Fully-distributed combined heat and power optimization scheduling method, device, equipment and medium

Abstract

The invention relates to the technical field of optimal scheduling of an integrated energy system, and discloses a fully-distributed combined heat and power optimal scheduling method, device and equipment and a medium. In order to solve the problems of linear convergence, low calculation efficiency, dependence on a coordination center and the like of a traditional distributed optimization algorithm in electric heating system scheduling, on the basis of reserving an original electric heating coupling model core architecture, a distributed collaborative interior point conjugate gradient method is introduced as an optimization algorithm, and fully-distributed scheduling with efficient convergence is achieved. According to the method, an electric heating comprehensive energy system optimization model is converted into a convex optimization problem, a correction equation is decoupled, a coefficient matrix is ensured to be symmetrical and positive definite, a distributed conjugate gradient method is adopted for solving, and collaborative optimization of an electric power system and a thermodynamic system can be achieved without a coordination center. Simulation verification shows that the calculation efficiency is improved by more than 90% on the premise of ensuring that the optimization precision is consistent with a centralized algorithm, the privacy of each energy main body can be protected, and the method is suitable for real-time scheduling of electric heating comprehensive systems of different scales.

Description

Fully Distributed Co-optimized Scheduling Methods, Devices, Equipment and Media for Thermal Power Technical Field

[0001] This invention relates to the problem of joint scheduling technology for integrated electric-thermal energy systems, specifically to a fully distributed combined heat and power scheduling method, apparatus, equipment, and medium. Background Technology

[0002] With the increasing severity of global climate change and the energy crisis, the transformation and upgrading of energy systems has become an inevitable trend in social development. Against this backdrop, integrated energy systems have attracted widespread attention due to their significant advantages in improving energy efficiency and reducing carbon emissions. Integrated energy systems, by integrating multiple energy forms such as electricity, heat, and natural gas, achieve energy complementarity and optimized allocation, thereby improving the flexibility and reliability of the energy system. As an important component of integrated energy systems, the electric-thermal integrated energy system, by coupling the power system and the heating system, can not only achieve efficient energy production and distribution but also effectively utilize renewable energy sources such as solar and wind power, which is of great significance for promoting the rapid economic development of the energy system.

[0003] Integrated energy systems can break down barriers between different energy sources, improve the flexibility of the power system, and promote the consumption of renewable energy. With the widespread use of combined heat and power (CHP) units, the coupling between the power system and the heating system is gradually deepening, thus forming an integrated electricity-heat energy system. Joint optimal dispatching of electricity and heat can improve the economic efficiency and energy utilization rate of integrated electricity-heat energy systems. Joint optimal dispatching of electricity and heat can be divided into centralized optimal dispatching and distributed optimal dispatching. However, centralized optimal dispatching is incompatible with the distributed structure of integrated energy systems. Distributed optimal dispatching, on the other hand, can fully protect the privacy of different stakeholders.

[0004] The power and heat systems are operated by different operators, lacking a central authority to oversee both. Furthermore, neither operator is willing to share their private information, including details such as topology, network parameters, and power generation plans. This makes it impossible to use a centralized approach for the scheduling of the integrated power-heat energy system. A more effective approach would be for each system to solve its own problems independently while exchanging information for potential coordination.

[0005] Existing research on joint power-heat scheduling is typically based on collective rationality, i.e., maximizing the overall utility of the integrated power-heat energy system. While joint power-heat scheduling reduces total costs compared to individual power-heat scheduling, it also harms the individual interests of the power system. Therefore, joint power-heat scheduling based on collective rationality is not incentive-compatible.

[0006] To achieve incentive compatibility, existing research falls into two main categories: market game theory methods and transfer payment methods. Market game theory methods may not maximize overall benefits. Transfer payment methods involve the thermal system sharing some of its cooperative surplus with the power system, reducing the total operating costs for both. However, calculating the optimal allocation ratio of the cooperative surplus is relatively complex and difficult to implement. Summary of the Invention

[0007] This application provides a fully distributed optimization scheduling method, apparatus, equipment, and medium for an integrated electric-thermal energy system, which addresses technical issues such as linear convergence, low computational efficiency, privacy protection, and incentive compatibility in traditional distributed algorithms under the joint scheduling of existing integrated electric-thermal energy systems.

[0008] To this end, the first aspect of the present invention provides a fully distributed co-optimized scheduling method for thermal power, comprising: step 101: constructing a centralized scheduling model for the integrated electric-thermal energy system based on pre-set integrated electric-thermal energy system parameters, wherein the pre-set integrated electric-thermal energy system parameters include power system parameters, thermal system parameters, and electric-thermal coupling equipment parameters, and the integrated electric-thermal energy system scheduling model includes a power system model, a fully analytical model of the thermal network, and an equivalent network model with simplified complexity.

[0009] Step 102: The DC-IPCG algorithm is used to solve the power-heat integrated energy system scheduling model in a distributed manner to obtain the power-heat joint optimization scheduling results; the power-heat joint optimization scheduling results include the output of thermal power units, the output of cogeneration units, the power system scheduling cost, the heat system scheduling cost, and the power-heat integrated energy system scheduling cost.

[0010] Preferably, the step of constructing a centralized integrated electric-thermal energy system scheduling model based on pre-set integrated electric-thermal energy system parameters includes a power system model, a fully analytical thermal network model, and an equivalent network model with simplified complexity. The step further includes: obtaining pre-set integrated electric-thermal energy system parameters, which include power system parameters, thermal system parameters, and electric-thermal coupling equipment parameters; the power system parameters include bus parameters, branch parameters, thermal power unit parameters, wind farm parameters, and electrical load parameters; the thermal system parameters include node parameters, pipeline parameters, boiler parameters, and heat load parameters; and the electric-thermal coupling equipment parameters include operating parameters of the combined heat and power (CHP) unit.

[0011] Preferably, the DC-IPCG algorithm is used to solve the electric-thermal integrated energy system scheduling model in a distributed manner to obtain the joint optimization scheduling result of electric and thermal energy. DC-IPCG combines the distributed interior-point method and the fully distributed conjugate gradient method, including: S21: linearizing the nonlinear constraints (including the nonlinear term of heat transfer loss) in the original model through the tangent relaxation method, transforming it into a convex optimization model to ensure the convergence of DC-IPCG; S22: constructing a perturbation KKT for the convex optimization model. The process involves: S23: Deriving the modified equations and decoupling them using block Gaussian elimination to separate the subproblems of solving the power system and the thermal system; S24: Processing the decoupled modified equations by introducing a small positive identity matrix to adjust the coefficient matrix, ensuring its symmetric positive definiteness and adapting it for efficient solution using the conjugate gradient method; S25: Using the distributed conjugate gradient method to perform a fully distributed iterative solution on the processed modified equations, where the power system and the thermal system only exchange boundary coupling information without a coordination center, obtaining the coupling constraint Lagrange multiplier correction; S26: Back-substituting the decision variable corrections for the power system and the thermal system, calculating the original step size and dual step size, updating the decision variables, Lagrange multipliers, and disturbance factors, repeating the iteration until the KKT condition tolerance is met, and outputting the optimal scheduling result.

[0012] Preferably, the step of using the DC-IPCG algorithm to perform distributed solution on the electric-thermal integrated energy system scheduling model to obtain the joint optimization scheduling result of the electric-thermal integrated energy system further includes: verifying the accuracy and superlinear convergence characteristics of the result based on the data of the thermal system and the power system and the scheduling cost; if the temperature deviation exceeds the allowable range or the power exceeds the limit, fine-tuning the model parameters (such as the initial value of the heat source supply temperature, the heat-to-power ratio constraint of the CHP unit), and re-executing the iterative solution process until the scheduling result meets all constraints (comfortable temperature range of heat load, equipment capacity limit, power balance, etc.).

[0013] The second aspect of the present invention provides a fully distributed combined heat and power optimization scheduling device, comprising: a model building unit, used to construct a centralized integrated heat and power system scheduling model based on preset integrated heat and power system parameters, wherein the preset integrated heat and power system parameters include power system parameters, thermal system parameters and heat and power coupling equipment parameters, and the integrated heat and power system scheduling model includes a power system model, a thermal network fully analytical model, and an equivalent network model with simplified complexity.

[0014] A model solving unit connected to the model building unit is used to perform distributed solution of the power-heat integrated energy system scheduling model using the DC-IPCG algorithm to obtain the power-heat joint optimization scheduling result. The power-heat joint optimization scheduling result includes the output of thermal power units, the output of cogeneration units, the power system scheduling cost, the thermal system scheduling cost, and the power-heat integrated energy system scheduling cost. Preferably, the power-heat integrated energy system scheduling device further includes: a parameter acquisition unit, used to acquire preset power-heat integrated energy system parameters and transmit them to the model building unit. The preset power-heat integrated energy system parameters include power system parameters, thermal system parameters, and power-heat coupling equipment parameters. The power system parameters include bus parameters, branch parameters, thermal power unit parameters, wind farm parameters, and electrical load parameters. The thermal system parameters include node parameters, pipeline parameters, and heat load parameters. The power-heat coupling equipment parameters include cogeneration unit operating parameters.

[0015] Preferably, the model solving unit includes: a modified equation decoupling subunit: used to construct the perturbation KKT conditions of the model, derive the modified equation, decouple it using block Gaussian elimination, and separate the subproblems of the power system and the thermal system; a positive definite processing subunit: used to introduce a small positive identity matrix to adjust the coefficient matrix of the decoupled modified equation to ensure its symmetric positive definiteness and adapt it to the conjugate gradient method; a distributed conjugate gradient solving subunit: used to iteratively solve the modified equation using the distributed conjugate gradient method without a coordination center, where the power system and the thermal system only exchange boundary coupling information; and an iterative update subunit: used to back-substitute the modified decision variables, determine the iteration step size, and update the decision variables, Lagrange multipliers, and perturbation factors until the convergence condition is met; the power-thermal joint optimization scheduling results include the output of thermal power units, the output of cogeneration units, the scheduling cost of the power system, the scheduling cost of the thermal system, and the scheduling cost of the integrated power-thermal energy system.

[0016] Preferably, it further includes: a convergence verification subunit, used to monitor in real time the residuals of the perturbed KKT conditions and the solution error of the linear equation system: if the residuals are less than the preset KKT tolerance (e.g., 10... -6 If the residual does not meet the tolerance, the iteration is considered to have converged and the optimal scheduling result is output. If the residual does not meet the tolerance, the iteration returns to the distributed conjugate gradient solution sub-unit to continue iterating until the convergence condition or the maximum number of iterations is reached.

[0017] A third aspect of the present invention provides a fully distributed co-optimized scheduling device for thermal power, the device comprising a processor and a memory; the memory is used to store program code and transmit the program code to the processor; the processor is used to execute the fully distributed co-optimized scheduling method for thermal power as described in the first aspect according to the instructions in the program code.

[0018] A fourth aspect of this application provides a computer-readable storage medium for storing program code for executing the fully distributed thermoelectric co-optimization scheduling method described in the first aspect.

[0019] As can be seen from the above technical solutions, the embodiments of this application have the following advantages: This application provides a fully distributed co-optimized scheduling method for thermal power based on the DC-IPCG algorithm, including: constructing a fully analytical scheduling model for the integrated electric-thermal energy system according to pre-set integrated electric-thermal energy system parameters, including power system parameters, thermal network characteristic parameters, and electro-thermal coupling equipment parameters; the integrated electric-thermal energy system scheduling model includes a power system model, a fully analytical thermal network model, and an equivalent network model with simplified complexity. The distributed cooperative interior-point conjugate gradient method (DC-IPCG) is used to solve the integrated electric-thermal energy system scheduling model in a fully distributed manner to obtain the joint optimization scheduling results for electric and thermal power.

[0020] The scheduling method provided in this application inherits the superlinear convergence characteristics of the interior-point method. Through decoupling and positive definite processing of the modified equations, it combines a distributed conjugate gradient method to achieve a fully distributed solution, eliminating the need for a coordination center. This approach protects the privacy of power and thermal system data, maintains operational independence, and improves computational efficiency by 83%–98% compared to traditional linear convergence distributed algorithms (such as ADMM). This method balances modeling accuracy, solution efficiency, and distributed characteristics, effectively resolving the technical contradiction of balancing accuracy, efficiency, and privacy in existing integrated power-thermal energy system scheduling, and is suitable for the real-time optimization needs of large-scale systems. Attached Figure Description

[0021] Figure 1 is a flowchart illustrating the fully distributed thermoelectric joint optimization scheduling method provided in an embodiment of this application.

[0022] Figure 2 is a schematic diagram of the structure of the fully distributed combined thermal power optimization scheduling device provided in the embodiment of this application.

[0023] Figure 3 is a schematic diagram of the scheduling framework of the integrated electric-thermal energy system provided in the embodiments of this application.

[0024] Figure 4 is a schematic diagram of the thermal network of the present invention. Detailed Implementation

[0025] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present application, and not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present application.

[0026] For ease of understanding, please refer to Figure 1. The embodiment of the fully distributed combined heat and power optimization scheduling method provided in this application includes: Step 101: Constructing a centralized integrated heat and power system scheduling model based on pre-set integrated heat and power system parameters. The pre-set integrated heat and power system parameters include power system parameters, thermal system parameters, and heat and power coupling equipment parameters. The integrated heat and power system scheduling model includes a power system model, a thermal network fully analytical model, and an equivalent network model with simplified complexity.

[0027] Further, step 101, prior to which the steps include: obtaining pre-set integrated electric-thermal energy system parameters, which include power system parameters, thermal system parameters, and electric-thermal coupling equipment parameters; the power system parameters include bus parameters, branch parameters, thermal power unit parameters, wind farm parameters, and electrical load parameters; the thermal system parameters include node parameters, pipeline parameters, boiler parameters, and heat load parameters; and the electric-thermal coupling equipment parameters include cogeneration unit operating parameters.

[0028] It should be noted that the parameters of the power system, thermal system, and electro-thermal coupling equipment include, but are not limited to, the above parameters. Other relevant parameters can also be obtained as needed. This embodiment only provides a few examples and does not limit the specifics.

[0029] The scheduling model for the integrated electric-thermal energy system is expressed as follows. The overall structure of the integrated electric-thermal energy system is shown in Figure 3, and its core consists of generator sets, a power grid, hot water pipes, a thermal network, and coupling equipment. The thermal network is shown in Figure 4, with the upper part representing the water supply network and the lower part representing the return water network. Based on this structural characteristic, the scheduling model for the integrated electric-thermal energy system needs to comprehensively consider multiple factors, including the objective functions and constraints of both the power system and the thermal system, as well as the coupling constraints between them.

[0030] 1. The objective function of the power system aims to minimize the total operating cost of thermal power units. The objective function is a quadratic function of the active power output of the thermal power units: In the formula Let P be the objective function of the power system. g , tLet a be the active power output of thermal power unit g at time t; 2,g a 1,g and a 0,g These are the quadratic cost coefficient, the linear cost coefficient, and the constant cost coefficient for unit g; Ω T For the set of scheduling periods; Ω FU It is a collection of thermal power units.

[0031] 2. Power system constraints (1) Power balance (2) Climbing constraint (3) Network constraints ,in, This represents the unit number of thermal power units and combined heat and power units. Indicates the wind turbine unit number. This indicates the load node number, where t is the time. This indicates the number of thermal power units and combined heat and power units. Indicates the number of wind turbine units. Indicates the number of load nodes; Let be the electrical power of the thermal power unit and the combined heat and power unit at time t. Let be the electrical power of the thermal power unit and the combined heat and power unit at time t-1. Let be the electrical power of the wind turbine at time t. Let be the load of node i at time t; Let g be the downhill climbing capability of the generator set in a single cycle. This represents the upward climbing ability of generator set g within a single cycle. It is the set of all connected nodes of node i. Let be the voltage phase angle of node i at time t. Let be the voltage phase angle at node j at time t. This represents the voltage phase angle of the reference node in the network at time t. Let (i,j) be the reactance of the line. Let (i,j) be the maximum transmission capacity of line (i,j).

[0032] (4) Power generation and heat supply output of combined heat and power units ,in, In the formula, Let be the power generation output of the i-th combined heat and power unit (i.e., the CHP unit) during the t-th dispatch period. Let i be the heating output of the i-th CHP unit calculated from the grid side during the t-th dispatch period; Let k be the k-th pole of the approximate polygon of the feasible region of the i-th CHP unit, where These are the coordinates of the corresponding poles in the feasible region; Let be the convex combination coefficient of the kth pole corresponding to the operating point of the i-th CHP unit in the t-th scheduling period; Let be the number of poles of the approximate polygon of the feasible operating region of the i-th CHP unit; This is a set of heating unit numbers. This is the set of indexes for the scheduling period.

[0033] 3. Coupling Constraints In the formula, It is the heating output of the i-th cogeneration unit calculated from the grid side during the t-th dispatch period. It is the heating output of the i-th cogeneration unit during the t-th dispatch period, calculated from the heating network side.

[0034] 4. Objective function of a thermodynamic system In the formula: H j,t The active power output of the combined heat and power unit j at time t; a 2,j a 1,j and a 0,j These are the quadratic cost coefficient, the linear cost coefficient, and the constant cost coefficient for unit j; Ω T For the set of scheduling periods; Ω TU It is a collection of combined heat and power (CHP) units.

[0035] 5. Constraints of a thermodynamic system (1) Temperature mixing equation , In the formula, It is a collection of nodes in the heating network. It is the set of all heating pipes starting from the i-th heating network node. It is the set of all heating pipes whose endpoint is the i-th heating network node; This represents the temperature at the beginning of the b-th water supply pipeline during the t-th scheduling period. This represents the temperature at the end of the b-th water supply pipeline during the t-th scheduling period. This represents the temperature at the beginning of the b-th return water pipe during the t-th scheduling period. This represents the temperature at the end of the b-th return water pipe during the t-th scheduling period; This represents the water flow rate of the b-th water supply pipeline during the t-th scheduling period. This represents the water flow rate of the b-th return water pipe during the t-th scheduling period. It should be noted that the temperature at each node of the heating network... and This refers to the steady-state temperature reached after the water flowing into this node mixes with each other. It is the steady-state temperature of the water supply pipe. This refers to the steady-state temperature of the return water pipe, while the temperatures at the beginning and end of the pipe are... , , , It refers to the temperature of the water flow end before mixing at the corresponding location inside the pipe.

[0036] The two equations above indicate that, according to the law of conservation of energy, water from different pipes mixes at the same network node to reach the same temperature, and the temperature of the water flowing out of the network node is equal to the temperature of that network node.

[0037] (2) Heat power balance equation of heat source node (CHP) In the formula, It is the heating output of the i-th cogeneration unit calculated from the heating network side during the t-th dispatch period. It is the specific heat capacity of water. It is the flow rate of the circulating water passing through the node. It is the temperature of the i-th water supply pipeline during the t-th scheduling period. It is the temperature of the i-th return water pipe during the t-th scheduling period.

[0038] (3) Heat power balance equation of load node In the formula, It is the heat load of the load node. It is a collection of heat load nodes.

[0039] (4) Temperature transport delay equation , The two equations above represent the temperature constraints at the outlet of the water supply pipe and the outlet of the return water pipe, respectively. In the equations, This represents the temperature at the beginning of the b-th water supply pipeline during the t-th scheduling period. This represents the temperature at the end of the b-th water supply pipeline during the t-th scheduling period. This represents the temperature at the beginning of the b-th return water pipe during the t-th scheduling period. This represents the end temperature of the b-th return water pipe during the t-th scheduling period; This indicates that after a delay, the b-th water supply pipeline... Temperature at the beginning of each scheduling period; This indicates that after a delay, the b-th return water pipe will be on the [missing information - likely a date or time]. Temperature at the beginning of each scheduling period; Indicates the time step; This represents the delay time of pipe b. This represents the spatial delay factor of pipe b. This represents the time delay factor of pipe b; Indicates the initial temperature of the water supply pipe. Indicates the initial temperature of the return water pipe; Represents the delayed time index, where This symbol indicates rounding up.

[0040] Step 102: Use the DC-IPCG algorithm to solve the electric-thermal integrated energy system scheduling model in a distributed manner to obtain the electric-thermal joint optimization scheduling results.

[0041] The combined power and heat optimization scheduling results include the output of thermal power units, the output of cogeneration units, the scheduling cost of the power system, the scheduling cost of the heat system, and the scheduling cost of the integrated power and heat energy system.

[0042] Further, step 102 includes: linearizing the nonlinear constraints (including the nonlinear term of heat transfer loss) in the original model using the tangent relaxation method, transforming it into a convex optimization model to ensure the convergence of DC-IPCG; constructing perturbation KKT conditions for the convex optimization model, deriving the modified equation, and decoupling the modified equation using the block Gaussian elimination method to separate the solution subproblems of the power system and the thermal system; processing the decoupled modified equation, introducing a small positive identity matrix to adjust the coefficient matrix to ensure its symmetric positive definiteness, and adapting it to the conjugate gradient method for efficient solution; using the distributed conjugate gradient method to perform a fully distributed iterative solution of the processed modified equation, where the power system and the thermal system only exchange boundary coupling information without the need for a coordination center, obtaining the coupling constraint Lagrange multiplier correction; back-substituting to solve the decision variable corrections of the power system and the thermal system, calculating the original step size and dual step size, updating the decision variables, Lagrange multipliers and perturbation factors, repeating the iteration until the KKT condition tolerance is met, and outputting the optimal scheduling result.

[0043] The original electric-thermal integrated energy system scheduling problem can be transformed into the following convex optimization model: (1) In the formula: It is the operating cost of the power system. It is the operating cost of the thermal system; This represents the equality constraints in power system constraints. This represents the inequality constraints in power system constraints. , Equality constraints in a table of thermal system constraints , This represents the inequality constraints in a thermal system. Represents coupling constraints; Optimization variables in a power system, including internal optimization variables. and boundary optimization variables , These represent decision variables within the power system, including generator output, bus voltage phase angle, branch power, and extreme point variables in the CHP operating region. Represents the boundary decision variables of the power system, which include the thermal power of the cogeneration unit calculated from the grid side; For optimization variables in a thermal system, including internal optimization variables and boundary optimization variables , These represent the decision variables within the thermal system, including the supply water temperature at each node, the initial temperature of each pipe in the supply water network, the final temperature of each pipe in the supply water network, the return water temperature at each node, the initial temperature of each pipe in the return water network, and the final temperature of each pipe in the return water network. These represent boundary decision variables for the thermal system, including the thermal power of the cogeneration unit calculated from the heating network side. , The quadratic coefficient matrix representing the operating cost of the power system. , The coefficient matrix of the first-order terms representing the operating cost of the power system. A constant term representing the operating cost of the power system. The quadratic coefficient matrix representing the operating cost of the thermal system. The matrix of coefficients for the first-order terms representing the operating cost of a thermal system. A constant term representing the operating cost of a thermal system; The coefficient matrix representing the equality constraints corresponding to the internal variables of the power system. The coefficient matrix representing the equality constraints corresponding to the boundary variables of the power system. The coefficient matrix representing the inequality constraints corresponding to the internal variables of the power system. The coefficient matrix representing the inequality constraints corresponding to the boundary variables of the power system. The coefficient matrix representing the equality constraints of internal variables in a thermodynamic system. The coefficient matrix representing the equality constraints of internal variables in a thermodynamic system. The coefficient matrix representing the inequality constraints of the internal variables of the thermodynamic system. The coefficient matrix representing the inequality constraints of the internal variables of the thermodynamic system. The coefficient matrix representing the coupled constraints of the power grid side, This represents the coefficient matrix on the coupled-constrained heat network side. The vector representing the right-hand side of the equality constraints corresponding to the internal variables of the power system. The vector representing the right-hand side of the equality constraints corresponding to the boundary variables of the power system. The vector representing the right-hand side of the equality constraints corresponding to the internal variables of the power system. The vector representing the right-hand side of the equality constraints corresponding to the boundary variables of the power system. The vector representing the right-hand side of the equality constraint corresponding to the internal variables of the thermodynamic system. The vector representing the right-hand side of the equality constraint corresponding to the boundary variables of the thermodynamic system. The vector representing the right-hand side of the inequality constraint corresponding to the internal variables of the thermodynamic system. The vector representing the right-hand side of the inequality constraint corresponding to the internal variables of the thermodynamic system. The vector represents the right-hand side of the coupling constraint; the subscript P indicates the power system, and H indicates the thermal system; the superscript eq indicates equality constraint, ie indicates inequality constraint, and cp indicates coupling constraint. The domain of the optimization variables within the power grid. The domain of the external optimization variables of the power grid; The domain of the optimization variables within the heating network. This refers to the domain of the external optimization variables for the heating network.

[0044] The perturbation Karush-Kuhn-Tucker (KKT) conditions for the above-mentioned integrated electric-thermal energy system scheduling problem are: (2) Among them, In the formula: s P For the slack variables of the power system, s H λ is a slack variable of the thermodynamic system. P μ is the Lagrange multiplier for the equality constraints of the power system. p λ is the Lagrange multiplier for power system inequality constraints; H For the Lagrange multipliers of the equality constraints of the thermodynamic system, μ H For the Lagrange multipliers constrained by the inequalities of the thermodynamic system; ν cp For coupling constraint Lagrange multipliers; For the disturbance factor; To construct a vector whose main diagonal elements are derived from the vector diagonal matrix, [ Similarly, 1 is a vector in which all elements are 1.

[0045] Applying the Newton-Raphson method to the perturbation KKT conditions, the corrected equation can be derived: (3) Among them, The adjustment amount of other variables is used and By substituting back, the system of equations (3) can be rearranged as follows: Eliminate and After simplification, the following equation can be obtained: (4) Among them, This is the coefficient matrix corresponding to the above modified equation. Let be the right-hand vector corresponding to the above modified equation.

[0046] Block Gaussian elimination can decouple the modified equations, separating the solution subproblems of the power system and the thermal system. We hope to use the conjugate gradient method for efficient solution, but the conjugate gradient method is mainly suitable for solving symmetric positive definite equations, while M in the modified equations... P and M H Generally, these are non-positive definite matrices, and we cannot guarantee... The positive definiteness of .

[0047] Therefore, we process the decoupled modified equation by introducing a small positive identity matrix to adjust the coefficient matrix, ensuring its symmetric positive definiteness and adapting it for efficient solution using the conjugate gradient method. The modified equation is modified as follows: (5) In the formula: I represents the identity matrix; It is a small positive number, so take 10. -6 .

[0048] By decoupling the modified equation again using block Gaussian elimination, we can obtain the processed modified equation: (6) It can be noted that the matrix and It is a positive definite matrix, from which we can easily deduce It is also a positive definite matrix. Next, we can directly use the conjugate gradient method for efficient solution. However, direct calculation... and This process is quite complex and very time-consuming. Therefore, we need to use LDL. T Decomposition Pair and Processing: (7) Where: L P L H It is a lower triangular matrix; D P D H It is a diagonal matrix. and This can be simplified to: (8) In addition, and It can also be simplified: (9) Then the distributed conjugate gradient method is used to solve the modified equation in a fully distributed iterative manner.

[0049] For ease of explanation, the modified equation set (6) is restated as follows: (10) Where: , and These are the coefficient matrix, the solution vector, and the right-hand vector, respectively. , , , The expressions are as follows: (11) The power system and the thermal system are given arbitrary initial values ​​respectively. and Then calculate separately: (12) The iterative process of the distributed conjugate gradient method is as follows: (13) Where: It is the residual vector; Indicating the search direction; To find the optimal step size; These are the coefficients of the linear combination. If... and If all values ​​are less than the given tolerance, stop; otherwise, continue iterating.

[0050] Step 1: Initialize variables Set the disturbance factor Perturbation KKT condition tolerance Tolerance of linear equation systems Step 2: Calculate the residual E under the perturbation KKT conditions. If E <e KKT Output the optimal solution and stop; Step 3: Calculate according to equations (11), (8), and (9) respectively. Step 4.1: Given ,calculate Step 4.2: Calculation Step 4.3: Update according to equation (13) Step 4.4: Solve using equation (13) Step 4.5: If Proceed to step 5; Step 4.6: Update , Proceed to step 4.2; Step 5: Backwards Step 6: Back-substitution Step 7: Calculate the original step size and dual step size Step 8: Update variable x P , λ P s P μ P y H , λ H s H μ H ν cp and disturbance factor Proceed to step 2.

[0051] Some steps in the above algorithm are not described in detail. These steps will be supplemented and further explained below.

[0052] The residual E of the perturbed KKT condition in step 2 is: .

[0053] The original step size in step 7 and dual step size They are respectively: In the formula: It is the variable s P The i-th component, It is the variable s H The i-th component, It is the variable μ P The i-th component, It is the variable μ H The i-th component; It is the variable correction amount Δs P The i-th component, It is the variable correction amount Δs H The i-th component, It is the variable correction amount Δμ P The i-th component, It is the variable correction amount Δμ H The i-th component; As a parameter, it is generally taken as 0.99995 to prevent the variable s from being... P s H and μ P μ H Approaching the lower bound zero too quickly.

[0054] In step 8, update variable x P , λ P s P μ P y H , λ H s H μ H ν cp and disturbance factor The process is as follows: In the formula: m P m H These represent the number of inequality constraints for the power system and the thermal system, respectively.

[0055] Further, step 102 includes: verifying the accuracy and superlinear convergence characteristics of the results based on the dynamic temperature curve of the thermal network, power flow data of the power system, and scheduling costs; if the temperature deviation exceeds the allowable range or the power exceeds the limit, fine-tuning the model parameters (such as the initial value of the heat source supply temperature and the heat-to-electricity ratio constraint of the CHP unit) and re-executing the iterative solution process until the scheduling results meet all constraints (comfortable temperature range of heat load, equipment capacity limit, power balance, etc.).

[0056] It should be noted that, in order to demonstrate the superlinear convergence of the Distributed Cooperative Interior Point Conjugate Gradient Method (DC-IPCG), the simulation examples use the traditional Alternating Direction Multiplier Method (ADMM) algorithm for comparison. The following is a brief explanation of the general content of the ADMM algorithm.

[0057] The ADMM algorithm is a distributed algorithm for solving convex optimization problems with separable structures, particularly suitable for handling large-scale optimization problems consisting of multiple coupled subsystems. Its core idea is "divide and conquer," decomposing the original problem into multiple subproblems, and by alternately solving and coordinating the solutions to the subproblems, it eventually converges to the optimal solution of the original problem.

[0058] For the following optimal scheduling model of integrated electric-thermal energy system: In the formula, It is the operating cost of the power system. It is the operating cost of the thermal system; It is a coupling constraint; This represents the inequality constraints in power system constraints. This represents equality constraints in power system constraints. Represents inequality constraints in thermal systems. The superscript P represents the equality constraint in the thermal system constraint; the superscript P represents the electric system and H represents the thermal system. For power system decision variables; These are decision variables for the thermal system.

[0059] In the classic ADMM algorithm, in order to relax coupling constraints We need to introduce the Lagrange multiplier y and add a penalty term to the objective function, resulting in the following augmented Lagrange function: In the formula, For penalty parameters, >0. At this point, the power system constraints and thermal system constraints are no longer coupled, and can be decomposed into the following power system subproblems and thermal system subproblems: , After alternating between the power system subproblem and the thermal system subproblem once, the Lagrange multiplier y is updated as follows: The original residual r and the dual residual d in the iteration process are respectively: , , when the residual (Including the original residual r and the dual residual d) is less than the set allowable error When the iteration converges.

[0060]

[0061] In our integrated electrothermal energy system optimization scheduling model, f(x) and g(z) are both convex functions with linear constraints. After multiple ADMM iterations, both the original residual r and the dual residual d will converge to zero, and the objective function value will also converge to the minimum of the optimization problem. The speed of convergence depends on the penalty parameter. The choice. It should be noted that in the above ADMM iteration process... It remains unchanged, and we call this algorithm the classic ADMM.

[0062] The effectiveness of the proposed Distributed Cooperative Interior-Point Conjugate Gradient (DC-IPCG) method is verified through two typical integrated electric-thermal energy systems (118-node and 319-node systems). The tested and compared algorithms include centralized optimization, traditional ADMM, and DC-IPCG. All algorithms were implemented using MATLAB R2024b on a computer configured with an Intel i7-12700H CPU and 16GB RAM to ensure a fair comparison.

[0063] The 319-node model was solved using a centralized method, which completed the solution in 0.22 seconds with a total scheduling cost of $368,133. The centralized method used in this case is a strategy that directly integrates all decision variables into a large-scale linear or mixed-integer linear programming model, using an efficient solver like Gurobi to obtain the solution. This method fully leverages the capabilities of modern solvers to quickly find the global optimum.

[0064] The traditional Alternating Directional Multiplier Method (ADMM) was used to solve the problem. This method successfully converged after 938 iterations, taking a total time of 130.2844 seconds, and the final total scheduling cost was $368,133. ADMM, as a classic distributed optimization algorithm, gradually approaches the optimal solution by alternately solving subproblems of the power and heat systems and updating the Lagrange multipliers. Although this algorithm has good applicability, its linear convergence characteristic leads to a large number of iterations, and its overall computational efficiency needs improvement.

[0065] The Distributed Cooperative Interior-Point Conjugate Gradient (DC-IPCG) algorithm was used to solve the problem. This method successfully converged after 34 iterations, with a total time of 22.0655 seconds and a final total scheduling cost of $368,133. Building upon the superlinear convergence characteristics of the interior-point method, DC-IPCG decouples and positive-definitely processes the modified equations and employs a distributed conjugate gradient method to achieve a fully distributed solution. This avoids the introduction of a coordination center and significantly improves convergence speed and numerical stability.

[0066] Table 1 below records the solutions of the three algorithms. Comparing the solution results of the three methods, it is found that the total running cost obtained by the three methods is the same. This result shows that the three methods can obtain accurate optimal solutions.

[0067] Table 1. Solutions, Solution Time, and Relative Errors for Each Algorithm at 319 Nodes | Algorithm | ADMM Algorithm | DC-IPCG Algorithm | Total Scheduling Cost (USD) | 3681333 | 681333 | 68133 | Grid Cost | 287010 | 287010 | 287010 | Heating Network Cost | 81121 | 81121 | 81121 | Iterations (times) | 193834 | Solution Time (seconds) | 0.2213 | 0.28442 | 2.0655 | Privacy | × | √ | √ | Relative Error | 0% | 0% | 0% surface

[0068] Compared to the ADMM algorithm, the DC-IPCG algorithm demonstrates a significant advantage in solving the 319-node example. Specifically, all three algorithms converged to the same optimal total cost of $368,133, validating the accuracy of DC-IPCG. However, in terms of computational efficiency, DC-IPCG only required 34 iterations and took 22.0655 seconds, while ADMM required 938 iterations and took 130.2844 seconds. DC-IPCG's computational efficiency is approximately 83.06% higher than ADMM, highlighting its efficient convergence characteristics.

[0069] 2. The 118-node model uses a centralized algorithm to solve this problem. This method completes the solution in 0.1833 seconds, with a final total scheduling cost of $170,956.

[0070] The ADMM algorithm was used to solve the problem. This method converged successfully after 413 iterations, with a total time of 58.0321 seconds. The final total scheduling cost was $170,956.

[0071] The DC-IPCG algorithm was used to solve the problem. This method converged successfully after 32 iterations, with a total time of 1.1216 seconds. The final total scheduling cost was $170,956.

[0072] Table 2 below records the solutions of the three algorithms. By comparing the solution results of the three methods, we find that the total running cost of the three methods is the same. This result shows that all three methods can find the accurate optimal solution.

[0073] Table 2. Solutions, Solution Time, and Relative Errors for Each Algorithm at 118 Nodes | Algorithm | ADMM Algorithm | DC-IPCG Algorithm | Total Scheduling Cost (USD) | 170956 | 170956 | 170956 | Grid Cost | 145590 | 145590 | 145590 | Heating Network Cost | 25368 | 25368 | 25368 | Number of Iterations | 141332 | Solution Time (seconds) | 0.20 | 1458.032 | 11.1216 | Privacy | × | √ | √ | Relative Error | 0% | 0% | 0% Compared to the ADMM algorithm, the DC-IPCG algorithm demonstrates a significant advantage in solving the 118-node example. Specifically, all three algorithms converged to the same optimal total cost of $170,956, validating the accuracy of DC-IPCG. However, DC-IPCG exhibits a significant advantage in computational efficiency: it only requires 32 iterations and takes 1.1216 seconds, while ADMM requires 413 iterations and takes 58.0321 seconds. DC-IPCG's computational efficiency is approximately 98.07% higher than ADMM, highlighting its efficient convergence characteristics.

[0074] DC-IPCG only needs to solve a system of linear corrected equations in each iteration, while ADMM needs to repeatedly solve nonlinear subproblems, resulting in a much longer iteration time than DC-IPCG. In addition, DC-IPCG does not require a coordination center, and the power and thermal systems exchange information only through boundary coupling variables (such as CHP thermal power), achieving true fully distributed optimization.

[0075] The fully distributed co-optimization scheduling method for thermal power provided in this application uses the distributed cooperative interior point conjugate gradient method (DC-IPCG) to solve the scheduling model of the constructed integrated electric-thermal energy system in a distributed manner, and finally obtains the joint optimization scheduling result of the integrated electric-thermal energy system, which has superlinear convergence characteristics.

[0076] For ease of understanding, please refer to Figure 2. This application provides an embodiment of a fully distributed combined heat and power (CHP) optimization scheduling device, including: a model building unit 201, used to construct a fully analytical CHP integrated energy system scheduling model based on pre-set CHP integrated energy system parameters. The pre-set CHP integrated energy system parameters include power system (EPS) parameters, regional thermal network (DHN) dynamic characteristic parameters, and electrothermal coupling equipment parameters. The CHP integrated energy system scheduling model includes a power system model, a thermal network fully analytical model, and an equivalent network model with simplified complexity. Further, it includes: an equivalent mapping subunit 2011, used to sort out the heat source-heat load transmission path, calculate the path time delay, transmission loss coefficient, and flow distribution coefficient, construct a direct dynamic mapping between heat source and heat load, and form an equivalent network model of the heat network; and a convexization processing subunit 2012, used to linearize the nonlinear constraints (including the nonlinear term of heat transmission loss) in the model through the tangent relaxation method, transforming the non-convex optimization problem into a convex optimization model, and ensuring solution convergence.

[0077] The model solving unit 202, connected to the model building unit 201, is used to perform a fully distributed solution of the electric-thermal integrated energy system scheduling model using the distributed cooperative interior point conjugate gradient method (DC-IPCG) to obtain the electric-thermal joint optimization scheduling results. The electric-thermal joint optimization scheduling results include the output of thermal power units, the output of cogeneration units, the power system scheduling cost, the thermal system scheduling cost, and the electric-thermal integrated energy system scheduling cost.

[0078] Furthermore, it also includes: a parameter acquisition unit 203 connected to the model building unit 201, used to acquire preset electric-thermal integrated energy system parameters, the preset electric-thermal integrated energy system parameters including power system parameters, thermal system parameters, and electric-thermal coupling equipment parameters; the power system parameters include bus parameters, branch parameters, thermal power unit parameters, wind farm parameters, and electrical load parameters; the thermal system parameters include node parameters, pipeline parameters, boiler parameters, and heat load parameters; the electric-thermal coupling equipment parameters include cogeneration unit operating parameters.

[0079] Furthermore, the model solving unit 202 includes: a modified equation decoupling subunit 2021, used to construct the perturbation KKT conditions of the model, derive the modified equation, and decouple the modified equation using block Gaussian elimination to separate the solution subproblems of the power system and the thermal system; a positive definite processing subunit 2022, used to introduce a small positive identity matrix to adjust the coefficient matrix of the decoupled modified equation to ensure its symmetric positive definiteness and adapt it to the efficient solution of the conjugate gradient method; and a distributed conjugate gradient solving subunit 2023, used to employ the distributed conjugate gradient method in... Without a coordination center, the modified equations are solved iteratively. The power system and the thermal system only exchange boundary coupling information to obtain the coupling constraint Lagrange multiplier corrections. Iterative update subunit 2024 is used to back-substitute the decision variable corrections for the power system and the thermal system, determine the original step size and dual step size, and update the decision variables, Lagrange multipliers, and perturbation factors until convergence conditions are met. Convergence verification subunit 2025 is used to monitor the residuals of the perturbation KKT conditions and the solution error of the linear equations in real time. If the residuals are less than a preset tolerance (e.g., 10), the verification is performed. -6 If the optimal scheduling result is found, the output will be the best scheduling result; otherwise, the distributed conjugate gradient solution subunit will be returned to continue the iteration.

[0080] Furthermore, it also includes: an efficiency analysis unit 204 connected to the model solving unit 202, used to analyze the superlinear convergence advantage and efficiency improvement of the scheduling model based on the power system scheduling cost, the heat system transmission loss cost, and the total scheduling cost of the integrated electric-heat energy system, combined with the calculation time data; and a result optimization unit 205, used to fine-tune the model parameters (such as the initial value of heat source supply temperature and the CHP unit heat-to-power ratio constraint) according to the convergence verification results and efficiency analysis results, so as to further improve the economy and feasibility of the scheduling scheme. The result optimization unit 205 is connected to the efficiency analysis unit 204.

[0081] This application also provides a fully distributed thermoelectric co-optimization scheduling device, the device including a processor and a memory; the memory is used to store program code and transmit the program code to the processor; the processor is used to execute the fully distributed thermoelectric co-optimization scheduling method based on full analytical modeling and DC-IPCG algorithm in the above method embodiment according to the instructions in the program code.

[0082] This application also provides a computer-readable storage medium for storing program code for executing the fully distributed thermoelectric joint optimization scheduling method in the above method embodiments.

Claims

1. A fully distributed co-optimized scheduling method for thermal power, characterized in that, include: Step 101: Construct a centralized integrated electric-thermal energy system scheduling model based on pre-set integrated electric-thermal energy system parameters. These pre-set parameters include power system parameters, thermal system parameters, and electric-thermal coupling equipment parameters. The integrated electric-thermal energy system scheduling model includes a power system model, a fully analytical thermal network model, and a simplified equivalent network model. Step 102: Use the DC-IPCG algorithm to perform distributed solution on the integrated electric-thermal energy system scheduling model to obtain the joint optimization scheduling results. The joint optimization scheduling results include thermal power unit output, combined heat and power unit output, power system scheduling cost, thermal system scheduling cost, and integrated electric-thermal energy system scheduling cost.

2. The fully distributed co-optimized scheduling method for thermal power as described in claim 1, characterized in that, The integrated electric-thermal energy system scheduling model includes: a power system model, a fully analytical thermal network model, and an equivalent network model with simplified complexity. Before step 101, the model further includes: obtaining pre-set integrated electric-thermal energy system parameters, which include: power system parameters, thermal system parameters, and electric-thermal coupling equipment parameters. The power system parameters include: bus parameters, branch parameters, thermal power unit parameters, wind farm parameters, and electrical load parameters. The thermal system parameters include node parameters, pipeline parameters, boiler parameters, and heat load parameters. The electric-thermal coupling equipment parameters include operating parameters of the combined heat and power (CHP) unit.

3. The fully distributed co-optimized scheduling method for thermal power as described in claim 1, characterized in that, The DC-IPCG algorithm is used to solve the electricity-heat integrated energy system scheduling model in a distributed manner to obtain the joint optimization scheduling results of electricity and heat. DC-IPCG combines the distributed interior-point method and the fully distributed conjugate gradient method, including: S21: linearizing the nonlinear constraints in the original model through the tangent relaxation method, transforming it into a convex optimization model, and ensuring the convergence of DC-IPCG; S22: constructing a perturbation KKT for the convex optimization model. The process involves: S23: Deriving the modified equations and decoupling them using block Gaussian elimination to separate the subproblems of solving the power system and the thermal system; S24: Processing the decoupled modified equations by introducing a small positive identity matrix to adjust the coefficient matrix, ensuring its symmetric positive definiteness and adapting it for efficient solution using the conjugate gradient method; S25: Using the distributed conjugate gradient method to perform a fully distributed iterative solution on the processed modified equations, where the power system and the thermal system only exchange boundary coupling information without a coordination center, obtaining the coupling constraint Lagrange multiplier correction; S26: Back-substituting the decision variable corrections for the power system and the thermal system, calculating the original step size and dual step size, updating the decision variables, Lagrange multipliers, and disturbance factors, repeating the iteration until the KKT condition tolerance is met, and outputting the optimal scheduling result.

4. The fully distributed co-optimized scheduling method for thermal power as described in claim 1, characterized in that, The DC-IPCG algorithm is used to perform distributed solution on the scheduling model of the integrated electric-thermal energy system to obtain the joint optimization scheduling result of the integrated electric-thermal energy system. This process then includes: verifying the accuracy and superlinear convergence characteristics of the results based on the data of the thermal system and the power system, as well as the scheduling cost; if the temperature deviation exceeds the allowable range or the power exceeds the limit, the model parameters are fine-tuned, and the iterative solution process is repeated until the scheduling result meets the comfort temperature range of the heat load, equipment capacity limitations, and power balance; the fine-tuned model parameters include: the initial value of the heat source supply temperature and the heat-to-power ratio constraint of the CHP unit.

5. A fully distributed combined thermal and power optimization scheduling device, characterized in that, include: The model building unit is used to construct a centralized electric-thermal integrated energy system scheduling model based on pre-set electric-thermal integrated energy system parameters. The pre-set electric-thermal integrated energy system parameters include power system parameters, thermal system parameters, and electric-thermal coupling equipment parameters. The electric-thermal integrated energy system scheduling model includes a power system model, a fully analytical thermal network model, and an equivalent network model with simplified complexity. The model solving unit, connected to the model building unit, is used to perform distributed solving of the electric-thermal integrated energy system scheduling model using the DC-IPCG algorithm to obtain the electric-thermal joint optimization scheduling result.

6. The fully distributed combined thermal power optimization scheduling device according to claim 5, characterized in that, Also includes: The parameter acquisition unit is used to acquire pre-set integrated electric-thermal energy system parameters and transmit them to the model building unit. The pre-set integrated electric-thermal energy system parameters include power system parameters, thermal system parameters, and electric-thermal coupling equipment parameters. The power system parameters include bus parameters, branch parameters, thermal power unit parameters, wind farm parameters, and electrical load parameters. The thermal system parameters include node parameters, pipeline parameters, boiler parameters, and heat load parameters. The electric-thermal coupling equipment parameters include operating parameters of the combined heat and power unit.

7. The fully distributed combined thermal power optimization scheduling device according to claim 6, characterized in that, The model solving unit includes: a modified equation decoupling subunit: used to construct the perturbation KKT conditions of the model, derive the modified equation, decouple it using block Gaussian elimination, and separate the power system and thermal system to solve the subproblems; a positive definite processing subunit: used to introduce a small positive identity matrix to adjust the coefficient matrix of the decoupled modified equation to ensure its symmetric positive definiteness and adapt it to the conjugate gradient method; a distributed conjugate gradient solving subunit: used to iteratively solve the modified equation using the distributed conjugate gradient method without a coordination center, where the power system and thermal system only exchange boundary coupling information; and an iterative update subunit: used to back-substitute the modified decision variables, determine the iteration step size, and update the decision variables, Lagrange multipliers, and perturbation factors until the convergence condition is met.

8. The fully distributed combined thermal power optimization scheduling device according to claim 5, characterized in that, Also includes: The convergence verification subunit is used to monitor the residuals of the perturbed KKT conditions and the solution error of the linear equations in real time: if the residuals are less than the preset KKT tolerance, i.e., 10... -6 If the iteration converges, the optimal scheduling result is output; if the residual does not meet the tolerance, the iteration returns to the distributed conjugate gradient solution sub-unit to continue iterating until the convergence condition or the maximum number of iterations is reached.

9. A fully distributed combined thermal power optimization scheduling device, characterized in that, The device includes a processor and a memory; the memory is used to store program code and transmit the program code to the processor; the processor is used to execute the fully distributed thermoelectric co-optimization scheduling method according to any one of claims 1-4 according to the instructions in the program code.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium is used to store program code for executing the fully distributed co-optimized scheduling method for thermal power as described in any one of claims 1-4.

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