# Reliability Optimization of Multi-Energy System Considering Energy Storage Devices Effects under Weather Uncertainties

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. MES Reliability Assessment Overview

#### 1.2. MES Reliability Optimization Overview

#### 1.3. Main Contributions

- The reliability assessment of multi-energy systems primarily focuses on single coupling systems, such as power–heat and power–gas systems, and assessments seldom focus on multi-energy systems that combine all three energy forms of power, heat, and natural gas;
- The established reliability modeling approach is very simplistic, ignoring component uncertainty and time-varying load in real-world situations;
- Most previous works solved the problem as a single optimization problem, with the goal of maximizing reliability or lowering cost as the sole objective, and there is still no detailed investigation of optimal storage system design for multi-energy system reliability.

- The power–heat–gas multi-energy system reliability with energy storage devices has been modeled, taking into account all the coupling components under weather uncertainties;
- The uncertainty modeling of PV and wind generation and time-varying load forecasting, including heat and gas demand, are considered. Moreover, a time varying cost model based on the sector customer damage function (SCDF) [29] is also adopted to calculate the EENS (expected energy not supplied) and the interruption cost in objective functions;
- A multi-objective reliability optimization problem is formulated considering both the system reliability index, SAIDI, and costs (including interruption cost and the installation cost of multi-energy storage devices) as objective functions. The optimization results are compared through the three widely used algorithms, i.e., the particle swarm algorithm, genetic algorithm, and evolutionary algorithm, to validate the feasibility and effectiveness of the suggested approach.

## 2. Overall Modeling Architecture of Multi-Energy System

#### 2.1. Multi-Energy System Components Modeling

#### 2.1.1. CHP Unit

#### 2.1.2. Gas Boiler

#### 2.1.3. P2G Device

#### 2.1.4. Energy Storage Devices

- Electricity storage devices

- 2.
- Heat storage devices

- 3.
- Gas storage devices

#### 2.1.5. Electric Vehicles

#### 2.2. Uncertainty Modeling

#### 2.2.1. Stochastic Modeling of Renewable Energy Generation

#### Wind Power Generation

#### Solar Power Generation

#### 2.2.2. Time-Varying Load Forecasting

- Input and output vectors are determined according to the specified heat and gas load.
- Construct a BP neural network model according to the input and output vectors.
- Commence network training for the BP neural network.
- Input test samples to conduct a network test on the trained BP neural network, and judge whether the error between the predicted value and the actual value is less than the set threshold. If so, perform Step 5.
- Obtain the required load prediction according to the predicted values.

#### 2.3. Time-Varying Load and Cost Model

## 3. Reliability Optimization Problem Formulation

#### 3.1. Reliability Indicator

#### 3.2. Economic Indicator

#### 3.3. Objective Functions

- Objective 1: Minimize the reliability index, SAIDI.

- 2.
- Objective 2: Minimize the interruption cost and storage device investment cost.

#### 3.4. Constraints

#### 3.4.1. Energy Balance Constraints

#### 3.4.2. Energy Storage Devices Constraints

#### 3.4.3. PV and Wind Turbine Constraints

#### 3.5. Normalization of Objective Functions

#### 3.6. Problem Formulation

#### 3.7. Multi-Objective Optimization Algorithms

- Step 1:
- Initialize population, generation size, the upper and lower boundary of decision variables (the placement of each particle should not exceed its energy network total buses), and simulation times.
- Step 2:
- Evaluate the objective functions using Monte Carlo simulation and store the non-dominated solutions in the repository.
- Step 3:
- Update the non-dominated solution.
- Step 4:
- Stop if the adaptive stop criterion and the maximum number of generations have been achieved; otherwise, proceed to step 2.
- Step 5:
- Obtain optimal solutions: optimal storage devices placement schemes and objective functions results.

## 4. Case Study

#### 4.1. Simulation Parameters

^{®}Core™ i5-7200 2.5 GHz CPU and 8 GB RAM. The simulation period for the MCS reliability evaluation is set as 20 years with a time step of one hour, with 100 MCS runs at each iteration to obtain reasonable results. The parameters for the Weibull distribution and beta distribution in the uncertainty modeling of a wind farm and PV are shown in Table 1 and Table 2, respectively [33].

#### 4.2. Simulation Results

^{5}× 1000 and achieves a SAIDI value of 0.0585, given in the number one case for NSGA-II, whereas MOPSO costs USD 2.1029 × 10

^{5}× 1000 and achieves the lowest SAIDI value of 0.0867, and SPEA2 costs USD 1.6200 × 10

^{5}× 1000 and achieves the lowest SAIDI value of 0.0673. From the three tables, it is not difficult to find out that SPEA2 outperformed MOPSO, but underperformed NSGA-II. However, it should be pointed out that higher reliability does not mean more storage devices, for MES reliability would relate to both storage device placement and the system interruption costs, and the second set of data has 41 storage devices while the fourth set of data has 49 storage devices in NSGA-II results, which can reflect this point of view. Table 10 compares the computational times of these three algorithms. It can be seen that NSGA-II and SPEA2 are faster than MOPSO.

## 5. Conclusions and Future Work

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

MES | Multi-energy system |

MCS | Monte Carlo simulation |

NSGA-II | Non-dominated sorting genetic algorithm II |

MOPSO | Multiple objective particle swarm optimization |

SPEA2 | Strength Pareto evolution algorithm 2 |

MOEA | Multi-objective evolutionary algorithm |

CHP | Combined heat and power |

P2G | Power to gas |

GB | Gas boiler |

PG | Power grid |

HN | Heat network |

GN | Gas network |

CCHP | Combined cooling, heat, and power |

V2G | Vehicle to grid |

FMEA | Failure mode and effect analysis |

ES | Electricity storage |

HS | Heat storage |

GS | Gas storage |

TVCM | Time-varying cost model |

CDF | Customer damage function |

SAIFI | System average interruption frequency index |

SAIDI | System average interruption duration index |

CAIDI | Customer average interruption duration index |

ASAI | Average service availability index |

EENS | Expected energy not supplied |

TTF | Time to failure |

TTR | Time to repair |

TTS | Time to switch |

## Appendix A

**Table A1.**An IEEE 39 bus system load and customer data [45].

Load Points | Average Load Level (MW) | Customer Type | Number of Customers |
---|---|---|---|

1 | 97.6 | 7 | 200 |

3 | 322 | 7 | 322 |

4 | 500 | 4 | 500 |

7 | 233.8 | 5 | 200 |

8 | 522 | 6 | 500 |

9 | 6.5 | 7 | 132 |

12 | 8.53 | 3 | 23 |

15 | 320 | 4 | 320 |

16 | 329 | 6 | 330 |

18 | 158 | 3 | 160 |

20 | 680 | 2 | 680 |

21 | 274 | 6 | 270 |

23 | 247.5 | 7 | 240 |

24 | 308.6 | 7 | 300 |

25 | 224 | 7 | 220 |

26 | 139 | 7 | 140 |

27 | 281 | 7 | 280 |

28 | 206 | 7 | 200 |

29 | 283.5 | 7 | 280 |

31 | 9.2 | 1 | 60 |

39 | 522 | 6 | 1000 |

**Table A2.**A 32-node heat network load and customer data [46].

Load Points | Average Load Level (MW) | Customer Type | Number of Customers |
---|---|---|---|

3 | 0.107 | 1 | 110 |

4 | 0.145 | 3 | 150 |

6 | 0.107 | 4 | 110 |

7 | 0.107 | 5 | 110 |

8 | 0.107 | 6 | 110 |

9 | 0.107 | 3 | 110 |

10 | 0.107 | 1 | 110 |

11 | 0.145 | 6 | 150 |

12 | 0.107 | 7 | 110 |

14 | 0.0805 | 7 | 80 |

16 | 0.0805 | 7 | 80 |

17 | 0.0805 | 7 | 80 |

18 | 0.0805 | 7 | 80 |

20 | 0.0805 | 7 | 80 |

21 | 0.0805 | 7 | 80 |

23 | 0.107 | 2 | 110 |

24 | 0.107 | 4 | 110 |

26 | 0.107 | 6 | 110 |

27 | 0.107 | 7 | 110 |

29 | 0.107 | 3 | 110 |

30 | 0.107 | 7 | 110 |

**Table A3.**A 20-node Belgian natural gas system load and customer data [47].

Load Points | Average Load Level (Mm^{3}/day) | Customer Type | Number of Customers |
---|---|---|---|

3 | 5.88 | 1 | 60 |

6 | 6.05 | 5 | 61 |

7 | 7.88 | 3 | 80 |

10 | 9.55 | 4 | 100 |

12 | 0.775 | 7 | 80 |

15 | 10.27 | 2 | 105 |

16 | 23.42 | 6 | 240 |

19 | 0.33 | 7 | 30 |

20 | 0.775 | 7 | 80 |

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**Figure 2.**Variation curve of wind farm output power with wind speed [36].

**Figure 6.**BP neural network load forecasting for: (

**a**) IEEE 39 bus system; (

**b**) 32-node heat network; (

**c**) 20-node natural gas network.

Weibull Distribution Parameters | k | c (m/s) | V_{ci} (m/s) | V_{r} (m/s) | V_{co} (m/s) | P_{r} (MW) |
---|---|---|---|---|---|---|

Value | 1.5 | 5 | 3 | 13 | 25 | 1000 |

Beta Distribution Parameters | α | β | A(m^{2}) | r_{max} (MW/m^{2}) | η | baseMVA |
---|---|---|---|---|---|---|

Value | 0.6869 | 2.132 | 70 | 100 | 0.14 | 100 |

BP Neural Network | Parameters Setting |
---|---|

Number of network layers | Input layer: 1; Hidden layer: 1; Output layer: 1 |

Number of neurons in each layer | Input layer: 4; Hidden layer: 9; Output layer: 1 |

Maximum number of iterations | 5000 |

Training target error | 0.2 |

Initial value of training learning rate | 0.1 |

Component | Cinstall_{i} | Capacity for MES |
---|---|---|

ES | 187 USD/MWh | 600 MWh |

HS | 6.05 USD/MWh | 0.5 MWh |

GS | 3.665 USD/MMBtu | 10 Mm^{3} |

Component | Capacity (MW) |
---|---|

PV | 100 |

WT | 500 |

GT | 120 |

MOPSO | NSGA-II | SPEA2 |
---|---|---|

Population size = 100 | Population size = 50 | Population size = 50 |

Generations = 200 | Generations = 200 | Generations = 200 |

Repository size =100 | Archive size = 50 | Archive size = 50 |

${c}_{1}$= 1.8 | Crossover rate = 0.7 | Crossover rate = 0.7 |

${c}_{2}$ = 2 | Mutation rate = 0.01 | Mutation rate = 0.01 |

w = 0.7 | ||

${\omega}_{damp}$ = 0.9 |

NSGA-II | Storage Device Optimal Location | Obj_{1}–SAIDI (h/Ca) | Obj_{2}–Cost (USD 1000) | ||
---|---|---|---|---|---|

Power Grid | Heat Network | Gas Network | |||

1 | Bus 1, 3, 6, 7, 12, 13, 15, 18, 19, 20, 21, 22, 25, 28, 29, 30, 31, 32, 35, 37, 39 | Bus 1, 2, 4, 5, 14, 15 | Bus 1, 2, 3, 5, 6, 7, 9, 10, 12, 13 | 0.0585 | 1.5028 × 10^{5} |

2 | Bus 1, 3, 4, 6, 7, 12, 13, 16, 18, 19, 20, 21, 22, 25, 28, 29, 30, 31, 32, 35, 37, 39 | Bus 1, 2, 4, 9, 12, 15 | Bus 2, 3, 5, 6, 7, 9, 10, 11, 12, 13, 15, 16, 19 | 0.0702 | 1.4132 × 10^{5} |

3 | Bus 1, 3, 4, 6, 7, 12, 13, 16, 18, 20, 21, 22, 25, 28, 29, 30, 31, 32, 35, 37, 39 | Bus 1, 3, 8, 14, 21 | Bus 2, 3, 5, 6, 7, 9, 10, 11, 12, 13, 15, 16, 19 | 0.0808 | 1.2859 × 10^{5} |

4 | Bus 1, 2, 3, 4, 5, 6, 7, 12, 13, 16, 18, 19, 20, 21, 22, 24, 25, 28, 29, 30, 31, 32, 35, 37, 39 | Bus 3, 11, 12, 13, 14, 17, 18, 21, 22, 23, 24 | Bus 2, 3, 5, 6, 7, 9, 10, 11, 12, 13, 15, 16, 19 | 0.0814 | 1.2354 × 10^{5} |

5 | Bus 1, 3, 4, 5, 6, 7, 12, 13, 18, 19, 20 21, 22, 25, 28, 29, 30, 31, 32, 35, 37, 39 | Bus 2, 3, 4, 5, 6, 10, 11, 20 | Bus 2, 3, 5, 6, 7, 9, 10, 11, 12, 13, 15, 16, 19 | 0.0944 | 1.1417 × 10^{5} |

6 | Bus 1, 2, 3, 4, 5, 6, 7, 12, 13, 14, 16, 18, 20 21, 22, 25, 28, 29, 30, 31, 32, 34, 37, 39 | Bus 2, 3, 4, 5, 6, 10, 11, 20 | Bus 2, 3, 5, 6, 7, 9, 10, 11, 12, 13, 16, 19 | 0.1167 | 1.0826 × 10^{5} |

7 | Bus 1, 2, 4, 6, 7, 12, 13, 16, 18, 19, 20, 21, 22, 25, 28, 29, 30, 31, 32, 34, 37, 39 | Bus 4 | Bus 2, 3, 5, 6, 7, 9, 10, 11, 12, 13, 15, 16, 19 | 0.1728 | 1.0461 × 10^{5} |

8 | Bus 1, 4, 5, 6, 7, 11, 12, 13, 16, 18, 19, 20, 22, 25, 28, 29, 30, 31, 32, 35, 37, 39 | Bus 5 | Bus 2, 3, 5, 6, 7, 9, 10, 11, 12, 13, 15, 16, 19 | 0.1765 | 1.0419 × 10^{5} |

MOPSO | Storage Device Optimal Location | Obj_{1}–SAIDI (h/Ca) | Obj_{2}–Cost (USD 1000) | ||
---|---|---|---|---|---|

Power Grid | Heat Network | Gas Network | |||

1 | Bus 1, 4, 5, 7, 11, 12, 14, 16, 17, 18, 19, 20, 23, 24, 25, 29, 30, 31, 34, 35, 37, 38 | Bus 2, 5, 7, 8, 9, 10, 12, 16, 17, 18, 20, 22, 23, 24, 25, 27, 28, 30, 31 | Bus 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 18, 19 | 0.0867 | 2.1029 × 10^{5} |

2 | Bus 2, 3, 4, 7, 8, 11, 16, 17, 18, 22, 23, 24, 25, 26, 27, 28, 31, 38, 39 | Bus 1, 2, 3, 4, 6, 7, 10, 12, 13, 14, 15, 16, 20, 21, 22, 23, 24, 26, 31 | Bus 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 14 | 0.1054 | 1.8381 × 10^{5} |

3 | Bus 1, 3, 5, 6, 8, 10, 11, 13, 14, 15, 16, 17, 19, 20, 21, 22, 26, 27, 28, 30, 31, 33, 36, 39 | Bus 1, 2, 3, 4, 6, 8, 10, 11, 13, 14, 15, 16, 18, 20, 22, 23, 24, 25, 26, 27, 29, 30, 32 | Bus 1, 2, 4, 6, 7, 8, 10, 12, 13, 16, 18 | 0.1371 | 1.7001 × 10^{5} |

4 | Bus 1, 2, 3, 4, 5, 6, 9, 16, 17, 19, 20, 22, 27, 28, 29, 30, 35, 36 | Bus 2, 3, 4, 5, 7, 9, 12, 13, 15, 16, 17, 18, 20, 23, 25, 26 | Bus 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 15 | 0.1999 | 1.3435 × 10^{5} |

5 | Bus 3, 4, 5, 7, 8, 9, 14, 19, 22, 30, 31 | Bus 1, 2, 3, 4, 7, 8, 9, 12, 14, 19, 20, 29 | Bus 3, 4, 6, 7, 9, 10, 15 | 0.2417 | 1.3032 × 10^{5} |

6 | Bus 1, 2, 4, 8, 10, 11, 12, 13, 14, 16, 17, 19, 26, 27, 28, 35 | Bus 3, 4, 5, 6, 8, 9, 11, 13, 14, 16, 17, 18, 23, 24, 25, 29 | Bus 2, 3, 4, 6, 7, 8, 10, 11, 12, 15, 19 | 0.4941 | 1.2588 × 10^{5} |

SPEA2 | Storage Device Optimal Location | Obj_{1}–SAIDI (h/Ca) | Obj_{2}–Cost (USD 1000) | ||
---|---|---|---|---|---|

Power Grid | Heat Network | Gas Network | |||

1 | Bus 1, 3, 4, 5, 6, 8, 9, 11, 14, 16, 17, 19, 22, 24, 28, 29, 31, 34 | Bus 1, 2, 3, 5, 6, 7, 9, 10, 11, 12, 14, 15, 16, 20, 21, 23, 25, 26 | Bus 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 14, 15, 19 | 0.0673 | 1.6200 × 10^{5} |

2 | Bus 2, 3, 4, 5, 6, 8, 9, 11, 14, 16, 17, 19, 22, 24, 28, 29, 31, 34 | Bus 1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 15, 16, 20, 21, 23, 25, 26 | Bus 1, 3, 4, 5, 6, 7, 8, 10, 11, 12, 14, 15, 19 | 0.0823 | 1.3749 × 10^{5} |

3 | Bus 2, 3, 4, 5, 6, 8, 9, 10, 11, 14, 17, 19, 25, 28, 30, 36, 38 | Bus 1, 2, 3, 4, 5, 7, 8, 12, 13, 14, 15, 16, 18, 20, 29 | Bus 1, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 16 | 0.0895 | 1.2237 × 10^{5} |

4 | Bus 1, 3, 6, 7, 9, 10, 12, 14, 17, 18, 23, 24, 28, 32 | Bus 1, 2, 3, 5, 6, 10, 12, 15, 18, 21, 22, 24 | Bus 1, 3, 4, 5, 6, 7, 10, 11, 12, 18, 19 | 0.1825 | 1.2120 × 10^{5} |

5 | Bus 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 15, 18, 22, 29, 30 | Bus 1, 2, 3, 4, 6, 7, 10, 16, 17, 20, 26, 28 | Bus 2, 3, 4, 5, 6, 7, 10, 13, 14, 18 | 0.2766 | 1.2066 × 10^{5} |

6 | Bus 1, 2, 4, 5, 6, 7, 8, 9, 10, 14, 16, 17, 21, 25, 32, 33, 37, 39 | Bus 2, 3, 4, 5, 7, 8, 9, 13, 17, 22, 29 | Bus 3, 6, 7, 8, 9, 10, 11, 12, 15, 17, 24, 30 | 0.3000 | 1.1218 × 10^{5} |

7 | Bus 1, 3, 4, 7, 8, 9, 10, 11, 12, 14, 18, 19, 24, 26, 28, 30, 33, 36, 39 | Bus 1, 4, 6, 8, 9, 11, 13, 15, 16, 18, 21, 23, 26, 27 | Bus 1, 3, 4, 5, 6, 7, 8, 10, 11, 12, 18, 20 | 0.4280 | 1.0934 × 10^{5} |

Optimization Algorithm | Execution Time (min) |
---|---|

NSGA-II | 288.67 |

MOPSO | 876.92 |

SPEA2 | 283.34 |

Reliability Indices | Before Optimization | After Optimization |
---|---|---|

SAIFI (1/Ca) | 0.1980 | 0.2641 |

SAIDI (h/Ca) | 1.4945 | 0.0585 |

CAIDI (h/Ca) | 7.5480 | 0.0600 |

ASAI | 0.9998 | 0.9999 |

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**MDPI and ACS Style**

Liao, Z.; Parisio, A.
Reliability Optimization of Multi-Energy System Considering Energy Storage Devices Effects under Weather Uncertainties. *Energies* **2022**, *15*, 696.
https://doi.org/10.3390/en15030696

**AMA Style**

Liao Z, Parisio A.
Reliability Optimization of Multi-Energy System Considering Energy Storage Devices Effects under Weather Uncertainties. *Energies*. 2022; 15(3):696.
https://doi.org/10.3390/en15030696

**Chicago/Turabian Style**

Liao, Ziyan, and Alessandra Parisio.
2022. "Reliability Optimization of Multi-Energy System Considering Energy Storage Devices Effects under Weather Uncertainties" *Energies* 15, no. 3: 696.
https://doi.org/10.3390/en15030696