CN109242366B - Multi-period power flow optimization method of electricity-gas interconnection comprehensive energy system - Google Patents

Multi-period power flow optimization method of electricity-gas interconnection comprehensive energy system Download PDF

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CN109242366B
CN109242366B CN201811310889.8A CN201811310889A CN109242366B CN 109242366 B CN109242366 B CN 109242366B CN 201811310889 A CN201811310889 A CN 201811310889A CN 109242366 B CN109242366 B CN 109242366B
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滕贤亮
杜刚
吴仕强
陈�胜
卫志农
孙国强
臧海祥
王文学
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Nari Technology Co Ltd
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Abstract

The invention discloses a multi-period power flow optimization method of an electricity-gas interconnection comprehensive energy system, which comprises the following steps: (1) acquiring information of a power-gas interconnection comprehensive energy system; (2) constructing a multi-period scheduling model of the electricity-gas interconnection comprehensive energy system according to the system information; (3) converting a nonlinear non-convex equation of the flow and the pressure of the natural gas pipeline in the electricity-gas interconnection comprehensive energy system multi-period scheduling model into a natural gas flow model in a reinforced second-order cone constraint form; (4) solving the converted electricity-gas interconnection comprehensive energy system multi-period scheduling model to obtain an optimal solution; (5) taking the optimal solution as an initial value, and performing linear iterative solution on the converted electricity-gas interconnection comprehensive energy system multi-period scheduling model by adopting a DCP method until the natural gas system strictly meets the load flow constraint; (6) and outputting the final solution at the end of iteration as the optimal power flow solution in the future time period. The invention can effectively optimize the multi-period tide.

Description

Multi-period power flow optimization method of electricity-gas interconnection comprehensive energy system
Technical Field
The invention relates to the technical field of electric interconnection, in particular to a multi-period power flow optimization method of an electric-electric interconnection comprehensive energy system.
Background
In view of the improvement of the specific gravity of the power generation side of the gas turbine and the application of the electric gas conversion technology in the power system, bidirectional energy flow between the power system and the natural gas system is made possible, and the development of the natural gas enables the power system and the natural gas system to be converted from being independent to being coupled with each other (gradually developing into strong coupling). Therefore, it is necessary to break through the independent planning and operation mode among the existing energy systems and construct a unified comprehensive energy system with multiple heterogeneous energy sources interconnected. Furthermore, the energy internet can be understood as the deep integration of internet thinking and technology on the basis of multi-type energy interconnection (i.e. comprehensive energy system), so that the construction of the comprehensive energy system also becomes an important link of the energy internet strategy in China. Compared with the existing energy system, the electricity-gas interconnection comprehensive energy system has the advantages that: 1) higher energy utilization efficiency and greater economic benefit; 2) the large-scale development and grid connection of renewable energy sources are promoted; 3) the flexibility and energy complementarity between systems are increased.
The natural gas system has a slow dynamic characteristic, so in short-time scale scheduling, the line-pack storage characteristic in a natural gas system pipeline needs to be considered. Meanwhile, the natural gas system power flow model is a nonlinear non-convex equation essentially, for non-convex optimization, only a local optimal solution can be obtained, and the convergence of the solution is easily influenced by an initial value. The operation optimization of the power system also faces the non-convex problem, but the direct current linear power flow model can replace the alternating current non-linear power flow model in engineering practice, so that the efficient linear power flow model in the optimization of the power system is available. However, for a natural gas system, the existing power flow model linearization model adopts a piecewise linearity method, a large number of integer variables need to be introduced, the calculation complexity is greatly increased, and if a small number of piecewise integer variables are considered, the piecewise linearity precision cannot meet the engineering practice requirements. Therefore, the natural gas system trend in an efficient convex optimization form is very important.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the problems in the prior art, the invention provides a multi-period power flow optimization method of an electricity-gas interconnection comprehensive energy system, wherein the method adopts second-order cone optimization to ensure the high efficiency and optimality of understanding, and adopts a DCP (difference-of-convergence) method to ensure the feasibility of understanding (namely, the strict physical constraint of a natural gas system can be met).
The technical scheme is as follows: the multi-period power flow optimization method of the electricity-gas interconnection comprehensive energy system comprises the following steps:
(1) respectively acquiring electric power system information and natural gas system information of the electric-gas interconnected comprehensive energy system;
(2) constructing a multi-period scheduling model of the electricity-gas interconnected comprehensive energy system according to the information of the electric power system and the information of the natural gas system;
(3) converting a nonlinear non-convex equation of the flow and the pressure of the natural gas pipeline in the electricity-gas interconnection comprehensive energy system multi-period scheduling model into a natural gas flow model in a reinforced second-order cone constraint form;
(4) solving the converted electricity-gas interconnection comprehensive energy system multi-period scheduling model to obtain an optimal solution;
(5) taking the optimal solution as an initial value, and performing linear iterative solution on the converted electricity-gas interconnection comprehensive energy system multi-period scheduling model by adopting a DCP method until the natural gas system strictly meets the load flow constraint;
(6) and outputting the final solution at the end of iteration as the optimal power flow solution in the future time period.
Further, the step (1) of obtaining the power system information includes: the method comprises the following steps of (1) power grid topology, branch parameter information, generator parameter information, electric load information in a future time period, and predicted value information of wind power; the natural gas system information is: the topology of the natural gas network, the parameter information of the pipeline, the pipeline filling storage capacity of the current pipeline, the parameter information of the gas source and the gas load information in the future period.
Further, the multi-period scheduling model of the electricity-gas interconnection comprehensive energy system established in the step (2) specifically comprises the following steps:
Figure GDA0002528530200000021
Figure GDA0002528530200000022
Figure GDA0002528530200000023
Figure GDA0002528530200000024
Figure GDA0002528530200000025
Figure GDA0002528530200000026
Figure GDA0002528530200000027
Figure GDA0002528530200000028
Figure GDA0002528530200000029
Figure GDA00025285302000000210
Figure GDA00025285302000000211
Figure GDA00025285302000000212
Figure GDA00025285302000000213
Figure GDA00025285302000000214
Figure GDA00025285302000000215
Figure GDA00025285302000000216
Figure GDA0002528530200000031
Figure GDA0002528530200000032
Figure GDA0002528530200000033
in the formula, a superscript 0 represents a reference operation scene, a subscript t represents time t, and i, j, m and n represent nodes in an energy system; the superscript max represents an upper limit value, and the superscript min represents a lower limit value; f. of0To optimize the objective function, NGAs a set of generators, NgAs a gas turbine assembly, NsIs a gas source set, NWFor a collection of wind farms, T0Is the number of time sections, CG,iAs cost factor of the generator, CS,mIs a cost coefficient of gas source, CW,iIn order to obtain the cost coefficient of the waste wind,
Figure GDA0002528530200000034
in order to obtain the percentage of the air to be abandoned,
Figure GDA0002528530200000035
the output of the generator is used as the output of the generator,
Figure GDA0002528530200000036
the lower limit and the upper limit of the output of the generator,
Figure GDA0002528530200000037
for the desired output of wind power, PL,i,tIn order to be an active load,
Figure GDA0002528530200000038
for active power on lines i-j, EN (i) is a set of nodes connected to node i, bijIs the susceptance of the line i-j, theta is the nodal phase angle vector,
Figure GDA0002528530200000039
the phase angle vector for node i, j at time t,
Figure GDA00025285302000000310
the lower limit and the upper limit of the active power of the lines i-j are set;
Figure GDA00025285302000000311
amount of natural gas consumed by gas turbine ηiFor the node i gas turbine set conversion efficiency,
Figure GDA00025285302000000312
for gas source output, FD,m,tFor natural gas load, GC (m), GP (m), GN (m) are the pressurizing station, gas turbine and pipeline set connected to node m,
Figure GDA00025285302000000313
in order to pressurize the absorbed flow of the station k,
Figure GDA00025285302000000314
in order to be able to pass the flow through the pressurizing station k,
Figure GDA00025285302000000315
the upper limit value of the flow passing through the pressurizing station k;
Figure GDA00025285302000000316
and
Figure GDA00025285302000000317
are respectively pipelinesm-n head end, tail end and mean flow, CmnIs the m-n pressure drop constant, pi, of the pipelinemAnd pinRespectively the pressures of the node m and the node n,
Figure GDA00025285302000000318
respectively as m and n pressures at t time node of reference operation scenem,tFor the node m pressure at time t,
Figure GDA00025285302000000319
lower and upper pressure limits at node m, respectively, G LmnThe pipeline of the pipeline m-n is filled with the gas storage amount,
Figure GDA00025285302000000320
filling and storing gas quantity K of pipelines m-n at t moment and t-1 moment of a reference operation scenemnThe pipeline filling parameters of the pipeline m-n are obtained;
Figure GDA00025285302000000321
for the energy consumption coefficient of the gas-driven pressurizing station,
Figure GDA00025285302000000322
the power generator is used for the maximum active power climbing,
Figure GDA00025285302000000323
respectively as the head pressure and the tail pressure of the pressurizing station,
Figure GDA00025285302000000324
and
Figure GDA00025285302000000325
for the upper and lower pressure boost ratio limits of the pressurizing station,
Figure GDA00025285302000000326
the lower limit and the upper limit of the output of the air source,
Figure GDA00025285302000000327
is the largest climbing of the air source,
Figure GDA00025285302000000328
for m-n channels, G LminThe lower limit of the pipeline amount of the pipeline, and GB is a pipeline set.
Further, the step (3) specifically comprises:
nonlinear non-convex equation for natural gas pipeline flow and pressure
Figure GDA0002528530200000041
Converting into a natural gas flow model in the form of enhanced second-order cone constraint as follows:
Figure GDA0002528530200000042
Figure GDA0002528530200000043
Figure GDA0002528530200000044
Figure GDA0002528530200000045
Figure GDA0002528530200000046
in the formula, the superscript 0 represents the reference operating scenario, the subscript t represents the time t,
Figure GDA0002528530200000047
Figure GDA0002528530200000048
the superscript max represents the corresponding upper limit, the superscript min represents the corresponding lower limit, πm,t、πn,tRespectively the node m and n pressures at the time t,<>Ta square term convex hull function is represented,
Figure GDA0002528530200000049
representing a bilinear term convex hull function, kmnRepresenting a squared term convex envelope variable, λmnRepresenting a bilinear term convex hull variable.
Further, the step (5) specifically comprises:
(5.1) solving the multi-period scheduling model of the electricity-gas interconnection comprehensive energy system to obtain an optimal solution x0；
(5.2) establishing a convex optimization problem:
Figure GDA00025285302000000410
s.t.smn≥0,x∈X
Figure GDA00025285302000000411
in the formula (f)0(x) An optimization objective function of a multi-period scheduling model of the electricity-gas interconnected comprehensive energy system is adopted, wherein X is a state variable, X is a feasible region of X, and X isrFor the optimal solution of state variables, s, to be solved in the r-th iterationmnAs a non-negative relaxation variable, βrFor the penalty weight coefficient, r is the current iteration number,
Figure GDA0002528530200000051
Figure GDA0002528530200000052
(5.3) mixing x0Performing DCP iterative solution as initial value of convex optimization problem, and gradually updating xrNumerical value until natural gas constraint violates index GapcAnd if the value is less than the preset value, ending the iteration.
Further, the natural gas constraint violation index Gap in the step (5.3)cThe calculation formula is as follows:
Figure GDA0002528530200000053
in the formula: x is the number of*After the current iteration is finishedThe value of the state variable of (a),
Figure GDA0002528530200000054
are respectively a state variable x*Of a corresponding value, i.e.
Figure GDA0002528530200000055
Has the advantages that: compared with the prior art, the invention has the following remarkable advantages: the invention adopts second-order cone optimization to ensure the high efficiency and optimality of understanding, and adopts a DCP method to ensure the feasibility of understanding (namely, the strict physical constraint of a natural gas system can be met).
Drawings
FIG. 1 is a schematic flow diagram of one embodiment of the present invention;
fig. 2 is a diagram of an integrated energy system consisting of an IEEE-39 node system and a belgium 20 node system.
Detailed Description
The embodiment provides a multi-period power flow optimization method for an electricity-gas interconnected comprehensive energy system, as shown in fig. 1, the method comprises the following steps:
and S1, respectively obtaining the electric power system information and the natural gas system information of the electric-gas interconnected comprehensive energy system.
Wherein, the power system information is: the method comprises the following steps of (1) power grid topology, branch parameter information, generator parameter information, electric load information in a future time period, and predicted value information of wind power; the parameter information of the natural gas system is as follows: the method comprises the steps of natural gas network topology, pipeline parameter information, line-pack pipeline filling storage of a current pipeline, parameter information of a gas source and gas load information in a future period.
S2, constructing a multi-period scheduling model of the electricity-gas interconnected comprehensive energy system according to the electric power system information and the natural gas system information:
Figure GDA0002528530200000056
Figure GDA0002528530200000057
Figure GDA0002528530200000058
Figure GDA0002528530200000061
Figure GDA0002528530200000062
Figure GDA0002528530200000063
Figure GDA0002528530200000064
Figure GDA0002528530200000065
Figure GDA0002528530200000066
Figure GDA0002528530200000067
Figure GDA0002528530200000068
Figure GDA0002528530200000069
Figure GDA00025285302000000610
Figure GDA00025285302000000611
Figure GDA00025285302000000612
Figure GDA00025285302000000613
Figure GDA00025285302000000614
Figure GDA00025285302000000615
Figure GDA00025285302000000616
in the formula, a superscript 0 represents a reference operation scene, a subscript t represents time t, and i, j, m and n represent nodes in an energy system; the superscript max represents an upper limit value, and the superscript min represents a lower limit value; f. of0To optimize the objective function, NGAs a set of generators, NgAs a gas turbine assembly, NsIs a gas source set, NWFor a collection of wind farms, T0Is the number of time sections, CG,iAs cost factor of the generator, CS,mIs a cost coefficient of gas source, CW,iIn order to obtain the cost coefficient of the waste wind,
Figure GDA00025285302000000617
in order to obtain the percentage of the air to be abandoned,
Figure GDA00025285302000000618
the output of the generator is used as the output of the generator,
Figure GDA00025285302000000619
the lower limit and the upper limit of the output of the generator,
Figure GDA00025285302000000620
for the desired output of wind power, PL,i,tIn order to be an active load,
Figure GDA00025285302000000621
for active power on lines i-j, EN (i) is a set of nodes connected to node i, bijIs the susceptance of the line i-j, theta is the nodal phase angle vector,
Figure GDA0002528530200000071
the phase angle vector for node i, j at time t,
Figure GDA0002528530200000072
the lower limit and the upper limit of the active power of the lines i-j are set;
Figure GDA0002528530200000073
amount of natural gas consumed by gas turbine ηiFor the node i gas turbine set conversion efficiency,
Figure GDA0002528530200000074
for gas source output, FD,m,tFor natural gas load, GC (m), GP (m), GN (m) are the pressurizing station, gas turbine and pipeline set connected to node m,
Figure GDA0002528530200000075
in order to pressurize the absorbed flow of the station k,
Figure GDA0002528530200000076
in order to be able to pass the flow through the pressurizing station k,
Figure GDA0002528530200000077
the upper limit value of the flow passing through the pressurizing station k;
Figure GDA0002528530200000078
and
Figure GDA0002528530200000079
respectively m-n head end, tail end and average flow, CmnIs the m-n pressure drop constant, pi, of the pipelinemAnd pinRespectively the pressures of the node m and the node n,
Figure GDA00025285302000000710
respectively as m and n pressures at t time node of reference operation scenem,tFor the node m pressure at time t,
Figure GDA00025285302000000711
lower and upper pressure limits at node m, respectively, G LmnThe pipeline of the pipeline m-n is filled with the gas storage amount,
Figure GDA00025285302000000712
filling and storing gas quantity K of pipelines m-n at t moment and t-1 moment of a reference operation scenemnThe pipeline filling parameters of the pipeline m-n are obtained;
Figure GDA00025285302000000713
for the energy consumption coefficient of the gas-driven pressurizing station,
Figure GDA00025285302000000714
the power generator is used for the maximum active power climbing,
Figure GDA00025285302000000715
respectively as the head pressure and the tail pressure of the pressurizing station,
Figure GDA00025285302000000716
and
Figure GDA00025285302000000717
for the upper and lower pressure boost ratio limits of the pressurizing station,
Figure GDA00025285302000000718
the lower limit and the upper limit of the output of the air source,
Figure GDA00025285302000000719
is the largest climbing of the air source,
Figure GDA00025285302000000720
for m-n channels, G LminThe lower limit of the pipeline amount of the pipeline, and GB is a pipeline set.
In the formula, the formula (1) is a multi-period optimization objective function, and comprises non-gas unit power generation cost, gas supply cost and wind abandoning cost. The air supply cost indirectly includes the power generation cost of the gas turbine, and therefore the power generation cost in (1) only takes into account the non-gas turbine unit. Equations (2) - (7) are power system operating constraints. The formula (2) is a node power balance constraint, and the formula (3) describes a linear relation between line power and a phase angle difference between a head end node and a tail end node in the direct current power flow model; the formula (4) and the formula (5) are respectively generator upper and lower limit constraint and climbing constraint; equation (6) is the line transmission capacity constraint. Equations (8) - (19) are natural gas system dynamic operating constraints. Equation (8) is a node flow balance constraint, and equations (9) and (10) describe a nonlinear relationship between the average flow of the pipeline and the pressure of the node at the head end and the tail end of the pipeline; the formula (11) shows that the difference of the flow rates of the head end and the tail end is equal to the fluctuation of the storage of two adjacent sections in the pipeline; formula (12) represents that pipeline inventory is proportional to head-to-tail end mean pressure; equation (13) describes a linear relationship between the flow absorbed by the pressurizing station and the flow through the pressurizing station; equation (14) is the pressurization station boost ratio constraint; equation (15) is the pressurization station delivery capacity constraint; equations (16) and (17) are the air supply capacity and the ramp constraints; the formula (18) is the constraint of the upper and lower limits of the node pressure; formula (19) is T0There is a lower bound on the natural gas system manifold at the time.
S3, converting the nonlinear non-convex equation of the natural gas pipeline flow and pressure in the electricity-gas interconnection comprehensive energy system multi-period scheduling model into a natural gas flow model in an enhanced second-order cone constraint form.
In the comprehensive energy system multi-section operation scheduling model formed by the formulas (1) - (19), the formula (9) is a nonlinear non-convex equation, and the corresponding nonlinear optimization model is difficult to avoid the problems of sensitivity to an initial value, poor numerical stability and the like. Formula (9) may be relaxed to formula (20) first, and further, the standard second order tapered formula of formula (20) is shown as formula (21).
Figure GDA0002528530200000081
Figure GDA0002528530200000082
While the numerical stability problem can be effectively avoided by relaxing equation (9) into the second order taper equation of equation (21), equation (21) is not necessarily the same as equation (9) at the optimal solution operating point, i.e., the second order taper relaxation is not necessarily strict. Based on the natural gas flow model, the invention provides a natural gas flow model with an enhanced second-order conical form.
The natural gas flow model of the enhanced second-order cone form deeply considers the formula (22) on the basis of the formula (21). Here, there are two points to be explained with respect to equation (22): 1) the combination of formula (21) and formula (22) is strictly equivalent to formula (9); 2) unlike equation (21), equation (22) remains non-convex.
Figure GDA0002528530200000083
The invention further proposes a method of Convex envelope (Convex envelope) to relax bilinear terms (essentially nonlinear non-Convex terms) in the formula (22). Then the left bilinear term in equation (22)
Figure GDA0002528530200000084
Formula (23) may be used instead, and for the right non-convex term in formula (22), the definition
Figure GDA0002528530200000085
The right part of formula (A-7) may be replaced with formula (24). Finally, equations (23) - (25) can be substituted for equation (22) using the convex envelope approach.
Figure GDA0002528530200000086
Figure GDA0002528530200000087
Figure GDA0002528530200000088
To this end, the formula (21) and the formulas (23) to (25) constitute a natural gas flow model of an enhanced second order tapered form.
And S4, solving the converted electricity-gas interconnection comprehensive energy system multi-period scheduling model to obtain an optimal solution.
And S5, taking the optimal solution as an initial value, and carrying out linear iterative solution on the converted electricity-gas interconnection comprehensive energy system multi-period scheduling model by adopting a DCP method until the natural gas system strictly meets the power flow constraint.
It can be noted that compared to the second-order cone natural gas flow model, the enhanced second-order cone model can provide a stricter optimal solution, however, the optimal solution still does not necessarily satisfy equation (9), i.e. the relaxation is not strictly established, and thus the invention further proposes a feasible solution for recovering the natural gas flow by using the DCP method. Defining:
Figure GDA0002528530200000091
Figure GDA0002528530200000092
then equation (22) can be expressed as:
gmn(x)-hmn(x)≤0 (26)
based on the current optimal solution xrThe DCP method linearizes the concave portion of formula (22) (i.e., h)mn(x) Then (22) is converted to the following form:
Figure GDA0002528530200000095
based on equation (27), the DCP solves the following optimization problem:
Figure GDA0002528530200000093
in the formula: x is a state variable, and X is a feasible field of X; smnAs a non-negative relaxation variable, βrFor the penalty weight coefficient, r is the number of iterations.
In the formula (28), a relaxation variable s is introducedmnThe solvability of the formula (28) can be ensured. DCP iterates to solve equation (28), updating x step by steprNumerical values up to Gap in formula (29)cSmall enough (i.e. original non-linear square)Equation (9) holds approximately true), and the iteration ends.
Figure GDA0002528530200000094
In the formula: gapcIs a constraint violation indicator.
And S6, outputting the final solution at the end of the iteration as the optimal power flow solution in the future time period.
The present invention was subjected to simulation tests as follows.
The test algorithm of the invention is shown in fig. 2, and is an integrated energy system consisting of an IEEE-39 node system and a belgium 20 node system. Table 1 shows the results of the optimization of the second order cone and the enhanced second order cone model, and it can be seen from the table that in the first stage optimization, the dual Gap of the enhanced second order cone model is compared with the second order cone modeloSmaller (0.43% VS 0.91%) and constraint violation index GapcAnd the smaller the optimization result of the enhanced second-order cone model is, the closer the optimization result of the enhanced second-order cone model is to the original nonlinear optimization result. Further, based on the first stage results, the second order cone model and the enhanced second order cone model both recover a feasible solution (Gap) at the second stagecSmall enough) but the enhanced second-order cone model is closer to the original nonlinear model (its Gap)oSmaller) and thus the table 1 results verify the validity of the enhanced second order cone model.
TABLE 1 comparison of second order cone and enhanced second order cone model optimization results
Figure GDA0002528530200000101
Here GapoOptimizing relative error between target values for a second order cone model and a non-linear model
While the invention has been described in connection with what is presently considered to be the most practical and preferred embodiment, it is to be understood that the invention is not to be limited to the disclosed embodiment, but on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims.

Claims (5)

1. A multi-period power flow optimization method of an electricity-gas interconnection comprehensive energy system is characterized by comprising the following steps:
(1) respectively acquiring electric power system information and natural gas system information of the electric-gas interconnected comprehensive energy system;
(2) constructing a multi-period scheduling model of the electricity-gas interconnected comprehensive energy system according to the information of the electric power system and the information of the natural gas system; the method specifically comprises the following steps:
Figure FDA0002528530190000011
Figure FDA0002528530190000012
Figure FDA0002528530190000013
Figure FDA0002528530190000014
Figure FDA0002528530190000015
Figure FDA0002528530190000016
Figure FDA0002528530190000017
Figure FDA0002528530190000018
Figure FDA0002528530190000019
Figure FDA00025285301900000110
Figure FDA00025285301900000111
Figure FDA00025285301900000112
Figure FDA00025285301900000113
Figure FDA00025285301900000114
Figure FDA00025285301900000115
Figure FDA00025285301900000116
Figure FDA00025285301900000117
Figure FDA00025285301900000118
Figure FDA00025285301900000119
in the formula, a superscript 0 represents a reference operation scene, a subscript t represents time t, and i, j, m and n represent nodes in an energy system; the superscript max represents an upper limit value, and the superscript min represents a lower limit value; f. of0To optimize the objective function, NGAs a set of generators, NgAs a gas turbine assembly, NsIs a gas source set, NWFor a collection of wind farms, T0Is the number of time sections, CG,iAs cost factor of the generator, CS,mIs a cost coefficient of gas source, CW,iIn order to obtain the cost coefficient of the waste wind,
Figure FDA0002528530190000021
in order to obtain the percentage of the air to be abandoned,
Figure FDA0002528530190000022
the output of the generator is used as the output of the generator,
Figure FDA0002528530190000023
the lower limit and the upper limit of the output of the generator,
Figure FDA0002528530190000024
for the desired output of wind power, PL,i,tIn order to be an active load,
Figure FDA0002528530190000025
for active power on lines i-j, EN (i) is a set of nodes connected to node i, bijIs the susceptance of the line i-j, theta is the nodal phase angle vector,
Figure FDA0002528530190000026
the phase angle vector for node i, j at time t,
Figure FDA0002528530190000027
the lower limit and the upper limit of the active power of the lines i-j are set;
Figure FDA0002528530190000028
amount of natural gas consumed by gas turbine ηiFor the node i gas turbine set conversion efficiency,
Figure FDA0002528530190000029
for gas source output, FD,m,tFor the natural gas load, GC (m), GP (m), GN (m) are a booster station, a gas turbine and a gas turbine respectively connected to node mThe collection of the pipelines is carried out,
Figure FDA00025285301900000210
in order to pressurize the absorbed flow of the station k,
Figure FDA00025285301900000211
in order to be able to pass the flow through the pressurizing station k,
Figure FDA00025285301900000212
the upper limit value of the flow passing through the pressurizing station k;
Figure FDA00025285301900000213
and
Figure FDA00025285301900000214
respectively m-n head end, tail end and average flow, CmnIs the m-n pressure drop constant, pi, of the pipelinemAnd pinRespectively the pressures of the node m and the node n,
Figure FDA00025285301900000215
respectively as m and n pressures at t time node of reference operation scenem,tFor the node m pressure at time t,
Figure FDA00025285301900000216
lower and upper pressure limits at node m, respectively, G LmnThe pipeline of the pipeline m-n is filled with the gas storage amount,
Figure FDA00025285301900000217
filling and storing gas quantity K of pipelines m-n at t moment and t-1 moment of a reference operation scenemnThe pipeline filling parameters of the pipeline m-n are obtained;
Figure FDA00025285301900000225
for the energy consumption coefficient of the gas-driven pressurizing station,
Figure FDA00025285301900000218
the power generator is used for the maximum active power climbing,
Figure FDA00025285301900000219
respectively as the head pressure and the tail pressure of the pressurizing station,
Figure FDA00025285301900000220
and
Figure FDA00025285301900000221
for the upper and lower pressure boost ratio limits of the pressurizing station,
Figure FDA00025285301900000222
the lower limit and the upper limit of the output of the air source,
Figure FDA00025285301900000223
is the largest climbing of the air source,
Figure FDA00025285301900000224
for m-n channels, G LminThe lower limit of the pipeline quantity of the pipeline is GB, and the pipeline set is GB;
(3) converting a nonlinear non-convex equation of the flow and the pressure of the natural gas pipeline in the electricity-gas interconnection comprehensive energy system multi-period scheduling model into a natural gas flow model in a reinforced second-order cone constraint form;
(4) solving the converted electricity-gas interconnection comprehensive energy system multi-period scheduling model to obtain an optimal solution;
(5) taking the optimal solution as an initial value, and performing linear iterative solution on the converted electricity-gas interconnection comprehensive energy system multi-period scheduling model by adopting a DCP method until the natural gas system strictly meets the load flow constraint;
(6) and outputting the final solution at the end of iteration as the optimal power flow solution in the future time period.
2. The method for multi-period power flow optimization of an electrical-pneumatic interconnected energy system according to claim 1, wherein: obtained in step (1)
The power system information is: the method comprises the following steps of (1) power grid topology, branch parameter information, generator parameter information, electric load information in a future time period, and predicted value information of wind power;
the natural gas system information is: the topology of the natural gas network, the parameter information of the pipeline, the pipeline filling storage capacity of the current pipeline, the parameter information of the gas source and the gas load information in the future period.
3. The method for multi-period power flow optimization of an electrical-pneumatic interconnected energy system according to claim 1, wherein: the step (3) specifically comprises the following steps:
nonlinear non-convex equation for natural gas pipeline flow and pressure
Figure FDA0002528530190000031
Converting into a natural gas flow model in the form of enhanced second-order cone constraint as follows:
Figure FDA0002528530190000032
Figure FDA0002528530190000033
Figure FDA0002528530190000034
Figure FDA0002528530190000035
Figure FDA0002528530190000036
in the formula, the superscript 0 represents the reference operating scenario, the subscript t represents the time t,
Figure FDA0002528530190000037
Figure FDA0002528530190000038
the superscript max represents the corresponding upper limit, the superscript min represents the corresponding lower limit, πm,t、πn,tRespectively the node m and n pressures at the time t,<>Ta square term convex hull function is represented,
Figure FDA0002528530190000039
representing a bilinear term convex hull function, kmnRepresenting a squared term convex envelope variable, λmnRepresenting a bilinear term convex hull variable.
4. The multi-period power flow optimization method of the electric-gas interconnection energy system according to claim 3, characterized in that: the step (5) specifically comprises the following steps:
(5.1) solving the multi-period scheduling model of the electricity-gas interconnection comprehensive energy system to obtain an optimal solution x0；
(5.2) establishing a convex optimization problem:
Figure FDA0002528530190000041
s.t.smn≥0,x∈X
Figure FDA0002528530190000042
in the formula (f)0(x) An optimization objective function of a multi-period scheduling model of the electricity-gas interconnected comprehensive energy system is adopted, wherein X is a state variable, X is a feasible region of X, and X isrFor the optimal solution of state variables, s, to be solved in the r-th iterationmnAs a non-negative relaxation variable, βrFor the penalty weight coefficient, r is the current iteration number,
Figure FDA0002528530190000043
Figure FDA0002528530190000044
(5.3) mixing x0Performing DCP iterative solution as initial value of convex optimization problem, and gradually updating xrNumerical value until natural gas constraint violates index GapcAnd if the value is less than the preset value, ending the iteration.
5. The method for multi-period power flow optimization of an electric-gas interconnected energy system according to claim 4, wherein: violation index of natural gas constraint Gap in step (5.3)cThe calculation formula is as follows:
Figure FDA0002528530190000045
in the formula: x is the number of*The value of the state variable after the current iteration is finished,
Figure FDA0002528530190000046
are respectively a state variable x*Of a corresponding value, i.e.
Figure FDA0002528530190000047
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