CN109583141B - Electricity-gas interconnection system unit combination linear model and system considering electricity-to-gas coupling - Google Patents

Electricity-gas interconnection system unit combination linear model and system considering electricity-to-gas coupling Download PDF

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CN109583141B
CN109583141B CN201811647144.0A CN201811647144A CN109583141B CN 109583141 B CN109583141 B CN 109583141B CN 201811647144 A CN201811647144 A CN 201811647144A CN 109583141 B CN109583141 B CN 109583141B
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generator set
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CN109583141A (en
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马洲俊
张明
张勇
臧海祥
王文学
郑玉平
孙国强
许洪华
陈逸如
马迪
洪露
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Shanghai Jiaotong University
State Grid Jiangsu Electric Power Co Ltd
Hohai University HHU
Nanjing Power Supply Co of State Grid Jiangsu Electric Power Co Ltd
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State Grid Jiangsu Electric Power Co Ltd
Hohai University HHU
Nanjing Power Supply Co of State Grid Jiangsu Electric Power Co Ltd
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Abstract

The invention relates to an electric-gas interconnection system unit combination linear model and system considering electric-gas conversion coupling, which aims at an electric-gas interconnection system, considers bidirectional coupling of an electric-gas conversion technology and a gas turbine and researches the unit combination problem. The solving efficiency of the existing nonlinear model and the linear model is calculated through simulation and compared, and the system operation cost and the operation state under two scenes of considering electricity to gas and not considering electricity to gas are analyzed at the same time.

Description

Electricity-gas interconnection system unit combination linear model considering electricity-to-gas coupling and system
Technical Field
The invention relates to an electricity-gas interconnection system unit combination linear model considering electricity-gas coupling, and belongs to the field of operation scheduling and control of an integrated energy system.
Background
In recent years, in order to solve the problems of environmental pollution, resource exhaustion and the like, the government of China makes great efforts on adjusting energy structures and changing energy utilization modes, and the revolution of energy production and consumption modes is actively promoted under the large background of energy Internet. An Integrated Energy System (IES) is used as an important component of an energy internet, and is a multi-energy coupling body which takes electric power as a main body and integrates various energy forms such as natural gas and the like, so that complementary mutual assistance among energy sources can be realized, the integrated consumption of renewable energy sources is facilitated, and the comprehensive utilization efficiency of the energy sources is improved.
Power to Gas (P2G) is a new technology that has been developed in recent years, and can convert electric energy into natural Gas for use or storage through electrolysis. The P2G is matched with a gas turbine to realize the bidirectional flow of energy between an electric power system and a natural gas system, and has a remarkable influence on the operation and scheduling of IES, so that the calculation of the P2G coupling in the unit combination UC (unit limitation) has stronger practical significance. For a study of P2G, MANUEL Gotz et al discussed the operating principles at P2G, established performance indicators, and evaluated economics. STEPHEN cleg et al analyzed the effect of applying P2G to an electro-pneumatic interconnection system. However, at present, the role of P2G is rarely taken into account in simplifying the UC problem.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a combined linear model of an electric-gas interconnection system unit considering electric-to-gas coupling.
The technical scheme of the invention is as follows: an electric-gas interconnection system unit combination linear model considering electric-to-gas coupling is established, a constraint equation set is obtained by considering safety constraints of a natural gas system and an electric power system, and a nonlinear part of the constraint equation set is linearized to obtain a linear model, wherein the linearization is as follows:
1) power equation of power line
The power system line power transmission constraint is converted into a linear equation by adopting a direct current model, and the influence of a phase shifter is considered, and is expressed as follows:
Figure BDA0001932260390000011
pf ij,min ≤pf ij,t ≤pf ij,max (23)
γ ij,min ≤γ ij,t ≤γ ij,max (24)
θ ref,t ＝0 (25)
in the formula: theta.theta. i,t 、θ j,t Voltage phase angles of nodes i and j at the moment t respectively; gamma ray ij,t Is a phase shift angle of a line ij at the time t; x is a radical of a fluorine atom ij Is the line ij reactance; pf ij,max 、pf ij,min Respectively an upper limit and a lower limit of transmission power of the line ij; gamma ray ij,max 、γ ij,min Respectively, the upper and lower limits of the phase shift angle of the line ij; theta ref,t Reference node voltage phase angle for time t;
2) minimum start-stop time constraint of generator set
The minimum start-stop time constraint of the generator set is converted into an equivalent linear constraint, and is expressed as follows:
Figure BDA0001932260390000021
Figure BDA0001932260390000022
a(Z)＝min{t+Z-1,T} (28)
b(Z)＝min{Z,T-t+1} (29)
Figure BDA0001932260390000023
Figure BDA0001932260390000024
in the formula:
Figure BDA0001932260390000025
respectively the minimum on-off time of the generator set i; u shape i,t Representing the running state of the generator set i at the time t, wherein delta (t-1) is a unit impact function; t is the number of time sections; u shape i,0 The initial state of the generator set is set; t is i 0 The time for the generator set to continuously run or stop;
3) natural gas pipeline flow equation
The natural gas system pipeline flow is as follows, for pipeline mn:
Figure BDA0001932260390000026
m and n are nodes at two ends of the pipeline, f mn,t Natural gas flow through the pipeline at time t, S mn,t Reflecting the direction of the pipeline flow at time t, c mn Is a constant, pi, related to many physical factors of the pipeline m,t 、π n,t Respectively are pressure values of nodes at two ends of the pipeline at the time t;
the two sides of equation (11) are squared simultaneously:
Figure BDA0001932260390000027
the method of piecewise approximating PLP is used to linearize equation (32), each linear piecewise is composed of a series of points A ═ x 1 ≤x 2 ≤≤x k Function value h (x) corresponding to B k ) Dividing to obtain;
4) start and stop cost of generator set
The start-stop cost of the generator set is expressed in the form of mixed integer linearity as follows:
C Start,i (t)≥0 (37)
C Start,i (t)≥C Start,i (U i,t -U i,t-1 ) (38)
in the formula: c Start,i (t) represents the start-up cost of the generator set i at time t;
5) expressing the natural gas flow consumed by the pressurizing station as a linear relationship of the natural gas flow through the pressurizing station;
6) the shutdown cost of the generator set is ignored;
7) neglecting the quadratic term of the electric-to-gas and gas turbine coupling relation, the gas turbine and electric-to-gas coupling relation is expressed as follows:
Figure BDA0001932260390000031
Figure BDA0001932260390000032
0≤P P2G,p,t ≤P P2G,p,max (21)
in the formula: q P2G,p,t The natural gas flow generated by the electric conversion gas p at the moment t is represented; q GT,q,t Representing the natural gas flow consumed by the gas turbine q at time t, k p2 、k p1 、k p0 The energy conversion coefficient of the electricity-to-gas p; p is GT,q,t The active power of the gas turbine q at the moment t; k is a radical of q2 、k q1 、k q0 Q energy conversion factor for the gas turbine; p P2G,p,max Converting the upper power limit for electric to gas;
and establishing and obtaining the combined linear model of the electric-gas hybrid system unit according to the linearization.
The invention also provides an electricity-gas interconnection system unit combination linear model system considering electricity-gas coupling, wherein a computer program runs in the system, and the computer program realizes the following steps:
1) acquiring parameter information of a power grid, comprising: the method comprises the following steps of (1) power grid topology, branch parameter information, generator parameter information and electric load information;
2) acquiring parameter information of an air network, comprising: the method comprises the following steps of (1) carrying out air network topology, pipeline parameter information, heat source parameter information and heat load information;
3) establishing an electric-gas interconnection comprehensive energy system unit combination model;
4) establishing a combined linear model of the comprehensive energy unit of the electrical interconnection system;
5) and (3) bringing the parameters of the power grid and the gas grid into the comprehensive energy unit combination linear model of the electrical interconnection system, outputting the state variable value, and completing the solution of the linear model, namely completing the performance analysis of the electrical interconnection system.
The invention considers the influence of P2G and establishes a linearized UC problem research model. Firstly, considering the safety constraints of a natural gas system and an electric power system, establishing a unit combination model of the electric-gas interconnection system, and then respectively giving a linearization method according to a plurality of highly nonlinear equation constraints in the model to obtain a linear model.
The invention has the beneficial effects that: the method aims at the lowest comprehensive operation cost of the whole system, considers various safety constraints of the power system and the natural gas system, establishes the combined linear model of the electric-gas interconnected system unit, obviously improves the solving efficiency, can be better applied to engineering, and ensures that the understanding has global optimality.
Drawings
Fig. 1 is a schematic diagram of piecewise linearization.
Fig. 2 is a system configuration diagram according to an embodiment of the present invention.
Fig. 3 is a graph showing a change in power load and natural gas load according to an embodiment of the present invention.
Fig. 4 is a P2G transformation curve of scenario one and scenario two according to the embodiment of the present invention.
Fig. 5 is a comparison of the unit output curves of the first scenario and the second scenario, where a) is a unit G1 output curve, and b) is gas turbine units G2 and G3 output curves.
Detailed Description
The technical process of the invention is described in detail below with reference to the accompanying drawings.
The method comprises the steps of establishing an electric-gas interconnection system unit combination model, obtaining a constraint equation set by considering safety constraints of a natural gas system and an electric power system, and linearizing a nonlinear part of the constraint equation set to obtain a linear model.
1. Establishing an objective function of a unit combination model of an electric-gas interconnection system
The combined model of the electric-gas hybrid system unit aims at the lowest comprehensive operation cost of the whole system, and the operation cost is the sum of the energy consumption cost, the electric-gas conversion cost and the unit start-stop cost. Wherein the energy consumption cost comprises the consumption cost of a generator set and the natural gas supply cost of a gas source point. To simplify the model, the present invention only considers the startup cost of the genset and ignores the shutdown cost. The objective function can be expressed as follows:
Figure BDA0001932260390000041
in the formula, F is the running cost of the whole system; t is the number of time sections; omega G Is a generator set; omega GT Is a gas turbine assembly; p G,i,t Representing the active output of the generator set i at the moment t; omega N Is a gas source point set; c N,j Is the natural gas price for gas source point j; q N,j,t Indicating gas sourceThe point j outputs the flow of the natural gas at the moment t; omega P2G Converting electricity into gas; c P2G,p Representing an operating cost factor of the electric transfer gas p; p P2G,p,t Representing the electric energy power consumed by the electric transfer gas p at the moment t; c Start,i Representing the starting cost of the generator set i; u shape i,t The running state of the generator set i at the time t is shown, 0 is a stop state, and 1 is a start state.
F (P) in formula (1) G,i,t ) The consumption cost of the generator set i at the time t is represented, and a polynomial form is adopted:
Figure BDA0001932260390000051
in the formula: a is i 、b i 、c i Is the consumption cost coefficient of the generator set i.
2. Electric power system constraints
The electric power system constraint considers the unit combination constraint, the generator set active output constraint, the generator set climbing rate constraint, the system rotation standby requirement, the generator set minimum start-stop time constraint and the active power balance constraint, and respectively represents as follows:
U i,t P G,i,min ≤P G,i,t ≤U i,t P G,i,max (3)
P G,i,t -P G,i,t-1 ≤R U,i (4)
P G,i,t-1 -P G,i,t ≤R D,i (5)
Figure BDA0001932260390000052
Figure BDA0001932260390000053
Figure BDA0001932260390000054
Figure BDA0001932260390000055
in the formula: p G,i,max 、P G,i,min Respectively the upper limit and the lower limit of the active output of the generator set i; r U,i 、R D,i The upper limit of the up-down climbing of the generator set i is respectively set; p L,i,t Is the active load of the node i at the moment t; SR t Rotating the system for standby at the moment t;
Figure BDA0001932260390000056
respectively representing the accumulated starting time and stopping time of the generator set i from the initial moment to the t-1 period;
Figure BDA0001932260390000057
Figure BDA0001932260390000058
respectively the minimum startup and shutdown time of the generator set i; j e represents all nodes connected with the node i; pf (p) of ij,t The real power flowing through line ij at time t.
3. Natural gas system constraints
The natural gas system mainly comprises a gas source point, a pipeline, a pressurizing station and the like. The natural gas supplied by the gas source point is transported by a pipeline and distributed to the load side; the pressurizing station is used for improving the node pressure of the natural gas network and supplementing the energy loss in the natural gas transmission process in time.
1) Air source point
The natural gas of the natural gas system is injected from gas source points, and the output natural gas flow of each gas source point has an upper limit and a lower limit, which are expressed as follows:
Q N,j,min ≤Q N,j,t ≤Q N,j,max (10)
in the formula: q N,j,max 、Q N,j,min Representing the maximum and minimum values of the natural gas flow output by source point j.
2) Pipeline
The natural gas pipeline flow is usually calculated by a nonlinear equation and is mainly related to the pressure values of the nodes at the two ends of the pipeline. For a pipe mn, under ideal adiabatic conditions, its steady state flow can be expressed as follows:
Figure BDA0001932260390000061
Figure BDA0001932260390000062
in the formula: f. of mn,t The natural gas flow rate flowing through the pipeline at the moment t; c. C mn Is a constant related to many physical factors of the pipeline; pi m,t 、π n,t Respectively are pressure values of nodes at two ends of the pipeline at the time t; s mn,t Reflecting the direction of the pipeline flow at the time t, wherein +1 is a positive direction and-1 is a negative direction.
Wherein the node pressure has upper and lower limit constraints expressed as follows:
π m,min ≤π m,t ≤π m,max (13)
in the formula: pi m,max 、π m,min Respectively an upper limit and a lower limit of the pressure value of the node m.
3) Pressurizing station
Because of frictional resistance, natural gas has certain pressure and energy loss in the transmission process, and in order to effectively transmit the natural gas, a partial pressurizing station needs to be installed in a natural gas system. The pressurizing station can raise the pressure of the natural gas pipeline, but consumes certain energy, and the energy is provided by natural gas flowing through the pressurizing station. The energy consumed by the pressurizing station is related to the natural gas flow rate through the pressurizing station, the pressurizing ratio, and the like, and can be expressed as follows:
Figure BDA0001932260390000063
Figure BDA0001932260390000064
in the formula: f. of com,k,t Represents the flow rate through the pressurizing station k at time t; h com,k,t Represents the energy consumed by the pressurizing station k at time t; k is a radical of 1 、k 2 β is a constant related to a number of physical factors of the pressurizing station; tau is com,k,t Representing the natural gas flow consumed by the pressurizing station k at the moment t; alpha is alpha k 、β k 、γ k Is the energy conversion coefficient.
The energy consumed by the compressor and the compression ratio are constrained by upper and lower limits, which are expressed as follows:
H com,k,min ≤H com,k,t ≤H com,k,max (16)
Figure BDA0001932260390000071
in the formula: h com,k,max 、H com,k,min Respectively an upper limit and a lower limit of energy consumed by the compressor k; r k,max 、R k,min Respectively, the upper and lower limits of the compression ratio of the compressor.
4) Flow balance
The natural gas system flow balance can be expressed as the algebraic sum of the natural gas flow rates of all the inflow nodes is zero, so the flow balance equation for each node can be expressed as:
Figure BDA0001932260390000072
in the formula: n belongs to m and represents all nodes connected with the node m; q P2G,p,t The natural gas flow generated by the electric conversion gas p at the moment t is represented; q GT,q,t Representing the natural gas flow consumed by the gas turbine q at time t; q L,m,t Representing the natural gas load at node m at time t.
4. Electric gas and gas turbine constraints
The invention adopts two elements of an electric conversion gas and a gas turbine to couple a power system and a natural gas system. The electricity-to-gas electrolysis can electrolyze the residual electric energy which is difficult to be absorbed into natural gas, and the natural gas can be used as the load of a power system and the gas source of a natural gas system; instead, the gas turbine may be considered a power source for the power system and a load for the natural gas system. The invention adopts polynomial expression to express the coupling relation between the gas turbine and the electric conversion gas, and can be expressed as follows:
Figure BDA0001932260390000073
Figure BDA0001932260390000074
0≤P P2G,p,t ≤P P2G,p,max (21)
in the formula: k is a radical of p2 、k p1 、k p0 The energy conversion coefficient of the electricity-to-gas p; p is GT,q,t The active power of the gas turbine q at the moment t; k is a radical of q2 、k q1 、k q0 Is the q energy conversion coefficient of the gas turbine; p P2G,p,max The upper power limit for electric-to-gas conversion.
5. Model linearization
In the established electricity-gas interconnection comprehensive energy system unit combination model, a power line power equation, a generator unit start-stop time constraint equation, a natural gas pipeline flow equation, a pressurization station energy consumption equation and the like all present high nonlinearity, so that model solution becomes very difficult. The conventional algorithm is easy to fall into local optimization, has low calculation efficiency and is difficult to adapt to a large-scale system. In order to overcome the problems, the section carries out linear processing on a nonlinear equation in a unit combination model of the electricity-gas interconnected comprehensive energy system, and converts an MINLP problem into an MILP problem so as to improve the solving efficiency of the model and ensure the global optimality of the model. The linearization process of the unit combination model of the electric-gas interconnection comprehensive energy system is described in detail below.
1) Power equation of power line
The power system line power transmission constraint is converted into a linear equation by adopting a direct current model, and the influence of a phase shifter is considered, and is expressed as follows:
Figure BDA0001932260390000081
pf ij,min ≤pf ij,t ≤pf ij,max (23)
γ ij,min ≤γ ij,t ≤γ ij,max (24)
θ ref,t ＝0 (25)
in the formula: theta i,t 、θ j,t Voltage phase angles of nodes i and j at the moment t respectively; gamma ray ij,t Is a phase shift angle of a line ij at the time t; x is the number of ij Is the line ij reactance; pf ij,max 、pf ij,min Respectively an upper limit and a lower limit of transmission power of the line ij; gamma ray ij,max 、γ ij,min Respectively, the upper and lower limits of the phase shift angle of the line ij; theta ref,t The reference node voltage phase angle is time t.
2) Minimum start-stop time constraint of generator set
Equations (7) and (8) are the minimum start-stop time constraint of the generator set, are complex nonlinear equations, and are converted into equivalent linear constraints, and are expressed as follows:
Figure BDA0001932260390000082
Figure BDA0001932260390000083
a(Z)＝min{t+Z-1,T} (28)
b(Z)＝min{Z,T-t+1} (29)
Figure BDA0001932260390000084
Figure BDA0001932260390000085
in the formula: delta (t-1) is a unit impact function; u shape i,0 For generating setsThe initial state of (a); t is i 0 The time for the generator set to continuously run or stop.
Therefore, the mutually coupled unit start-stop time constraint is converted into independent calculation for each time interval, and the difficulty of model solution is greatly reduced.
3) Natural gas pipeline flow equation
The natural gas system pipeline flow equation (11) is in the form of square root, is a non-convex height nonlinear equation, and firstly squares the two sides of the equation simultaneously:
Figure BDA0001932260390000091
when formula (32) is observed, all variables in formula (iv) are h (x) ═ x 2 Are all defined in the interval [ A, B ]]The above univariate function, so that it can be linearized by adopting a piece-wise approximation (PLP) method, as shown in fig. 1. Each linear segment is composed of a series of points A ═ x 1 ≤x 2 ≤…≤x k Function value h (x) corresponding to B k ) And (5) dividing to obtain.
In the formula (32), f is mn,t 、π m,t And pi n,t Are all square terms, so taking the node pressure pi as an example, for the function h (pi) ═ pi 2 Carrying out piecewise linearization:
Figure BDA0001932260390000092
Figure BDA0001932260390000093
wherein, delta i Reflects each linear segment H i H i+1 And satisfies the following conditions:
0≤δ i ≤1 (35)
binary variable psi i Satisfies the following conditions:
δ i+1 ≤ψ i ≤δ i ，ψ i ∈{0，1} (36)
when psi i When 1, there is delta i 1 and 0. ltoreq. delta i+1 Less than or equal to 1; when psi i When equal to 0, there is delta i ＝δ i+1 ＝0。
4) Generating set start-stop cost
The start-stop cost of the generator set can be expressed in the form of mixed integer linearity as follows:
C Start,i (t)≥0 (37)
C Start,i (t)≥C Start,i (U i,t -U i,t-1 ) (38)
in the formula: c Start,i (t) represents the start-up cost of genset i at time t.
In addition, the natural gas flow consumed by the pressurizing station is expressed as a linear relation of the natural gas flow flowing through the pressurizing station, and secondary terms of a generating set cost expression, an electric conversion gas and a gas turbine coupling relation are ignored, so that a generating set combination linear model of the electric-gas hybrid system is established.
The effect of the model of the present invention is illustrated by example simulation.
The embodiment of the invention adopts an electricity-gas interconnection system which is constructed by a 6-node power system and a modified 10-node natural gas system, the systems are coupled through an electricity-gas conversion device and a gas turbine, and the system structure is shown in figure 2. The 6-node power system has 1 generator set G1 and 2 gas turbines G2 and G3. Wherein phase shifters are arranged between nodes 3-6 of the power system; the natural gas system has 2 source points W with pressurizing stations between nodes 3-5. Gas turbines G2 and G3 are connected to natural gas system nodes 1 and 6, respectively. The P2G facility is installed between the power node 1 and the natural gas node 4. The 24 hour curves for the electrical load and the natural gas load are shown in fig. 3.
The starting costs of the generator set G1 and the gas turbines G2, G3 are $ 350, $ 500, $ 400, respectively; the power generation cost of the generator set G1 is 3.23 $/MBtu; the purchase cost of the natural gas is 3.23 $/kcf; the operating conversion cost of the P2G is 20 $/kcf.
In order to comprehensively compare the difference between the nonlinear model and the linear model and analyze the influence of the P2G equipment on the combination of the electric-gas interconnected comprehensive energy system units, the invention sets the following 2 scenes for comparison and analysis:
scene one: considering the P2G device, the total system is a mixed integer nonlinear Model (MINLP);
scene two: considering the P2G plant, the power network, natural gas pipeline and plant combined part uses a mixed integer linear Model (MILP), the model of the invention;
table 1 shows the results of the generated energy, gas purchase amount, calculation time, and the like for the two scenes.
TABLE 1 comparison of scene one and scene two results
Figure BDA0001932260390000101
In the aspect of solving time, as can be seen from the comparison results in table 1, the solving time required by the MILP model of the second scene is greatly reduced as compared with that of the MILP model of the first scene, and thus the MILP model can effectively improve the solving efficiency of the unit combination problem of the electrical-electrical interconnection system. When the system scale is larger or the number of the access units is larger, the improvement of the solving efficiency is more obvious, the model expression can be simplified by adopting a linear model, and the problems of low calculation efficiency, long time, non-convergence and the like can be effectively solved.
In the aspect of economic cost, the total power generation amount of the system of the scene two is 5911.99MW, compared with the system of the scene one, the power generation amount is increased by 205.92MW, and the increase amplitude is 3.60%; compared with the scene one, the gas purchase amount of the system is reduced by 5235.82kcf, the reduction amplitude is 3.92%, and the total operation cost of the system is reduced by 2.17%.
Fig. 4 and 5 show the operating state of P2G and the capacity condition of each unit in scenario one and scenario two, respectively. It can be found that, at 8: 00 to 23: between periods 00, the P2G behavior for both models is exactly the same, and at 0: 00 to 7: during the 00 time period, the P2G plant using the MILP model needs to convert more electrical power to meet the natural gas load requirements of the system. Meanwhile, for the output condition of each unit, the stop-start condition and the output condition of the gas turbine units G2 and G3 under the scene one and the scene two are completely consistent, and the stop-start condition of the gas turbine unit G1 under the two models of MINLP and MINLP is consistent, but only 8: 00 to 23: the output conditions are the same between the 00 time periods, and the output of the scene two adopting the MILP model is higher in the rest time periods, which is related to the fact that the P2G converts more electric energy in the time periods. The reason for the above difference is that in the range of 0: 00 to 8: in the period of 00, the electric load is reduced more quickly than the natural gas load, and the power generating unit increases the output to compensate the natural gas load through the P2G device. This is also the reason why the total power generation amount is higher in the second scenario compared to the first scenario and the total natural gas purchase amount is reduced on the premise that the load demand is not changed.
In summary, although the adoption of the MILP model leads to the increase of the total system cost, the change of the generated energy, the purchased gas amount and the P2G running state, and the accuracy of the model is slightly reduced, the error is relatively small, the solving efficiency is remarkably improved, the method can be better applied to engineering, and the understanding is guaranteed to have global optimality.

Claims (4)

1. An electric-gas interconnection system unit combination linear model considering electric-to-gas coupling is characterized in that an electric-gas interconnection system unit combination model is established, safety constraints of a natural gas system and a power system are considered, a constraint equation set is obtained, nonlinear parts in the constraint equation set are linearized to obtain a linear model, and the linearization is as follows:
1) power equation of power line
The power system line power transmission constraint is converted into a linear equation by adopting a direct current model, and the influence of a phase shifter is considered, and is expressed as follows:
Figure FDA0003694588090000011
pf ij,min ≤pf ij,t ≤pf ij,max (23)
γ ij,min ≤γ ij,t ≤γ ij,max (24)
θ ref,t ＝0 (25)
in the formula: pf ij,t For transmission power, theta, of line ij at time t i,t 、θ j,t Voltage phase angles of nodes i and j at the moment t respectively; gamma ray ij,t Is a phase shift angle of a line ij at the time t; x is the number of ij Is the line ij reactance; pf ij,max 、pf ij,min Respectively an upper limit and a lower limit of transmission power of the line ij; gamma ray ij,max 、γ ij,min Respectively, the upper and lower limits of the phase shift angle of the line ij; theta ref,t Reference node voltage phase angle for time t;
2) minimum start-stop time constraint of generator set
The minimum start-stop time constraint of the generator set is converted into an equivalent linear constraint, and is expressed as follows:
Figure FDA0003694588090000012
Figure FDA0003694588090000013
a(Z)＝min{t+Z-1,T} (28)
b(Z)＝min{Z,T-t+1} (29)
Figure FDA0003694588090000014
Figure FDA0003694588090000015
in the formula:
Figure FDA0003694588090000016
respectively the minimum startup and shutdown time of the generator set i; u shape i,t Representing the running state of the generator set i at the time t, wherein delta (t-1) is a unit impact function; t is time sectionCounting; u shape i,0 The initial state of the generator set is set; t is i 0 The time for the generator set to continuously run or stop;
3) natural gas pipeline flow equation
The natural gas system pipeline flow is as follows, for pipeline mn:
Figure FDA0003694588090000021
m and n are nodes at two ends of the pipeline, f mn,t Natural gas flow through the pipeline at time t, S mn,t Reflecting the direction of the pipeline flow at time t, c mn Is a constant, pi, related to many physical factors of the pipeline m,t 、π n,t Respectively are pressure values of nodes at two ends of the pipeline at the moment t;
the two sides of equation (11) are squared simultaneously:
Figure FDA0003694588090000022
the method of piecewise approximating PLP is adopted to linearize the equation (32), each linear piecewise is composed of a series of points A ═ x 1 ≤x 2 ≤…≤x k Function value h (x) corresponding to B k ) Dividing to obtain;
4) start and stop cost of generator set
The start-stop cost of the generator set is expressed in the form of mixed integer linearity as follows:
C Start,i (t)≥0 (37)
C Start,i (t)≥C Start,i (U i,t -U i,t-1 ) (38)
in the formula: c Start,i (t) represents the start-up cost of the generator set i at time t;
5) expressing the natural gas flow consumed by the pressurizing station as a linear relationship of the natural gas flow through the pressurizing station;
6) the shutdown cost of the generator set is ignored;
7) neglecting the quadratic term of the electric-to-gas and gas turbine coupling relation, the gas turbine and electric-to-gas coupling relation is expressed as follows:
Figure FDA0003694588090000023
Figure FDA0003694588090000024
0≤P P2G,p,t ≤P P2G,p,max (21)
in the formula: q P2G,p,t The natural gas flow generated by the electric conversion gas p at the moment t is represented; q GT,q,t Representing the natural gas flow consumed by the gas turbine q at time t, k p2 、k p1 、k p0 The energy conversion coefficient of the electricity-to-gas p; p GT,q,t The active power output of the gas turbine q at the moment t; k is a radical of q2 、k q1 、k q0 Is the q energy conversion coefficient of the gas turbine; p P2G,p,max Converting an upper power limit for electric to gas;
and establishing and obtaining the combined linear model of the electric-gas hybrid system unit according to the linearization.
2. The electric-to-gas interconnection system unit combination linear model considering electric-to-gas coupling as claimed in claim 1, wherein the power system safety constraints include unit combination constraints, generator set active output constraints, generator set ramp rate constraints, system rotation standby requirements, generator set minimum start-stop time constraints, and active power balance constraints, and the natural gas safety constraints include safety operation constraints of gas source points, pipelines, pressurizing stations, and flow balance.
3. The linear model of claim 1 or 2, wherein the linear model of the electrical-to-gas interconnection system unit combination is designed to minimize the overall system comprehensive operation cost, the comprehensive operation cost is the sum of energy consumption cost, electrical-to-gas conversion cost and unit start-up cost, the energy consumption cost includes generator unit consumption cost and natural gas supply cost at the source point, and the objective function is expressed as follows:
Figure FDA0003694588090000031
in the formula, F is the comprehensive operation cost of the whole system; t is the number of time sections; omega G Is a generator set; omega GT Is a gas turbine assembly; p G,i,t Representing the active output of the generator set i at the moment t; omega N Is a gas source point set; c N,j Is the natural gas price at gas source point j; q N,j,t The flow rate of the natural gas output by the gas source point j at the time t is shown; omega P2G Is an electricity-to-gas collection; c P2G,p Representing the running cost coefficient of the electric conversion gas p; p P2G,p,t Representing the electric energy power consumed by the electric conversion gas p at the moment t; c Start,i Representing the starting cost of the generator set i; u shape i,t Representing the running state of the generator set i at the time t, 0 representing a shutdown state, and 1 representing a starting state;
f (P) in formula (1) G,i,t ) Representing the consumption cost of the generator set i at the time t, and adopting a polynomial form:
Figure FDA0003694588090000032
in the formula: a is i 、b i 、c i Is the consumption cost coefficient of the generator set i.
4. An electric-gas interconnection system unit combination linear model system considering electric-to-gas coupling is characterized in that a computer program runs in the system, and the computer program realizes the following steps:
1) acquiring parameter information of a power grid, comprising: the method comprises the following steps of (1) power grid topology, branch parameter information, generator parameter information and electric load information;
2) acquiring parameter information of an air network, comprising: the method comprises the following steps of (1) carrying out air network topology, pipeline parameter information, heat source parameter information and heat load information;
3) establishing an electric-gas interconnection comprehensive energy system unit combination model;
4) establishing an electric-to-gas interconnection system unit combination linear model considering electric-to-gas coupling according to claim 1;
5) and (3) bringing parameters of the power grid and the gas grid into the electric-gas interconnection system unit combination linear model considering the electric-gas coupling, outputting a state variable value, and completing the solution of the linear model, namely completing the performance analysis of the electric interconnection system.
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