# An Optimization Ensemble for Integrated Energy System Configuration Strategy Incorporating Demand–Supply Coordination

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## Abstract

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## 1. Introduction

- To handle the complicated coupling relations among supply and demand sides in an IES, this paper proposes an energy configuration optimization strategy based on a multi-model ensemble to ensure better resource allocation and arrangement, especially in more complex data distribution scenarios.
- To cope with the high-dimensional data conditions, the ICA approach is deployed to establish a linear transformation from high-dimensional inputs to unmixing independent components in the feature space, which can reduce the noise and thus improve computing efficiency.
- To solve the heterogeneous and uncertain data problems, the SAQGM methodology is designed for subsequent energy configuration optimizations, where the quantum bit representation is built to reduce computation complexity in multi-state component scenarios, the double-chain formation of chromosomes is formed to diminish the uncertainty when encoding, and the dynamic adaptation quantum gate is implemented to successively amend parameters.

## 2. IES Coupling Model

#### 2.1. Coupling Relationships between Supply and Demand

#### 2.2. Coupling Relationships between Supply and Demand

#### 2.2.1. Economical Cost

_{b}denotes the integrated system investment cost; ${c}_{t}^{E}$, ${c}_{t}^{G}$, and ${c}_{t}^{H}$ represent the acquisition unit price of electric network resources, natural gas network resources, and thermal network resources, respectively; and ${E}_{t}^{E}$, ${E}_{t}^{G}$, and ${E}_{t}^{H}$ demonstrate the amount of resources acquired by the electricity network, the amount of resources acquired by the natural gas network, and the amount of resources acquired by the thermal network, respectively.

_{r}represents the cost to be spent by the equipment in operation, ${c}_{t}$ is the maintenance cost required for the physical equipment to output unit power per unit time period, and ${P}_{t}$ denotes the power output of the equipment per unit time period.

_{l}depicts the additional cost of energy loss during operation; ${\beta}_{E}$, ${\beta}_{H}$, and ${\beta}_{G}$ denote the additional loss coefficients of energy in the operation process for electric network resources, thermal network resources, and natural gas network resources, respectively; ${W}_{E}^{sup}$, ${W}_{H}^{sup}$, and ${W}_{G}^{sup}$ delineate the supply of electric power resources, thermal power resources, and natural gas resources, respectively; and ${W}_{E}^{req}$, ${W}_{H}^{req}$, and ${W}_{G}^{req}$ represent the demand for electricity, heat, and natural gas resources, respectively.

_{c}is the user comfort cost, i.e., the cost expended by the user to compensate for the user’s comfort not being affected when the energy demand changes; ${\mu}_{t}$ denotes the proportional coefficient of user comfort cost per unit time period; and ${L}_{E}$, ${L}_{H}$, and ${L}_{G}$ illustrate the load difference between the user’s energy demand change and the initial demand.

#### 2.2.2. Environmental Cost

#### 2.2.3. Constraints

- Power balance constraint:

- 2.
- Equipment operation constraint:

- 3.
- Energy price constraint:

## 3. ICA-SAQGM Ensemble

#### 3.1. ICA Model

- 1.
- Calculate the mean value of X and obtain the de-averaged value Y according to the following equation:$$Y=X-M$$

- 2.
- Find the covariance matrix of $Y:C=cov\left(Y,{Y}^{T}\right)$, the diagonal array of eigenvalues of the matrix Q, and the eigenvectors $\alpha $. Let $U={Q}^{-1/2}{\alpha}^{T}$, and the processed data can be obtained via the following equation:$$H=U\times Y$$

- 3.
- Initialize the random matrix, ${\mathit{W}}^{\left(0\right)}$, and assume that the modulus of the column vector is 1. Set k as the iteration indicator, such that $k=0$.

- 4.
- Use the following equation for numerical iterations of ${\stackrel{~}{w}}_{j}^{\left(k\right)}$:$${\stackrel{~}{w}}_{j}^{\left(k\right)}=\mathit{E}\left\{H\xb7G\left({\stackrel{~}{w}}_{j}^{\left(k-1\right)T}\xb7H\right)\right\}-\mathit{E}\left\{H\xb7g\left({\stackrel{~}{w}}_{j}^{\left(k-1\right)T}\xb7H\right)\right\}\times {\stackrel{~}{w}}_{j}^{\left(k-1\right)}$$

- 5.
- Perform the matrix orthogonalization and normalization on $\mathit{W}$:$${\stackrel{~}{w}}_{j}^{\left(k\right)}\to \sum _{i=1}^{m}\left({w}_{j}^{{\left(k\right)}^{r}}{w}_{i}\right){w}_{i}$$$${\stackrel{~}{w}}_{j}^{\left(k\right)}\to \frac{{w}_{j}^{\left(k\right)}}{\left|\right|{w}_{j}^{\left(k\right)}\left|\right|}$$

- 6.
- When $|{\stackrel{~}{w}}_{j}^{\left(k\right)T}{\stackrel{~}{w}}_{j}^{(k-1)}-1|<\epsilon $, then $j=j+1$; otherwise, there is no convergence, and must return to Step 3.

- 7.
- When $j=m$, the matrix $\mathit{W}$ can be generated, and then the independent components, S, can be figured out according to Equation (17).

#### 3.2. SAQGM Methodology

#### 3.2.1. Objective Description: Quantum Bit Representation Scheme

#### 3.2.2. Quantum Bit Coding: Double-Chain Formation

#### 3.2.3. Evolution Strategy: Dynamic Adaptation Quantum Gate

#### 3.2.4. Procedure

- Initialize the quantum position chromosome population, Q(t), with l quantum position chromosomes and assume θ
_{0}to be the initial iteration angle and the mutation probability, P_{m}, to be 0.05. - Probe all chromosomes, encode the quantum bits via the double-chain coding model, and calculate the fitness, as well as the gradient.
- Evaluate the solution set, S(t); solve the optimal solution; and store.
- If the termination condition is not reached, S(t) is generated via the previous time series of the chromosome population Q(t − 1) in each round of the iteration.
- Adjust the rotation angle and the probability magnitude, and then update Q(t) via the self-adaptive quantum gate, U(t);
- The optimal solution is stored in S(t) until the termination condition is reached.

## 4. Empirical Case Study

#### 4.1. Data Base

#### 4.2. Results Analysis

**Scenario 1:**To verify the optimization performance of the ICA-SAQGM ensemble, the particle swarm optimization (PSO) [31], the BP neural network (BPNN) [32], and the standard quantum genetic model (QGM) [33] are deployed for comparison. The maximum time of iterations of all of these algorithms is set to 300 times. The total daily cost of the studied IES is optimized, and the resulting curves are illustrated in Figure 5.

**Scenario 2:**In order to assess the optimized IES considering the coupling relationship between supply and demand, three patterns are utilized: Pattern 1, standard IES operations; Pattern 2, IES operations considering the coupling relationships; and Pattern 3, optimized IES operations with the coupling relationships. Figure 5 delineates the operating curves of these three patterns.

## 5. Conclusions

- An IES operation model containing the coupling relationships between supply and demand sides was built which can incorporate the underlying connections between the energy sources and loads when designing strategies.
- The ICA model was established for dimensionality reduction, which maps the high-dimensional heterogeneous inputs into the linear combinations of independent components for data unmixing. Therefore, it is used to further improve the computing efficiency.
- The SAQGM optimization procedure was designed to enhance the comprehensiveness and efficiency, where the quantum bit representation scheme is built to decrease the computation burden in multi-state scenarios, the double-chain formation of chromosomes is deployed to ameliorate the performance when encoding, and the dynamic adaptation quantum gate was implemented to modify the parameters.
- An empirical case study was conducted to validate the performance of the proposed method during real applications. The results prove that the configuration strategy based on this methodology can reduce investment, operation costs, and pollution emissions significantly.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 6.**Comparison of operation curves by three patterns. (

**a**) Electric load curve. (

**b**) Heating load curve.

Equipment | Efficiency | Lower Limit | Upper Limit |
---|---|---|---|

Transformer | Power: 0.9 | Power purchase: 0 kW | Power purchase: 4200 kW |

Gas turbine | Power: 0.35 Heating: 0.42 | Electricity/heat production: 1000 kW/1080 kW | Electricity/heat production: 4000 kW/4200 kW |

Gas boiler | Heating: 0.91 | Heat production capacity: 1000 kW | Heat production capacity: 6300 kW |

Air conditioning | Cooling: 3.7 | Production capacity: 0 kW | Production capacity: 4000 kW |

Heat exchangers | Heating: 1.2 | Production capacity: 0 kW | Production capacity: 6000 kW |

Absorption chillers | Cooling: 1.2 | Production capacity: 0 kW | Production capacity: 4000 kW |

External heating | Heating: 1 | Heat purchase: 0 kW | Heat purchase: 4000 kW |

External gas supply | Air supply: 1 | Gas purchase: 0 m^{3} | Gas purchase limit: 1350 m^{3} |

Energy Type | Parameters | Price/CNY |
---|---|---|

Electricity | Peak hours | 1.00 |

Off-peak hours | 0.60 | |

Low hours | 0.30 | |

Heating | Upper limit | 0.75 |

Lower limit | 0.35 | |

Natural Gas | / | 3.33 |

Model | Average Total Daily Cost/CNY | Average Pollution Emissions/Ton | Average Convergence Iterations | Mean Variance |
---|---|---|---|---|

PSO | 53,662 | 1.69 | 284 | 0.7731 |

BPNN | 52,013 | 1.48 | 233 | 0.5215 |

QGM | 50,978 | 1.26 | 136 | 0.2781 |

ICA-SAQGM | 47,681 | 1.02 | 47 | 0.1833 |

Model |

Pattern | Pattern 1 | Pattern 2 | Pattern 3 |
---|---|---|---|

Investment cost/CNY | 46,914 | 44,832 | 42,002 |

Equipment running cost/CNY | 4522 | 3964 | 3482 |

Loss cost/CNY | 3022 | 2552 | 1889 |

User comfort cost/CNY | 0 | 1231 | 0 |

Total daily cost/CNY | 54,458 | 52,579 | 47,373 |

Pollutant emissions/ton | 1.02 | 1.02 | 1.02 |

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## Share and Cite

**MDPI and ACS Style**

Sun, C.; Jiang, X.; Jia, Z.; Yu, K.; Xiang, S.; Su, J.
An Optimization Ensemble for Integrated Energy System Configuration Strategy Incorporating Demand–Supply Coordination. *Sustainability* **2023**, *15*, 15248.
https://doi.org/10.3390/su152115248

**AMA Style**

Sun C, Jiang X, Jia Z, Yu K, Xiang S, Su J.
An Optimization Ensemble for Integrated Energy System Configuration Strategy Incorporating Demand–Supply Coordination. *Sustainability*. 2023; 15(21):15248.
https://doi.org/10.3390/su152115248

**Chicago/Turabian Style**

Sun, Chenhao, Xiwei Jiang, Zhiwei Jia, Kun Yu, Sheng Xiang, and Jianhong Su.
2023. "An Optimization Ensemble for Integrated Energy System Configuration Strategy Incorporating Demand–Supply Coordination" *Sustainability* 15, no. 21: 15248.
https://doi.org/10.3390/su152115248