A multi-objective optimization scheduling method for combined electric-thermal systems considering thermal inertia

Abstract

The application belongs to the technical field of electric-thermal combined optimal scheduling, and discloses a multi-objective optimal scheduling method of an electric-thermal combined system considering thermal inertia, comprising the following steps: constructing an electric-thermal combined system containing a large-scale heat pipe network, a thermal power unit, a CHP, a wind turbine and an electric boiler, fully considering heat network heat transmission delay, loss and heat storage capacity to establish a thermal inertia dynamic model, combining multiple operation constraints to construct a multi-objective optimal scheduling model and solving the model through an MOPSO algorithm, solving the contradiction between insufficient unit regulation capacity and new energy fluctuation during the heating period; the screening mode of the Pareto optimal solution set and the optimal compromise solution takes into account the economy and reliability, ensures the stability of the heat load supply, optimizes the energy resource allocation, and has extremely strong practical application value and popularization significance.

Description

Technical Field

[0001] This invention belongs to the field of electrothermal joint optimization scheduling technology, and relates to a multi-objective optimization scheduling method for electrothermal joint systems that takes thermal inertia into account. Background Technology

[0002] Improving the utilization of new energy sources such as wind and solar power while reducing the use of fossil fuels is a trend and requirement for energy development. Currently, the mainstream heat supply model in Northeast China is combined heat and power (CHP). Constrained by the priority of winter heating, CHP units generally adopt a "heat-driven power generation" operating mechanism, meaning that power generation output is determined based on heat load demand. While this model ensures residential heating, it also greatly limits the flexibility of adjusting unit power generation output. At the same time, Northeast China possesses abundant wind and solar resources, and the installed capacity of new energy power generation continues to climb, forming a large-scale development pattern. However, the contradiction between the high demand for both electricity and heat during the heating season and the absorption of new energy sources is becoming increasingly prominent, becoming a core bottleneck restricting the efficient operation of the regional energy system. The aforementioned contradictions directly lead to a series of technical problems: First, the intermittent and fluctuating nature of new energy power generation clashes with the insufficient regulation capacity of generating units under the "heat-driven power generation" model, resulting in frequent wind curtailment during the heating season, a significant decrease in the utilization rate of new energy, and prominent energy waste. Second, to alleviate the pressure of new energy consumption, the system needs to be additionally configured with peak-shaving resources, which increases the overall operating cost. Third, existing solutions all have obvious limitations—while energy storage technologies such as electrochemical energy storage and thermal storage tanks can improve regulation capacity, their equipment investment costs are high; when electric boilers, heat pumps, and other electrothermal conversion equipment operate alone, their consumption effect is poor due to load matching. The existing heating network in Northeast China possesses natural thermal storage capacity due to its thermal inertia characteristics. Therefore, based on the existing heating network, there is an urgent need for a scheduling strategy that can optimize the combined heat and power system by considering multiple complex constraints such as the output constraints of cogeneration units, the operating constraints of the heating network, and the fluctuation constraints of new energy output. Summary of the Invention

[0003] The purpose of this invention is to solve the problem that existing technologies cannot optimize the scheduling strategy of electric heating combined systems based on the heating characteristics of heating networks, and to provide a multi-objective optimization scheduling method for electric heating combined systems that considers thermal inertia.

[0004] To achieve the above objectives, the present invention employs the following technical solution: A multi-objective optimization scheduling method for an electrothermal combined system considering thermal inertia includes: Construct a scenario for an integrated electric and thermal system that includes a large-scale thermal pipeline network, thermal power units, combined heat and power (CHP) systems, wind turbine units, and electric boilers; Based on the working status of thermal power units, combined heat and power (CHP) units, wind turbine units, and electric boilers, equipment models are established. Considering the heat transfer delay, heat transfer loss and heat storage capacity of large-scale heating networks, a dynamic model of the thermal inertia of the heating network is established to determine the operating constraints of the heating system. Based on the constructed system scenario, equipment model, and thermal inertia dynamic model of the heating network, a multi-objective optimization scheduling model is constructed, which includes multiple constraints such as power balance, wind power output, equipment operation, and thermal system operation, with the goal of minimizing system power generation cost and wind curtailment rate. The multi-objective optimization scheduling model is solved based on the multi-objective particle swarm optimization algorithm MOPSO to obtain the Pareto optimal solution set, and the optimal solution is selected to realize the collaborative optimization scheduling of the electrothermal combined system.

[0005] A further improvement of the present invention is that: Furthermore, the scenario of constructing an electrothermal integrated system scenario including a large-scale heating network, thermal power units, cogeneration CHP, wind turbine units, and electric boilers specifically involves: the electrical energy generated by the cogeneration CHP, thermal power units, and wind turbine units entering the power grid; the heat energy generated by the cogeneration CHP entering the heating network; the power grid driving the heat energy generated by the electric boiler entering the heating network; external electrical loads connected to the power grid; and external heat loads connected to the heating network.

[0006] Furthermore, the establishment of an equipment model based on the operating status of large-scale thermal pipeline networks, thermal power units, cogeneration CHP, wind turbines, and electric boilers specifically includes: the operating status of thermal power units, cogeneration CHP, wind turbines, and electric boilers includes: power generation constraints of thermal power units, power ramp-up constraints of thermal power units, operating constraints of cogeneration CHP, power and electrothermal conversion efficiency constraints of electric boilers, overall thermal power balance constraints of the system, and electrical power balance constraints of the system.

[0007] The power generation constraints and power ramping constraints of thermal power units are as follows: , in, For the first Each thermal power unit during the period The power generation capacity; and For the first Minimum and maximum power generation of each thermal power unit; For generator sets Downhill ramp rate constraint; For generator sets The upward ramp rate constraint.

[0008] The feasible operating domain for combined heat and power (CHP) is based on thermal power. The horizontal axis represents electrical power. The vertical axis represents the region formed by the corner points of the combined heat and power (CHP) plant, along with the horizontal and vertical axes. The electrothermal power coordinates of its corner points are as follows: The relationship between the electrothermal power of a combined heat and power (CHP) unit and the coordinates of its corner points is as follows: , , in, This is the total number of corner points of the combined heat and power (CHP) plant. It is the corner number of the combined heat and power (CHP) plant. It is the first Taiwan Cogeneration CHP Electric power during a period of time It is the first Taiwan Cogeneration CHP Thermal power over a period of time This represents the heat energy output of the combined heat and power (CHP) plant. Represents the electrical energy output of the combined heat and power (CHP) plant; Combination coefficient Satisfy the following formula: , , The power and electrothermal conversion efficiency constraints for electric boilers are: , in, For electric boilers during time periods Power consumption This represents the maximum power consumption of the electric boiler. For the electrothermal conversion efficiency of electric boilers, For electric boilers during time periods The heat output power; The system power balance constraint is: , in, For thermal power units during the time period The power generation capacity; For CHP cogeneration during the period Power generation capacity, For wind farms during time periods The absorption capacity; For electric boilers during time periods Power consumption For the system in time period The predicted value of electricity load demand; The system thermal power balance constraint is: , in, For the system in time period Heat load requirements; For time period The actual heat supply of the internal combined heat and power (CHP) unit; The power constraint of the wind turbine is: , in, For time period The predicted output of the wind farm, For time period The absorption capacity of the wind farm.

[0009] Furthermore, before establishing the dynamic model of the heating network's thermal inertia and determining the operational constraints of the thermal system, the process also includes: determining the heating network pipeline system between the heat source and the heat load; the heating network pipeline system includes: the heat source, the primary pipeline network, the heat exchange station, the secondary pipeline network, and the heat load; water in the heat source flows into the heat exchange station through the primary pipeline network, undergoes heat exchange at the heat exchange station, and then enters the heat load through the secondary pipeline network, thus completing the water supply from the heat source to the heat load; water entering the heat load enters the heat exchange station through the secondary pipeline network, undergoes heat exchange at the heat exchange station, and then enters the heat source through the primary pipeline network, thus completing the return water from the heat source to the heat load.

[0010] Furthermore, considering the heat transfer delay, heat transfer loss, and heat storage capacity of large-scale heating networks, a dynamic model of the heating network's thermal inertia is established to determine the operational constraints of the heating system. Specifically: For the heat source node, the heat energy generated by the heat source is: , in, The heat energy supplied to the heat source The specific heat capacity of water, For time period The mass flow rate of water heated by the heat source. The return water temperature, For water supply temperature; For the heat load node, the heat received by the heat load is: , in, The heat provided by the heating network to the heat load nodes. for The mass flow rate of water passing through the heat load node during the time period; The supply and return water temperatures are limited by the allowable temperature of the pipeline. The supply and return water temperature constraints are as follows: , in, , The maximum and minimum allowable water temperatures for the water supply pipeline. , The maximum and minimum allowable water temperatures for the return water pipe; For each node in the heating network pipeline, the mass flow rate of the inflowing and outflowing hot water is equal, and its mathematical expression is: , In the formula, Based on nodes A collection of pipes starting from [the origin]. The end node of the pipeline is a node A collection of pipes, For time period pipeline The mass flow rate of the hot water in the container; For time period Internal pipes The mass flow rate of the hot water circulating in the middle; Assuming no heat loss during the hot water mixing process, when hot water with different temperature parameters is transported to the same confluence node via independent pipes, thermal mixing will occur within the node. After the mixing process is complete, the hot water output from this node to each branch pipe will have the same temperature. The mathematical expression for this is: , in, For time period pipeline The temperature of the hot water at the outlet; For time period pipeline The temperature of the hot water at the inlet; Considering the heat transfer delay and heat transfer loss; when calculating the heat transfer delay, heat transfer loss is initially ignored, and the heat transfer delay is calculated as follows: , , in, For pipelines The hot water at the outlet Temperature during the period For pipelines Hot water at the entrance Temperature during the period; For pipelines The total mass of the reheated water For pipelines radius, For pipelines Length, For the first The time delay of heat transfer in the pipeline; When considering the heat loss of hot water during transmission, its temperature change is as follows: , in, The ambient temperature of the pipeline; The value is the thermal conductivity of the pipe material.

[0011] Furthermore, the construction of a multi-objective optimization scheduling model, which includes multiple constraints such as power balance, wind power output, equipment operation, and thermal system operation, with the objectives of minimizing system power generation cost and wind curtailment rate, is as follows: With the objectives of minimizing power generation cost and minimizing wind curtailment rate as the scheduling goals, the objective function expression is as follows: , , , in, The function expression for system operating cost. Here is the function expression for the system's wind curtailment rate. The power generation cost of all CHP units in the system is calculated using the following formula: , The power generation cost of all thermal power units in the system is calculated using the following formula: , in, For the first A CHP during the period Power generation capacity, For the first A CHP during the period The heating power; For thermal power units During the period The power generation capacity; The power consumption of the electric boiler; This is the operating cost coefficient for electric heating equipment; For combined heat and power units Operating costs; This refers to the operating cost of conventional generating units; , , , , , and , , This represents the cost coefficient for generating electricity from CHP units and conventional thermal power units.

[0012] Furthermore, the multi-objective optimization scheduling model is solved using the multi-objective particle swarm optimization algorithm MOPSO to obtain the Pareto optimal solution set, and the optimal solution is selected, specifically as follows: Set the number of particles N, the maximum number of iterations M, and the inertia weight in the Multi-Objective Particle Swarm Optimization (MOPSO) algorithm. Learning factors c1 and c2, maximum external archive capacity Particle velocity range Location range ; Initialize individual optimal solution External archive A of the multi-objective particle swarm optimization algorithm MOPSO; Randomly select a global guide particle from external archive A. The particle velocity is updated; the particle adjusts its position according to the updated velocity, and the position boundary of the particle is corrected to prevent the particle from running out of the position boundary. Calculate the new position of the particle objective function value and its current optimal target value Compare and update according to non-dominant relations. Then update external archive A; The new self-optimal solution for all particles Add the solutions to the temporary set Q, then sort all solutions in the temporary set Q using the non-dominated method, remove dominated solutions, and obtain a new non-dominated set. ; When the number of iterations reaches the preset upper limit M, or when the non-dominated solution of the external archive A does not change significantly for several consecutive generations, the algorithm terminates and the final optimized Pareto solution set is obtained. The objective function is normalized, and weights are set for different objectives. The weighted deviation of each solution in the Pareto solution set is calculated. The maximum weighted deviation of each solution is then taken, and the solution with the smallest maximum weighted deviation is taken as the optimal compromise solution.

[0013] Furthermore, the initialization of the individual optimal solution The external archive A of the multi-objective particle swarm optimization algorithm MOPSO is as follows: The particle's own optimal solution This is the non-dominated solution found in the particle's history search, meaning no other solution is superior to it across all targets; at initialization, the particle has no history information, so its initial position is set to its own optimal position. , The global guiding particle is randomly selected from external archive A. Update the particle velocity, specifically: , in, This represents the current iteration number. For inertial weights, two independent uniformly random numbers in [0,1] are used. Sub-particles The global guided solution of the first Dimensional components; where the inertia weight adopts a linear decreasing strategy, specifically: , The particles adjust their positions based on the updated velocity, while simultaneously correcting the particle position boundaries to prevent particles from running out of the boundaries. Specifically: The formula for limiting particle velocity is as follows: , The particle adjusts its position based on the updated velocity, thus moving within the search space; the position update formula is: The position boundaries are corrected using a truncation method to ensure that the particles are in the solution space: , Furthermore, the calculation of the new position of the particle objective function value and its current optimal target value Compare and update according to non-dominant relations. Then update external save file A, specifically as follows: , Furthermore, the new self-optimal solution for all particles Add to the temporary set Q, specifically: , The process involves sorting all solutions in the temporary set Q using a non-dominated algorithm, removing dominated solutions, and obtaining a new non-dominated set. Specifically: , in, The crowding level is a preset upper limit for archiving. It measures the sparsity of the solution around the target space. The greater the crowding level, the more open the solution is around, and the more it needs to be preserved to maintain diversity.

[0014] The objective function is normalized, weights are assigned to different objectives, the weighted deviation of each solution in the Pareto solution set is calculated, the maximum weighted deviation of each solution is taken, and the solution with the smallest maximum weighted deviation is taken as the optimal compromise solution. Specifically: , in, For the i-th solution In the Normalized values ​​on each objective For the first The minimum value of each objective in the Pareto solution set. For the first The maximum value of each objective in the Pareto solution set.

[0015] Compared with the prior art, the present invention has the following beneficial effects: This invention constructs an integrated electric-thermal system comprising a large-scale heating network, thermal power units, CHP (heating power plant), wind turbines, and electric boilers. It establishes a dynamic thermal inertia model, fully considering heat transfer delays, losses, and thermal storage capacity within the heating network. A multi-objective optimization scheduling model is constructed based on multiple operational constraints and solved using the MOPSO algorithm. This effectively resolves the contradiction between insufficient unit regulation capacity and fluctuations in renewable energy sources during the heating season. Simultaneously, it minimizes system power generation costs, avoids high investments in additional energy storage equipment, expands the scheduling space through the natural thermal storage capacity of the heating network, and enhances the flexibility of the electric-thermal system's coordinated operation. The Pareto optimal solution set and optimal compromise solution selection method balance economic efficiency and reliability, ensuring stable heat load supply while optimizing energy resource allocation. This invention possesses significant practical application value and promotional value. Attached Figure Description

[0016] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 This is a flowchart illustrating the multi-objective optimization scheduling method for an electrothermal combined system considering thermal inertia according to the present invention. Figure 2 This is a structural diagram of the electrothermal combined system in this invention; Figure 3 This is a schematic diagram of the solar thermal load curve and the wind power forecast curve; Figure 4 A feasible domain diagram for the operation of the CHP unit; Figure 5 This is a basic structural diagram of a thermal system; Figure 6 This is a cross-sectional view of the heating pipeline; Figure 7 The power scheduling results are shown in the example diagram; Figure 8 The thermal power scheduling result diagram is shown in the example. Figure 9 The following is a diagram showing the scheduling results of the hourly wind curtailment rate in an example. Figure 10 A graph showing the intraday supply and demand of thermal energy to reflect the effect of thermal inertia. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0019] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0020] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0021] In the description of the embodiments of the present invention, it should be noted that if terms such as "upper," "lower," "horizontal," or "inner" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship commonly used when the product of the invention is in use, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the present invention. Furthermore, terms such as "first" and "second" are only used to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0022] Furthermore, the use of the term "horizontal" does not imply that the component must be absolutely horizontal, but rather that it can be slightly tilted. For example, "horizontal" simply means that its direction is more horizontal than "vertical," and does not mean that the structure must be completely horizontal, but can be slightly tilted.

[0023] In the description of the embodiments of the present invention, it should also be noted that, unless otherwise explicitly specified and limited, the terms "set," "install," "connect," and "link" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in the present invention according to the specific circumstances.

[0024] The present invention will now be described in further detail with reference to the accompanying drawings: See Figure 1 This invention discloses a multi-objective optimization scheduling method for an electrothermal combined system considering thermal inertia, comprising: S101, constructing a combined electric and thermal system scenario including a large-scale thermal pipeline network, thermal power units, cogeneration CHP, wind turbine units and electric boilers; See Figure 2 The electrical energy generated by the combined heat and power (CHP) generator, thermal power units, and wind power units enters the power grid, while the heat energy generated by the CHP generator enters the heating network; the power grid drives electric boilers to generate heat which enters the heating network; the power grid is connected to external electrical loads; and the heating network is connected to external heat loads.

[0025] S102, Based on the working status of thermal power units, combined heat and power (CHP) units, wind turbine units and electric boilers, establish equipment models; The operating status of the thermal power unit, cogeneration CHP, wind power unit, and electric boiler includes: thermal power unit power generation constraints, thermal power unit power ramping constraints, cogeneration CHP operation constraints, electric boiler power and electrothermal conversion efficiency constraints, overall system thermal power balance constraints, and system electrical power balance constraints.

[0026] The basic parameter data input for the combined electric and thermal power system includes: daily wind power forecast data, operating parameter data for conventional thermal power units, CHP units, and electric boilers; mass flow rate, temperature limits, pipe length, diameter, and other parameters of hot water in the heating network; and daily heating load data. Electricity and thermal load data curves and wind power forecast curves are shown below. Figure 3 As shown.

[0027] The power generation constraints and power ramping constraints of thermal power units are as follows: , in, For the first Each thermal power unit during the period The power generation capacity; and For the first Minimum and maximum power generation of each thermal power unit; For generator sets Downhill ramp rate constraint; For generator sets The upward ramp rate constraint.

[0028] See Figure 4 The feasible operating domain for the combined heat and power (CHP) is based on thermal power. The horizontal axis represents electrical power. The vertical axis represents the region formed by the corner points of the combined heat and power (CHP) plant, along with the horizontal and vertical axes. The electrothermal power coordinates of its corner points are as follows: The relationship between the electrothermal power of a combined heat and power (CHP) unit and the coordinates of its corner points is as follows: , , in, This is the total number of corner points of the combined heat and power (CHP) plant. It is the corner number of the combined heat and power (CHP) plant. It is the first Taiwan Cogeneration CHP Electric power during a period of time It is the first Taiwan Cogeneration CHP Thermal power over a period of time This represents the heat energy output of the combined heat and power (CHP) plant. Represents the electrical energy output of the combined heat and power (CHP) plant; Combination coefficient Satisfy the following formula: , , The power and electrothermal conversion efficiency constraints of the electric boiler are as follows: , in, For electric boilers during time periods Power consumption This represents the maximum power consumption of the electric boiler. For the electrothermal conversion efficiency of electric boilers, For electric boilers during time periods The heat output power; The system power balance constraint is: , in, For thermal power units during the time period The power generation capacity; For CHP cogeneration during the period Power generation capacity, For wind farms during time periods The absorption capacity; For electric boilers during time periods Power consumption For the system in time period The predicted value of electricity load demand; The system thermal power balance constraint is: , in, For the system in time period Heat load requirements; For time period The actual heat supply of the internal combined heat and power (CHP) unit; The power constraint of the wind turbine is: , in, For time period The predicted output of the wind farm, For time period The absorption capacity of the wind farm.

[0029] S103. Considering the heat transfer delay, heat transfer loss and heat storage capacity of large-scale heating networks, a dynamic model of the thermal inertia of the heating network is established to determine the operating constraints of the heating system. Before establishing a dynamic model of the heating network's thermal inertia and determining the operational constraints of the thermal system, the process also includes: determining the heating network piping system from the heat source to the heat load; see [link to relevant documentation]. Figure 5 The heating network pipeline system includes: a heat source, a primary pipeline, a heat exchange station, a secondary pipeline, and a heat load; water in the heat source flows into the heat exchange station through the primary pipeline, and after heat exchange at the heat exchange station, it enters the heat load through the secondary pipeline, thus completing the water supply to the heat load; water entering the heat load enters the heat exchange station through the secondary pipeline, and after heat exchange at the heat exchange station, it enters the heat source through the primary pipeline, thus completing the return water to the heat source.

[0030] The process considers the heat transfer delay, heat transfer loss, and heat storage capacity of large-scale heating networks, establishing a dynamic model of the heating network's thermal inertia to determine the operational constraints of the heating system. Specifically: For the heat source node, the heat energy generated by the heat source is: , in, The heat energy supplied to the heat source The specific heat capacity of water, For time period The mass flow rate of water heated by the heat source. The return water temperature, For water supply temperature; For the heat load node, the heat received by the heat load is: , in, The heat provided by the heating network to the heat load nodes. for The mass flow rate of water passing through the heat load node during the time period; The supply and return water temperatures are limited by the allowable temperature of the pipeline. The supply and return water temperature constraints are as follows: , in, , The maximum and minimum allowable water temperatures for the water supply pipeline. , The maximum and minimum allowable water temperatures for the return water pipe; For each node in the heating network pipeline, the mass flow rate of the inflowing and outflowing hot water is equal, and its mathematical expression is: , In the formula, Based on nodes A collection of pipes starting from [the origin]. The end node of the pipeline is a node A collection of pipes, For time period pipeline The mass flow rate of the hot water in the container; For time period Internal pipes The mass flow rate of the hot water circulating in the middle; Assuming no heat loss during the hot water mixing process, when hot water with different temperature parameters is transported to the same confluence node via independent pipes, thermal mixing will occur within the node. After the mixing process is complete, the hot water output from this node to each branch pipe will have the same temperature. The mathematical expression for this is: , in, For time period pipeline The temperature of the hot water at the outlet; For time period pipeline The temperature of the hot water at the inlet; Considering heat transfer delay and heat transfer loss; heat transfer delay refers to the time it takes for the temperature to change from the inlet of the pipe to slowly diffuse to the outlet, rather than immediately affecting the outlet, and this time delay is approximately the same as the total travel time of the hot water from the inlet to the outlet. Heat loss refers to the physical process by which hot water loses heat to the environment through the pipe walls via conduction, convection, or radiation during pipe transportation due to the temperature difference between the hot water and the external environment, ultimately leading to a decrease in its own temperature. The cross-section of the heating pipe is shown below. Figure 6 As shown.

[0031] When calculating the heat transfer delay, heat transfer loss is not considered initially. The calculation of the heat transfer delay is as follows: , , in, For pipelines The hot water at the outlet Temperature during the period For pipelines Hot water at the entrance Temperature during the period; For pipelines The total mass of the reheated water For pipelines radius, For pipelines Length, For the first The time delay of heat transfer in the pipeline; When considering the heat loss of hot water during transmission, its temperature change is as follows: , in, The ambient temperature of the pipeline; The value is the thermal conductivity of the pipe material.

[0032] S104, based on the constructed system scenario, equipment model and thermal inertia dynamic model of the heating network, constructs a multi-objective optimization scheduling model with multiple constraints including power balance, wind power output, equipment operation and thermal system operation, with the goal of minimizing system power generation cost and minimizing wind curtailment rate; With the objectives of minimizing power generation cost and minimizing wind curtailment rate as the scheduling goals, the objective function expression is as follows: , , , in, The function expression for system operating cost. Here is the function expression for the system's wind curtailment rate. The power generation cost of all CHP units in the system is calculated using the following formula: , The power generation cost of all thermal power units in the system is calculated using the following formula: , in, For the first A CHP during the period Power generation capacity, For the first A CHP during the period The heating power; For thermal power units During the period The power generation capacity; The power consumption of the electric boiler; This is the operating cost coefficient for electric heating equipment; For combined heat and power units Operating costs; This refers to the operating cost of conventional generating units; , , , , , and , , This represents the cost coefficient for generating electricity from CHP units and conventional thermal power units.

[0033] S105. The multi-objective optimization scheduling model is solved based on the multi-objective particle swarm optimization algorithm MOPSO to obtain the Pareto optimal solution set, and the optimal solution is selected to realize the collaborative optimization scheduling of the electrothermal combined system.

[0034] The objective function is simplified as follows: , , , The objective function is ,in, To meet The constraints of the equations. To meet The constraints of the inequalities There are N decision variables.

[0035] The multi-objective particle swarm optimization algorithm (MOPSO) is used to solve the constructed multi-objective optimization scheduling model, specifically as follows: Set the number of particles N, the maximum number of iterations M, and the inertia weight in the Multi-Objective Particle Swarm Optimization (MOPSO) algorithm. Learning factors c1 and c2, maximum external archive capacity Particle velocity range Location range ; Initialize individual optimal solution External archive A of the multi-objective particle swarm optimization algorithm MOPSO; Randomly select a global guide particle from external archive A. The particle velocity is updated; the particle adjusts its position according to the updated velocity, and the position boundary of the particle is corrected to prevent the particle from running out of the position boundary. Calculate the new position of the particle objective function value and its current optimal target value Compare and update according to non-dominant relations. Then update external archive A; The new self-optimal solution for all particles Add the solutions to the temporary set Q, then sort all solutions in the temporary set Q using the non-dominated method, remove dominated solutions, and obtain a new non-dominated set. ; When the number of iterations reaches the preset upper limit M, or when the non-dominated solution of the external archive A does not change significantly for several consecutive generations, the algorithm terminates and the final optimized Pareto solution set is obtained. The objective function is normalized, and weights are set for different objectives. The weighted deviation of each solution in the Pareto solution set is calculated. The maximum weighted deviation of each solution is then taken, and the solution with the smallest maximum weighted deviation is taken as the optimal compromise solution.

[0036] The initialization of the individual optimal solution The external archive A of the multi-objective particle swarm optimization algorithm MOPSO is as follows: The particle's own optimal solution This is the non-dominated solution found in the particle's history search, meaning no other solution is superior to it across all targets; at initialization, the particle has no history information, so its initial position is set to its own optimal position. , The global guiding particle is randomly selected from external archive A. Update the particle velocity, specifically: , in, This represents the current iteration number. For inertial weights, two independent uniformly random numbers in [0,1] are used. Sub-particles The global guided solution of the first Dimensional components; where the inertia weight adopts a linear decreasing strategy, specifically: , The particles adjust their positions based on the updated velocity, while simultaneously correcting the particle position boundaries to prevent particles from running out of the boundaries. Specifically: The formula for limiting particle velocity is as follows: , The particle adjusts its position based on the updated velocity, thus moving within the search space; the position update formula is: , The position boundaries are corrected using a truncation method to ensure that the particles are in the solution space: , The calculation of the new position of the particle objective function value and its current optimal target value Compare and update according to non-dominant relations. Then update external save file A, specifically as follows: , The new optimal solution for all particles Add to the temporary set Q, specifically: , The process involves sorting all solutions in the temporary set Q using a non-dominated algorithm, removing dominated solutions, and obtaining a new non-dominated set. Specifically: , in, The crowding level is a preset upper limit for archiving. It measures the sparsity of the solution around the target space. The greater the crowding level, the more open the solution is around, and the more it needs to be preserved to maintain diversity.

[0037] With the kth For example, the steps for calculating congestion are as follows: For each objective function ,Will The solution in the middle Sort in ascending order, and set the crowding degree of the first and last solutions to infinity after sorting. , intermediate solution The crowding degree is the sum of the distances between adjacent solutions in each objective dimension: ; In the formula, , yes exist The first and second solutions after sorting. , yes middle The maximum and minimum values.

[0038] The objective function is normalized, weights are assigned to different objectives, the weighted deviation of each solution in the Pareto solution set is calculated, and the solution with the largest weighted deviation is selected as the optimal compromise solution. Specifically: ; in, For the first One solution In the Normalized values ​​on each objective.

[0039] In this example, The target weight is set to 1 or 2. The formula for calculating the maximum weighted deviation of each solution is: ; In this embodiment, the combined electric and thermal system example consists of a 33-node power system and a 32-node thermal system. The optimized scheduling method proposed in this invention utilizes the thermal inertia of the thermal network, eliminating the need for real-time thermal power balance and increasing the scheduling space. Simultaneously, the thermal inertia of the thermal network provides heat storage capacity, effectively improving the system's absorption of wind energy. Furthermore, the multi-objective optimization algorithm proposed in this invention improves wind energy utilization while reducing system operating costs. Overall, this invention has high practical application value. The solution results for the example are as follows: Figures 7-10 As shown, by Figure 7 It can be seen that the power scheduling result of this embodiment; is derived from Figure 8 It can be seen that the thermal power scheduling result of this embodiment; is derived from Figure 9 It can be seen that the scheduling result of the hourly wind curtailment rate in this embodiment; is derived from Figure 10 As can be seen, this embodiment shows the transformation of intraday heat energy supply and demand curves under the influence of thermal inertia. The system operating cost was reduced by 9.6%, the wind curtailment rate decreased to 8%, and the overall wind power utilization rate reached 92%.

[0040] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A multi-objective optimization scheduling method for an electrothermal combined system considering thermal inertia, characterized in that, include: Construct a scenario for an integrated electric and thermal system that includes a large-scale thermal pipeline network, thermal power units, combined heat and power (CHP) systems, wind turbine units, and electric boilers; Based on the working status of thermal power units, combined heat and power (CHP) units, wind turbine units, and electric boilers, equipment models are established. Considering the heat transfer delay, heat transfer loss and heat storage capacity of large-scale heating networks, a dynamic model of the thermal inertia of the heating network is established to determine the operating constraints of the heating system. Based on the constructed system scenario, equipment model, and thermal inertia dynamic model of the heating network, a multi-objective optimization scheduling model is constructed, which includes multiple constraints such as power balance, wind power output, equipment operation, and thermal system operation, with the goal of minimizing system power generation cost and wind curtailment rate. The multi-objective optimization scheduling model is solved based on the multi-objective particle swarm optimization algorithm MOPSO to obtain the Pareto optimal solution set, and the optimal solution is selected to realize the collaborative optimization scheduling of the electrothermal combined system.

2. The multi-objective optimization scheduling method for an electrothermal combined system considering thermal inertia according to claim 1, characterized in that, The scenario of constructing an electrothermal integrated system including a large-scale heating network, thermal power units, cogeneration CHP, wind turbines, and electric boilers is as follows: the electrical energy generated by the cogeneration CHP, thermal power units, and wind turbines enters the power grid; the heat energy generated by the cogeneration CHP enters the heating network; and the power grid drives the heat energy generated by the electric boilers to enter the heating network. External electrical loads connected to the power grid; external heat loads connected to the heating network.

3. The multi-objective optimization scheduling method for an electrothermal combined system considering thermal inertia according to claim 2, characterized in that, The equipment model is established based on the working status of large-scale thermal pipeline networks, thermal power units, combined heat and power (CHP) plants, wind turbines, and electric boilers. Specifically, the working status of thermal power units, CHP plants, wind turbines, and electric boilers includes: power generation constraints of thermal power units, power ramp-up constraints of thermal power units, operating constraints of CHP plants, power and electrothermal conversion efficiency constraints of electric boilers, overall thermal power balance constraints of the system, and electrical power balance constraints of the system. The power generation constraints and power ramping constraints of thermal power units are as follows: ， in, For the first Each thermal power unit during the period The power generation capacity; and For the first Minimum and maximum power generation of each thermal power unit; For generator sets Downhill ramp rate constraint; For generator sets The upward ramp rate constraint; The feasible operating domain for combined heat and power (CHP) is based on thermal power. The horizontal axis represents electrical power. The vertical axis represents the region formed by the corner points of the combined heat and power (CHP) plant, along with the horizontal and vertical axes. The electrothermal power coordinates of its corner points are as follows: The relationship between the electrothermal power of a combined heat and power (CHP) unit and the coordinates of its corner points is as follows: ， ， in, This is the total number of corner points of the combined heat and power (CHP) plant. It is the corner number of the combined heat and power (CHP) plant. It is the first Taiwan Cogeneration CHP Electric power during a period of time It is the first Taiwan Cogeneration CHP Thermal power over a period of time This represents the heat energy output of the combined heat and power (CHP) plant. Represents the electrical energy output of the combined heat and power (CHP) plant; Combination coefficient Satisfy the following formula: ， ， The power and electrothermal conversion efficiency constraints for electric boilers are: ， in, For electric boilers during time periods Power consumption This represents the maximum power consumption of the electric boiler. For the electrothermal conversion efficiency of electric boilers, For electric boilers during time periods The heat output power; The system power balance constraint is: ， in, For thermal power units during the time period The power generation capacity; For CHP cogeneration during the period Power generation capacity, For wind farms during time periods The absorption capacity; For electric boilers during time periods Power consumption For the system in time period The predicted value of electricity load demand; The system thermal power balance constraint is: ， in, For the system in time period Heat load requirements; For time period The actual heat supply of the internal combined heat and power (CHP) unit; The power constraint of the wind turbine is: ， in, For time period The predicted output of the wind farm, For time period The absorption capacity of the wind farm.

4. The multi-objective optimization scheduling method for an electrothermal combined system considering thermal inertia according to claim 3, characterized in that, Before establishing the dynamic model of the heating network's thermal inertia and determining the operating constraints of the thermal system, the process also includes: determining the heating network pipeline system between the heat source and the heat load; the heating network pipeline system includes: the heat source, the primary pipeline network, the heat exchange station, the secondary pipeline network, and the heat load; water in the heat source flows into the heat exchange station through the primary pipeline network, undergoes heat exchange at the heat exchange station, and then enters the heat load through the secondary pipeline network, thus completing the water supply to the heat load; water entering the heat load enters the heat exchange station through the secondary pipeline network, undergoes heat exchange at the heat exchange station, and then enters the heat source through the primary pipeline network, thus completing the return water to the heat source.

5. The multi-objective optimization scheduling method for an electrothermal combined system considering thermal inertia according to claim 4, characterized in that, The process considers the heat transfer delay, heat transfer loss, and heat storage capacity of large-scale heating networks, establishing a dynamic model of the heating network's thermal inertia to determine the operational constraints of the heating system. Specifically: For the heat source node, the heat energy generated by the heat source is: ， in, The heat energy supplied to the heat source The specific heat capacity of water, For time period The mass flow rate of water heated by the heat source. The return water temperature, For water supply temperature; For the heat load node, the heat received by the heat load is: ， in, The heat provided by the heating network to the heat load nodes. for The mass flow rate of water passing through the heat load node during the time period; The supply and return water temperatures are limited by the allowable temperature of the pipeline. The supply and return water temperature constraints are as follows: ， in, , The maximum and minimum allowable water temperatures for the water supply pipeline. , The maximum and minimum allowable water temperatures for the return water pipe; For each node in the heating network pipeline, the mass flow rate of the inflowing and outflowing hot water is equal, and its mathematical expression is: ， In the formula, Based on nodes A collection of pipes starting from [the origin]. The end node of the pipeline is a node A collection of pipes, For time period pipeline The mass flow rate of the hot water in the container; For time period Internal pipes The mass flow rate of the hot water circulating in the middle; Assuming no heat loss during the hot water mixing process, when hot water with different temperature parameters is transported to the same confluence node via independent pipes, thermal mixing will occur within the node. After the mixing process is complete, the hot water output from this node to each branch pipe will have the same temperature. The mathematical expression for this is: ， in, For time period pipeline The temperature of the hot water at the outlet; For time period pipeline The temperature of the hot water at the inlet; Considering the heat transfer delay and heat transfer loss; when calculating the heat transfer delay, heat transfer loss is initially ignored, and the heat transfer delay is calculated as follows: ， ， in, For pipelines The hot water at the outlet Temperature during the period For pipelines Hot water at the entrance Temperature during the period; For pipelines The total mass of the reclaimed water For pipelines radius, For pipelines Length, For the first The time delay of heat transfer in the pipeline; When considering the heat loss of hot water during transmission, its temperature change is as follows: ， in, The ambient temperature of the pipeline; The value is the thermal conductivity of the pipe material.

6. The multi-objective optimization scheduling method for an electrothermal combined system considering thermal inertia according to claim 5, characterized in that, The construction of the multi-objective optimization scheduling model, which includes multiple constraints such as power balance, wind power output, equipment operation, and thermal system operation, aims to minimize system power generation cost and wind curtailment rate. Specifically: With the objectives of minimizing power generation cost and minimizing wind curtailment rate as the scheduling goals, the objective function expression is as follows: ， ， ， in, The function expression for system operating cost. Here is the system's wind curtailment rate function expression. The power generation cost of all CHP units in the system is calculated using the following formula: ， The power generation cost of all thermal power units in the system is calculated using the following formula: ， in, For the first A CHP during the period Power generation capacity, For the first A CHP during the period The heating power; For thermal power units During the period The power generation capacity; The power consumption of the electric boiler; This is the operating cost coefficient for electric heating equipment; For combined heat and power units Operating costs; This refers to the operating cost of conventional generating units; , , , , , and , , This represents the cost coefficient for generating electricity from CHP units and conventional thermal power units.

7. The multi-objective optimization scheduling method for an electrothermal combined system considering thermal inertia according to claim 6, characterized in that, The multi-objective optimization scheduling model is solved using the multi-objective particle swarm optimization algorithm (MOPSO) to obtain the Pareto optimal solution set, and the optimal solution is selected. Specifically: Set the number of particles N, the maximum number of iterations M, and the inertia weight in the Multi-Objective Particle Swarm Optimization (MOPSO) algorithm. Learning factors c1 and c2, maximum external archive capacity Particle velocity range Location range ; Initialize individual optimal solution External archive A of the multi-objective particle swarm optimization algorithm MOPSO; Randomly select a global guide particle from external archive A. The particle velocity is updated; the particle adjusts its position according to the updated velocity, and the position boundary of the particle is corrected to prevent the particle from running out of the position boundary. Calculate the new position of the particle objective function value and its current optimal target value Compare and update according to non-dominant relations. Then update external archive A; The new self-optimal solution for all particles Add the solutions to the temporary set Q, then sort all solutions in the temporary set Q using the non-dominated method, remove dominated solutions, and obtain a new non-dominated set. ; When the number of iterations reaches the preset upper limit M, or when the non-dominated solution of the external archive A does not change significantly for several consecutive generations, the algorithm terminates and the final optimized Pareto solution set is obtained. The objective function is normalized, and weights are set for different objectives. The weighted deviation of each solution in the Pareto solution set is calculated. The maximum weighted deviation of each solution is then taken, and the solution with the smallest maximum weighted deviation is taken as the optimal compromise solution.

8. The multi-objective optimization scheduling method for an electrothermal combined system considering thermal inertia according to claim 7, characterized in that, The initialization of the individual optimal solution The external archive A of the multi-objective particle swarm optimization algorithm MOPSO is as follows: The particle's own optimal solution This is the non-dominated solution found in the particle's history search, meaning no other solution is superior to it across all targets; at initialization, the particle has no history information, so its initial position is set to its own optimal position. ， The global guiding particle is randomly selected from external archive A. Update the particle velocity, specifically: ， in, This represents the current iteration number. For inertial weights, two independent uniformly random numbers in [0,1] are used. Sub-particles The global guided solution of the first Dimensional components; where the inertia weight adopts a linear decreasing strategy, specifically: ， The particles adjust their positions based on the updated velocity, while simultaneously correcting the particle position boundaries to prevent particles from running out of the boundaries. Specifically: The formula for limiting particle velocity is as follows: ， The particle adjusts its position based on the updated velocity, thus moving within the search space; the position update formula is: The position boundaries are corrected using a truncation method to ensure that the particles are in the solution space: 。 9. The multi-objective optimization scheduling method for an electrothermal combined system considering thermal inertia according to claim 8, characterized in that, The calculation of the new position of the particle objective function value and its current optimal target value Compare and update according to non-dominant relations. Then update external save file A, specifically as follows: 。 10. The multi-objective optimization scheduling method for an electrothermal combined system considering thermal inertia according to claim 9, characterized in that, The new optimal solution for all particles Add to the temporary set Q, specifically: ， The process involves sorting all solutions in the temporary set Q using a non-dominated algorithm, removing dominated solutions, and obtaining a new non-dominated set. Specifically: ， in, The crowding is a preset upper limit for archiving. The crowding measures the sparsity of the solution around the target space. The greater the crowding, the more open the solution is around, and the more it needs to be preserved to maintain diversity. The objective function is normalized, weights are assigned to different objectives, the weighted deviation of each solution in the Pareto solution set is calculated, and the solution with the largest weighted deviation is selected as the optimal compromise solution. Specifically: ， in, For the i-th solution In the Normalized values ​​on each objective For the first The minimum value of each objective in the Pareto solution set. For the first The maximum value of each objective in the Pareto solution set.

Images