CN109636052B - Collaborative planning method of gas-electricity combined system - Google Patents

Collaborative planning method of gas-electricity combined system Download PDF

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CN109636052B
CN109636052B CN201811561201.3A CN201811561201A CN109636052B CN 109636052 B CN109636052 B CN 109636052B CN 201811561201 A CN201811561201 A CN 201811561201A CN 109636052 B CN109636052 B CN 109636052B
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范宏
刘巧宏
鲁家阳
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Shanghai University of Electric Power
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Abstract

The invention relates to a collaborative planning method of a gas-electricity combined system, which comprises the following steps: 1) considering the safety constraint of the power system and simultaneously considering the safety constraint of the natural gas system and the gas-electricity coupling constraint condition, and establishing a collaborative planning model of the gas-electricity combined system; 2) and taking the planning scheme of the gas-electricity combined system as particles, and solving the collaborative planning model of the gas-electricity combined system by adopting a particle swarm algorithm to obtain the optimal planning scheme of the natural gas pipeline and the electric power line, namely the number of newly-built pipelines and lines on each pipeline and line corridor. Compared with the prior art, the method has the advantages of environmental protection, search performance enhancement, good planning effect and the like.

Description

Collaborative planning method of gas-electricity combined system
Technical Field
The invention relates to the field of gas-electricity combined energy supply systems, in particular to a collaborative planning method of a gas-electricity combined system.
Background
With the increasing consumption of natural gas and the increasing proportion of natural gas power generation, the connection between a natural gas system and a power system is more and more tight. The traditional planning method only aims at a single energy system, and the planning problem of a combined energy supply system needs to be solved urgently. In the conventional planning method, because the degree of association between the two systems is not high, special planning and optimal configuration are usually performed only on a single energy supply system, which may cause problems of repeated investment of equipment, low utilization rate and the like, and reduce the economy of energy supply. Under the background, on the basis of the existing research results, a collaborative planning model of the gas-electricity combined system is established, the economy and the environmental protection of a planning scheme are comprehensively considered, the optimal construction scheme of a natural gas pipeline and a power line is determined, finally, an example of the combined energy supply system is established, and the correctness of the provided method is tested.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a collaborative planning method of a gas-electricity combined system.
The purpose of the invention can be realized by the following technical scheme:
a collaborative planning method of a gas-electricity combined system comprises the following steps:
1) considering the safety constraint of the power system and simultaneously considering the safety constraint of the natural gas system and the gas-electricity coupling constraint condition, and establishing a collaborative planning model of the gas-electricity combined system;
2) and taking the planning scheme of the gas-electricity combined system as particles, and solving the collaborative planning model of the gas-electricity combined system by adopting a particle swarm algorithm to obtain the optimal planning scheme of the natural gas pipeline and the electric power line, namely the number of newly-built pipelines and lines on each pipeline and line corridor.
In the step 1), an objective function of a collaborative planning model of the gas-electricity combined system is as follows:
MinF＝Cinv+Cop+Ccarbon
Figure BDA0001913299040000021
Figure BDA0001913299040000022
Figure BDA0001913299040000023
wherein, CinvTo investment costs, CopFor operating costs, CcarbonIn order to reduce the cost of carbon emission,
Figure BDA0001913299040000024
and
Figure BDA0001913299040000025
the investment costs N of the candidate lines l and the candidate pipelines p in the planning periodlAnd NpThe number of newly built loops, omega, on the line l and the pipeline p respectivelyClineFor a set of power lines to be built, omegaCpipeIs a collection of natural gas pipelines to be built,
Figure BDA0001913299040000026
Figure BDA0001913299040000027
the unit natural gas price of the gas source and the unit output cost of the coal-fired generator, SsNatural gas supply quantity, P, as a source of gas sgIs the active power output of the generator g, omegaSupplierIs a collection of gas sources in the natural gas network, omegaCGAs a collection of non-gas-turbine units, TmaxFor the number of hours of maximum annual load use,
Figure BDA00019132990400000216
is the carbon price, ξ1And xi2The carbon emission coefficients of the coal-fired power generating unit and the gas power generating unit are respectively.
In the step 1), the constraint conditions of the collaborative planning model of the gas-electricity combined system comprise equipment construction constraint, power system constraint and natural gas system constraint.
The equipment construction constraint is specifically as follows:
the number of newly built loops of each power line and pipeline in the planning period cannot exceed the limit:
Figure BDA0001913299040000028
Figure BDA0001913299040000029
wherein the content of the first and second substances,
Figure BDA00019132990400000210
and
Figure BDA00019132990400000211
the new loop upper limit is respectively set on the electric power line l and the pipeline p.
The power system constraints include:
and (3) power balance constraint:
Figure BDA00019132990400000212
wherein the content of the first and second substances,
Figure BDA00019132990400000213
and
Figure BDA00019132990400000214
respectively node-generator incidence matrix, node-line incidence matrix and node-load incidence matrix, Pg，
Figure BDA00019132990400000215
G output and load d of generatorelecSize of (D), PlIs the magnitude of the current of the line l, omegaGen、ΩEloadAnd ΩelecRespectively, the set of generators, power loads and nodes in the power system, omegaAlineM is the node number in the power system for the planned power line set;
and (3) output restraint of the generator:
Figure BDA0001913299040000031
wherein the content of the first and second substances,
Figure BDA0001913299040000032
and
Figure BDA0001913299040000033
the upper limit and the lower limit of the output of the generator g are respectively;
node voltage constraint:
Vmin≤Vm≤Vmax m∈Ωelec
wherein, VminAnd VmaxThe upper limit and the lower limit of the voltage of the node m are respectively;
line active power constraint:
Figure BDA0001913299040000034
|Pl|≤Pl max
wherein the content of the first and second substances,
Figure BDA0001913299040000035
respectively as the head and tail end nodes m of the line1,m2Phase angle of (A), XlIs the reactance of the power line l, Pl maxIs the power transmission limit of the power line i.
The natural gas system constraints include:
and (3) natural gas flow balance constraint:
Figure BDA0001913299040000036
wherein A iss、
Figure BDA0001913299040000037
AcAnd ApRespectively a node-gas source incidence matrix, a node-gas load incidence matrix, a node-compressor incidence matrix and a node-pipeline incidence matrix, omegaGload，ΩCp，ΩgasRespectively, gas load set, compressor set and node set, omega, in the natural gas systemApipeFor the planned set of natural gas pipelines, n is the node number in the natural gas system, QdgasIs loaded by gasgasSize, τcFor obtaining the compressor air consumption after conversion, fpIs the natural gas flow between the pipelines p;
and (3) node pressure constraint:
Figure BDA0001913299040000038
wherein the content of the first and second substances,
Figure BDA0001913299040000039
and
Figure BDA00019132990400000310
respectively, the upper limit anda lower limit;
and (3) air outlet restriction of an air source point:
Figure BDA00019132990400000311
wherein the content of the first and second substances,
Figure BDA00019132990400000312
and
Figure BDA00019132990400000313
the upper limit and the lower limit of the gas output of the gas source s are respectively set;
compressor restraint:
Figure BDA00019132990400000314
wherein the content of the first and second substances,
Figure BDA0001913299040000041
and
Figure BDA0001913299040000042
respectively the upper and lower compression ratio limits for compression c,
Figure BDA0001913299040000043
and
Figure BDA0001913299040000044
respectively are the pressure values of the head end and the tail end of the compressor c;
electrical and gas network association constraints:
Figure BDA0001913299040000045
wherein r isk、qkAnd bkRespectively the fuel factor, omega, of the gas turbineECNRepresenting a set of associated nodes, Ω, in an electrical power systemGCNRepresenting a set of associated nodes in a natural gas system.
In the step 2), in order to enhance the initial search performance of the particle swarm algorithm, a nonlinear dynamic inertia weight is used for initial search, and the expression of the inertia weight omega is as follows:
Figure BDA0001913299040000046
where t is the current iteration number, tmaxIs the maximum number of iterations, ωstartAnd ωendThe initial value and the terminal value of the inertia weight are respectively used as parameters for controlling the smooth degree of the curve of the inertia weight omega along with the change of the iteration times t.
In the step 2), in order to reduce the possibility that the particle swarm algorithm falls into premature convergence, the speed updating formula is improved by adding an average extreme value of the population particles, and the improved particle swarm speed formula is as follows:
Figure BDA0001913299040000047
wherein the content of the first and second substances,
Figure BDA0001913299040000048
for the optimal solution of particle i in the d-th dimension,
Figure BDA0001913299040000049
for the current optimal solution of the whole population in the d-th dimension,
Figure BDA00019132990400000410
is the average extreme value of all the particles in the t generation, r1、r2、r3Is uniformly distributed in [0,1 ]]Random number in the interval, D is the dimension of the particle group,
Figure BDA00019132990400000411
the position of the d-th dimension of particle i at the t-th iteration,
Figure BDA00019132990400000412
and
Figure BDA00019132990400000413
the velocity of the d-th dimension of the particle i at the t-th and t + 1-th iterations, c, respectively1、c2As a learning factor, c3Is a constant.
Compared with the prior art, the invention has the following advantages:
firstly, considering the environmental protection: the invention takes the investment cost, the operation cost and the carbon emission cost as objective functions, and can consider the environmental protection of the planning scheme while ensuring the economy.
Secondly, enhancing the search performance: the nonlinear dynamic inertia weight is adopted, and the average extreme value of the population particles is added in the velocity updating formula, so that the traditional particle swarm algorithm is improved, the initial search performance of the algorithm is enhanced, the possibility that the algorithm falls into premature convergence is reduced, and the planning result is ensured to be the optimal solution.
Thirdly, the planning effect is good: the planning result shows that the proposed collaborative planning method not only reduces the total planning cost, but also greatly reduces the carbon emission of the system.
Drawings
FIG. 1 is a flow chart of the present invention.
FIG. 2 is a schematic diagram of a gas-electric combined system.
Fig. 3 is a flow chart of a modified particle swarm algorithm.
FIG. 4 is a schematic diagram of an exemplary system.
Fig. 5 is a diagram of the scheme results after independent planning.
Fig. 6 is a diagram of the plan results after co-planning.
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments.
As shown in fig. 1, the present invention provides a collaborative planning method for a gas-electricity combined system, which includes the following steps:
s1, considering the safety constraint of the power system and the safety constraint of the natural gas system and the gas-electricity coupling constraint condition, and establishing a collaborative planning model of the gas-electricity combined system;
s2, comprehensively considering the economy and the environmental protection of the planning scheme, and determining the optimal construction scheme of the natural gas pipeline and the power line;
s3, constructing an example of a combined energy supply system, and testing the correctness of the provided method.
Compared with the traditional power grid planning, the collaborative planning model of the gas-electricity combined system in the step S1 considers the safety constraint of the power system and also considers the safety constraint of the natural gas system and the gas-electricity coupling constraint condition. And finally, determining an optimal investment scheme on the basis of meeting the conditions. The method comprises the following steps:
step S11: objective function
The objective function of the energy planning problem is generally to minimize the investment and operation costs of the planning scheme, and considering the national regulation and control of greenhouse gas emission and the opening of the national carbon trading market, the present invention adds the carbon emission cost of the system to one of the objective functions, which is expressed as:
MinF＝Cinv+Cop+Ccarbon
in the formula: cinvDenotes the investment cost, CopRepresents the running cost, CcarbonRepresenting the cost of carbon emissions.
Investment cost CinvIncluding the construction costs of power lines and the construction costs of natural gas pipelines.
Figure BDA0001913299040000051
In the formula:
Figure BDA0001913299040000052
and
Figure BDA0001913299040000053
the investment costs N of the candidate lines l and the candidate pipelines p in the planning periodlAnd NpThe number of newly built loops, omega, on the line l and the pipeline p respectivelyClineFor sets of power lines to be builtOmega ofCpipeFor collections of natural gas lines to be built
Running cost CopIncluding the gas supply cost of the gas source and the fuel cost of the non-gas turbine unit.
Figure BDA0001913299040000061
In the formula:
Figure BDA0001913299040000062
the unit natural gas price of the gas source and the unit output cost of the coal-fired generator, SsNatural gas supply quantity, P, as a source of gas sgIs the active power output of the generator g; omegaSupplierIs a collection of gas sources in the natural gas network, omegaCGAs a collection of non-gas-turbine units, TmaxThe number of annual maximum load utilization hours.
Carbon emission cost CcarbonMainly considering the carbon emission cost of the generator
Figure BDA0001913299040000063
In the formula:
Figure BDA0001913299040000064
is the carbon price; xi1And xi2Carbon emission coefficients of a coal-fired power generator set and a gas power generator set are respectively set; n is a radical ofEGGThe number of the gas generator sets.
Step S12: constraint conditions
(1) Equipment construction constraints
In the planning period, the number of newly built loops of each power line and pipeline cannot exceed the limit
Figure BDA0001913299040000065
Figure BDA0001913299040000066
In the formula:
Figure BDA0001913299040000067
and
Figure BDA0001913299040000068
respectively setting newly built return number upper limits on the power line l and the pipeline p;
(2) electric power system constraints
1) Power balance constraint
Any node i in the power system should satisfy active power balance
Figure BDA0001913299040000069
In the formula:
Figure BDA00019132990400000610
and
Figure BDA00019132990400000611
respectively node-generator incidence matrix, node-line incidence matrix and node-load incidence matrix, Pg，
Figure BDA00019132990400000612
G output and load d of generatorelecSize of (D), PlIs the magnitude of the current of the line l, omegaGen、ΩEloadAnd ΩelecRespectively, the set of generators, power loads and nodes in the power system, omegaAlineFor the planned power line set, m is the node number in the power system.
2) Generator output restraint
For the generator, the constraint of upper and lower output limits needs to be satisfied
Figure BDA00019132990400000613
3) Node voltage constraint
Vmin≤Vm≤Vmax m∈Ωelec
In the formula: vminAnd VmaxRespectively, the upper limit and the lower limit of the voltage of the power node m.
4) Line active power constraint
In an electric power system, direct current power flow is considered
Figure BDA0001913299040000071
|Pl|≤Pl max
In the formula:
Figure BDA0001913299040000072
the phase angles of the nodes at the head and the tail of the line are XlIs the reactance of the power line l, Pl maxIs the power transmission limit of the power line i.
(3) Natural gas system constraints
1) Natural gas flow balance constraint
Similar to the power system node power balance constraint, any node in the natural gas system should also satisfy the node power balance constraint, which is usually expressed in terms of natural gas flow
Figure BDA0001913299040000073
In the formula: a. thes、
Figure BDA0001913299040000074
AcAnd ApRespectively a node-gas source incidence matrix, a node-gas load incidence matrix, a node-compressor incidence matrix and a node-pipeline incidence matrix, omegaGload，ΩCp，ΩgasRespectively a gas load set, a compressor set and a node set in the natural gas system; omegaApipeA set of planned natural gas pipelines; n is a node number in the natural gas system;
Figure BDA00019132990400000711
is loaded by gasgasSize, τcFor obtaining the compressor air consumption after conversion, fpIs the natural gas flow between the pipelines p.
The natural gas pipeline flow equation is related to the pressure at two ends of the pipeline and various physical characteristics of the pipeline, and is not in a common form, and the gas flow in a specific situation is generally described by a nonlinear equation. Under ideal conditions, the natural gas flow f in the pipeline ppCan be expressed as
Figure BDA0001913299040000075
Figure BDA0001913299040000076
In the formula:
Figure BDA0001913299040000077
and
Figure BDA0001913299040000078
the pressure of the gas at the two ends of the pipeline respectively;
Figure BDA0001913299040000079
the parameters of the pipeline, related to the diameter and length of the pipeline,
Figure BDA00019132990400000710
is a direction parameter.
Because natural gas can rub with the periphery of the pipe wall in the conveying stage, if the compressor is not considered in the planning process, the air pressure and the flow of a load point far away from an air source point in the planning scheme can not meet the requirements, and the defects exist in the practical application. This patent assumes that the compressors in the system are all gas turbine driven electrical compressors, and calculatesWhen the compressor consumes energy, the electric energy H consumed by the compressor c is calculated by the following formulacEquivalent as the amount of consumed natural gas τcAs part of the natural gas load.
Figure BDA0001913299040000081
Figure BDA0001913299040000082
In the formula: alpha is alphac、βcAnd gammacIs the energy conversion efficiency constant of the compressor c; b iscConstants related to temperature, compressor c efficiency, and natural gas heating value; f. ofcIs the flow through compressor c; zcIs a constant related to the compression factor of the compressor c and the heating value of the natural gas;
Figure BDA0001913299040000083
and
Figure BDA0001913299040000084
respectively are the pressure values of the head end and the tail end of the compressor c.
2) Nodal pressure constraint
Figure BDA0001913299040000085
In the formula:
Figure BDA0001913299040000086
and
Figure BDA0001913299040000087
respectively, the upper pressure limit and the lower pressure limit of the natural gas node n.
3) Gas source point outgassing constraint
Figure BDA0001913299040000088
In the formula:
Figure BDA0001913299040000089
and
Figure BDA00019132990400000810
are respectively gas sources siThe upper limit and the lower limit of the air output.
4) Compressor restraint
Figure BDA00019132990400000811
In the formula:
Figure BDA00019132990400000812
and
Figure BDA00019132990400000813
respectively, the upper and lower compression ratio limits for compression c.
5) Electrical and gas network association constraints:
gas turbine output PjCorresponding natural gas supply QiIn a non-linear functional relationship
Figure BDA00019132990400000814
In the formula, rk、qkAnd bkRespectively the fuel factor, omega, of the gas turbineECNRepresenting a set of associated nodes, Ω, in an electrical power systemGCNRepresenting a set of associated nodes in a natural gas system.
In step S2, based on the research results of the relevant documents, the standard particle swarm algorithm is improved as follows:
(1) nonlinear dynamic inertial weight
The initial search performance of the algorithm can be enhanced by adopting the nonlinear dynamic inertia weight, and the expression of the inertia weight omega is as follows:
Figure BDA00019132990400000815
in the formula: t is the current iteration number; t is tmaxIs the maximum iteration number; omegastartAnd ωendRespectively an initial value and an end value of the inertia weight; the parameter is a parameter for controlling the smooth degree of the curve of omega along with the change of the iteration times t, and is 3 in the invention.
(2) Mean extremum of population
In order to reduce the possibility that the algorithm falls into premature convergence, an average extreme value term of the particle swarm is added into a velocity updating formula, and the improved particle swarm velocity formula is as follows:
Figure BDA0001913299040000091
in the formula:
Figure BDA0001913299040000092
for the optimal solution of particle i in the d-th dimension,
Figure BDA0001913299040000093
for the current optimal solution of the whole population in the d-th dimension,
Figure BDA0001913299040000094
is the average extreme value of all the particles in the t generation, r1、r2、r3Is uniformly distributed in [0,1 ]]Random number in the interval, D is the dimension of the particle group,
Figure BDA0001913299040000095
the position of the d-th dimension of particle i at the t-th iteration,
Figure BDA0001913299040000096
and
Figure BDA0001913299040000097
the velocity of the d-th dimension of the particle i at the t-th and t + 1-th iterations, c, respectively1、c2For learningFactor, c3Constant, take 1.5.
The collaborative planning step for solving the gas-electricity combined system by applying the improved particle swarm optimization is shown in fig. 3, wherein the population scale is 50, and the maximum iteration time is 200.
In step S3, a collaborative planning model of the integrated gas-electric system provided by the present invention is calculated by the integrated gas-electric system formed by the modified IEEE 39 node system and the 12-node natural gas system. The power grid side comprises 10 generators ( nodes 34, 37 and 38 are gas units and are associated nodes of a natural gas system, the nodes are connected with the natural gas system nodes 12, 5 and 11), 17 power loads and 46 power lines, and at most 3 lines can be expanded on each existing line corridor; the gas network side comprises 3 natural gas sources, 2 compressors, 8 gas loads and 9 pipelines, and at most 2 lines can be expanded on each existing pipeline corridor. The candidate lines and pipes are shown in fig. 4.
When the analysis is carried out, the electric power generation amount and the load level of the power system are assumed to be 1.5 times of the reference year, the capacity of the natural gas source and the natural gas load level are assumed to be 1.3 times of the reference year, the utilization hours of the maximum load of the system is 5200 hours, and the electric power load data and the natural gas load data are shown in tables 1 and 2. The investment costs of the power lines and the natural gas pipelines are 100 ten thousand yuan/km and 200 ten thousand yuan/km, respectively. The price of carbon dioxide is 23 yuan/ton, the carbon emission coefficient of a gas unit is 0.549 ton/MW & h, the carbon emission coefficient of a coal-fired unit is 0.976 ton/MW & h, the power generation cost of the coal-fired unit is 0.3 yuan/kW & h, the power generation cost of the gas unit is added into the supply cost of natural gas, and the price of the natural gas is 73.624 yuan/kcf.
TABLE 1 Electrical load data
Figure BDA0001913299040000098
Figure BDA0001913299040000101
To verify the feasibility of the constructed planning model, 2 different scenarios were set. Scene 1: independent planning is respectively carried out on the two systems without considering the joint relation; scene 2: and (4) taking the joint relation into consideration, and performing collaborative planning on the gas-electricity joint system. The planning results in both scenarios are shown in table 3, and the numbers in parentheses represent the number of extensions of the line or pipe.
Table 2 gas load data
Figure BDA0001913299040000102
The results were analyzed as follows:
TABLE 3 System planning results under different scenarios
Figure BDA0001913299040000103
Through comparison of planning results, it can be seen that scene 2 mainly expands natural gas pipelines 2-5, 9-11 and 3-12 near coupling nodes 5, 11 and 12 in the aspect of a natural gas system, and 1 more pipelines 9-11 and 3-12 are expanded relative to the planning result of scene 1, so that the capability of natural gas to deliver natural gas to a gas power plant is enhanced. In the power system, scenario 2 creates more circuits 28-29 and 2-25 around the gas generators 37, 38 than scenario 1. The line capacity around the gas generators 37, 38 is increased, and the total number of newly built power lines is reduced by 2 loops compared with scenario 1. However, the overall investment cost of scenario 2 is still slightly higher than that of scenario 1 due to the higher construction cost of the pipeline.
TABLE 4 planning cost analysis
Scene Investment cost/billion yuan Operating cost per billion yuan Carbon emission cost per billion yuan Total cost/billion yuan
1 14.922 126.623 9.375 150.920
2 15.871 125.047 8.940 149.858
Difference value -0.949 1.576 0.435 1.094
Although the investment cost of the independent planning is 9.49 million less than that of the collaborative planning, the total operation cost and the carbon emission cost are higher than those of the collaborative planning, so that the overall cost of the collaborative planning is lower than that of the independent planning, 1.062 billion yuan is saved totally, and 1.8913 x 10^6 tons of carbon dioxide are reduced. In conclusion, the collaborative planning not only reduces the total planning cost, but also greatly reduces the carbon emission of the system.

Claims (3)

1. A collaborative planning method of a gas-electricity combined system is characterized by comprising the following steps:
1) considering the safety constraint of the power system and simultaneously considering the safety constraint of the natural gas system and the gas-electricity coupling constraint condition, establishing a collaborative planning model of the gas-electricity combined system, wherein the objective function of the collaborative planning model of the gas-electricity combined system is as follows:
MinF＝Cinv+Cop+Ccarbon
Figure FDA0002733653240000011
Figure FDA0002733653240000012
Figure FDA0002733653240000013
wherein, CinvTo investment costs, CopFor operating costs, CcarbonIn order to reduce the cost of carbon emission,
Figure FDA0002733653240000014
and
Figure FDA0002733653240000015
the investment costs N of the candidate lines l and the candidate pipelines p in the planning periodlAnd NpThe number of newly built loops, omega, on the line l and the pipeline p respectivelyClineFor a set of power lines to be built, omegaCpipeIs a collection of natural gas pipelines to be built,
Figure FDA0002733653240000016
Figure FDA0002733653240000017
the unit natural gas price of the gas source and the unit output cost of the coal-fired generator, SsNatural gas supply quantity, P, as a source of gas sgIs the active power output of the generator g, omegaSupplierIs a daySet of gas sources in natural gas network, omegaCGAs a collection of non-gas-turbine units, TmaxFor the number of hours of maximum annual load use,
Figure FDA0002733653240000018
is the carbon price, ξ1And xi2Carbon emission coefficients of a coal-fired power generator set and a gas power generator set are respectively set;
the constraint conditions of the collaborative planning model of the gas-electricity combined system comprise equipment construction constraint, electric power system constraint and natural gas system constraint, wherein the equipment construction constraint specifically comprises the following steps:
the number of newly built loops of each power line and pipeline in the planning period cannot exceed the limit:
Figure FDA0002733653240000019
Figure FDA00027336532400000110
wherein the content of the first and second substances,
Figure FDA00027336532400000111
and
Figure FDA00027336532400000112
respectively setting newly built return number upper limits on the power line l and the pipeline p;
the power system constraints include:
and (3) power balance constraint:
Figure FDA0002733653240000021
wherein the content of the first and second substances,
Figure FDA0002733653240000022
and
Figure FDA0002733653240000023
respectively node-generator incidence matrix, node-line incidence matrix and node-load incidence matrix, Pg，
Figure FDA0002733653240000024
G output and load d of generatorelecSize of (D), PlIs the magnitude of the current of the line l, omegaGen、ΩEloadAnd ΩelecRespectively, the set of generators, power loads and nodes in the power system, omegaAlineM is the node number in the power system for the planned power line set;
and (3) output restraint of the generator:
Figure FDA0002733653240000025
g∈ΩGen
wherein the content of the first and second substances,
Figure FDA0002733653240000026
and
Figure FDA0002733653240000027
the upper limit and the lower limit of the output of the generator g are respectively;
node voltage constraint:
Vmin≤Vm≤Vmax m∈Ωelec
wherein, VminAnd VmaxThe upper limit and the lower limit of the voltage of the node m are respectively;
line active power constraint:
Figure FDA0002733653240000028
m1,m2∈ΩAline
|Pl|≤Pl max
wherein the content of the first and second substances,
Figure FDA0002733653240000029
respectively as the head and tail end nodes m of the line1,m2Phase angle of (A), XlIs the reactance of the power line l, Pl maxIs the power transmission limit of the power line l;
the natural gas system constraints include:
and (3) natural gas flow balance constraint:
Figure FDA00027336532400000210
wherein A iss、Agl、AcAnd ApRespectively a node-gas source incidence matrix, a node-gas load incidence matrix, a node-compressor incidence matrix and a node-pipeline incidence matrix, omegaGload，ΩCp，ΩgasRespectively, gas load set, compressor set and node set, omega, in the natural gas systemApipeFor the planned set of natural gas pipelines, n is the node number in the natural gas system, QdgasIs loaded by gasgasSize, τcFor obtaining the compressor air consumption after conversion, fpIs the natural gas flow between the pipelines p;
and (3) node pressure constraint:
Figure FDA00027336532400000211
n∈Ωgas
wherein the content of the first and second substances,
Figure FDA0002733653240000031
and
Figure FDA0002733653240000032
respectively, an upper limit and a lower limit of the pressure of the node n;
and (3) air outlet restriction of an air source point:
Figure FDA0002733653240000033
s∈ΩSupplier
wherein the content of the first and second substances,
Figure FDA0002733653240000034
and
Figure FDA0002733653240000035
the upper limit and the lower limit of the gas output of the gas source s are respectively set;
compressor restraint:
Figure FDA0002733653240000036
c∈ΩCp
wherein the content of the first and second substances,
Figure FDA0002733653240000037
and
Figure FDA0002733653240000038
respectively the upper and lower compression ratio limits for compression c,
Figure FDA0002733653240000039
and
Figure FDA00027336532400000310
respectively are the pressure values of the head end and the tail end of the compressor c;
electrical and gas network association constraints:
Figure FDA00027336532400000311
k∈ΩECN,j∈ΩGCN
wherein r isk、qkAnd bkRespectively the fuel factor, omega, of the gas turbineECNRepresenting a set of associated nodes, Ω, in an electrical power systemGCNRepresenting a set of associated nodes in a natural gas system;
2) and taking the planning scheme of the gas-electricity combined system as particles, and solving the collaborative planning model of the gas-electricity combined system by adopting a particle swarm algorithm to obtain the optimal planning scheme of the natural gas pipeline and the electric power line, namely the number of newly-built pipelines and lines on each pipeline and line corridor.
2. The collaborative planning method for a gas-electric combined system according to claim 1, wherein in the step 2), in order to enhance the initial search performance of the particle swarm optimization, a nonlinear dynamic inertia weight is used for the initial search, and the expression of the inertia weight ω is:
Figure FDA00027336532400000312
where t is the current iteration number, tmaxIs the maximum number of iterations, ωstartAnd ωendThe initial value and the terminal value of the inertia weight are respectively used as parameters for controlling the smooth degree of the curve of the inertia weight omega along with the change of the iteration times t.
3. The collaborative planning method for a gas-electric combined system according to claim 2, wherein in the step 2), in order to reduce the possibility that the particle swarm algorithm falls into premature convergence, the improvement is made by adding an average extreme value of the swarm particles in the velocity update formula, and the improved swarm velocity formula is:
Figure FDA00027336532400000313
d＝1,2,...,D
wherein the content of the first and second substances,
Figure FDA00027336532400000314
for the optimal solution of particle i in the d-th dimension,
Figure FDA00027336532400000315
for the current optimal solution of the whole population in the d-th dimension,
Figure FDA00027336532400000316
is the average extreme value of all the particles in the t generation, r1、r2、r3Is uniformly distributed in [0,1 ]]Random number in the interval, D is the dimension of the particle group,
Figure FDA0002733653240000041
the position of the d-th dimension of particle i at the t-th iteration,
Figure FDA0002733653240000042
and
Figure FDA0002733653240000043
the velocity of the d-th dimension of the particle i at the t-th and t + 1-th iterations, c, respectively1、c2As a learning factor, c3Is a constant.
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