Multi-objective optimization study of CCHP-GSHP-PV-ST system under different climatic zone conditions

In this research, a system with multiple energy sources of combined cooling, heating, and power (CCHP)/ground source heat pump (GSHP)/photovoltaic (PV)/solar thermal collector (ST) (CCHP-GSHP-PV-ST system) is constructed. And this system is combined with the operation strategy of following total electric demand, that is, giving priority to meeting the electrical load of the building, the additional power of the coupling system, and the power of driving the GSHP. Therefore, a model for multi-objective optimization of the CCHP-GSHP-PV-ST system based on energy, environment, and economic indicators is established, and the optimization model is resolved using the genetic algorithm. The load simulation of office buildings in representative cities of five climate zones in China (Harbin (severe cold climate), Beijing (cold climate), Kunming (mild climate), Guangzhou (hot summer and warm winter climate), Changsha (hot summer and cold winter climate)) was selected as the basis for coupling system optimization, and the multi-objective optimization study of CCHP-GSHP-PV-ST system under different climate zone conditions was carried out. The findings indicate: (1) Under various climatic zone conditions, the coupling system’s optimized composition varies a little; (2) The multi-energy coupled system of office buildings in Beijing (cold climate) has primary energy saving rates, carbon dioxide emission reduction rates, annual total cost saving rates, and comprehensive performance that are respectively 46.06%, 60.43%, 44.05%, and 50.18% better than the split-production system when compared to other climate zones.


Introduction
The rapid development of the economy leads to increased energy consumption and environmental pollution.The traditional energy supply system is unable to solve the above problems.Fossil energy can guarantee reliable supply, but it will bring environmental problems.Renewable energy is environmentally friendly, but affected by climate conditions, which cannot guarantee sustainable supply.Different energy sources have different characteristics.Therefore, the multi-energy system of clean fossil fuel and sustainable energy can not only ensure the stability of the energy supply but also deal with environmental pollution [1] .GSHP has great advantages in energy, economy, and environment, and to ensure the advantages of the system of multiple energy coupling, it is necessary to optimize the configuration and operation mode of the system of multiple energy coupling.
The optimal scheme of the PV-T/GSHP/CCHP coupling system is determined [2] , and the findings indicate that the life cycle cost, total electricity consumption, and boiler natural gas usage of the optimized multi-energy coupling system are significantly reduced.Li et al. [3] compare the comprehensive performance of the combined cooling, heating and power, and ground source heat pump under the five operation strategies and the comprehensive performance of CCHP and GSHP in parallel, and points out that the two systems have the greatest benefits when deeply coupled and under electrical load following (FEL) strategy.Wang et al. [4] used the established two-stage model for optimization to determine the optimal capacity of the equipment in the PV-T/CCHP coupling system, and the findings indicate that the annual total cost-saving rate, primary energy-saving rate, and carbon dioxide emission reduction rate of the optimized multi-energy coupling system increased, which verified the effectiveness of the optimization model.Wang et al. [5] created an optimization model for PV/CCHP coupling systems in response to climate change, and it was discovered that the best operating plan under these circumstances can successfully prevent the imbalance between energy supply and demand brought on by extremely high temperatures.Yang and Zhai [6] optimized the equipment capacity of the PV/CCHP coupling system and analyzed the performance of the system of multiple energy coupling under the two strategies of FEL and FTL.Chu et al. [7] analyzed the performance of the PV-T/CCHP coupling system under the two strategies of FEL and thermal load following (FTL) from the aspects of energy, economy, and environment.Yang et al. [8] used the advantages of redundant design to optimize the PV-T/CCHP coupling system and analyzed the performance of the system of multiple energy coupling.Wen et al. [9] established a model of the PV/GSHP/CCHP coupling system in TRNSYS software, and compared the energy-saving, environmental protection, and economy of the PV/GSHP/CCHP coupling system under two different operation strategies (FTL and FEL).Wu et al. [10] suggested a PV/GSHP/CCHP coupling system in combination with an organic Rankine cycle.He then developed a multi-objective optimization model based on sustainability indicators (technical, economic, environmental, and social performance) to determine the coupling system's ideal configuration.It was discovered that the coupling system had high sustainability indicators when the heat distribution was 75%.Kazemian et al. [11] proposed two high-performance GSHP/CCHP coupling system composition schemes and established optimization models.Using the central composite design method and the statistical optimization method based on the expectation function, respectively, he solved the model and arrive at the best configuration for the two systems.Wang then examined the economics of the two systems when their capacities are equal.Bae et al. [12] set up an experimental device for the PV-T/GSHP coupling system, examined how well it performed in the heating and cooling modes and contrasted the coupling system's economic benefits with the conventional system.The results show that, in the event of rising electricity prices and government subsidies, the coupling system's initial investment cost payback period was 15 years.
Analysis of the aforementioned research reveals that there aren't many studies that take the influence of climatic conditions on the best design of multi-energy coupling systems into account.As a result, the focus of this paper is on the optimization of multi-energy coupling systems in various climate zones.Based on the concept that the coupling of CCHP with renewable energy and GSHP can reduce primary energy consumption and alleviate environmental pollution, this paper constructs a CCHP-GSHP-PV-ST system, and establishes the optimization model of CCHP-GSHP-PV-ST system, and uses a genetic algorithm to build the optimization model.As a result, the CCHP-GSHP-PV-ST system's capacity and operating mode are optimized to improve the operation efficiency and energy utilization efficiency of the coupling system, this paper adopts the operation strategy of following the total electric demand [13] , that is, giving priority to meeting the building electrical load, driving the power of the multi-energy coupling system and driving the power of GSHP.In this study, office buildings in five representative Chinese cities representing various climate zones were chosen: Harbin (severe cold climate), Beijing (cold climate), Kunming (mild climate), Guangzhou (hot summer and warm winter climate), and Changsha (hot summer and cold winter climate).
, -the public grid's electricity;  represents the electricity produced by GE;  -the electricity produced by PV;  -the building electricity load;  -how much power the GSHP uses;  -the additional electricity of the system of multiple energy coupling;  , -the additional electricity produced for the public grid.
The heat balance of the system is: +  +  ,  , −  ,  , +  = -the heating load that HE provided;  -the cooling load offered by AR;  -the heat provided by ST;  -the heat replenished by NB;  , -the heat output from HST;  , -the heat input to HST;  is the recovery heat from GE;  , and  , are the state parameter of HST (  , (0  1) +  , (0  1) = 1 );  is the efficiency of HE;  is the coefficient of performance of AR.
The mathematical model of the gas engine (GE) unit can be expressed as [14] : where  is the hourly electric efficiency of the GE;  ,  and  are related parameters;  is the load factor of the GE;  is the actual hourly electricity output of the GE;  is the nominal capacity of the GE;  is the hourly electricity generated from GE;  is the key value to control whether run GE.
The mathematical model of the photovoltaic (PV) unit can be expressed as [15,16] : -the PV area;  -the solar radiation coming from an angle of ;  -the reference module efficiency;  -the PV module's temperature coefficients; γ -the PV module's solar irradiance; the temperature of PV cells;  -the nominal operating cell temperature ( usually values around 45℃);  -the local latitude;  -the radiation from a beam on a flat surface;  -the sporadic radiation on a flat surface;  -the surface reflectance;  -the tilt factor of the beam radiation;  -the hour angle;  -the inclination of the solar;  -day.
The mathematical model of the GSHP unit can be expressed as: =  (  +   ).
The mathematical model of the ST unit can be expressed as [17,18] : -the ST area;  -optical efficiency;  -correction factor;  -correction factor;  -the external air temperature.The mathematical model of the HST unit can be expressed as: The mathematical model of the HE unit can be expressed as: Where  -the load ratio;  -the building's heating load.
The mathematical model of the AR unit can be expressed as [19] : (20)  -the building's cooling load;  -the COP of the AR;  -the load factor;  ,  ,  and  -related parameters.

Reference system
The GSHP system is the reference system.The public grid supplies the building's primary electricity needs as well as the additional electricity needed for the reference system.The GSHP, which is powered by electricity from the public grid, handles the building's cooling and heating needs.

Optimal model
The optimal model, which includes optimal variables, operation strategies, optimal objectives, constraints, and an optimal algorithm, aims to determine the nominal capacity and operation mode of the multi-energy system.

Optimal variables and operation strategies
The parameters that determine the system's capacity and mode of operation are the optimal variables.The GSHP's rated capacity, the key value used to determine whether to operate the PGU, the ratio of the GSHP's cooling/heating output to the building's cooling/heating load, the area of the PV array, and the area of the ST are the five variables that affect the paper.The CCHP-GSHP-PV-ST system can produce its best results once the aforementioned variables are established.
The GSHP, coupling system's additional power, and meeting the building's electrical load, is given priority in this paper's operation strategy, which follows total electric demand.

Optimal objective
Figure 1 shows that the natural gas used by the GE and NB, as well as the conventional fossil fuel used by the public grid make up the system's energy input.Energy, economy, and the environment are all taken into account in the ideal objective, which is expressed as: where λ , λ , and λ are the weight number for every single objective (λ = λ = λ = 1/3);  and  are the energy consumption of CCHP-GSHP-PV-ST and GSHP system respectively;  and  are the carbon dioxide emission of the system of multiple energy coupling and GSHP system respectively;  and  are the annual total cost of the system of multiple energy coupling and GSHP system respectively, which are expressed as: -the natural gas that GE used (   *  ⁄ );  -the natural gas that NB used (  ⁄ );  -the energy sources that the public grid uses ( ,   ); K -the price of capital recovery;  -the equipment capacity in the multi-energy system;  -the equipment unit cost;  -the annual CO2 emission of the multi-energy system; T -the carbon tax; L -the natural gas cost per kilowatt hour;  , -the electricity cost of public grid; L , -electricity feed-in tariff.φ -CO2 emission factor of natural gas; φ -CO2 emission coefficient when electricity is produced in the public grid;  , , -the energy sources consumed by the public grid ( , ,   ); K -the capital recovery cost;  -the equipment capacity in GSHP system;  -the equipment unit cost; -the annual CO2 emission of the GSHP system; T -the carbon tax;  , -the cost of public grid electricity.

Constraints
The constraints are the boundary to obtain the optimal results in the optimal model: (1) Electricity, heating, and cooling balance of the system of multiple energy coupling, which is expressed in Section 2; (2) The equipment's output must not be higher than its rated capacity.

Optimal algorithm
The stochastic optimization algorithm used in this study, the genetic algorithm, is used to build the optimization model.The genetic algorithm is based on Mendel's genetics and Darwin's theory of evolution, and it has a high degree of robustness, convergence, and adaptation value.The genetic algorithm's flowchart is shown in Figure 2. The population size is 40, the genetic algebra is 500, the selection rate was 0.9, the crossover rate was 0.7, and the mutation rate was 0.05.These are the relevant parameters of the genetic algorithm.Beijing (cold climate), Kunming (mild climate), Guangzhou (mild climate), and Changsha (hot summer and cold winter climate)-were chosen for load simulation in this study.This simulation served as the foundation for the optimization of coupled systems.

Building load
The office buildings representing the cities in the five different climate zones have the same basic information: the total area is 9600 m 2 , the area is 1200 m 2 , the body size factor is 0.288, and different envelope parameters are set to distinguish each climate zone.All the parameters are set according to the specification.Figure 3 shows the monthly cooling/heating loads of office buildings representing cities in five different climate zones.This figure shows that the load characteristics of various climatic zones are evident.Because of the parameter setting, the monthly electric load of the same building type in different climate zones is the same, as shown in Figure 4.

Parameter information
The parameters need to be specified to get the optimal results.Tables 1 -3 show the characteristic parameters of the equipment in the system, environment and economic parameters, and unit price of equipment respectively.The range of the ideal variables is displayed in Table 4. Table 1.The equipment's defining characteristics in the coupled system [6,20] Units Values Photovoltaic  = 25℃;  = 12.5%; γ = 0.12;  = 0.The efficiency of the electric grid  =0.35 Grid transmission efficiency  = 0.91 Table 2. Environmental and financial standards for electricity and natural gas [6] Items The area of PV [0,1000] The area of ST [0,1000] Note: The total area of PV and ST cannot exceed 1000 m 2 .

Results and analysis
After solving the optimization model by the genetic algorithm, the optimal variables can be obtained, and the optimal composition of the coupling system, the best operating modes, and the capacities for each piece of equipment can be determined through the optimal variables.The optimization results of the coupling system under different climatic zone conditions are as follows.

Optimal system composition and optimal capacity
Based on the optimization results, the system composition of Harbin (severe cold climate), Beijing (cold climate), Guangzhou (hot summer and warm winter climate), and Changsha (hot summer and cold winter climate) are the same, and the coupling system is all CCHP-GSHP-PV-ST system.The coupling system in Kunming (mild climate) is the CCHP-PV-ST system.
Figure 5 shows the optimal capacity of the multi-energy system for offices in five typical cities following the total electric demand strategy.Under the operational approach of following total electric demand, the capacity of GE is large; Since Kunming's year-round cooling load and year-round heating load are small, there is no GSHP in Kunming's coupling system; For climate zones with greater cold/heating loads on buildings, the greater the capacity of heat exchangers (HE) and absorption refrigeration (AR) units is, the greater the NB is.6 shows the area distribution of photovoltaic and solar collectors representing urban office buildings in different climate zones.The area distribution of photovoltaic and solar collectors in Kunming is different from that of other cities due to the city's low cooling and heating load and the absence of ground source heat pumps; provided that the combined of photovoltaic and solar collectors does not exceed 1000 m 2 , the photovoltaic area decreases with an increase in cooling load while solar collector area increases with an increase in cooling load.Figure 7 shows the energy ratio in heating mode for office buildings in representative cities of five different climatic zones under the following total electric demand operation strategies.The recovery of heat from a gas engine (GE), heat from a solar thermal collector (ST), heat from a heat storage tank (HST), heat from a GSHP (GSHP), and heat from a natural gas boiler (NB) can all be used to meet the heating load at a given time, as shown in Figure 1.
The waste heat from the GE, the heat provided by the ST, the heat provided by the HST, the heat provided by the GSHP, and the heat provided by the NB can completely meet the heat load of the office building when heating the coupling system of office buildings in Harbin, Beijing, Guangzhou, and Changsha; In addition to the heat provided by the GE, the heat provided by the NB also contributes significantly.The coupling system of the Kunming office building lacks a GSHP, and the heat ratio in heating mode is made up of four components: GE waste heat, ST heat, HST heat, and NB heat, with GE heat having the largest share.Under the following total electric demand operation strategies, Figure 8 displays the energy ratio in cooling mode for office buildings in representative cities of five different climatic zones.The system of multiple energy coupling in Kunming uses the following total electric demand operation strategies and lacks a GSHP, so the energy ratio consists of four parts.In addition to the heat from GE, the NB, and ST primarily satisfy the remaining requirements.Other than the heat from GE and ST, the remaining insufficient heat is provided by the NB for the other four cities, where the cooling load from GSHP makes up a relatively small portion.
Figure 9 shows the energy ratio of electricity for office buildings in representative cities of five different climatic zones under the following total electric demand operation strategies.The electricity supplied by PV and GE is preferentially met by the building's electrical load, along with the additional power from the coupling system and the electricity powering the ground source heat pump.The public grid supplies the remainder, and under certain circumstances, the excess electricity can be exported to the public grid.Figure 9 shows that the five gas internal combustion engines representing the city's office buildings provide the majority of the electricity; the coupling system of Harbin office buildings produces the most electricity for the public grid due to the office buildings' highly variable hourly cooling and heating loads.5 displays the energy, environmental, economic, and comprehensive performance of the coupling system representing urban office buildings in various climate zones under the operational strategy of following total electric demand.The coupling system of Beijing's office buildings performs best in energy metering.Due to the lack of a ground source heat pump in the coupling system of the Kunming office building, the environmental indicators show that the use of a GSHP can significantly reduce carbon dioxide emissions; Beijing's office buildings required a significant initial investment in the coupling system, but compared to the other four cities, Beijing's primary energy consumption and carbon dioxide emissions are the smallest, making the total annual cost the lowest; The coupling system of the Beijing office building had the best overall performance among the five representative cities, followed by Harbin.This finding suggests that the coupling system performed better overall in the region with a colder climate.In general, the optimized CCHP-GSHP-PV-ST system has better energy savings, environmental protection, and economy when compared to the production system.

Conclusion
The CCHP-GSHP-PV-ST system is optimized in this paper for various climatic conditions.The system of multiple energy coupling and its mathematical model were built, and the optimal configuration and operation mode of the CCHP-GSHP-PV-ST system were established based on the comprehensive indicators of primary energy saving rate, carbon dioxide emission reduction rate, and annual total cost saving rate as the optimization goal.The monthly load simulations of office buildings in representative cities in five different climate zones in China were also included.Analysis of the optimization's results was done.The following are this paper's main conclusions: (1) The five climate zones' office buildings have a large capacity of gas engines (GE) thanks to their operational strategy of following total electric demand.
(2) The optimal coupling system composition for Kunming's office buildings is different from that of the other four cities because of the smaller cooling and heating loads in those buildings (Kunming's coupling system is CCHP-PV-ST, while the coupling systems in the other four cities are CCHP-GSHP-PV-ST. (3) The energy ratio distribution of each energy supply equipment in the coupling system of office buildings in various climate zones was analyzed under the operation strategy of following total electric demand, and the results demonstrated that the electricity provided by GE predominated the electric energy ratio distribution.The coupling system's energy ratio distribution for heating mode and cooling mode is dominated by the heat from the GE and the NB.
(4) Compared with the split-production system, the comprehensive performance of the coupling system after optimization in Harbin, Beijing, Kunming, Guangzhou, and Changsha was 49.29%, 50.18%, 39.91%, 43.46%, and 42.83%, respectively.And the findings indicated that the encompassing performance of the system of multiple energy coupling in the colder climate zone was better.

Figure 3 .
Figure 3.The monthly heating and cooling load in five typical cities for Office buildings

Figure 5 .
Figure 5.The nominal capacity for Office in five typical cities

Figure 6 .
Figure 6.The area distribution of PV and ST4.3.3.The energy ratio of the multi-energy systemThe source components of heating load, cooling load, and electricity load, or energy ratio are shown in the following figures to more clearly illustrate the function of each sub-unit of the energy system.

Figure 7 .Figure 8 .
Figure 7.The energy ratio for the heating load

Figure 9 .
Figure 9.The energy ratio for electricity 4.3.4.Energy, environment, economic indicators and comprehensive performance Table5displays the energy, environmental, economic, and comprehensive performance of the coupling system representing urban office buildings in various climate zones under the operational strategy of following total electric demand.The coupling system of Beijing's office buildings performs best in energy metering.Due to the lack of a ground source heat pump in the coupling system of the Kunming office building, the environmental indicators show that the use of a GSHP can significantly reduce carbon dioxide emissions; Beijing's office buildings required a significant initial investment in the coupling system, but compared to the other four cities, Beijing's primary energy consumption and carbon dioxide emissions are the smallest, making the total annual cost the lowest; The coupling system of the Beijing office building had the best overall performance among the five representative cities, followed by Harbin.This finding suggests that the coupling system performed better overall in the region with a colder climate.In general, the optimized CCHP-GSHP-PV-ST system has better energy savings, environmental protection, and economy when compared to the production system.Table5.Energy, environment, economic indicators, and comprehensive performance

Table 5 .
Energy, environment, economic indicators, and comprehensive performance