# Seasonal Operation Strategy Optimization for Integrated Energy Systems with Considering System Cooling Loads Independently

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## Abstract

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## 1. Introduction

- (1)
- In most previous studies, the CHP heat to power ratio and energy system heat to power ratio in different seasons were selected as a constant when optimizing CHP operation. In this paper, the state of the art CHP unit with an additionally fired waste heat boiler was introduced to optimize the CHP heat to power ratio in different seasons. The results showed that the average daily fuel costs could be reduced by 5.2% if the CHP heat to power ratio was optimized seasonally.
- (2)
- Compared to the existing literature, system cooling loads were independently considered rather than treated as a part of thermal or electrical loads when optimizing a system operation. Results showed that the peak–valley gap of the power system could be significantly reduced, especially in summer (about 40.7% reduction) if the cooling loads were independently considered.
- (3)
- Different from early research, this paper adopted a time-of-use gas price rather than a constant gas price to optimize the energy system operation. This is because it is believed that the rapid development of CHP and gas boilers can lead to the shortage of natural gas at peak time. Simulation results showed that the average daily thermal production costs could be reduced by 7% when applying the time-of-use gas price. Additionally, adopting time-of-use gas price was conductive to optimizing system configuration.

## 2. Energy Hub Modeling for an Integrated Energy System

#### 2.1. The Energy Hub Model

_{EV}and P

_{WT}are greater than zero, the electric vehicle power exchange station and hot water tank are in discharge state. In addition, when P

_{C}is greater than zero, the ice storage system is in an ice melting state. Moreover, diesel consumed in CHP cannot increase CHP electricity output efficiency, but it can improve combustion efficiency, and this will be introduced in detail in the next part.

#### 2.2. Different Energy Carriers’ Output Power Modeling and Operation Constraints

#### 2.2.1. CHP Output Power and Operation Constraints Modeling

_{a1}, K

_{a2}, K

_{b1}, and K

_{b2}are set as 4.4483, 1.2857, 0.0051209, and 0.00038 in this paper [18]. Therefore, the mathematical expression of CHP heat conversion efficiency and the supplementary volume of diesel oil can be expressed as:

#### 2.2.2. Diesel Generator Output Power and Operation Constraints Modeling

#### 2.2.3. Gas Boiler Output Power and Operation Constraints Modeling

#### 2.2.4. Ice Storage System Output Power and Operation Constraints Modeling

_{Cout}) can be expressed as:

#### 2.2.5. Hot Water Tank Output Power and Operation Constraints Modeling

#### 2.2.6. Electric Vehicle Power Exchange Station Output Power and Operation Constraints Modeling

_{min}and SOC

_{max}are set as 10% and 100%, respectively.

## 3. System Optimal Operation Strategy

#### 3.1. Objective Function

#### 3.2. Optimization Algorithm

## 4. Case Study

## 5. Results and Analysis

#### 5.1. Optimization Results of CHP Heat to Power Ratio

_{o}) increased at first and then decreased. The overall efficiency of CHP can reach its maximum value of 78.2% when the heat to power ratio of CHP is 337%. However, CHP overall efficiency started to decrease shortly after it reached its maximum value. This was because, with the increase of the supplementary volume of diesel oil, the temperature of the waste heat boiler’s exhaust smoke rose as well, which made the supplemented diesel oil have a lesser effect on improving the waste heat boiler’s efficiency and eventually reduced CHP overall efficiency.

#### 5.2. The Influence of Cooling Loads on System Operation

_{C}

_{1}and P

_{C}

_{2}represent the operation states of two ice storage devices. When the cooling loads are greater than zero, the ice storage system is in the ice melting state; otherwise, the ice storage system is in the ice making state. In addition, P

_{T}

_{1}is the equivalent average daily electrical load curve before independently considering cooling loads (the cooling loads are converted to real time electrical loads). P

_{T}

_{2}is the equivalent average daily electrical load curve after independently considering cooling loads (the cooling loads can participate in the demand response program).

_{DE}

_{1}and P

_{DE}

_{2}in Figure 8 represent the average daily output power of diesel generators before and after the cooling loads were independently considered.

#### 5.3. System Fuel Costs Optimization under the Time-of-Use Gas Price

_{WT}is greater than zero. It is worth noting that the heat stored in the hot water tank is about 8–11% greater than the heat released by the hot water tank. This is because a hot water tank always has standby losses and the standby losses vary between different seasons.

_{V}

_{2G}is greater than zero, the power exchange station works as a generator, or alternatively, the power exchange station works as loads.

## 6. Conclusions

- (1)
- Taking the seasonal factor into consideration when optimizing the CHP heat to power ratio, the average system fuel costs can be reduced by 5.2% and the CHP heat to power ratio will match up to the system heat to power ratio.
- (2)
- By considering the cooling loads independently and utilizing the ice storage system to participate in the power system demand response, the system electrical load curve can be regulated in an indirect way. Simulation results also revealed that the peak–valley gap of electrical loads was reduced by 40.7% in summer under the premise of ensuring the cooling loads. Meanwhile, by regulating the system electrical load curve, the installation capacity of the diesel generator can be fully utilized.
- (3)
- The proposed optimal operation strategy makes full use of the load shifting capability of the hot water tank to improve system stability and to respond to the time-of-use gas price simultaneously. However, due to the limited battery installation capacity, the load shifting capability of the electric vehicle power exchange station is constrained.

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A. List of Symbols

Nomenclature | Meaning | Nomenclature | Meaning |

L_{e} | Electrical loads | L_{h} | Thermal loads |

L_{c} | Cooling loads | ω | Ratio of power consumed by ice storage system to total power consumption |

α | Ratio of diesel consumed by diesel generator to total diesel consumption | β | Ratio of natural gas consumed by CHP to total natural gas consumption |

η_{DE} | Diesel generator output efficiency | η_{CHPe} | CHP output electricity efficiency |

η_{CHPh} | CHP output heat efficiency | η_{GB} | Gas boiler generator efficiency |

P_{D} | Inputs of diesel | P_{G} | Inputs of natural gas |

P_{EV} | Discharge power of electric vehicle power exchange station | P_{WT} | Discharge power of hot water tank |

P_{C} | Ice storage system ice making power | R_{CHP} | Heat to power ratio of CHP |

P_{CHPh} | Thermal output power of a CHP unit | P_{CHPe} | Electrical output power of a CHP unit |

P_{CHPin} | Input power of CHP | K_{a1}, K_{a2}, K_{b1} ,K_{b2} | Boost factors of CHP heat to power ratio |

P_{0 }(t) | Supplementary volume of diesel oil at time t | P_{DE} | Diesel generator output power |

P_{DEin} | Input power of a diesel generator | P_{DEmax} | Maximum operating power of a diesel generator |

P_{DEmin} | Minimum starting power of a diesel generator | P_{GB} | Gas boiler output power |

P_{GBin} | Input power of a gas boiler | a1 | Exhaust smoke heat loss |

a2 | Incomplete combustion loss | a3 | Heat dissipation loss |

Q_{GB_H} (t) | Operation capacity of a gas boiler | Q_{GB_Hmin} | Minimum operation capacity of a gas boiler |

Q_{GB_Hmax} | Maximum operation capacity of a gas boiler | T_{GB_ON }(t) | Accumulated operation time of the gas boiler at time t |

T_{GB_OFF} (t) | Accumulated turn-off time of the gas boiler at time t | T_{GB_ONmin} | Minimum accumulated operation time of the gas boiler |

T_{GB_OFFmin} | Minimum accumulated turn-off time of the gas boiler | P_{Cout} | Output refrigerating power of the ice storage system |

P_{Cin} | Input electrical power of the ice storage system | EER | Energy efficiency ratio of the ice storage system |

Q_{Cice} | Ice making capacity of the ice storage tank | Q_{Cicemin} | Minimum ice making capacity of the ice storage tank |

Q_{Cicemax} | Maximum ice making capacity of the ice storage tank | Q_{Cw} | Ice melting capacity of the ice storage tank |

Q_{Cwmin} | Minimum ice melting capacity of the ice storage tank | Q_{Cwmax} | Maximum ice melting capacity of the ice storage tank |

M_{C_ICE }(t) | Ice making mode | M_{C_W }(t) | Ice melting mode |

Q_{WT }(t) | Total thermal energy stored in the hot water tank at time t | ε_{WT} | Self discharge rate of a hot water tank |

Q_{WTh }(t) | Thermal energy stored in the hot water tank at time t | Q_{WTr }(t) | Thermal energy released by the hot water tank at time t |

Q_{WTmin} | Minimum amount of thermal energy that can be stored in the hot water tank | Q_{WTmax} | Maximum amount of thermal energy that can be stored in the hot water tank |

Q_{WThmin} | Minimum amount of thermal energy that can flow in the hot water tank within a certain time period | Q_{WThmax} | Maximum amount of thermal energy that can flow in the hot water tank within a certain time period |

Q_{WTrmin} | Minimum amount of thermal energy that can release by the hot water time within a certain time period | Q_{WTrmax} | Maximum amount of thermal energy that can release by the hot water time within a certain time period |

t_{SC} | Starting time of charging battery | t_{c1} | Starting time of low power demand |

t_{c2} | Ending time of low power demand | t_{chg} | Total charging time |

T_{g} | Period of low demand time | t_{SD} | Starting time of discharging battery |

t_{d1} | Starting time of peak power demand | t_{d2} | Ending time of peak power demand |

t_{chd} | Total discharging time | T_{f} | Period of peak demand time |

k | Random number between 0 and 1 | Q_{EV }(t) | Electrical energy stored in electric vehicle power exchange station at time t |

L_{EV} | Electric vehicles’ daily energy consumption | SOC | State of Charge |

SOC_{min} | Minimum state of Charge | SOC_{max} | Maximum state of Charge |

Q_{EV} | Rated energy storage capacity of electric vehicle power exchange station | F | Total fuel costs of the system |

Q_{G }(t) | Amount of natural gas (in cubic meter) consumed by the system at time t | Q_{D }(t) | Amount of diesel (in liter) consumed by the system at time t |

C_{G }(t) | Real time natural gas price (in US $/cubic meter) at time t | C_{D }(t) | Real time diesel price (in US $/liter) at time t |

η_{o} | Overall efficiency of CHP | R_{CHPmin} | Minimum CHP heat to power ratio |

Q_{e} | Total electrical energy generated by CHP | Q_{h} | Total thermal energy generated by CHP |

Q_{in} | Sum of the calorific value of diesel and natural gas consumed by CHP | - | - |

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**Figure 6.**Simulation results of the relationship between CHP heat to power ratio and its overall efficiency.

**Figure 7.**Optimal output of two ice storage devices and average daily electrical load curve of the integrated energy system in (

**a**) spring; (

**b**) summer; (

**c**) autumn; (

**d**) winter.

**Figure 8.**Output power of the diesel generator before and after cooling loads were independently considered.

**Figure 9.**Optimal thermal storage output and time-of-use gas price in (

**a**) spring; (

**b**) summer; (

**c**) autumn; (

**d**) winter.

**Figure 10.**Optimal output power of the electric vehicle power station and time-of-use gas price in (

**a**) spring; (

**b**) summer; (

**c**) autumn; (

**d**) winter.

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**MDPI and ACS Style**

Li, K.; Yan, H.; He, G.; Zhu, C.; Liu, K.; Liu, Y.
Seasonal Operation Strategy Optimization for Integrated Energy Systems with Considering System Cooling Loads Independently. *Processes* **2018**, *6*, 202.
https://doi.org/10.3390/pr6100202

**AMA Style**

Li K, Yan H, He G, Zhu C, Liu K, Liu Y.
Seasonal Operation Strategy Optimization for Integrated Energy Systems with Considering System Cooling Loads Independently. *Processes*. 2018; 6(10):202.
https://doi.org/10.3390/pr6100202

**Chicago/Turabian Style**

Li, Kecheng, Huaguang Yan, Guixiong He, Chengzhi Zhu, Kaicheng Liu, and Yuting Liu.
2018. "Seasonal Operation Strategy Optimization for Integrated Energy Systems with Considering System Cooling Loads Independently" *Processes* 6, no. 10: 202.
https://doi.org/10.3390/pr6100202