CN111416349A - Collaborative planning method for electrical interconnection comprehensive energy system - Google Patents
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Abstract
The collaborative planning method of the electrical interconnection comprehensive energy system provided by the invention takes the constraint of new facility installation conditions, the constraint of a power distribution system and the constraint of a natural gas system as constraint conditions, and takes the minimum total cost of the comprehensive energy system as an optimization target to construct a collaborative planning model of the comprehensive energy system; determining a collaborative planning scheme of the comprehensive energy system according to the collaborative planning model; the power distribution system constraints include: the method comprises the following steps of (1) output constraint of an externally connected power grid, output constraint of a distributed gas turbine unit, radial constraint of a power distribution network, rotating standby capacity constraint, power distribution network constraint and reliability constraint; the natural gas system constraints include: the method comprises the following steps of urban gate station output constraint, natural gas network constraint and natural gas adequacy constraint. According to the collaborative planning method of the electrical interconnection comprehensive energy system, the collaborative planning is carried out on the comprehensive energy system, and a collaborative planning scheme with low cost, high reliability and stable operation can be obtained.
Description
Technical Field
The invention relates to the technical field of energy system planning, in particular to a collaborative planning method for an electrical interconnection comprehensive energy system.
Background
In the primary energy of the energy Internet, except for renewable energy sources such as wind, light and the like, natural gas energy sources have environmental protection and economic advantages. In terms of environmental benefits, natural gas power generation emits almost no sulfur dioxide and smoke, while the carbon dioxide emission of CCHP (combined cooling, heating and power) using natural gas as fuel is only 1/4 of coal-fired power generation. In the aspect of economic benefit, the natural gas power plant has the advantages of low construction cost, high power generation efficiency and the like.
In addition, the natural gas power generation has flexible adjusting capacity and peak shaving performance, and can play a role of a peak shaving power supply in an energy internet. It is anticipated that natural gas will exceed coal and oil, along with renewable energy sources, becoming the primary energy source.
Under the large background of multi-energy network development, the planning of multi-energy networks is increasingly emphasized, wherein the collaborative planning of a power distribution network and a natural gas network is taken as a typical scene of multi-energy network planning in cities, and the core of the planning is that under the condition of natural gas and electric load prediction in a planning target time period, various constraints of a power distribution network and a natural gas pipeline are comprehensively considered, and the optimal investment decision scheme of the power distribution network and the natural gas network is determined so as to ensure the safe and economic operation of a comprehensive energy system.
The problem of collaborative planning of a power distribution network and a natural gas network is always a difficult point in the field of comprehensive energy system planning, and the main problem lies in the complexity of multi-time-space nonlinearity and non-convexity presented by the coupling of power distribution system constraint and natural gas system constraint; meanwhile, considering uncertainty, a monte carlo-based random scene generation planning method is often adopted in the industry to solve the problem of comprehensive energy system planning. The two are superposed, so that the calculated amount is increased rapidly, and the calculation time is long and the efficiency is low.
At present, most technical schemes start from a mathematical model of a simplification (linearization) problem, and adopt network flow analysis in a gas transmission network to carry out linearization treatment, but the simplification does not meet the requirement of general natural gas system planning. Also, there are considered to be improved energy hubs of renewable energy, each energy hub being an energy coupling unit; and (3) carrying out energy network classification on the planning area, wherein each energy hub supplies an energy network of a secondary level in the energy network, so that the whole energy network can be represented as a multi-layer planning model with the energy hubs as nodes, but the method is not in line with the actual energy network at the present stage.
Therefore, how to comprehensively consider the constraint conditions of the power distribution system and the natural gas network and cooperatively plan the comprehensive energy system for interconnecting the power distribution network and the natural gas network becomes a technical problem to be solved.
Disclosure of Invention
The invention aims to provide a collaborative planning method for an electrical interconnection comprehensive energy system, so as to effectively plan the comprehensive energy system for interconnection of a power distribution network and a natural gas network.
The purpose of the invention can be realized by the following technical scheme:
a collaborative planning method of an electrical interconnection comprehensive energy system is characterized in that a collaborative planning model of the comprehensive energy system is constructed by taking new facility installation condition constraint, power distribution system constraint and natural gas system constraint as constraint conditions and taking the minimum total cost of the comprehensive energy system as an optimization target;
wherein the total cost is the sum of the investment cost and the operation cost of the comprehensive energy system;
determining a collaborative planning scheme of the comprehensive energy system according to the collaborative planning model;
the power distribution system constraints specifically include: the method comprises the following steps of (1) output constraint of an externally connected power grid, output constraint of a distributed gas turbine unit, radial constraint of a power distribution network, rotating standby capacity constraint, power distribution network constraint and reliability constraint;
the natural gas system constraints specifically include: the method comprises the following steps of urban gate station output constraint, natural gas network constraint and natural gas adequacy constraint.
Optionally, the investment cost cinvCan be expressed as:
in the formula (I), the compound is shown in the specification,
and
respectively represent distribution lines, distribution trunk pipelines, urban gate stations and distributed gas sigmal,ij,f,tInvestment cost of the unit in the t year in the planning period; λ represents a discount rate; t represents a planning period; a variable 0-1 representing commissioning f-type distribution lines between distribution system nodes i, j in the t year within the planning period; sigmap,ij,f,tA variable 0-1 representing commissioning of f-type pipelines between natural gas network nodes i, j in the t year within the planning period; sigmags,i,f,tA variable 0-1 representing commissioning a type f urban gate station at natural gas network node i in the t year within the planning period; sigmaDG,i,f,tA variable 0-1 representing commissioning of the f-type distributed gas turbine group at a power distribution system node i in the t year within the planning period; omegal、Ωp、ΩgsAnd ΩDGRespectively representing candidate sets of a distribution line, a distribution main pipeline, an urban gate station and a distributed gas turbine set; omegalf、Ωpf、ΩgsfAnd ΩDGfRespectively representing candidate type sets of a distribution line, a distribution main pipeline, an urban gate station and a distributed gas turbine set; u shapel,ij,fRepresenting the investment cost of commissioning f-type distribution lines between distribution system nodes i, j in the t year of the planning period; u shapep,ij,fRepresenting the investment cost of commissioning f-type pipelines between natural gas network nodes i, j in the t year within the planning period; u shapegs,i,fRepresenting the investment cost of commissioning a type f urban gate station at natural gas network node i in the t year of the planning period; u shapeDG,i,fRepresenting the investment cost of commissioning a f-type distributed gas unit at power distribution system node i in year t within the planning period.
Optionally, the operation cost includes operation cost of each element in a planning period and reliability cost caused by load shedding due to energy shortage, and the operation cost copCan be expressed as:
in the formula (I), the compound is shown in the specification,
and respectively representing the operation cost of the city gate station, the distributed gas generator set, the distributed wind generator set and the externally connected power grid in the t year in the planning period. Egs、EDGAnd EgridRespectively representing the set of the urban gate station, the distributed gas turbine set and the externally connected power grid which exist in the initial planning year;
and
respectively representing the variable cost of unit output of the city gate station, the distributed gas turbine set and the external connection power grid in the t year in the planning period;
representing the fixed cost of operation of the f-type distributed gas turbine unit in the t year in the planning period; sgs,i,t(τ)、PDG,i,t(τ) and Pgrid,i,t(τ) represents the output of the city gate station, the distributed gas turbine units and the externally connected power grid at the τ th moment of the t year in the planning period respectively; c. CENS(t) represents the load shedding cost of the t year within the planning period; enA set of nodes representing a power distribution system;
representing the load shedding at node i of the distribution system at the time t of the year t within the planning period, VO LLiRepresenting a unit loss of power at node i of the power distribution system.
Alternatively, the installation condition constraint may be expressed as:
optionally, the externally connected grid output constraint may be expressed as:
Pgrid,i,t(τ)≤Pgrid,i,max，Qgrid,i,t(τ)≤Qgrid,i,max；
in the formula, Pgrid,i,max、Qgrid,i,maxRespectively representing the maximum active output and the maximum reactive output of an externally connected power grid connected with a power distribution network node i; qgrid,i,t(τ) represents the reactive power contribution of the externally connected grid at node i of the power distribution network at time τ of the t year within the planned cycle.
Optionally, the output constraint of the distributed gas turbine group may be expressed as:
in the formula (I), the compound is shown in the specification,
representing the maximum and minimum power of the distributed gas turbine at node i of the power distribution network, respectively;
respectively representing the maximum and minimum reactive power of the distributed gas turbine set at the node i of the power distribution network; qDG,i,t(τ) represents the reactive power contribution of the distributed gas turbine group at the distribution network node i.
Alternatively, the spinning reserve capacity constraint may be expressed as:
in the formula (I), the compound is shown in the specification,
representing the rated power of the distributed gas turbine set at the node i of the power distribution system when planning the initial year;
representing the maximum external power grid output connected with the power distribution system at the node i when planning the initial year;
representing the rated power of the distributed gas turbine unit input by the type f at the node i in the planning period;
represents the maximum load at node i for the t year within the planning period; rD,tRepresenting the reserve capacity of the t year within the planning period, the value of which is related to the maximum load of the distribution system.
Optionally, the power distribution network constraint may be expressed as:
Vmin≤Vi,t(τ)≤Vmax；
in the formula, PD,i,t(τ)、QD,i,t(τ) represents the active and reactive loads at node i at time τ of the t year in the planning cycle, respectively;
respectively representing the active load shedding amount and the reactive load shedding amount at a node i at the time tau in the t year in a planning period; pl,ij,t(τ)、Ql,ij,t(τ) and Sl,ij,t(τ) respectively representing the active power flow, the reactive power flow and the apparent power of distribution lines ij existing in the planning initial year at the time τ in the t year in the planning period; pl,ij,f,t(τ)、Ql,ij,f,t(τ) and Sl,ij,f,t(tau) respectively representing the active power flow, the reactive power flow and the apparent power of the newly-added f-type distribution line ij at the time tau in the t year in the planning period;
and
respectively representing the capacity upper limit of the distribution line ij of the type f existing in the initial planning year and the capacity upper limit of the distribution line ij of the type f newly added in the t year in the planning period; vi,t(τ)、Vj,t(τ) represents the voltage amplitudes at node i and node j, respectively, at time τ of the t year in the planning period; vmin、VmaxRepresenting upper and lower limits of the node voltage amplitude; r isij,oAnd xij,oRespectively representing conductance and susceptance matrix elements of distribution lines ij existing in the initial planning year; r isl,ij,fAnd xl,ij,fRespectively representing the conductance and susceptance matrix elements of the newly added f-type distribution line ij; m is a sufficiently large positive number.
Alternatively, the natural gas network constraint may be expressed as:
vmin≤vi,t(τ)≤vmax，
in the formula, vi,t(τ) represents the gas pressure at natural gas node i at time τ of year t within the planned cycle; v. ofmaxAnd vminRespectively representing the upper limit value and the lower limit value of the natural gas node air pressure;
representing the electric-to-gas power at the natural gas node i in the t year in the planning period; sDg,i,t(τ) denotes the natural gas negative at natural gas node i at time τ of the t year in the planning cycleLoading;
representing the gas load of a distributed gas turbine set at a natural gas node i at the time tau in the t year in a planning period; sp,ij,t(τ) represents the power flow at the natural gas main pipeline ij at the time τ of the t year in the planning period; sp,ij,f,t(τ) represents the flow at τ time f type natural gas main pipeline ij in the t year of the planning period;
representing the upper limit of the power flow at the natural gas main pipeline ij existing in the planning initial year;
and (4) representing the upper limit of the power flow at the f-type natural gas main pipeline ij in the t year in the planning period.
Optionally, a fixed complex variable decomposition iterative method is adopted for solving, the collaborative planning model is decomposed into an integer planning investment decision main problem and a linear planning operation sub-problem, different decomposition cut set information is formed according to the decomposition form and the solving result of the sub-problem and returned to the main problem, coordination and information interaction of the main problem and the sub-problem are realized, and iterative solving of the main problem and the sub-problem is carried out.
The invention provides a collaborative planning method of an electrical interconnection comprehensive energy system, which takes new facility installation condition constraint, power distribution system constraint and natural gas system constraint as constraint conditions, takes the minimum total cost of the comprehensive energy system as an optimization target, and constructs a collaborative planning model of the comprehensive energy system; wherein the total cost is the sum of the investment cost and the operation cost of the comprehensive energy system; determining a collaborative planning scheme of the comprehensive energy system according to the collaborative planning model; the power distribution system constraints specifically include: the method comprises the following steps of (1) output constraint of an externally connected power grid, output constraint of a distributed gas turbine unit, radial constraint of a power distribution network, rotating standby capacity constraint, power distribution network constraint and reliability constraint; the natural gas system constraints specifically include: the method comprises the following steps of urban gate station output constraint, natural gas network constraint and natural gas adequacy constraint. According to the collaborative planning method of the electrical interconnection comprehensive energy system, the collaborative planning is carried out on the comprehensive energy system, and a collaborative planning scheme with low cost, high reliability and stable operation can be obtained.
Drawings
Fig. 1 is a projection schematic diagram of an improved decomposition method of a collaborative planning method of an electrical interconnection comprehensive energy system provided by the invention;
FIG. 2 is a diagram illustrating a relationship between sub-problems of the improved collaborative planning method for the electrical interconnection comprehensive energy system provided by the present invention;
FIG. 3 is a generalized decomposition algorithm flow chart of the collaborative planning method for the electrical interconnection comprehensive energy system provided by the present invention;
FIG. 4 is a decoupling structure diagram of the collaborative planning method for the electrical interconnection comprehensive energy system provided by the invention;
FIG. 5 is a modified decoupling architecture diagram of the collaborative planning method for an electrical interconnection integrated energy system provided by the present invention;
FIG. 6 is a flowchart of a decoupling-based method of collaborative planning for an electrically interconnected integrated energy system according to the present invention;
fig. 7 is a topology structure diagram of a 54-node power distribution system of the collaborative planning method for the electrical interconnection comprehensive energy system according to the embodiment of the present invention;
fig. 8 is a 19-node natural gas network topology structure diagram of the collaborative planning method for the electrical interconnection comprehensive energy system according to the embodiment of the present invention;
fig. 9 is a planned power distribution system network topology structure diagram in a load scene two of the collaborative planning method for an electrical interconnection comprehensive energy system according to the embodiment of the present invention;
fig. 10 is a planned natural gas network topology structure diagram in a load scene two of the collaborative planning method for the electrical interconnection comprehensive energy system according to the embodiment of the present invention.
Detailed Description
The embodiment of the invention provides a collaborative planning method for an electrical interconnection comprehensive energy system, which is used for effectively planning a comprehensive energy system for interconnection of a power distribution network and a natural gas network.
To facilitate an understanding of the invention, the invention will now be described more fully with reference to the accompanying drawings. Preferred embodiments of the present invention are shown in the drawings. This invention may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete.
Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. The terminology used in the description of the invention herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used herein, the term "and/or" includes any and all combinations of one or more of the associated listed items.
DistFlow: a method for solving power flow calculation of a power distribution network is used for solving a state equation by using active power, reactive power and a node voltage square as system state variables and utilizing a Newton-Raphson method.
Mixed integer programming: under the constraint of equality or inequality, the problem of maximizing (or minimizing) a certain function requires that some variables must be integers is generally called Mixed Integer Programming (MIP) problem, and the problem of Mixed Programming of natural gas and distribution network after linearization in the invention is also a Mixed Integer Programming problem.
GUROBI: the method is a new generation of large-scale mathematical programming optimizer developed by Gurobi corporation of America, and has higher optimization speed and precision.
CP L EX A mathematical optimization technique, mainly used to improve efficiency, implement strategies quickly and increase profitability Complex business problems can be represented as a mathematical Programming model using CP L EX.
According to the collaborative planning method of the electrical interconnection comprehensive energy system, provided by the embodiment of the invention, a collaborative planning model of the comprehensive energy system is constructed by taking new facility installation condition constraint, power distribution system constraint and natural gas system constraint as constraint conditions and taking the minimum total cost of the comprehensive energy system as an optimization target;
wherein the total cost is the sum of the investment cost and the operation cost of the comprehensive energy system;
determining a collaborative planning scheme of the comprehensive energy system according to the collaborative planning model;
the power distribution system constraints specifically include: the method comprises the following steps of (1) output constraint of an externally connected power grid, output constraint of a distributed gas turbine unit, radial constraint of a power distribution network, rotating standby capacity constraint, power distribution network constraint and reliability constraint;
the natural gas system constraints specifically include: the method comprises the following steps of urban gate station output constraint, natural gas network constraint and natural gas adequacy constraint.
The collaborative planning method for the electrical interconnection comprehensive energy system provided by the embodiment of the invention comprises two parts, namely modeling and solving algorithm, wherein the modeling is divided into: the description of the objective function and the description of the constraint condition are two parts. The solving algorithm firstly introduces the algorithm adopted by the patent as a basis, and then provides a scheme for solving the mathematical model for solving the planning problem of the natural gas network and the power distribution system.
The collaborative planning method for the electrical interconnection comprehensive energy system provided by the embodiment of the invention comprehensively considers the constraints of the natural gas network and the power distribution system and the output constraints of each unit, and determines the optimal investment decision scheme of the natural gas network and the power distribution system so as to ensure the safe and economic operation of the collaborative system. The objective function of the collaborative planning problem comprises two parts, namely investment costs of a distribution line, urban gate station expansion, a distributed gas turbine set and a gas distribution main pipeline; and total operating costs consisting of operating costs of the distributed gas turbine plants and the city gate stations, electricity purchased from the external power grid, and costs due to load shedding due to energy shortage. The optimization goal is to minimize the total cost, which can be described in the form:
minCtotal＝Cinv+Cop(1)
in the formula: c. CinvAnd copRespectively representing the investment cost and the operation cost in the planning period.
The investment cost is the investment cost and the total investment cost of each element in the planning period, and can be described by the following formulas:
investment cost cinvCan be expressed as:
in the formula (I), the compound is shown in the specification,
and
respectively represent distribution lines, distribution trunk pipelines, urban gate stations and distributed gas sigmal,ij,f,tInvestment cost of the unit in the t year in the planning period; λ represents a discount rate; t represents a planning period; a variable 0-1 representing commissioning f-type distribution lines between distribution system nodes i, j in the t year within the planning period; sigmap,ij,f,tA variable 0-1 representing commissioning of f-type pipelines between natural gas network nodes i, j in the t year within the planning period; sigmags,i,f,tA variable 0-1 representing commissioning a type f urban gate station at natural gas network node i in the t year within the planning period; sigmaDG,i,f,tTo representIn the t year in the planning period, commissioning 0-1 variables of the f-type distributed gas turbine set at a power distribution system node i; omegal、Ωp、ΩgsAnd ΩDGRespectively representing candidate sets of a distribution line, a distribution main pipeline, an urban gate station and a distributed gas turbine set; omegalf、Ωpf、ΩgsfAnd ΩDGfRespectively representing candidate type sets of a distribution line, a distribution main pipeline, an urban gate station and a distributed gas turbine set; u shapel,ij,fRepresenting the investment cost of commissioning f-type distribution lines between distribution system nodes i, j in the t year of the planning period; u shapep,ij,fRepresenting the investment cost of commissioning f-type pipelines between natural gas network nodes i, j in the t year within the planning period; u shapegs,i,fRepresenting the investment cost of commissioning a type f urban gate station at natural gas network node i in the t year of the planning period; u shapeDG,i,fRepresenting the investment cost of commissioning a f-type distributed gas unit at power distribution system node i in year t within the planning period.
The operation cost of the integrated energy system includes the operation cost of each element in the planning period and the reliability cost caused by load shedding due to energy shortage, and can be described in the following formulas:
in the formula (I), the compound is shown in the specification,
and respectively representing the operation cost of the city gate station, the distributed gas generator set, the distributed wind generator set and the externally connected power grid in the t year in the planning period. Egs、EDGAnd EgridRespectively representing the set of the urban gate station, the distributed gas turbine set and the externally connected power grid which exist in the initial planning year;
and
respectively representing the variable cost of unit output of the city gate station, the distributed gas turbine set and the external connection power grid in the t year in the planning period;
representing the fixed cost of operation of the f-type distributed gas turbine unit in the t year in the planning period; sgs,i,t(τ)、PDG,i,t(τ) and Pgrid,i,t(τ) represents the output of the city gate station, the distributed gas turbine units and the externally connected power grid at the τ th moment of the t year in the planning period respectively; c. CENS(t) represents the load shedding cost of the t year within the planning period; enA set of nodes representing a power distribution system;
representing the load shedding at node i of the distribution system at the time t of the year t within the planning period, VO LLiRepresenting a unit loss of power at node i of the power distribution system.
According to the collaborative planning method for the electrical interconnection comprehensive energy system, the constraint conditions of the collaborative planning model mainly comprise two aspects of installation condition constraint of new facilities and physical operation constraint of a power distribution system and a natural gas network.
The installation condition constraint means that in a planning period, any distribution line, a distribution main pipeline, a city gate station and a distributed gas turbine set are required to avoid repeated investment construction, and the installation condition constraint can be described by the following formulas:
wherein the power distribution system constraints include:
(1) output restraint of the external connection power grid: the output constraints for any externally connected grid node can be described by the following equations:
Pgrid,i,t(τ)≤Pgrid,i,max(16)
Qgrid,i,t(τ)≤Qgrid,i,max(17)
in the formula, Pgrid,i,max、Qgrid,i,maxRespectively representing the maximum active output and the maximum reactive output of an externally connected power grid connected with a power distribution network node i; qgrid,i,t(τ) represents the reactive power contribution of the externally connected grid at node i of the power distribution network at time τ of the t year within the planned cycle.
(2) Output constraint of the distributed gas turbine set: the output constraints for any distributed gas turbine plant can be described by the following equations:
in the formula (I), the compound is shown in the specification,
representing the maximum and minimum power of the distributed gas turbine at node i of the power distribution network, respectively;
respectively representing the maximum and minimum reactive power of the distributed gas turbine set at the node i of the power distribution network; qDG,i,t(τ) represents the reactive power contribution of the distributed gas turbine group at the distribution network node i.
(3) Radial constraint of the distribution network: in general, the distribution network always operates in an open-loop manner, which can be described by the following equation:
nl,t＝nn,t-1 (20)
in the formula, nl,tIndicating the number of distribution lines; n isn,tRepresenting the number of power distribution system nodes.
(4) Rotating reserve capacity constraint: in the planning period, in order to ensure that the power distribution system can operate safely and reliably, the rotating reserve capacity constraint of the power distribution system needs to be satisfied in any year in the planning period, which can be described by the following formula:
in the formula (I), the compound is shown in the specification,
representing the rated power of the distributed gas turbine set at the node i of the power distribution system when planning the initial year;
representing the maximum external power grid output connected with the power distribution system at the node i when planning the initial year;
distributed gas representing f-type input at inode in planning cycleRated power of the unit;
represents the maximum load at node i for the t year within the planning period; rD,tRepresenting the reserve capacity of the t year within the planning period, the value of which is related to the maximum load of the distribution system.
(5) Power distribution network constraints: because the power distribution system flow has the nonlinear and non-convex characteristic, the problem is difficult to obtain the global optimum, and even the optimization problem can not be converged. For a short-term optimization scheduling problem, parameters of a power distribution system need to be accurately evaluated, and the nonlinear and non-convex characteristics of power flow of the power distribution system are difficult to avoid. However, for long-term planning problems, the non-linearity will greatly increase the difficulty of solving the problem, and even make convergence difficult. To improve computational efficiency, it is desirable and effective to employ linearized power distribution system flow models in long-term planning problems, partially sacrificing model accuracy. Therefore, the invention adopts simplified linear DistFlow constraint to describe the power distribution network flow, and adopts a Big-M method to process the flow of a newly added line, so that the power distribution network flow constraint is changed into a linear constraint, the convergence of the problem is greatly improved, and the optimization problem is ensured to be finally converged to a global optimal point. The power distribution network constraints may be described by the following equations:
Vmin≤Vi,t(τ)≤Vmax(28)
in the formula, PD,i,t(τ)、QD,i,t(τ) represents the active and reactive loads at node i at time τ of the t year in the planning cycle, respectively;
respectively representing the active load shedding amount and the reactive load shedding amount at a node i at the time tau in the t year in a planning period; pl,ij,t(τ)、Ql,ij,t(τ) and Sl,ij,t(τ) respectively representing the active power flow, the reactive power flow and the apparent power of distribution lines ij existing in the planning initial year at the time τ in the t year in the planning period; pl,ij,f,t(τ)、Ql,ij,f,t(τ) and Sl,ij,f,t(tau) respectively representing the active power flow, the reactive power flow and the apparent power of the newly-added f-type distribution line ij at the time tau in the t year in the planning period;
and
respectively representing the capacity upper limit of the distribution line ij of the type f existing in the initial planning year and the capacity upper limit of the distribution line ij of the type f newly added in the t year in the planning period; vi,t(τ)、Vj,t(τ) represents the voltage amplitudes at node i and node j, respectively, at time τ of the t year in the planning period; vmin、VmaxRepresenting upper and lower limits of the node voltage amplitude; r isij,oAnd xij,oRespectively representing conductance and susceptance matrix elements of distribution lines ij existing in the initial planning year; r isl,ij,fAnd xl,ij,fRespectively representing the conductance and susceptance matrix elements of the newly added f-type distribution line ij; m is a positive number large enough, for example, to take the total installed capacity of the power distribution system.
(6) And (3) reliability constraint: in order to evaluate the reliability of the comprehensive energy system, a reliability index of load shedding amount is introduced. The annual load shedding of the integrated energy system should be limited to a certain threshold and can be described by the following equation:
in the formula, EUEmax,tAnd the upper limit of the threshold value of the annual load shedding amount of the integrated energy system is represented.
The natural gas network constraint in the embodiment of the invention is described as follows:
natural gas systems, similar to electrical power systems, transport natural gas from oil and gas wellheads to individual end users through natural gas pipeline networks. Similarly, the operation of the natural gas system is subject to pipeline capacity and other technical constraints, such as node gas quantity balance constraint, node gas pressure upper and lower limit constraint, and the like. The flow rate of natural gas flowing through a natural gas pipeline is affected by many factors, the most important of which include the length of the natural gas pipeline, the inner diameter, the friction coefficient, the ambient temperature, the altitude, the air pressure at both ends, and the like. And because the flow of the natural gas pipeline and the factors have a complex nonlinear relationship, the modeling difficulty of the natural gas system is increased.
(1) And (3) output constraint of the urban gate station: the city gate station output constraint for any natural gas node can be described by the following equation:
in the formula (I), the compound is shown in the specification,
respectively representing the minimum and maximum output of the urban gate station at natural gas node i.
(2) Natural gas network constraints: natural gas system modeling is a very complex nonlinear problem. The nonlinear natural gas flow constraint often makes the feasible domain of the problem non-convex, and is difficult to ensure to obtain the global optimal solution, even the effective convergence can not be achieved. For a short-term optimization scheduling problem, the parameters of the natural gas system need to be accurately evaluated, and the nonlinear and non-convex characteristics of the natural gas system flow are difficult to avoid. However, for long-term planning problems, the non-linearity will greatly increase the difficulty of solving the problem, and even make convergence difficult. To improve computational efficiency, it is desirable and effective to employ a linearized natural gas system flow model in a long-term planning problem, partially sacrificing model accuracy. In order to make the optimization problem converge to the global optimum point, only the upper and lower limit constraints of the pipeline capacity are considered in the planning model. The natural gas network constraints can be described by the following equations:
vmin≤vi,t(τ)≤vmax(31)
in the formula, vi,t(τ) represents the gas pressure at natural gas node i at time τ of year t within the planned cycle; v. ofmaxAnd vminRespectively representing the upper limit value and the lower limit value of the natural gas node air pressure;
the electric gas conversion power (the power of a natural gas device generated by consuming electric power and can be regarded as a reverse natural gas generator set) at the natural gas node i in the t year in the planning period is represented; sDg,i,t(τ) represents the natural gas load at natural gas node i at time τ of year t within the planning period;
representing the gas load of a distributed gas turbine set at a natural gas node i at the time tau in the t year in a planning period; sp,ij,t(tau) watchShowing the trend of the natural gas main pipeline ij at the time T in the t year in the planning period; sp,ij,f,t(τ) represents the flow at τ time f type natural gas main pipeline ij in the t year of the planning period;
representing the upper limit of the power flow at the natural gas main pipeline ij existing in the planning initial year;
and (4) representing the upper limit of the power flow at the f-type natural gas main pipeline ij in the t year in the planning period.
(3) Natural gas adequacy constraint: in a planning period, in order to ensure safe and reliable operation of the integrated energy system, the natural gas supply amount in any year needs to satisfy the natural gas adequacy constraint, which can be described by the following formula:
in the formula, ηDG,iRepresenting the gas conversion efficiency of the distributed gas turbine at natural gas node i.
The embodiment of the invention solves the collaborative planning model of the comprehensive energy system by adopting a fixed complex variable decomposition iterative method.
The problem decomposition algorithm can be used to solve Mixed Integer L initial programming (MI L P) problems involving complex variables at the expense of iteration.
Consider the mixed integer linear programming (MI L P) problem as follows:
(P)Max cTx+dTy
s.t. Ax+Gy≤b； (36)
in the formula, y ∈ Zm，x∈Rn(ii) a Where the variable y is considered to be a "complex variable (integer variable)", its presence increases the difficulty of solving the problem (1), and if its value can be fixed, the solution of the problem becomes rather simple.
MI L P problem equation (36) can be expressed as follows:
Max{dTy+max(cTx|Ax≤b-Gy)} (37)
when the integer variable y is fixed, a linear programming problem related to y is obtained, namely, the maximum problem in parentheses of the formula (2):
Max cTx
s.t. Ax≤b-Gy (38)
in the formula, x ∈ Rn；
The dual problems are as follows:
Min uT(b-Gy)
s.t. ATu≥c (39)
in the formula, u ∈ Rm；
If Q ═ u ∈ Rm|ATu ≧ c } is empty, there is no feasible solution to the dual problem, as can be seen from the dual theorem, problem (38) is either unbounded or infeasible.
Without assuming that
The convex polyhedron Q is independent of y, and u is on Q no matter what the value of y isTAssuming that the set of polar directions of the feasible region Q is vs (S ∈ S) and the set of polar points is up (P ∈ P), according to the basic theory of linear programming, there are:
1) when the feasible domain Q of the dual problem (39) has a polar orientation v, so that vT(b-Gy)<0, then the problem (39) is unbounded and the problem (38) is unbounded, so MI L P equation (35) has no solution.
2) When the problem (38) has an optimal solution, there must be some pole u of Q, so that the optimal solution is uT(b-Gy)。
Thus, a mixed integer linear program can be written as follows:
Max{dTy+min(up)T(b-Gy)}
s.t. (Vs)T(b-Gy)≥0 (40)
wherein S ∈ S, y ∈ Zm；
The above equation can be equated with the mixed linear integer programming problem as follows:
Maxη
s.t. η≤dTy+(up)T(b-Gy) (41)
wherein, P ∈ P, (V)s)T(b-Gy)≥0，s∈S，y∈Zm。
Although equation (41) theoretically considers a large number of linear constraints, only a small part of the constraints are active constraints at the optimal solution, and therefore, a relatively simple expression form can be constructed by using poles and pole directions corresponding to the active constraints.
The decomposition algorithm solving steps are as follows:
the method comprises the following steps: and (5) initializing. Iterative technique k 1, parameter M>1. For problem (36), take the set Q ═ { u ∈ Rm|ATu ≧ c } initial pole index set
And polar direction index set
Here P1 and S1 may be empty sets. The feasible domain initial relaxed form of the equivalent expression of the question (36) is:
step two: and solving the problem.
1) If it is
The original problem (36) is not feasible and the algorithm terminates;
2) if the problem (42) is unbounded, a feasible solution (y (k), η k) can be found such that η k > M, otherwise, an optimal solution (y (k), η k) thereof is obtained.
Step three: the problem (38) is solved.
1) If the problem (38) is not upper bound, the original problem is not upper bound and the algorithm terminates.
2) If the optimal value of the problem (38)
The optimal solution to the problem is x (k), which is the optimal solution to the dual problem u (k). When c is going toTx(k)+dTy (k) is equal to or greater than η k, (x (k), y (k)) is the optimal solution to the original problem (36), the algorithm terminates when cTx(k)+dTy(k)<η k, η ≦ d in the representationTy+(up)TThe (b-Gy) constraint will be a positive constraint that comes into play, let Pk +1 be Pk ∪ { k },
3) if the problem (38) feasible region is an empty set, then a satisfy (v) of the set Q can be obtainedT(b-Gy(k)) Polar direction v < 0kAt this time, (v) in the representationk)T(b-Gy) ≥ 0 is a functional constraint allowing Sk+1＝Sk∪{k}，
And updating the iteration count k to k +1, and turning to the step two.
Problem (41) is generally referred to as the main problem, and problem (38) is referred to as the sub-problem. In the main problem, the constraint formed by the poles and the pole directions corresponding to the feasible domains of the sub-problem pair is decomposition and segmentation.
It should be noted that, since the set Q and the pole index set and the pole direction index set are necessarily finite sets, and the cardinality of the pole or the pole direction of the decomposition algorithm is increased by 1 in each iteration process, the decomposition algorithm is necessarily stopped after a finite number of iterations.
For linear programming problems involving complex variables, if the complex variable values are fixed at a given value, the original problem either becomes easy to solve or can be decomposed in blocks. This is often the case in practical engineering and scientific problems. This decomposition allows us to solve linear programming problems involving integer variables in steps, at the cost of iteration.
Only mixed integer linear programming can be solved by using a decomposition iteration method, and the method is not helpful for mixed integer nonlinear programming (the problem oriented by the invention). To solve this situation, it needs to be generalized to the field of nonlinear programming.
The following are the basic principles of the algorithm and the algorithm flow used by the embodiments of the present invention. Let the general mathematical form of mixed integer nonlinear programming be:
Max f(x，y)
s.t.g(x，y)≥0 (43)
in the formula, y ∈ Zm，x∈RnThe variable y is considered to be a "complex variable". If y is fixed to some determined value, then the problem (43) is a more easily solved problem with respect to x.
The general problem (43) has some of the following characteristics:
1) after fixing the variable y, the problem (43) can be divided into a series of independent optimization problems, and each problem only contains a part of the variable x.
2) After fixing the variable y, the problem (43) has a special structure, such as a typical transportation problem, which can be solved using an efficient method.
The problems with the characteristics are presented in a large number of practical application and optimization works of mathematical programming problems, and the main purpose of discussing the problems is to design effective solving steps by utilizing the special structure of the problems.
First, the original question (43) is projected onto the y-plane, with:
Max v(y)
s.t.y∈V (44)
in the formula, y ∈ Zm；
Wherein the content of the first and second substances,
s.t.g(x，y)≥0 (45)
and
wherein, x ∈ Rn(ii) a v (y) is the optimum value of the original problem (43) after the variable y is fixed. Given y as a complex variable, the calculation (45) is easier than the original problem (43). Since v (y) will be involved multiple times in the solution, equation (47) can be used instead of (44):
s.t.g(x，y)≥0 (47)
the set V is composed of y corresponding to when the problem (47) is feasible. Feasible field Z of question (44)m∩ V can be regarded as the projection of the problem (43) in the y-space feasible domain, and equation (47) is generally referred to as a subproblem, the principle of projection is illustrated in FIG. 1 by taking the projection of the original problem onto the y-plane as an example.
The problem (44) is equivalent to the original problem (43), and the optimal solution (x, y) of the original problem (43) is easily obtained from the optimal solution y of the problem (44), wherein x is the optimal solution when y is y in (47).
The problem (44) is an effective way to solve the original problem (43), however, the problem (44) is difficult to solve in that the functions V and V are expressed by equations (45) and (46) defining them. This difficulty is solved by designing approximations that decompose the cut plane configurations V and V.
From the fundamental principle of decomposition and the nonlinear dual theory, the following theorem can be proved to hold.
1) The same is true if the problem (43) is not feasible or has an unbounded optimal solution, if and only if (44). If (x, y) is the optimal solution to the problem (43), then y must be the optimal solution to the problem (44). If y is the optimal solution to the problem and x is (45) the supremum obtained when y is y, then (x, y) must be the optimal solution to the original problem (43).
2) Let us assume the feasible region R of xnFor non-empty convex sets, for each fixed y ∈ ZmG is the feasible region RnThe set Zy ═ z ∈ RnG (x, y) ≧ Z } for fixed y ∈ ZmIs a closed set.Then, points y (k) ∈ ZmA sufficient requirement in set V is that y (k) satisfies the following definition:
wherein the content of the first and second substances,
3) let us assume the feasible region R of xnFor non-empty convex sets, for each fixed y ∈ ZmF and g are feasible fields RnFor any fixed y (k) ∈ Zm∩ V, then at least one of ① V (y) is finite, and the problem (47) has a corresponding optimal multiplier when y is y (k), ② V (y) is finite, and f (x, y (k)) and g (x, y (k)) are feasible regions R of xnA continuous function of RnFor a closed interval, the optimal solution to the problem (47) is a non-empty set, bounded for ≧ 0.③ v (y (k)) + ∞thus, the optimal solution to the problem (47) for y ═ y (k) equals it is at Zm∩ V, i.e. dual
Under the assumptions of the above theorems (2) and (3), the main problem equivalent to the original problem (43) can be obtained:
the problem (51) can also be written as follows, using the infimum bound as the minimum lower bound of the problem:
in the formula (I), the compound is shown in the specification,
the problem (52) is solved by the relaxation problem, namely solving the relaxation main problem of the original problem as follows:
if the solution results of the relaxation problem cannot satisfy the neglected constraints, new constraints are generated into the problem until the solution results satisfy all the neglected constraints, at which point the optimal solution has been found, or a certain termination condition is reached.
As shown in fig. 2, the improved decomposition algorithm obtains the main problem and the sub problem of the original problem through the steps of mapping, duality, relaxation, and the like, and solves the problem through continuous iteration of the main problem and the sub problem. The upper graph shows the relationship among all the sub-problems, wherein the main problem is obtained after the mapping/dual of the original problem, and the loose main problem only comprises partial constraints of the main problem; the integer variable value is defined to obtain an atomic problem.
The generalized decomposition algorithm steps are as follows:
the method comprises the following steps: initialization, order
k is 1; given convergence criterion>0, initializing a discrete variable y (k) satisfying y (k) ∈ Zm∩V。
Step two: solving the subproblem (47) by using y (k) to obtain a dual multiplier u (k) corresponding to inequality constraint; p is 1, q is 0,
step three: solving the current relaxation main problem (53), and enabling y (k +1) to be an optimal solution, wherein the optimal value isz＝η，zRepresents the lower bound of the original optimization problem (43) if
And outputting the optimal solution (x (k), y (k)) and stopping iteration.
Step four: and solving the subproblem (47) when y is equal to y (k + 1).
① if v(k+1)Is limited. If v is(k+1)≤z-, the iteration terminates. Otherwise, p is p +1, resulting in dual multiplier u (if not present, an approximately optimal multiplier satisfies
And
time and memory
Is the upper bound of the original optimization problem (43).
② the sub-problem (40) is not feasible if y is y (k +1), and λ ∈Λ can be obtained to satisfy
And q is q +1, k is k +1, and the process returns to the step three.
As mentioned above
I.e. the optimal cut connecting the main sub-problem,
i.e. a feasible decomposition cut of the connected major and minor problems.
If the condition assumption ② of theorem 3) is ignored, given that the feasible domain of variable y is a finite discrete set, the assumption of theorem 2) is satisfied, then the generalized decomposition converges within a finite step for a given >0, even for ═ 0.
When an improved decomposition method is applied to solve some non-convex non-linear programming problems, the non-convex characteristics of the problems can be separated from the convex characteristics by judicious selection of complex variables and isolation of the convex parts of the original problems in the main problems. The objective is to generate convex non-linear programming subproblems in four steps of the algorithm, while obtaining a globally optimal solution to the main problem (for linear, convex non-linear, linear integer programming problems).
Fig. 3 is an algorithm flow of the improved decomposition method, and it should be noted that the improved decomposition method only provides a framework for solving MIP, and the decomposed main sub-problem can be solved by selecting an appropriate optimization algorithm or tool. The main problem is a mixed integer programming problem, which can be solved by using a decomposition cut plane method, a branch and bound method and the like. The subproblems belonging to the nonlinear programming can be solved using interior point methods or other intelligent algorithms. It should be noted that when the projection problem of the original problem is a non-convex case, the improved decomposition method cannot guarantee convergence to the globally optimal solution.
The embodiment of the invention decomposes the collaborative planning mathematical model of the natural gas network and the power distribution system into two constraint optimization problems by the decoupling method provided by the invention: an integer programming investment decision main problem and a linear programming operation sub-problem. The integral planning main problem is used for determining investment decision variables of each element in a planning period; the linear programming operation subproblem is used for determining the output condition of each unit at each moment in the programming period; and different decomposition cut set information is formed according to the decomposition form and the solving result of the subproblems and returned to the main problem, so that the coordination and information interaction of the main problem and the subproblems are realized, and the iterative solving of the main problem and the subproblems is carried out, as shown in fig. 4.
When the main problem is solved, the formula (1) is projected to the discrete variable x space of the investment decision according to the decoupling theorem, so that a projection model which is completely equivalent to the formula (1) and only expressed by the discrete variable x of the investment decision is provided, and the main problem of the original problem is formed. The objective function of the main problem is that the investment cost of each element in the planning period and the running cost of the comprehensive energy system returned by the subproblems are minimum to the function of the investment decision variable x, and can be described by the following formula:
Min Jmaster＝cinv(x)+β(x) (54)
according to the decoupling theorem, β (x) can be expressed as the decomposition cut constraint for the main problem by the following equation:
β(x)≥Jsub+cut1_benders(x) (55)
in the formula, cut _ markers 1(x) represents the optimized decomposition cut set of the investment decision discrete variable x function connecting the main question and the subproblem returned by the operation subproblem; j. the design is a squaresubAnd representing the optimization result returned by the operation subproblem.
Meanwhile, the main investment decision problem also needs to meet installation condition constraint, radial constraint of a power distribution network, rotary standby constraint and natural gas adequacy constraint.
From the mathematical model of the main problem described above, it can be determined that the main problem is a 0-1 integer programming problem, and the CP L EX solver can be called to rapidly solve under the modeling environment of MAT L AB + YA L MIP, CP L EX integrates the advantages of numerous methods such as branch-and-bound and splitting cut planes, and the like, can rapidly solve the 0-1 integer programming problem (IP), is convenient for a user to modify the model, and is suitable for application of large-scale problems.
The objective function of the operation sub-problem is that the operation cost of the integrated energy system is the minimum under the condition of the given discrete variable x of the investment decision of the integrated energy system, and can be described by the following formula:
Min Jsub(x)＝min{cop(y)} (56)
in the formula, y represents a continuous variable of the original problem.
Meanwhile, the operation sub-problem needs to meet the output constraint of an external connection power grid of the power system, the output constraint of a distributed gas turbine unit, the constraint of a power distribution network, the constraint of reliability, the output constraint of an urban gate station and the constraint of a natural gas network.
From the above model, if there is an element overload in the system for the investment decision scheme x of a given integrated energy system, that is, the investment decision scheme x is an infeasible scheme, the constraint condition of the subproblem cannot be satisfied, and the subproblem has no feasible solution. At this time, virtual power generation power and virtual electrical loads, and virtual gas supply power and virtual gas loads may be introduced in the power distribution system node and the natural gas network node where overload is concerned. And the overloaded element is eliminated by adjusting the magnitude of the virtual output force and the virtual load. Obviously, the minimum value of the sum of the virtual outlets and the virtual loads of the individual distribution systems and natural gas network nodes required to eliminate the overload element is a function of the discrete variable x of the investment decision. Therefore, a virtual operation subproblem can be introduced to describe the influence of virtual output and virtual load of each power distribution system and natural gas network node on the main problem investment decision discrete variable x. The objective function of the virtual run sub-problem can be described by:
in the formula (I), the compound is shown in the specification,
respectively representing virtual power generation active power and reactive power of each node of the power distribution system;
respectively representing virtual active and reactive loads of each node of the power distribution system;
and respectively representing the virtual gas supply power and the virtual gas load of each node of the natural gas network.
Therefore, the node power balance constraints of the power distribution system and the natural gas network should be modified to be represented by the following equations:
the virtual output and the virtual load of the power distribution system and the natural gas network node need to meet the following various constraints:
in addition to the power balance constraints of each power distribution system and natural gas network node and the upper and lower limit constraints of virtual output and virtual load, which are described in the above formulas, other constraints of the virtual operation subproblems and the constraints of the operation subproblems have the same form, and the two problems are judged by the mathematical models of the two problems and can be linear programming problems, and a GUROBI solver can be called to rapidly solve under the MAT L AB + YA L MIP modeling environment.
Therefore, the constraint item of the main problem also needs to add the information returned by the virtual operation subproblem. The constraint that the virtual run sub-problem returns to the main problem can be described by:
Jvir+cut2_benders(x)≤0 (67)
in the formula: j. the design is a squarevirRepresenting an optimization result of the virtual run sub-problem; cut _ markers 2(x) represents an infeasible decomposition cut set of investment decision discrete variable x functions connecting the main and sub-problems returned by the virtual run sub-problem.
Thus, according to the form of the decomposition division found by the above run subproblem and the virtual run subproblem, the decomposition division constraint of the main problem at the k-th iteration should be modified as shown in the following equation:
in the formula: and p and q are the accumulated number of feasible decomposition cuts and infeasible decomposition cuts in the kth iteration. Meanwhile, the decoupling structure diagram should be modified as shown in fig. 5.
The information interaction between the main question and the subproblems is realized by decomposition and segmentation, and the information interaction is generated by constraint of the subproblems and dual multipliers corresponding to the constraint. The addition of the decomposition-partition constraints returned by the sub-problem to the main problem will modify the optimization space of the main problem. Since the multiplier has marginal meaning, the decomposition and segmentation constraint cannot represent all information of the subproblems, and thus the main problem solution result does not necessarily satisfy the constraint corresponding to the subproblems although the decomposition and segmentation constraint is satisfied. Therefore, after the main problem is solved, the generated sub-problem of the decomposition and segmentation needs to be calculated again, and the process is a process of up-and-down iteration of the main problem and the sub-problem. And the structure of different decomposition cuts has great influence on the quality of problem solving.
In order to obtain the resolution of the run subproblem or the virtual run subproblem, the following constraints are not added to the run subproblem and the virtual run subproblem:
in the formula (I), the compound is shown in the specification,
and
is the optimized value of the investment decision variable at the kth iteration of the main problem.
The dual multipliers corresponding to the run subproblem and the virtual run subproblem and the above constraints are respectively
from the constraints and corresponding dual multipliers, the decomposition of the problem of the runners is divided into the following equations:
cut1_benders(k)＝cut11_benders(k)+cut12_benders(k)+cut13_benders(k)+cut14_benders(k)
(74)
similarly, the decomposition of the virtual run subproblem is divided into the following formulas:
cut2_benders(k)＝cut21_benders(k)+cut22_benders(k)+cut23_benders(k)+cut24_benders(k)
(79)
cut1_ markers to be divided(k)Or cut2_ markers(k)And the method is added into the decomposition cut constraint of the main problem, and influences the determination of the investment decision discrete variable of the main problem in the next iteration. The decomposition and segmentation provided by the invention can effectively improve the speed of the algorithm converging to a feasible solution and finally converging to a global optimum point.
FIG. 6 shows a flowchart and an algorithm for solving the co-planning problem of the natural gas network and the power distribution system based on the decoupling method① initializing data including topology and parameters of distribution system and natural gas network, electric load and gas load of each node of distribution system and natural gas network, economic cost and technical information of each investment element, ② determining line type of candidate distribution line, pipe diameter of natural gas main pipe, and candidate site and capacity of distributed gas turbine set and city gate station, ③ planning cycle, scene prediction of load level 5630 optimizing main problem of investment decision under a certain determined load level, and obtaining investment decision scheme, ⑤ judging whether the investment decision scheme obtained in step ④ meets constraint condition, if yes, updating network topology and parameters of comprehensive energy system, otherwise, the problem is not solved, ⑤ optimizing subproblems under different load scenes, ⑥ judging whether the subproblems are feasible solution, if yes, obtaining operation cost and reliability cost of subproblems, if the subproblems are feasible solution, 2 judging UB-829, if no feasible solution is available, generating synergetic solution of natural gas distribution system, if no more than 4934,
and
⑧, if the operation subproblem has no feasible solution, optimizing the virtual operation subproblem, and obtaining the optimized objective function value of the virtual operation subproblem and the dual multiplier of the corresponding constraint, and generating the infeasible decomposition segmentation of the virtual operation subproblem and returning to the step ④.
The collaborative planning method of the electrical interconnection comprehensive energy system provided by the embodiment of the invention takes a river area power distribution system with 138 nodes and a comprehensive energy system of a natural gas network with 119 nodes as examples, and a collaborative planning mathematical model provided by the invention is programmed and solved under the MatlabR2010b + Yalmip environment, so that the effectiveness of the algorithm is verified, wherein the main problem of the collaborative planning model is that a 0-1 integer planning problem can be solved through a CP L EX solver, and a linear planning problem is formed by adopting a DistFlow power flow model for sub-problems and virtual sub-problems, and can be solved through a ROGUBI solver.
In order to meet the predicted electrical load demand, the embodiment has 131 candidate feeders, 162 natural gas pipelines, 14 candidate distributed gas turbine units and 18 natural gas plant stations, and each natural gas plant station and distributed gas turbine unit has two different candidate capacities. The positions of the candidate feeders and the candidate distributed gas turbine groups are shown in fig. 8. The two candidate capacities of the candidate natural gas station are respectively 30MVA and 50MVA, and the two candidate capacities of the candidate distributed gas turbine set are respectively 5MVA and 7 MVA. The feeder impedance parameters and candidate feeder impedance parameters of the power distribution system in the planning initial year are shown in tables 1-1, 1-2 and 1-3, the active and reactive loads of the power distribution system in each node are shown in table 2, and the power supply capacity and type of the power distribution system in the planning initial year are shown in table 3.
In order to meet the predicted gas load demand, the embodiment has 22 candidate pipelines and 2 candidate capacity expansion gate stations, each candidate pipeline has one candidate capacity, and each natural gas city gate station has two different candidate capacity expansion capacities, namely 30MW and 50 MW. The locations of the candidate pipe and candidate city gate stations are shown in fig. 9. The capacity and the candidate capacity expansion capacity of the urban gate station in the planning initial year are shown in a table 4, the non-electric natural gas load at each node of the natural gas network is shown in a table 5, and the pipeline capacity and the candidate pipeline capacity of the natural gas network in the planning initial year are shown in a table 6.
TABLE 1-1
TABLE 2
| Node point | Active power | Reactive power | Node point | Active power | |
| 1 | 0.02423 | 0.00796 | 26 | 0.00692 | 0.00228 |
| 2 | 0.00865 | 0.00284 | 27 | 0.00865 | 0.00284 |
| 3 | 0.00404 | 0.00133 | 28 | 0.00404 | 0.00133 |
| 4 | 0.00635 | 0.00209 | 29 | 0.00808 | 0.00265 |
| 5 | 0.01500 | 0.00493 | 30 | 0.01500 | 0.00493 |
| 6 | 0.00404 | 0.00133 | 31 | 0.00404 | 0.00133 |
| 7 | 0.00577 | 0.00190 | 32 | 0.00850 | 0.00279 |
| 8 | 0.01096 | 0.00360 | 33 | 0.01673 | 0.00550 |
| 9 | 0.00692 | 0.00228 | 34 | 0.00692 | 0.00228 |
| 10 | 0.01673 | 0.00550 | 35 | 0.00519 | 0.00171 |
| 11 | 0.00173 | 0.00057 | 36 | 0.00173 | 0.00057 |
| 12 | 0.01038 | 0.00341 | 37 | 0.01212 | 0.00398 |
| 13 | 0.00635 | 0.00209 | 38 | 0.00550 | 0.00181 |
| 14 | 0.00577 | 0.00190 | 39 | 0.00500 | 0.00164 |
| 15 | 0.00808 | 0.00265 | 40 | 0.00700 | 0.00230 |
| 16 | 0.01096 | 0.00360 | 41 | 0.04500 | 0.01479 |
| 17 | 0.00404 | 0.00133 | 42 | 0.00600 | 0.00197 |
| 18 | 0.00692 | 0.00228 | 43 | 0.00650 | 0.00214 |
| 19 | 0.00808 | 0.00265 | 44 | 0.00700 | 0.00230 |
| 20 | 0.00462 | 0.00152 | 45 | 0.00400 | 0.00131 |
| 21 | 0.01038 | 0.00341 | 46 | 0.00900 | 0.00296 |
| 22 | 0.00635 | 0.00209 | 47 | 0.00500 | 0.00164 |
| 23 | 0.00577 | 0.00190 | 48 | 0.00400 | 0.00131 |
| 24 | 0.00288 | 0.00095 | 49 | 0.00250 | 0.00082 |
| 25 | 0.00519 | 0.00171 | 50 | 0.00400 | 0.00131 |
TABLE 3
| Node point | Capacity of power supply | Type of |
| 51 | 0.1 | Gas engine set |
| 52 | 0.1 | Gas engine set |
| 53 | 0.15 | Transformer connected with |
| 54 | 0.15 | Transformer connected with external power supply |
TABLE 4
| Node point | Planning initial annual capacity | Candidate capacity type one | Candidate capacity type one |
| 1 | 0.6 | 0.3 | 0.5 |
| 17 | 0.4 | 0.3 | 0.5 |
TABLE 5
| Node point | Power of | Node point | Power of |
| 1 | 0.0174 | 10 | 0.031467 |
| 2 | 0.0103 | 11 | 0.033667 |
| 3 | 0.0123 | 12 | 0.01385 |
| 4 | 0.0113 | 13 | 0.01986 |
| 5 | 0.0212 | 14 | 0.031067 |
| 6 | 0.0160 | 15 | 0.022933 |
| 7 | 0.0750 | 16 | 0.020367 |
| 8 | 0.0137 | 17 | 0.042 |
| 9 | 0.0120 |
TABLE 6
The coupling nodes of the power distribution system and the natural gas system are as follows: the distribution system node 8 corresponds to a natural gas network node 15; the power distribution system node 9 corresponds to a natural gas network node 11; the power distribution system node 12 corresponds to the natural gas network node 2; the distribution system node 18 corresponds to the natural gas network node 10; the distribution system node 41 corresponds to the natural gas network node 6; the distribution system node 51 corresponds to the natural gas network node 17; the distribution system node 52 corresponds to the natural gas network node 1; and assume that future increases in energy load are all supplied by the natural gas network.
In order to verify the validity of the collaborative planning model proposed by the present invention, 2 different cases were analyzed. The first case is: firstly, planning a power distribution system considering a distributed gas turbine set, and in the model, assuming that the power distribution system is not constrained by a natural gas network, namely that the natural gas supply is sufficient and not limited; thereafter, natural gas network planning is performed to meet the non-electrical load as well as the gas load generated by the electrical demand. The second case is the coordinated planning of the power distribution system and the natural gas network in consideration of the natural gas network constraint proposed by the invention.
Table 7 shows the comparison of the planning costs of 2 cases (unit: million yuan), and table 7 shows the comparison of the planning costs of 2 different cases in the second load scenario. Compared with case two, in case one, the operating cost of the power distribution system is reduced from 72.42 million yuan to 67.983 million yuan in case two due to the fact that the constraint of a natural gas network is not considered, but the investment cost of a feeder line and a distributed gas turbine set is increased. Overall, the total power distribution system cost 95.1223 million dollars for case two is greater than 95.0355 million dollars for case one. Although case one reduces the overall cost of the power distribution system, the operating cost and the investment cost of the natural gas system are both increased, resulting in an increase in the overall cost of the natural gas system by 1.78% compared to case two. The net result is that the total cost of the integrated energy system of case two is 1.14% lower than that of case one.
TABLE 7
Tables 8 to 11 are the planning results of the distributed gas turbine set, the feeder line, the natural gas pipeline and the city gate station of the integrated energy system under three different load scenes.
As shown in table 8, in order to meet the electrical load demand in the planning period of the next 10 years in the load scenario two, it is necessary to operate 6 distributed gas turbines in the planning period of the next 10 years, respectively, a distributed gas turbine having a rated capacity of 5MVA in the corresponding year at the power distribution system nodes 12, 8, 18, and 51, and a distributed gas turbine having a rated capacity of 7MVA in the corresponding year at the power distribution system nodes 41 and 9.
TABLE 8
As shown in table 9, in the second load scenario, in order to smoothly transmit power from one node to another node, 24 candidate distribution feeders need to be put into operation in different years in the planning period of the next 10 years, including expansion on the original distribution feeder and a new distribution feeder to satisfy the potential load node.
TABLE 9
As shown in table 10, in order to smoothly transmit the natural gas from one node to another node in the second load scenario, 8 natural gas pipelines need to be put into operation in the corresponding year in the planning period of the next 10 years.
As shown in table 11, in order to satisfy the non-electrical load and the gas load generated by the electrical demand in the planning period of the next 10 years in the load scenario two, it is necessary to expand the original natural gas city gate stations in the planning period of the next 10 years in the corresponding year, and expand the city gate stations on the natural gas nodes 18 by 30MW and expand the city gate stations on the natural gas nodes 19 by 50MW, respectively.
TABLE 11
For example, table 12 shows the comparison of the planning costs (millions of yuan) of the various items in different load scenarios, and table 12 shows the planning costs of the integrated energy system for meeting the power load and the natural gas load in the planning period of the next 10 years in different load scenarios.
TABLE 12
As shown in fig. 9 and 10, the method provided by the present invention is used to obtain a topology structure diagram of a power distribution system network and a topology structure diagram of a natural gas network by optimization and solution in a load scenario two.
The effectiveness of the collaborative planning method for the electrical interconnection comprehensive energy system provided by the embodiment of the invention is verified by the comprehensive energy system consisting of the 54-node power distribution system and the 19-node natural gas network.
The problem of joint planning of natural gas and a power distribution network is a nonlinear and non-convex planning problem, and a collaborative planning mathematical model is changed into a mixed integer linear planning problem by linearizing nonlinear and non-convex power distribution line power flow constraint and natural gas main pipeline power flow constraint in a modeling stage of the embodiment of the invention, so that the global convergence and the calculation efficiency of the problem are greatly improved.
With the continuous expansion of the scale of the power system and the scale of the natural gas system, the scale of the collaborative planning problem of the comprehensive energy system is also continuously expanded, and the direct solving by directly using the existing algorithm or solving software still has great difficulty. The embodiment of the invention adopts a decoupling-based method to reasonably decompose the problems, effectively simplifies the problems and reduces the risk of dimension disaster caused by the increase of the system scale.
The above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.
Claims (10)
1. A collaborative planning method of an electrical interconnection comprehensive energy system is characterized in that a collaborative planning model of the comprehensive energy system is constructed by taking new facility installation condition constraint, power distribution system constraint and natural gas system constraint as constraint conditions and taking the minimum total cost of the comprehensive energy system as an optimization target;
wherein the total cost is the sum of the investment cost and the operation cost of the comprehensive energy system;
determining a collaborative planning scheme of the comprehensive energy system according to the collaborative planning model;
the power distribution system constraints specifically include: the method comprises the following steps of (1) output constraint of an externally connected power grid, output constraint of a distributed gas turbine unit, radial constraint of a power distribution network, rotating standby capacity constraint, power distribution network constraint and reliability constraint;
the natural gas system constraints specifically include: the method comprises the following steps of urban gate station output constraint, natural gas network constraint and natural gas adequacy constraint.
2. The collaborative planning method for an electrically interconnected integrated energy system according to claim 1, wherein the investment cost cinvCan be expressed as:
in the formula (I), the compound is shown in the specification,
and
respectively represent distribution lines, distribution trunk pipelines, urban gate stations and distributed gas sigmal,ij,f,tInvestment cost of the unit in the t year in the planning period; λ represents a discount rate; t represents a planning period; a variable 0-1 representing commissioning f-type distribution lines between distribution system nodes i, j in the t year within the planning period; sigmap,ij,f,tA variable 0-1 representing commissioning of f-type pipelines between natural gas network nodes i, j in the t year within the planning period; sigmags,i,f,tA variable 0-1 representing commissioning a type f urban gate station at natural gas network node i in the t year within the planning period; sigmaDG,i,f,tA variable 0-1 representing commissioning of the f-type distributed gas turbine group at a power distribution system node i in the t year within the planning period; omegal、Ωp、ΩgsAnd ΩDGRespectively representing candidate sets of a distribution line, a distribution main pipeline, an urban gate station and a distributed gas turbine set; omegalf、Ωpf、ΩgsfAnd ΩDGfRespectively representing candidate type sets of a distribution line, a distribution main pipeline, an urban gate station and a distributed gas turbine set; u shapel,ij,fRepresenting the investment cost of commissioning f-type distribution lines between distribution system nodes i, j in the t year of the planning period; u shapep,ij,fRepresenting the investment cost of commissioning f-type pipelines between natural gas network nodes i, j in the t year within the planning period; u shapegs,i,fRepresenting the investment cost of commissioning a type f urban gate station at natural gas network node i in the t year of the planning period; u shapeDG,i,fRepresenting the investment cost of commissioning a f-type distributed gas unit at power distribution system node i in year t within the planning period.
3. The collaborative planning method for an electrical interconnection energy integrated system according to claim 2, wherein the operation cost includes operation costs of each element in a planning period and reliability cost due to load shedding due to energy shortage, and the operation cost copCan be expressed as:
in the formula (I), the compound is shown in the specification,
respectively representing the operation of the city gate station, the distributed gas generator set, the distributed wind generator set and the externally connected power grid in the t year in the planning periodAnd (4) cost. Egs、EDGAnd EgridRespectively representing the set of the urban gate station, the distributed gas turbine set and the externally connected power grid which exist in the initial planning year;
and
respectively representing the variable cost of unit output of the city gate station, the distributed gas turbine set and the external connection power grid in the t year in the planning period;
representing the fixed cost of operation of the f-type distributed gas turbine unit in the t year in the planning period; sgs,i,t(τ)、PDG,i,t(τ) and Pgrid,i,t(τ) represents the output of the city gate station, the distributed gas turbine units and the externally connected power grid at the τ th moment of the t year in the planning period respectively; c. CENS(t) represents the load shedding cost of the t year within the planning period; enA set of nodes representing a power distribution system;
representing the load shedding at node i of the distribution system at the time t of the year t within the planning period, VO LLiRepresenting a unit loss of power at node i of the power distribution system.
4. The collaborative planning method for an electrically interconnected integrated energy system according to claim 3, wherein the installation condition constraint is expressed as:
5. the collaborative planning method for an electrically interconnected integrated energy system according to claim 4, wherein the output constraints of the externally connected power grid are expressed as:
Pgrid,i,t(τ)≤Pgrid,i,max，Qgrid,i,t(τ)≤Qgrid,i,max；
in the formula, Pgrid,i,max、Qgrid,i,maxRespectively representing the maximum active output and the maximum reactive output of an externally connected power grid connected with a power distribution network node i; qgrid,i,t(τ) represents the reactive power contribution of the externally connected grid at node i of the power distribution network at time τ of the t year within the planned cycle.
6. The collaborative planning method for an electrically interconnected integrated energy system according to claim 5, wherein the output constraint of the distributed gas turbine is expressed as:
in the formula (I), the compound is shown in the specification,
representing the maximum and minimum power of the distributed gas turbine at node i of the power distribution network, respectively;
respectively representing the maximum and minimum reactive power of the distributed gas turbine set at the node i of the power distribution network; qDG,i,t(τ) represents the reactive power contribution of the distributed gas turbine group at the distribution network node i.
7. The collaborative planning method for an electrically interconnected integrated energy system according to claim 6, wherein the rotational reserve capacity constraint is expressed as:
in the formula (I), the compound is shown in the specification,
representing the rated power of the distributed gas turbine set at the node i of the power distribution system when planning the initial year;
representing the maximum external power grid output connected with the power distribution system at the node i when planning the initial year;
representing the rated power of the distributed gas turbine unit input by the type f at the node i in the planning period;
represents the maximum load at node i for the t year within the planning period; rD,tRepresenting the reserve capacity of the t year within the planning period, the value of which is related to the maximum load of the distribution system.
8. The collaborative planning method for an electrically interconnected integrated energy system according to claim 7, wherein the distribution network constraint is expressed as:
Vmin≤Vi,t(τ)≤Vmax；
in the formula, PD,i,t(τ)、QD,i,t(τ) represents the active and reactive loads at node i at time τ of the t year in the planning cycle, respectively;
respectively representing the active load shedding amount and the reactive load shedding amount at a node i at the time tau in the t year in a planning period; pl,ij,t(τ)、Ql,ij,t(τ) and Sl,ij,t(τ) respectively representing the active power flow, the reactive power flow and the apparent power of distribution lines ij existing in the planning initial year at the time τ in the t year in the planning period; pl,ij,f,t(τ)、Ql,ij,f,t(τ) and Sl,ij,f,t(tau) respectively representing the active power flow, the reactive power flow and the apparent power of the newly-added f-type distribution line ij at the time tau in the t year in the planning period;
and
respectively representing the capacity upper limit of the distribution line ij of the type f existing in the initial planning year and the capacity upper limit of the distribution line ij of the type f newly added in the t year in the planning period; vi,t(τ)、Vj,t(τ) represents the voltage amplitudes at node i and node j, respectively, at time τ of the t year in the planning period; vmin、VmaxRepresenting upper and lower limits of the node voltage amplitude; r isij,oAnd xij,oRespectively representing the conductance and susceptance matrix elements of the distribution line ij which has existed in the initial year of the planningA peptide; r isl,ij,fAnd xl,ij,fRespectively representing the conductance and susceptance matrix elements of the newly added f-type distribution line ij; m is a sufficiently large positive number.
9. The collaborative planning method for an electrically interconnected integrated energy system according to claim 8, wherein the natural gas network constraint is expressed as:
vmin≤vi,t(τ)≤vmax，
in the formula, vi,t(τ) represents the gas pressure at natural gas node i at time τ of year t within the planned cycle; v. ofmaxAnd vminRespectively representing the upper limit value and the lower limit value of the natural gas node air pressure;
representing the electric-to-gas power at the natural gas node i in the t year in the planning period; sDg,i,t(τ) represents the natural gas load at natural gas node i at time τ of year t within the planning period;
representing the gas load of a distributed gas turbine set at a natural gas node i at the time tau in the t year in a planning period; sp,ij,t(τ) represents the power flow at the natural gas main pipeline ij at the time τ of the t year in the planning period; sp,ij,f,t(τ) represents the flow at τ time f type natural gas main pipeline ij in the t year of the planning period;
representing the upper limit of the power flow at the natural gas main pipeline ij existing in the planning initial year;
and (4) representing the upper limit of the power flow at the f-type natural gas main pipeline ij in the t year in the planning period.
10. The collaborative planning method for the electrical interconnection comprehensive energy system according to any one of claims 1 to 9, characterized in that a fixed complex variable decomposition iteration method is adopted for solving, the collaborative planning model is decomposed into an integer planning investment decision main problem and a linear planning operation sub-problem, different decomposition cut set information is formed according to the decomposition form and the solving result of the sub-problem and returned to the main problem, coordination and information interaction of the main problem and the sub-problem are realized, and iterative solution of the main problem and the sub-problem is performed.
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