A method for constructing a security domain for an integrated electrothermal energy system

Abstract

This invention discloses a method for constructing a safety domain for an integrated electrothermal energy system, belonging to the field of energy system modeling and operation analysis. Specifically, it includes: establishing a dynamic model of the integrated electrothermal energy system, including a power system model, a quality regulation thermal system dynamic model, and a combined heat and power (CHP) unit dynamic model; constructing a safety domain model for the integrated electrothermal energy system that considers thermal dynamics, taking into account the nonlinear and nonconvex characteristics of the safety domain; employing an optimization-verification-based concave hull method to solve for the safety domain boundary and characterize the safety domain, addressing the nonlinear and nonconvex characteristics of the safety domain; compared with existing technologies, this application comprehensively considers the thermal dynamics of equipment and network sides in the integrated electrothermal energy system, accurately characterizing the operating characteristics of the integrated electrothermal energy system; and by solving for the limiting operating point using the optimization-verification-based concave hull method, ensuring the absolute safety of the obtained safety domain, providing theoretical guidance for the operation analysis of the integrated electrothermal energy system.

Description

Technical Field

[0001] This invention relates to the field of energy system modeling and operation analysis, specifically to a method for constructing a security domain for an integrated electrothermal energy system. Background Technology

[0002] Due to the global energy crisis and environmental problems, heating systems are gradually shifting from traditional coal-based supply to electricity-based supply to improve energy efficiency and reduce carbon emissions. Against this backdrop, integrated power-heat energy systems have seen widespread development. Cogeneration units and other coupled equipment are key components for coordinated optimization and joint control. However, the close coupling between the power and heating systems also increases the risk of cascading failures and poses additional threats to the power system. For example, a blizzard in a region causing a large-scale power outage and heating interruption exposes the vulnerability of integrated power-heat energy systems. Therefore, a comprehensive analysis of the operational safety of integrated power-heat energy systems is of great significance.

[0003] Existing research typically solves for the safety region through traversal simulation or hyperplane fitting. However, traversal simulation requires generating a sufficient number of scenarios for analysis, making it unsuitable for online analysis; while hyperplane fitting requires extensive model simplification, resulting in lower accuracy. Furthermore, in integrated electrothermal energy systems, thermal dynamics are a crucial factor affecting the safety of combined operation; however, this characteristic is generally neglected in existing research, further reducing the accuracy of the constructed safety region. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention proposes a method for constructing a security domain for an integrated electrothermal energy system.

[0005] The objective of this invention can be achieved through the following technical solutions:

[0006] A method for constructing a security domain for an integrated electrothermal energy system includes the following steps:

[0007] A dynamic model of an integrated electric and thermal energy system is established, which includes a power system model based on power conservation, a quality regulation thermal system dynamic model based on pipeline heat transfer, node heat exchange, node temperature fusion and pipeline-node temperature correlation, and a cogeneration unit dynamic model based on the capacity of the cogeneration unit.

[0008] A safety domain model for the integrated electrothermal energy system is constructed by combining the operational safety constraints of the dynamic model of the integrated electrothermal energy system. Considering the nonlinear and nonconvex characteristics of the safety domain of the integrated electrothermal energy system, the concave hull method is used to solve the boundary of the safety domain and characterize the safety domain.

[0009] Furthermore, the power system model includes nodal power conservation equations and branch power conservation equations, as follows:

[0010]

[0011]

[0012]

[0013]

[0014] In the formula, i and j represent node numbers, t is a time stamp, and V i,t P represents the voltage magnitude at node i at time t. Gi,t and P Li,t Q represents the active power produced by the generator at node i at time t and the active power consumed by the load. Gi,t and Q Li,t G represents the reactive power produced by the generator at node i at time t and the reactive power consumed by the load. ij and B ij θ represents the conductance and susceptance between node i and node j. ij,t P represents the phase angle difference between node i and node j at time t. l,ij,t and Q l,ij,t This represents the active and reactive power transmitted between node i and node j at time t.

[0015] Furthermore, the dynamic model of the quality-regulated thermodynamic system includes pipe heat transfer equations, node heat exchange equations, node temperature fusion equations, and pipe-node temperature correlation equations, as detailed below:

[0016]

[0017]

[0018]

[0019]

[0020] In the formula, Φ and Θ represent the pipe set and node set of the thermal system, respectively, and T j,x,t v represents the relative temperature at point x on pipe j at time t. j C represents the flow velocity of water in pipe j. w m is the specific heat capacity of water. j Let λ be the mass flow rate of the water in the pipe. j φ represents the thermal resistance coefficient of pipe j. i,t Let Ti,t represent the heat power consumed by node i at time t. The relative supply and return water temperatures at node i at time t are represented by L, and the pipe length is Φ. ji and Φ j o Let each represent a pipe set that flows into and out of node j, respectively.

[0021] The analytical solution of equation (5) can be expressed as:

[0022]

[0023] In the formula, δ represents the step function. Let ψ(j,tx / v) represent the temperature distribution at x-vt along pipe j at the initial time, and let ψ(j,tx / v) represent the temperature distribution at the inlet of pipe j at time tx / v.

[0024] Furthermore, the dynamic model of a combined heat and power (CHP) unit includes a coal-fired boiler, steam turbine, generator, and steam-water heat exchanger; the construction of the dynamic model of a CHP unit includes the following steps:

[0025] The input fuel for a coal-fired boiler can be expressed as:

[0026] φ B,t =K B1 m B,t (10)

[0027] In the formula, K B1 φ is the unit calorific value of the fuel. B,t The m represents the heat input to the boiler at time t. B,t This represents the mass flow rate input to the boiler at time t;

[0028] The energy conservation principle within the boiler is expressed as:

[0029]

[0030] In the formula, K B2 For the combustion efficiency of the boiler, K B3 K is the heat storage coefficient of the boiler. T1 For the boiler gain, p T,t Let φ be the pressure of the steam turbine at time t. H,t p represents the power used for heating at time t. B,t The pressure of the coal-fired boiler at time t;

[0031] The energy conservation within a steam turbine can be expressed as:

[0032]

[0033] In the formula, K T2 To represent the inlet opening of a steam turbine, K T3 For the gain of the steam turbine, K T4 P is the time delay factor for the steam turbine. T,tLet t be the electrical power generated by the steam turbine at time t;

[0034] The pressure of the coal-fired boiler and the pressure of the steam turbine meet the following requirements:

[0035]

[0036] In the formula, K B4 This is the coefficient of friction of the boiler;

[0037] The energy conservation within a steam-water heat exchanger can be expressed as:

[0038]

[0039] In the formula, K H1 K represents the heat storage coefficient of the heat exchanger. H2 The thermal conductivity of the heat exchanger is represented by m. H,t This represents the mass flow rate of water undergoing heat exchange in the heat exchanger at time t. and This represents the inlet and outlet temperatures of the steam-water heat exchanger at time t;

[0040] The ordinary differential equations are discretized using the implicit Euler method. Equations (11), (12), and (14) can be discretized as follows:

[0041]

[0042]

[0043]

[0044] In the formula, Δt is the time step, and p B,t-Δt P T,t-Δt and This represents the pressure of the coal-fired boiler, the electrical power input to the steam turbine, and the outlet temperature of the steam-water heat exchanger at time t-Δt.

[0045] Furthermore, the operational safety constraints of the dynamic model of the integrated power and heat energy system include the operational safety constraints of the power system model, the operational safety constraints of the dynamic model of the quality regulation heat system, and the operational safety constraints of the dynamic model of the cogeneration unit, specifically including:

[0046] The operational safety constraints of the power system include branch transmission power constraints, upper and lower limits of generator active and reactive power constraints, upper and lower limits of node voltage amplitude constraints, and voltage phase angle constraints, as shown in equations (18) to (21), respectively.

[0047]

[0048]

[0049] V i min ≤V i,t ≤V i max (20)

[0050] -π≤θ i,t ≤π (21)

[0051] In the formula, This represents the maximum apparent power transmitted between node i and node j. and Let represent the lower limits of the active and reactive power of the generator at node i, respectively. and These represent the upper limits of the active and reactive power of the generator at node i, respectively. and These represent the lower and upper limits of the voltage amplitude at node i, respectively.

[0052] The coupling constraints between the power system and the combined heat and power unit can be expressed as:

[0053] P T,t =P G,t (twenty two)

[0054] The operational safety constraints of a quality-regulating thermal system include the supply and return water temperature constraints at the nodes, which can be expressed as:

[0055]

[0056] In the formula, and This represents the upper and lower limits of the water supply temperature at node i at time t. and The upper and lower limits of the return water temperature at node i at time t are represented; the coupling constraints between the thermal system and the cogeneration unit can be expressed as:

[0057] m G =-m H (twenty four)

[0058]

[0059] In the formula, This represents the water supply temperature of the heat source node at time t. Equation (24) indicates that the inlet and outlet mass flow rates of the steam-water heat exchanger are the same as the mass flow rates of the heat source node; Equation (25) indicates that the outlet temperature of the steam-water heat exchanger is the same as the supply water temperature of the heat source node, and the inlet temperature of the steam-water heat exchanger is the same as the return water temperature of the heat source node.

[0060] The operational safety constraints of a combined heat and power (CHP) unit include the mass flow rate constraint of the input fuel, the pressure constraint of the coal-fired boiler, the pressure constraint of the steam turbine, the heating power constraint, the power supply constraint, and the electrothermal power coupling constraint, as shown in equations (26) to (31), respectively.

[0061]

[0062]

[0063]

[0064]

[0065]

[0066] P T,t +φ H,t ≤K B2 φ B,t (31).

[0067] Furthermore, the construction of the security domain model for the integrated electric and thermal energy system includes the following steps:

[0068] The variables of the integrated energy system at any time t are divided into controllable variables X. t and the controlled variable Y t The controllable variables include the active power of generators in the power system, the input fuel mass in the combined heat and power unit, the heating power of the heat source in the thermal system, and the supply water temperature, which are expressed as follows:

[0069]

[0070] In the formula, Let t represent the controllable variables in the power system at time t. Denotes the controllable variables in the thermodynamic system at time t. φ represents the controllable variable in the cogeneration unit at time t. G,t This represents the heating power of the heat source node at time t;

[0071] The controlled variables include the active and reactive power of branches in the power system, the voltage amplitude and phase angle at nodes, the return water temperature at heat source nodes and the supply water temperature at load nodes in the thermal system, and the input heat, coal-fired boiler and steam turbine pressure, steam-water heat exchanger outlet temperature, and power supply in the combined heat and power unit, which can be expressed as:

[0072]

[0073] In the formula, Denotes the controlled variables in the power system at time t. Denotes the controlled variable in the thermodynamic system at time t. This represents the controlled variable in the cogeneration unit at time t. This represents the water supply temperature at the load node at time t;

[0074] The security domain model of an integrated electrothermal energy system considering thermal dynamics can be expressed as:

[0075]

[0076] In the formula, Ω j Represents the security domain, X1,…,X j Let Y1, ..., Yj be the controllable variables from time 1 to time j. j Let f represent the controlled variables from time 1 to time j, f be the set of equality constraints in the safety domain model, including equations (1) to (4), (6) to (10), (13), (15) to (17), (22), (24), and (25); g be the set of inequality constraints in the safety domain model, including equations (18) to (21), (23), and (26) to (31).

[0077] Furthermore, considering the nonlinear and nonconvex characteristics of the safety domain of the integrated electrothermal energy system, the concave hull method is used to solve for the safety domain boundary, and the safety domain is characterized by the following steps:

[0078] The problem of modeling the safe domain is transformed into the problem of solving the safe domain boundary; Equation (34) is transformed into two sets of nonlinear optimization problems, and the safe domain boundary is characterized by solving the limit running point; the two sets of optimization problems can be expressed as follows:

[0079]

[0080]

[0081] Equations (35) and (36) represent the lower and upper limits of operation of the integrated electrothermal energy system taking thermal dynamics into account, respectively; where F j F represents the vector of all state variables within the integrated energy system at time j. j,i Let A1 represent the i-th variable in the integrated energy system at time j, and let A2 represent the upper bound vector of the inequality constraints.

[0082] Considering the non-convex and nonlinear characteristics of the safety domain model, the limit operating points obtained by solving equations (35) and (36) are subjected to safety verification; ε is defined as the safety margin, if the i-th variable F in the integrated energy system at time j is obtained from the solution. j,i If the upper limit of safe operation is violated, the corresponding optimization problem is corrected as follows:

[0083] min Fj,i

[0084] stf(X1,…,X j ,Y1,…,Y j )=0 (37)

[0085] A1≤g(X1,…,X j ,Y1,…,Y j )≤A2-ε

[0086] If the solution yields the i-th variable F within the integrated energy system at time j... j,i If the upper limit of safe operation is violated, the corresponding optimization problem is corrected as follows:

[0087] min F j,i

[0088] stf(X1,…,X j ,Y1,…,Y j )=0 (38)

[0089] A1+ε≤g(X1,…,X j ,Y1,…,Y j )≤A2

[0090] Based on the limit operating point that meets the safety verification, the boundary of the safety domain is characterized by the concave hull method, and the safety domain of the integrated electrothermal energy system taking into account thermal dynamics is determined.

[0091] The beneficial effects of this invention are:

[0092] Compared with existing technologies, this invention comprehensively considers the thermal dynamics of equipment and network sides in an integrated electrothermal energy system, accurately characterizing the operating characteristics of the integrated electrothermal energy system; by solving the limit operating point using the concave hull method based on optimization-verification, it ensures the absolute safety of the obtained safety domain, providing theoretical guidance for the operation analysis of integrated electrothermal energy systems. Attached Figure Description

[0093] The invention will now be further described with reference to the accompanying drawings.

[0094] Figure 1 A typical electrothermal integrated energy system structure diagram in an embodiment of the present invention;

[0095] Figure 2 A flowchart illustrating the method for constructing a security domain for an integrated electrothermal energy system considering thermal dynamics, as described in an embodiment of the present invention.

[0096] Figure 3 This is a topology diagram of the integrated electrothermal energy system in an embodiment of the present invention;

[0097] Figure 4This is a topology diagram of the thermal system in an embodiment of the present invention;

[0098] Figure 5 This is a time-varying curve of the area of ​​the safety domain formed by generator 1 and generator 2 in the power system in an embodiment of the present invention. Detailed Implementation

[0099] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0100] In the description of this specification, references to terms such as "an embodiment," "example," "specific example," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0101] against Figure 1 As shown in the typical integrated energy system, a method for constructing the security domain of an electrothermal integrated energy system that takes into account thermal dynamics is proposed, and its process is as follows: Figure 2 As shown, the method includes the following steps:

[0102] Establish a dynamic model of the integrated energy system of electricity and heat, including a power system model, a quality regulation thermal system dynamic model, and a combined heat and power unit dynamic model;

[0103] Based on operational safety constraints, a safety domain model for an integrated electrothermal energy system that takes thermal dynamics into account is constructed.

[0104] To address the nonlinear and nonconvex characteristics of the safety domain in an integrated electrothermal energy system, a concave hull method based on optimization and verification is employed to solve for the safety domain boundary and characterize the safety domain.

[0105] Establishing a dynamic model of the integrated electric and thermal energy system, including a power system model, a quality regulation thermal system dynamic model, and a combined heat and power unit dynamic model, involves the following steps:

[0106] Establish a power system model, including the equations for nodal power conservation and branch power conservation:

[0107]

[0108]

[0109]

[0110]

[0111] In the formula, i and j represent node numbers, t is a time stamp, and V i,t P represents the voltage magnitude at node i at time t. Gi,t and P Li,t Q represents the active power produced by the generator and the active power consumed by the load at node i at time t. Gi,t and Q Li,t G represents the active power produced by the generator and the active power consumed by the load at node i at time t. ij and B ij θ represents the conductance and susceptance between node i and node j. ij,t P represents the phase angle difference between node i and node j at time t. l,ij,t and Q l,ij,t This represents the active and reactive power transmitted between node i and node j at time t.

[0112] A dynamic model of the quality-regulated thermodynamic system is established, including the pipe heat transfer equation, the node heat exchange equation, the node temperature fusion equation, and the pipe-node temperature correlation equation, as shown in equations (5) to (8), respectively:

[0113]

[0114]

[0115]

[0116]

[0117] In the formula, Φ and Θ represent the pipe set and node set of the thermal system, respectively, and T j,x,t v represents the relative temperature at point x on pipe j at time t. j C represents the flow velocity of water in pipe j. w m is the specific heat capacity of water. j Let λ be the mass flow rate of the water in the pipe. j φ represents the thermal resistance coefficient of pipe j. i,t This represents the heat power consumed by node i at time t. and The relative supply and return water temperatures at node i at time t are represented by L, and the pipe length is Φ. j i and Φ j o Let j represent the pipeline sets that flow into and out of node j, respectively.

[0118] The analytical solution of equation (5) can be expressed as:

[0119]

[0120] In the formula, δ represents the step function. Let ψ(j,tx / v) represent the temperature distribution at x-vt along pipe j at the initial time, and let ψ(j,tx / v) represent the temperature distribution at the inlet of pipe j at time tx / v.

[0121] A dynamic model of a combined heat and power (CHP) unit is established, including a coal-fired boiler, steam turbine, generator, and steam-water heat exchanger. The input fuel for the coal-fired boiler can be represented as:

[0122] φ B,t =K B1 m B,t (10)

[0123] In the formula, K B1 φ is the unit calorific value of the fuel. B,t The m represents the heat input to the boiler at time t. B,t Let represent the mass flow rate input to the boiler at time t. The energy conservation within the boiler is expressed as:

[0124]

[0125] In the formula, K B2 For the combustion efficiency of the boiler, K B3 K is the heat storage coefficient of the boiler. T1 For the boiler gain, p T,t Let φ be the pressure of the steam turbine at time t. H,t p represents the power used for heating at time t. B,t Let be the pressure of the coal-fired boiler at time t. The energy conservation within the steam turbine can be expressed as:

[0126]

[0127] In the formula, K T2 To represent the inlet opening of a steam turbine, K T3 For the gain of the steam turbine, K T4 P is the time delay factor for the steam turbine. T,t Let be the electrical power generated by the steam turbine at time t. The pressures of the coal-fired boiler and the steam turbine satisfy the following:

[0128]

[0129] In the formula, K B4 Let be the coefficient of friction of the boiler. The energy conservation within the steam-water heat exchanger can be expressed as:

[0130]

[0131] In the formula, K H1 K represents the heat storage coefficient of the heat exchanger. H2 The thermal conductivity of the heat exchanger is represented by m. H,t This represents the mass flow rate of water undergoing heat exchange in the heat exchanger at time t. and This represents the inlet and outlet temperatures of the steam-water heat exchanger at time t.

[0132] The ordinary differential equations are discretized using the implicit Euler method. Equations (11), (12), and (14) can be discretized as follows:

[0133]

[0134]

[0135]

[0136] In the formula, Δt is the time step, and p B,t-Δt P T,t-Δt and This represents the pressure of the coal-fired boiler, the electrical power input to the steam turbine, and the outlet temperature of the steam-water heat exchanger at time t-Δt.

[0137] Based on operational safety constraints, a safety domain model for an integrated electrothermal energy system considering thermal dynamics is constructed, including the following steps:

[0138] For power systems, operational safety constraints include branch transmission power constraints, upper and lower limits of generator active and reactive power constraints, upper and lower limits of node voltage amplitude constraints, and voltage phase angle constraints, as shown in equations (18) to (21), respectively.

[0139]

[0140]

[0141] V i min ≤V i,t ≤V i max (20)

[0142] -π≤θ i,t ≤π (21)

[0143] In the formula, This represents the maximum apparent power transmitted between node i and node j. and Let represent the lower limits of the active and reactive power of the generator at node i, respectively. and These represent the upper limits of the active and reactive power of the generator at node i, respectively. and These represent the lower and upper limits of the voltage amplitude at node i, respectively.

[0144] Furthermore, the coupling constraints between the power system and the combined heat and power unit can be expressed as:

[0145] P T,t =P G,t (twenty two)

[0146] For a quality-controlled thermal system, operational safety constraints mainly include the supply and return water temperature constraints at the nodes, which can be expressed as:

[0147]

[0148] In the formula, and This represents the upper and lower limits of the water supply temperature at node i at time t. and The upper and lower limits of the return water temperature at node i at time t are represented; the coupling constraints between the thermal system and the cogeneration unit can be expressed as:

[0149] m G =-m H (twenty four)

[0150]

[0151] In the formula, This represents the water supply temperature of the heat source node at time t. Equation (24) indicates that the inlet and outlet mass flow rates of the steam-water heat exchanger are the same as the mass flow rates of the heat source node; Equation (25) indicates that the outlet temperature of the steam-water heat exchanger is the same as the supply water temperature of the heat source node, and the inlet temperature of the steam-water heat exchanger is the same as the return water temperature of the heat source node.

[0152] For combined heat and power (CHP) units, the main operational safety constraints include the mass flow rate constraint of the input fuel, the pressure constraint of the coal-fired boiler, the pressure constraint of the steam turbine, the heating power constraint, the power supply constraint, and the electrothermal power coupling constraint, as shown in equations (26) to (31), respectively.

[0153]

[0154]

[0155]

[0156]

[0157]

[0158] P T,t +φ H,t ≤K B2 φ B,t (31)

[0159] Based on the safety operation constraints of each system, a safety domain model of the integrated electrothermal energy system is established. First, the variables of the integrated energy system at any time t are divided into controllable variables X. t and the controlled variable Y t The controllable variables include the active power of generators in the power system, the input fuel mass in the combined heat and power (CHP) unit, the heating power of the heat source in the thermal system, and the supply water temperature, which are expressed as follows:

[0160]

[0161] In the formula, Let t represent the controllable variables in the power system at time t. Denotes the controllable variables in the thermodynamic system at time t. φ represents the controllable variable in the cogeneration unit at time t. G,t This represents the heating power of the heat source node at time t.

[0162] The controlled variables include the active and reactive power of branches in the power system, the voltage amplitude and phase angle at nodes, the return water temperature at heat source nodes and the supply water temperature at load nodes in the thermal system, and the input heat, coal-fired boiler and steam turbine pressure, steam-water heat exchanger outlet temperature, and power supply in the combined heat and power unit, which can be expressed as:

[0163]

[0164] In the formula, Denotes the controlled variables in the power system at time t. Denotes the controlled variable in the thermodynamic system at time t. This represents the controlled variable in the cogeneration unit at time t. This represents the water supply temperature of the load node at time t.

[0165] Therefore, considering the thermal dynamics, the safety domain Ω of the integrated electrothermal energy system at time j is... j It can be represented as:

[0166]

[0167] In the formula, Ω j Represents the security domain, X1,…,X j Let Y1, ..., Yj be the controllable variables from time 1 to time j. jLet f represent the controlled variables from time 1 to time j, f be the set of equality constraints in the safety domain model, including equations (1) to (4), (6) to (10), (13), (15) to (17), (22), (24), and (25); g be the set of inequality constraints in the safety domain model, including equations (18) to (21), (23), and (26) to (31).

[0168] To address the nonlinear and nonconvex characteristics of the safety domain in an integrated electrothermal energy system, a concave hull method based on optimization and verification is employed to solve for the safety domain boundary and characterize the safety domain. The method includes the following steps:

[0169] The problem of modeling the safety region is transformed into solving the safety region boundary. Equation (34) is transformed into two sets of nonlinear optimization problems, and the safety region boundary is characterized by solving the limit running point. The two sets of optimization problems can be expressed as follows:

[0170]

[0171]

[0172] Equations (35) and (36) represent the lower and upper limits of operation of an integrated electrothermal energy system taking thermal dynamics into account, respectively. Where F... j F represents the vector of all state variables within the integrated energy system at time j. j,i Let A1 represent the i-th variable in the integrated energy system at time j, and let A2 represent the upper bound vector of the inequality constraints.

[0173] Considering the nonconvex and nonlinear characteristics of the safety domain model, the limit operating points obtained from solving equations (35) and (36) are subjected to safety verification. ε is defined as the safety margin; if the i-th variable F in the integrated energy system at time j is obtained from the solution... j,i If the upper limit of safe operation is violated, the corresponding optimization problem is corrected as follows:

[0174] min F j,i

[0175] stf(X1,…,X j ,Y1,…,Y j )=0 (37)

[0176] A1≤g(X1,…,X j ,Y1,…,Y j )≤A2-ε

[0177] If the solution yields the i-th variable F within the integrated energy system at time j... j,i If the upper limit of safe operation is violated, the corresponding optimization problem is corrected as follows:

[0178] min F j,i

[0179] stf(X1,…,X j ,Y1,…,Y j )=0 (38)

[0180] A1+ε≤g(X1,…,X j ,Y1,…,Y j )≤A2

[0181] By using the concave hull method to characterize the boundary of the safety domain at the limit operating point that meets the safety verification, a safety domain for the integrated electrothermal energy system that takes into account thermal dynamics is constructed.

[0182] by Figure 2 Taking the system shown as an example, the structure of the thermal system is as follows: Figure 3 As shown. The calculation period is 6 hours, the time step is 5 minutes, and the simulated operating characteristics of the combined heat and power unit are as follows. Figure 4 As shown, the time-varying curves of the safety domain areas of generator 1 and generator 2 calculated based on the optimization-verification concave hull method are as follows: Figure 5 As shown.

[0183] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the claimed invention.

Claims

1. A method for constructing a security domain in an integrated electrothermal energy system, characterized in that, Includes the following steps: A dynamic model of an integrated electric and thermal energy system is established, which includes a power system model based on power conservation, a quality regulation thermal system dynamic model based on pipeline heat transfer, node heat exchange, node temperature fusion and pipeline-node temperature correlation, and a cogeneration unit dynamic model based on the capacity of the cogeneration unit. A safety domain model for the integrated electrothermal energy system is constructed by combining the operational safety constraints of the dynamic model of the integrated electrothermal energy system. Considering the nonlinear and nonconvex characteristics of the safety domain of the integrated electrothermal energy system, the concave hull method is used to solve for the boundary of the safety domain and characterize the safety domain. The dynamic model of the thermodynamic system with quality regulation includes the pipe heat transfer equation, the node heat exchange equation, the node temperature fusion equation, and the pipe-node temperature correlation equation, as detailed below: (5) (6) (7) (8) In the formula, Φ and Θ represent the pipe set and node set of the thermal system, respectively. express t Time Pipeline j superior x The relative temperature at that location Indicates pipeline j Water flow velocity, The specific heat capacity of water, The mass flow rate of the water in the pipe. Indicates pipeline j thermal resistance coefficient, express t Time Node i The heat power consumed, and express t Time Node i The relative supply and return water temperatures, L Indicates the length of the pipe. and Representing inflow and outflow nodes respectively. j Pipeline collection; The analytical solution of equation (5) can be expressed as: (9) In the formula, δ Represents the step function. Indicates the initial time of the pipeline j superior x - v Temperature distribution at point t express t - x / v Time Pipeline j Temperature distribution at the entrance; The dynamic model of a combined heat and power (CHP) unit includes a coal-fired boiler, steam turbine, generator, and steam-water heat exchanger; the construction of the dynamic model of a CHP unit. Includes the following steps: The input fuel for a coal-fired boiler can be expressed as: (10) In the formula, This refers to the unit calorific value of the fuel. express t The constant heat input to the boiler, express t Input the boiler's mass flow rate continuously; The energy conservation principle within the boiler is expressed as: (11) In the formula, For the combustion efficiency of the boiler, The heat storage coefficient of the boiler. For the boiler gain, for t The pressure of the steam turbine at all times, express t The power used for heating at all times. for t The pressure of the coal-fired boiler at all times; The energy conservation within a steam turbine can be expressed as: (12) In the formula, To indicate the inlet opening of a steam turbine, For the gain of the steam turbine, For the delay factor of the steam turbine, for t The electrical power generated by the steam turbine at any given time; The pressure of the coal-fired boiler and the pressure of the steam turbine meet the following requirements: (13) In the formula, This is the coefficient of friction of the boiler; The energy conservation within a steam-water heat exchanger can be expressed as: (14) In the formula, Indicates the heat storage coefficient of the heat exchanger. Indicates the thermal conductivity of the heat exchanger. express t The mass flow rate of water undergoing heat exchange in the heat exchanger at all times. and express t The inlet and outlet temperatures of the steam-water heat exchanger are constantly monitored. The ordinary differential equations are discretized using the implicit Euler method. Equations (11), (12), and (14) can be discretized as follows: (15) (16) (17) In the formula, For time step, , and express The constant pressure of the coal-fired boiler, the electrical power input to the steam turbine, and the outlet temperature of the steam-water heat exchanger.

2. The method for constructing a security domain for an integrated electrothermal energy system according to claim 1, characterized in that, The power system model includes nodal power conservation equations and branch power conservation equations, as detailed below: (1) (2) (3) (4) In the formula, i and j These represent the node numbers respectively. t As a time marker, V i,t express t Time Node i voltage amplitude, P Gi,t and P Li,t express t Time Node i The active power produced by the generator and the active power consumed by the load. Q Gi,t and Q Li,t express t Time Node i The reactive power produced by the generator and the reactive power consumed by the load, G ij and B ij Represents a node i and nodes j The conductivity and susceptance between them θ ij,t express t Time Node i and nodes j The phase angle difference between them P l,ij,t and Q l,ij,t express t Time Node i and nodes j The active and reactive power transmitted between them.

3. The method for constructing a security domain for an integrated electrothermal energy system according to claim 2, characterized in that, The operational safety constraints of the dynamic model of the integrated power and heat energy system include the operational safety constraints of the power system model, the operational safety constraints of the dynamic model of the quality regulation heat system, and the operational safety constraints of the dynamic model of the combined heat and power unit. Specifically, they include: The operational safety constraints of the power system include branch transmission power constraints, upper and lower limits of generator active and reactive power constraints, upper and lower limits of node voltage amplitude constraints, and voltage phase angle constraints, as shown in equations (18) to (21), respectively. (18) (19) (20) (21) In the formula, Represents a node i and nodes j The maximum apparent power transmitted between them, and Representing nodes respectively i The lower limits of active and reactive power of the generator at the location, and Representing nodes respectively i The upper limits of active and reactive power of the generator at the location, and Representing nodes respectively i The lower and upper limits of the voltage amplitude at the location; The coupling constraints between the power system and the combined heat and power unit can be expressed as: (22) The operational safety constraints of a quality-regulating thermal system include the supply and return water temperature constraints at the nodes, which can be expressed as: (23) In the formula, and express t Time Node i The upper and lower limits of the water supply temperature, and express t Time Node i The upper and lower limits of the return water temperature; the coupling constraints between the thermal system and the cogeneration unit can be expressed as: (24) (25) In the formula, express t The water supply temperature at the heat source node at all times. express t The return water temperature of the heat source node at any time; Equation (24) indicates that the inlet and outlet mass flow rates of the steam-water heat exchanger are the mass flow rates of the heat source node; Equation (25) indicates that the outlet temperature of the steam-water heat exchanger is the supply water temperature of the heat source node, and the inlet temperature of the steam-water heat exchanger is the return water temperature of the heat source node. The operational safety constraints of a combined heat and power (CHP) unit include the mass flow rate constraint of the input fuel, the pressure constraint of the coal-fired boiler, the pressure constraint of the steam turbine, the heating power constraint, the power supply constraint, and the electrothermal power coupling constraint, as shown in equations (26) to (31), respectively. (26) (27) (28) (29) (30) (31)。 4. The method for constructing a security domain for an integrated electrothermal energy system according to claim 3, characterized in that, The construction of the security domain model for the integrated electric and thermal energy system includes the following steps: will any t The variables of a time-integrated energy system are divided into controllable variables. X t and controlled variables Y t The controllable variables include the active power of generators in the power system, the input fuel mass in the combined heat and power unit, the heating power of the heat source in the thermal system, and the supply water temperature, which are expressed as follows: (32) In the formula, express t Controllable variables in a power system at any given time express t Controllable variables in a thermodynamic system at any given time express t Controllable variables in a cogeneration unit at all times express t The heating power of the heat source node at any given time; The controlled variables include the active and reactive power of branches in the power system, the voltage amplitude and phase angle at nodes, the return water temperature at heat source nodes and the supply water temperature at load nodes in the thermal system, and the input heat, coal-fired boiler and steam turbine pressure, steam-water heat exchanger outlet temperature, and power supply in the combined heat and power unit, which can be expressed as: (33) In the formula, express t Controlled variables in the power system at any given time express t Controlled variables in a thermodynamic system at any given time express t Controlled variables in a constant-time cogeneration unit express t The water supply temperature at each load node at any given time; The security domain model of an integrated electrothermal energy system considering thermal dynamics can be expressed as: (34) In the formula, Ω j Indicates a security domain. X 1,..., X j Indicates time 1 to time 2. j Controllable variables, Y 1, ..., Y j Indicates time 1 to time 2. j The controlled variables, f The set of equality constraints in the security domain model includes equations (1) to (4), (5) to (10), (13), (15) to (17), (22), (24), and (25); g The set of inequality constraints in the safety domain model includes equations (18) to (21), (23), and (26) to (31).

5. The method for constructing a security domain for an integrated electrothermal energy system according to claim 4, characterized in that, To address the nonlinear and nonconvex characteristics of the safety region in an integrated electrothermal energy system, the concave hull method is employed to solve for the safety region boundary. The safety region is characterized through the following steps: The problem of modeling the safe domain is transformed into the problem of solving the safe domain boundary; Equation (34) is transformed into two sets of nonlinear optimization problems, and the safe domain boundary is characterized by solving the limit running point; the two sets of optimization problems can be expressed as follows: (35) (36) Equations (35) and (36) represent the lower and upper limits of the operation of the integrated electrothermal energy system, taking into account thermal dynamics, respectively; where, express j At any given moment, the vector of all state variables within the integrated energy system is... express j The first in the integrated energy system at all times i One variable, The vector representing the lower bound of the inequality constraint. The upper bound vector representing the inequality constraint; Considering the non-convex and nonlinear characteristics of the safety domain model, the limit operating points obtained by solving equations (35) and (36) are subjected to safety verification; define ε For a safety margin, if the solution obtained is j The first in the integrated energy system at all times i Variables If the upper limit of safe operation is violated, the corresponding optimization problem is corrected as follows: (37) If the solution is obtained j The first in the integrated energy system at all times i Variables If the upper limit of safe operation is violated, the corresponding optimization problem is corrected as follows: (38) Based on the limit operating point that meets the safety verification, the boundary of the safety domain is characterized by the concave hull method, and the safety domain of the integrated electrothermal energy system taking into account thermal dynamics is determined.

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