CN112163329A - Thermodynamic system matrix model construction method and electronic equipment - Google Patents
Thermodynamic system matrix model construction method and electronic equipment Download PDFInfo
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Abstract
The embodiment of the invention provides a thermodynamic system matrix model construction method and electronic equipment, wherein the method comprises the following steps: s101, determining connection lines among all nodes, establishing an incidence matrix representing topological relation among all nodes based on the connection lines among all nodes, and establishing a heat transfer constraint equation based on the incidence matrix, wherein all the nodes are obtained by dividing all heat treatment processes in a thermodynamic system; s102, establishing a system incidence matrix in a matrix block superposition mode according to each incidence matrix, and establishing a system heat transfer constraint equation in a matrix block superposition mode according to each heat transfer constraint equation; s103, performing matrix analysis on the system incidence matrix and the system heat transfer constraint equation, determining a target solution condition, and establishing a system integral constraint equation according to a matrix analysis result and the target solution condition. The method is generally suitable for the complex thermodynamic system model construction process on the premise of ensuring the calculation accuracy, reduces the calculation difficulty and improves the calculation efficiency.
Description
Technical Field
The invention relates to the technical field of energy system modeling, in particular to a thermodynamic system matrix model construction method and electronic equipment.
Background
Aiming at a comprehensive energy system integrating a plurality of energy systems such as electricity, heat, gas and the like, when the comprehensive regulation and control of different forms of energy are researched by a model, a thermodynamic system model constructed by a traditional thermodynamic system modeling method has strong nonlinearity, so that the calculation efficiency is low and the convergence is difficult when different energy system models are integrated and solved.
When an energy transportation process is considered, ohm law and kirchhoff voltage and current law are generally adopted in a power system to describe element transmission and system topological characteristics respectively so as to construct a power flow constraint. In a modeling method of a linear network, these power flow constraints can be conveniently solved by a matrix iterative algorithm, such as the newton-raphson method. The heat transfer process of the thermodynamic system consists of two coupled sub-processes: one is the heat transfer sub-process that accompanies the fluid flow and the other is the heat transfer sub-process between the two different fluids in the heat exchange device. As a key device in a thermodynamic system, the heat exchange device simultaneously comprises two sub-processes which are simultaneously influenced mutually, so that the heat transfer constraint of the heat exchange device has high nonlinearity. Therefore, when a thermodynamic system generally comprising heat exchange equipment is solved, special algorithms such as a simultaneous equation method, a sequential module method, a simultaneous module method and the like are generally needed, the key of the algorithms is to perform cycle iteration in a mode of stacking component models, and the calculation difficulty is high and the calculation efficiency is low.
Therefore, many researchers adopt methods such as neglect, approximate simplification, linearization under specific scenes and the like for nonlinear heat transfer constraint, the methods meet the analysis requirements of the electric heating comprehensive energy system in terms of calculation difficulty, but all the methods have certain limitations, and particularly the calculation accuracy of the methods is obviously reduced.
In summary, the nonlinearity of the conventional thermodynamic system modeling method is a cause that the method is difficult to apply in the analysis of the integrated energy system, and the heat transfer characteristic cannot be completely reflected by adopting a simplified method with limitations. Therefore, researchers research a heat exchanger thermal resistance method based on heat transfer process linearization, and further develop a heat flow modeling method for establishing an equivalent circuit model, but the model construction process of the method is based on experience and depends on graph derivation, the modeling process is complex and difficult, and the application of the method in a large-scale comprehensive energy system is limited.
Disclosure of Invention
Aiming at the problems in the prior art, the embodiment of the invention provides a thermodynamic system matrix model construction method and electronic equipment.
In a first aspect, an embodiment of the present invention provides a thermodynamic system matrix model building method, including:
s101, determining connection lines among all nodes, establishing an incidence matrix representing topological relation among all nodes based on the connection lines among all nodes, and establishing a heat transfer constraint equation based on the incidence matrix, wherein all the nodes are obtained by dividing all heat treatment processes in a thermodynamic system;
s102, establishing a system incidence matrix in a matrix block superposition mode according to each incidence matrix, and establishing a system heat transfer constraint equation in a matrix block superposition mode according to each heat transfer constraint equation;
s103, performing matrix analysis on the system incidence matrix and the system heat transfer constraint equation, determining a target solution condition, and establishing a system integral constraint equation according to a matrix analysis result and the target solution condition.
Further, the S101 in the thermodynamic system matrix model building method includes:
s1011, dividing independent nodes for each heat treatment process according to a fluid inlet mode and a fluid outlet mode, and determining the connection line and the direction between the nodes according to the fluid flow continuity;
s1012, establishing each incidence matrix to respectively reflect the topological relation between each node and each connecting line in each heat treatment process based on a graph theory description method;
and S1013, respectively establishing topological constraint equations between the temperature vectors and the temperature difference vectors based on the incidence matrixes, and respectively establishing heat transfer constraint equations for the heat treatment processes based on the coefficient matrixes of the temperature vectors, the temperature difference vectors and the heat flow vectors.
Further, in S1011, the method further includes: the method comprises the steps of adding a reference node for a single-strand flow heating process, determining a heat input connecting line from the reference node to an inlet node for the single-strand flow heating process, and determining a heat transfer connecting line between different inlet nodes for a heat exchange process.
Further, the S102 in the thermodynamic system matrix model construction method includes:
s1021, summing the incidence matrixes to obtain a summed incidence matrix, adding an internal incidence matrix reflecting the internal topological relation of different parts to the summed incidence matrix in a diagonal form, adding an external incidence matrix reflecting the topological relation of external nodes and reference nodes, and performing price reduction treatment to obtain the system incidence matrix;
s1022, fusing the heat transfer constraint equations to obtain a general heat transfer constraint equation reflecting the whole heat treatment process, determining all matrixes and vectors in the general heat transfer constraint equation, adding the matrixes and vectors reflecting the heat transfer constraint conditions of the external nodes and the reference nodes, adding the matrixes and vectors reflecting the internal heat transfer conditions of different parts, and obtaining all the matrixes and vectors of the system heat transfer constraint equation.
Further, in S1022, the determining all the matrices and vectors in the general heat transfer constraint equation includes: the device comprises a diagonal matrix, a temperature difference matrix, a heat flow vector coefficient matrix, a temperature vector coefficient matrix and an independent heat flow vector.
Further, the thermodynamic system matrix model construction method comprises the following steps:
each of the matrices has exchangeability of rows and columns.
Further, the target solution condition in S103 includes: a heat flow solution condition that causes the heat flow to have a unique solution, a boundary condition that causes each parameter in the system correlation matrix and the system heat transfer constraint equation to be closed.
Further, the heat flow definite solution condition is a definite solution condition which is derived by searching a maximum linear independent set of a column vector set and defining the heat flow as zero, wherein the column vector set is obtained by analyzing and extracting each coefficient matrix in a system incidence matrix and a system heat transfer constraint equation;
correspondingly, the boundary condition is given by a coefficient matrix input mode aiming at an external node temperature constraint equation, wherein the external node is determined according to a system incidence matrix based on graph theory description knowledge.
In a second aspect, an embodiment of the present invention provides an electronic device, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor, and the processor, when executing the computer program, implements the thermodynamic system matrix model building method as described above.
In a third aspect, an embodiment of the present invention provides a non-transitory computer-readable storage medium, on which a computer program is stored, and the computer program, when executed by a processor, implements the thermodynamic system matrix model building method as described above.
The thermodynamic system matrix model construction method and the electronic equipment provided by the embodiment of the invention effectively establish a system incidence matrix and a system heat transfer constraint equation based on the topological relation among nodes in each process, carrying out matrix analysis on the system incidence matrix and the system heat transfer constraint equation to determine a target solution condition, establishing a system integral constraint equation according to a matrix analysis result and the target solution condition, thereby forming a thermodynamic system model solving algorithm for carrying out integral solution by utilizing a linear network, and also being an automatic model generation method capable of directly deducing a corresponding control equation from a system physical model, the method can be generally suitable for the thermodynamic system model construction process of the comprehensive energy system on the premise of ensuring the calculation accuracy, effectively reduces the calculation difficulty, and improves the calculation efficiency.
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In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
Fig. 1 is a schematic flow chart of a thermodynamic system matrix model building method according to an embodiment of the present invention;
FIG. 2 is a schematic flow chart of another thermodynamic system matrix model building method according to an embodiment of the present invention;
FIG. 3 is a schematic flow chart of another thermodynamic system matrix model building method according to an embodiment of the present invention;
FIG. 4 is a schematic diagram illustrating a heat exchange process of a heat exchanger in the method according to the embodiment of the invention;
FIG. 5 is a schematic diagram of a flow separation process in a method provided by an embodiment of the invention;
FIG. 6 is a schematic diagram of the flow mixing process in a method provided by an embodiment of the invention;
FIG. 7 is a schematic diagram of a single stream heating process in accordance with an embodiment of the present invention;
FIG. 8 is a schematic diagram of an exemplary district heating system to which the method provided by the embodiments of the present invention is applied;
fig. 9 is a schematic structural diagram of an electronic device according to an embodiment of the present invention.
Reference numerals:
910: a processor; 920: a communication interface; 930: a memory; 940: a communication bus.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, 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 some, but not all, embodiments of the present invention. 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.
The embodiment of the invention provides a thermodynamic system matrix model construction method, which comprises the following steps:
s101, determining connection lines among all nodes, establishing an incidence matrix representing topological relation among all nodes based on the connection lines among all nodes, and establishing a heat transfer constraint equation based on the incidence matrix, wherein all the nodes are obtained by dividing all heat treatment processes in a thermodynamic system;
s102, establishing a system incidence matrix in a matrix block superposition mode according to each incidence matrix, and establishing a system heat transfer constraint equation in a matrix block superposition mode according to each heat transfer constraint equation;
s103, performing matrix analysis on the system incidence matrix and the system heat transfer constraint equation, determining a target solution condition, and establishing a system integral constraint equation according to a matrix analysis result and the target solution condition.
The thermodynamic system matrix model construction method provided by the embodiment of the invention can be generally applied to the thermodynamic system model construction process of the comprehensive energy system on the premise of ensuring the calculation accuracy, and can also improve the calculation efficiency.
The thermodynamic system matrix model construction method according to the embodiment of the invention is described in detail below with reference to the accompanying drawings.
In a first aspect, an embodiment of the present invention provides a thermodynamic system matrix model building method, and fig. 1 is a schematic flow chart of the thermodynamic system matrix model building method provided in the embodiment of the present invention, as shown in fig. 1, the method includes:
s101, determining connection lines among all nodes, establishing an incidence matrix representing topological relation among all nodes based on the connection lines among all nodes, and establishing a heat transfer constraint equation based on the incidence matrix, wherein all the nodes are obtained by dividing all heat treatment processes in a thermodynamic system;
the heat treatment process in the thermodynamic system is divided into typical processes such as a heat exchanger heat exchange process, a flow separation process, a flow mixing process, a single-flow heating process and the like. According to the division of different heat treatment processes, the thermodynamic system is divided into different parts, parts nodes and parts connecting lines, namely the nodes are divided according to the modes of a fluid inlet and a fluid outlet. And determining the connection line between the nodes and the direction of the connection line according to the fluid flow continuity. Based on the connection lines among the nodes, according to a matrix description method for the relationship between the nodes and the connection lines in the graph theory, the network theory is used for defining each node and each connection line in different heat treatment processes, the topological relationship among the different heat treatment processes of the thermodynamic system is established in a mode of the nodes, the connection lines and the incidence matrix, and the incidence matrix reflecting the topological relationship is established. Based on the incidence matrix, a topological constraint equation between the temperature vector and the temperature difference vector is established, and then a coefficient matrix of the temperature vector, the temperature difference vector and the heat flow vector is introduced, so that a general form equation reflecting heat transfer constraint conditions in different heat treatment processes is established and used as a heat transfer constraint equation. That is, in the system research, the characteristics of each component of the researched physical system and the characteristics of the topological relation among the components are input, the incidence matrix of each component reflecting the topological relation among the components is constructed, and the heat transfer constraint equation in the general matrix expression reflecting the heat transfer constraint of each component is constructed.
In the step S101, a heat transfer constraint equation is established, a heat exchanger thermal resistance method based on heat transfer constraints of a linearized heat exchanger and a commonly used energy conservation equation are used, and heat transfer constraints of different processes are described in a unified manner by a general matrix equation, so that establishment of normalized matrix models of different heat treatment processes is facilitated. If necessary, for the thermal processes of other thermal systems than the above thermal processes, similar node and link division methods may also be used to establish corresponding matrix models.
The graph-theoretic description and matrix model of the topological relationship between the components includes matrices and vectors describing the correlation matrix of the topological relationship between the components and the heat transfer constraints between the components. Especially considering the need to connect the external node to the reference node, all the matrices and vectors in the correlation matrix and heat transfer constraint equation corresponding to step S101 need to be given.
S102, establishing a system incidence matrix in a matrix block superposition mode according to each incidence matrix, and establishing a system heat transfer constraint equation in a matrix block superposition mode according to each heat transfer constraint equation;
and establishing a system incidence matrix in a matrix block superposition mode according to each incidence matrix, establishing a system heat transfer constraint equation in a matrix block superposition mode according to each heat transfer constraint equation, and specifically establishing a graph theory description and a matrix model of a system-level heat transfer process in a stacked matrix block mode, wherein the graph theory description and the matrix model comprise processing of the incidence matrix and the heat transfer constraint equation. On the basis of the incidence matrix among the systems, the incidence matrix reflecting the topological relation among different components is continuously added in a diagonal form, an increment incidence matrix considering the topological relation increased when an external node is connected with a reference node is supplemented, and the system incidence matrix finally describing the topological relation among the nodes of the system is obtained by reducing the order and is used for integrally reflecting the topological relation among the components. Based on a heat transfer constraint equation in a general form, all matrixes and vectors of the heat transfer constraint equation among the components in the system are described by using graph theory, increment matrixes and increment vectors when external nodes are connected with reference nodes are additionally considered, and the matrixes and vectors inside the components are added, so that the heat transfer constraint equation of the system for describing the overall heat transfer constraint condition of the system and all the matrixes and vectors thereof are constructed in a matrix block superposition mode.
S103, performing matrix analysis on the system incidence matrix and the system heat transfer constraint equation, determining a target solution condition, and establishing a system integral constraint equation according to a matrix analysis result and the target solution condition;
performing matrix analysis on the system incidence matrix and the system heat transfer constraint equation determined in the step S102 to determine a target solution condition. And obtaining a system heat transfer constraint equation by utilizing the incidence matrix, wherein the system heat transfer constraint equation comprises three equations, the first equation corresponds to a kirchhoff current law equation in electricity, the second equation corresponds to a kirchhoff voltage law equation, and the third equation corresponds to a voltage-current relation equation reflecting the characteristics of the electrical elements on a branch. These equations are established in a general form, and actually, only the correlation matrix in each heat treatment process obtained in step S101 and the coefficient matrix determined from the correlation matrix need to be calculated. Since the equations are all linear equations which are matrixed, a common matrix equation solving algorithm is adopted for solving the equations.
And establishing a system integral constraint equation according to the matrix analysis result and the target solution condition. And giving a target solution condition or a required solution condition, wherein the target solution condition comprises a heat flow solution condition which enables the heat flow to have a unique solution and a boundary condition which enables the system parameter to be closed. And finding out a definite solution condition which enables a system model to have a unique solution through analyzing the system incidence matrix and the coefficient matrix, thereby establishing the system overall constraint equation and the corresponding definite solution condition.
The thermodynamic system matrix model construction method provided by the embodiment of the invention is a clear and standardized thermodynamic system model construction method based on graph theory description and matrix operation, a system incidence matrix and a system heat transfer constraint equation are effectively established based on the topological relation among nodes of each process, the system incidence matrix and the system heat transfer constraint equation are subjected to matrix analysis to determine a target solution condition, then a system overall constraint equation is established according to a matrix analysis result and the target solution condition, the thermodynamic system matrix model solution algorithm which utilizes a linear network to carry out overall solution is also an automatic model generation method which can directly derive a corresponding linearized control equation from components and topological relation of a physical model without graph derivation, and the method can be generally applied to the complex thermodynamic system model construction process of a comprehensive energy system on the premise of ensuring calculation accuracy, the method effectively reduces the calculation difficulty and improves the calculation efficiency, and is favorable for realizing standardization, automation and normalization of the modeling process of the complex thermodynamic system.
Fig. 2 is a schematic flow chart of another thermodynamic system matrix model building method provided in an embodiment of the present invention, and on the basis of the embodiment shown in fig. 1, as shown in fig. 2, step S101 in the thermodynamic system matrix model building method further includes:
s1011, dividing independent nodes for each heat treatment process according to a fluid inlet mode and a fluid outlet mode, and determining the connection line and the direction between the nodes according to the fluid flow continuity;
the heat treatment process in the thermodynamic system is divided into typical processes such as a heat exchanger heat exchange process, a flow separation process, a flow mixing process, a single-flow heating process and the like. According to the division of different heat treatment processes, the thermodynamic system is divided into different parts, parts nodes and parts connecting lines, namely the nodes are divided according to the modes of a fluid inlet and a fluid outlet. And determining the connection line between the nodes and the direction of the connection line according to the fluid flow continuity.
S1012, establishing each incidence matrix to respectively reflect the topological relation between each node and each connecting line in each heat treatment process based on a graph theory description method;
based on the connection lines among the nodes, according to a matrix description method for the relationship between the nodes and the connection lines in the graph theory, the network theory is used for defining each node and each connection line in different heat treatment processes, the topological relationship among the different heat treatment processes of the thermodynamic system is established in a mode of the nodes, the connection lines and the incidence matrix, and the incidence matrix reflecting the topological relationship is established.
And S1013, respectively establishing topological constraint equations between the temperature vectors and the temperature difference vectors based on the incidence matrixes, and respectively establishing heat transfer constraint equations for the heat treatment processes based on the coefficient matrixes of the temperature vectors, the temperature difference vectors and the heat flow vectors.
Based on the incidence matrix, a topological constraint equation between the temperature vector and the temperature difference vector is established, and then a coefficient matrix of the temperature vector, the temperature difference vector and the heat flow vector is introduced, so that a general form equation reflecting heat transfer constraint conditions in different heat treatment processes is established and used as a heat transfer constraint equation. That is, in the system research, the characteristics of each component of the researched physical system and the characteristics of the topological relation among the components are input, the incidence matrix of each component reflecting the topological relation among the components is constructed, and the heat transfer constraint equation in the general matrix expression reflecting the heat transfer constraint of each component is constructed.
On the basis of the above embodiment, in S1011, the method further includes: the method comprises the steps of adding a reference node for a single-strand flow heating process, determining a heat input connecting line from the reference node to an inlet node for the single-strand flow heating process, and determining a heat transfer connecting line between different inlet nodes for a heat exchange process.
And a reference node, namely a reference node for supplementing energy input, is additionally arranged for the single-flow heating process. Aiming at the heat exchange process of a heat exchanger. A heat transfer link reflecting the heat transfer path between different fluid inlet nodes is also established. A connection line reflecting a heat input path between the reference node and the inlet node is also established for the single stream heating process. Therefore, different heat treatment processes are subjected to targeted treatment, and the overall treatment accuracy is improved.
Fig. 3 is a schematic flowchart of another thermodynamic system matrix model building method according to an embodiment of the present invention, and based on the embodiment shown in fig. 2, as shown in fig. 3, step S102 in the thermodynamic system matrix model building method further includes:
s1021, summing the incidence matrixes to obtain a summed incidence matrix, adding an internal incidence matrix reflecting the internal topological relation of different parts to the summed incidence matrix in a diagonal form, adding an external incidence matrix reflecting the topological relation of external nodes and reference nodes, and performing price reduction treatment to obtain the system incidence matrix;
the method comprises the steps of establishing a system incidence matrix in a matrix block superposition mode according to each incidence matrix, establishing a system heat transfer constraint equation in a matrix block superposition mode according to each heat transfer constraint equation, specifically, summing the incidence matrices to obtain a sum incidence matrix, adding an internal incidence matrix reflecting the internal topological relation of different components in a diagonal form to the sum incidence matrix, supplementing an increment incidence matrix considering the increased topological relation when an external node is connected with a reference node, and performing step reduction processing to obtain the system incidence matrix finally describing the topological relation among the nodes of the system, wherein the system incidence matrix is used for integrally reflecting the topological relation between the components.
S1022, fusing the heat transfer constraint equations to obtain a general heat transfer constraint equation reflecting the whole heat treatment process, determining all matrixes and vectors in the general heat transfer constraint equation, adding the matrixes and vectors reflecting the heat transfer constraints of external nodes and reference nodes, adding the matrixes and vectors reflecting the internal heat transfer conditions of different parts, and obtaining all matrixes and vectors of the system heat transfer constraint equation;
and fusing the heat transfer constraint equations obtained in the step S1013 to obtain a general heat transfer constraint equation reflecting all heat treatment processes, determining all matrixes and vectors in the general heat transfer constraint equation by using graph theory description based on the general heat transfer constraint equation, adding the matrixes and vectors reflecting the heat transfer constraints of the external nodes and the reference nodes, adding the matrixes and vectors reflecting the internal heat transfer conditions of different parts, and constructing a system heat transfer constraint equation describing the overall heat transfer constraint condition of the system and all the matrixes and vectors thereof in a matrix block overlapping manner.
On the basis of the above embodiment, in S1022, the determining all the matrices and vectors in the general heat transfer constraint equation includes: the device comprises a diagonal matrix, a temperature difference matrix, a heat flow vector coefficient matrix, a temperature vector coefficient matrix and an independent heat flow vector. Thereby comprehensively reflecting various heat transfer constraints in the thermodynamic system based on the graph theory description.
On the basis of the above embodiment, the thermodynamic system matrix model construction method further includes:
each of the matrices has exchangeability of rows and columns.
Because the matrix equation has exchangeability of rows and columns, the final form of constructing the matrix model of the system is not unique, and the arrangement sequence corresponding to the components, the nodes and the connecting lines is also not unique. In the method provided by the embodiment of the invention, the matrix block superposition mode is to divide and reassemble the component characteristics and the association between the components, so that the method is very favorable for the automatic and batch processing of a large-scale complex thermodynamic system by a computer program.
On the basis of the above embodiment, the target solution condition in S103 includes: a heat flow solution condition that causes the heat flow to have a unique solution, a boundary condition that causes each parameter in the system correlation matrix and the system heat transfer constraint equation to be closed.
On the basis of the above embodiment, the heat flow solution condition is a solution condition that the heat flow derived by searching the maximum linearly independent group of the column vector group is determined to be zero, wherein the column vector group is obtained by analyzing and extracting each coefficient matrix in the system incidence matrix and the system heat transfer constraint equation;
correspondingly, the boundary condition is given by a coefficient matrix input mode aiming at an external node temperature constraint equation, wherein the external node is determined according to a system incidence matrix based on graph theory description knowledge.
The heat flow definite solution condition extracts a column vector group which meets the condition through the analysis of a system incidence matrix and a coefficient matrix, finds a maximum linear irrelevant group of the column vector group through mathematical processing, derives the heat flow which needs to give the definite solution condition and gives the definite solution condition of zero; external nodes of the system are found out according to the correlation matrix characteristics based on graph theory description knowledge, constraint equations of temperature vectors, temperature difference vectors and the like of the nodes are given in a matrix mode, and finally boundary conditions are given in a coefficient matrix input mode. Since the way to mathematically find the very large linearly independent set of column vector sets is not unique, the objects of the derived heat flow solution conditions are not unique, but the number of objects obtained by different methods is unique. And finding out a definite solution condition which enables a system model to have a unique solution through analyzing the system incidence matrix and the coefficient matrix, thereby establishing the system overall constraint equation and the corresponding definite solution condition.
Fig. 4 is a schematic diagram illustrating a heat exchange process of a heat exchanger in the method according to the embodiment of the present invention, and a counter-flow heat exchanger is taken as an example for illustration, and other types of heat exchangers can be treated in the same manner. As shown in FIG. 4, the correlation matrix describing the topological relationship of the heat treatment process is
The 1 st and 2 nd columns represent the topological relation of working medium flowing between the node 1 and the node 2 and between the node 3 and the node 4, the 3 rd column represents the topological relation of heat transfer between the node 1 and the node 3, the element 1 represents the starting point of a connecting line of the topological relation, and the element-1 represents the end point of the connecting line of the topological relation. Using the correlation matrix, a topological constraint between the temperature vector T and the temperature differential vector Δ T can be established as
By introducing the coefficient matrix H of the heat flow vector, the heat transfer constraint equation can be written in the form of a matrix
Wherein phi1→2Phi of3→4Is heat flow accompanying the flow of working medium, phi1→3Is the heat flow transferred between the fluids, m is the mass flow of the working medium, cpIs the constant pressure heat capacity (mc) of the fluid working mediump) Subscript 1 represents fluid between nodes 1,2, subscript 2 represents fluid between nodes 3, 4, R is the thermal resistance of the counterflow heat exchanger, and is expressed as
Wherein K is the heat exchange coefficient of the heat exchanger, and A is the heat exchange area of the heat exchanger.
FIG. 5 is a schematic diagram illustrating the principle of the flow separation process in the method according to the embodiment of the present invention, and the correlation matrix describing the topological relationship of the thermal treatment process is shown in FIG. 5
Using the correlation matrix, a topological constraint between the temperature vector T and the temperature differential vector Δ T can be established as
Since the temperature is not changed during the flow separation process, the coefficient matrix corresponding to the heat transfer constraint equation is zero.
FIG. 6 is a schematic diagram illustrating the principle of the flow mixing process in the method according to the embodiment of the present invention, and the correlation matrix describing the topological relationship of the thermal treatment process is shown in FIG. 6
Using the correlation matrix, a topological constraint between the temperature vector T and the temperature differential vector Δ T can be established as
By introducing a coefficient matrix J of temperature vectors, the heat transfer constraint equation can be written in matrix form as
Wherein λ1＝(mcp)1/[(mcp)1+(mcp)2]And λ2＝(mcp)1/[(mcp)1+(mcp)2]Is the proportionality coefficient of the inlet heat capacity flow to the outlet heat capacity flow.
Fig. 7 is a schematic diagram illustrating a principle of a single-stream heating process in the method according to the embodiment of the present invention, as shown in fig. 7, the heat treatment process is applicable to heat input processes such as an electric heat pump, a cogeneration unit, and the like, and a virtual reference node r needs to be introduced to represent heat input besides the input and output nodes 1 and 2, where the reference node r is similar to a ground node in a circuit, and the temperature can be assumed to be 0. The correlation matrix describing the topological relationship of the heat treatment process is
Using the correlation matrix, a topological constraint between the temperature vector T and the temperature differential vector Δ T can be established as
By introducing the coefficient matrix H of the heat flow vector, the heat transfer constraint equation can be written in matrix form as
Wherein phi1→2Is heat flow accompanying the flow of working medium, phir→1Representing a unidirectional input of heat.
Through the analysis, the temperature difference-heat flow-temperature heat transfer constraint equation of different processes can be written into a general form by analogy with a voltage-current relation equation described by a tabulation method in the theory of an electric network
FΔT+HΦ+JT＝Φs+Ts (13)
Wherein F is a diagonal matrix and describes whether a temperature difference term exists in the heat transfer constraint equation, and delta T is a temperature difference matrix; q is the heat flow vector, H is the corresponding coefficient matrix; t is the temperature vector, J is the corresponding coefficient matrix; qsAnd TsAre independent heat flow and temperature vectors.
Fig. 8 is a schematic diagram of a typical district heating system to which the method according to the embodiment of the present invention is applied, and as shown in fig. 8, the specific components include a heat exchanger device HE, a flow separation process SP, a flow mixing process MP, and an electric heat pump HP. Each node is represented by a serial number 1-20, connecting lines among the components are represented by dotted line arrows 1-7, and solid line arrows represent the flowing direction of the fluid working medium. The hot water of the primary network from the CHP enters a heat exchange station HE1 through a node 1 to heat secondary network water, the secondary network water is divided into two flows and passes through radiators HE2 and HE3 to heat indoor air, and the return water of the secondary network is mixed and then added into an electric heat pump HP to serve as an auxiliary heat source. The matrix modeling method for the typical district heating system is as follows:
(1) constructing a matrix model reflecting overall topological characteristics and heat transfer characteristics of the system
The incidence matrix reflecting the topological relation among the components in the example is
Here, the incidence matrix is written after being inverted for page beauty. For the transposed correlation matrix, each column represents a node (20 in the figure) and each row represents a branch (7 in the figure). The column with element 1 represents the start of a branch and the column with element-1 represents the end of a branch.
At this stage, the incidence matrix only describes the topological relation among the components, and then the topological relation inside the components needs to be added and added into the incidence matrix describing the topological relation among the nodes of the system. Depending on the type of each component, the final topological correlation matrix is
Because a single-strand flow process introduces a reference node, a column needs to be added to the whole transposed incidence matrix, and the topological relation inside other components is added to the original incidence matrix along the diagonal in the form of a block matrix. It is worth mentioning that even if there are multiple single-stream processes, only one common reference node may be used.
The third step is to close the flow path of the non-closed loop, which is similar to connecting an open node in the circuit to ground to form a closed loop circuit. In this example, there are six external nodes 1,2,7,8,11,12, so connecting them to the reference node adds six rows in the transposed correlation matrix in the form of six rows
Where A is3Is a 21 x 28 matrix describing the overall topological relationship of the 21 nodes and 28 branches. At the same time due to the matrixThe sum of all column vectors must be zero vector, and it can be known from graph theory that A is deleted3Any row of (a) still retains all the topological connection information. Therefore, can be substituted by3Deleting the last row representing the reference node, and adding A3Reduced to a reduced incidence matrix A4And the correlation matrix is used for describing the topological relation among the nodes of the system.
Given the general form of the heat transfer constraint equation, the matrices and vectors describing the heat transfer constraints between the components can be given as
FCC＝diag(1,1,1,1,1,1,1) (17)
HCC＝07×7 (19)
JCC＝07×21 (21)
TCC＝(T1,...,T20)T (22)
Qs,CC＝Ts,CC＝07×1 (23)
And the six branches connecting the external node and the reference node give the heat transfer constraint equation of the six branches as a matrix and a vector
FRB＝diag(1,1,1,1,1,1) (24)
HRB＝06×6 (26)
JRB＝06×21 (28)
TRB＝(T1,...,T20)T (29)
Qs,RB＝06×1 (30)
Using these matrices and vectors describing the heat transfer constraints between components in the system plus matrices and vectors within the components, one can construct a matrix and vector describing the overall heat transfer constraint equations for the system as
F＝diag(FCC,FHE,1,FHE,2,FHE,3,FSP,FMP,FHP,FRB) (31)
ΔT＝(ΔTCC,ΔTHE,1,ΔTHE,2,ΔTHE,3,ΔTSP,ΔTMP,ΔTHP,ΔTRB)T (32)
H＝diag(HCC,HHE,1,HHE,2,HHE,3,HSP,HMP,HHP,HRB) (33)
T＝(T1,...,T20)T (36)
Qs＝(Qs,CC,Qs,HE,1,Qs,HE,2,Qs,HE,3,Qs,SP,Qs,MP,Qs,HP,Qs,RB)T (37)
Ts＝(Ts,CC,Ts,HE,1,Ts,HE,2,Ts,HE,3,Ts,SP,Ts,MP,Ts,HP,Ts,RB)T (38)
Using the matrices and vectors obtained above, the heat transfer constraint equation for the system as a whole can be written as
A4Q＝0 (39)
ΔT-A4 TT＝0 (40)
FΔT+HQ+JT＝Ts+Qs (41)
The first equation corresponds to a kirchhoff current law equation in the electricity, the second equation corresponds to a kirchhoff voltage law equation, and the third equation corresponds to a voltage-current relation equation reflecting the characteristics of the electrical elements on the branch.
(2) Giving the necessary solution conditions for model solution
Construct A by looking for the presence of non-zero elements in only columns 10, 13, 16, 22 in Hu＝(v1,…,v9,v11,v12,v14,v15,v17,…,v21,v23,…,v28) Finding the maximum linearly independent set of matrix column vectors { v }a(1),va(2),…,va(m)The remaining column vectors form a set { v }b(1),vb(2),…,vb(n)}. The conditions for the solution can be given as
(Qb(1),Qb(2)...,Qb(n))T＝0 (42)
The method for searching the maximum linear independent group in mathematics is not unique, the simplest method is a traversal method, namely, the most columns which can enable the matrix rank constructed by the column vector group to be unchanged are sequentially taken out, and the remaining column vectors form the maximum linear independent group of the original vector.
In addition, for three open-circuit fluids (primary network water and indoor temperature), three temperature or heat flow boundaries need to be given, external nodes of the fluids can be found out according to correlation matrix characteristics based on graph theory knowledge, and constraint equations of the node temperatures are given in a matrix mode
CmTs,RB＝Cv (43)
Where C ismAnd CvRespectively a 3 x 6 matrix and a 3 x 1 vector. Given the inlet temperatures as an example, the equation can be written as
Wherein T isc,i(i-1-3) is a given boundary temperature.
In the schematic diagram of the typical district heating system principle shown in fig. 8, when the typical district heating system applies a thermodynamic system matrix model construction method, it effectively establishes a system incidence matrix and a system heat transfer constraint equation based on the topological relation between nodes of each process, and performs matrix analysis on the system incidence matrix and the system heat transfer constraint equation to determine a target solution condition, and then establishes a system overall constraint equation according to the matrix analysis result and the target solution condition, which is a thermodynamic system model solution algorithm that performs overall solution using a linear network, and is an automatic model generation method that can directly derive a corresponding linearized control equation from components and topological relation of a physical model without graph derivation, and the method can be universally applied to the complex thermodynamic system model construction process of an integrated energy system on the premise of ensuring calculation accuracy, the method effectively reduces the calculation difficulty and improves the calculation efficiency, is favorable for realizing standardization, automation and normalization of the modeling process of the complex thermodynamic system, and can effectively avoid errors caused by manual operation.
In a second aspect, an embodiment of the present invention provides an electronic device, and fig. 9 is a schematic structural diagram of the electronic device provided in the embodiment of the present invention, as shown in fig. 9, the electronic device includes: a processor (processor)910, a communication Interface (Communications Interface)920, a memory (memory)930, and a communication bus 940, wherein the processor 910, the communication Interface 920, and the memory 930 communicate with each other via the communication bus 940. Processor 910 may invoke logic instructions in memory 930 to perform a thermodynamic system matrix model building method comprising:
s101, determining connection lines among all nodes, establishing an incidence matrix representing topological relation among all nodes based on the connection lines among all nodes, and establishing a heat transfer constraint equation based on the incidence matrix, wherein all the nodes are obtained by dividing all heat treatment processes in a thermodynamic system;
s102, establishing a system incidence matrix in a matrix block superposition mode according to each incidence matrix, and establishing a system heat transfer constraint equation in a matrix block superposition mode according to each heat transfer constraint equation;
s103, performing matrix analysis on the system incidence matrix and the system heat transfer constraint equation, determining a target solution condition, and establishing a system integral constraint equation according to a matrix analysis result and the target solution condition.
Furthermore, the logic instructions in the memory 930 may be implemented in software functional units and stored in a computer readable storage medium when the logic instructions are sold or used as independent products. Based on such understanding, the technical solution of the present invention may be embodied in the form of a software product, which is stored in a storage medium and includes several instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the steps of the thermodynamic system matrix model building method according to the embodiments of the present invention. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk or an optical disk, and other various media capable of storing program codes.
In a third aspect, an embodiment of the present invention provides a non-transitory computer-readable storage medium, on which a computer program is stored, where the computer program, when executed by a processor, implements a thermodynamic system matrix model building method as described above, where the method includes:
s101, determining connection lines among all nodes, establishing an incidence matrix representing topological relation among all nodes based on the connection lines among all nodes, and establishing a heat transfer constraint equation based on the incidence matrix, wherein all the nodes are obtained by dividing all heat treatment processes in a thermodynamic system;
s102, establishing a system incidence matrix in a matrix block superposition mode according to each incidence matrix, and establishing a system heat transfer constraint equation in a matrix block superposition mode according to each heat transfer constraint equation;
s103, performing matrix analysis on the system incidence matrix and the system heat transfer constraint equation, determining a target solution condition, and establishing a system integral constraint equation according to a matrix analysis result and the target solution condition.
The above-described embodiments of the apparatus are merely illustrative, and the units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of the present embodiment. One of ordinary skill in the art can understand and implement it without inventive effort.
Through the above description of the embodiments, those skilled in the art will clearly understand that each embodiment can be implemented by software plus a necessary general hardware platform, and certainly can also be implemented by hardware. With this understanding in mind, the above-described technical solutions may be embodied in the form of a software product, which can be stored in a computer-readable storage medium such as ROM/RAM, magnetic disk, optical disk, etc., and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute the methods described in the embodiments or some parts of the embodiments.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.
Claims (10)
1. A thermodynamic system matrix model construction method is characterized by comprising the following steps:
s101, determining connection lines among all nodes, establishing an incidence matrix representing topological relation among all nodes based on the connection lines among all nodes, and establishing a heat transfer constraint equation based on the incidence matrix, wherein all the nodes are obtained by dividing all heat treatment processes in a thermodynamic system;
s102, establishing a system incidence matrix in a matrix block superposition mode according to each incidence matrix, and establishing a system heat transfer constraint equation in a matrix block superposition mode according to each heat transfer constraint equation;
s103, performing matrix analysis on the system incidence matrix and the system heat transfer constraint equation, determining a target solution condition, and establishing a system integral constraint equation according to a matrix analysis result and the target solution condition.
2. The thermodynamic system matrix model construction method as claimed in claim 1, wherein the S101 includes:
s1011, dividing independent nodes for each heat treatment process according to a fluid inlet mode and a fluid outlet mode, and determining the connection line and the direction between the nodes according to the fluid flow continuity;
s1012, establishing each incidence matrix to respectively reflect the topological relation between each node and each connecting line in each heat treatment process based on a graph theory description method;
and S1013, respectively establishing topological constraint equations between the temperature vectors and the temperature difference vectors based on the incidence matrixes, and respectively establishing heat transfer constraint equations for the heat treatment processes based on the coefficient matrixes of the temperature vectors, the temperature difference vectors and the heat flow vectors.
3. The thermodynamic system matrix model building method according to claim 2, wherein in S1011, the method further comprises: the method comprises the steps of adding a reference node for a single-strand flow heating process, determining a heat input connecting line from the reference node to an inlet node for the single-strand flow heating process, and determining a heat transfer connecting line between different inlet nodes for a heat exchange process.
4. The thermodynamic system matrix model construction method as claimed in claim 2, wherein the S102 includes:
s1021, summing the incidence matrixes to obtain a summed incidence matrix, adding an internal incidence matrix reflecting the internal topological relation of different parts to the summed incidence matrix in a diagonal form, adding an external incidence matrix reflecting the topological relation of external nodes and reference nodes, and performing price reduction treatment to obtain the system incidence matrix;
s1022, fusing the heat transfer constraint equations to obtain a general heat transfer constraint equation reflecting the whole heat treatment process, determining all matrixes and vectors in the general heat transfer constraint equation, adding the matrixes and vectors reflecting the heat transfer constraint conditions of the external nodes and the reference nodes, adding the matrixes and vectors reflecting the internal heat transfer conditions of different parts, and obtaining all the matrixes and vectors of the system heat transfer constraint equation.
5. The thermodynamic system matrix model building method according to claim 4, wherein in the step S1022, the determining all the matrices and vectors in the general heat transfer constraint equation includes: the device comprises a diagonal matrix, a temperature difference matrix, a heat flow vector coefficient matrix, a temperature vector coefficient matrix and an independent heat flow vector.
6. The thermodynamic system matrix model construction method as claimed in claim 5, comprising:
each of the matrices has exchangeability of rows and columns.
7. The thermodynamic system matrix model construction method as claimed in claim 5, wherein the target solution condition in S103 includes: a heat flow solution condition that causes the heat flow to have a unique solution, a boundary condition that causes each parameter in the system correlation matrix and the system heat transfer constraint equation to be closed.
8. The thermodynamic system matrix model construction method according to claim 7, wherein the heat flow solution condition is a solution condition derived by finding a maximum linearly independent set of column vector sets and setting the heat flow to zero, wherein the column vector sets are obtained by analyzing and extracting coefficient matrixes in a system correlation matrix and a system heat transfer constraint equation;
correspondingly, the boundary condition is given by a coefficient matrix input mode aiming at an external node temperature constraint equation, wherein the external node is determined according to a system incidence matrix based on graph theory description knowledge.
9. An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor implements the thermodynamic system matrix model construction method according to any one of claims 1 to 8 when executing the computer program.
10. A non-transitory computer-readable storage medium, on which a computer program is stored, which, when being executed by a processor, implements the thermodynamic system matrix model building method according to any one of claims 1 to 8.
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