# Resilience-Oriented Optimal Operation Strategy of Active Distribution Network

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## Abstract

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## 1. Introduction

- Among the existing similar research, there is no optimal operational strategy applied in power systems that takes resilience, economy, and environmental protection all into account, and act as objective functions. In particular, the proposed strategy can notably enhance resilience without significantly increasing the operational costs and pollutant emissions.
- In the proposed multi-objective optimal problem, NSGA-II is applied to investigate the solution which has an extremely low CPU time. This paper presents the Pareto optimal fronts to illustrate the optimization results.
- The optimal strategy proposed in this paper can be widely used in different DER-integrated power systems, such as microgrid, etc.

## 2. Methods and Model

#### 2.1. DER Integrated ADN Operation Model

#### 2.2. Resilience-Oriented Robust Optimal Model

#### 2.2.1. Resilience Definition and Metric

_{L}(t) in Figure 2 represents the power function of the total load remaining in the DG, that has been studied in this paper. The system operates in its original state at time t

_{o}, then an unpredicted incident occurs at time t

_{i}and lasts until time t

_{d}, when the functionality is considered to be entirely lost. Thus, the system operates in the disrupted state from time t

_{e}to time t

_{d}, where the total loads remained reach to the minimum. The recovery/resilient action triggers at time t

_{r}. Finally, as a result of the resilient action, the system recovers to the final state with power function value P

_{L}(t

_{f}) at time t

_{f}.

#### 2.2.2. Economical Index

#### 2.2.3. Environmental Index

_{2}emission can be employed as an example and represent the pollutant degree in this paper. Based on the above analysis, the total CO

_{2}emission can be calculated as (3) [9]. Where ${F}_{g,t}$ is the amount of fuel consumed by traditional generation units, ${\omega}_{f}$ is the CO

_{2}emission coefficient of fuel consumption.

#### 2.2.4. Robust Optimal Objectives Considering the Uncertainty

#### 2.2.5. Constraints

_{es,t}represents the state of charge of ESS showed in (19) [22] and must be restricted by the specific limit in (20) [22].

#### 2.3. Robust Solution Methodology

#### 2.3.1. Min-Max Problem Decoupling based on BD

_{1}is constructed in (22).

_{1}is added to the constraints to ensure the set of DVs can satisfy the constraints in the optimization model with arbitrary values of UVs:

#### 2.3.2. Multi-Objective Problem Solving based on NSGA-II

^{2}) computational complexity. A selection operator exists in NSGA-II to create a mating pool by making a combination of parents and offspring populations and select the best N solution. From the amount of simulation results on a number of different test problems, which were made by many researchers, such as Kalyanmoy Deb, NSGA-II outperforms other EAs in terms of finding much better spread of solutions, as well as better convergence near the true Pareto-optimal front.

## 3. Results and Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

Indices: | |

i | Index for loads. |

p | Index for PV panels. |

w | Index for WTs. |

g | Index for Gs. |

es | Index for ESSs. |

t | Index for time. |

Sets: | |

PV | Set of PV panels. |

WT | Set of WTs. |

G | Set of Gs. |

ESS | Set of electrical storage stations. |

U | Set of uncontrollable sources. |

X | Set of dispatchable variables. |

L | Set of load. |

Constants: | |

${\omega}_{f}$ | CO_{2} emission coefficient of the fuel. |

${P}_{i}^{L}$ | Nominal value of the load. |

${\widehat{P}}_{i}^{L}$ | Maximal fluctuation of the load. |

${P}_{p}^{\mathrm{PV}}$ | PV nominal output power. |

${\widehat{P}}_{p}^{\mathrm{PV}}$ | PV output power maximal fluctuation. |

${P}_{w}^{\mathrm{WT}}$ | WT nominal output power. |

${\widehat{P}}_{w}^{\mathrm{WT}}$ | WT output power maximal fluctuation. |

${P}_{g}^{\mathrm{min}},{P}_{g}^{\mathrm{max}}$ | G minimal/maximal output power |

$\mathsf{\Delta}{P}_{g}^{RD},\mathsf{\Delta}{P}_{g}^{RU}$ | MT ramp down/ramp up power. |

${P}_{es}^{ch,\mathrm{min}},{P}_{es}^{ch,\mathrm{max}}$ | ESS minimal/maximal charging power. |

${P}_{es}^{dch,\mathrm{min}},{P}_{es}^{dch,\mathrm{max}}$ | ESS minimal/maximal discharging power. |

Variables: | |

$R(t)$ | Resilience of the DER integrated ADN. |

$C(t)$ | Total cost of the DER integrated ADN. |

$\mathrm{C}{\mathrm{O}}_{2}(t)$ | Total CO_{2} emission. |

${P}_{es}^{}$ | ESS charging/discharging power. |

${\tilde{P}}_{p}^{\mathrm{PV}}$ | PV panel actual output power. |

${\tilde{P}}_{w}^{\mathrm{WT}}$ | WT actual output power. |

${P}_{m}$ | MT output power. |

${Q}_{es}$ | ESS stored energy. |

${I}_{es}^{dch},{I}_{es}^{ch}$ | Discharging and charging statues of ESS. |

$SO{C}_{es,t}$ | State of charge of ESS |

${F}_{g}$ | The amount of fuel consumed byG. |

${P}_{L}$ | Total power supply for loads. |

${C}_{}^{SU},{C}_{}^{SD}$ | Startup/shutdown cost. |

${C}^{ch},{C}^{dch}$ | Charge/discharge cost. |

${C}^{\mathrm{G}}(\cdot )$ | Generation cost. |

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**Figure 1.**Two-stage controlled distributed energy resources (DER) integrated active distribution network (ADN) model.

**Figure 5.**(

**a**) The fluctuated curve of photovoltaic (PV) on Node-4; (

**b**) The fluctuated curve of wind turbines (WT) on Node-7; (

**c**) The fluctuated curve of total electric load demand.

**Figure 8.**(

**a**) The relationship between resilience and cost based on the cross-section of the Pareto surface; (

**b**) the relationship between resilience and pollutant emission based on the cross-section of the Pareto surface.

Node Number | Generation Type | Rated Capacity |
---|---|---|

4 | PV | 1.8 MW |

5 | ESS | 1.5 MW·h |

7 | WT | 3.5 MW |

9 | ESS | 1.5 MW·h |

10 | G | 3 MW |

11 | PV | 1.25 MW |

12 | ESS | 1.5 MW·h |

14 | G | 3 MW |

15 | G | 3 MW |

16 | WT | 3 MW |

19 | ESS | 1.5 MW·h |

20 | ESS | 1.5 MW·h |

22 | PV | 2 MW |

24 | WT | 4.5 MW |

26 | WT | 2.5 MW |

27 | PV | 1.5 MW |

29 | G | 3 MW |

31 | WT | 3.5 MW |

32 | G | 3 MW |

34 | ESS | 2MW·h |

G | ESS |
---|---|

${P}_{G}^{\mathrm{min}}=0.3\mathrm{MW}$ | ${P}_{es}^{ch,\mathrm{min}}=0.25\mathrm{MW}$ |

${P}_{G}^{\mathrm{max}}=3\mathrm{MW}$ | ${P}_{es}^{ch,\mathrm{max}}=1.5\mathrm{MW}$ |

$\mathsf{\Delta}{P}_{g}^{RD}=0.6\mathrm{MW}/\mathrm{h}$ | ${P}_{es}^{dch,\mathrm{min}}=0.25\mathrm{MW}$ |

$\mathsf{\Delta}{P}_{g}^{RU}=0.9\mathrm{MW}/\mathrm{h}$ | ${P}_{es}^{dch,\mathrm{max}}=1.5\mathrm{MW}$ |

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**MDPI and ACS Style**

Wang, J.; Zheng, X.; Tai, N.; Wei, W.; Li, L.
Resilience-Oriented Optimal Operation Strategy of Active Distribution Network. *Energies* **2019**, *12*, 3380.
https://doi.org/10.3390/en12173380

**AMA Style**

Wang J, Zheng X, Tai N, Wei W, Li L.
Resilience-Oriented Optimal Operation Strategy of Active Distribution Network. *Energies*. 2019; 12(17):3380.
https://doi.org/10.3390/en12173380

**Chicago/Turabian Style**

Wang, Jun, Xiaodong Zheng, Nengling Tai, Wei Wei, and Lingfang Li.
2019. "Resilience-Oriented Optimal Operation Strategy of Active Distribution Network" *Energies* 12, no. 17: 3380.
https://doi.org/10.3390/en12173380