Aircraft energy and heat system modeling method based on graph theory
By modeling the aircraft's energy and thermal system based on graph theory, the problem of difficult to model the strongly coupled energy and thermal system in multi-electric aircraft in the existing technology is solved, and efficient and accurate modeling and control of complex systems is achieved.
Patent Information
- Application Number
- CN202510056436.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-01-14
- Publication Date
- 2025-05-23
AI Technical Summary
The prior art is difficult to effectively model strongly coupled energy-thermal systems spanning multiple physical domains and multiple time scales in multi-electric aircraft.
Using a graph theory-based method, dynamic equations are established by defining vertices and edges in the graph theory model, and state changes and energy flow of each vertices in the system are described. The specific steps include determining the number of vertices, edges and connection relationships in the graph theory model, defining the matrices E, M, D and C, deriving dynamic equations, and calculating the edge power flow.
It realizes unified automated modeling of complex aircraft energy and thermal systems, can clearly understand the changes in key state quantities and energy flow, and is suitable for control objects in multiple time scales and multiple physical domains, improving the computing efficiency and accuracy of modeling.
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Figure CN120030752A_ABST
Abstract
Description
Technical Field
[0001] The present application belongs to the technical field of aircraft energy and thermal system modeling, and specifically relates to an aircraft energy and thermal system modeling method based on graph theory. Background Art
[0002] As aircraft electrical systems gradually replace traditional power systems, the coupling between aircraft engines, electrical systems, and thermal management systems becomes increasingly complex. Electrification brings many performance and efficiency advantages, but it also brings more thermal management challenges.
[0003] In commercial aviation, thermal management is one of the factors that hinder the development of more electric propulsion systems. In the future, the aircraft will be a large system composed of multiple subsystems, and its energy is converted and consumed between multiple systems. The time scale of regulation of each subsystem ranges from voltage regulation in milliseconds to fuel tank temperature regulation in minutes.
[0004] Developing mathematical models that can describe multiple time scales and multiple spatial scales in these complex systems can promote the development and research of model-based advanced control algorithms. In view of this, this application is proposed. Summary of the invention
[0005] The purpose of this application is to provide an aircraft energy and thermal system modeling method based on graph theory to solve the technical problem of difficulty in modeling strongly coupled energy and thermal systems across multiple physical domains and multiple time scales in more-electric aircraft.
[0006] The technical solution of this application is:
[0007] A graph-theory-based aircraft energy and thermal system modeling method, comprising:
[0008] Determine the number of source vertices N in the graph theory model s , the number of dynamic vertices is N v , the number of sink vertices is N t , the number of edges is N e , the number of input variables is N uC , the edges introduced by the source vertex are not counted in N e inside;
[0009] Definition N e ×2 matrix E is used to describe the directed edges connecting the vertices in the system;
[0010] The matrix M is automatically generated from the matrix E to describe the relationship between each vertex and the edges connected to it;
[0011] Take the first N of the matrix M v Column matrix
[0012] Definition N v ×Ns The matrix D is used to describe the edges introduced by the source vertex;
[0013] Get the capacity C of each dynamic vertex i , forming an N v The diagonal matrix C of order;
[0014] Obtain the dynamic equations describing the entire system: in, is a column vector consisting of the state values of all dynamic vertices, P is a column vector consisting of the edges derived from all dynamic vertices, P in A column vector of all the edges that originate from the source vertex.
[0015] According to at least one embodiment of the present application, the above-mentioned aircraft energy and thermal system modeling method based on graph theory further includes:
[0016] Definition N e ×N uC The matrix B is used to describe the input variable u of the system;
[0017] Definition N e ×4 matrix E_Coeff, used to characterize the edge power flow calculation coefficients;
[0018] Substitute the elements of matrix B and matrix E_Coeff into the formula to calculate P:
[0019] P = (a + u) (bx tail +cx head +d);
[0020] Among them, x tail With x head are the state values of the tail vertex and the head vertex of P respectively; u is the input corresponding to edge P. When P does not correspond to any input, u=0; a, b, c, d are the edge power flow calculation coefficients.
[0021] According to at least one embodiment of the present application, the above-mentioned aircraft energy and thermal system modeling method based on graph theory further includes:
[0022] Number each vertex in the graph theory model.
[0023] According to at least one embodiment of the present application, in the above-mentioned graph theory-based aircraft energy and thermal system modeling method, in the i-th row of the matrix E, the first column is the tail vertex number of the i-th edge, and the second column is the head vertex number of the i-th edge.
[0024] According to at least one embodiment of the present application, in the above-mentioned aircraft energy and thermal system modeling method based on graph theory, M=[m ij ];
[0025]
[0026] According to at least one embodiment of the present application, in the above-mentioned graph theory-based aircraft energy and thermal system modeling method, for the i-th source vertex, when it is connected to the dynamic vertex j, fill 1 in the j-th row and i-th column of the matrix D, and let D(j,i)=1, otherwise take 0.
[0027] According to at least one embodiment of the present application, in the above-mentioned graph theory-based aircraft energy and thermal system modeling method, for the i-th input, assuming that the power flow calculation on the j-th edge requires input i, then the j-th row and i-th column of the matrix B is 1, and B(j,i)=1, otherwise it is 0. BRIEF DESCRIPTION OF THE DRAWINGS
[0028] Figure 1 is a schematic diagram of a graph theory model provided in an embodiment of the present application;
[0029] Figure 2 is a schematic diagram of an aircraft energy and thermal system modeling method based on graph theory provided in an embodiment of the present application;
[0030] Figure 3 is a schematic diagram of a graph theory model of a cold plate component provided in an embodiment of the present application;
[0031] Figure 4 is a schematic diagram of an energy system architecture provided by an embodiment of the present application;
[0032] Figure 5 is a schematic diagram of a thermal management system architecture provided in an embodiment of the present application;
[0033] Figure 6 It is a schematic diagram of an energy system architecture provided in an embodiment of the present application being abstracted into a graph theory model;
[0034] Figure 7 It is a schematic diagram of the thermal management system architecture provided in the embodiment of the present application abstracted as a graph theory model.
[0035] In order to better illustrate the present embodiment, some contents of the drawings may be omitted, enlarged or reduced, which is only used for illustrative purposes and should not be construed as limiting the present application. DETAILED DESCRIPTION
[0036] In order to make the technical solution and advantages of the present application clearer, the technical solution of the present application will be described in further detail in detail and in detail with reference to the accompanying drawings. It can be understood that the specific embodiments described here are only partial embodiments of the present application, which are only used to explain the present application, not to limit the present application. It should be noted that, for the convenience of description, only the parts related to the present application are shown in the accompanying drawings, and other related parts can refer to the general design.
[0037] In addition, unless otherwise defined, the technical terms or scientific terms used in the description of this application should be the common meanings understood by those skilled in the art in the field to which this application belongs. The term "include" used in the description of this application means that the concepts appearing before the term include the concepts listed after the term and their equivalents, without excluding other related concepts.
[0038] According to the aircraft energy and thermal system architecture, a graph theory-based model of components and systems is established. Typical components of the system include generators, DC buses, batteries, loads, boost pumps, cold plates, heat exchangers, liquid storage tanks, etc.
[0039] The state quantity x of the component directly affected by the input and output power flow is used as a vertex in the graph model. For components of a thermal management system, this state quantity x is often the temperature. If a part of a real component transfers power P to another part, then in the graph model, a directed edge is drawn from one vertex to another vertex. For an edge P representing power flow, when P is connected by vertex x 1 Lead to x 2 When 1 is the tail vertex of edge P, point x 2 It is the head vertex of edge P. The vertices of a certain edge model can be divided into three categories: source vertex: the vertex that introduces energy from the outside world or other components to the component; dynamic vertex: the vertex that contains the state quantity that needs attention inside the component; sink vertex: the vertex that draws energy from the component to the outside world or other components.
[0040] According to the law of conservation of energy, a dynamic equation of the influence of power flow on the state quantity x is established, and each state vertex x is extracted from the dynamic equation i Capacitance C i . Thus, the dynamic equation is rewritten into the form of (1):
[0041]
[0042] According to the form of the dynamic equation (1), we can get: i Vertices with larger values correspond to states with larger time scales, C i The vertex with smaller value corresponds to the state quantity with smaller time scale. For the target component, the number of its overall input and output power flows and the number of dynamic vertices are determined, and then the dynamic model of the target component in graph theory form is obtained.
[0043] The above is the graph theory modeling technology for a single component. For a system or subsystem composed of multiple components, its graph theory model is also composed of the graph theory models of its internal components. The sink vertex of a component model may be the source vertex of another component in the system, and the source vertex of a component model may be the sink vertex of another component in the system. This reflects the modular characteristics of graph theory modeling, which can clearly describe the energy flow and state changes within the system.
[0044] Based on the above, the present application provides a graph-theory-based aircraft thermal system modeling method, so as to obtain a unified and automated form when modeling components / systems in the thermal system, such as Figure 1 As shown in the figure, determine the structure of the model, that is, the number of vertices, edges, vertex connection relationships, etc. in the model, and derive the capacitance C of each vertex based on physical principles such as the law of conservation of energy. i The method of obtaining and converting the equation form to calculate the power flow.
[0045] Determine the number of source vertices N in the graph theory model s , the number of dynamic vertices is N v , the number of sink vertices is N t , the number of edges is N e , the number of input variables is N uC , the edges introduced by the source vertex are not counted in N e inside.
[0046] Number each vertex in the graph theory model.
[0047] Definition N e ×2 matrix E is used to describe the directed edges connecting the vertices in the system. The first column of the ith row in matrix E is the number of the tail vertex of the ith edge, and the second column is the number of the head vertex of the ith edge. Matrix E also gives the numbers of the edges in the graph theory model.
[0048] After the definition of matrix E is completed, the matrix M can be automatically generated from matrix E = [m ij ], and its generation method is shown in formula (2):
[0049]
[0050] The matrix M describes the relationship between each vertex and the edges connected to it. For the complete matrix M, take its first N v Column matrix Will be involved in the calculation of the model's dynamic equations.
[0051] Definition N v ×N sThe matrix D is used to describe the edges introduced by the source vertex. For the i-th source vertex, when it is connected to the dynamic vertex j, fill 1 in the j-th row and i-th column of the matrix D, that is, let D(j,i) = 1, otherwise it is 0.
[0052] The capacitance C of each dynamic vertex is obtained by measuring i , forming an N v The diagonal matrix C of order.
[0053] When the matrix After the matrix D is defined, the dynamic equation describing the entire system can be obtained:
[0054]
[0055] in, is a column vector consisting of the state values of all dynamic vertices, P is a column vector consisting of the edges derived from all dynamic vertices, P in is a column vector of all the edges from the source vertex. It can be verified that when it is expanded row by row, it is the dynamic equation of a single vertex.
[0056] The above definitions are mainly used to establish the system dynamic equations to determine the calculation method of the vertex state value change. In order to clarify the calculation method of the entire graph theory model, it is also necessary to define the calculation method of the edge power flow. In practical applications, in order to simplify the calculation, the calculation of the edge power flow is often linearized, that is, the calculation formula of the edge power flow P is (is an element in the P matrix):
[0057] P = (a + u) (bx tail +cx head +d)………(4)
[0058] Among them, x tail With x head are the state values of the tail vertex and the head vertex of P, respectively. u is the input corresponding to edge P. When P does not correspond to any input, u = 0. a, b, c, d are the edge power flow calculation coefficients. The main steps of normalizing the power flow calculation of the entire model are as follows.
[0059] Definition N e ×N uC The matrix B is used to characterize the situation of the system input variable u. For the i-th input, assuming that the power flow calculation on the j-th edge requires input i, then the j-th row and i-th column of the matrix B are 1, that is, let B(j,i) = 1, otherwise it is 0. With the help of matrix B, we can find out whether a certain edge corresponds to a certain input and the corresponding input number.
[0060] Definition N e×4 matrix E_Coeff is used to characterize the edge power flow calculation coefficients. For the i-th edge, assume that the four coefficients a, b, c, and d in equation (4) are a 0 ,b 0 ,c 0 ,d 0 Then let the four columns of the i-th row of the matrix E_Coeff be a 0 ,b 0 ,c 0 ,d 0 , that is, let E_Coeff(i,1)=a 0 ,E_Coeff(i,2)=b 0 ,E_Coeff(i,3)=c 0 E_Coeff(i,4)=d 0 .
[0061] For a certain edge power flow, when it does not contain input u, its calculation method is E_Coeff(i,1)*(E_Coeff(i,2)*x tail +E_Coeff(i,3)*x head +E_Coeff(i,4)), when it contains input u, it is calculated as (E_Coeff(i,1)+u)*(E_Coeff(i,2)*x tail +E_Coeff(i,3)*x head +E_Coeff(i,4)).
[0062] Therefore, the calculation method of edge power flow has been defined. In summary, by establishing the above matrix, the standardized graph model of a system / component is established. If other constraints need to be added, other matrices can be introduced.
[0063] The plant model in graph theory form is simple, decomposable, modular, and can be used for model-based control, such as MPC algorithms. In addition, for model-based control of large interconnected systems, model fidelity and computational efficiency must be balanced.
[0064] The graph-theory-based aircraft thermal system modeling method disclosed in the above-mentioned embodiment can clearly understand the changes in key state quantities and energy flow in the thermal system, can cope with the establishment of predictive models for control objects in multiple time scales and multiple physical domains, and can accurately model systems containing multiple energy domains in a computationally efficient manner, while accurately capturing the dynamics of the power flow system and reducing computing time and computing resources used.
[0065] In a specific embodiment, the aircraft energy and thermal system modeling method based on graph theory disclosed in the above embodiment is used to model the cold plate component in the thermal management system as follows.
[0066] According to the energy flow analysis, the cold plate components are abstracted as follows Figure 3 The graph model shown in Figure 2, where the vertex x 1 is the cold plate wall temperature, vertex x 2 is the fluid outlet temperature at the cold plate, vertex x 3 For downstream parts; S 1 The component cooled by the cold plate is directed to the vertex x 1 The edge of S represents the heat load of the component; 2 is the component of the cold plate flow, which leads to the vertex x 2 The edge represents the internal energy of the liquid flowing out from the upstream. That is, the cold plate model includes 2 source vertices, 2 dynamic vertices, 1 sink vertex, 2 edges, and 1 input (flow). That is, N s =2, N v =2, N t =1,N e =2, N uC =1.
[0067] Derive the form of the dynamic equation for a given component. According to the first law of thermodynamics:
[0068] △U=QW.
[0069] The cold plate component does not do any work, so W = 0. For the heat Q, we have:
[0070]
[0071] For the internal energy U, we have:
[0072] U=MC p T;
[0073]
[0074] The mass changes of vertex x1 and vertex x2 can be ignored, so So we get the formula:
[0075]
[0076] This can be rewritten as:
[0077]
[0078] Where C = MC p is the vertex capacity. For vertex x 1 The cold plate wall is solid, so C 1 =MC p , M is the mass of the cold plate. For vertex x 2 , it is a liquid, so C 2=ALρC p , A is the cross-sectional area of the flow channel, L is the length of the flow channel, and ρ is the density of the fluid. This completes the definition of the vertex capacity.
[0079] Vertex x 1 to x 2 The edge between represents the heat power brought by the convection heat transfer between the cold plate wall and the liquid, so its calculation method is P = hAΔT = hA(x 1 -x 2 ), h is the convective heat transfer coefficient. 2 to x 3 The edge between represents the internal energy of the liquid due to the transfer of mass from one part to another, so its calculation method should be is the flow rate, defined as input u.
[0080] According to the edges derived from the dynamic vertices, we get So we get According to the connection relationship of the source vertices, the matrix is obtained The model dynamic equation is obtained Expanding by rows easily verifies that it satisfies the dynamic equations for a single vertex.
[0081] Input u refers to the vertex x 2 Flow to vertex x 3 The flow rate is, so the matrix According to the above principle, we can get the matrix So the edge power related matrix has been defined.
[0082] In another specific embodiment, the aircraft energy and thermal system modeling method based on graph theory disclosed in the above embodiment is used to Figure 4 , Figure 5 The energy system architecture and thermal management system architecture are modeled as follows. The energy system architecture and thermal management system architecture are abstracted into graph theory models. Figure 6 , Figure 7 shown.
[0083] In the graph theory model of the energy system, vertex 1 corresponds to the battery, vertices 2 and 5 correspond to the generator, vertices 4, 5, 8, and 9 correspond to the bus, vertices 6 and 7 correspond to the generator, vertices 10 to 19 correspond to the load, and the sink vertices of T1, T2, T3, T4, T1, and T5 represent the waste heat of the components connected to the thermal management system.
[0084] P1, P5, P6, P7, and P9 of the thermal management system represent pump power, and the sum of their powers is the power of LVL6 in the energy system, which is vertex 19 in the energy system graph model; P2, P3, P4, P8, and P10 in the thermal management system represent the waste heat of the converter, battery, and generator in the energy system, which is vertices T1, T2, T3, T4, and T5 in the energy system graph model. These vertices are the coupling parts of the two subsystems.
[0085] After establishing the graph theory framework, it is necessary to uniformly define various related matrices.
[0086] The dynamic equations of the vertices are derived according to the basic physical characteristics of the components and the physical theorems they follow.
[0087] For energy systems, the vertex C value is sometimes used to characterize the transient behavior of components, and sometimes it can be derived from the law of conservation of energy. For example, for battery components, assuming the capacity is Q and the voltage is V, according to the definition of SOC, we have:
[0088]
[0089]
[0090]
[0091] Since SOC is the state quantity of the battery vertex, the capacitance of the battery vertex is selected as QV.
[0092] According to the structure of the graph, we can get the matrix:
[0093]
[0094] At the same time, we get the matrix M and
[0095] According to the connection relationship of the source vertices, the matrix D is obtained.
[0096] The model dynamic equation is obtained
[0097] Expanding by rows easily verifies that it satisfies the dynamic equations for a single vertex.
[0098] In energy systems, the power flow is derived from the balance relationship, so there is no need for the matrix E_Coeff.
[0099] For thermal management systems, most components can derive dynamic equations using the first law of thermodynamics. According to the first law of thermodynamics:
[0100] △U=QW
[0101] The cold plate component does not do any work, so W = 0. For the heat Q, we have:
[0102]
[0103] For the internal energy U, we have:
[0104] U=MC p T;
[0105]
[0106] Vertex x 1 With vertex x 2 The mass change can be ignored, so So we get the formula:
[0107]
[0108] Rewrite it as:
[0109]
[0110] Where C = MC p is the vertex capacitance. Therefore, for the vertex representing the solid state, the capacitance C is directly taken as MC p Calculated in the following way, where M is the solid mass; for the vertex representing the fluid state, the capacitance C is ALρC p It is calculated by , where A is the cross-sectional area of the flow channel, L is the length of the flow channel, and ρ is the density of the fluid.
[0111] For the calculation of edge power flow P, there are generally two forms in the thermal management system. One is to represent the solid vertex x 1 With liquid vertex x 2 The heat power brought by the convective heat transfer between the two is calculated as P = hAΔT = hA(x 1 -x 2 ), h is the convective heat transfer coefficient. Another way to express the heat transfer rate of a fluid from a pipe outlet x is 3 Pass to another pipe outlet x 4 The internal energy of the liquid brought about by this is calculated as is the flow rate, defined as input u.
[0112] According to the edges derived from the dynamic vertices, we get
[0113] At the same time, we get the matrix M and
[0114] According to the connection relationship of the source vertices, the matrix D is obtained.
[0115] The model dynamic equation is obtained
[0116] Expanding by rows easily verifies that it satisfies the dynamic equations for a single vertex.
[0117] There are 13 pipeline flows in this architecture. According to the architecture of the figure, we can get the matrix B. According to the above principle, we can get the matrix: So the edge power related matrix has been defined.
[0118] So far, the technical solution of the present application has been described in conjunction with the preferred embodiments shown in the accompanying drawings. Those skilled in the art should understand that the scope of protection of the present application is obviously not limited to these specific embodiments. Without departing from the principles of the present application, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions after these changes or substitutions will fall within the scope of protection of the present application.
Claims
1. A graph-theory-based aircraft energy and thermal system modeling method, characterized in that: include: Determine the number of source vertices N in the graph theory model s , the number of dynamic vertices is N v , the number of sink vertices is N t , the number of edges is N e , the number of input variables is N uC , the edges introduced by the source vertex are not counted in N e inside; Definition N e ×2 matrix E is used to describe the directed edges connecting the vertices in the system; The matrix M is automatically generated from the matrix E to describe the relationship between each vertex and the edges connected to it; Take the first N of the matrix M v Column matrix Definition N v ×N s The matrix D is used to describe the edges introduced by the source vertex; Get the capacity C of each dynamic vertex i , forming an N v The diagonal matrix C of order; Obtain the dynamic equations describing the entire system: in, is a column vector consisting of the state values of all dynamic vertices, P is a column vector consisting of the edges derived from all dynamic vertices, P in A column vector of all the edges that originate from the source vertex.
2. The aircraft energy and thermal system modeling method based on graph theory according to claim 1 is characterized in that: Also includes: Definition N e ×N uC The matrix B is used to describe the input variable u of the system; Definition N e ×4 matrix E_Coeff, used to characterize the edge power flow calculation coefficients; Substitute the elements of matrix B and matrix E_Coeff into the formula to calculate P: P=(a+u)(bx tail +cx head +d); Among them, x tail With x head are the state values of the tail vertex and the head vertex of P respectively; u is the input corresponding to edge P. When P does not correspond to any input, u=0; a, b, c, d are the edge power flow calculation coefficients.
3. The aircraft energy and thermal system modeling method based on graph theory according to claim 2 is characterized in that: Also includes: Number each vertex in the graph theory model.
4. The aircraft energy and thermal system modeling method based on graph theory according to claim 3 is characterized in that: In the i-th row of matrix E, the first column is the number of the tail vertex of the i-th edge, and the second column is the number of the head vertex of the i-th edge.
5. The aircraft energy and thermal system modeling method based on graph theory according to claim 4 is characterized in that: M=[m ij ]; 6. The aircraft energy and thermal system modeling method based on graph theory according to claim 5 is characterized in that: For the i-th source vertex, when it is connected to the dynamic vertex j, fill 1 in the j-th row and i-th column of the matrix D, and let D(j,i) = 1, otherwise it is 0.
7. The aircraft energy and thermal system modeling method based on graph theory according to claim 6 is characterized in that: For the i-th input, assuming that the power flow calculation on the j-th edge requires input i, then the j-th row and i-th column of the matrix B is 1, and B(j,i)=1, otherwise it is 0.