# A Robust Economic Framework for Integrated Energy Systems Based on Hybrid Shuffled Frog-Leaping and Local Search Algorithm

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. The Integrated Energy System Model

_{R}is the set of time; and ${\rho}_{{t}^{\u2019}}^{e0}$ and ρ represents t actual load price and base price, respectively.

_{GT}, electric energy purchase cost CEM, and energy conversion and storage equipment operation and maintenance cost C

_{M}, represented as:

## 3. Proposed Method

#### 3.1. Objective Function

_{1}and C

_{2}are start-up and shut-down costs of CHP units in the first stage, and operation costs and purchasing costs in the second stage, while $Ma{x}_{\psi ,L}$ are the upper, middle, and lower decision variables.

#### 3.2. Constraints

_{max}and S

_{min}are the energy storage device’s maximum and minimum capacity states, respectively; S

_{all}is the total capacity of the energy storage device; μ represents attrition rate; ${Q}_{s,t}^{C}$, ${Q}_{s,t}^{D}$ are charge/discharge energy work, respectively; and ${\eta}_{C}$ is charging efficiency rate.

#### 3.3. Optimisation Algorithm

_{i}= [x

_{i1}, x

_{i2},…, x

_{iN}]. According to their fitness, the frogs are listed in descending order. In this algorithm, the mth frog goes to the mth memeplex, and frog m + 1 returns to the first memeplex. The frog position with the best fitness is represented by X

_{b}, and the frog position with the worst fitness is introduced with X

_{w}. Xg also defines the global best fitness. Following that, a particular technique is performed to improve the fitness of the frog with the lowest fitness level, such as:

_{b}is substituted with X

_{g}. Without any enhancement in results, a novel result can be arbitrarily created to interchange that frog.

## 4. Result and Discussion

#### 4.1. Model Parameter Setting

^{3}, respectively. The scheduling period T is 24, and the unit time interval is 1 h. Table 1 shows the ACA scheduling parameters. Gas turbine parameters, heat/cold storage system parameters, and other equipment parameters are detailed in [26].

#### 4.2. Analysis of Model Optimisation Results

#### 4.3. Influence of Uncertain Factors

_{RE}and ψ

_{DR}, it can be seen that the change in the comprehensive demand response uncertain budget has a more significant impact on the operation cost and average slack power of IES than the change in the scenic output uncertain budget.

## 5. Conclusions

- (1)
- Considering the unpredictability of the price of energy purchases, IES operators can choose the best energy buy strategy in real-time, based on the particular market price realization scenario, enhancing the system’s operational economy;
- (2)
- The economic scheduling model considering multiple uncertainties proposed in this paper can further enhance the economy and security of system operation, in accordance with the characteristics of uncertain sources when comparing the HSFLA–LS model with the deterministic scheduling model and the model considering only a single uncertainty;
- (3)
- The best way to operate the IES and identify the best output for the ACA device is to use a hybrid SFLA–LS algorithm. The result that has the biggest effect on the system’s security and overall economy is the modification to apply to the comprehensive demand response uncertainty budget.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

Variable | Definition |

ACA | Adiabatic compressed air |

CCHP | Combined cooling heat and power |

GA | Genetic algorithm |

HSFLA–LS | Hybrid shuffled frog leaping and local search |

IDR | Integrated demand response |

IES | Integrated energy system |

PSO | Particle swarm optimisation |

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**Figure 6.**Influence of purchasing price uncertainty on the model. (

**a**) Cost function; (

**b**) Energy function.

Parameter | Values |
---|---|

Rated compression power/kW | 100 |

Rated power/kW | 100 |

Gas storage chamber volume/m^{3} | 5.5 × 10^{5} |

Initial pressure of the gas storage chamber/bar | 47.5 |

Upper pressure of gas storage chamber/bar | 55 |

Lower limit of air storage chamber pressure/bar | 40 |

Unit capacity maintenance cost/(USD/kWh) | 0.729 |

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**MDPI and ACS Style**

Abdalla, A.N.; Ju, Y.; Nazir, M.S.; Tao, H.
A Robust Economic Framework for Integrated Energy Systems Based on Hybrid Shuffled Frog-Leaping and Local Search Algorithm. *Sustainability* **2022**, *14*, 10660.
https://doi.org/10.3390/su141710660

**AMA Style**

Abdalla AN, Ju Y, Nazir MS, Tao H.
A Robust Economic Framework for Integrated Energy Systems Based on Hybrid Shuffled Frog-Leaping and Local Search Algorithm. *Sustainability*. 2022; 14(17):10660.
https://doi.org/10.3390/su141710660

**Chicago/Turabian Style**

Abdalla, Ahmed N., Yongfeng Ju, Muhammad Shahzad Nazir, and Hai Tao.
2022. "A Robust Economic Framework for Integrated Energy Systems Based on Hybrid Shuffled Frog-Leaping and Local Search Algorithm" *Sustainability* 14, no. 17: 10660.
https://doi.org/10.3390/su141710660