CN110717632A - Natural gas pipeline transient operation optimization method - Google Patents

Natural gas pipeline transient operation optimization method Download PDF

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CN110717632A
CN110717632A CN201910982144.4A CN201910982144A CN110717632A CN 110717632 A CN110717632 A CN 110717632A CN 201910982144 A CN201910982144 A CN 201910982144A CN 110717632 A CN110717632 A CN 110717632A
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刘恩斌
彭善碧
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Southwest Petroleum University
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Abstract

The invention discloses a natural gas pipeline transient operation optimization method, which comprises the steps of establishing a transient optimization model comprising compressor operation energy consumption and compressor switching cost, wherein the transient optimization model selects the outlet pressure of a compressor station and the number of starting-up compressor stations which change along with time as optimization variables; establishing constraint conditions of the transient optimization model, wherein the constraint conditions comprise transient natural gas pipeline constraint, node constraint, compressor and station site constraint and terminal conditions; solving the transient optimization model through a heuristic algorithm to obtain an optimal feasible solution; and the natural gas pipeline operates by utilizing the optimal feasible solution to realize transient optimization. The transient optimization model has high solving speed, can avoid frequent switching of the compressor, reduce the switching cost of the compressor, avoid the problem of reducing the output by excessively utilizing the pipe stock in order to reduce the energy consumption, and ensure the stable operation of a natural gas pipeline system.

Description

Natural gas pipeline transient operation optimization method
Technical Field
The invention belongs to the technical field of natural gas scheduling, and particularly relates to a natural gas pipeline transient operation optimization method.
Background
For a long time, natural gas supply in China mainly comprises pipeline natural gas, which accounts for more than 85% of natural gas supply markets in China. However, when the natural gas long-distance pipeline is actually operated, the natural gas long-distance pipeline is influenced by gas supply of a gas source and fluctuation of gas consumption of users, and the operation state of the natural gas long-distance pipeline is constantly changed. In addition, the structure of the large pipe network and the boundary conditions of the input and the output of the large pipe network are very complex, and the steady-state optimization model cannot meet the actual operation condition of the pipe network. Therefore, in the operation management process of the natural gas conveying pipeline system, the simulation and analysis by adopting the transient optimization technology are more accurate and reliable.
The natural gas pipeline transient operation optimizing technology is that when parameters in boundary conditions of natural gas pipelines are in a constantly changing state, a transient optimization method is adopted to set a compressor station operation scheme in a period of time aiming at corresponding transient problems, and the compressor station operation scheme comprises control measures of outlet pressure, a compressor unit on-off scheme, air supply flow and the like which change along with time, so that the lowest operation cost is realized. However, the existing transient operation optimization model has the disadvantages of large number of related variables, complex constraint conditions and difficult model solution.
Disclosure of Invention
In order to solve the problems, the invention aims to provide a natural gas pipeline transient operation optimization method, which considers the changes of the gas inlet and outlet quantities of a gas source and a gas terminal along with time, and establishes a transient optimization mathematical model by combining the constraint conditions of the upstream and downstream pressures, the flow, the split delivery quantity, the lowest station inlet pressure, the performance of a compressor, the risk of starting and stopping operation of the compressor and the like, and provides a fast and effective heuristic algorithm solution model.
The technical scheme of the invention is as follows:
a natural gas pipeline transient operation optimization method comprises the following steps: establishing a transient optimization model comprising compressor operation energy consumption and compressor switching cost, wherein the transient optimization model selects the outlet pressure of a compressor station and the number of starting-up compressor stations which change along with time as optimization variables; establishing constraint conditions of the transient optimization model, wherein the constraint conditions comprise transient natural gas pipeline constraint, node constraint, compressor and station site constraint and terminal conditions; solving the transient optimization model through a heuristic algorithm to obtain an optimal feasible solution; and the natural gas pipeline operates by utilizing the optimal feasible solution to realize transient optimization.
Further, the transient optimization model is as follows:
Figure BDA0002235539970000011
in the formula:
s is the number of compressor stations;
t is the number of time layers;
Pt spower consumed by the compressor at time horizon t, kW;
kt sthe number of compressors operated at the s-th station at time horizon t;
tau is a set time interval;
Ct s，upkw.h consumption of compressor on at station s at time horizon t;
Ct s，downkw.h consumption of compressor shutdown at station s at time horizon t;
kt s，upthe number of the starting-up stations is increased when the station is at the time layer t compared with the last time layer;
kt s，downthe number of the start-up stations is reduced in the s-th station in the time layer t compared with the previous time layer.
Further, the transient natural gas pipeline constraints are:
neglecting the transient influence of temperature, the motion of the gas in the gas transmission pipeline necessarily satisfies mass conservation and momentum conservation, and the mass conservation and momentum conservation equation is as follows:
Figure BDA0002235539970000021
in the formula:
Figure BDA0002235539970000023
is a defined reduced pressure;
C0is a constant number of times, and is,
Figure BDA0002235539970000024
R0is the universal gas constant, kJ/(kmol. K);
ρ0is the density of natural gas in the standard state in kg/m3；
Figure BDA0002235539970000025
Is the average temperature, K;
a is the sectional area of the pipeline, m2；
q is the flow rate, m3/s；
p is pressure, Pa;
g is the acceleration of gravity, m/s2；
h is elevation, m;
λ is the friction coefficient, dimensionless;
d is the pipe diameter m;
further, when the numerical solution is performed, the equations (2) and (3) are discretized by using an implicit difference format.
The pressure at each node in the pipeline and the flow in the pipeline are both within threshold ranges:
Figure BDA0002235539970000026
Figure BDA0002235539970000027
in the formula:
pmin、pmaxrespectively minimum and maximum pressure, Pa;
pt i、pt jcompressor entering pressure and compressor exiting pressure Pa at the t-th time layer respectively;
qmin、qmaxminimum and maximum flow, m, respectively3/s；
qt i、qt jThe compressor inlet flow and outlet flow at the t time layer，m3/s。
Further, the node constraint is: each node v in the pipeline must follow the mass conservation law and the consumption of fuel gas must be subtracted from the gas flow at the compressor end node:
Figure BDA0002235539970000031
in the formula:
qp+、qp-respectively the flow into the pipeline and the flow out of the pipeline, m3/s；
qs+、qs-Inlet and outlet flows, m, of the compressors of station s, respectively3/s；
fs(t) consumption of fuel gas at the s-th station, m3/s；
Ni p+、Ni p-The number of pipelines is equal, P + represents an inlet, P-represents an outlet and is dimensionless;
Ni s+、Ni s-the number of the compressor stations is equal, S + represents an inlet, S-represents an outlet, and the dimension is not existed;
boundary conditions for gas flow pressure and flow are set at node v:
Figure BDA0002235539970000032
Figure BDA0002235539970000033
in the formula:
pv tis the pressure at node v at time t, Pa;
pv min、pv maxrespectively the minimum and maximum values of pressure, Pa;
qt vfor the traffic of node v at time t, m3/s；
qt v，min、qt v，maxRespectively the minimum and maximum flow, Pa.
Further, the compressor and battlefield constraints are:
(1) compressor feasible region:
in the formula:
Ht sthe variable of the pressure head at the s station at the t time layer is m;
hs3、hs2、hs1all are pressure head curve coefficients without dimension;
Qt sis the actual flow rate, m, of each compressor in operation in the s station at the t time horizon3/s；
St sThe rotating speed of the s station at the t time layer is r/min;
ss1、ss2the coefficient of a surge curve is dimensionless;
ss3、ss4the coefficient of the stagnation curve is dimensionless;
Smin、Smaxrespectively the minimum rotating speed and the maximum rotating speed, r/min;
(2) adjusting a compressor:
the flow and the pressure in the pipeline are relatively stable along with the change of time by limiting the inlet flow of the compressor station and adjusting the outlet pressure of the compressor station;
optionally, the compressor station outlet pressure is not adjusted when the pressure fluctuations are less than 0.2 MPa.
1) When the s-th station is in the t-th time layer, when at least one compressor is started:
the compressor flow in equation (9) is a function of the gas pressure, irrespective of the temperature:
Figure BDA0002235539970000041
Figure BDA0002235539970000042
in the formula:
r is a gas constant, J/(mol. K);
qt s，actis the actual flow of the s-th station in the t-th time layer, m3/s；
Figure BDA0002235539970000043
Compressor inlet pressure, Pa, at the s-th time horizon;
qt s+compressor inlet flow, m, for the s-th station at the t-th time horizon3/s；
clb q，s、cub q，sRespectively the minimum value and the maximum value of the current limiting proportion;
in equation (9), the head variation of the compressor is determined by the pressures entering and exiting the compressor:
Figure BDA0002235539970000044
Figure BDA0002235539970000045
in the formula:
γsis the adiabatic expansion coefficient of the compressor of the s station and is dimensionless;
pt s，actis the actual pressure, Pa, of the station at time t;
clb p，sis the minimum value of the voltage regulation proportion;
when there are both gas driven compressors and electrically driven compressors:
Figure BDA0002235539970000051
Figure BDA0002235539970000052
in the formula:
qt s，consumfuel gas consumption at time t, m for station s3/s；
ns elecThe number of the electrically driven compressors of the s station;
dgasthe air consumption coefficient of the compressor is dimensionless;
qt s-compressor outlet flow rate, m, for the s-th station at the t-th time horizon3/s；
2) When the s-th station is in the t-th time layer, all the compressors are not started, namely kt sWhen 0, the gas is allowed to pass through the compressor station at will:
Figure BDA0002235539970000054
(3) minimum run time and minimum downtime constraints:
Figure BDA0002235539970000055
in the formula:
bt sifor the on-off state of the s-th station compressor i at the t-time level,
when b ist si＝0(i＝1，……，ns comp) When, it indicates that the compressor is in the off state;
when b ist si＝1(i＝1，……，ns comp) When, it means that the compressor is in operation;
ns compis the s th stationTotal number of compressors;
ton、toffminimum run time and minimum down time, respectively.
Further, the terminal conditions are: in the T time frame, the total gas volume at the end point is required to be at least as large as the starting point, i.e.:
Figure BDA0002235539970000057
in the formula:
V1 evolume of gas at the beginning of time T, m3；
VT eVolume of gas at end of time T, m3。
Further, when the transient optimization model is solved by using the heuristic algorithm, for the pipelines, the outlet flow of each pipeline is required to be within the threshold range of the inlet flow, and the outlet pressure is required to be within the threshold range of the outlet pressure of the same pipeline at the previous time layer, namely, the outlet pressure and the flow of the pipeline are determined to be in the following form, and for the pipelines, the heuristic algorithm is used for solving the transient optimization modelfp(p)＝(i，j)∈Ep，Comprises the following steps:
Figure BDA0002235539970000063
Figure BDA0002235539970000064
in the formula:
clb q，p、cub q，p、clb p，p、cub p，pare all constants;
qt p+、qt p-flow into the pipeline and flow out of the pipeline at the t time layer, m3/s；
pt-1 jThe pipeline outlet pressure at the t-1 time layer is Pa.
Further, when equations (21) and (22) are solved, the solution is performed using the data structure of the stack.
Compared with the prior art, the invention has the following advantages:
the transient optimization model has high solving speed, can avoid frequent switching of the compressor, reduce the switching cost of the compressor, avoid the problem of reducing the output by excessively utilizing the pipe stock in order to reduce the energy consumption, and ensure the stable operation of a natural gas pipeline system.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
FIG. 1 is a schematic structural diagram of a gas transmission trunk pipeline model according to the optimization method for transient operation of a natural gas pipeline;
FIG. 2 is a schematic diagram of an implicit center difference method of the optimization method for transient operation of a natural gas pipeline according to the present invention;
FIG. 3 is a schematic diagram of a compressor crotch characteristic curve according to the optimization method for transient operation of a natural gas pipeline;
FIG. 4 is a schematic diagram of a randomly generated solution set tree when the natural gas pipeline transient operation optimization method of the present invention is used for solving;
FIG. 5 is a graph illustrating the mileage at each station and the number of compressors configured according to one embodiment;
FIG. 6 is a schematic diagram of initial conditions for operating pressure and flow for the embodiment of FIG. 5;
FIG. 7 is a schematic diagram of boundary conditions of gas usage by a user in the embodiment of FIG. 5;
FIG. 8 is a diagram illustrating the optimization results of the full line pressure in the embodiment of FIG. 5;
FIG. 9 is a diagram illustrating the optimization results of the full-line flow in the embodiment of FIG. 5;
FIG. 10 is a diagram illustrating the optimized result of the inventory management in the embodiment of FIG. 5;
FIG. 11 is a graphical illustration of the results of the outbound pressure optimization of the compressor stations 1-12 of the embodiment of FIG. 5;
FIG. 12 is a graphical representation of the outbound pressure optimization results of the compressor stations 13, 15-17, 19, 20, 22, 24, 26, 29 of the embodiment of FIG. 5;
FIG. 13 is a schematic diagram of the power optimization results of the compressor stations 1-12 of the embodiment of FIG. 5;
FIG. 14 is a graph illustrating the power optimization results of the compressor stations 13, 15-17, 19, 20, 22, 24, 26, 29 of the embodiment of FIG. 5;
FIG. 15 is a schematic diagram of the results of optimizing the gas consumption of the compressor stations 1-13, 15-17, 19, 29 of the embodiment of FIG. 5;
fig. 16 is a schematic diagram of the results of optimizing the gas consumption of the compressor stations 9, 20, 22, 24, 26 of the embodiment of fig. 5.
Detailed Description
The invention is further illustrated with reference to the following figures and examples.
The invention provides a natural gas pipeline transient operation optimization method, which comprises the following steps: establishing a transient optimization model comprising compressor operation energy consumption and compressor switching cost, wherein the transient optimization model selects compressor station outlet pressure and the number of compressor station starting machines which change along with time as optimization variables; establishing constraint conditions of the transient optimization model, wherein the constraint conditions comprise transient natural gas pipeline constraint, node constraint, compressor and station site constraint and terminal conditions; solving the transient optimization model through a heuristic algorithm to obtain an optimal feasible solution; the natural gas pipeline operates by utilizing the optimal feasible solution to realize transient optimization.
When the operation of the natural gas pipeline is optimized, the structure of the actual gas pipeline is very complex, so that the pipeline structure is abstracted into a simplified structure which can be expressed by mathematics. For a natural gas main pipeline, a directed graph as shown in fig. 1 was used for simulation.
In a specific embodiment, a transient optimization model comprising two parts of compressor operation energy consumption and compressor switching cost is established firstly, and the transient optimization model is as follows:
in the formula:
s is the number of compressor stations;
t is the number of time layers;
Pt spower consumed by the compressor at time horizon t, kW;
kt sthe number of compressors operated at the s-th station at time horizon t;
tau is a set time interval;
Ct s，upkw.h consumption of compressor on at station s at time horizon t;
Ct s，downkw.h consumption of compressor shutdown at station s at time horizon t;
kt s，upthe number of the starting-up stations is increased when the station is at the time layer t compared with the last time layer;
kt s，downthe number of the start-up stations is reduced in the s-th station in the time layer t compared with the previous time layer.
For the natural gas main pipeline, the gas flow of each station in the pipeline is determined according to the gas source condition and the user demand and cannot be used as an optimization variable, so the transient optimization model selects the outlet pressure of the compressor stations and the number of the compressor stations which change along with the time as the optimization variables, and the transient operation optimization of the natural gas main pipeline is realized.
Secondly, establishing constraint conditions of the transient optimization model, wherein the constraint conditions comprise transient natural gas pipeline constraint, node constraint, compressor and station site constraint and terminal conditions.
Optionally, the transient natural gas pipeline constraint is: neglecting the transient influence of temperature, the motion of the gas in the gas transmission pipeline necessarily satisfies mass conservation and momentum conservation, and the mass conservation and momentum conservation equation is as follows:
Figure BDA0002235539970000081
Figure BDA0002235539970000082
in the formula:
Figure BDA0002235539970000083
is a defined reduced pressure;
C0is a constant number of times, and is,
Figure BDA0002235539970000084
R0is the universal gas constant, kJ/(kmol. K);
ρ0is the density of natural gas in the standard state in kg/m3；
Figure BDA0002235539970000085
Is the average temperature, K;
a is the sectional area of the pipeline, m2；
q is the flow rate, m3/s；
p is pressure, Pa;
g is the acceleration of gravity, m/s2；
h is elevation, m;
λ is the friction coefficient, dimensionless;
d is the pipe diameter m;
optionally, when performing numerical solution, discretizing equations (2) and (3) by using an implicit difference format as shown in fig. 2:
Figure BDA0002235539970000086
in the formula:
respectively the reduced pressure, Pa, of the node i and the node j of the t +1 time layer;
Figure BDA0002235539970000092
respectively the reduced pressure, Pa, of the node i and the node j in the t time layer;
qi t+1、qj t+1the flow rates of the time layer node i and the node j of t +1, m3/s；
LpIs the distance step, m;
qt i、qt jtraffic of node i and node j of t time layer, m3/s；
pi t+1、pj t+1The pressure intensities, Pa, of the node i and the node j of the t +1 time layer respectively; (ii) a
hpM is the height difference corresponding to the distance step length;
Ip t+1、Rp t+1the nonlinear term caused by friction and dissipation is expressed as:
Figure BDA0002235539970000093
Figure BDA0002235539970000094
Figure BDA0002235539970000095
in the formula:
pt ithe station-entering pressure of the compressor at the t time layer is Pa;
alpha is a coefficient and is dimensionless.
The pressure at each node in the pipeline and the flow in the pipeline are both within threshold ranges:
Figure BDA0002235539970000097
in the formula:
pmin、pmaxrespectively minimum and maximum pressure, Pa;
pt i、pt jcompressor entering pressure and compressor exiting pressure Pa at the t-th time layer respectively;
qmin、qmaxminimum and maximum flow, m, respectively3/s。
Optionally, the node constraint is: each node v in the pipeline must follow the law of conservation of mass and the consumption of fuel gas must be subtracted from the gas flow at the compressor end node:
Figure BDA0002235539970000098
in the formula:
qp+、qp-respectively the flow into the pipeline and the flow out of the pipeline, m3/s；
qs+、qs-Inlet and outlet flows, m, of the compressors of station s, respectively3/s；
fs(t) consumption of fuel gas at the s-th station, m3/s；
Ni p+、Ni p-The number of pipelines is equal, P + represents an inlet, P-represents an outlet and is dimensionless;
Ni s+、Ni s-the number of the compressor stations is equal, S + represents an inlet, S-represents an outlet, and the dimension is not existed;
boundary conditions for gas flow pressure and flow are set at node v:
Figure BDA0002235539970000101
Figure BDA0002235539970000102
in the formula:
pv tis the pressure at node v at time t, Pa;
pv min、pv maxrespectively the minimum and maximum values of pressure, Pa;
qt vfor the traffic of node v at time t, m3/s；
qt v，min、qt v，maxRespectively the minimum and maximum flow, Pa.
Optionally, the compressor and battlefield constraints are:
(1) compressor feasible region: as shown in the compressor head characteristic graph of fig. 3, each compressor has an optimum operating point, and the area formed by the adjacent states of the optimum operating point is the operating area of the compressor:
Figure BDA0002235539970000103
in the formula:
Ht sthe variable of the pressure head at the s station at the t time layer is m;
hs3、hs2、hs1the coefficients of the pressure head curve are dimensionless;
Qt sis the actual flow rate, m, of each compressor in operation in the s station at the t time horizon3/s；
St sAt the t time layers the rotation speed of the station, r/min;
ss1、ss2the coefficient of a surge curve is dimensionless;
ss3、ss4the coefficient of the stagnation curve is dimensionless;
Smin、Smaxrespectively the minimum rotating speed and the maximum rotating speed, r/min;
in equation (9), the head variation of the compressor is determined by the pressures entering and exiting the compressor:
Figure BDA0002235539970000104
in the formula:
γsis the adiabatic expansion coefficient of the s station compressor;
r is a gas constant, J/(mol. K);
in equation (9), the flow rate of the compressor is a function of the gas pressure without taking into account the temperature:
Figure BDA0002235539970000111
in the formula:
qt s+compressor inlet flow, m, for the s-th station at the t-th time horizon3/s；
Compressor inlet pressure, Pa, at the s-th time horizon;
(2) adjusting a compressor:
in actual production, the inbound pressure and flow rate can not exactly meet the constraint conditions of the formula (28) and the formula (29), so that the flow rate and pressure change in the pipeline along with time are relatively stable and the model solution is fast and effective by introducing measures of 'flow limiting' and 'pressure regulating', namely, by limiting the inlet flow rate of the compressor station and regulating the outlet pressure of the compressor station;
optionally, the compressor station outlet pressure is not adjusted when the pressure fluctuations are less than 0.2 MPa.
1) When the s-th station is in the t-th time layer, when at least one compressor is started:
the actual flow rate of the compressor in equation (9) is redefined as equation (29) without considering the temperature:
Figure BDA0002235539970000113
Figure BDA0002235539970000114
in the formula:
qt s，actis the actual flow of the s-th station in the t-th time layer, m3/s；
clb q，s、cub q，sRespectively the minimum value and the maximum value of the current limiting proportion;
in equation (9), the head pressure actual variable of the compressor is redefined by equation (28):
in the formula:
pt s，actis the actual pressure, Pa, of the station at time t;
clb p，sis the minimum value of the voltage regulation proportion;
when the s-th station has both gas-driven compressors and electrically-driven compressors, the total number of compressors of the s-th station is equal to the sum of the number of electrically-driven compressors of the s-th station and the number of gas-driven compressors of the s-th station. The gas driven compressor will consume some of the gas to provide compressor power, so the outbound flow rate will be slightly lower than the inbound flow rate. Known gas consumption by a factor dgasPreference being given to compression of the electric drive type, in proportion to the compressor powerMachine:
Figure BDA0002235539970000121
Figure BDA0002235539970000122
in the formula:
qt s，consumfuel gas consumption at time t, m for station s3/s；
ns elecThe number of the electrically driven compressors of the s station;
dgasthe air consumption coefficient of the compressor is dimensionless;
qt s-compressor outlet flow rate, m, for the s-th station at the t-th time horizon3/s；
2) When the s-th station is in the t-th time layer, all the compressors are not started, namely kt sWhen 0, the gas is allowed to pass through the compressor station at will:
Figure BDA0002235539970000123
through the pressure regulating and current limiting measures introduced in the compressor regulation, the method is beneficial to optimizing the calculation process, abandoning invalid solutions and accelerating the solving speed of the model.
(3) Minimum run time and minimum downtime constraints:
due to the technical condition limitation of the compressor, the compressor can be restarted after the compressor needs to be kept in a closed state for a certain time, and the time is called as minimum shutdown time; similarly, the compressor can only be in operation when the minimum operating time is not reached. The minimum run-time and minimum downtime constraint models are:
Figure BDA0002235539970000125
Figure BDA0002235539970000126
in the formula:
bt sifor the on-off state of the s-th station compressor i at the t-time level,
when b ist si＝0(i＝1，……，ns comp) When, it indicates that the compressor is in the off state;
when b ist si＝1(i＝1，……，ns comp) When, it means that the compressor is in operation;
ns compthe total number of compressors of the s station;
ton、toffminimum run time and minimum down time, respectively.
The formula (18) and the formula (19) ensure that the compressor must operate at least t after being openedonTime horizon, or at least t must be maintained after compressor shutdownoffShutdown state of time horizon. Through the constraint of minimum running time and minimum shutdown time, frequent switching of the compressor in the optimization scheme can be avoided, the switching cost of the compressor is reduced, and the stable running of a natural gas pipeline system is ensured.
Optionally, the terminal condition is: in the T time frame, the total gas volume at the end point is required to be at least as large as the starting point, i.e.:
Figure BDA0002235539970000131
in the formula:
V1 evolume of gas at the beginning of time T, m3；
VT eVolume of gas at end of time T, m3。
The lower the output of the natural gas pipeline is, the lower the energy consumption is, and the problem that the output is reduced by excessively utilizing the pipe stock in order to reduce the energy consumption can be avoided by adding the terminal condition constraint, so that the continuous and stable operation of a pipeline system is ensured.
And then, solving the transient optimization model through a heuristic algorithm to obtain an optimal feasible solution.
When solving and calculating, firstly, solving by adopting a random generation method, considering the distribution of the trunk pipeline according to the compressor stations, dividing the trunk pipeline into different calculating units: each computing unit consists of a compressor station and pipes connected downstream of the compressor station, between which there are separate delivery stations into and out of which gas can flow. Assuming that there are U computing units in total, each unit is denoted as U (1, 2, … …), U (n)s cmp≠0)。
For a computational unit, to ensure a feasible solution to the piping equation, the appropriate compressor station outlet pressure should first be selected. For compressor station s: n iss cmp＞0，fs(s)＝(i，j)∈EsGiven inlet pressure pt iAnd inlet flow rate qt s+And determining the compressor station outlet pressure.
For a pipe, it is required that the outlet flow rate of each pipe is within a threshold range of the inlet flow rate, and the outlet pressure needs to be within a threshold range of the outlet pressure of the same pipe at the previous time level, i.e. the outlet pressure and flow rate of the pipe are determined in the form for whichfp(p)＝(i，j)∈Ep，
Figure BDA0002235539970000133
Comprises the following steps:
Figure BDA0002235539970000135
in the formula:
clb q，p、cub q，p、clb p，p、cub p，pare all constants;
qt p+、qt p-flow into the pipeline and flow out of the pipeline at the t time layer, m3/s；
pt-1 jThe pipeline outlet pressure at the t-1 time layer is Pa.
By analyzing the piping equation, it can be seen that, given an inlet flow, the piping outlet pressure increases with increasing inlet pressure and the outlet flow decreases with increasing inlet pressure, within an allowable pressure range. Thus, when the outlet pressure and outlet flow are determined, according to the set targets: equations (21), (22) can yield two cases, and assuming that each case yields a return value ret, there are:
(1) if the outlet flow is too small or the outlet pressure is too large, and the outlet pressure of the compressor needs to be reduced, ret is 1;
(2) if the outlet flow is too large or the outlet pressure is too small, the outlet pressure of the compressor needs to be increased, and then ret is 2;
when the flow changes are particularly large, the switching condition can be continuously ensured by a 'flow limiting' measure to avoid the situation of solving failure, namely, the step length delta q of limiting the flow is selected in advance, and when the outlet pressure of the compressor station reaches the upper limit or the lower limit, the flow entering the compressor is determined to be increased or decreased according to the change of the inlet flow relative to the upper time layer, namely:
when in use
Figure BDA0002235539970000141
When it is used, order
Figure BDA0002235539970000142
When in use
Figure BDA0002235539970000143
When it is used, order
Figure BDA0002235539970000144
Based on this, under the given previous t time layer pipeline running state, the feasible solution of the t +1 th time layer pipeline is obtained by adopting a random search method, and the calculation steps for generating the solution are as follows:
(1) inputting the operating parameters of the first t time layers and the gas source conditions of the t +1 th time layer of the pipeline, and letting pcom＝pt+1 in，qcom＝qt+1 in，pdic＝pt p，0；
(2) For each calculation unit, pcom、qcomCalculating the range [ p ] of compressor station outlet pressuresmin，pmax]；
(3) According to the range [ pmin，pmax]And the pressure limiting condition of the pipeline to obtain an upper and a lower bounds p of the initial outlet pressureub，plb；
(4) If p isdic＝pminAnd ret is 1 or pdic＝pmaxAnd ret is 2, the switching condition is judged to obtain qt+1 s，actAnd update the range [ p ]min，pmax]Retrieving the upper and lower bounds p of the searchub，plb；
(5) Solving the pipeline equations in sequence, if the pipeline equations are all in the fluctuation range, entering the step (6), and if not, obtaining a return value ret and returning to the step (4);
(6) if the calculation of all the calculation units is completed, k is obtainedt+1 s、qt+1 s，act、pt+1 s，act、pt+1 p，d、qt+1 p，dAnd if the calculation of all the calculation units is not finished, returning to the step (2).
Optionally, the random search method adopts a Beta distribution, that is:
when ret is 1, let pdic＝plb+V(pdic-plb)；
When ret is 2, let pdic＝pub-V(pub-pdic)。
After the solution is obtained by the random generation method, a group of solutions of the previous t +1 time layers is obtained by using the solution of the previous t time layer, and the number B of generated solutions can be selected in advance. Thus, given an initial solution t, one t ═ 0 can be obtained using the method described above; 1; … …, respectively; a T-level solution set tree, as shown in fig. 4, where the vertices for the T-T 'lines represent the feasible solutions of one previous T' level. If the total number of layers T in the calculated time is larger, the number of times of calculating the solution is exponentially increased along with the time-interval number, so that a depth-first search method (DFS) is adopted for the previous T time-interval solution; specifically, given the previous t-level solution, for the generated B solutions, a "superior" solution is selected for further calculation, and the next "superior" solution in the set of solutions is calculated until the solution and all feasible solutions generated by the solution are explored.
Regarding how to define the "better" solution, in conjunction with equations (21), (22), consider that the "current limiting" effect is the smallest solution selected each time, so that the first found previous T-layer solution has approximately the smallest "current limiting" effect. When the minimum 'current limit' influence solution meets the requirement of the expected 'current limit' range, the other solutions are compared in the expected range to obtain a solution with lower energy consumption. Optionally, the above algorithm is implemented by using a data structure of a stack.
Alternatively, the solution efficiency is improved by discarding the solutions of the following cases:
(1) the energy consumption is large, namely for a feasible solution of the previous T layers (T < T), the total power consumption is Wt; at this time, if a feasible solution is obtained and the total power consumption is WT, the feasible solution in the previous T period is discarded when Wt/T > WT/T, such as Wt/T ≧ 3 WT/T.
(2) The flow fluctuation is large, and the feasible solution that the flow fluctuation is larger than the limit value is directly abandoned; for solutions outside the desired range but within the limited range, the solutions are discarded according to probabilities, such as 5%, 10%, 20%, 50%, 70%, etc., and are discarded directly after the T-period feasible solution is obtained.
(3) When the two situations continuously appear, the node jumps back to a certain previous node. The hopping method is determined based on the remaining number of computations, i.e., after the upper limit of the number of computations is determined in advance, if the remaining number of computations is more at the time of hopping, the number of discarded nodes is more.
The optimal feasible solution, namely the solution with the lowest pipeline overall energy consumption, is obtained by the method.
And finally, the natural gas pipeline operates by utilizing the optimal feasible solution, so that transient optimization is realized.
In a specific embodiment, taking the west-east pipeline 1 as an example, the total length of the pipeline is 3840km, and the designed output is 170 x 108t/a, the pipe diameter is 1016mm, the wall thickness is 17.5mm, and the whole line has 41 stations, wherein 22 gas compression stations and 33 compressors. The length of the tube between each station and the number of compressors starting up each station are shown in FIG. 5. An optimization period is 24 hours from 8 o 'clock to 7 o' clock on the next day, and the time step is 1 hour.
The air source pressure at the starting point of the pipeline is 6.5MPa, the air source pressures of stations No. 1, 15, 22 and 32 are respectively injected into stations No. 4539.9 ten thousand square/day, 437 ten thousand square/day, 194 ten thousand square/day and 750 ten thousand square/day, the pressure and flow parameters under the stable operation state of the pipeline are shown in figure 6, the pressure and flow parameters are the initial conditions of transient optimization, namely the operation parameters at 7 am, the maximum operation pressure of the pipeline is 9.8MPa, the minimum pressure is 5.7MPa, no user exists at the front section of the pipeline (before station No. 14), and the pipeline operates stably. The users of the pipeline are mainly concentrated in the second half, and the total number of 19 stations with gas output is calculated, and the change curve of the gas output of each station along with time is calculated based on the imbalance coefficient of the gas consumption provided by the pipeline company due to the unstable gas consumption of the users, as shown in fig. 7. In FIG. 7, time step 1 is 8 am, time step 24 is 7 am, and it can be seen from FIG. 7 that 8-12 am, 17-22 am the peak of gas consumption, 6 am the peak of gas consumption, and 23-7 am the valley of gas consumption.
Based on the initial conditions and the dynamic change of the gas consumption of each user, the transient operation optimization method provided by the invention is adopted to optimize and obtain the transient optimal operation scheme as shown in the figures 8-16. The optimization model and the algorithm established by the invention adopt a common computer (CPU: COrei5) to calculate, the time is less than 15 minutes, the calculation speed is high, and the actual engineering requirements are met.
The optimization result of the operating pressure is shown in fig. 8, the pressure operating conditions of the time steps 1, 9, 17 and 24 are listed, and it can be seen that due to fluctuation of the air consumption of the user, the operating pressure at each moment also fluctuates, the time steps 1 and 9 are at an air consumption peak, the pressure difference of the whole line is large, the time steps 17 and 24 are at an air consumption valley, and the pressure difference of the whole line is reduced, so that the energy consumption of the operation result of the transient optimization can be obviously reduced.
The full-line flow distribution situation corresponding to the transient optimization result is shown in fig. 9, the full-line flow distribution situations of time steps 1, 9, 17 and 24 are listed, it can be seen that full-line operation pressure fluctuation is caused by non-uniform gas consumption of a user, so that full-line flow fluctuation is caused, the time step 24 is a gas consumption valley, and the full-line flow is the lowest. The result of the inventory optimization is shown in fig. 10, and can be seen by combining fig. 9 and fig. 10:
(1) the flow rate is gradually increased from time step 1, because the user is mainly concentrated after 2900km of the pipeline, the time step 1 is the peak of gas utilization at 8 am, the flow rate of the pipeline is the maximum after 2900km, the flow rate of the pipeline is lower before 2900km, the pipeline storage is the maximum at the moment, and the demand of the user can be met by utilizing the pipeline storage and peak regulation.
(2) The time step 9 is 16 pm, the pipeline flow before 2900km reaches the peak, the flow is gradually reduced after 2900km, and the pipeline pipe is gradually supplemented so as to deal with the next peak of gas utilization.
(3) Time step 17 is 24 am, time step 24 is 7 am, the time period is gas utilization valley, the pipeline flow before 2900km is large, then the gas utilization valley is gradually reduced, the gas utilization valley is minimum at time step 24, and the pipeline flow after 2900km is small. The optimization solution is in a steady increase state after the 16 th time layer, and at this time, although the gas consumption of the user is reduced, in order to maintain the smooth operation of the pipeline, the optimal scheme keeps larger operation flow, so that the gas storage is increased for the user to use next day.
As shown in fig. 11 and 12, it can be seen that the flow rate of the pipeline and the generated friction loss are changed along with the dynamic change of the air consumption of the user, and the outlet pressure of the compressor is dynamically adjusted based on the change of the friction loss of the pipeline, so that a great amount of energy can be saved. However, if the compressor outlet pressure is frequently adjusted, the difficulty of operation increases, and therefore, in combination with the actual situation of the control center, it is preferable that no adjustment is taken when the pressure fluctuation is within 0.2 MPa.
The power optimization results for each compressor station are shown in fig. 13 and 14, which are close to the trend of the compressor outlet pressure.
The results of optimizing the gas consumption of each compressor station are shown in fig. 15 and 16, and the total gas consumption of the optimized operation plan obtained by summarizing the energy consumption of each time tier is 177.47 ten thousand square, and the power consumption is 1.49 × 106kWh, total energy consumption obtained by converting gas consumption into electricity consumption throughout the day is 6.448 x 106kWh. By adopting the steady-state optimization algorithm in the prior art, the total energy consumption of the whole day is 6.654 multiplied by 106Compared with the prior art, the invention reduces the total energy consumption by about 3.1 percent, ensures the stable operation of the pipeline, reduces the energy consumption and saves the cost.
Although the present invention has been described with reference to a preferred embodiment, it should be understood that various changes, substitutions and alterations can be made herein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (10)

1. A natural gas pipeline transient operation optimization method is characterized by comprising the following steps:
establishing a transient optimization model comprising compressor operation energy consumption and compressor switching cost, wherein the transient optimization model selects the outlet pressure of a compressor station and the number of starting-up compressor stations which change along with time as optimization variables;
establishing constraint conditions of the transient optimization model, wherein the constraint conditions comprise transient natural gas pipeline constraint, node constraint, compressor and station site constraint and terminal conditions;
solving the transient optimization model through a heuristic algorithm to obtain an optimal feasible solution;
and the natural gas pipeline operates by utilizing the optimal feasible solution to realize transient optimization.
2. The natural gas pipeline transient operation optimization method of claim 1, wherein the transient optimization model is:
in the formula:
s is the number of compressor stations;
t is the number of time layers;
Pt spower consumed by the compressor at time horizon t, kW;
kt sthe number of compressors operated at the s-th station at time horizon t;
tau is a set time interval;
Ct s，upkw.h consumption of compressor on at station s at time horizon t;
Ct s，downkw.h consumption of compressor shutdown at station s at time horizon t;
kt s，upthe number of the starting-up stations is increased when the station is at the time layer t compared with the last time layer;
kt s，downthe number of the start-up stations is reduced in the s-th station in the time layer t compared with the previous time layer.
3. The natural gas pipeline transient operation optimization method of claim 2, wherein the transient natural gas pipeline constraints are:
neglecting the transient influence of temperature, the motion of the gas in the gas transmission pipeline necessarily satisfies mass conservation and momentum conservation, and the mass conservation and momentum conservation equation is as follows:
Figure FDA0002235539960000012
Figure FDA0002235539960000013
in the formula:
is a defined reduced pressure;
C0is a constant;
q is the flow rate, m3/s；
A is the sectional area of the pipeline, m2；
ρ0Is the density of natural gas in the standard state in kg/m3；
p is pressure, Pa;
g is the acceleration of gravity, m/s2；
h is elevation, m;
λ is the friction coefficient, dimensionless;
d is the pipe diameter m;
the pressure at each node in the pipeline and the flow in the pipeline are both within threshold ranges:
Figure FDA0002235539960000021
Figure FDA0002235539960000022
in the formula:
pmin、pmaxrespectively minimum and maximum pressure, Pa;
pt i、pt jcompressor entering pressure and compressor exiting pressure Pa at the t-th time layer respectively;
qmin、qmaxminimum and maximum flow, m, respectively3/s；
qt i、qt jThe compressor inlet flow and outlet flow m at the t time layer3/s。
4. The natural gas pipeline transient operation optimization method of claim 3, wherein when the numerical solution is performed, the formula (2) and the formula (3) are discretized by using an implicit difference format.
5. The natural gas pipeline transient operation optimization method of claim 2, wherein the node constraints are: each node v in the pipeline must follow the law of conservation of mass and the consumption of fuel gas must be subtracted from the gas flow at the compressor end node:
Figure FDA0002235539960000023
in the formula:
qp+、qp-respectively the flow into the pipeline and the flow out of the pipeline, m3/s；
qs+、qs-Inlet and outlet flows, m, of the s-th compressor, respectively3/s；
fs(t) consumption of fuel gas at the s-th station, m3/s；
Ni p+、Ni p-The number of pipelines is equal, P + represents an inlet, P-represents an outlet and is dimensionless;
Ni s+、Ni s-the number of the compressor stations is equal, S + represents an inlet, S-represents an outlet, and the dimension is not existed;
boundary conditions for gas flow pressure and flow are set at node v:
Figure FDA0002235539960000031
in the formula:
pv tis the pressure at node v at time t, Pa;
pv min、pv maxrespectively the minimum and maximum values of pressure, Pa;
qt vfor the traffic of node v at time t, m3/s；
qt v，min、qt v，maxRespectively the minimum and maximum flow, Pa.
6. The natural gas pipeline transient operation optimization method of claim 2, wherein the compressor and battlefield constraints are:
(1) compressor feasible region:
in the formula:
Ht sthe variable of the pressure head at the s station at the t time layer is m;
hs3、hs2、hs1all are pressure head curve coefficients without dimension;
Qt sis the actual flow rate, m, of each compressor in operation in the s station at the t time horizon3/s；
St sThe rotating speed of the s station at the t time layer is r/min;
ss1、ss2the coefficient of a surge curve is dimensionless;
ss3、ss4the coefficient of the stagnation curve is dimensionless;
Smin、Smaxrespectively the minimum rotating speed and the maximum rotating speed, r/min;
(2) adjusting a compressor:
the flow and the pressure in the pipeline are ensured to be relatively stable along with the change of time by limiting the inlet flow of the compressor station and adjusting the outlet pressure of the compressor station;
1) when the s-th station is in the t-th time layer, when at least one compressor is started:
the compressor flow in equation (9) is a function of the gas pressure, irrespective of the temperature:
Figure FDA0002235539960000033
Figure FDA0002235539960000034
in the formula:
r is a gas constant, J/(mol. K);
Figure FDA0002235539960000041
is the average temperature, K;
qt s，actis the actual flow of the s-th station in the t-th time layer, m3/s；
Figure FDA0002235539960000042
Compressor inlet pressure, Pa, at the s-th time horizon;
qt s+compressor inlet flow, m, for the s-th station at the t-th time horizon3/s；
clb q，s、cub q，sRespectively the minimum value and the maximum value of the current limiting proportion;
in equation (9), the head variation of the compressor is determined by the pressures entering and exiting the compressor:
Figure FDA0002235539960000043
Figure FDA0002235539960000044
in the formula:
γsis the adiabatic expansion coefficient of the compressor of the s station and is dimensionless;
pt s，actis the actual pressure, Pa, of the station at time t;
clb p，sis the minimum value of the voltage regulation proportion;
when there are both gas driven compressors and electrically driven compressors:
Figure FDA0002235539960000045
in the formula:
qt s，consumfuel gas consumption at time t, m for station s3/s；
ns elecThe number of the electrically driven compressors of the s station is dimensionless;
dgasthe air consumption coefficient of the compressor is dimensionless;
qt s-compressor outlet flow rate, m, for the s-th station at the t-th time horizon3/s；
2) When the s-th station is in the t-th time layer, all the compressors are not started, namely kt sWhen 0, the gas is allowed to pass arbitrarily through the compressor station:
Figure FDA0002235539960000047
Figure FDA0002235539960000048
(3) minimum run time and minimum downtime constraints:
Figure FDA0002235539960000049
Figure FDA00022355399600000410
in the formula:
bt sifor the on-off state of the s-th station compressor i at the t-time level,
when b ist si＝0(i＝1，……，ns comp) When, it indicates that the compressor is in the off state;
when b ist si＝1(i＝1，……，ns comp) When, it means that the compressor is in operation;
ns compthe total number of compressors of the s station is dimensionless;
ton、toffminimum run time and minimum down time, s, respectively.
7. The natural gas pipeline transient operation optimization method of claim 6, wherein an outlet pressure of the compressor station is not adjusted when the pressure fluctuations are less than 0.2 MPa.
8. The natural gas pipeline transient operation optimization method of claim 2, wherein the terminal conditions are: in the T time frame, the total gas volume at the end point is required to be at least as large as the starting point, i.e.:
Figure FDA0002235539960000051
in the formula:
V1 evolume of gas at the beginning of time T, m3；
VT eVolume of gas at end of time T, m3。
9. The natural gas pipeline transient operation optimization method of claim 2, wherein when solving the transient optimization model by using the heuristic algorithm, for the pipelines, the outlet flow of each pipeline is required to be within a threshold range of the inlet flow, and the outlet pressure is required to be within a threshold range of the outlet pressure of the same pipeline at the previous time level, that is, the outlet pressure and the flow of the pipeline are determined in the form that, for the pipeline, the outlet pressure and the flow of the pipeline are determined in the last time level
Figure FDA0002235539960000052
fp(p)＝(i，j)∈Ep，
Figure FDA0002235539960000053
Comprises the following steps:
Figure FDA0002235539960000055
in the formula:
clb q，p、cub q，p、clb p，p、cub p，pare all constants;
qt p+、qt p-flow into the pipeline and flow out of the pipeline at the t time layer, m3/s；
pt-1 jThe pipeline outlet pressure at the t-1 time layer is Pa.
10. The natural gas pipeline transient operation optimization method according to claim 9, wherein when the equations (21) and (22) are solved, the data structure of the stack is used for solving.
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