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The hybridization of two or more energy sources into a single power station is one of the widely discussed solutions to address the demand and supply havoc generated by renewable production (wind-solar/photovoltaic (PV), heating power, and cooling power) and its energy storage issues. Hybrid energy sources work based on the complementary existence of renewable sources. The combined cooling, heating, and power (CCHP) is one of the significant systems and shows a profit from its low environmental impact, high energy efficiency, low economic investment, and sustainability in the industry. This paper presents an economic model of a microgrid (MG) system containing the CCHP system and energy storage considering the energy coupling and conversion characteristics, the effective characteristics of each microsource, and energy storage unit is proposed. The random forest regression (RFR) model was optimized by the gravitational search algorithm (GSA). The test results show that the GSA-RFR model improves prediction accuracy and reduces the generalization error. The detail of the MG network and the energy storage architecture connected to the other renewable energy sources is discussed. The mathematical formulation of energy coupling and energy flow of the MG network including wind turbines, photovoltaic (PV), CCHP system, fuel cell, and energy storage devices (batteries, cold storage, hot water tanks, and so on) are presented. The testing system has been analysed under load peak cutting and valley filling of energy utilization index, energy utilization rate, the heat pump, the natural gas consumption of the microgas turbine, and the energy storage unit. The energy efficiency costs were observed as 88.2% and 86.9% with heat pump and energy storage operation comparing with GSA-RFR-based operation costs as 93.2% and 93% in summer and winter season, respectively. The simulation results extended the rationality and economy of the proposed model.

The government and legislative authorities incentives to use new energies, concerns about the high and rising price of fossil fuels including its scarcity, and environmental issues are the most important motivations for the integration of renewable energy resources into conventional power systems [

A component-based analysis for the CCHP system outlined by [

In grid-connected insulated modes, the characteristics of MG are flexible operating and can improve grid efficiency and safety [

The MG with the energy storage system has become a promising component of future implementation of the smart grid [

Microgrid energy design and power flow.

When the supply of cold (heat) power is insufficient, it can be used to make up the shortage while the gas boiler is used as auxiliary supply equipment for cold (heat) load [

The optimal scheduling model of the MG with heat pump and energy storage established is a mixed-integer nonlinear programming problem. The general solution expression of the model is as follows:_{M} is the total operating cost of the system, _{F} (_{M}(_{S} (_{E} (_{C} (

The fuel cost is calculated as follows:_{NG} and _{NG} represent the unit cost of natural gas and low calorific natural gas, _{GB} (t) is the output thermal power efficiency of the gas-fired boiler, _{FC} is the fuel cell power, _{FC} is the fuel cell efficiency, respectively, while

The operation and maintenance cost is calculated as follows:_{M,t} is the unit maintenance cost for generating unit; _{M,j} is the number of controllable units; _{CG,i}_{ES} is the unit maintenance cost of the energy storage device; and

The unit start-up cost is calculated as follows:_{i} (_{S,i} is the controllable unit start-up cost.

The electricity cost is calculated as follows:_{grid},_{sup} (t) and _{grid,dem} (t) are the power supply and demand power of the power grid during the period _{dem} (t) is the electricity demand price.

The refrigeration (heat) profit is calculated as follows:_{c} and _{h} are the predicted costs of cooling and heat load during the period, respectively; _{co} (t) is the unit cooling and _{he} (t) is the heating source.

The energy balance constraints are calculated as follows:_{BS} (_{CS} (_{HS} (_{load} (

The grid power constraints are calculated as follows:_{sup, max} is the maximum power supply and _{dem, min} is the demand power for the grid. The multiple energy sources coordinate the coupling and conversion to minimize the total operating cost of the system.

The controllable unit constraints are calculated as follows:_{ES} is the capacity of the energy storage unit, _{ch, max} is the maximum input power, and _{dis, max} is the maximum output power of the energy storage.

The energy storage unit constraints are calculated as follows:_{max} and _{min} are the maximum and minimum state of the energy storage, respectively.

The GSA algorithm needs to determine the fitness function to evaluate the advantages and disadvantages of the RFR model corresponding to each node. The crossover will produce a new particle as follows:_{i} and _{j}; and _{i} new and _{i}. For excellent particles, the strategy of dynamic updating inertia factor is adopted.

In the early stage,

The mean square of residual was selected as follows:^{2}_{y} is the variance of the predicted cost and ^{2}_{RF} is the mean square of residual error. The random forest can calculate the importance of each input feature [33], as shown in the following equation:_{k} is the importance of node _{j} is the node with the feature _{k}, _{1}, and _{2} are the mean square errors of node

The procedure of the proposed algorithm is shown in Figure

GSA-RFR algorithm procedure.

In this paper, the MG system under grid connection is selected as a case study and is optimized. The network mainly includes wind turbine, photovoltaic cells, fuel cells, CCHP, and energy storage units. The specific model shows the advantages of clean energy, wind turbines, and photovoltaic cells which are given priority in their output, and the MPPT operation mode is adopted. Figure

Predictive curves of the wind, photovoltaic output, cooling, heating, and electrical loads in (a) summer season and (b) winter season.

The power generation cost of the unit is not included, only the operation and maintenance cost of the new energy unit is considered. For the different energy supply requirements in summer and winter in the MG parameter, two typical seasons were selected for analysis, and corresponding optimization scheduling strategies were formulated. The operating parameters of the microenergy parameter are shown in Table

Operating parameters of the MG network.

Source type | Minimum power (kW) | Maximum power (kW) | Minimum power (h) | Minimum shutdown (h) | Maintenance cost ($/kW.h) |
---|---|---|---|---|---|

Wind | 0 | 50 | — | — | 0.029 |

Photovoltaic | 0 | 30 | — | — | 0.025 |

Power grid | −60 | 60 | — | — | — |

Gas turbine | 15 | 65 | 3 | 2 | 0.025 |

Fuel cell | 5 | 40 | 3 | 2 | 0.028 |

GSHP | 0 | 30 | 2 | 2 | 0.027 |

Energy storage unit parameters.

Self-consumption of energy storage | Charging and discharging | Self-consumption | Maximum input power (kW) | Maximum output power (kW) | Minimum state | Maximum state | Initial cost (kW.h) | Capacity (kW.h) | Maintenance cost ($/kW.h) |
---|---|---|---|---|---|---|---|---|---|

Electric energy storage | 0.99 | 0.001 | 37.5 | 37.5 | 0.2 | 0.8 | 30 | 150 | 0.0018 |

Thermal energy storage | 0.89 | 0.01 | 25 | 25 | 0 | 0.9 | 10 | 100 | 0.0016 |

Cold energy storage | 0.90 | 0.01 | 25 | 25 | 0 | 0.9 | 10 | 100 | 0.0015 |

Parameter of MG network.

Parameter | Cost | Parameter | Cost | Parameter | Cost |
---|---|---|---|---|---|

_{C} | 1.40 | _{L} | 0.16 | _{GB} | 0.9 |

_{H} | 1.31 | _{rec} | 0.87 | _{co/$/kWh} | 0.1 |

_{HPC} | 3.0 | _{HPH} | 2.98 | _{he/$/kWh} | 0.1 |

To validate the economic and energy-saving effects of the proposed model, the operation optimization model without heat pump and cold storage unit was selected for comparison. On a certain summer day, the optimization results without ground source heat pump and energy storage unit are shown in Figure

Summer heat pump and cold storage optimization.

The CCHP system must first supply the demand for cooling load, and the microgas turbine operates in the mode of “fixing electricity with cold.” If the cooling load is insufficient, the gas boiler will make up the shortfall. In this mode of operation, the CCHP system needs to follow the changes in cooling power at all times. Due to the restriction of the energy coupling relationship, the adjustment capability of its electric power is greatly restricted, and it cannot be added to the optimized operation of the system autonomously. Therefore, the cost of the system in this operating mode is relatively high. The optimization results of electricity and cooling power of the MG with heat pump and cold storage in summer are shown in Figure

Optimization results with heat pump and cold storage in summer: (a) electric power and (b) cooling power.

The results show that the cooling load in the MG is jointly met by the CCHP system, energy storage unit, and heat pump device. The power required by the heat pump and the electrical load in the grid is composed of wind turbines, photovoltaic cells, grid power, CCHP systems, fuel cells, and battery equipment connect during the period of 0–7 and 23-24, and the demand for electricity and cooling load of the MG is relatively low. At this time, the electricity supply price of the external power grid is the lowest, and the power generation costs of distributed microsources (microturbines and fuel cells) in the grid are higher than the electricity supply price of the power grid. Therefore, the electrical load is first to supply from the grid to supply the user's electrical energy needs, and the shortage is supplemented by the fuel cell, the cold load is supplied by the ground source heat pump, and the CCHP system is in a shutdown state during this period. Since the heat pump cooling consumes less electric power, the supply of electrical load can fully meet the requirements during the periods of 7–10, 15–17, and 20–22, and the supply and sale price of external power grids were moderate. The generation cost of distributed microsources in the grid is higher than the power supply price and lower than the price of power demand. The insufficient part chooses to supply power from the grid microsources of the system which is preferentially called to meet the user's electrical energy demand. If the demand for the cooling load is small, the heat pump is driven by electric energy for cooling; if the demand for the cooling load is large, the CCHP system will start for cooling energy during the period of 10–15 and 18–21, and the price of supply electricity and sold by the external power grid is the highest. The electricity demand price of the power grid is higher than the generation cost of distributed microsources, and each microsource is at rated power as much as possible and demands electricity to obtain economic profits. The CCHP system is selected to supply the cooling load demand, and the heat pump equipment is shut down during the entire optimized dispatch period. When the external electricity price is low, releases the electrical energy is released; when the external electricity price is high, the battery stores electrical energy. The charging and discharging state is determined by the grid electricity price. The cold storage unit can absorb the cold energy output by the ground source heat pump at night and release it when the cold load demand is high during the day. The energy storage unit can realize the peak-valley difference transfer of the load within the grid, thereby reducing the total operating cost of the MG.

According to the heating needs of users in winter, the operating state of the heat recovery device in the MG parameter CCHP system is switched to operate in the combined heat and power mode, and the cycle state of the heat pump compressor is changed for heating. On typical winter days, the optimization results of MG power and thermal power without heat pump and heat storage are shown in Figure

Optimization results in winter without heat pump and heat storage: (a) electric power; (b) thermal power.

Optimization results in winter with heat pump and heat storage: (a) electric power; (b) thermal power.

Peak-shaving, valley-filling, and energy efficiency indicators under the two modes.

Operation mode | Season | Peak shaving and valley filling/kW.h | Energy efficiency (%) |
---|---|---|---|

With heat pumped | Summer | 460 | 88.2 |

Winter | 369.5 | 86.9 | |

GSA-RFR | Summer | 428.9 | 93.2 |

Winter | 343 | 93 |

To test the advantages of introducing ground source heat pumps and energy storage units in the MG, the peak-cutting, valley-filling, and energy utilization indexes in the grid were analysed. The peak-cutting and valley-filling index _{n} is evaluated by the minimum square sum of various load change rates during the dispatch period, and the energy utilization index _{m} is evaluated by the total energy input and output ratio presented in (^{3}, and the low heating cost is 9.68 kW h/m^{3}. The electricity cost curve of the microgrid indicated and authenticated the proposed GSA-RFR optimization, while without optimization and GA, PSO approaches show comparatively higher values, which are not in favour of system operation (Figure

Electricity cost of microgrid.

Costs of the MG parameter under the two scheduling methods.

Parameters | Cost ($/day) | ||||
---|---|---|---|---|---|

Summer | Winter | ||||

Unit fuel cost | With heat pump and cold storage | GSA-RFR optimization | With heat pump and cold storage | GSA-RFR optimization | |

Gas turbine | 220.9 | 275.2 | 1241 | 947 | |

Fuel cell | 39.4 | 0 | 209 | 245 | |

Gas-fired boiler | 89.6 | 263.9 | 24.5 | 0 | |

Energy interaction cost | Electricity supply cost | 181.8 | 202.7 | 68 | 141.2 |

Electricity demand | 63.8 | 68.8 | 122 | 127.2 | |

Operation and maintenance cost | 3.98 | 9 | 73 | 71.9 | |

The unit starts and stop cost | 258.7 | 260.3 | 4.19 | 9.3 | |

Heating profit | 1103.8 | 842.7 | 316.9 | 317 | |

Total operation cost | 1030.5 | 689.7 | 1182 | 970 |

The demand for cold load in summer is low, and the demand for heat load in winter is high. There is a certain difference between the two. If the heat pump is used to supply electricity from the power grid for heating at night and the CCHP system is not started, the energy supply needs of users cannot be met. If the unit capacity of the ground source heat pump is further increased, there will be a situation where the equipment utilization rate is low and the initial investment cost is higher. The costs of the MG parameter under the two scheduling methods in winter are shown in Table

The peak-shaving, valley-filling, and energy utilization indicators of the MG are shown in Table

To analyse the advantages of the different modes, a comparative analysis of the comprehensive cost of the MG under the two scheduling modes is carried out, as shown in Figure

A final comparison of GSA-RFR and with heat pump.

The perfection in the modelling of the energy storage system with economic optimization characteristics is the key features of next-generation energy technologies. Nonetheless, there are still issues to developing a physically attractive/efficient and energy storage system that is cost-effective for electronic as well as hybrid vehicles. The model we are going to use to test this is a mixed-integer program. By given data, the integrated parameters, the output cost, and the total cost of the grid are obtained. The simulation verification shows that the integration of the heat pumps and energy storage units into the MG parameter can improve the coupling relationship of the three energy sources of the CCHP system. The MG sources including wind, photovoltaic, CCHP systems, fuel cells, and energy storage unit complementary and coordinated operation are also realized. According to the analysis of the peak-cutting, valley-filling, and energy utilization indexes, the heat pump can improve the energy utilization rate and reduce the natural gas consumption of the microgas turbine, and the energy storage unit has the function of realizing load peak cutting and valley filling. Energy efficiency’s numerical costs validated the proposed GSA-RFR optimization, which is calculated as 93.2% and 93%, comparing 88.2% and 86.9% of heat pump and energy storage costs in the summer and winter season, respectively. Owing to the limitations of the RFR model, if the actual cost exceeds the range, the prediction result may produce a greater deviation. This problem can be improved by expanding the range nodes. The proposed model provided a certain reference for the modelling planning and optimal scheduling of the MG parameter. This study is expected to be a significant contribution concerning the maturity of energy storage technologies for microgrid application, which is likely to dominate the electricity market need.

_{CH}:

Cooling (heating) profit of the system

Combined cooling, heating, and power

_{E}:

Interactive cost of electric energy

Consortium for solutions in electric reliability systems

_{ES}:

The capacity of the energy storage

_{F}:

Unit fuel cost

_{M}:

Operation and maintenance cost

_{NG},

_{NG}:

Unit cost of natural gas and low calorific natural gas

_{S}:

Unit start-up cost

_{S,i}:

Controllable unit start-up cost

_{M}:

Total operating cost of the system

_{c},

_{h}:

Predicted costs of cooling and heat load

_{dem}:

Electricity demand price

_{ES}:

Unit maintenance cost of the energy storage device

_{M,j}:

Number of controllable units

Controllable unit

Microgrid

_{BS}:

Power of the storage battery

_{CGi}:

Output thermal power efficiency of the gas-fired boiler

_{ch, max,}

_{dis, max}:

Charging/discharging output power

_{dem, min}:

Demand power

_{grid}:

Active power

_{grid},

_{pur},

_{grid,dem}:

Supply and demand power

_{load}:

Predicted cost of the electric load

_{pur, max}:

Maximum supply and demand of power

Photovoltaic

_{co}:

Unit cooling

_{CS}:

Cold storage

_{GB}:

Low calorific cost of natural gas

_{grid}:

Reactive power

_{he}:

Heating source

_{HS}:

Hot water storage tank

Time

Optimization period

Shutdown time

Start-up time

_{max}and

_{min}:

Maximum and minimum state of the energy storage.

The data used to support this study are cited in the manuscript.

The authors declare that they have no conflicts of interest.

M. S. N. was responsible for conceptualization, formal analysis, and methodology of the study and wrote the original draft. S. D. reviewed and edited the manuscript and developed software. W. A. S. validated the study and reviewed and edited the manuscript. M. A. performed formal analysis. A. Y. K was responsible for original draft preparation and investigation. A. N. A. was involved in conceptualization, investigation, formal analysis, and reviewing and editing of the manuscript. P .S. was involved in investigation and reviewing and editing of the manuscript.

All the authors are highly grateful to their affiliated institutes and universities for providing all the necessary services.