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Scientific Reports volume 15, Article number: 21016 (2025)
1720
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Aiming at the problems of complex characteristics such as nonlinearity, multivariable, and strong coupling in the energy optimization process of thermal power plant station under the carbon reduction constraints due to the multiple types of equipment and large amount of operation data in the multi-energy system (MES), an energy optimization method of multi-energy system considering distributed photovoltaic coordinated carbon reduction is proposed in this paper. Firstly, the energy characteristic model of the MES in the production process of energy input, output and conversion is established. The interaction between various systems, equipment and other elements of the MES is deeply studied, and the energy characteristic analysis method of the MES is proposed. Secondly, the relationship between fuel balance, heat balance, power balance, and carbon emission of the MES is analyzed, and the carbon emission intensity model of the MES is established. Then, an energy optimization model of the MES with the objectives of minimizing operating cost and maximizing carbon emission reduction is established, and a deep reinforcement learning algorithm is used to solve the model. Finally, based on the operation data of a power plant in a certain area in Northeast china, a MES simulation model is established to simulate and verify the effectiveness of the energy optimization method proposed in this paper.
With the accelerated transition of the energy structure towards clean and low-carbon, the dual control of energy consumption in the power system is shifting to dual control of carbon emissions1,2. In the medium and short term, thermal power plants, as the main supporting power source, will still be the primary source of energy consumption for residents for a certain period. Therefore, for thermal power plants, how to enhance carbon emission reduction levels while exporting electricity under the premise of energy balance in the plant is an urgent issue that needs to be studied and resolved in the future low-carbon power generation transformation and planning and construction of thermal power plants3,4.
As the scale of renewable energy generation such as wind power and PV increases, thermal power plants need to adapt to the system’s response and carbon reduction requirements under the integration of renewable energy. To achieve this, thermal power plants have been vigorously developing comprehensive energy flexibility retrofit upgrades, including heat energy storage technologies, electric boilers, waste heat recovery technologies, and carbon capture technologies. These upgrades not only enhance the regulation capabilities of thermal power plants but also provide support for reducing carbon emissions5. However, during the operation of thermal power plants with the wind-PV-electricity-heat-storage coupling framework, multi-significant challenges arise in multi-energy balance optimization, which further increases the difficulty of carbon reduction6.
In the field of carbon reduction technologies for thermal power plants, some studies have been conducted. In the literature5, the coupling regulation characteristics of carbon capture power plants are investigated, and the scheduling model incorporating flexibility regulation requirements is established to achieve low-carbon and economic operation of the carbon capture power plants. In the literature7, a pollution reduction and carbon efficiency evaluation and optimization method for coal-fired power plants is established with a case plant analyzed and evaluated. In the literature8, based on the analysis of energy flow characteristics in carbon capture power plants, a load distribution model minimizing carbon emissions and generation costs is established, reducing carbon emissions while optimizing the load distribution of thermal power units. From the perspective of environmental pollution assessment, the lifecycle power generation and environmental impacts of coal-fired units, carbon capture coal-fired units, and photovoltaic-carbon capture integrated coal-fired units are analyzed and evaluated in the literature9. In the literature10, the carbon reduction strategies for thermal power plants under a carbon trading mechanism are explored, studying the operation method of thermal power plants using carbon capture, utilization, and storage (CCUS) technologies. In the literature11, a coordinated optimization scheduling model of multi-regional energy systems coupling wind, PV, hydro, and carbon capture is studied, achieving complementary regulation between carbon capture thermal power units and renewable energy sources and reducing the carbon emission intensity of thermal power units to a certain extent. To meet the low-carbon transition requirements of coal-fired units, low-carbon retrofitting schemes are investigated in the literature12, such as sludge co-firing, biomass coupling, and rooftop photovoltaic construction. A comprehensive lifecycle evaluation model for coal-fired power plant retrofitting is established, enabling the lifecycle analysis and evaluation of different retrofitting schemes12.
The existing research primarily focuses on the carbon capture and carbon reduction methods of thermal power units and the environmental assessment under the operation of thermal power units. However, there is a lack of consideration of ‘source-grid-load’ coordination and the optimization of complementary coordination among various energy sources. With the increase of multi-type resources on the grid side and multi-energy consumption demand on the load side, the development of carbon reduction strategies for thermal power plants also needs to consider the coordination between source, grid, and load, as well as the complementary integration of various energy sources to optimize the multi-energy characteristics within thermal power plants. Therefore, the problems that still need to be studied and solved can be summarized as follows:
Can various types of resources, such as distributed photovoltaic, battery energy storage, heat energy storage and other resources, provide support for the low-carbon operation of the thermal power plant station or the MES?
Can the coordination between multiple ‘source-grid-load’ units further promote the carbon reduction and consumption reduction of the thermal power plant or the MES?
How to consider and solve the nonlinear and multivariable influencing factors in the low-carbon energy optimization process of the thermal power plant station or the MES, which are characterized by a large number of equipment and a vast amount of operational data?
To address the energy characteristics of energy input, output, and conversion processes in thermal power plants, and considering the source-grid coordinated carbon reduction mechanism, an energy optimization model of the MES considering distributed photovoltaic coordination and carbon reduction is proposed. Taking the MES as the research object, the energy characteristics of the system are analyzed, and a carbon emission intensity model is established to link the operational output, energy balance characteristics, and carbon emissions of the energy supply equipment within the system. Taking the operational costs and carbon emission costs of the MES are set as optimization objectives, an energy optimization model of the MES is established. This model is solved using a deep reinforcement learning algorithm. Finally, based on the operational data of a power station in Northeast China, a simulation model is constructed to verify the feasibility and effectiveness of the proposed method.
The key contributions of this paper are as follows:
The supply equipment model of the MES is established. The energy balance characteristics of the MES are analyzed, and a carbon emission intensity model for the system is established. Specifically, by analyzing the operating characteristics of each energy supply equipment and their energy characteristics in the process of energy input, output and conversion, an energy supply equipment model of the MES is established. Furthermore, by analyzing the strong coupling relationship between energy balance characteristics and carbon emissions of the MES, the carbon emission intensity model of the MES is established, which provides a basis for subsequent energy optimization.
The energy optimization model of the MES considering system operational costs and carbon emission costs is established. Specifically, with the objectives of minimizing the operating cost and carbon emission cost of the MES, and considering the power balance constraint, equipment output constraint, and load adjustable range constraint of the MES, an energy optimization method of the MES is proposed.
The energy optimization framework of the MES based on the Deep Deterministic Policy Gradient (DDPG) algorithm is proposed, and the model is solved using the DDPG algorithm. Specifically, by describing the energy optimization problem of the MES as a Markov decision process. The state set, action set, and reward value function are defined, and the strategy network and value network of the DDPG algorithm are used to solve the problem. Meanwhile, during the solution process, the priority experience playback mechanism and the Ornstein-Uhlenbeck process are introduced to generate random noise, which enhances the exploration ability and learning effect of the DDPG algorithm for solving the optimization model.
In general, the research work in this paper provides new ideas and methods for energy optimization of thermal power plants under carbon emission reduction constraints. By establishing an energy optimization model of the MES and using deep reinforcement learning algorithm to solve it, not only the energy optimization of the MES is realized, but also the carbon emission of the system is significantly reduced.
The structure of the paper is as follows:
Section “Multi-energy system model” analyzes the energy balance and carbon emission characteristics of the MES, and establishes the corresponding mathematical models. Section “Energy optimization model of multi-energy system” establishes the energy optimization model of the MES considering system operational costs and carbon emission costs. Section “Energy optimization model of multi-energy system based on deep reinforcement learning” proposes the solution process for the energy optimization using deep reinforcement learning. Section “Simulation analysis” encompasses the establishment of the simulation model and the validation of the proposed method. Section “Conclusion and research outlook” concludes the findings and research outlook of this study.
The structure of the MES studied is shown in Fig. 1. The MES includes combined heat and power (CHP) unit, renewable energy equipment, heat storage equipment, electric boiler, heat recovery boiler, battery energy storage equipment, carbon capture equipment, and multi-energy load, among others. In addition to the internal electric and heat energy consumption needs of different production processes and the buildings within the MES, the MES exports electric and heat energy to meet the electricity and heat demands of residents through power transmission lines and heat supply networks.
Structure diagram of the MES.
For the structure shown in Fig. 1, the main energy supply equipment in the system is first models and analyzes as follows:
CHP unit model.
In this paper, the back-pressure CHP unit is studied, and the relationship between the electrical energy output and heat energy output of the unit is described as:
.
where ({P_{RDLG,t}}) and ({Q_{RDLG,t}}) are the electrical energy output value and heat energy output value of the CHP unit, respectively; (eta _{{RDLG}}^{{text{P}}}) is the electrical energy output efficiency of the CHP unit; (eta _{{RDLG}}^{{text{Q}}}) is the heat energy output efficiency of the CHP unit.
Electric boilers and heat recovery boiler model.
The heat output characteristics of electric boiler and heat recovery boiler are described as:
.
where ({Q_{{text{EB}},t}}) and ({Q_{{text{WHB}},t}}) are the heat output values of the electric boiler and heat recovery boiler, respectively; (eta _{{{text{EB}}}}^{{}}) is the heat energy output efficiency of the electric boiler; (eta _{{{text{WHB}}}}^{{}}) is the waste heat reuse efficiency of the heat recovery boiler; (CO{P_{{text{WHB}},h}}) is the coefficient of waste heat production of the heat recovery boiler.
The role of the heat recovery boiler in this context is to utilize the waste heat recovery technology to improve the flexibility of the operation and regulation of the CHP unit within the MES by reusing the high-temperature flue gases from the operation of the CHP unit for re-heating.
Heat storage equipment and battery energy storage equipment model.
The charging and discharging characteristics of heat storage equipment and battery energy storage equipment are described as:
where ({S_{{text{BES/TS}},t}}) is the amount of electric ore heat stored in the battery energy storage equipment or heat storage equipment at the time t; BES/TS is the meaning of the battery energy storage equipment or heat storage equipment; (P_{{{text{BES/TS}},t}}^{{chg}}) and (P_{{{text{BES/TS}},t}}^{{dis}}) are the electric storage power or heat storage power, electric discharge power or heat discharge power of the battery energy storage equipment or heat storage equipment, respectively; (eta _{{{text{BES/TS}}}}^{{chg}}) and (eta _{{{text{BES/TS}}}}^{{dis}}) are the electric storage efficiency or heat storage efficiency, electric discharge efficiency or heat discharge efficiency of the battery energy storage equipment or heat storage equipment, respectively; (eta _{{{text{BES/TS}}}}^{{loss}}) is the electric storage loss coefficient or heat storage loss coefficient of the battery energy storage equipment or heat storage equipment; (mu _{{{text{BES/TS}},t}}^{{chg}}) and (mu _{{{text{BES/TS}},t}}^{{dis}}) are the storage and discharge state variables of the battery energy storage equipment or heat storage equipment, respectively, and the values of the variables are 0 or 1; (hbox{max} P_{{{text{BES/TS}},t}}^{{chg}}) and (hbox{max} P_{{{text{BES/TS}},t}}^{{dis}}) are the maximum values of electric storage power or heat storage power, electric discharge power or heat discharge power of the battery energy storage equipment or heat storage equipment, respectively; (hbox{min} {S_{{text{BES/TS}},t}}) and (hbox{max} {S_{{text{BES/TS}},t}}) are the minimum and maximum values of the amount of electric power or heat stored in the battery energy storage equipment or heat storage equipment at time t, respectively.
Equation (3) uses a same mathematical model to describe the charging and discharging characteristics of both heat energy storage equipment and battery energy storage equipment. This equipment is installed in addition to the existing power station equipment to enhance the flexible regulation capabilities of the combined heat and power (CHP) units in terms of both electric and heat energy.
Carbon capture equipment model.
Within the MES, the carbon capture equipment is installed to adsorb, capture, and sequester carbon dioxide compounds from the carbonaceous flue gas generated after the operation of a CHP unit or coal-fired unit to reduce the carbon emissions of the system. Therefore, the operational characteristics of carbon capture equipment can be described as follows:
where ({P_{{text{CCE}},t}}) is the energy consumption for carbon capture operation of the carbon capture equipment; ({P_{{text{MES}},{text{g,}}t}}) is the total value of the electrical power output of the generating units in the MES; (C{O_{{text{CCE}},t}}) is the amount of carbon captured by the carbon capture equipment; (C{O_{{text{MES}},t}}) is the total amount of carbon dioxide produced during the operation of the MES; ({alpha _{{text{CCE}}}}) is the unit power consumption coefficient for carbon capture operation of the carbon capture equipment; ({beta _{{text{CCE}}}}) is the carbon capture capacity of the carbon capture equipment; ({gamma _{{text{MES}}}}) is the amount of carbon dioxide produced per unit of electrical energy output during the operation of the MES; (hbox{max} {beta _{{text{CCE}}}}) is the maximum carbon capture capacity of the carbon capture equipment; (JC{O_{{text{MES}},t}}) is the actual net carbon emissions during the operation of the MES.
Multiple energy loads model.
Within the MES, there is also a portion of electric and heat energy consuming equipment or buildings, that meeting certain conditions:
where ({P_{{text{MES}},{text{load}},t}}) is the controllable electric load power within the MES; (hbox{min} {P_{{text{MES}},{text{load}}}}) and (hbox{max} {P_{{text{MES}},{text{load}}}}) are the minimum and maximum values of the controllable electric load power within the MES, respectively; ({Q_{{text{MES}},{text{hload}},t}}) is the heat load power of the building within the MES; ({T_{{text{in}},t}}) and ({T_{{text{out}},t}}) are the internal and external ambient temperatures of the building within the MES, respectively; ({A_{{text{MES}},{text{hb}}}}) is the heated building area within the MES; ({C_{{text{MES}},{text{hb}}}}) is the heat capacity per unit of heating area of the heated building within the MES; ({L_{{text{MES}},{text{hb}}}}) is the heat value lost per unit of temperature difference per unit of heating area of the heated building within the MES.
Fuel balance characterization
From the MES shown in Fig. 1, the factors affecting the fuel balance characteristics of the MES with natural gas and coal combustion as energy fuel input are analyzed as follows:
There is a certain intermediate link (coal yard, gas storage tank) for the energy fuel input of the MES, which ensures reliable fuel supply to the unit, so the fuel balance characteristics of the MES are affected by the amount of coal stored in the coal yard, the amount of gas stored in the gas storage tanks, and the gas pressure;
Generating units that use coal as energy input, the coal will have certain changes in heat and moisture content in the intermediate stages of storage and transportation, which will also have an impact on the fuel balance characteristics of the MES.
Based on the above, the fuel balance characteristics of the MES should satisfy the following constraints when equipment such as the CHP unit is in normal operation:
where ({N_{{text{MES}},rc}}) is the total amount of incoming fuel for the MES; ({N_{{text{MES}},rl}}) is the amount of incoming fuel for the MES; ({N_{{text{MES}},fs}}) is the amount of non-production fuel for the MES; (Delta {N_{{text{MES}},rb}}) is the value of the change in storage of natural gas, coal and other fuels for the MES; and ({N_{{text{MES}},ms}}) is the value of the loss of storage of natural gas, coal and other fuels for the MES.
Heat balance characterization
Existing thermal power station or gas power plant, analyzing the heat energy balance characteristics of the plant unit equipment operation process, mainly through the new generating unit assessment experiments, the efficiency of the already operating generating unit overhaul session experiments, and a series of other experiments on the analysis of the energy balance characteristics of the whole plant station. Therefore, for the MES, analyzing and optimizing their heat energy balance characteristics can also help to improve the operational efficiency and carbon reduction capacity of the MES.
The heat energy balance characteristics of the MES should satisfy the following balance constraints when the MES unit equipment is in normal operation:
.
where ({Q_{{text{MES}},sr}}) is the fuel heat input value of the unit in the MES; ({Q_{{text{MES}},1}}) is the effective heat output value of the boiler of the unit in the MES; ({Q_{{text{MES}},2}}) is the exhaust heat loss value of the unit in the MES; ({Q_{{text{MES}},3}}) is the heat loss value due to incomplete combustion of combustible gases in the input unit of the MES; ({Q_{{text{MES}},4}}) is the heat loss value due to incomplete combustion of solid fuels in the MES; ({Q_{{text{MES}},5}}) is the heat loss value of the boiler of the unit in the MES. loss value; ({Q_{{text{MES}},6}}) is the value of heat energy loss caused by other reasons in the MES; ({Q_{{text{MES}},m}}) is the calorific value of the incoming fuel of the unit in the MES; ({Q_{{text{MES}},y}}) is the calorific value of the incoming oil fuel of the unit; ({Q_{{text{MES}},yx}}) is the physical sensible heat calorific value of the incoming fuel for the unit in the MES; ({Q_{{text{MES}},nf}}) is the airborne heat value of the fuel mixture for the unit in the MES.
Electric energy balance characterization
The analysis of electric energy balance characteristics of the MES is to analyze and study the electricity flow process of generating units, electricity equipment, electricity storage equipment and other links within the MES, to clarify the electric energy production links of the MES that can further reduce carbon emissions, and at the same time, to improve the power generation efficiency of the MES13. In this regard, the electric energy balance characteristics of the MES should satisfy the following relationships:
where ({W_{{text{MES}},{text{g}}}}) is the total value of electrical energy output of generating units in the MES; (sum {{W_{{text{MES,s}}}}}) is the value of electrical energy consumption of each electrical equipment in the MES; ({W_{{text{MES}},{text{out}}}}) is the value of electrical energy exported from the MES; ({W_{{text{MES}},{text{og}}}}) is the value of electrical energy purchased from the MES.
On the basis of the results of the analysis of the energy characteristics of the MES, the strong coupling relationship between the operation output of the energy supply equipment, the energy balance characteristics and the carbon emissions within the MES is studied14. The model of the carbon emission intensity of the MES is established.
During the operation of the MES, carbon dioxide emissions are mainly generated from the combustion of coal, natural gas and other fuels in the unit and the desulfurization process of high-temperature flue gas after combustion. Therefore, ignoring the fuel that not fully combusted carbon element emissions and dust, VOCs and other pollutants in the case of unorganized carbon emissions, and on the basis of the principle that the carbon emissions are equal when the MES outputs electrical power from ({P_{{text{MES}},{text{g,}}t}}) to ({P_{{text{MES}},{text{g,}}t+1}})over a time period (Delta t), the carbon emissions intensity model of the MES based on the principle of equal area is established, specifically:
where ({E_{{text{MES}},{text{g,}}t}}) is the carbon emission intensity value of the MES in time period (Delta t); ({P_{{text{MES}},{text{g,}}t}}) is the total value of electric power output of generating units in the MES; (gamma _{{text{MES}}}) is the amount of carbon dioxide produced by outputting a unit of electric power during the operation of the MES; ({a_{{text{MES}},{text{g}}}}), ({b_{{text{MES}},{text{g}}}}), and ({c_{{text{MES}},{text{g}}}}) are the fitting coefficients of the energy-cost curve of the MES, respectively.
Based on Eq. (4), the carbon emission intensity model of the MES containing carbon capture equipment is further analyzed as:
where (E_{{{text{MES}},{text{g,}}t}}^{{{text{CCE}}}}) is the carbon emission intensity value of the MES in time period (Delta t) after the addition of carbon capture equipment; (e_{{{text{MES}},{text{g,}}t}}^{{{text{CCE}}}}left( {P_{{{text{MES}},{text{g,}}t}}^{{{text{out}}}}} right)) is the value of the dynamic change of carbon emission intensity of the MES; (P_{{{text{MES}},{text{g,}}t}}^{{{text{out}}}}) is the net output value of electric power during the operation of the MES; (sum {{P_{{text{MES,s,}}t}}}) is the consumed electric power of the electric equipment in the MES; ({P_{{text{MES}},{text{og,}}t}}) is the purchased electric power of the MES.
The purpose of energy optimization considering distributed photovoltaic coordination and carbon reduction is to optimize the energy balance characteristics of the MES by coordinating the energy supply resources, distributed photovoltaic, etc., with the grid-side controllable electric loads and heat load resources. Therefore, the operating costs and carbon emission costs of the MES are considered as the energy optimization objectives.
Operating costs.
The operating costs of the MES can be expressed as:
where ({f_{MES,{text{op}}}}) is the operating costs of the MES; ({f_{{text{BES/TS}}}}), ({f_{MES,rc}}), and ({f_{{text{Gload}}}}) are the storage and discharge costs, fuel consumption costs, and grid-side controllable electric and thermal load resource regulation costs for thermal storage and heat storage equipment and battery energy storage equipment within the MES, respectively; ({c_{RDLG}}), ({c_{{text{EB}}}}), ({c_{{text{WHB}}}}), ({c_{{text{CCE}}}}), and ({c_{text{e}}}) are the unit operating cost of the CHP unit, unit operating cost of electric boilers, unit operating cost of heat recovery boiler, unit operating cost of carbon capture equipment, and unit cost of purchased electricity, respectively.
The storage and discharge costs for thermal storage and heat storage equipment and battery energy storage equipment within the MES can be specifically expressed as follows:
where (P_{{{text{BES}},t}}^{{chg}}) and (P_{{{text{BES}},t}}^{{dis}}) are the storage and discharge power of the battery energy storage equipment, respectively; (c_{{{text{BES}}}}^{{chg}}) and (c_{{{text{BES}}}}^{{dis}}) are the cost per unit of stored and discharged power of battery energy storage equipment, respectively; (P_{{{text{TS}},t}}^{{chg}}) and (P_{{{text{TS}},t}}^{{dis}}) are the heat storage and heat release power of the heat storage equipment; (c_{{{text{TS}}}}^{{chg}}) and (c_{{{text{TS}}}}^{{dis}}) are the unit cost of heat storage and heat release, respectively.
The cost of fuel consumption in the MES can be specifically expressed as:
where ({c_{MES}}) is the unit cost of fuel consumption for the operation of the MES.
The cost of grid-side controllable electric and thermal load resource regulation can be specifically expressed as:
where (P_{{{text{G}},{text{e}},t}}^{{{text{load}}}}) is the net-side controllable electric load power; (hbox{max} P_{{{text{G}},{text{e}},t}}^{{{text{load}}}}) is the maximum value of the power of the controllable electric load on the grid side; (P_{{{text{G}},{text{h}},t}}^{{{text{load}}}}) and (P_{{{text{G}},{text{h}},t}}^{{{text{load,pr}}}}) are the net-side controllable heat load power, preferred controllable heat load power; (hbox{min} P_{{{text{G}},h,t}}^{{{text{load}}}}) and (hbox{max} P_{{{text{G}},h,t}}^{{{text{load}}}}) are the minimum and maximum values of controllable heat load power on the grid side; ({c_{{text{Ge}}}}) and ({c_{{text{Gh}}}}) are the unit cost of regulation for grid-side controllable electric loads, unit cost of regulation for grid-side controllable heat loads, respectively.
Therefore, the energy optimization objective function for minimizing the operating cost of the MES can be expressed as:
Carbon emissions costs
In the MES studied in this paper, the amount of carbon emission costs will depend on the amount of actual carbon emissions from the power station after carbon capture equipment, and on the other hand, it will also be affected by the coordination of the carbon reduction process of the source and network resources, and both aspects can be regarded as embodied in the amount of carbon allowances of the MES. Therefore, a carbon emission cost function of the MES is established by analyzing the MES carbon quota.
The historical method was used to determine the carbon allowances for the MES, and the calculation process was as follows:
where (C{E_{MES,{text{CO2}}}}) is the value of total carbon allowances for MES; (CE_{{MES,{text{CO2}}}}^{{text{e}}}) is the value of carbon allowances for the actual power supply output of power generating equipment (CHP unit, battery energy storage equipment, wind power) within the MES; (CE_{{MES,{text{CO2}}}}^{{text{h}}}) is the value of carbon allowances for the actual heat output of heat-producing equipment (CHP unit, electric boiler, heat recovery boiler, and heat storage equipment) within the MES; (CE_{{MES,{text{CO2}}}}^{{{text{CCS}}}}) is the value of carbon allowances for the actual heat output of carbon capture equipment within the MES.
The calculation process can be expressed as:
where ({chi _{text{e}}}) is the generation benchmark coefficients for generating equipment within the MES, i.e., different benchmark coefficients for different generating classes of unit equipment; ({chi _{text{x}}}) is the correction factor for the effect of changes in grid-side load on the actual supply output of generating equipment within the MES; ({chi _{text{h}}}) is the heat supply benchmark coefficients for heat production equipment within the MES, that is, different benchmark coefficients for different heat supply levels of unit equipment.
According to the results of carbon quota calculation of the MES mentioned above, and combined with the carbon quota allocated to the MES by the grid or government in the actual operation process, a reward and punishment mechanism for carbon emission of the MES is established. The reality is that when the actual carbon emissions of the MES are higher than the carbon allowances allocated to the MES by the grid or government, the MES needs source-grid coordination to obtain more carbon allowances and pay the penalty for the higher portion of the carbon allowances. When the actual carbon emissions of the MES are lower than the carbon quota allocated to the MES by the grid or government, the MES can receive a certain bonus or subsidy by coordinating the carbon quota. The carbon emission reward and punishment mechanism of the MES is described as a segmented function:
where ({f_{{text{CE,u}}}}) is the reward and penalty costs of carbon emissions from the MES; (sum {JC{O_{MES,t}}}) is the total actual net carbon emissions from the MES; ({C_{{text{CE}}}}) is the unit cost of source-side-grid-side coordination of carbon allowances for the MES; (kappa) is the reward and penalty scaling parameters for carbon emissions from the MES under source-grid coordination; (C{E_{text{d}}}) is the scope of carbon emission penalty zoning for the MES under source-grid coordination.
Further, the energy optimization objective function for minimizing the carbon emission cost of the MES can be expressed as:
where ({f_{MES{text{,CE}}}}) is the carbon costs; ({c_{{text{CO2}}}}) is the carbon unit cost of the MES.
The objective function of energy optimization for the whole MES is expressed as:
The constraints to be satisfied are:
Electric power balance constraints of the MES
where ({P_{{text{NEW}},t}}) is the part of the renewable energy equipment within the MES outputs electrical power; ({P_{{text{EB}},t}}) is the power consumption of electric boilers in the MES; ({P_{MES,{text{load1}},t}}) is the uncontrollable electrical load power within the MES; (P_{{{text{G}},{text{e}},t}}^{{{text{load,1}}}}) is the net-side uncontrollable electric load power.
Heat power balance constraints of the MES
Capacity constraints for energy supply equipment in the MES
.
where (hbox{min} {P_{{text{RDLG}},t}}) and (hbox{max} {P_{{text{RDLG}},t}}) are the minimum and maximum values of the electrical energy output of the CHP unit; (hbox{min} {Q_{{text{EB}},t}}) and (hbox{max} {Q_{{text{EB}},t}}) are the minimum and maximum values of the heat output of the electric boiler; (hbox{min} {Q_{{text{WHB}},t}}) and (hbox{max} {Q_{{text{WHB}},t}}) are the minimum and maximum values of heat output of the heat recovery boiler.
The output constraints for thermal storage and battery energy storage equipment are shown in Eq. (3), and the operational constraints for carbon capture equipment are shown in Eq. (4).
Adjustable range constraints for multi-energy loads within the MES.
The regulation range of the controllable electric load power within the MES is shown in Eq. (5), and the regulation range of the building thermal load power inside the MES is limited by the internal temperature of the building, expressed as:
where (hbox{min} {T_{{text{in}},t}}) and (hbox{max} {T_{{text{in}},t}}) are the minimum and maximum values of the internal temperature of the building in the MES.
Based on the energy optimization model of the MES considering distributed photovoltaic coordinated carbon reduction established in the previous section, the energy optimization problem of the MES is described as a Markov decision process, and gives the state set, energy optimization action set and reward value function of the energy optimization process of the MES.
State set.
The state set of the energy optimization process of the MES includes the output power ({P_{{text{NEW}},t}}) of the renewable energy equipment in the MES, the grid-side uncontrollable electric load power (P_{{{text{G}},{text{e}},t}}^{{{text{load,1}}}}), the uncontrollable electric load power ({P_{{text{MES}},{text{load1}},t}}), the unit cost of purchased electricity ({c_{text{e}}}), the total carbon quota value (C{E_{{text{MES}},{text{CO2}}}}) of the MES, the internal environment temperature ({T_{{text{in}},t}})and external environment temperature ({T_{{text{out}},t}}) of the building inside the MES, and the optimization time t. The state set of the energy optimization process of the MES can be expressed as:
Energy optimization action set.
The objective of the energy optimization model of the MES considering distributed photovoltaics for coordinated carbon reduction is to determine the optimal electric output value ({P_{RDLG,t}}) and the heat energy output value ({Q_{RDLG,t}}) of the CHP unit, the heat output value ({Q_{{text{EB}},t}}) of electric boilers, the heat output value ({Q_{{text{WHB}},t}}) of heat recovery boiler, the storage power (P_{{{text{BES}},t}}^{{chg}}) of the battery energy storage equipment, the discharge power (P_{{{text{BES}},t}}^{{dis}}) of the battery energy storage equipment, the heat storage power (P_{{{text{TS}},t}}^{{chg}}) of the heat storage equipment, the heat discharge power (P_{{{text{TS}},t}}^{{dis}}) of the heat storage equipment, the energy consumption ({P_{{text{CCE}},t}}) of carbon capture operation of the carbon capture equipment, the controlled electric load power ({P_{{text{MES}},{text{load}},t}}) with the MES, and the grid-side controllable electric load power (P_{{{text{G}},{text{e}},t}}^{{{text{load}}}}). The energy optimization actions set in the energy optimization process of the MES can be expressed as:
The value range of energy optimization action decision quantity ({A_{{text{MES}},t}}) of the MES should meet the above constraints
Reward value function.
The energy optimization objective function of the MES is to minimize the operating cost and carbon emission cost given by Eq. (19), then the MES should obtain the reward function during the optimization period t, which can be expressed as:
State transition probability distribution function.
The process of transferring the state ({S_{{text{MES}},t}}) to ({S_{{text{MES}},t+1}})in the energy optimization process of the MES is controlled by the decision quantity of the energy optimization action of the MES, and is also affected by the uncertain factors such as the output of renewable energy equipment to a certain extent15,16,17. Therefore, in this paper, the probability distribution satisfied by the state transition in the energy optimization process of the MES is set to meet the uniform distribution.
State-energy optimization action value function.
During the energy optimization process of the MES, the state-energy optimization action value function under the energy optimization action set ({A_{{text{MES}}}}) can be expressed as:
where ({Q_{{text{MES}},{pi _{{text{MTP}}}}}}left( {S,A} right)) is the state-energy optimization action value function; ({{mathbb{E}}^{{pi _{{text{MES}}}}}}left{ cdot right})is the expectation under the energy-optimized action set; ({vartheta _k}) is the proportional discount factor, and the value range is [0,1].
Based on the above description of Markov decision process, the purpose of the MES energy optimization problem shown in Eq. (19) is the energy optimization strategy ({pi _{{text{MES}}}}^{*}). It is equivalent to what kind of energy/power characteristics should each energy supply equipment in the MES carry out actual operation, so as to obtain the maximum value of the state-energy optimization action value function given by Eq. (27), which is described as:
Deep reinforcement learning based model to solve the energy optimization model established in this paper considering distributed photovoltaic coordinated carbon reduction, the actual process to solve the optimal energy optimization strategy is relatively difficult. The deep reinforcement learning algorithm18 can meet the requirements of energy optimization and solution of the MES through data learning and training and network solution.
In this paper, the deep deterministic strategy gradient algorithm is used to solve the Markov decision process for energy optimization of the MES. The energy optimization model solving framework of the MES is shown in Fig. 2. Among them, the input layer of the energy optimization strategy network of the solution process is 8-dimensional process state ({S_{{text{MES}},t}}), and the output layer is 11-dimensional energy optimization action decision quantity ({A_{{text{MES}},t}}), The input layer of the network consists of 8-dimensional pass state ({S_{{text{MES}},t}}) and 11-dimensional energy optimization action decision quantity ({A_{{text{MES}},t}}). The output layer consists of state-energy optimization action value function ({Q_{{text{MES}},{pi _{{text{MTP}}}}}}left( {S,A} right)). Therefore, the energy optimization strategy network and value network diagram of the energy optimization solution process of the MES based on the deep deterministic strategy gradient algorithm are shown in Fig. 3.
In this paper, when DDPG algorithm is used to solve the energy optimization model of the MES, the historical operation data of the MES are used to train the energy optimization strategy network and value network. After the network training process is completed, the parameters of energy optimization strategy network and value network can be determined, and then the energy optimization solution is carried out. When the energy optimization task begins, the MES agent first solves the output power of each energy attack device in the MES at the current time period through the energy optimization strategy network and the value network according to the process state. The controllable load adjustment amount and the controllable load adjustment amount on the network side, and at the same time can calculate the reward (that is, the operating cost, carbon emission cost). The MES then starts the energy optimization solution for the next period according to the process state of the next period.
Solution framework of energy optimization model.
Energy optimization strategy network and value network of the DDPG algorithm solving process.
The input data of the model solution process includes the following:
Operation Parameters of Energy Equipment: These include the operation parameters of combined heat and power unit, electric boiler and waste heat boiler, heat storage equipment, and battery energy storage equipment, as well as the carbon capture operation energy consumption and carbon capture parameters of carbon capture equipment, etc.
Historical Operation Data of Electric and Heat Loads: These include uncontrollable electric loads on the grid side, uncontrollable electric loads inside the system, controllable electric load power on the grid side, controllable electric loads inside the system, and building heat loads inside the system, etc.
Output data of renewable energy, that is, the historical output data of photovoltaic power
Carbon Emission Data of Thermal Power Plant Station or MES: These include the total output value of the electric power of generator units within the MES, the total amount of CO2 produced during the operation of the MES, and the amount of CO2 produced per unit of electric energy output during the operation of the MES.
Other Data, Including Equipment Operating Costs and Carbon Emission Costs: These include the operation cost of generation equipment within the MES, the unit operation cost of electric boiler, the unit operation cost of waste heat boiler, the unit operation cost of carbon capture equipment, and the unit cost of unit electricity purchases, as well as fuel consumption data and energy storage efficiency data, etc.
The above model input data can be obtained by using data sensors and monitoring equipment to collect data from the thermal power plant or the MES through experimental measurements and on-site operation monitoring. For price cost data, it can be obtained by querying the market transaction price. The data from different channels are fused and processed to build a more comprehensive model data input. Meanwhile, pre-processing operations such as cleaning, denoising, and format conversion are carried out to improve the quality and availability of the model input data.
The process of solving is shown in Fig. 4. The specific process is as follows:
Solving process.
Algorithm network parameter initialization, including energy optimization strategy network and value network training times Nx, energy optimization strategy network and value network weight coefficient, data sampling mini-batch number Nc, proportional discount coefficient, data experience playback pool size, hidden layer number, neuron number, and other equipment parameters and so on to initialize the setting.
Set the number of cycles: j = 1.
Input MES agent state set ({S_{{text{MES}},t}});
Initialize and set a random noise variable ({varsigma _{{text{MES}},t}}), the random noise variable ({varsigma _{{text{MES}},t}}) is generated based on the Ornstein-Uhlenbeck process19, which is used to enhance the energy optimization ability of the MES agents in the DDPG algorithm.
Set the simulation period t = 1, and the energy optimization time T.
The MES agent is based on the state set ({S_{{text{MES}},t}}), solve the energy optimization action decision quantity ({A_{{text{MES}},t}}).
The MES agent performs energy optimization action ({A_{{text{MES}},t}}) and obtains the state set ({S_{{text{MES}},t+1}}) of the next optimization period.
Calculate the reward function ({R_{{text{MES}},t}}) that the MES should obtain during the optimization period t, and the data tuple (left( {{S_{{text{MES}},t}},{A_{{text{MES}},t}},{R_{{text{MES}},t}},{S_{{text{MES}},t+1}}} right)) at this time is stored in the data experience playback pool.
Set k = 1.
The sampling experience probability ({p_{{text{MES}},k}}) is set to sample data, the importance sampling weight ({W_{{text{MES}},k}}) is calculated, and the priority ({p_{{text{MES}},k}}) of the kth data sampling experience is updated (the function of this process is to store the important data tuples retained in the experience pool by introducing the priority experience playback mechanism20, so as to promote the learning and solving of the MES agents in the energy optimization process).
Determine whether k reaches the number of data sampling mini-batch Nc, when k does not reach, set k=k+1, continue to perform step (10); instead execute the next step.
Update the value network of the energy optimization, use the sampling strategy gradient to update the energy optimization strategy network, and update the energy optimization strategy network and the value network weight coefficient.
To determine whether the optimization period t is greater than the energy optimization time T, if it is greater than, the next step is performed; conversely, t = t + 1, and execute step (6).
Determine whether the number of cycles j is greater than the number of training iterations Nx, if greater, then perform the next step; conversely, j = j + 1, and execute step (2).
Output the energy optimization results of the MES in all optimization periods.
In the process of multi-energy energy optimization of the system, the primary optimization task is to optimize the energy regulation balance characteristics of each energy supply equipment in the MES under the premise of economic and carbon emission constraints. Therefore, based on the MES shown in Fig. 1, a simulation model is established for analysis. Among them, renewable energy equipment is mainly photovoltaic facilities on the roofs of buildings inside and around the power station, and the setting of other simulation parameters is shown in Table 1.
In addition, when the DDPG algorithm is used to solve the problem, the number of data sampling mini-batch Nc is 128, the size of data experience playback pool is 15,000, the number of hidden layers is 2, the number of neurons in hidden layer 1 is 200, the number of neurons in hidden layer 2 is 100, the proportional discount coefficient ({vartheta _k}) is 0.95, and the activation function of hidden layer is set as ReLU function.
Load and PV data for two typical days.
In order to analyze the optimization effect of the proposed energy optimization model, this paper selects the grid-side power, heat load data and photovoltaic facility output data of typical working days and typical non-working days for analysis and verification. The data of typical working days and typical non-working days are shown in Fig. 5.
Figure 6 shows the energy optimization results of the MES under typical working days. It can be seen from the results in the figure that the MES can meet the consumption demand of the power load and the grid-side power load at different times by coordinating the energy output characteristics of the energy supply equipment in the plant. During the daytime period, the power output of the CHP unit in the MES increases. In order to meet the constraints of carbon emissions, the carbon capture capacity of the carbon capture equipment increases during this period, and the power consumption increases; the discharge period of battery energy storage equipment is concentrated in the evening period (18:00–23:00). In addition to the midnight period (1:00–5:00), the charging period is also charged during the daytime period (10:00–15:00). For the change of controllable electric load, the power consumption of controllable electric load in the factory and controllable electric load on the grid side is reduced during the daytime, and the power regulation ability is increased. For the adjustment of heat load, the heating temperature during the 12:00–19:00 period is higher than that in other periods, which corresponds to the increase of heat energy output of the CHP unit during this period. The heat storage equipment also stores a large amount of heat energy during this period, which is convenient to supplement the heat energy demand in other periods. Therefore, the heating temperature in other periods has been maintained at about 21.8 °C. The above results show that the MES can meet the needs of users and reduce the operating cost of the system to a certain extent by coordinating the energy supply resources of the MES and the controllable load on the grid side.
Energy optimization results of the MES under typical working days.
Figure 7 shows the energy optimization results of the MES under typical non-working days. Compared with the energy optimization results of typical working days, the energy optimization results of MES under typical non-working days are similar. The MES can still meet the energy demand of the plant and the grid side at different times by coordinating the energy supply resources in the plant and the controllable load on the grid side. For the adjustment of heat load, the heating temperature has been maintained at about 21.6 °C for most of the time, and the maximum temperature is lower than 24 °C, which is maintained in the range of 21–24 °C.
Energy optimization results of multi-energy power station under typical non-working days.
In order to further analyze the ability of the MES energy supply resources and grid-side controllable electric load and heat load resources to coordinate carbon reduction, three source-network coordination scenarios are set up for comparison and analysis. That is:
Scenario 1: The energy optimization of the multi energy system is carried out without considering the coordination ability of the controllable load resources on the network side, that is, the electric load and heat load on the network side are not adjustable, and the temperature of the heating area is maintained at a constant value.
Scenario 2: Considering the coordination ability of the controllable load resources on the grid side, that is, the power load and heat load on the grid side are controllable, the deep convolutional neural network algorithm is used to optimize the energy of the MES21.
Scenario 3: Considering the coordination ability of controllable load resources on the grid side, that is, the electric load and heat load on the grid side are controllable within the constraint range, the DDPG algorithm is used to optimize the energy of the MES. The simulation results in different scenarios are as follows:
The results of Tables 2 and 3 show that the total energy optimization cost of the MES under Scenario 3 is much lower than that under Scenario 1. The energy optimization cost of Scenario 3 on typical working days and typical non-working days is reduced by 18.99% and 20.34%. The carbon reduction of Scenario 3 is much higher than that of Scenario 1. The carbon reduction of Scenario 3 on typical working days and typical non-working days is increased by 24.45% and 22.81%. For Scenario 2 and Scenario 3, although the model solving algorithm is different, the energy optimization results and carbon emission reduction results of the MES are similar, and the results of Scenario 3 are better, which indirectly shows that the algorithm in this paper has certain advantages.
Compared with Scenario 1, the MES under Scenario 3 can adjust the energy supply resources of the MES and the controllable load on the grid side, and adjust the heat load within a certain temperature range, so as to give full play to the cooperative adjustment ability of the source-grid side resources, reduce the operation cost of the MES, and improve the carbon reduction ability of the MES.
Aiming at the characteristics of energy input, output, conversion and loss in the production process of thermal power plant station, as well as the carbon reduction mechanism of source-network coordination, an energy optimization method of the MES considering distributed photovoltaics coordinated carbon reduction is proposed. The following conclusions are obtained:
By analyzing the multi-energy power characteristics of the MES in the production process of energy input and output, the energy optimization model of the MES is established.
The method in this paper can coordinate the energy supply resources of the MES with the controllable electric load and heat load resources on the grid side, give full play to the adjustment and adjustment ability of the MES and controllable load resources on the grid side, realize the energy optimization and reduce the carbon emission of the MES.
The energy optimization model of the MES considering distributed photovoltaic coordinated carbon reduction established in this paper can reduce the total energy optimization cost of the MES to a certain extent.
Future research will focus on conducting large-scale pilot applications and tests in actual thermal power plants to verify the practical effectiveness of the model and further optimize the model based on actual operational data. Meanwhile, in-depth study of policies and market mechanisms, such as carbon trading and subsidy policies, is to promote the optimal operation and carbon emission reduction of the MES. Exploring new technologies, such as artificial intelligence and Internet of Things, can improve the intelligence level and optimization ability of the MES. interdisciplinary research is carried out to provide a more comprehensive solution for the optimization of the MES by combining the knowledge of energy engineering, economics, environmental science and other fields.
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.
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This work is supported by the National Science and Technology Major Project (2024ZD0802000) and Science and Technology Plan Project of Liaoning Province (2023JH1/10400050).
Shenyang University of Technology, Shenyang, 110870, China
Shi Qiu, Shuo Liu, Guoqiang Lu, Kun Zhang & Yun Teng
State Grid Qinghai Electric Power Company, Xining, 810008, China
Guoqiang Lu
Department of Energy Technology, Aalborg University, 9220, Aalborg, Denmark
Zhe Chen
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Shi Qiu, Shuo Liu, and Guoqiang Lu wrote the original manuscript, prepared the data, and carried out the simulation verification. Kun Zhang, Yun Teng, and Zhe Chen proposed the research method of the manuscript, and reviewed and proofread the content of the manuscript.
Correspondence to Kun Zhang.
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Qiu, S., Liu, S., Lu, G. et al. Energy optimization model of multi-energy system considering distributed photovoltaic coordinated carbon reduction. Sci Rep 15, 21016 (2025). https://doi.org/10.1038/s41598-025-06870-5
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