CN113343531B - Method for acquiring dynamic energy flow of electricity-gas integrated energy system based on explicit difference - Google Patents

Method for acquiring dynamic energy flow of electricity-gas integrated energy system based on explicit difference Download PDF

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CN113343531B
CN113343531B CN202110684263.9A CN202110684263A CN113343531B CN 113343531 B CN113343531 B CN 113343531B CN 202110684263 A CN202110684263 A CN 202110684263A CN 113343531 B CN113343531 B CN 113343531B
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王程
吴科宏
毕天姝
王敬尧
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North China Electric Power University
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Abstract

The invention discloses an electricity-gas comprehensive energy system dynamic energy flow obtaining method based on explicit difference, which comprises the steps of firstly obtaining the linear relations between the mass flow and pressure of any node in different areas in a natural gas pipeline difference grid, boundary conditions and initial conditions according to a difference equation of the mass flow and the pressure; constructing a two-port model of mass flow and pressure of any node on the natural gas pipeline differential grid, which are related to boundary conditions and initial conditions, according to the obtained linear relation; and embedding the two-port model into a dynamic energy flow calculation model of the electric-gas comprehensive energy system to obtain the dynamic energy flow of the electric-gas comprehensive energy system. The method converts the partial differential equation of the natural gas pipeline flow into a time domain linear algebraic model, is convenient to embed a time domain optimization model, can greatly reduce the state variable scale and the model calculation cost compared with the traditional finite difference method, and improves the calculation efficiency.

Description

Method for acquiring dynamic energy flow of electricity-gas integrated energy system based on explicit difference
Technical Field
The invention relates to the technical field of power systems, in particular to a method for acquiring dynamic energy flow of an electricity-gas comprehensive energy system based on explicit difference.
Background
The electricity-gas comprehensive energy system is a novel energy system integrating generation, transmission, distribution and consumption of heterogeneous energy such as electric energy and natural gas, can effectively improve the comprehensive energy efficiency and the wind-light power generation consumption level of a user side terminal, is an important component of a clean, low-carbon, safe and efficient energy system in China, and is a beneficial way for realizing the carbon peak reaching, carbon neutralization and medium-long term targets in China. The calculation of the electricity-gas coupling energy flow is the basis for realizing the efficient operation of the regional electricity-gas comprehensive energy system, the active power flow distribution rule of the power system can be approximately depicted by a direct current power flow model with low calculation cost and high accuracy, the energy flow distribution rule of the natural gas system is described by a partial differential equation, and the calculation and analysis cost is high.
At present, the existing research adopts an implicit finite difference method to convert a partial differential equation into a linear algebraic equation to realize the high-precision calculation of the electricity-gas energy flow, but because a large amount of auxiliary variables and constraints are introduced at the same time, the calculation cost is higher; meanwhile, a plurality of research works try to construct a natural gas dynamic model with high precision and low complexity in a frequency domain and a complex frequency domain, but an equivalent conversion condition of a time domain-frequency domain/a complex frequency domain needs to be additionally added during calculation of the electric-gas coupling energy flow, so that the scale of the electric-gas coupling energy flow calculation model is increased, and the calculation efficiency is reduced.
Disclosure of Invention
The invention aims to provide a method for acquiring dynamic energy flow of an electricity-gas integrated energy system based on explicit difference.
The purpose of the invention is realized by the following technical scheme:
an electric-gas integrated energy system dynamic energy flow obtaining method based on explicit difference comprises the following steps:
step 1, obtaining linear relations between mass flow and pressure of any node in different areas in a natural gas pipeline differential grid, boundary conditions and initial conditions according to a differential equation of the mass flow and the pressure;
step 2, constructing a two-port model of mass flow and pressure of any node on the natural gas pipeline differential grid with respect to boundary conditions and initial conditions according to the linear relation obtained in the step 1;
and 3, embedding the two-port model into a dynamic energy flow calculation model of the electric-gas comprehensive energy system to obtain the dynamic energy flow of the electric-gas comprehensive energy system.
According to the technical scheme provided by the invention, the partial differential equation of the natural gas pipeline flow is converted into the time domain linear algebraic model by the method, so that the time domain optimization model is conveniently embedded, and compared with the traditional finite difference method, the method can greatly reduce the state variable scale and the model calculation cost and improve the calculation efficiency.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the description below are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.
Fig. 1 is a schematic flow chart of a method for acquiring a dynamic energy flow of an electric-gas integrated energy system based on explicit difference according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a dynamic three-layer explicit differential grid of a natural gas pipeline according to an embodiment of the present invention;
fig. 3 is a schematic diagram of region division of the differential mesh according to the embodiment of the present invention;
FIG. 4 is a schematic diagram of the differential type of the regions 1 and 2 according to the embodiment of the present invention;
FIG. 5 is a schematic diagram of the differential form of the regions 3 and 4 according to the embodiment of the present invention;
FIG. 6 is a schematic view of an exemplary electro-pneumatic energy system topology according to the present invention;
FIG. 7 is a schematic view of a single pipe according to an exemplary embodiment of the present invention;
FIG. 8 is a graph showing a comparison of single pipe results for two processes in accordance with an exemplary embodiment of the present invention;
FIG. 9 is a schematic view of topology and pipeline parameters of an exemplary natural gas testing system in accordance with the present invention;
FIG. 10 is a schematic view of the gas pressure at each node and the mass flow at the head and tail ends of each pipeline of the natural gas system of the illustrated embodiment of the present invention;
FIG. 11 is a graph illustrating a comparison of the load of the power system and the output of the generator according to an exemplary embodiment of the present invention;
FIG. 12 is a graph illustrating the comparison of gas pressure and gas turbine consumption for a natural gas system according to an exemplary embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention are clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present invention without making any creative effort, shall fall within the protection scope of the present invention.
In the following, embodiments of the present invention will be described in further detail with reference to the accompanying drawings, and as shown in fig. 1, a flow chart of a method for obtaining a dynamic power flow of an electrical-gas integrated energy system based on explicit difference provided by embodiments of the present invention is schematically illustrated, where the method includes:
step 1, obtaining linear relations between mass flow and pressure of any node in different areas in a natural gas pipeline differential grid, boundary conditions and initial conditions according to a differential equation of the mass flow and the pressure;
in this step, first, the second-order hyperbolic partial differential equation of the mass flow is expressed as:
Figure BDA0003123813320000031
the second order hyperbolic partial differential equation for pressure is expressed as:
Figure BDA0003123813320000032
wherein M is natural gas mass flow, pi is natural gas pressure, c is gas sound velocity, lambda is friction coefficient, D is pipeline diameter, x is space variable, t is time variable,
Figure BDA0003123813320000033
is the average flow velocity->
Figure BDA0003123813320000034
Is the sign of the partial derivative;
then, the solution is regionalized into discrete points according to the natural gas pipeline differential grid, as shown in fig. 2, which is a schematic diagram of a dynamic three-layer explicit differential grid of the natural gas pipeline according to an embodiment of the present invention,
Figure BDA0003123813320000035
representing the mass flow M at node (j, k) (x＝j,t＝k) ；
Discretizing the differential equation into a differential equation, approximating a second order partial derivative using a second order center difference quotient, represented as:
Figure BDA0003123813320000036
Figure BDA0003123813320000037
wherein tau is a time infinitesimal; h is a spatial infinitesimal; u (x) j ,t k ) Representing the pressure or mass flow at the point with the space serial number j (j is more than or equal to 0 and less than or equal to N) and the time serial number k (T is more than or equal to 0 and less than or equal to T) in the differential grid;
the first order partial derivative of approximate time using the forward difference quotient is expressed as:
Figure BDA0003123813320000038
substituting equations (3), (4) and (5) into the second-order hyperbolic partial differential equation (1) of the mass flow rate, the algebraic form of the difference with respect to the mass flow rate is obtained as:
Figure BDA0003123813320000041
reusing spatial direction transformations
Figure BDA0003123813320000042
Combined vertical type (5) and (6) are obtained
Figure BDA0003123813320000043
In the formula, K 1 、K 2 、K 3 、K 4 Is a difference coefficient whose value is:
Figure BDA0003123813320000044
by giving boundary conditions and initial conditions, solving a differential expression (8) of a second-order hyperbolic partial differential equation about mass flow, and for a section of natural gas pipeline, assuming that the head-end air pressure and the tail-end mass flow are known, the following steps are provided:
Figure BDA0003123813320000045
in the formula (I), the compound is shown in the specification,
Figure BDA0003123813320000046
denotes the gas pressure pi at the inlet (x = N) of the conduit (x＝N,t) ；Π in (t) is a function of the pipeline inlet gas pressure over time; />
Figure BDA0003123813320000047
Represents the mass flow M at the outlet of the pipe (x = 0) (x＝0,t) ；M out (t) is the initial value of the mass flow at the outlet of the pipeline;
assuming that the system is in a steady state at the initial moment, the mass flow is satisfied
Figure BDA0003123813320000048
Considering that the state quantity of equation (8) contains only mass flow, the pressure boundary condition of equation (9) needs to be converted into a mass flow boundary condition, for which the first-order partial derivative of the forward difference quotient approximation space is used:
Figure BDA0003123813320000049
the united type (1), (5) and (11) equivalently converts the pressure boundary condition (9) into a mass flow boundary condition:
Figure BDA00031238133200000410
in the formula (I), the compound is shown in the specification,
Figure BDA00031238133200000411
indicating the gas pressure pi at the node (j, k) (x＝j,t＝k) ；
The boundary conditions of the three-layer explicit difference equation for the mass flow are thus obtained, namely equations (9), (12); and initial conditions, i.e. formulae (9), (10);
similarly, firstly, according to the second-order hyperbolic partial differential equation (2) of the pressure, the differential algebraic form of the pressure is obtained through the joint type equations (3), (4) and (5):
Figure BDA0003123813320000051
secondly, the initial conditions of the formula (13) are the air pressure of each node at the initial time and the air pressure change rate at the initial time;
the joint type (5) and (11) obtain the air pressure of each node at the initial moment as follows:
Figure BDA0003123813320000052
assuming that the system is in a steady state at the initial time, the air pressure change rate at the initial time is:
Figure BDA0003123813320000053
finally, considering that the state quantity of equation (13) contains only pressure, it is necessary to convert the mass flow boundary into a pressure boundary, which is satisfied at the pipe outlet according to equation (9):
Figure BDA0003123813320000054
boundary conditions for three-layer explicit differential equations for pressure are thus obtained, namely equations (9), (16); and the initial conditions, i.e., equations (14), (15).
Step 2, constructing a two-port model of mass flow and pressure of any node on the natural gas pipeline differential grid with respect to boundary conditions and initial conditions according to the linear relation obtained in the step 1;
in this step, firstly, according to the difference in distance between the point to be solved and the boundary point and the initial point on the natural gas pipeline differential grid, the area to be solved is divided into four areas, as shown in fig. 3, which is a schematic diagram of area division of the differential grid according to the embodiment of the present invention, and the respective areas are:
1) Region 1 (k =1, j < N); 2) Region 2 (k =1,j = n); 3) Region 3 (k is more than or equal to 2 and less than or equal to T, j is more than or equal to 1 and less than N); 4) Region 4 (k ≦ T, j = N, 2 ≦ k);
firstly, a two-port model of mass flow of any node on a natural gas pipeline differential grid with respect to boundary conditions and initial conditions is constructed, specifically:
(1) Region 1: when k =1, j < N, as shown in fig. 4, is a schematic diagram of a differential form of the regions 1 and 2 according to the embodiment of the present invention, and the differential form of the mass flow is as shown in fig. 4 (a), specifically:
Figure BDA0003123813320000055
assuming that the mass flow of each node of the pipeline at the initial moment is equal to the mass flow at the tail end of the pipeline, when k is less than 2,
Figure BDA0003123813320000056
and then, satisfy:
Figure BDA0003123813320000057
substituting formula (18) into formula (17) yields:
Figure BDA0003123813320000061
in the formula (I), the compound is shown in the specification,
Figure BDA0003123813320000062
represents->
Figure BDA0003123813320000063
And &>
Figure BDA0003123813320000064
The linear correlation coefficient of (a) has a value of:
Figure BDA0003123813320000065
(2) And (4) area 2: when k =1,j = n, the differential form of the mass flow rate is as shown in fig. 4 (b), specifically:
Figure BDA0003123813320000066
in the formula:
Figure BDA0003123813320000067
when the region 1 and the region 2 are combined into the region A, and the equations (19) and (20) are observed, when k =1,1 ≦ j ≦ N (i.e., region 1+ region 2), the mass flow satisfies:
Figure BDA0003123813320000068
the matrix form of the formula (21) is
Figure BDA0003123813320000069
In the formula:
Figure BDA00031238133200000610
Figure BDA00031238133200000611
(3) And (4) area 3: when k is more than or equal to 2 and less than or equal to T and j is more than or equal to 1 and less than N, as shown in FIG. 5, the differential form of the areas 3 and 4 in the embodiment of the present invention is schematically shown, and the differential form of the mass flow is shown in FIG. 5 (a), and satisfies the following conditions:
Figure BDA00031238133200000612
(4) And (4) region: when k is 2 ≦ T, j = N, the differential form of the mass flow rate satisfies, as shown in fig. 5 (b):
Figure BDA00031238133200000613
when the area 3 and the area 4 are combined into an area B, and the formula (23) and the formula (24) are observed, when k is more than or equal to 2 and less than or equal to T and j is more than or equal to 1 and less than or equal to N (namely the area 3+ the area 4), the mass flow satisfies:
Figure BDA00031238133200000614
/>
so far, the two-port form of the mass flow of the area A and the area B is obtained, the area A and the area B are combined, when k is more than or equal to 1 and less than or equal to T, j is more than or equal to 1 and less than or equal to N, the mass flow satisfies the following conditions:
Figure BDA0003123813320000071
in the formula, A j ,B j Matrix of difference coefficients, m, of (T x T) respectively j The mass flow for a node with spatial index j is a (T × 1) matrix:
Figure BDA0003123813320000072
equation (26) is a two-port model of the mass flow of any node on the natural gas pipeline differential grid with respect to the boundary condition and the initial condition;
then, a two-port model of the pressure of any node on the natural gas pipeline differential grid with respect to the boundary condition and the initial condition is constructed, specifically:
(1) Region 1: when k =1, j < N, it is found from the differential form of the pressure that:
Figure BDA0003123813320000073
when k =0 and j is equal to or greater than 1 and equal to or less than N, the air pressure at each node at the initial time is satisfied as shown in equation (27):
Figure BDA0003123813320000074
in the formula
Figure BDA0003123813320000075
The rate of change of the gas pressure at the initial time and the boundary conditions at the outlet of the pipeline are brought into (27) to obtain:
Figure BDA0003123813320000076
the formula (29) is arranged as
Figure BDA0003123813320000077
Wherein:
Figure BDA0003123813320000081
the matrix form of equation (30) is:
Figure BDA0003123813320000082
in the formula:
Figure BDA0003123813320000083
Figure BDA0003123813320000084
(2) Region 2: when k =1,j = n, the pressure satisfies:
Figure BDA0003123813320000085
in the formula:
Figure BDA0003123813320000086
(3) Region 3: when k is more than or equal to 2 and less than or equal to T and j is more than or equal to 1 and less than N, the pressure satisfies the following conditions:
Figure BDA0003123813320000087
(4) Region 4: when k is more than or equal to 2 and less than or equal to T, j = N, the pressure satisfies:
Figure BDA0003123813320000088
combining 4 areas, and when k is more than or equal to 1 and less than or equal to T and j is more than or equal to 1 and less than or equal to N, the pressure is satisfied as follows:
Figure BDA0003123813320000089
in the formula, C j ,D j Difference coefficient matrices, n, of (T x T) respectively j The pressure at a node with spatial index j is a (T1) matrix:
Figure BDA00031238133200000810
thus, a two-port model of the pressure of any node on the natural gas pipeline differential grid with respect to the boundary condition and the initial condition is obtained, namely equation (35).
In the specific implementation, because the state quantities of the head end and the tail end of the natural gas pipeline are only related to the boundary conditions and the initial conditions, the time domain two-port model does not contain state variables of other space micro elements, and compared with a traditional finite difference method, the state variable scale and the model calculation cost are greatly reduced.
In addition, the two-port model of the mass flow and the pressure of any node on the natural gas pipeline differential grid with respect to the boundary condition and the initial condition can be further represented by combining:
Figure BDA0003123813320000091
when the initial conditions are head end air pressure and tail end mass flow, the head end mass flow and the tail end air pressure of the pipeline meet the following conditions:
Figure BDA0003123813320000092
thereby obtaining a time domain two-port model (37) of the gas pressure and the mass flow at the head end and the tail end of the natural gas pipeline.
And 3, embedding the two-port model into a dynamic energy flow calculation model of the electric-gas comprehensive energy system to obtain the dynamic energy flow of the electric-gas comprehensive energy system.
In this step, the operation cost of the regional electricity-gas integrated energy system includes the traditional unit power generation cost and the natural gas source gas supply cost, and the objective function of the dynamic energy flow is the minimum operation cost, namely:
Figure BDA0003123813320000093
in the formula (I), the compound is shown in the specification,
Figure BDA0003123813320000094
calculating a set of time periods for the powerflow; />
Figure BDA0003123813320000095
Is a traditional unit set; c. C gc Is the g th c Cost coefficient of the conventional unit; />
Figure BDA0003123813320000096
Is the g th c The conventional unit is in time period t e Internal output forces; />
Figure BDA0003123813320000097
Calculating the number of time segments for the natural gas energy flow; />
Figure BDA0003123813320000098
Is a medium-pressure gas source set; c. C w The cost coefficient of the w gas source; />
Figure BDA0003123813320000099
For the w-th gas source in the time period t g Mass flow rate inside;
for example, as shown in fig. 6, a topological schematic diagram of an electric-gas integrated energy system according to an example of the present invention is composed of a 13-node natural gas system and a 12-node power system, and includes three power generators (one conventional thermal power generating unit and two gas power generating units, which are respectively connected to nodes 8 and 9 of the natural gas system); 10 electrical loads; three conventional gas loads; two gas turbine gas loads.
The energy flow model of the natural gas system satisfies the following constraints:
(1) Pipeline air pressure-mass flow constraint:
according to the time domain two-port model of the gas pressure and the mass flow at the head end and the tail end of the natural gas pipeline, the gas pressure and the mass flow at the head end and the tail end of the p-th pipeline meet the following conditions:
Figure BDA0003123813320000101
in the formula (I), the compound is shown in the specification,
Figure BDA0003123813320000102
respectively representing mass flow and air pressure matrixes at the head end of the p-th pipeline in all time periods;
Figure BDA0003123813320000103
respectively representing the mass flow and the air pressure matrix of the p-th pipeline tail end in all time periods;
(2) Air pressure and mass flow restraint of an air source:
Figure BDA0003123813320000104
(3) Node mass flow balance constraint:
for natural gas node n g And the sum of the mass flow of all pipelines connected with the node and the net injection mass flow of the node is zero:
Figure BDA0003123813320000105
in the formula, n g Is a natural gas node;
Figure BDA0003123813320000106
to access the skyGas node n g The set of gas sources of (a); />
Figure BDA0003123813320000107
Is the end and natural gas node n g A set of connected pipes; />
Figure BDA0003123813320000108
Is a head end and natural gas node n g A set of connected pipes; d is an element of D g (n g ) To be located at natural gas node n g A load set of (a);
(4) And (3) node air pressure constraint:
Figure BDA0003123813320000109
in the formula (I), the compound is shown in the specification,Π、
Figure BDA00031238133200001010
the lower limit and the upper limit of the natural gas node air pressure are set;
the power flow model of the power system satisfies the following constraints:
because the power network of the regional electric-gas comprehensive energy system belongs to a power distribution network, the topology of the regional electric-gas comprehensive energy system is generally radial, and the power Flow of the power system can be approximated by combining a Branch Flow power Flow model and a second-order conical convex relaxation technology;
(1) Node active and reactive power balance constraint:
Figure BDA00031238133200001011
Figure BDA00031238133200001012
in the formula, n e Is a power system node;
Figure BDA00031238133200001013
for the node n of the power system e Tradition ofThe set of the units;
Figure BDA00031238133200001014
for node n of the power system e A set of gas turbine units; />
Figure BDA00031238133200001015
For node n of the power system e A set of electrical loads; />
Figure BDA0003123813320000111
For the line head section and the node n of the power system e A set of connected power lines of (c); />
Figure BDA0003123813320000112
For line end and power system node n e A set of connected power lines; />
Figure BDA0003123813320000113
The active power and the reactive power of the traditional unit are obtained; />
Figure BDA0003123813320000114
The active power and the reactive power of the thermal power generating unit are obtained; />
Figure BDA0003123813320000115
Active and reactive loads for the power system; p lt 、Q lt The active power and the reactive power of the line are obtained; r is a radical of hydrogen l 、x l The resistance and reactance of the circuit are shown; i is lt Is the square of the branch current; />
Figure BDA0003123813320000116
Is the ground conductance of the node;
Figure BDA0003123813320000117
is the square of the node voltage;
(2) The line voltage drop equation and the line current equation of the second-order cone-convex relaxation are as follows:
Figure BDA0003123813320000118
Figure BDA0003123813320000119
in the formula, v l-t Is the line end voltage; v. of l+t Is the line first section voltage;
(3) And (3) generator capacity constraint:
the active power and reactive power upper and lower limits of the generator are constrained as follows:
Figure BDA00031238133200001110
in the formula (I), the compound is shown in the specification,
Figure BDA00031238133200001111
for node n of the power system e A set of generator sets;P、/>
Figure BDA00031238133200001112
the upper limit and the lower limit of active power of the generator are set;Q、/>
Figure BDA00031238133200001113
the upper limit and the lower limit of the reactive power of the generator are set;
the constraints after the electrical-to-electrical coupling are:
(1) The active power and gas consumption of gas power generation are restricted:
Figure BDA00031238133200001114
in the formula, eta is energy conversion efficiency;
(2) The time coupling constraint of the power energy flow calculation variable and the natural gas energy flow calculation variable is as follows:
Figure BDA00031238133200001115
in the formula (I), the compound is shown in the specification,
Figure BDA00031238133200001116
is an upper rounding function; and N is the ratio of the time resolution of the electric and gas decision variables.
The following describes the advantages of the above dynamic power flow acquisition method with specific examples:
1) The results of the calculations of the Implicit finite Difference Method (IDM) and the Method described in this example (Explicit Difference model, explicit Difference Method, EDM) were compared for a single natural gas pipeline. Fig. 7 is a schematic diagram of a single pipeline according to an exemplary embodiment of the present invention, where the length of the natural gas pipeline is 7783 m, the diameter of the pipeline is 0.5 m, the head-end pressure is maintained at a constant pressure of 0.4MPa, and the end load is changed at intervals of 150 seconds. The lengths of the defined temporal and spatial bins are 0.5 seconds and 181 meters, respectively.
Fig. 8 is a schematic diagram showing comparison of results of a single pipeline in two methods according to the example of the present invention, and when the mass flow at the outlet of the pipeline changes in a step manner, the mass flow at the inlet obtained by the two calculation methods does not change immediately, and the change has an obvious "time lag" phenomenon. In the aspect of calculation time, a computer configured as an Intel i5-8400 2.8ghz, 169b memory is used, the calculation time of the implicit differential model is 27.36 seconds, while the calculation time of the time domain two-port model provided by the invention is 1.07 seconds, and the speed is increased by more than 25 times, so that the advantage of the method in the aspect of calculation efficiency is embodied.
2) The validity of the natural gas pipeline time domain two-port model constructed in the text is verified by adopting a 4-node natural gas system algorithm, and meanwhile, the time consumption is calculated by comparing with an implicit differential model, as shown in fig. 9, a schematic diagram of the topology and pipeline parameters of the natural gas testing system of the embodiment of the invention is shown, wherein a node 1 is a gas source (GW 1), the gas pressure is constant at 0.4MPa, and nodes 3 and 4 are gas loads (GL 1 and GL 2).
Fig. 10 is a schematic diagram of dynamic curves of pressure at each node and mass flow at the head end and the tail end of each pipeline of the natural gas system according to the example of the present invention, where boundary conditions are pi 1, md1, and Md2, which respectively represent pressure at node 1, and loads Md1 and Md2 in the natural gas system. II 2-EDM, II 3-EDM and II 4-EDM respectively represent the air pressure of the nodes 2, 3 and 4 calculated according to the EDM; min1-EDM, min2-EDM, and Min3-EDM represent mass flow rates into the pipes 1#, 2#, and 3# calculated by EDM, respectively. By taking IDM as comparison, the maximum deviation of the node air pressure and the pipeline mass flow obtained by EDM solution with the same differential precision is 0.29 percent and 0.47 percent respectively. It should be noted that the two calculation results are not identical because the difference formats used by the two methods are different, and in order to eliminate the influence of the boundary condition values on the calculation speed, several groups of loads are randomly generated, and the two methods are respectively used for calculating the natural gas system load flow, and the lengths of the limited time and space elements are 1 second and 362 meters respectively. The average time consumption of the method is 4.21 seconds, while the average time consumption of the implicit differential model is 131.38 seconds, which represents the great advantage of the technology in the aspect of solving efficiency.
3) Dynamic energy flow calculation example for regional electricity-gas comprehensive energy system
The topology of the regional electricity-gas comprehensive energy system is shown in fig. 6, and the regional electricity-gas comprehensive energy system is composed of a 13-node natural gas system and a 12-node electric power system and comprises three generators; a traditional thermal power generating unit. The two gas turbine units are respectively connected with natural gas system nodes 8 and 9; a gas well; the system comprises ten electric loads; three conventional gas loads; two gas turbine gas loads. The time interval length of the electric power system model is selected to be 15 minutes, energy flow calculation results of the electric-gas comprehensive energy system in the region within 6 hours are considered, the time interval and the space interval are 24 time intervals, the length of a limited time infinitesimal and the length of a limited space infinitesimal in the natural gas system model are respectively 9 seconds and 3303 meters, 40000 variables are obtained, 56450 constraint conditions are obtained, and the model solving time is 8.66 seconds.
Fig. 11 is a graph showing the comparison between the load of the power system and the output of the generator according to the example of the present invention, fig. 12 is a graph showing the comparison between the gas pressure of the natural gas system and the gas consumption of the gas turbine according to the example of the present invention, and fig. 11 and 12 show that: the method provided by the embodiment of the invention can rapidly depict the dynamic energy flow of the electricity-gas integrated energy system, and the dynamic model can reflect the dynamic process of the air pressure in the natural gas system and can better reflect the real condition of the operation of the combined system.
It is noted that those skilled in the art will recognize that embodiments of the present invention are not described in detail herein.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (3)

1. An explicit differential-based method for acquiring dynamic power flow of an electric-gas integrated energy system, the method comprising:
step 1, obtaining linear relations between mass flow and pressure of any node in different areas in a natural gas pipeline differential grid, boundary conditions and initial conditions according to a differential equation of the mass flow and the pressure;
the process of the step 1 specifically comprises the following steps:
first, the second order hyperbolic partial differential equation of mass flow is expressed as:
Figure FDA0004126506920000011
the second order hyperbolic partial differential equation of pressure is expressed as:
Figure FDA0004126506920000012
wherein M is natural gas mass flow, pi is natural gas pressure, c is gas sound velocity, lambda is friction coefficient, D is pipeline diameter, x is space variable, t is time variable,
Figure FDA0004126506920000013
is the average flow velocity->
Figure FDA0004126506920000014
Is the sign of the partial derivative;
and then regionalizing the solution into discrete points according to the natural gas pipeline differential grid, wherein:
Figure FDA0004126506920000015
representing the mass flow M at node (j, k) (x＝j,t＝k) ；
Discretizing the differential equation into a differential equation, approximating a second order partial derivative using a second order center difference quotient, represented as:
Figure FDA0004126506920000016
Figure FDA0004126506920000017
wherein tau is a time infinitesimal; h is a spatial infinitesimal; u (x) j ,t k ) Representing the pressure or mass flow at the point with the space serial number j (j is more than or equal to 0 and less than or equal to N) and the time serial number k (T is more than or equal to 0 and less than or equal to T) in the differential grid;
the first order partial derivative of approximate time using the forward difference quotient is expressed as:
Figure FDA0004126506920000018
substituting equations (3), (4) and (5) into the second-order hyperbolic partial differential equation (1) for mass flow yields the algebraic form of the difference with respect to mass flow as:
Figure FDA0004126506920000019
reusing spatial direction transformations
Figure FDA0004126506920000021
Combined vertical type (5) and (6) are obtained
Figure FDA0004126506920000022
In the formula, K 1 、K 2 、K 3 、K 4 Is a difference coefficient whose value is:
Figure FDA0004126506920000023
/>
by giving boundary conditions and initial conditions, solving a differential expression (8) of a second-order hyperbolic partial differential equation about mass flow, and for a section of natural gas pipeline, assuming that the head-end air pressure and the tail-end mass flow are known, the following steps are provided:
Figure FDA0004126506920000024
in the formula (I), the compound is shown in the specification,
Figure FDA0004126506920000025
denotes the gas pressure pi at the inlet (x = N) of the conduit (x＝N,t) ；Π in (t) is a function of the pipeline inlet gas pressure over time; />
Figure FDA0004126506920000026
Represents the mass flow M at the outlet of the pipe (x = 0) (x＝0,t) ；M out (t) is an initial value of mass flow at the outlet of the pipeline;
assuming that the system is in a steady state at the initial moment, the mass flow is satisfied
Figure FDA0004126506920000027
Considering that the state quantity of equation (8) contains only mass flow, the pressure boundary condition of equation (9) needs to be converted into a mass flow boundary condition, for which the first order partial derivative of the forward difference quotient approximation space is used:
Figure FDA0004126506920000028
the united type (1), (5) and (11) equivalently converts the pressure boundary condition (9) into a mass flow boundary condition:
Figure FDA0004126506920000029
in the formula (I), the compound is shown in the specification,
Figure FDA00041265069200000210
indicating the gas pressure pi at the node (j, k) (x＝j,t＝k) ；
The boundary conditions of the three-layer explicit difference equation for the mass flow are thus obtained, namely equations (9), (12); and initial conditions, i.e. formulae (9), (10);
in a similar way, firstly, according to a second-order hyperbolic partial differential equation (2) of the pressure, a differential algebraic form of the pressure is obtained in a joint type (3), (4) and (5):
Figure FDA0004126506920000031
secondly, the initial conditions of the formula (13) are the air pressure of each node at the initial time and the air pressure change rate at the initial time;
the joint type (5) and (11) obtain the air pressure of each node at the initial moment as follows:
Figure FDA0004126506920000032
assuming that the system is in a steady state at the initial time, the air pressure change rate at the initial time is:
Figure FDA0004126506920000033
finally, considering that the state quantity of equation (13) contains only pressure, it is necessary to convert the mass flow boundary into a pressure boundary, which is satisfied at the pipe outlet according to equation (9):
Figure FDA0004126506920000034
boundary conditions for three-layer explicit differential equations for pressure are thus obtained, namely equations (9), (16); and initial conditions, i.e. formulae (14), (15);
step 2, constructing a two-port model of mass flow and pressure of any node on the natural gas pipeline differential grid with respect to boundary conditions and initial conditions according to the linear relation obtained in the step 1;
in step 2, according to the difference in distance between the point to be solved and the boundary point and the initial point on the natural gas pipeline differential grid, the area to be solved is divided into four areas, which are:
1) Region 1 (k =1, j < N); 2) Region 2 (k =1,j = n); 3) Region 3 (k is more than or equal to 2 and less than or equal to T, j is more than or equal to 1 and less than N); 4) Region 4 (2 ≦ k ≦ T, j = N);
firstly, a two-port model of mass flow of any node on a natural gas pipeline differential grid with respect to boundary conditions and initial conditions is constructed, specifically:
(1) Region 1: when k =1, j < N, the differential form of the mass flow is in particular:
Figure FDA0004126506920000035
assuming that the mass flow of each node of the pipeline at the initial moment is equal to the mass flow at the tail end of the pipeline, when
Figure FDA0004126506920000036
And then, satisfy:
Figure FDA0004126506920000037
substituting formula (18) into formula (17) yields:
Figure FDA0004126506920000041
in the formula (I), the compound is shown in the specification,
Figure FDA0004126506920000042
represents->
Figure FDA0004126506920000043
And &>
Figure FDA0004126506920000044
The linear correlation coefficient of (a) has a value of:
Figure FDA0004126506920000045
(2) And (4) area 2: when k =1,j = n, the differential form of the mass flow rate is specifically:
Figure FDA0004126506920000046
in the formula:
Figure FDA0004126506920000047
when the region 1 and the region 2 are combined into the region a and the equations (19) and (20) are observed, when k =1,1 ≦ j ≦ N, that is, the region 1+ the region 2, the mass flow satisfies:
Figure FDA0004126506920000048
the matrix form of the formula (21) is
Figure FDA0004126506920000049
In the formula:
Figure FDA00041265069200000410
Figure FDA00041265069200000411
(3) Region 3: when k is more than or equal to 2 and less than or equal to T and j is more than or equal to 1 and less than N, the difference form of the mass flow satisfies the following conditions:
Figure FDA00041265069200000412
(4) Region 4: when k is more than or equal to 2 and less than or equal to T and j = N, the difference form of the mass flow satisfies the following conditions:
Figure FDA00041265069200000413
combining the area 3 and the area 4 into an area B, and observing the formula (23) and the formula (24), when k is more than or equal to 2 and less than or equal to T and j is more than or equal to 1 and less than or equal to N, namely the area 3+ the area 4, the mass flow satisfies:
Figure FDA00041265069200000414
so far, the two-port form of the mass flow of the area A and the area B is obtained, the area A and the area B are combined, when k is more than or equal to 1 and less than or equal to T, j is more than or equal to 1 and less than or equal to N, the mass flow satisfies the following conditions:
Figure FDA0004126506920000051
in the formula, A j ,B j Difference coefficient matrices, m, of (T × T) respectively j The mass flow for a node with spatial index j is a (T × 1) matrix:
Figure FDA0004126506920000052
equation (26) is a two-port model of the mass flow of any node on the natural gas pipeline differential grid with respect to the boundary condition and the initial condition;
then, a two-port model of the pressure of any node on the natural gas pipeline differential grid with respect to the boundary condition and the initial condition is constructed, specifically:
(1) Region 1: when k =1,j < N, as can be seen from the differential form of the pressure, the following is satisfied:
Figure FDA0004126506920000053
when k =0 and j is equal to or greater than 1 and equal to or less than N, the air pressure at each node at the initial time is satisfied as shown in equation (27):
Figure FDA0004126506920000054
in the formula
Figure FDA0004126506920000055
The rate of change of the gas pressure at the initial time and the boundary conditions at the outlet of the pipeline are brought into (27) to obtain:
Figure FDA0004126506920000056
the formula (29) is arranged as
Figure FDA0004126506920000057
Wherein:
Figure FDA0004126506920000058
the matrix form of equation (30) is:
Figure FDA0004126506920000061
in the formula:
Figure FDA0004126506920000062
Figure FDA0004126506920000063
(2) Region 2: when k =1,j = n, the pressure satisfies:
Figure FDA0004126506920000064
in the formula:
Figure FDA0004126506920000065
(3) Region 3: when k is more than or equal to 2 and less than or equal to T and j is more than or equal to 1 and less than N, the pressure satisfies the following conditions:
Figure FDA0004126506920000066
(4) Region 4: when k is more than or equal to 2 and less than or equal to T, j = N, the pressure satisfies:
Figure FDA0004126506920000067
combining 4 areas, and when k is more than or equal to 1 and less than or equal to T and j is more than or equal to 1 and less than or equal to N, the pressure satisfies the following conditions:
Figure FDA0004126506920000068
in the formula, C j ,D j Difference coefficient matrices, n, of (T x T) respectively j The pressure at a node with spatial index j is a (T1) matrix:
Figure FDA0004126506920000069
thus, a two-port model of the pressure of any node on the natural gas pipeline differential grid with respect to the boundary condition and the initial condition is obtained, namely an equation (35);
and step 3, embedding the two-port model into a dynamic energy flow calculation model of the electric-gas integrated energy system to obtain the dynamic energy flow of the electric-gas integrated energy system.
2. The method for acquiring dynamic power flow of an electric-gas integrated energy system based on explicit difference as claimed in claim 1, wherein in step 2, the two-port model of mass flow and pressure of any node on the natural gas pipeline difference grid with respect to boundary condition and initial condition is further represented by:
Figure FDA0004126506920000071
when the initial conditions are head end air pressure and tail end mass flow, the head end mass flow and the tail end air pressure of the pipeline meet the following conditions:
Figure FDA0004126506920000072
thereby obtaining a time domain two-port model (37) of the gas pressure and the mass flow at the head end and the tail end of the natural gas pipeline.
3. The method for acquiring the dynamic energy flow of the electric-gas integrated energy system based on the explicit difference as claimed in claim 2, wherein in step 3, the operation cost of the regional electric-gas integrated energy system includes the conventional unit power generation cost and the natural gas source gas supply cost, and the objective function of the dynamic energy flow is to minimize the operation cost, that is:
Figure FDA0004126506920000073
in the formula (I), the compound is shown in the specification,
Figure FDA0004126506920000074
calculating a set of time periods for the powerflow; />
Figure FDA0004126506920000075
Is a traditional unit set; c. C gc Is the g th c Cost coefficient of the conventional unit; />
Figure FDA0004126506920000076
Is the g th c The conventional unit is in time period t e Internal output force; />
Figure FDA0004126506920000077
As natural gasCalculating the number of time segments by the energy flow; />
Figure FDA00041265069200000713
Is a medium-pressure gas source set; c. C w The cost coefficient of the w gas source; />
Figure FDA0004126506920000078
For the w gas source during the time period t g Mass flow rate inside;
the energy flow model of the natural gas system satisfies the following constraints:
(1) Pipeline air pressure-mass flow constraint:
according to the time domain two-port model of the head end and tail end air pressure and mass flow of the natural gas pipeline, the head end and tail end air pressure and mass flow of the p-th pipeline meet the following requirements:
Figure FDA0004126506920000079
in the formula (I), the compound is shown in the specification,
Figure FDA00041265069200000710
respectively representing mass flow and air pressure matrixes at the head end of the p-th pipeline in all time periods; />
Figure FDA00041265069200000711
Respectively representing the mass flow and the air pressure matrix of the p-th pipeline tail end in all time periods;
(2) Air pressure and mass flow restraint of an air source:
Figure FDA00041265069200000712
(3) Node mass flow balance constraint:
for natural gas node n g And the sum of the mass flow of all pipelines connected with the node and the net injection mass flow of the node is zero:
Figure FDA0004126506920000081
in the formula, n g Is a natural gas node;
Figure FDA0004126506920000082
for accessing natural gas node n g The gas source set of (2); />
Figure FDA0004126506920000083
Is the end and natural gas node n g A set of connected pipes; />
Figure FDA0004126506920000084
Is a head end and natural gas node n g A set of connected pipes; d is an element of D g (n g ) To be located at natural gas node n g A load set of (a);
(4) And (3) node air pressure constraint:
Figure FDA0004126506920000085
in the formula (I), the compound is shown in the specification,Π、
Figure FDA0004126506920000086
the lower limit and the upper limit of the natural gas node air pressure are set; />
The power flow model of the power system satisfies the following constraints:
(1) Node active and reactive power balance constraint:
Figure FDA0004126506920000087
Figure FDA0004126506920000088
in the formula, n e Is a power system node;
Figure FDA0004126506920000089
for node n of the power system e A set of legacy units; />
Figure FDA00041265069200000810
For node n of the power system e A set of gas turbine units; />
Figure FDA00041265069200000811
For node n of the power system e A set of electrical loads;
Figure FDA00041265069200000812
for the line head section and the node n of the power system e A set of connected power lines of (c); />
Figure FDA00041265069200000813
For line end and power system node n e A set of connected power lines; />
Figure FDA00041265069200000814
The active power and the reactive power of the traditional unit are obtained; />
Figure FDA00041265069200000815
Active power and reactive power of the thermal power generating unit; />
Figure FDA00041265069200000816
Active and reactive loads for the power system; p lt 、Q lt The active power and the reactive power of the line are obtained; r is l 、x l The resistance and reactance of the circuit are shown; I.C. A lt Is the square of the branch current; />
Figure FDA00041265069200000817
Is the ground conductance of the node; />
Figure FDA00041265069200000818
Is the square of the node voltage;
(2) The line voltage drop equation and the line current equation of the second-order cone-convex relaxation are as follows:
Figure FDA00041265069200000819
Figure FDA0004126506920000091
in the formula, v l-t Is the line end voltage; v. of l+t Is the line first section voltage;
(3) And (3) generator capacity constraint:
the active power and reactive power upper and lower limits of the generator are constrained as follows:
Figure FDA0004126506920000092
Figure FDA0004126506920000093
in the formula (I), the compound is shown in the specification,
Figure FDA0004126506920000094
for the node n of the power system e A set of generator sets;P、/>
Figure FDA0004126506920000095
the upper limit and the lower limit of the active power of the generator are set;Q、/>
Figure FDA0004126506920000096
the reactive power of the generator,A lower limit;
the constraints after the electrical-to-electrical coupling are:
(1) The active power and gas consumption of gas power generation are restricted:
Figure FDA0004126506920000097
in the formula, eta is energy conversion efficiency;
(2) The time coupling constraint of the power energy flow calculation variable and the natural gas energy flow calculation variable is as follows:
Figure FDA0004126506920000098
/>
in the formula (I), the compound is shown in the specification,
Figure FDA0004126506920000099
a rounding function is applied to the upper part; and N is the ratio of the time resolution of the electric and gas decision variables. />
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