CN117034787B - Modelica modeling and genetic algorithm-based coal-fired boiler operation method - Google Patents
Modelica modeling and genetic algorithm-based coal-fired boiler operation method Download PDFInfo
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Abstract
The invention discloses a coal-fired boiler operation method based on Modelica modeling and genetic algorithm. An accurate coal-fired boiler physical model is established by adopting a ClaRaPlus library in Modelica, the maximum generating capacity is used as an optimization target, and the optimal input parameter combination of the air supply quantity, the coal burning quantity and the water supply quantity is solved by using a genetic algorithm. Firstly, carrying out thermal engineering and flow performance simulation on a boiler by using a coal-fired boiler power generation model, then exporting the boiler model into an FMU file, loading the FMU model by using a fmpy package in a Python environment, constructing a genetic algorithm framework, and optimizing an input parameter combination. The method realizes the efficient, environment-friendly and economic operation of coal-fired power generation, provides a brand-new thought for the deep fusion of virtual simulation and actual process, enables the optimization result to effectively guide the dispatching and control of the actual power plant, and has important engineering application value.
Description
Technical Field
The invention relates to the field of boiler system operation, in particular to a coal-fired boiler operation method based on Modelica modeling and genetic algorithm.
Background
Coal-fired power generation plays an important role in the current world power supply, and a coal-fired boiler is core equipment of a power generation link. Optimizing the operation of the coal-fired boiler can not only improve the power generation efficiency and reduce the production cost, but also reduce the environmental pollution emission and promote the sustainable development of the power industry. Therefore, research and improvement of the coal-fired boiler technology are beneficial to realizing energy conservation and emission reduction, improving the peak shaving capacity of a system, reducing the risk of new construction cost and transforming to environment-friendly power generation for coal-electric enterprises, and have important significance in promoting the stable, efficient and clean development of the power industry.
The optimization control of the coal burning amount, the water feeding amount and the primary side air feeding amount of the coal burning boiler is the key point for improving the economical efficiency and the environmental protection of the coal burning boiler. The reasonable parameter configuration not only can improve the combustion efficiency and reduce the fuel consumption, but also can reduce the generation of pollutants and reduce the emission of pollutants such as nitrogen oxides, sulfur dioxide and the like. Therefore, the three key input parameters are synergistically optimized, and the method has important significance for promoting the economical efficiency and the environmental protection of the operation of the coal-fired boiler.
Disclosure of Invention
The invention provides a coal-fired boiler operation method based on Modelica modeling and genetic algorithm. According to the method, the boiler parameter combination configuration for realizing the maximum power generation amount can be obtained by optimizing the input parameters in the normal operation state of the boiler. The method provides reliable reference and optimization direction for the economic operation of the actual boiler, and provides a feasible new thought for the optimal control of the coal-fired boiler.
A coal-fired boiler operation method based on Modelica modeling and genetic algorithm comprises the following steps:
step S1, a simulation model is established according to a coal-fired boiler operation system, wherein the simulation model comprises two sub-models of a boiler system and a steam-water system; wherein the boiler system submodel comprises a pulverizer, a cold ash bucket, a burner, a combustion chamber, an economizer and a wall surface part with a convection bank; the air supply and the coal enter a pulverizer together to finish the preparation of the coal dust, the coal dust and the air mixture enter a combustor to burn, and the high-temperature flue gas is further combusted through a combustion chamber and an economizer and is heated by a steam pipeline;
the steam-water system sub-model comprises a steam turbine, a condenser, a reheater, a water supply tank, a pump and a valve; the water supply pump pumps water from the water supply tank and enters the steam pipeline to be heated and vaporized by the boiler side system, the vaporized high-temperature and high-pressure steam enters the steam turbine to generate electricity, the steam turbine exhaust steam enters the condenser to condensate back water, and the condensate water enters the heater and the water supply tank to complete circulation.
Step S2, setting the generated energy as an optimization target, and adding an input/output interface related to optimization into the model, wherein the output interface is as follows: the generator model is used for calculating the generated energy; an input interface: and (3) primary side air supply quantity, coal supply quantity and water supply quantity, and guiding out an FMU dynamic link library file.
And S3, importing a pre-established coal-fired boiler operation system model in the Python environment, configuring parameters of a model input interface, and connecting the interface with the exported FMU dynamic link library file.
And S4, compiling the following functions according to the flow of a genetic algorithm, wherein the main steps comprise randomly initializing a population, designing an fitness function taking the maximum power generation amount as a target, selecting individuals according to fitness, performing genetic crossover and mutation to generate a new population, and judging iteration termination conditions.
And S5, setting control parameters required by a genetic algorithm, including upper and lower limit cross probability, variation probability, population number and population size of each generation of input parameters, and carrying out iterative operation and simulation optimization based on the set parameters.
In summary, the invention firstly establishes a physical model of the operation process of the coal-fired boiler by using Modelica software according to the technological process and thermodynamic principle of the coal-fired boiler. And then generating an FMU model, and adopting a genetic algorithm to carry out multi-parameter optimization so as to realize maximization of the generated energy. Specifically, the method of the invention sets a wide input parameter variation range and designs a fitness function aiming at generating capacity. In the genetic iteration process, the population is gathered towards an optimal region along with the principle of 'superior and inferior elimination', so that the population is prevented from falling into local optimal. Through continuous genetic iteration, the invention can quickly locate the optimal matching of parameters, and realize the effective global optimization of the complex coal-fired boiler process.
Drawings
FIG. 1 is a flow chart of the method of operation of the coal-fired boiler of the present invention based on Modelica modeling and genetic algorithm.
Fig. 2 is a flowchart of a coal-fired boiler operation method based on Modelica modeling and genetic algorithm for implementing loading operation FMU model in Python according to an embodiment of the present invention.
Fig. 3 is a cross operation method diagram of the coal-fired boiler operation method based on Modelica modeling and genetic algorithm provided by the embodiment of the invention.
Fig. 4 is a diagram of a variation operation method of the coal-fired boiler operation method based on Modelica modeling and genetic algorithm according to the embodiment of the present invention.
FIG. 5 is a graph of power generated by a steam turbine at steady state for various combinations of Modelica modeling and genetic algorithm based methods of operating a coal-fired boiler according to embodiments of the present invention.
Description of the embodiments
In order that the subject matter, technical solutions and advantages of the present invention may be more clearly understood, the present invention will be described in detail below with reference to the accompanying drawings and examples. It should be noted that the following description of the specific embodiments is for the purpose of illustrating the invention only and is not to be construed as limiting the invention. Furthermore, the embodiments of the present invention and the technical features in the embodiments may be combined with each other as long as they do not collide therewith.
A coal-fired boiler operation method based on Modelica modeling and genetic algorithm comprises the following steps:
step S1, a simulation model is established according to a coal-fired boiler operation system, wherein the simulation model comprises a boiler system and a steam-water system. The boiler system submodel comprises a pulverizer, a ash cooling hopper, a burner, a combustion chamber, an economizer, a wall surface with a convection bank and the like; the air supply and the coal enter a pulverizer together to finish the preparation of the coal dust, the coal dust and the air mixture enter a combustor to burn, and the high-temperature flue gas is further combusted through a combustion chamber and an economizer and is heated by a steam pipeline;
the steam-water system sub-model comprises a steam turbine, a condenser, a reheater, a water supply tank and related pumps and valves; the water supply pump pumps water from the water supply tank and enters the steam pipeline to be heated and vaporized by the boiler side system, the vaporized high-temperature and high-pressure steam enters the steam turbine to generate electricity, the steam turbine exhaust steam enters the condenser to condensate back water, and the condensate water enters the heater and the water supply tank to complete circulation.
Each component in the simulation model of the coal-fired boiler operation system selects a ClaRa component library of Modelica, so that continuous steady-state operation and transient state working condition changes of the coal-fired boiler can be accurately reproduced. Wherein the boiler system model comprises key components of a boiler system, including a coal system, a combustion system, a wall heat exchange system and the like. The fuel used in the combustion chamber includes, but is not limited to, coal, natural gas, and other renewable sources of combustion energy. The steam-water system sub-model comprises main component equipment of steam-water circulation, all the sub-models can be mutually related, so that the exchange of parameters in the steam-water circulation is realized, and the simulation of the whole system is realized.
Step S2, setting the generated energy as an optimization target, and adding an input/output interface related to optimization into the model, wherein the output interface is as follows: the generator model is used for calculating the generated energy; an input interface: and (3) primary side air supply quantity, coal supply quantity and water supply quantity, and guiding out an FMU dynamic link library file.
And S3, importing a pre-established coal-fired boiler operation system model in the Python environment, configuring parameters of a model input interface, and connecting the interface with the exported FMU dynamic link library file.
The invention exports the model into the FMU standard format, can be integrated into different software environments to carry out analog simulation, and improves the portability of the model. Simulation of the Modelica model in Python uses fmpy library to import FMU files in the Python environment.
Step S4, according to the flow of the genetic algorithm, writing the following functions, wherein the main steps comprise: randomly initializing a population, designing an fitness function with the maximum power generation as a target, selecting individuals according to the fitness, performing genetic crossover and mutation to generate a new population, and judging iteration termination conditions.
The genetic algorithm is a heuristic search algorithm based on a natural selection principle and a natural genetic mechanism, and good genetic genes (optimal targets) are continuously inherited to offspring through simulating the natural mechanism (selection, crossover and mutation operations) of biological genetic evolution in nature, so that the probability of generating optimal solutions by offspring is increased.
And S5, setting control parameters required by a genetic algorithm, including upper and lower limit cross probability, variation probability, population number and population size of each generation of input parameters, and carrying out iterative operation and simulation optimization based on the set parameters.
The genetic algorithm control parameters of the invention, including the upper and lower limits of input parameters, crossover probability, variation probability, population number and population size of each generation, can be configured in a self-defined way according to specific application requirements.
Examples
The invention relates to a high-efficiency operation method of a coal-fired boiler based on Modelica modeling and genetic algorithm, which mainly comprises the following steps:
step 1: referring to fig. 1, a simulation model of a coal-fired boiler operation system is firstly established in a Modelica language environment, the simulation model is mainly divided into two parts, a boiler system sub-model and a steam-water system sub-model, the boiler system sub-model mainly comprises a pulverizer, a cold ash bucket, a burner, a combustion chamber with an inner tube bundle and an economizer, and is used for simulating the scene of coal dust processing and coal-fired high-temperature and high-pressure steam production, and the connection mode is as follows: the air quantity and coal enter a pulverizer to finish the preparation of the coal powder, the coal powder and the air mixture enter a combustor to burn, and the high-temperature flue gas is further combusted through a combustion chamber, an economizer and the like and is heated by a steam pipeline. The steam-water system sub-model mainly comprises a steam turbine, a condenser, a water supply tank, a superheater and pipeline valves and is used for simulating the conditions of steam expansion acting and circulating water supply, and the steam-water system sub-model is built into a 580MW coal-fired power plant steam circulation model in the embodiment. The connection mode is as follows: the water supply pump pumps water from the water supply tank and enters the steam pipeline to be heated and vaporized by the boiler side system, the vaporized high-temperature and high-pressure steam enters the steam turbine to generate electricity, the steam turbine exhaust steam enters the condenser to condensate back water, and the condensate water enters the heater and the water supply tank to complete the system circulation. In the established coal-fired boiler model, different air supply quantity, coal supply quantity and water supply quantity (Input) have different generated energy (Output), so that the air supply quantity, the coal supply quantity and the water supply quantity cannot be definitely calibrated to a certain value in the model, but are made into an Input interface Input form, so that the maximum Output can be found by optimizing the Input by utilizing a Genetic Algorithm (GA) in python.
In the process of packaging the coal-fired boiler model, a fmu form is derived, and fmu is essentially a model packaging file with an interface. By invoking this fmu on the Python software, a joint simulation of Python and modica is achieved, whereas given the specific value of Input described above in Python, output can be calculated in the modica model.
In python, the specific flow of the genetic algorithm is to Input the initial value of Input first, calculate Output, if it is not the optimal individual (i.e. Input), execute the operations of selection, crossover and mutation on the individual until the optimal individual is Output in the iteration number.
Step 2: an input interface of a simulation model of the coal-fired boiler operation system is arranged, and the input interface comprises primary side air supply quantity, coal supply quantity and a water supply tank and is used as an optimization object of a genetic algorithm. Setting the generated energy of an output interface of a simulation model of a coal-fired boiler operation system, wherein the generated energy is calculated by the following process:
first calculating the turnover angular velocity generated by the steam turbine[rad/s]：/>
Wherein, [rad]is the absolute angular velocity of the flange, ts]For time, d is the derivative sign, i.eDeriving the time t.
Calculating electrical energy due to turbine shaft rotation:/>
【Kg.m 2 Moment of inertia, 1500.
The FMU dynamic link library file is generated using Modelica's built-in solver (Dassl) co-simulation.
Step 3: fig. 2 shows a specific flow of implementing the load running FMU model in Python, and in Python 3.10 environment, numpy 1.25.1 and fmpy 0.3.15 are installed. The FMU dynamic link library file is first extracted using the unizip dir function of fmpy, model_description function description model, and model is instantiated via FMU _instance. The FMU _input is then used to determine the input variables of the FMU, namely the air supply, coal supply and water supply, the type being set to the floating point type. Finally, the start and end times of the simulation are set in the simulation_ fmu, the simulation is run, and the power generation amount is output as a control target.
Step 4: FIG. 2 shows a method for optimizing an FMU model by using a genetic algorithm, and the specific process is as follows:
process 1), first creating an initial population, namely initializing the model, and accepting the input parameter values including maximum value, minimum value, population size, cross rate, mutation rate and propagation algebra by an initialization method. The maximum value and the minimum value are the upper limit and the lower limit of the variable; the population size is a feasible solution domain, and the number of a group of solutions is selected according to the fitness function; the crossing rate is the probability of random crossing of components in two feasible solutions to generate a new solution, the value range is 0-1, the value is generally 0.6-0.9, the crossing rate is too high, the good solution can be lost, and the new solution is difficult to generate due to the too low crossing rate; the mutation rate is a certain component part in the random mutation feasible solution, the probability of generating a new solution is generated, the value range is 0-1, the value is generally 0.001-0.1, the algorithm is similar to random search due to the fact that the mutation rate is too high, local optimum is easy to fall into, the prior information cannot be effectively utilized, and population diversity is reduced due to the fact that the mutation rate is too low; the propagation algebra is the required iteration number, i.e. the algebra calculated by evolution from the initial population.
The population size is the number of a group of feasible solutions, the higher the population number is, the higher the calculation accuracy is, but the lower the calculation speed is, the reverse is, the lower the population number is, the lower the calculation accuracy is, but the calculation speed is higher. The crossover is a random crossover of the components of two feasible solutions, creating a new solution. Variation is a component of a random variation feasible solution. Both are ways to generate new populations. The propagation algebra is how many times the total needs to be simulated.
And 2) taking the generated energy in the step 2 as a control target, selecting the condition of maximum generated energy during each iteration, and recording corresponding input parameters.
Process 3) selecting individuals according to the electricity generation value using a roulette selection method, the method being implemented as follows:
(1) Calculate eachIndividual fitnessWherein->Representing a different set of individuals and having a different set of individuals,sequence number for each different individual, +.>Is the population number.
(2) Calculating the probability that each individual is selected to the next generation population:
(3) Calculating the cumulative probability for each individual:
(4) A random number r is generated between 0, 1.
(5) The individual in the cumulative probability interval where r is located is selected, and a large selected probability with a large fitness can be assumed.
(6) Repeating (4) and (5) n times, selecting the m corresponding individualsThe following crossover operation is facilitated. Process 4), in the genetic algorithm, the crossover operation is a process of exchanging information of the two selected generation solutions to generate new child solutions, as shown in fig. 3. The invention adopts a double-point crossing method, which comprises the specific steps of selecting two feasible solutions (1) and two feasible solutions (2) from a first generation solution according to the adaptability. Two intersections are randomly selected on the code strings of the feasible solution (1) and the feasible solution (2). The code segments between these two intersections are swapped to generate two second-generation solutions (1) and (2). Thus, through the exchange of genetic information, the second generation not only maintains the excellent genes of the first generation, but also can generate new combinations, thereby improving population diversity and acquisitionThe probability of the solution is better.
Process 5), mutation is another genetic operation in the genetic algorithm that produces a new solution. It is achieved by randomly modifying the coded bits of certain individuals as shown in fig. 4. In this example, we use a single-point mutation method, which specifically includes randomly selecting one feasible solution from the feasible solutions of the first generation (new solutions generated by the crossover operation). The variation point is randomly selected and the code for that point is changed (e.g., 2 to 5 in the example) so that a second generation solution is created. Mutation is a probabilistic event, typically setting a smaller probability of mutation, such as 0.01. This can avoid excessive randomness while maintaining population diversity. When the effect of crossover manipulation is weaker, appropriate mutation can produce new superior genes, helping to obtain a better solution.
Step 5: setting control parameters required by a genetic algorithm, wherein the population number is 40, the crossover rate is 0.8, the mutation rate is 0.1, and the propagation algebra is 5000.
The upper and lower limits of the variables are:
wherein,is primary side air supply quantity (kg/s),>and->The upper limit and the lower limit of the primary side air supply quantity are respectively 100 and 800; />For the coal feed (kg/s),. About.>And->The upper limit and the lower limit of the coal feeding amount are respectively 1 and 100; />For water supply amount->And->The upper and lower limits of the water supply amount are respectively 50 and 800.，/>，/>Are within the viable range.
The optimization simulation is carried out, and FIG. 5 lists the power generation curves of the steam turbine at steady state under several different combination conditions, wherein the optimal combination parameter configuration is as follows: the primary side air supply amount was 505.331kg/s, the coal supply amount was 42.88kg/s, the water supply amount was 420kg/s, and the power generation amount within one hour was 620.582MWh. The method can find the optimal parameter configuration, provide reference and guidance for on-site operation, and realize energy conservation, consumption reduction and economic development. Specifically, the method can guide reasonable configuration of parameters of the coal-fired boiler, reduce fuel consumption, improve power generation efficiency and reduce pollutant emission. In addition, the method can be widely applied to optimization of other industrial processes by means of model establishment and parameter optimization thought, and the purposes of saving resources and reducing cost are achieved by determining the optimal technological parameters.
According to the invention, an accurate coal-fired boiler physical model is established by adopting a ClaRaPlus library in Modelica, the maximum generating capacity is used as an optimization target, and the optimal input parameter combination of the air supply quantity, the coal burning quantity and the water supply quantity is solved by using a genetic algorithm. First, a model of a coal-fired boiler including a combustion chamber, a superheater, a steam turbine, and the like is developed by using Modelica language, and a thermal engineering and flow performance simulation is performed on the boiler. And then, exporting the boiler model into an FMU file, loading the FMU model by using an fmpy package in a Python environment, constructing a genetic algorithm framework, and optimizing the input parameter combination. The technology realizes high-efficiency, environment-friendly and economic operation of coal-fired power generation, provides a brand-new thought for deep fusion of virtual simulation and actual process, enables an optimization result to effectively guide scheduling and control of an actual power plant, and has important engineering application value.
The above description is only of the preferred embodiments of the present invention and is not intended to limit the present invention, but various modifications and variations can be made by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (7)
1. The coal-fired boiler operation method based on Modelica modeling and genetic algorithm is characterized by comprising the following steps of:
step S1, a simulation model is established according to a coal-fired boiler operation system, and each component in the coal-fired boiler operation system simulation model adopts a ClaRa component library of Modelica, so that continuous steady-state operation and transient state working condition changes of the coal-fired boiler can be accurately reproduced;
the simulation model comprises two sub-models of a boiler system and a steam-water system; wherein the boiler system submodel comprises a pulverizer, a cold ash bucket, a burner, a combustion chamber, an economizer and a wall surface part with a convection bank; the air supply and the coal enter a pulverizer together to finish the preparation of the coal dust, the coal dust and the air mixture enter a combustor to burn, and the high-temperature flue gas is further combusted through a combustion chamber and an economizer and is heated by a steam pipeline;
the steam-water system sub-model comprises a steam turbine, a condenser, a reheater, a water supply tank, a pump and a valve; the water supply pump pumps water from the water supply tank and enters the steam pipeline to be heated and vaporized by the boiler side system, the vaporized high-temperature and high-pressure steam enters the steam turbine to generate electricity, the steam turbine exhaust steam enters the condenser to condensate back water, and the condensate water enters the heater and the water supply tank to complete circulation;
step S2, setting the generated energy as an optimization target, and adding an input/output interface related to optimization into a simulation model, wherein the output interface is as follows: for calculating the amount of power generation; an input interface: setting air supply quantity, coal supply quantity and water supply quantity, and guiding out an FMU dynamic link library file;
s3, importing a pre-established coal-fired boiler operation system model in a Python environment, configuring parameters of a model input interface, and connecting the interface with an exported FMU dynamic link library file;
s4, establishing a random initialization population, designing an fitness function taking the maximum power generation amount as a target, selecting individuals according to fitness, performing genetic crossover and mutation to generate a new population, and judging iteration termination conditions according to the flow of a genetic algorithm;
and S5, setting control parameters required by a genetic algorithm, including upper and lower limits, crossover probability, variation probability, population number and population size of each generation of input parameters, and carrying out iterative operation and simulation optimization based on the set parameters.
2. The method for operating a coal-fired boiler based on Modelica modeling and genetic algorithm according to claim 1, wherein the power generation amount in step S2 is calculated by:
first, the rotational speed omega generated by the turbine is calculated:
the method comprises the steps that the sheet.phi is the absolute angular speed of a flange, t is time, d is a derivative symbol, namely, the sheet.phi derives the time t;
calculating the electrical energy E generated by the rotation of the turbine shaft:
wherein J is moment of inertia.
3. The method for operating a coal-fired boiler based on Modelica modeling and genetic algorithm according to claim 1, wherein the simulation of Modelica model in step S3 in Python utilizes fmpy library to import FMU dynamic link library file in Python environment.
4. The method for operating a coal-fired boiler based on Modelica modeling and genetic algorithm according to claim 1, wherein the individual is selected according to fitness in step S4, and the roulette selection method is used, and the method is implemented as follows:
(1) Calculating each individual fitness f (x i ) I=1, 2,..m, where x is i Representing different individuals, i is the serial number of each different individual, and m is the population number;
(2) Calculating the probability that each individual is selected to the next generation population:
(3) Calculating the cumulative probability for each individual:
(4) Generating a random number r between [0,1 ];
(5) The individual in the cumulative probability interval where r is positioned is selected, and the selected probability with large adaptability is large;
(6) Repeating (4) and (5) m times, and selecting the m corresponding individuals x i The following crossover operation is facilitated.
5. The method for operating a coal-fired boiler based on Modelica modeling and genetic algorithm according to claim 1, wherein the crossing operation in step S4 is a double-point crossing and the mutation operation is a single-point mutation.
6. The method for operating a coal-fired boiler based on Modelica modeling and genetic algorithm according to claim 1, wherein the upper and lower limits of the parameters in step S5 are:
x 1_low ≤x 1 ≤x 1_high ，
x 2_low ≤x 2 ≤x 2_high ，
x 3_low ≤x 3 ≤x 3_high ，
wherein x is 1 Is the primary side air supply quantity x 1_high And x 1_low The upper limit and the lower limit of the primary side air supply quantity are respectively; x is x 2 For coal feed, x 2_high And x 2_low The upper limit and the lower limit of the coal feeding amount are respectively; x is x 3 To feed water volume x 3_high And x 3_low The upper and lower limits of the water supply amount are respectively set.
7. The method for operating a coal-fired boiler based on Modelica modeling and genetic algorithm according to claim 1, wherein the genetic algorithm control parameters in the step S5 comprise upper and lower limits of input parameters, crossover probability, variation probability, population number and population size of each generation, and are configured in a self-defining manner according to specific application requirements.
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| CN111222237A (en) * | 2019-12-30 | 2020-06-02 | 国网北京市电力公司 | Modeling processing method and device for direct-heating electric heating equipment |
| CN111765445A (en) * | 2020-07-01 | 2020-10-13 | 河北工业大学 | Boiler on-line combustion optimization control method and system and computer equipment |
| CN115081900A (en) * | 2022-06-30 | 2022-09-20 | 国网北京市电力公司 | Modeling method and device of integrated energy system and electronic equipment |
| CN116819945A (en) * | 2023-05-31 | 2023-09-29 | 北京工业大学 | Pressure difference control method for multi-cold-source annular cooling system based on reinforcement learning |
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| CN111222237A (en) * | 2019-12-30 | 2020-06-02 | 国网北京市电力公司 | Modeling processing method and device for direct-heating electric heating equipment |
| CN111765445A (en) * | 2020-07-01 | 2020-10-13 | 河北工业大学 | Boiler on-line combustion optimization control method and system and computer equipment |
| CN115081900A (en) * | 2022-06-30 | 2022-09-20 | 国网北京市电力公司 | Modeling method and device of integrated energy system and electronic equipment |
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