CN112417698A - Dynamic two-port thermodynamic system model based on quality adjustment - Google Patents

Dynamic two-port thermodynamic system model based on quality adjustment Download PDF

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CN112417698A
CN112417698A CN202011336938.2A CN202011336938A CN112417698A CN 112417698 A CN112417698 A CN 112417698A CN 202011336938 A CN202011336938 A CN 202011336938A CN 112417698 A CN112417698 A CN 112417698A
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顾伟
张苏涵
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Abstract

The invention discloses a dynamic two-port thermodynamic system model based on quality adjustment, which comprises: 10) establishing a matrix uniform format based on a thermodynamic system dynamic model of a differential format; 20) determining the port type of a dynamic thermodynamic system in a water supply network, and establishing a dynamic two-port thermodynamic system model in the water supply network; 30) determining the port type of the dynamic thermodynamic system in the backwater net, and establishing a dynamic two-port thermodynamic system model in the backwater net. The model establishes direct relation between the boundary condition and the initial condition and the state evolution of the thermodynamic system, quantitatively describes the influence degree of the boundary condition and the initial condition on the state distribution in the thermodynamic system, is favorable for intuitively analyzing the operation flexibility and the safety of the thermodynamic system, and can depict the response of the system to external disturbance.

Description

Dynamic two-port thermodynamic system model based on quality adjustment
Technical Field
The invention belongs to the field of energy system modeling and operation analysis, and particularly relates to a dynamic two-port thermodynamic system model based on quality regulation.
Background
The gradual increase of energy consumption and environmental pressure promote the change of low-carbon green energy network technology, and cities serve as main bodies of energy consumption and change, and forward multi-energy-flow and multi-dynamic complex energy networks are changed. The centralized heat supply power system serves as an important component of the urban energy network, and the comprehensive utilization efficiency of the energy system and the consumption capacity of renewable energy can be remarkably improved through interconnection and intercommunication and energy optimization management of the centralized heat supply power system, the power system and the natural gas system. The time scales of operation and management of different energy networks are greatly different, real-time, reliable and consistent network information needs to be acquired based on an accurate simulation model and technology, however, as the multi-energy network belongs to management and operation of different companies, interactive information is very limited, and attention needs to be paid to information protection in the process of joint simulation and operation optimization.
The simulation calculation of the heat supply pipe network is essentially to define a group of state variables to describe the key characteristics of the system, and then to analyze the system mechanism to obtain the change process of all the state variables under given excitation. Because the heat supply pipe network model is a group of nonlinear partial differential equations, the existing mainstream method is to differentiate the pipe model by space-time segmentation, and to perform recursive calculation on the state distribution in the system according to boundary conditions and initial conditions. However, to ensure the computational efficiency, the number of segments required on each pipeline is generally large, so that the whole recursion process is low in computational efficiency, and it is difficult to visually and quantitatively characterize the response degree of the state quantity in the thermodynamic system to the external excitation.
In view of the above disadvantages, it is necessary to develop a dynamic two-port thermodynamic system model that considers both the physical characteristics of the system and the network topology characteristics from the modeling perspective, and establish a direct connection between the external excitation and the state quantity in the system, so as to describe the dynamic process of the system quickly and accurately, which is more beneficial to the simulation calculation and the optimized operation of multiple subjects, and conforms to the application conditions in the actual engineering.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: aiming at the problems that the existing model analysis depends on a recursion relation, the calculation efficiency is low, the response degree of state quantity in a thermodynamic system to external excitation is difficult to visually and quantitatively depict, and the like, the method provides a dynamic two-port thermodynamic system model based on quality adjustment. And then, converting the traditional recursive pipeline temperature distribution calculation process into a matrix type unified format by introducing a partial constant vector and a constant coefficient matrix. On the basis, a correlation matrix describing the topological connection relation in the system is established, and the correlation matrix and the pipeline flow are segmented according to the precision requirement. And finally, combining the segmented correlation matrix, the segmented pipeline flow and the unified matrix pipeline temperature distribution equation with the node temperature equation to form a two-port model only comprising an input port and an output port.
In order to solve the technical problem, the technical scheme adopts a dynamic two-port thermodynamic system model based on quality adjustment, and the method comprises the following steps:
step 10), establishing a matrix uniform format based on a thermodynamic system dynamic model of a differential format;
step 20) determining the port type of a dynamic thermodynamic system in the water supply network, and establishing a dynamic two-port thermodynamic system model in the water supply network;
and step 30) determining the port type of the dynamic thermodynamic system in the backwater network, and establishing a dynamic two-port thermodynamic system model in the backwater network.
As a further description of the present invention, the step 10) specifically includes:
step 101) establishing a thermodynamic system dynamic model, including a pipeline temperature distribution equation in a partial differential format and a linear node temperature mixed equation:
Figure BDA0002797434510000021
(∑mout)Tout＝(∑minTin) \*MERGEFORMAT (2)
wherein T is the pipeline temperature; m is the mass flow of the pipeline, v is the flow velocity of the pipeline, and lambda is the heat conductivity coefficient of the pipeline; t isaIs ambient temperature; cρThe specific heat capacity of the working medium; m isoutFor pipe flow into the node, minAn outgoing flow that is a node; x represents a spatial scale and t represents a temporal scale; t isoutIs the node outflow temperature, TinTo linearize the end temperature of the node inflow pipe, the equation (1) is linearized using an implicit differential format, which can be expressed as
Figure BDA0002797434510000031
Figure BDA0002797434510000032
In the formula, mu1-4Coefficient terms representing different temperature components; the coefficient terms of α and β are constructed for convenience of description; tau and h are respectively differential space-time step length; k represents a differential time step, i represents a differential space step;
step 102) establishing a matrix uniform format for describing the temperature distribution of the pipeline based on the differential thermodynamic system dynamic model:
Figure BDA0002797434510000033
in the formula (I), the compound is shown in the specification,
Figure BDA0002797434510000034
and
Figure BDA0002797434510000035
respectively representing segmented pipeline temperature vectors at the k +1 moment and the k moment; m represents the number of spatial segments of the pipeline;
Figure BDA0002797434510000036
representing the temperature corresponding to each segmented point on the pipeline at the moment k; u and V are constant matrices composed of the coefficients in the equation (3), and are respectively expressed as:
Figure BDA0002797434510000037
Figure BDA0002797434510000038
χ and γ represent the vectors used to characterize the boundary conditions of the temperature of the pipeline, respectively. χ is used to delineate a known set of boundary conditions, wherein χi＝μ4Ta(1. ltoreq. i. ltoreq.M), for a pipeline of known boundary conditions, χ0Equal to the boundary condition of the pipeline, otherwise χ0Equal to 0; gamma is used to delineate a set of unknown boundary conditions, which can be expressed as
Figure BDA0002797434510000041
In the formula (I), the compound is shown in the specification,
Figure BDA0002797434510000042
for the corrected head end temperature-node temperature correlation matrix of the segmented pipeline in the water supply network, the head end temperature-node water supply temperature correlation matrix of the segmented pipeline is used
Figure BDA0002797434510000043
And (6) obtaining.
Figure BDA0002797434510000044
Behavior 0 of the pipe set corresponding to the known boundary condition,
Figure BDA0002797434510000045
corresponding dimension is (M +1) Np×NhIn which N ispIndicating the number of thermodynamic system pipe sections, NhRepresenting the number of thermodynamic system nodes;
pipeline starting temperature T in thermodynamic systempsNamely the mixed water supply temperature T of the nodes,nThrough a correlation matrix A of pipeline initial temperature-node water supply temperaturesAssociation, which can be expressed as
Tps＝AsTs,n \*MERGEFORMAT (9)
Wherein A issThe ith row of (1) the jth element as,ij1 denotes that the starting temperature of conduit i equals the supply water temperature at node j, otherwise as,ij0. Accordingly, the method can be used for solving the problems that,
Figure BDA0002797434510000046
the values of the medium elements can be expressed as:
Figure BDA0002797434510000047
step 103) deriving a matrix uniform format for describing the temperature distribution of the pipeline in the backwater net, wherein the equations (5) - (7) are still applicable to the backwater net due to the topology structure of the backwater net being the same as that of the water supply net, and the difference is characterized in that boundary conditions are depicted, and the equations (8) - (10) are respectively transformed in the backwater net:
Tps＝ArTr,n \*MERGEFORMAT (11)
Figure BDA0002797434510000048
wherein, Tr,nIndicating the node mixed return water temperature, ArRepresents a correlation matrix of the initial temperature of the pipeline and the return water temperature of the node, ArThe ith row of (1) the jth element ar,ij1 represents that the initial temperature of the pipeline i is equal to the return water temperature of the node j, otherwise ar,ij＝0，
Figure BDA0002797434510000049
For the corrected head end temperature-node temperature correlation matrix of the segmented pipeline in the backwater network, the head end temperature-node backwater temperature correlation matrix of the pipeline based on the segmentation
Figure BDA00027974345100000410
The acquisition step is carried out by the user,
Figure BDA00027974345100000411
behavior 0 of the pipe set corresponding to the known boundary condition,
Figure BDA00027974345100000412
has a dimension of (M +1) Np×Nh. Accordingly, the method can be used for solving the problems that,
Figure BDA00027974345100000413
the values of the medium elements can be expressed as:
Figure BDA0002797434510000051
as a further explanation of the present invention, the step 20) determines the port type of the dynamic thermodynamic system in the water supply network, and establishes a dynamic two-port thermodynamic system model in the water supply network, specifically as follows:
step 201) in the dynamic thermodynamic model, the distribution of the node state in the water supply network is mainly determined by boundary conditions and initial conditions, so that in the dynamic two-port model in the water supply network, the input port is the boundary conditions and the initial conditions of the pipeline temperature at the given k moment, and the output port is the node water supply temperature distribution at the k +1 moment;
step 202) a net outflow flow matrix Ms, out of nodes in the water supply network, comprising node outflow to pipe sections and node flows, may be expressed as
Ms,out＝diag(As,outm+d) \*MERGEFORMAT (14)
In the formula, As,outAs an association matrix of nodes and outflow conduits in the water supply network, as,out,ij1 denotes the flow from node i to conduit j, as,out,ij0 means that the flow from node i is independent of pipe j; d represents the node injection flow; net injection flow to nodes in water supply network
Figure BDA0002797434510000052
Can be equivalently the endmost injection node segmented by the pipeline, can be represented as
Figure BDA0002797434510000053
Wherein M' represents the segmented pipeline flow, and the dimension of the segmented pipeline flow is (M +1) NpX 1, which can be expressed as:
Figure BDA0002797434510000054
Figure BDA0002797434510000055
a node and inflow pipe association matrix representing segments in a water supply network, having a dimension Nh×(M+1)NpFrom the correlation matrix AsinAnd (6) obtaining. a iss,in,ij1 denotes that pipe j flows into node i, otherwise as,in,ij0. Accordingly, the method can be used for solving the problems that,
Figure BDA0002797434510000056
Figure BDA0002797434510000057
middle element
Figure BDA0002797434510000058
The values of (a) can be expressed as:
Figure BDA0002797434510000059
substituting the formula (5), the formula (14) -the formula (17) into the formula (2), a matrix-type dynamic model in the water supply network can be expressed as
Figure BDA0002797434510000061
In the formula (I), the compound is shown in the specification,
Figure BDA0002797434510000062
the tabular value is equal to the node water supply temperature vector for the given boundary condition,
Figure BDA0002797434510000063
representing an unknown node supply water temperature vector,
Figure BDA0002797434510000064
a water supply temperature vector representing the pipe section for a given boundary condition,
Figure BDA0002797434510000065
a temperature vector representing a pipe segment for which no boundary condition is given; ms,bdAnd Ms,gdAre respectively a matrix MsA medium element corresponding to the components of the node of the known supply water temperature and the node of the unknown supply water temperature;
Figure BDA0002797434510000066
and
Figure BDA0002797434510000067
are respectively a matrix
Figure BDA0002797434510000068
Middle element;
Figure BDA0002797434510000069
and
Figure BDA00027974345100000610
are respectively vector
Figure BDA00027974345100000611
A medium element corresponding to the components of the node of the known supply water temperature and the node of the unknown supply water temperature;
Ms，
Figure BDA00027974345100000612
and
Figure BDA00027974345100000613
respectively representing a coefficient matrix and a constant vector of the middle dynamic two-port model in the water supply network, wherein the coefficient matrix and the constant vector are respectively represented as follows:
Figure BDA00027974345100000614
suppose that
Figure BDA00027974345100000615
The initial condition of the water supply temperature of the pipeline after the given time k is segmented is shown, and according to the formula (18), the dynamic two-port model can be shown as follows:
Figure BDA00027974345100000616
in the formula (I), the compound is shown in the specification,
Figure BDA00027974345100000617
and
Figure BDA00027974345100000618
respectively is a constant coefficient matrix and a constant vector of the dynamic two-port model in the water supply network.
As a further explanation of the present invention, the step 30) determines the port type of the dynamic thermodynamic system in the backwater network, and establishes a dynamic two-port thermodynamic system model in the backwater network, specifically as follows:
step 301) in the dynamic thermodynamic model, the distribution of the node states in the backwater network is mainly determined by boundary conditions and initial conditions, therefore, in the dynamic two-port model in the backwater network, the input port is the boundary condition and the initial condition of the pipeline temperature at the given k moment, the output port is the node backwater temperature distribution at the k +1 moment,
step 302) Net outflow matrix M of nodes in the Return networkr,outIncluding the outflow from the node to the pipe section and the node flow, can be expressed as
Mr,out＝diag(Ar,outm-d) \*MERGEFORMAT (21)
In the formula, Ar,outIs an incidence matrix of nodes and outflow pipes in the backwater network, ar,out,ij1 denotes the flow from node i to conduit j, ar,out,ij0 means that the flow out of node i is independent of pipe j. Net injection flow to nodes in a backwater net
Figure BDA0002797434510000071
Can be equivalently the endmost injection node segmented by the pipeline, can be represented as
Figure BDA0002797434510000072
Figure BDA0002797434510000073
A node and inflow pipe association matrix representing segments in a water supply network, having a dimension Nh×(M+1)NpFrom the correlation matrix Ar,inAnd (6) obtaining. a isr,in,ij1 denotes that pipe j flows into node i, otherwise ar,in,ij0. Accordingly, the method can be used for solving the problems that,
Figure BDA0002797434510000074
middle element
Figure BDA0002797434510000075
The values of (a) can be expressed as:
Figure BDA0002797434510000076
substituting the formula (5), the formula (21) and the formula (23) into the formula (2), a matrix type dynamic model in the backwater net can be expressed as
Figure BDA0002797434510000077
In the formula (I), the compound is shown in the specification,
Figure BDA0002797434510000078
the tabular value is equal to the node return water temperature vector for the given boundary condition,
Figure BDA0002797434510000079
representing an unknown node return water temperature vector,
Figure BDA00027974345100000710
a return water temperature vector for the pipe section representing a given boundary condition,
Figure BDA00027974345100000711
a temperature vector representing a pipe segment for which no boundary condition is given; mr,bdAnd Mr,gdAre respectively a matrix MrA medium element corresponding to the components of a node of known return water temperature and a node of unknown return water temperature;
Figure BDA00027974345100000712
and
Figure BDA00027974345100000713
are respectively a matrix
Figure BDA00027974345100000714
Middle element; jdybr, bd and
Figure BDA00027974345100000715
are respectively vector
Figure BDA00027974345100000716
A medium element corresponding to the components of a node of known return water temperature and a node of unknown return water temperature; mr，
Figure BDA00027974345100000717
And
Figure BDA00027974345100000718
respectively representing a coefficient matrix and a constant vector of the middle dynamic two-port model in the backwater net,respectively expressed as:
Figure BDA00027974345100000719
suppose that
Figure BDA0002797434510000081
And (3) representing the initial condition of the return water temperature of the pipeline after the given segmentation at the moment k, wherein according to the formula (18), the dynamic two-port model can be represented as follows:
Figure BDA0002797434510000082
in the formula (I), the compound is shown in the specification,
Figure BDA0002797434510000083
and
Figure BDA0002797434510000084
respectively is a constant coefficient matrix and a constant vector of the dynamic two-port model in the backwater net.
The invention has the beneficial effects that: compared with the prior art, the invention has the following beneficial effects: the model directly links the boundary conditions, the initial conditions and the state quantity of the system to be solved, so that the calculation efficiency of the thermodynamic system time sequence simulation is effectively improved; the weight coefficient for connecting the two ports reflects the influence degree of the input end on the output end, and the response of the output end to the input end can be quantitatively described; in addition, because the complex thermodynamic system model is a two-port model, for different operation scenes, the thermodynamic system can obtain the operation state of the network only by opening the input and output ports.
Drawings
In order to more clearly illustrate the embodiments or technical solutions in the prior art of the present invention, the drawings used in the description of the embodiments or prior art will be briefly described below, and it is obvious for those skilled in the art that other drawings can be obtained based on these drawings without creative efforts.
FIG. 1 illustrates an embodiment of the present invention;
FIG. 2 is a flow chart of timing simulation using a dynamic two-port heat network model according to an embodiment of the present invention;
FIG. 3 is a block diagram of a thermodynamic system employed in an embodiment of the present invention;
FIG. 4 is a comparison of the time sequence of the variation of the end temperature of the pipe 6 with the variation of the heat source temperature in the dynamic port model and the static model according to the embodiment of the present invention;
Detailed Description
The technical solutions in the embodiments of the present invention will be 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 of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Examples
The thermodynamic system shown in fig. 3 is taken as an example for explanation. And each pipeline is divided into 50 ends, the time step is 40s, the ambient temperature is-10 ℃, the co-simulation is carried out for 20000s, and a sinusoidal disturbance is added at a heat source at 800s-1400s and is used for observing the response of the system to external excitation.
As shown in fig. 1, an embodiment of the present invention provides a dynamic two-port thermodynamic system model based on quality adjustment, including the following steps:
step 10), establishing a matrix uniform format based on a thermodynamic system dynamic model of a differential format;
step 20) determining the port type of a dynamic thermodynamic system in the water supply network, and establishing a dynamic two-port thermodynamic system model in the water supply network;
and step 30) determining the port type of the dynamic thermodynamic system in the backwater network, and establishing a dynamic two-port thermodynamic system model in the backwater network.
In the above embodiment, the step 10) specifically includes:
step 101) establishing a thermodynamic system dynamic model, including a pipeline temperature distribution equation in a partial differential format and a linear node temperature mixed equation:
Figure BDA0002797434510000091
(∑mout)Tout＝(∑minTin) \*MERGEFORMAT (2)
wherein T is the pipeline temperature; m is the mass flow of the pipeline, v is the flow velocity of the pipeline, and lambda is the heat conductivity coefficient of the pipeline; t isaIs ambient temperature; cρThe specific heat capacity of the working medium; m isoutFor pipe flow into the node, minAn outgoing flow that is a node; x represents a spatial scale and t represents a temporal scale; t isoutIs the node outflow temperature, TinTo linearize the end temperature of the node inflow pipe, the equation (1) is linearized using an implicit differential format, which can be expressed as
Figure BDA0002797434510000101
Figure BDA0002797434510000102
In the formula, mu1-4Coefficient terms representing different temperature components; the coefficient terms of α and β are constructed for convenience of description; tau and h are respectively differential space-time step length; k represents the time step of the difference and i represents the space step of the difference.
Step 102) establishing a matrix uniform format for describing the temperature distribution of the pipeline based on the differential thermodynamic system dynamic model:
Figure BDA0002797434510000103
in the formula (I), the compound is shown in the specification,
Figure BDA0002797434510000104
and
Figure BDA0002797434510000105
respectively representing segmented pipeline temperature vectors at the k +1 moment and the k moment; m represents the number of spatial segments of the pipeline;
Figure BDA0002797434510000106
representing the temperature corresponding to each segmented point on the pipeline at the moment k; u and V are constant matrices composed of the coefficients in the equation (3), and are respectively expressed as:
Figure BDA0002797434510000107
Figure BDA0002797434510000108
χ and γ represent the vectors used to characterize the boundary conditions of the temperature of the pipeline, respectively. χ is used to delineate a known set of boundary conditions, wherein χi＝μ4Ta(1. ltoreq. i. ltoreq.M), for a pipeline of known boundary conditions, χ0Equal to the boundary condition of the pipeline, otherwise χ0Equal to 0; gamma is used to delineate a set of unknown boundary conditions, which can be expressed as
Figure BDA0002797434510000109
In the formula (I), the compound is shown in the specification,
Figure BDA00027974345100001010
for the corrected head end temperature-node temperature correlation matrix of the segmented pipeline in the water supply network, the head end temperature-node water supply temperature correlation matrix of the segmented pipeline is used
Figure BDA00027974345100001011
And (6) obtaining.
Figure BDA00027974345100001012
Corresponds to knownBehavior 0 of the pipe set of the boundary condition,
Figure BDA0002797434510000111
corresponding dimension is (M +1) Np×NhIn which N ispIndicating the number of thermodynamic system pipe sections, NhRepresenting the number of thermodynamic system nodes;
pipeline starting temperature T in thermodynamic systempsNamely the mixed water supply temperature T of the nodes,nThrough a correlation matrix A of pipeline initial temperature-node water supply temperaturesAssociation, which can be expressed as
Tps＝AsTs,n \*MERGEFORMAT (9)
Wherein A issThe ith row of (1) the jth element as,ij1 denotes that the starting temperature of conduit i equals the supply water temperature at node j, otherwise as,ij0. Accordingly, the method can be used for solving the problems that,
Figure BDA0002797434510000112
the values of the medium elements can be expressed as:
Figure BDA0002797434510000113
step 103) deriving a matrix uniform format for describing the temperature distribution of the pipeline in the backwater net, wherein the equations (5) - (7) are still applicable to the backwater net due to the topology structure of the backwater net being the same as that of the water supply net, and the difference is characterized in that boundary conditions are depicted, and the equations (8) - (10) are respectively transformed in the backwater net:
Tps＝ArTr,n \*MERGEFORMAT (11)
Figure BDA0002797434510000114
wherein, Tr,nIndicating the node mixed return water temperature, ArRepresents a correlation matrix of the initial temperature of the pipeline and the return water temperature of the node, ArThe ith row of (1) the jth element ar,ij1 denotes that the initial temperature of the pipe i is equal to the pitchReturn water temperature at point j, otherwise ar,ij＝0，
Figure BDA0002797434510000115
For the corrected head end temperature-node temperature correlation matrix of the segmented pipeline in the backwater network, the head end temperature-node backwater temperature correlation matrix of the pipeline based on the segmentation
Figure BDA0002797434510000116
The acquisition step is carried out by the user,
Figure BDA0002797434510000117
behavior 0 of the pipe set corresponding to the known boundary condition,
Figure BDA0002797434510000118
has a dimension of (M +1) Np×Nh. Accordingly, the method can be used for solving the problems that,
Figure BDA0002797434510000119
the values of the medium elements can be expressed as:
Figure BDA00027974345100001110
in the above embodiment, the step 20) specifically includes:
step 201) in the dynamic thermodynamic model, the distribution of the node state in the water supply network is mainly determined by boundary conditions and initial conditions, so that in the dynamic two-port model in the water supply network, the input port is the boundary conditions and the initial conditions of the pipeline temperature at the given k moment, and the output port is the node water supply temperature distribution at the k +1 moment;
step 202) Net outflow matrix M for nodes in Water supply networks,outIncluding the outflow from the node to the pipe section and the node flow, can be expressed as
Ms,out＝diag(As,outm+d) \*MERGEFORMAT (14)
In the formula, As,outFor nodes and outflow conduits in water supply networksThe correlation matrix of as,out,ij1 denotes the flow from node i to conduit j, as,out,ij0 means that the flow from node i is independent of pipe j; d represents the node injection flow; net injection flow to nodes in water supply network
Figure BDA0002797434510000121
Can be equivalently the endmost injection node segmented by the pipeline, can be represented as
Figure BDA0002797434510000122
Wherein M' represents the segmented pipeline flow, and the dimension of the segmented pipeline flow is (M +1) NpX 1, which can be expressed as:
Figure BDA0002797434510000123
Figure BDA0002797434510000124
a node and inflow pipe association matrix representing segments in a water supply network, having a dimension Nh×(M+1)NpFrom the correlation matrix AsinAnd (6) obtaining. a iss,in,ij1 denotes that pipe j flows into node i, otherwise as,in,ij0. Accordingly, the method can be used for solving the problems that,
Figure BDA0002797434510000125
Figure BDA0002797434510000126
middle element
Figure BDA0002797434510000127
The values of (a) can be expressed as:
Figure BDA0002797434510000128
substituting the formula (5), the formula (14) -the formula (17) into the formula (2), a matrix-type dynamic model in the water supply network can be expressed as
Figure BDA0002797434510000129
In the formula (I), the compound is shown in the specification,
Figure BDA00027974345100001210
the tabular value is equal to the node water supply temperature vector for the given boundary condition,
Figure BDA00027974345100001211
representing an unknown node supply water temperature vector,
Figure BDA00027974345100001212
a water supply temperature vector representing the pipe section for a given boundary condition,
Figure BDA00027974345100001213
a temperature vector representing a pipe segment for which no boundary condition is given; ms,bdAnd Ms,gdAre respectively a matrix MsA medium element corresponding to the components of the node of the known supply water temperature and the node of the unknown supply water temperature;
Figure BDA0002797434510000131
and
Figure BDA0002797434510000132
are respectively a matrix
Figure BDA0002797434510000133
Middle element;
Figure BDA0002797434510000134
and
Figure BDA0002797434510000135
are respectively vector
Figure BDA0002797434510000136
Middle element, corresponding toThe components of the node of the known supply water temperature and the node of the unknown supply water temperature;
Ms，
Figure BDA0002797434510000137
and
Figure BDA0002797434510000138
respectively representing a coefficient matrix and a constant vector of the middle dynamic two-port model in the water supply network, wherein the coefficient matrix and the constant vector are respectively represented as follows:
Figure BDA0002797434510000139
suppose that
Figure BDA00027974345100001310
The initial condition of the water supply temperature of the pipeline after the given time k is segmented is shown, and according to the formula (18), the dynamic two-port model can be shown as follows:
Figure BDA00027974345100001311
in the formula (I), the compound is shown in the specification,
Figure BDA00027974345100001312
and
Figure BDA00027974345100001313
respectively is a constant coefficient matrix and a constant vector of the dynamic two-port model in the water supply network.
In the above embodiment, the step 30) specifically includes:
step 301) in the dynamic thermodynamic model, the distribution of the node states in the backwater network is mainly determined by boundary conditions and initial conditions, therefore, in the dynamic two-port model in the backwater network, the input port is the boundary condition and the initial condition of the pipeline temperature at the given k moment, the output port is the node backwater temperature distribution at the k +1 moment,
step 302) backwater netThe net outgoing flow matrix M of the node inr,outIncluding the outflow from the node to the pipe section and the node flow, can be expressed as
Mr,out＝diag(Ar,outm-d) \*MERGEFORMAT (21)
In the formula, Ar,outIs an incidence matrix of nodes and outflow pipes in the backwater network, ar,out,ij1 denotes the flow from node i to conduit j, ar,out,ij0 means that the flow out of node i is independent of pipe j. Net injection flow to nodes in a backwater net
Figure BDA00027974345100001314
Can be equivalently the endmost injection node segmented by the pipeline, can be represented as
Figure BDA0002797434510000141
Figure BDA0002797434510000142
A node and inflow pipe association matrix representing segments in a water supply network, having a dimension Nh×(M+1)NpFrom the correlation matrix Ar,inAnd (6) obtaining. a isr,in,ij1 denotes that pipe j flows into node i, otherwise ar,in,ij0. Accordingly, the method can be used for solving the problems that,
Figure BDA0002797434510000143
middle element
Figure BDA0002797434510000144
The values of (a) can be expressed as:
Figure BDA0002797434510000145
substituting the formula (5), the formula (21) and the formula (23) into the formula (2), a matrix type dynamic model in the backwater net can be expressed as
Figure BDA0002797434510000146
In the formula (I), the compound is shown in the specification,
Figure BDA0002797434510000147
the tabular value is equal to the node return water temperature vector for the given boundary condition,
Figure BDA0002797434510000148
representing an unknown node return water temperature vector,
Figure BDA0002797434510000149
a return water temperature vector for the pipe section representing a given boundary condition,
Figure BDA00027974345100001410
a temperature vector representing a pipe segment for which no boundary condition is given; mr,bdAnd Mr,gdAre respectively a matrix MrA medium element corresponding to the components of a node of known return water temperature and a node of unknown return water temperature;
Figure BDA00027974345100001411
and
Figure BDA00027974345100001412
are respectively a matrix
Figure BDA00027974345100001413
Middle element; jdybr, bd and
Figure BDA00027974345100001414
are respectively vector
Figure BDA00027974345100001415
A medium element corresponding to the components of a node of known return water temperature and a node of unknown return water temperature; mr，
Figure BDA00027974345100001416
And
Figure BDA00027974345100001417
respectively representing the coefficient matrix and the constant vector of the middle dynamic two-port model in the backwater net, and respectively representing as follows:
Figure BDA00027974345100001418
suppose that
Figure BDA00027974345100001419
And (3) representing the initial condition of the return water temperature of the pipeline after the given segmentation at the moment k, wherein according to the formula (18), the dynamic two-port model can be represented as follows:
Figure BDA00027974345100001420
in the formula (I), the compound is shown in the specification,
Figure BDA00027974345100001421
and
Figure BDA00027974345100001422
respectively is a constant coefficient matrix and a constant vector of the dynamic two-port model in the backwater net. Calculating the temperature distribution of the thermodynamic system at different moments in the simulation process using said equation (26), wherein at a simulation time of 800-1400 s a sinusoidal disturbance is added at the boundary condition, i.e. T is changeds,bdThe values at 800s-1400s were kept constant for the rest of the time, and the results of the calculations are shown by taking the temperatures at the ends of the pipes 1 and 5 as examples. As shown in fig. 4, the temperature at the end of the pipe responds to the excitation disturbance at the heat source after a delay, the length of which is related to the distance. Compared with the traditional model, the model provided by the invention does not need layer-by-layer iteration, directly depicts the response of the pipeline temperature to the heat source disturbance, has high calculation efficiency, and is favorable for giving intuitive guidance suggestion on the adjustment mode of the heat source in advance.
According to the dynamic two-port heat supply network model based on mass adjustment, provided by the embodiment of the invention, the boundary condition, the initial condition and the state quantity of the system to be solved are directly linked together, so that the calculation efficiency of the thermodynamic system time sequence simulation is effectively improved; the weight coefficient for connecting the two ports reflects the influence degree of the input end on the output end, and the response of the output end to the input end can be quantitatively described; in addition, because a complex thermodynamic system model is a two-port model, the thermodynamic system can obtain the running state of the network only by opening the input port and the output port in different running scenes, so that the internal information is protected.
It will be appreciated by those skilled in the art that various changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention. The present embodiments are, therefore, to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the spirit and scope of the invention, and any equivalents thereto, such as those skilled in the art, are intended to be embraced therein.

Claims (4)

1. A dynamic two-port thermodynamic system model based on quality adjustment is characterized in that the model construction comprises the following steps:
step 10), establishing a matrix uniform format based on a thermodynamic system dynamic model of a differential format;
step 20) determining the port type of a dynamic thermodynamic system in the water supply network, and establishing a dynamic two-port thermodynamic system model in the water supply network;
and step 30) determining the port type of the dynamic thermodynamic system in the backwater network, and establishing a dynamic two-port thermodynamic system model in the backwater network.
2. The dynamic two-port thermodynamic system model based on quality adjustment according to claim 1, wherein the step 10) is based on a thermodynamic system dynamic model in a differential format to establish a matrix uniform format, and the specific steps are as follows:
step 101) establishing a thermodynamic system dynamic model, including a pipeline temperature distribution equation in a partial differential format and a linear node temperature mixed equation:
Figure FDA0002797434500000011
(∑mout)Tout＝(∑minTin) \*MERGEFORMAT (2)
wherein T is the pipeline temperature; m is the mass flow of the pipeline, v is the flow velocity of the pipeline, and lambda is the heat conductivity coefficient of the pipeline; t isaIs ambient temperature; cρThe specific heat capacity of the working medium; m isoutFor pipe flow into the node, minAn outgoing flow that is a node; x represents a spatial scale and t represents a temporal scale; t isoutIs the node outflow temperature, TinTo linearize the end temperature of the node inflow pipe, the equation (1) is linearized using an implicit differential format, which can be expressed as
Figure FDA0002797434500000012
Figure FDA0002797434500000021
In the formula, mu1-4Coefficient terms representing different temperature components; the coefficient terms of α and β are constructed for convenience of description; tau and h are respectively differential space-time step length; k represents a differential time step, i represents a differential space step;
step 102) establishing a matrix uniform format for describing the temperature distribution of the pipeline based on the differential thermodynamic system dynamic model:
Figure FDA0002797434500000022
in the formula (I), the compound is shown in the specification,
Figure FDA0002797434500000023
and
Figure FDA0002797434500000024
respectively representing segmented pipeline temperature vectors at the k +1 moment and the k moment; m represents the number of spatial segments of the pipeline;
Figure FDA0002797434500000025
representing the temperature corresponding to each segmented point on the pipeline at the moment k; u and V are constant matrices composed of the coefficients in the equation (3), and are respectively expressed as:
Figure FDA0002797434500000026
Figure FDA0002797434500000027
χ and γ represent the vectors used to characterize the boundary conditions of the temperature of the pipeline, respectively. χ is used to delineate a known set of boundary conditions, wherein χi＝μ4Ta(1. ltoreq. i. ltoreq.M), for a pipeline of known boundary conditions, χ0Equal to the boundary condition of the pipeline, otherwise χ0Equal to 0; gamma is used to delineate a set of unknown boundary conditions, which can be expressed as
Figure FDA0002797434500000028
In the formula (I), the compound is shown in the specification,
Figure FDA0002797434500000029
for the corrected head end temperature-node temperature correlation matrix of the segmented pipeline in the water supply network, the head end temperature-node water supply temperature correlation matrix of the segmented pipeline is used
Figure FDA00027974345000000210
And (6) obtaining.
Figure FDA00027974345000000211
Behavior 0 of the pipe set corresponding to the known boundary condition,
Figure FDA00027974345000000212
corresponding dimension is (M +1) Np×NhIn which N ispIndicating the number of thermodynamic system pipe sections, NhRepresenting the number of thermodynamic system nodes;
pipeline starting temperature T in thermodynamic systempsNamely the mixed water supply temperature T of the nodes,nThrough a correlation matrix A of pipeline initial temperature-node water supply temperaturesAssociation, which can be expressed as
Tps＝AsTs,n \*MERGEFORMAT (9)
Wherein A issThe ith row of (1) the jth element as,ij1 denotes that the starting temperature of conduit i equals the supply water temperature at node j, otherwise as,ij0. Accordingly, the method can be used for solving the problems that,
Figure FDA0002797434500000031
the values of the medium elements can be expressed as:
Figure FDA0002797434500000032
step 103) deriving a matrix uniform format for describing the temperature distribution of the pipeline in the backwater net, wherein the equations (5) - (7) are still applicable to the backwater net due to the topology structure of the backwater net being the same as that of the water supply net, and the difference is characterized in that boundary conditions are depicted, and the equations (8) - (10) are respectively transformed in the backwater net:
Tps＝ArTr,n \*MERGEFORMAT (11)
Figure FDA0002797434500000033
wherein，Tr,nIndicating the node mixed return water temperature, ArRepresents a correlation matrix of the initial temperature of the pipeline and the return water temperature of the node, ArThe ith row of (1) the jth element ar,ij1 represents that the initial temperature of the pipeline i is equal to the return water temperature of the node j, otherwise ar,ij＝0，
Figure FDA0002797434500000034
For the corrected head end temperature-node temperature correlation matrix of the segmented pipeline in the backwater network, the head end temperature-node backwater temperature correlation matrix of the pipeline based on the segmentation
Figure FDA0002797434500000035
Figure FDA0002797434500000036
The acquisition step is carried out by the user,
Figure FDA0002797434500000037
behavior 0 of the pipe set corresponding to the known boundary condition,
Figure FDA0002797434500000038
has a dimension of (M +1) Np×Nh. Accordingly, the method can be used for solving the problems that,
Figure FDA0002797434500000039
the values of the medium elements can be expressed as:
Figure FDA00027974345000000310
3. the dynamic two-port thermodynamic system model based on quality adjustment according to claim 2, wherein the step 20) determines the type of the dynamic thermodynamic system port in the water supply network, and establishes the dynamic two-port thermodynamic system model in the water supply network as follows:
step 201) in the dynamic thermodynamic model, the distribution of the node state in the water supply network is mainly determined by boundary conditions and initial conditions, so that in the dynamic two-port model in the water supply network, the input port is the boundary conditions and the initial conditions of the pipeline temperature at the given k moment, and the output port is the node water supply temperature distribution at the k +1 moment;
step 202) Net outflow matrix M for nodes in Water supply networks,outIncluding the outflow from the node to the pipe section and the node flow, can be expressed as
Ms,out＝diag(As,outm+d) \*MERGEFORMAT (14)
In the formula, As,outAs an association matrix of nodes and outflow conduits in the water supply network, as,out,ij1 denotes the flow from node i to conduit j, as,out,ij0 means that the flow from node i is independent of pipe j; d represents the node injection flow; net injection flow to nodes in water supply network
Figure FDA0002797434500000041
Can be equivalently the endmost injection node segmented by the pipeline, can be represented as
Figure FDA0002797434500000042
Wherein M' represents the segmented pipeline flow, and the dimension of the segmented pipeline flow is (M +1) NpX 1, which can be expressed as:
Figure FDA0002797434500000043
Figure FDA0002797434500000044
a node and inflow pipe association matrix representing segments in a water supply network, having a dimension Nh×(M+1)NpFrom the correlation matrix AsinAnd (6) obtaining. a iss,in,ij1 denotes that pipe j flows into node i, otherwise as,in,ij0. Accordingly, the method can be used for solving the problems that,
Figure FDA0002797434500000045
middle element
Figure FDA0002797434500000046
The values of (a) can be expressed as:
Figure FDA0002797434500000047
substituting the formula (5), the formula (14) -the formula (17) into the formula (2), a matrix-type dynamic model in the water supply network can be expressed as
Figure FDA0002797434500000051
In the formula (I), the compound is shown in the specification,
Figure FDA0002797434500000052
the tabular value is equal to the node water supply temperature vector for the given boundary condition,
Figure FDA0002797434500000053
representing an unknown node supply water temperature vector,
Figure FDA0002797434500000054
a water supply temperature vector representing the pipe section for a given boundary condition,
Figure FDA0002797434500000055
a temperature vector representing a pipe segment for which no boundary condition is given; ms,bdAnd Ms,gdAre respectively a matrix MsA medium element corresponding to the components of the node of the known supply water temperature and the node of the unknown supply water temperature;
Figure FDA0002797434500000056
Figure FDA00027974345000000520
Figure FDA0002797434500000057
and
Figure FDA0002797434500000058
are respectively a matrix
Figure FDA0002797434500000059
Middle element;
Figure FDA00027974345000000510
and
Figure FDA00027974345000000511
are respectively vector
Figure FDA00027974345000000512
A medium element corresponding to the components of the node of the known supply water temperature and the node of the unknown supply water temperature;
Ms，
Figure FDA00027974345000000513
and
Figure FDA00027974345000000514
respectively representing a coefficient matrix and a constant vector of the middle dynamic two-port model in the water supply network, wherein the coefficient matrix and the constant vector are respectively represented as follows:
Figure FDA00027974345000000515
suppose that
Figure FDA00027974345000000516
Representing initial conditions of the water supply temperature of the pipeline after the given k-time segmentation, and according to the formula (18), a dynamic two-port model supplies waterThe net can be represented as:
Figure FDA00027974345000000517
in the formula (I), the compound is shown in the specification,
Figure FDA00027974345000000518
and
Figure FDA00027974345000000519
respectively is a constant coefficient matrix and a constant vector of the dynamic two-port model in the water supply network.
4. The dynamic two-port thermodynamic system model based on quality adjustment according to claim 3, wherein the step 30) determines the type of the dynamic thermodynamic system port in the backwater network, and establishes the dynamic two-port thermodynamic system model in the backwater network, specifically as follows:
step 301) in the dynamic thermodynamic model, the distribution of the node states in the backwater network is mainly determined by boundary conditions and initial conditions, therefore, in the dynamic two-port model in the backwater network, the input port is the boundary condition and the initial condition of the pipeline temperature at the given k moment, the output port is the node backwater temperature distribution at the k +1 moment,
step 302) Net outflow matrix M of nodes in the Return networkr,outIncluding the outflow from the node to the pipe section and the node flow, can be expressed as
Mr,out＝diag(Ar,outm-d) \*MERGEFORMAT (21)
In the formula, Ar,outIs an incidence matrix of nodes and outflow pipes in the backwater network, ar,out,ij1 denotes the flow from node i to conduit j, ar,out,ij0 means that the flow out of node i is independent of pipe j. Net injection flow to nodes in a backwater net
Figure FDA0002797434500000061
Can be equivalently segmented by the last of the pipesEnd injection node, which can be represented as
Figure FDA0002797434500000062
Figure FDA0002797434500000063
A node and inflow pipe association matrix representing segments in a water supply network, having a dimension Nh×(M+1)NpFrom the correlation matrix Ar,inAnd (6) obtaining. a isr,in,ij1 denotes that pipe j flows into node i, otherwise ar,in,ij0. Accordingly, the method can be used for solving the problems that,
Figure FDA0002797434500000064
middle element
Figure FDA0002797434500000065
The values of (a) can be expressed as:
Figure FDA0002797434500000066
substituting the formula (5), the formula (21) and the formula (23) into the formula (2), a matrix type dynamic model in the backwater net can be expressed as
Figure FDA0002797434500000067
In the formula (I), the compound is shown in the specification,
Figure FDA0002797434500000068
the tabular value is equal to the node return water temperature vector for the given boundary condition,
Figure FDA0002797434500000069
representing an unknown node return water temperature vector,
Figure FDA00027974345000000610
a return water temperature vector for the pipe section representing a given boundary condition,
Figure FDA00027974345000000611
a temperature vector representing a pipe segment for which no boundary condition is given; mr,bdAnd Mr,gdAre respectively a matrix MrA medium element corresponding to the components of a node of known return water temperature and a node of unknown return water temperature;
Figure FDA00027974345000000612
Figure FDA00027974345000000713
Figure FDA0002797434500000071
and
Figure FDA0002797434500000072
are respectively a matrix
Figure FDA0002797434500000073
Middle element; jdybr, bd and
Figure FDA0002797434500000074
are respectively vector
Figure FDA0002797434500000075
A medium element corresponding to the components of a node of known return water temperature and a node of unknown return water temperature; mr，
Figure FDA0002797434500000076
And
Figure FDA0002797434500000077
respectively representing the coefficient matrix and the constant vector of the middle dynamic two-port model in the backwater net, and respectively representing as follows:
Figure FDA0002797434500000078
suppose that
Figure FDA0002797434500000079
And (3) representing the initial condition of the return water temperature of the pipeline after the given segmentation at the moment k, wherein according to the formula (18), the dynamic two-port model can be represented as follows:
Figure FDA00027974345000000710
in the formula (I), the compound is shown in the specification,
Figure FDA00027974345000000711
and
Figure FDA00027974345000000712
respectively is a constant coefficient matrix and a constant vector of the dynamic two-port model in the backwater net.
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