# Period Cycle Optimization of Integrated Energy Systems with Long-Term Scheduling Consideration

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. System’s Optimization Algorithms

#### 2.1.1. Objective Function

#### 2.1.2. Constraint Conditions

^{3}/h) is converted into power (kW) by using the calorific value of natural gas (kWh/m

^{3}).

#### 2.1.3. Economic Viability

#### 2.1.4. Energy and Component Cycle Optimization Method

- Define decision variables. The primary decision variables in this approach encompass component parameters and energy attributes.
- Establish operating cycles. Following the scenario simulation method, determine the total operating duration and operating cycles to assess the initial design solution set periodically.
- Configure optimization scheme parameters based on the decision variables and operational cycles; set optimization scheme parameters.
- Simulate real-time operations. Utilizing component capacities, energy attributes, and operational cycles defined in the initial design solutions, simulate the operational states and power profiles of each component to meet the energy demands and constraints of the current real-time scenario.
- Compute scheme performance. Based on the real-time scenario simulation results, calculate the power profiles of various components, total energy cost, total carbon emissions, and total energy consumption over the operational cycle.
- Evaluate schemes. Assess the optimization and improvements needed for the current operational cycle based on the performance from the simulation.
- Determine the termination conditions. If the simulated runtime reaches the predefined operational time, exit the ECC optimization method and output all the result data. Otherwise, continue with step 8.
- Update optimization schemes. According to the results of the simulation and evaluation, retain certain optimization schemes within the collection and remove others to accommodate new optimization methods. Then, return to step 4 to continue the cycle simulation.

#### 2.2. Case Study

## 3. Results and Discussion

#### 3.1. Real-Time Scheduling Data

#### 3.2. Energy Conservation and Emission Reduction

_{2}, SO

_{2}, NO

_{X}, and PM

_{2.5}are 226.6, 830.5, 25.0, 12.5, and 8.3 tons. These reductions can be equivalently translated into the planting of 833,010 trees. The data indicate that the system, driven by electricity and natural gas as energy sources, can effectively achieve energy saving and emission reduction through multiple cycle optimizations, with significant initial optimization results.

#### 3.3. Economic Feasibility

## 4. Conclusions

- The energy and component cycling optimization method proposed in this paper, considering the capacity of energy devices and loads, can effectively reduce costs and carbon emissions.
- Conducting an economic feasibility assessment on the integrated energy system enables more efficient prediction and evaluation of whether the system is worth investing in and operating.
- By appropriately increasing the usage of pricing clean energy sources such as natural gas in the integrated energy system to offset the use of expensive peak–valley electricity, while reducing the capacity and load scheduling of thermal and cooling storage devices, the system’s operational efficiency can be significantly improved.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

Abbreviations | $Q$ | energy consumption | |

EEMs | energy efficiency measures | $C$ | energy cost |

MILP | Mixed-Integer Linear Programming | $E$ | carbon emissions |

PV | photovoltaic | $lr$ | load rate |

GA | genetic algorithm | $f$ | objective function |

ILPSO | Improved Particle Swarm Optimization method | $g$ | constraint function |

PAR | peak-to-average ratio | $G$ | overall gain |

CHP | combined heat and power | $INCOME$ | total income |

ECC | energy and component cycle | $COST$ | total expense |

$NPV$ | net present value | $C$ | total equipment |

$IRR$ | internal rate of return | $pvf$ | present value factor |

IMF | International Monetary Fund | ${P}_{st}$ | flow of energy |

Indices | $k$ | cost | |

$i$ | energy components | $\phi $ | equipment depreciation coefficient |

$n$ | number of decision variables | $\epsilon $ | equipment residual value coefficient |

$m$ | number of constraint functions | $hm$ | refrigeration unit |

$t$ | time | $br$ | lithium bromide absorption chiller |

Parameters | $cu$ | CHP | |

$prod$ | production | $gb$ | gas boiler |

$stor$ | energy storage | $pg$ | power grid |

$buy$ | energy purchase | $ng$ | natural gas station |

$depr$ | fixed asset depreciation | $si$ | solar radiation |

$resi$ | equipment residual value | $wt$ | wind turbine |

$sell$ | energy sales | $hp$ | ground source heat pump |

$total$ | total energy or price | $s{t}_{i}$ | energy storage power |

$c$ | equipment | ${\eta}^{c}$ | energy storage efficiency |

$b\in B$ | system’s energy demand | ${\eta}^{d}$ | energy transfer efficiency |

$s\in S$ | load intervals | ${\delta}_{c}$ | storage energy efficient |

$t\in T$ | time steps | ${\delta}_{d}$ | output energy efficient |

$elec$ | electricity loads | $q$ | consumption factor |

$heat$ | heat loads | $P$ | energy prices |

$cold$ | cool loads | $e$ | emission factor |

$gas$ | gas loads | $C{F}_{i}$ | cash inflows |

$capa$ | equipment capacity | $C{F}_{0}$ | initial capital investment |

$out$ | output power | $r$ | periodic interest rate |

$re$ | energy |

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**Figure 1.**Schematic representation of the case. (In the figure, yellow lines represent electricity, green represents natural gas, red represents heat load and blue represents cold load).

**Figure 2.**Load profiles of various energy components within one operating cycle. ((

**a**) represents the power load curve of each energy equipment in a period; (

**b**) represents the heat load curve of each energy equipment in a period; (

**c**) represents the cold load curve of each energy equipment in a period).

Item (Unit) | Maximum Capacity | Minimum Capacity | Annual Price |
---|---|---|---|

Photovoltaic (kW) | 80 | 0 | 50 USD/kw |

CHP (kW) | 600 | 0 | 40 USD/kw |

Gas boiler (kW) | 1200 | 0 | 6 USD/kw |

Lithium bromide refrigerator (kW) | 1000 | 0 | 15 USD/kw |

Double-working condition main engine (kW) | 900 | 0 | 17 USD/kw |

Airborne main engine (kW) | 300 | 0 | 15 USD/kw |

Electric energy storage (kWh) | 1500 | 0 | 20 USD/kwh |

Heat storage tank (m^{3}) | 50 | 0 | 170 USD/m^{3} |

Ice storage tank (m^{3}) | 50 | 0 | 170 USD/m^{3} |

Item | Price (USD/kWh) | Emission Factor (kg/kWh) | Consumption Factor (kWh/kWh) | Energy Purchase Tax Rate (%) |
---|---|---|---|---|

Power grid electricity | 0.04/0.09/0.15 | 0.78 | 1.00 | 13 |

Natural gas | 0.04 | 0.22 | 1.00 | 9 |

Item (Unit) | Value |
---|---|

Capital ratio (%) | 45 |

Lending rate (%) | 3 |

Repayment period (year) | 4 |

Surtax rate (%) | 0.1 |

Income tax rate (%) | 25 |

Benchmark return rate (%) | 12 |

Facility deduction tax rate (%) | 1 |

Equipment depreciation year (year) | 3 |

Item (Unit) | Value |
---|---|

Runtime (h) | 8760 |

Run optimized population size | 20 |

Run optimization iterations | 25 |

Mutation operator | 1.8 |

Cross operator | 0.62 |

Optimization Period | Carbon Emission Reduction of the System/t | Other Emission Gas Reduction of the System/t | Proportion/% |
---|---|---|---|

1~5 | 91.90 | 30.19 | 11.07% |

6~10 | 162.28 | 53.30 | 19.55% |

11~15 | 185.15 | 60.82 | 22.30% |

16~20 | 193.11 | 63.43 | 23.26% |

21~25 | 197.74 | 64.91 | 23.82% |

Item (Unit) | Value |
---|---|

Total investment cost (million) | 509.40 |

Pre-tax IRR (%) | 23.14 |

Post-tax IRR (%) | 21.96 |

Pre-tax NPV (million) | 66.38 |

Post-tax NPV (million) | 59.27 |

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**MDPI and ACS Style**

Ye, D.; Deng, S.
Period Cycle Optimization of Integrated Energy Systems with Long-Term Scheduling Consideration. *Algorithms* **2023**, *16*, 530.
https://doi.org/10.3390/a16110530

**AMA Style**

Ye D, Deng S.
Period Cycle Optimization of Integrated Energy Systems with Long-Term Scheduling Consideration. *Algorithms*. 2023; 16(11):530.
https://doi.org/10.3390/a16110530

**Chicago/Turabian Style**

Ye, Daoyu, and Shengxiang Deng.
2023. "Period Cycle Optimization of Integrated Energy Systems with Long-Term Scheduling Consideration" *Algorithms* 16, no. 11: 530.
https://doi.org/10.3390/a16110530