts forward higher requirements on the energy supply reliability of an electrical coupling system, the maximum energy supply capacity is used as an important index of the energy supply reliability of the system, and accurate evaluation of the maximum energy supply capacity plays a crucial role in guiding the planning design and load management of the electrical coupling system. Different from the maximum power supply capacity of the traditional power grid, the evaluation of the maximum power supply capacity of the electrical coupling system needs to fully consider the coupling relation between the power grid and the air grid and take the influence of large-scale wind power access in the power grid into consideration. For this purpose, an evaluation method for the maximum energy supply capacity of the electrical coupling system considering the opportunity constraint is provided.
Disclosure of Invention
The invention aims to provide an electric coupling system maximum energy supply capacity evaluation method considering opportunity constraint, which is used for constructing an electric coupling system maximum energy supply capacity evaluation model considering random wind energy output combined with opportunity constraint and decomposing the model into a power grid and gas grid submodel for distributed iterative solution based on a target cascade analysis method. The established model provides a theoretical basis for the evaluation of the maximum energy supply capacity of the electric coupling system considering the random wind energy output under the information privacy protection requirement.
The purpose of the invention can be realized by the following technical scheme:
an evaluation method of maximum energy supply capacity of an electrical coupling system considering opportunity constraint, the evaluation method comprising the steps of:
s1, establishing an objective function of the maximum energy supply capacity model of the electric coupling system;
s2, considering the joint opportunity constraint of the random wind energy output, and establishing a power distribution network operation constraint condition in the maximum energy supply capacity model;
s3, establishing a gas network operation constraint condition in the maximum energy supply capacity model;
s4, establishing a constraint condition of coupling operation of the power distribution network and the gas network in the maximum energy supply capacity model;
s5, converting the fan output joint opportunity constraint in the maximum energy supply capacity model into an equivalent mixed integer linear constraint group by adopting a Boolean reconstruction method;
s6, converting the maximum energy supply capacity model into a mixed integer second-order cone programming model containing a penalty term by adopting a convex-concave method;
s7, relaxing the electric and gas coupling constraints, and decomposing the maximum energy supply capacity model into a power distribution network maximum power supply capacity sub-model and a gas network maximum gas supply capacity sub-model;
and S8, based on a target cascade analysis method, carrying out distributed iterative solution on the power distribution network maximum power supply capacity sub-model and the air network maximum air supply capacity sub-model.
Further, the objective function in S1 is:
Figure BDA0003338775910000021
in the formula (I), the compound is shown in the specification,
Figure BDA0003338775910000022
respectively representing the active load and the reactive load of the node i,
Figure BDA0003338775910000023
respectively representing the active and reactive load increase base power of the node i, kappai、κmThe respective magnifications of the electrical load and the air load are shown.
Further, in S2, the power distribution network operation constraint conditions in the maximum energy supply capability model include:
Figure BDA0003338775910000024
Figure BDA0003338775910000025
Figure BDA0003338775910000026
Figure BDA0003338775910000027
Figure BDA0003338775910000031
Figure BDA0003338775910000032
Figure BDA0003338775910000033
Figure BDA0003338775910000034
Figure BDA0003338775910000035
Figure BDA0003338775910000036
Figure BDA0003338775910000037
Figure BDA0003338775910000038
Figure BDA0003338775910000039
Figure BDA00033387759100000310
Figure BDA00033387759100000311
Figure BDA00033387759100000312
Figure BDA00033387759100000313
Figure BDA00033387759100000314
Figure BDA00033387759100000315
Figure BDA00033387759100000316
Figure BDA00033387759100000317
in the formula, subscripts ij, i, u, v, w, g and t respectively represent lines, nodes, substations, fans, electric gas conversion equipment, gas turbines and scheduling periods, sets u (i), v (i), w (i) and g (i) respectively represent substations, fans, electric gas conversion equipment and gas turbines which are connected with the nodes i, and pi (i) and delta (i) respectively represent first-section nodes of the lines which take the nodes i as tail-end nodes in the power distribution networkSet, line end node set with node i as head end node, set
Figure BDA00033387759100000319
Representing a collection of distribution network nodes, a collection U representing a collection of substation nodes,
Figure BDA00033387759100000318
representing a set of faulty substation connected lines;
Figure BDA0003338775910000041
respectively representing the fan power factor, pu,t、pv,t、pw,t、pg,tRespectively represents the active power of a transformer substation u, a fan v, an electric-to-gas device w and a gas turbine g, and qu,t、qv,t、qg,tRespectively representing the reactive power v of the substation u, the fan v and the gas turbine gi,tRepresenting the voltage square of node i, iij,tRepresents the current squared value of line ij; alpha (alpha) ("alpha")ijVariables 0-1, x representing the operating states of distribution line ij, respectivelyij、xjiA 0-1 variable indicating whether line ij is in forward and reverse operation; rij、XijRespectively representing the resistance and reactance of the line ij,
Figure BDA0003338775910000042
representing the ratio of the electric load to the peak load during a time period t, M representing a larger positive integer, Vi、
Figure BDA0003338775910000043
Respectively represent the minimum and maximum values of the voltage at the node i,
Figure BDA0003338775910000044
represents the maximum value of the current of line ij,
Figure BDA0003338775910000045
respectively representing the maximum value of the active and reactive power flowing through the line ij,
Figure BDA0003338775910000046
respectively represents the maximum value of active power of a transformer substation, electric gas conversion equipment and a gas turbine,
Figure BDA0003338775910000047
respectively representing the maximum reactive power of the substation and the gas turbine, RUPtG,w、RUGT,gRespectively represents the maximum value RD of the upward climbing power of the electric gas conversion equipment w and the gas turbine gPtG,w、RDGT,gRespectively represents the maximum value, eta, of the downward climbing power of the electric gas conversion equipment w and the gas turbine gGT、ηPtGRespectively representing the conversion efficiency of a gas turbine and an electric gas conversion device, P { A } represents the occurrence probability of an event A, xiv,tThe predicted value of the active power output of the random fan, theta represents the probability level of satisfying the joint chance constraint, kappai、
Figure BDA0003338775910000048
Representing the minimum and maximum values of the amplification of the electrical load,
Figure BDA0003338775910000049
respectively representing the virtual power flow variables, D, of the lines ijiRepresenting the virtual load amount of node i.
Further, in S3, the operation constraint conditions of the air grid specifically include:
Figure BDA00033387759100000410
Figure BDA00033387759100000411
Figure BDA00033387759100000412
Figure BDA00033387759100000413
Figure BDA00033387759100000414
Figure BDA00033387759100000415
Figure BDA00033387759100000416
Figure BDA0003338775910000051
Figure BDA0003338775910000052
Figure BDA0003338775910000053
Figure BDA0003338775910000054
in the formula, subscripts mn, m, s respectively represent a pipeline, a gas node, and a gas source node, sets s (m), v (m), g (m) respectively represent a gas source, an electric gas conversion device, and a gas turbine set connected to node m, P, C respectively represent a conventional pipeline and a compressor pipeline set, and pi (m) and delta (m) respectively represent a pipeline first section node set using node m as a tail end node and a pipeline tail end node set using node i as a head end node in a gas network; f. ofmn,tDenotes the average flow of gas through the pipe mn, fs,t、fv,t、fg,tRespectively representing the gas flow rate, f, of the electric gas-converting plant v, gas turbine g, of the gas source sm,t、fn,tRespectively representing the gas flow rates of nodes m, n, [ pi ]m,t、πn,tRespectively representing the pressure, χ, at nodes m, nmn,tRepresenting a pipeline inventory;
Figure BDA0003338775910000055
the air load at the node m is shown,
Figure BDA0003338775910000056
the gas load of the node m is shown to increase the base power,
Figure BDA0003338775910000057
represents the ratio of air load to peak load, k, in time period tm、
Figure BDA0003338775910000058
Representing the minimum and maximum values of the magnification of the air load, pim、
Figure BDA0003338775910000059
Respectively representing the minimum and maximum values of the air pressure at node m, Fs、
Figure BDA00033387759100000510
Respectively representing the minimum and maximum values of the s flow of the source gas, Fm、
Figure BDA00033387759100000511
Respectively represent the minimum and maximum air flow of the node m,
Figure BDA00033387759100000512
the pressure rise and the gas loss coefficient of the compressor are shown,
Figure BDA00033387759100000513
the pipeline storage coefficient is represented by the index,
Figure BDA00033387759100000514
representing the coefficients of the viruss equation.
Further, the constraint conditions for the operation of coupling the distribution network and the air network in S4 specifically include
Figure BDA00033387759100000515
Figure BDA00033387759100000516
In the formula, phi represents the gas-electric conversion coefficient, etaGT、ηPtGRespectively showing the conversion efficiency of the gas turbine and the electric gas conversion equipment.
Further, the S5 specifically includes:
s51, preprocessing the fan predicted power data set, wherein the uncertain fan output vector xi of each time period t is a V-dimensional variable, and V represents the number of fans; setting a fan prediction data set to be omega in each period, and setting the k-th prediction vector in the set omega to be
Figure BDA0003338775910000061
ωkThe probability distribution and the marginal probability distribution of (d) are respectively F (omega)k)＝P(ξ≥ωk)、
Figure BDA0003338775910000062
S52, collecting any fan v
Figure BDA0003338775910000063
Will ZvAll of (1)
Figure BDA0003338775910000064
Is arranged in descending order to form a segmentation point sequence c1v＞c2v＞...＞cnvvWherein n isvRepresenting the number of the division points corresponding to the fan v;
s53 collecting set
Figure BDA0003338775910000065
Where x represents the Cartesian product of the sets, the sets
Figure BDA0003338775910000066
Splitting into theta full sets
Figure BDA0003338775910000067
And theta is not sufficient set
Figure BDA0003338775910000068
According to the formula (2.36), will
Figure BDA0003338775910000069
Performing 0-1 projection to obtain
Figure BDA00033387759100000610
Wherein each vector
Figure BDA00033387759100000611
Corresponding n-dimensional 0-1 vector
Figure BDA00033387759100000612
n＝∑v∈V nv；
Figure BDA00033387759100000613
S54, converting the fan output joint opportunity constraint (2.10) into the following equivalent mixed integer linear constraint group;
Figure BDA00033387759100000614
Figure BDA00033387759100000615
Figure BDA00033387759100000616
in the formula, civ,tDenotes the division point, u, of the fan v at time tiv,tIs corresponding n dimensions 0-1Variable, representation set
Figure BDA00033387759100000617
Middle vector
Figure BDA00033387759100000618
In that
Figure BDA00033387759100000619
The corresponding n-dimensional 0-1 vector.
Further, the S6 specifically includes:
s61, rewriting the equality constraints (2.5) and (2.32) as a set of inequalities consisting of the difference between two convex functions as follows:
Figure BDA00033387759100000620
Figure BDA00033387759100000621
Figure BDA00033387759100000622
Figure BDA00033387759100000623
s62 solving the relaxation model (2.44) and recording the initial solution
Figure BDA0003338775910000071
And
Figure BDA0003338775910000072
wherein Obj represents the objective function;
Obj＝max (2.1)
s.t.(2.2)-(2.4),(2.6)-(2.9),(2.11)-(2.22),(2.23)-(2.31), (2.44)
(2.33)-(2.35),(2.37)-(2.39),(2.40),(2.42)
s63, expanding the right side of the constraint conditions (2.41) (2.43) by using a first-order Taylor formula according to the initial solution and adding a relaxation variable
Figure BDA0003338775910000073
As shown in equation (2.45) (2.46);
Figure BDA0003338775910000074
Figure BDA0003338775910000075
s64, iteratively solving the model (2.47) of the objective function containing the relaxation variable penalty term, and stopping iteration if the equations (2.48) and (2.49) are met after each solution; otherwise, record
Figure BDA0003338775910000076
And
Figure BDA0003338775910000077
updating the penalty term according to a formula (2.50) and entering next iteration; where the superscript h denotes the number of iterations, p(h)Indicating a penalty term of the slack variable, psi1、ψ2Denotes a convergence criterion, tau denotes a penalty update step, pmaxRepresenting a maximum value of the penalty term;
Figure BDA0003338775910000078
Figure BDA0003338775910000079
Figure BDA00033387759100000710
ρ(h+1)＝min{τρ(h),ρmax} (2.50)
further, the S7 specifically includes:
relaxing the electric and gas coupling constraints (2.34) (2.35), and decomposing the model (2.44) into a power grid maximum power supply capacity sub-model and a gas grid maximum gas supply capacity sub-model;
Figure BDA0003338775910000081
Figure BDA0003338775910000082
wherein, Objp、ObjgRespectively representing the maximum power supply capacity of the power distribution network and the maximum air supply capacity of the air network containing punishment items, lambdag,t、γg,tRespectively representing the primary and secondary penalty terms, lambda, of the gas turbinew,t、γw,tRespectively represent the first punishment item and the second punishment item of the electric gas conversion equipment,
Figure BDA0003338775910000083
representing the interaction variables passed by the air network to the distribution network,
Figure BDA0003338775910000084
representing the interaction variables that the distribution network passes to the gas network.
Further, the S8 specifically includes:
s81, setting initial values of interaction variables of the power distribution network and the gas network
Figure BDA0003338775910000085
Initial value of primary and secondary punishment item
Figure BDA0003338775910000086
The penalty item updates the step length sigma and the maximum iteration number LmaxConvergence criterion psi3、ψ4Taking the iteration number l as 1;
s82 fetching
Figure BDA0003338775910000087
Solving the power grid sub-model (2.51) according to S3; get
Figure BDA0003338775910000088
Solving the air net submodel (2.52) with reference to S3; if the formulae (2.53) and (2.54) are satisfied, or L ═ LmaxCombining iteration; otherwise, updating the first and second punishment terms according to a formula (2.55), taking l as l +1, and entering the next iteration;
Figure BDA0003338775910000089
Figure BDA00033387759100000810
Figure BDA00033387759100000811
the invention has the beneficial effects that:
1. according to the method, the coupling relation of the power grid and the air network is fully considered, the influence of the output randomness of the fan is considered, and a maximum energy supply capacity evaluation model of the electric coupling system is established;
2. according to the evaluation method, the fact that the power grid and the gas grid belong to different main bodies is considered, privacy protection requirements exist, and the practical engineering requirements cannot be met by adopting a unified solving framework. The method is based on a target cascade decomposition method, decomposes the integral model into a power grid sub-model and a power grid sub-model for distributed independent solution, and meets the actual engineering requirements better.
Drawings
The invention will be further described with reference to the accompanying drawings.
FIG. 1 is a flow chart of the evaluation method of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
As shown in fig. 1, a flowchart of a method for evaluating a maximum energy supply capacity of an electrical coupling system considering opportunity constraint according to the present invention includes the following steps:
s1, constructing an electric coupling system maximum energy supply capacity evaluation model considering random wind energy output based on joint opportunity constraint; :
s11, comprehensively considering the maximum power supply capacity of the power distribution network and the maximum air supply capacity of the air network, and establishing an objective function of the maximum power supply capacity as follows:
Figure BDA0003338775910000091
in the formula (I), the compound is shown in the specification,
Figure BDA0003338775910000092
respectively representing the active load and the reactive load of the node i,
Figure BDA0003338775910000093
respectively representing the active and reactive load increase base power of the node i, kappai、κmThe magnifications of the electrical load and the gas load are shown respectively.
S12, considering uncertainty fan joint opportunity constraint, and establishing a power distribution network flow constraint group as follows:
Figure BDA0003338775910000101
Figure BDA0003338775910000102
Figure BDA0003338775910000103
Figure BDA0003338775910000104
Figure BDA0003338775910000105
Figure BDA0003338775910000106
Figure BDA0003338775910000107
Figure BDA0003338775910000108
Figure BDA0003338775910000109
Figure BDA00033387759100001010
Figure BDA00033387759100001011
Figure BDA00033387759100001012
Figure BDA00033387759100001013
Figure BDA00033387759100001014
Figure BDA00033387759100001015
Figure BDA00033387759100001016
Figure BDA00033387759100001017
Figure BDA00033387759100001018
Figure BDA00033387759100001019
Figure BDA00033387759100001020
Figure BDA00033387759100001021
in the formula, subscripts ij, i, u, v, w, g and t respectively represent lines, nodes, substations, fans, electric gas conversion equipment, gas turbines and scheduling time periods, sets u (i), v (i), w (i) and g (i) respectively represent substations, fans, electric gas conversion equipment and gas turbines which are connected with the nodes i, and pi (i) and delta (i) respectively represent a line first section node set taking the nodes i as tail end nodes and a line tail end node set taking the nodes i as head end nodes in a power distribution network, and the sets
Figure BDA00033387759100001113
Representing a collection of distribution network nodes, a collection U representing a collection of substation nodes,
Figure BDA00033387759100001112
representing a set of faulty substation connected lines;
Figure BDA0003338775910000111
respectively representing the fan power factor, pu,t、pv,t、pw,t、pg,tRespectively representing the active power of a transformer substation u, a fan v, an electric gas conversion device w and a gas turbine g, qu,t、qv,t、qg,tRespectively representing the reactive power v of the substation u, the fan v and the gas turbine gi,tRepresenting the voltage square of node i, iij,tRepresents the current squared value of line ij; alpha is alphaijVariables 0-1, x representing the operating states of distribution line ij, respectivelyij、xjiA 0-1 variable indicating whether line ij is in forward and reverse operation; rij、XijRespectively representing the resistance and reactance values of the line ij,
Figure BDA0003338775910000112
representing the ratio of the electric load to the peak load during a time period t, M representing a larger positive integer, Vi、
Figure BDA0003338775910000113
Respectively represent the minimum and maximum values of the voltage at the node i,
Figure BDA0003338775910000114
represents the maximum value of the current of line ij,
Figure BDA0003338775910000115
respectively representing the maximum value of the active and reactive power flowing through the line ij,
Figure BDA0003338775910000116
respectively represents the maximum value of active power of a transformer substation, electric gas conversion equipment and a gas turbine,
Figure BDA0003338775910000117
respectively representing the maximum reactive power of the substation and the gas turbine, RUPtG,w、RUGT,gRespectively represents the maximum value RD of the upward climbing power of the electric gas conversion equipment w and the gas turbine gPtG,w、RDGT,gRespectively represents the maximum value, eta, of the downward climbing power of the electric gas conversion equipment w and the gas turbine gGT、ηPtGRespectively representing the conversion efficiency of a gas turbine and an electric gas conversion device, P { A } represents the occurrence probability of an event A, xiv,tA predicted value of the active power output of the random wind turbine, theta represents a probability level of satisfying joint chance constraints,κ i、
Figure BDA0003338775910000118
representing the minimum and maximum values of the amplification of the electrical load,
Figure BDA0003338775910000119
respectively representing the virtual power flow variable, D, of the line ijiRepresenting the virtual load amount of node i.
S13, establishing a gas network flow constraint group as follows:
Figure BDA00033387759100001110
Figure BDA00033387759100001111
Figure BDA0003338775910000121
Figure BDA0003338775910000122
Figure BDA0003338775910000123
Figure BDA0003338775910000124
Figure BDA0003338775910000125
Figure BDA0003338775910000126
Figure BDA0003338775910000127
Figure BDA0003338775910000128
Figure BDA0003338775910000129
in the formula, subscripts mn, m, s respectively represent a pipeline, a gas node, and a gas source node, sets s (m), v (m), g (m) respectively represent a gas source, an electric gas conversion device, and a gas turbine set connected to node m, P, C respectively represent a conventional pipeline and a compressor pipeline set, and pi (m) and delta (m) respectively represent a pipeline first section node set using node m as a tail end node and a pipeline tail end node set using node i as a head end node in a gas network; f. ofmn,tDenotes the average flow of gas through the pipe mn, fs,t、fv,t、fg,tRespectively showing the gas flow rate f of the gas source s electric gas conversion equipment v and the gas turbine gm,t、fn,tRespectively representing the gas flow rates of nodes m, n,. pim,t、πn,tRespectively representing the pressure, χ, at nodes m, nmn,tRepresenting a pipeline inventory;
Figure BDA00033387759100001210
the gas load at the node m is represented,
Figure BDA00033387759100001211
the gas load of the node m is shown to increase the base power,
Figure BDA00033387759100001212
representing the proportion of air load to peak load over time period t,κ m、
Figure BDA00033387759100001213
the minimum and maximum values of the air load magnification are shown,Π m、
Figure BDA00033387759100001214
respectively representing the minimum and maximum values of the air pressure at node m, Fs、
Figure BDA00033387759100001215
Respectively represent the minimum value and the maximum value of the gas flow of the gas source s,F m、
Figure BDA00033387759100001216
respectively represent the minimum and maximum air flow of the node m,
Figure BDA00033387759100001217
the pressure rise and the gas loss coefficient of the compressor are shown,
Figure BDA00033387759100001218
the pipeline storage coefficient is represented by the index,
Figure BDA00033387759100001219
representing the coefficients of the viruss equation.
S14, establishing the coupling constraint of the distribution network and the air network as follows:
Figure BDA00033387759100001220
Figure BDA0003338775910000131
in the formula, phi represents the gas-electric conversion coefficient, etaGT、ηPtGRespectively showing the conversion efficiency of the gas turbine and the electric gas conversion equipment.
S2, converting the fan output joint opportunity constraint into an equivalent mixed integer linear constraint group by adopting a Boolean reconstruction method;
and S21, preprocessing the fan predicted power data set, wherein the uncertain fan output vector xi of each time period t is a V-dimensional variable, and V represents the number of fans. Setting a fan prediction data set to be omega in each period, and setting the k-th prediction vector in the set omega to be
Figure BDA0003338775910000132
ωkThe probability distribution and the marginal probability distribution of (d) are respectively F (omega)k)＝P(ξ≥ωk)、
Figure BDA0003338775910000133
S22, collecting any fan v
Figure BDA0003338775910000134
Will ZvAll of
Figure BDA0003338775910000135
Is arranged in descending order to form a segmentation point sequence c1v＞c2v＞...＞cnvvWherein n isvAnd representing the number of the division points corresponding to the fan v.
S23 collecting set
Figure BDA0003338775910000136
Where x represents the Cartesian product of the sets, the sets
Figure BDA0003338775910000137
Splitting into theta full sets
Figure BDA0003338775910000138
And theta incomplete set
Figure BDA0003338775910000139
According to the formula (3.36), will
Figure BDA00033387759100001310
Performing 0-1 projection to obtain
Figure BDA00033387759100001311
Wherein each vector
Figure BDA00033387759100001312
Corresponding n-dimensional 0-1 vector
Figure BDA00033387759100001313
n＝∑v∈V nv。
Figure BDA00033387759100001314
And S24, converting the fan output joint opportunity constraint (3.10) into the following equivalent mixed integer linear constraint group.
Figure BDA00033387759100001315
Figure BDA00033387759100001316
Figure BDA00033387759100001317
In the formula, civ,tDenotes the division point, u, of the fan v at time tiv,tRepresenting sets for corresponding n-dimensional 0-1 variables
Figure BDA00033387759100001318
Middle vector
Figure BDA00033387759100001319
In that
Figure BDA00033387759100001320
The corresponding n-dimensional 0-1 vector.
S3, converting the model into a mixed integer second-order cone programming model containing a penalty term by adopting a convex-concave method;
s31, rewriting the equality constraints (3.5) and (3.32) as a set of inequalities consisting of the difference between two convex functions as follows:
Figure BDA0003338775910000141
Figure BDA0003338775910000142
Figure BDA0003338775910000143
Figure BDA0003338775910000144
s32 solving the relaxation model (3.44) and recording the initial solution
Figure BDA0003338775910000145
And
Figure BDA0003338775910000146
where Obj represents the objective function.
Obj＝max(3.1)
s.t.(3.2)-(3.4),(3.6)-(3.9),(3.11)-(3.22),(3.23)-(3.31), (3.44)
(3.33)-(3.35),(3.37)-(3.39),(3.40),(3.42)
S33, according to the initial solution, the right side of the constraint conditions (3.41) (3.43) is processed by using the first-order Taylor formulaUnrolling and adding relaxation variables
Figure BDA0003338775910000147
As shown in equation (3.45) (3.46).
Figure BDA0003338775910000148
Figure BDA0003338775910000149
S34, iteratively solving the model (3.47) of the objective function containing the relaxation variable penalty term, and stopping iteration if the equations (3.48) and (3.49) are met after each solution; otherwise, record
Figure BDA00033387759100001410
And
Figure BDA00033387759100001411
and updating the penalty term according to a formula (3.50) and entering the next iteration. Where the superscript h denotes the number of iterations, p(h)Indicating a penalty term of the slack variable, psi1、ψ2Denotes a convergence criterion, tau denotes a penalty update step, pmaxA penalty term maximum is indicated.
Figure BDA00033387759100001412
Figure BDA00033387759100001413
Figure BDA0003338775910000151
ρ(h+1)＝min{τρ(h),ρmax} (3.50)
And S4, decomposing the model into power grid and gas grid submodels based on a target cascade analysis method, and performing distributed iterative solution.
And S41, relaxing the electrical and gas coupling constraints (3.34) (3.35), and decomposing the model (3.44) into a power grid maximum power supply capacity sub-model and a gas grid maximum gas supply capacity sub-model.
Figure BDA0003338775910000152
Figure BDA0003338775910000153
Wherein, Objp、ObjgRespectively representing the maximum power supply capacity of the power distribution network and the maximum air supply capacity of the air network containing punishment items, lambdag,t、γg,tRespectively representing the primary and secondary penalty terms, lambda, of the gas turbinew,t、γw,tRespectively representing the first punishment item and the second punishment item of the electric gas conversion equipment,
Figure BDA0003338775910000154
representing the interaction variables passed by the air network to the distribution network,
Figure BDA0003338775910000155
representing the interaction variables that the distribution network passes to the gas network.
S42, setting initial values of interaction variables of the power distribution network and the gas network
Figure BDA0003338775910000156
Initial value of primary and secondary punishment item
Figure BDA0003338775910000157
The penalty item updates the step length sigma and the maximum iteration number LmaxConvergence criterion psi3、ψ4The iteration number l is 1.
S43 fetching
Figure BDA0003338775910000158
Solving the grid submodel according to S3Type (3.51); get the
Figure BDA0003338775910000159
Refer to S3 to solve the air net submodel (3.52). If the formulae (3.53) and (3.54) are satisfied, or L ═ LmaxCombining iteration; otherwise, updating the first and second penalty terms according to the formula (3.55), taking l as l +1, and entering the next iteration.
Figure BDA00033387759100001510
Figure BDA0003338775910000161
Figure BDA0003338775910000162
In the description herein, references to the description of "one embodiment," "an example," "a specific example," etc., mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
The foregoing shows and describes the general principles, essential features, and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed.

Claims (9)

1. An evaluation method for maximum energy supply capacity of an electric coupling system considering opportunity constraint, which is characterized by comprising the following steps:
s1, establishing an objective function of the maximum energy supply capacity model of the electric coupling system;
s2, considering the joint opportunity constraint of the output of the random fan, and establishing a power distribution network operation constraint condition in the maximum energy supply capacity model;
s3, establishing a gas network operation constraint condition in the maximum energy supply capacity model;
s4, establishing a constraint condition of coupling operation of the power distribution network and the gas network in the maximum energy supply capacity model;
s5, converting the fan output joint opportunity constraint in the maximum energy supply capacity model into an equivalent mixed integer linear constraint group by adopting a Boolean reconstruction method;
s6, converting the maximum energy supply capacity model into a mixed integer second-order cone programming model containing a penalty term by adopting a convex-concave method;
s7, relaxing the electric and gas coupling constraints, and decomposing the maximum energy supply capacity model into a power distribution network maximum power supply capacity sub-model and a gas network maximum gas supply capacity sub-model;
and S8, based on the target cascade analysis method, performing distributed iterative solution on the power distribution network maximum power supply capacity sub-model and the air network maximum air supply capacity sub-model.
2. The method for evaluating the maximum energy supply capacity of the electric coupling system considering the opportunity constraint according to claim 1, wherein the objective function in S1 is:
Figure FDA0003659455830000011
in the formula, Pi d、Pi d,0Respectively representing the active load of the node i and the active load increase basic power,
Figure FDA0003659455830000012
Figure FDA0003659455830000013
respectively representing the gas load of the node m and the gas load increase basic power, kappai、κmThe magnifications of the electrical load and the gas load are shown respectively.
3. The method for evaluating the maximum power supply capacity of the electrical coupling system considering the opportunity constraint is characterized in that in the S2, the power distribution network operation constraint conditions in the maximum power supply capacity model include:
Figure FDA0003659455830000021
Figure FDA0003659455830000022
Figure FDA0003659455830000023
Figure FDA0003659455830000024
Figure FDA0003659455830000025
Figure FDA0003659455830000026
Figure FDA0003659455830000027
Figure FDA0003659455830000028
Figure FDA0003659455830000029
Figure FDA00036594558300000210
Figure FDA00036594558300000211
Figure FDA00036594558300000212
Figure FDA00036594558300000213
Figure FDA00036594558300000214
Figure FDA00036594558300000215
Figure FDA00036594558300000216
Figure FDA00036594558300000217
Figure FDA00036594558300000218
Figure FDA00036594558300000219
Figure FDA00036594558300000220
Figure FDA0003659455830000031
in the formula, subscripts ij, i, u, v, w, g and t respectively represent lines, nodes, transformer substations, fans, electric gas conversion equipment, gas turbines and scheduling periods, sets U (i), V (i), W (i) and G (i) respectively represent transformer substations, fans, electric gas conversion equipment and gas turbine sets connected with the nodes i, and pi (i) and delta (i) respectively represent a line first section node set taking the nodes i as tail end nodes and a line tail end node set taking the nodes i as head end nodes in a power distribution network, and sets
Figure FDA00036594558300000313
Representing a collection of distribution network nodes, a collection U representing a collection of substation nodes,
Figure FDA0003659455830000032
representing a set of faulty substation connected lines;
Figure FDA0003659455830000033
respectively representing the fan power factor, pu,t、pv,t、pw,t、pg,tRespectively representing the active power of a transformer substation u, a fan v, an electric gas conversion device w and a gas turbine g, qu,t、qv,t、qg,tRespectively representing a transformer substation u, a fan v and a gas turbineReactive power of machine g, vi,tRepresenting the voltage square of node i, iij,tRepresents the current squared value of line ij; alpha is alphaijVariables 0-1, x representing the operating states of distribution line ij, respectivelyij、xjiA 0-1 variable indicating whether line ij is in forward and reverse operation;
Figure FDA0003659455830000034
respectively representing the reactive load of the node i, the reactive load increase base power, Rij、XijRespectively representing the resistance and reactance values of the line ij,
Figure FDA0003659455830000035
representing the proportion of the electrical load to the peak load for a period of time t, M representing a larger positive integer,V i、
Figure FDA0003659455830000036
respectively represent the minimum and maximum values of the voltage at the node i,
Figure FDA0003659455830000037
represents the maximum value of the current of line ij,
Figure FDA0003659455830000038
respectively representing the maximum value of the active and reactive power flowing through the line ij,
Figure FDA0003659455830000039
respectively represents the maximum value of active power of a transformer substation, electric gas conversion equipment and a gas turbine,
Figure FDA00036594558300000310
respectively representing the maximum reactive power of the substation and the gas turbine, RUPtG,w、RUGT,gRespectively represents the maximum value RD of the upward climbing power of the electric gas conversion equipment w and the gas turbine gPtG,w、RDGT,gThe maximum power of the electric gas conversion equipment w and the power of the gas turbine g climbing downwards are respectively shownLarge value of ηGT、ηPtGRespectively representing the conversion efficiency of a gas turbine and an electric gas conversion device, P { A } represents the occurrence probability of an event A, xiv,tA predicted value of the active power output of the random wind turbine, theta represents a probability level of satisfying joint chance constraints,κ i、
Figure FDA00036594558300000311
representing the minimum and maximum values of the amplification of the electrical load,
Figure FDA00036594558300000312
respectively representing the virtual power flow variable, D, of the line ijiRepresenting the virtual load amount of node i.
4. The method for evaluating the maximum energy supply capacity of the electrical coupling system considering the opportunity constraint as recited in claim 1, wherein in the step S3, the operation constraint conditions of the air grid specifically include:
Figure FDA0003659455830000041
Figure FDA0003659455830000042
Figure FDA0003659455830000043
Figure FDA0003659455830000044
Figure FDA0003659455830000045
Figure FDA0003659455830000046
Figure FDA0003659455830000047
Figure FDA0003659455830000048
Figure FDA0003659455830000049
Figure FDA00036594558300000410
Figure FDA00036594558300000411
in the formula, subscripts mn, m, s respectively represent a pipeline, a gas node, and a gas source node, sets s (m), v (m), g (m) respectively represent a gas source, an electric gas conversion device, and a gas turbine set connected to node m, P, C respectively represent a conventional pipeline and a compressor pipeline set, and pi (m) and delta (m) respectively represent a pipeline first section node set using node m as a tail end node and a pipeline tail end node set using node i as a head end node in a gas network; f. ofkm,t、fmn,tRespectively, the average gas flow, f, flowing through the pipelines km, mns,t、fv,t、fg,tRespectively representing the gas flow rate, f, of the electric gas-converting plant v, gas turbine g, of the gas source sm,t、fn,tRespectively representing the gas flow rates of nodes m, n,. pim,t、πn,tRespectively representing the pressure, χ, at nodes m, nmn,tRepresenting a pipeline inventory;
Figure FDA00036594558300000412
the gas load at the node m is represented,
Figure FDA00036594558300000413
the gas load of the node m is shown to increase the base power,
Figure FDA00036594558300000414
representing the air load to peak load ratio for a period of time t,κ m、
Figure FDA00036594558300000415
the minimum and maximum values of the air load magnification are shown,Π m、
Figure FDA00036594558300000416
respectively represent the minimum value and the maximum value of the air pressure of the node m,F s、
Figure FDA00036594558300000417
respectively represent the minimum and maximum gas flow of the gas source s,F m、
Figure FDA00036594558300000418
respectively represent the minimum and maximum air flow of the node m,
Figure FDA00036594558300000419
the pressure rise and the gas loss coefficient of the compressor are shown,
Figure FDA00036594558300000420
the pipeline storage coefficient is represented by the index,
Figure FDA00036594558300000421
the coefficients of the wegener equation are expressed.
5. The method as claimed in claim 1, wherein the constraint conditions for operation of coupling the distribution grid with the air grid in S4 include
Figure FDA0003659455830000051
Figure FDA0003659455830000052
In the formula, phi represents the gas-electric conversion coefficient, etaGT、ηPtGThe conversion efficiencies of the gas turbine and the electric power conversion equipment are respectively shown.
6. The method for evaluating the maximum energy supply capacity of the electrical coupling system considering the opportunity constraint according to claim 1, wherein the S5 specifically comprises:
s51, preprocessing the fan predicted power data set, wherein the uncertain fan output vector xi of each time period t is a V-dimensional variable, and V represents the number of fans; setting a fan prediction data set to be omega in each period, and setting the k-th prediction vector in the set omega to be
Figure FDA0003659455830000053
ωkThe probability distribution and the marginal probability distribution of (d) are respectively F (omega)k)＝P(ξ≥ωk)、
Figure FDA0003659455830000054
S52, collecting any fan v
Figure FDA0003659455830000055
Will ZvAll of
Figure FDA0003659455830000056
Is arranged in descending order to form a segmentation point sequence c1v＞c2v＞...＞cnvvWherein n isvRepresenting the number of the division points corresponding to the fan v;
s53, collecting the set
Figure FDA0003659455830000057
Where x represents the Cartesian product of the sets, the sets
Figure FDA0003659455830000058
Splitting into theta full sets
Figure FDA0003659455830000059
And theta is not sufficient set
Figure FDA00036594558300000510
According to the formula (1.36), will
Figure FDA00036594558300000511
Performing 0-1 projection to obtain
Figure FDA00036594558300000512
Wherein each vector
Figure FDA00036594558300000513
Corresponding n-dimensional 0-1 vector
Figure FDA00036594558300000514
n＝∑v∈Vnv；
Figure FDA00036594558300000515
S54, converting the fan output joint opportunity constraint (1.10) into an equivalent mixed integer linear constraint group;
Figure FDA00036594558300000516
Figure FDA0003659455830000061
Figure FDA0003659455830000062
in the formula, civ,tDenotes the division point, u, of the fan v at time tiv,tRepresenting sets for corresponding n-dimensional 0-1 variables
Figure FDA0003659455830000063
Middle vector
Figure FDA0003659455830000064
In that
Figure FDA0003659455830000065
The corresponding n-dimensional 0-1 vector.
7. The method for evaluating the maximum energy supply capacity of the electrical coupling system considering the opportunity constraint according to claim 1, wherein the S6 specifically comprises:
s61, rewrite the equality constraints (1.5) and (1.32) as an inequality group consisting of the difference between two convex functions as follows:
Figure FDA0003659455830000066
Figure FDA0003659455830000067
Figure FDA0003659455830000068
Figure FDA0003659455830000069
s62 solving the relaxation model (1.44) and recording the initial solution
Figure FDA00036594558300000610
And
Figure FDA00036594558300000611
wherein Obj represents the objective function;
Figure FDA00036594558300000612
s63, expanding the right side of the constraint conditions (1.41) (1.43) by using a first-order Taylor formula according to the initial solution, and adding a relaxation variable
Figure FDA00036594558300000613
As shown in equation (1.45) (1.46);
Figure FDA00036594558300000614
Figure FDA00036594558300000615
s64, iteratively solving the model (1.47) of the objective function containing the relaxation variable penalty term, and stopping iteration if the equations (1.48) and (1.49) are met after each solution; otherwise, record
Figure FDA00036594558300000616
And
Figure FDA0003659455830000071
updating the penalty term according to a formula (1.50) and entering next iteration; where the superscript h denotes the number of iterations, p(h)Representing a penalty of a relaxation variable, #1、ψ2Denotes the convergence criterion, τ denotes the penalty term update step, ρmaxRepresenting a maximum value of the penalty term;
Figure FDA0003659455830000072
Figure FDA0003659455830000073
Figure FDA0003659455830000074
ρ(h+1)＝min{τρ(h),ρmax} (1.50)。
8. the method for evaluating the maximum energy supply capacity of the electrical coupling system considering the opportunity constraint as recited in claim 1, wherein the S7 specifically comprises:
relaxing the electrical and electrical coupling constraints (1.34) (1.35), and decomposing the model (1.44) into a power grid maximum power supply capacity sub-model and a gas grid maximum gas supply capacity sub-model;
Figure FDA0003659455830000075
Figure FDA0003659455830000076
wherein, Objp、ObjgRespectively representing the maximum power supply capacity of the power distribution network and the maximum air supply capacity of the air network containing punishment items, lambdag,t、γg,tIndividual watchIndicating the primary and secondary penalty term, λ, of the gas turbinew,t、γw,tRespectively representing the first punishment item and the second punishment item of the electric gas conversion equipment,
Figure FDA0003659455830000077
representing the interaction variables passed by the air network to the distribution network,
Figure FDA0003659455830000078
representing the interaction variables that the distribution network passes to the gas network.
9. The method for evaluating the maximum energy supply capacity of the electrical coupling system considering the opportunity constraint as recited in claim 1, wherein the S8 specifically comprises:
s81, setting initial values of interaction variables of the power distribution network and the gas network
Figure FDA0003659455830000081
Initial value of primary and secondary punishment item
Figure FDA0003659455830000082
The penalty item updates the step length sigma and the maximum iteration number LmaxConvergence criterion psi3、ψ4Taking the iteration number l as 1;
s82 fetching
Figure FDA0003659455830000083
Solving the power grid sub-model (1.51) according to S3; get
Figure FDA0003659455830000084
Solving the gas net submodel (1.52) with reference to S3; if the formulae (1.53) and (1.54) are satisfied, or L ═ LmaxCombining iteration; otherwise, updating the first and second punishment terms according to a formula (1.55), taking l as l +1, and entering the next iteration;
Figure FDA0003659455830000085
Figure FDA0003659455830000086
。
Figure FDA0003659455830000087
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