# A Metaheuristic-Based Micro-Grid Sizing Model with Integrated Arbitrage-Aware Multi-Day Battery Dispatching

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

#### 1.1. Background and Motivation

#### 1.2. Literature Review

#### 1.3. Knowledge Gaps

#### 1.4. Novel Contributions

- Formulating a robust metaheuristic-based MG equipment capacity planning optimisation model tailored towards community-scale, 100%-renewable and -reliable energy projects.
- Developing an arbitrage-aware, dynamic, look-ahead, predictive dispatch strategy for the optimal scheduling of MGs—charging/discharging of energy storage systems and energy exchanges with the main power grid—over a moving 72-h dispatch horizon.
- Nesting the developed forward-looking operational planning problem—formulated to optimally respond to the dynamic nature of system conditions over a moving three-day period—within the proposed metaheuristic-based MG sizing model to jointly optimise the design and dispatch of MG systems.

#### 1.5. Paper Organisation

## 2. Test-Case Micro-Grid

#### 2.1. Wind Turbines

#### 2.2. PV Panels

^{2}) at time-step $t$, $DF$ is the degradation rate, ${A}_{S}$ is the panel’s surface area (m

^{2}), ${\eta}_{r}$ denotes the panel’s efficiency, ${\eta}_{pc}$ is the built-in inverter’s efficiency, $\mu $ denotes the PV temperature coefficient of power (%/°C), ${T}_{c,ref}$ denotes the reference cell temperature (°C), ${T}_{c}\left(t\right)$ is the effective cell temperature (°C), $NOCT$ represents the nominal operating cell temperature (°C), whereas ${T}_{a,NOCT}$ and ${G}_{T,NOCT}$, respectively, denote the ambient temperature (°C) and solar irradiance (W/m

^{2}) at nominal operating cell conditions.

#### 2.3. Battery Storage

#### 2.4. Inverter

## 3. Methodology

#### 3.1. Targeted Arbitrage Opportunities

#### 3.2. Optimal Capacity Planning Problem

#### Metaheuristic Optimisation Algorithm

#### 3.3. Multi-Day Energy Dispatch Scheduling Problem

**,**respectively, denote the 72-h column vectors of operational cost (expenditure), imported power, exported power, spot prices, and feed-in tariffs, $\Delta t$ represents the length of each time-step (1 h), whereas the term ${10}^{-6}{\Vert \mathit{u}\Vert}_{1}$ is a penalty factor, which ensures that the battery bank does not undergo any uneconomic cycles. Specifically, the penalty term can be calculated as follows:

#### 3.4. Overview of the Overall Method

## 4. Case Study: Simulation Results and Discussion

#### 4.1. Input Data

#### 4.2. Comparative Optimal MG Sizing Results

#### 4.3. Economics of Daily Energy Arbitrage

#### Impact on the Optimal MG Sizing

#### 4.4. Validation of the Equilibrium Optimiser

## 5. Conclusions and Future Work

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Illustration of the power output–wind speed characteristics of a WT (adapted with permission from Ref. [28]. 2019, Elsevier).

**Figure 3.**Illustration of the three-point rainflow-cycle-counting algorithm in battery storage applications (adapted with permission from Ref. [33]. 2020, Elsevier).

**Figure 4.**Illustration of the general updating rule of the EO (adapted with permission from Ref. [41]. 2020, Elsevier).

**Figure 5.**Illustration of the collaboration of the equilibrium candidates in a representative 2D solution space (adapted with permission from Ref. [41]. 2020, Elsevier).

**Figure 7.**Flowchart of the metaheuristic-based MG sizing modelling framework with co-optimised dispatch decisions.

**Figure 8.**Totarabank Subdivision: (

**a**) location on a New Zealand map; and (

**b**) satellite photograph with the location of premises overlaid (Satellite image courtesy of Google Maps).

**Figure 9.**Monthly-averaged 24-h daily profiles for: (

**a**) power loads; (

**b**) solar radiation; (

**c**) temperature; (

**d**) wind speed; and (

**e**) spot electricity price.

**Figure 10.**Summary statistics of the hourly variations of the battery SOC for the system optimised under the multi-day dispatch strategy.

**Figure 11.**Monthly mean daily profiles for the energy content of the battery bank with and without a nested scheduling optimisation framework.

**Figure 12.**Sensitivity of the total arbitrage trade with respect to changes in the buyback rate and the capital cost of the battery energy storage system.

Reference | Components | Real Input Data | Two-Stage Modelling | Arbitrage | Multi-Day Rolling Horizon | ||||
---|---|---|---|---|---|---|---|---|---|

Grid | PV | WT | BESS | Diesel | |||||

[12] | × | ✓ | × | ✓ | × | × | ✓ | × | × |

[13] | ✓ | ✓ | × | ✓ | × | ✓ | × | × | × |

[14] | ✓ | ✓ | ✓ | ✓ | × | × | × | × | × |

[15] | ✓ | ✓ | × | ✓ | ✓ | × | ✓ | × | × |

[16] | ✓ | ✓ | ✓ | ✓ | × | × | × | × | × |

[17] | × | ✓ | × | ✓ | ✓ | ✓ | ✓ | × | × |

[18] | × | ✓ | ✓ | ✓ | ✓ | ✓ | × | × | × |

[19] | × | ✓ | × | ✓ | × | ✓ | ✓ | × | × |

[20] | × | ✓ | × | ✓ | ✓ | ✓ | × | × | × |

[21] | × | ✓ | × | ✓ | × | ✓ | × | × | × |

[22] | × | ✓ | ✓ | ✓ | × | × | × | × | × |

[23] | × | ✓ | ✓ | ✓ | × | ✓ | × | × | × |

[24] | ✓ | ✓ | × | ✓ | × | ✓ | × | × | × |

[25] | × | ✓ | ✓ | ✓ | × | × | × | × | × |

This study | ✓ | ✓ | ✓ | ✓ | × | ✓ | ✓ | ✓ | ✓ |

Component | Capital Cost | Replacement Cost | Operation and Maintenance Cost | Lifetime | Efficiency | Source(s) |
---|---|---|---|---|---|---|

PV panel | NZD 1135/kW | NZD 915/kW | NZD 5/kW/year | 25 years | 17.11% | [5,47,48] |

Wind turbine | NZD 1290/kW | NZD 1020/kW | NZD 191/kW/year | 25 years | N/A ^{a} | [49,50,51] |

Battery pack ^{b} | NZD 1073/kWh | NZD 504/kWh | NZD 2.1/kWh/year | 15 years | 90% ^{c} | [52,53] |

Hybrid inverter | NZD 533/kW | NZD 533/kW | NZD 1.3/kW/year | 15 years | 96% | [54,55] |

^{a}Not applicable, as the WT generator’s power output is estimated based on the associated power (characteristic) curve.

^{b}Charge/discharge power capacity of the battery pack is equal to 3 kW and its energy throughput equals 3.03 MWh.

^{c}Round-trip efficiency.

**Table 3.**Comparative MG sizing results optimised under the multi-day (proposed), one-day, and cycle-charging dispatch strategies.

Output | Dispatch Strategy | ||
---|---|---|---|

Multi-Day Scheduling | One-Day Scheduling | Cycle-Charging | |

Total net present cost [NZD] | 55,175 | 60,244 | 69,466 |

Levelised cost of energy [NZD/kWh] | 0.19 | 0.22 | 0.27 |

Total discounted renewable energy generation [kWh] | 1,248,446 | 1,773,003 | 2,754,411 |

Solar PV generator size [kW] | 8 | 10 | 16 |

WT generator size [kW] | 11 | 17 | 20 |

Li-ion battery storage size [kWh] | 31 | 19 | 12 |

Multi-mode inverter size [kW] | 7 | 8 | 9 |

TNPC of the components [NZD] | 99,581 | 86,383 | 84,610 |

Total net energy purchased [kWh] | −249,471 | −175,170 | −302,882 |

TNPC of the net electricity imports [NZD] | −44,406 | −26,139 | −15,144 |

Total excess renewable energy curtailment [kWh] | 1509 | 11,738 | 19,121 |

Battery bank autonomy ^{a} [h] | 11.2 | 7.1 | 4.5 |

^{a}Defined as the ratio of the optimal size of storage to the mean total annual load, battery bank autonomy represents the number of hours the battery bank alone would be able to meet the local loads over a year-long operation of the system [36].

**Table 4.**Comparative modelling results under the existing situation, realistic projection case, and the extreme case scenarios.

Output | Scenario | ||
---|---|---|---|

Existing Situation (Status Quo) ^{a} | Realistic Projection | Extreme-Case Projection | |

Total net present cost [NZD] | 50,148 | 26,270 | 15,142 |

Total net energy arbitrage trade profit [NZDm] | 0.09 | 0.11 | 0.13 |

Optimal battery bank size [kWh] | 30 | 48 | 51 |

Optimal multi-mode inverter size [kW] | 7 | 12 | 15 |

^{a}The small changes in the model outputs relative to the base-case planning and scheduling co-optimisation results are attributable to the down-sampled input data, as well as deactivating the MG system’s access to the wholesale spot market through a financially responsible market participant, and therefore, considering a fixed feed-in tariff.

Algorithm | Parameter Settings | Reference |
---|---|---|

GA | Mutation rate = 0.05, crossover probability = 0.1, mutation probability = 0.9 | [60] |

PSO | Acceleration coefficients = 2, inertia weight = 0.7 | [61] |

Hybrid GA-PSO | Mutation rate = 0.05, crossover probability = 0.1, mutation probability = 0.9, acceleration coefficients = 2, inertia weight = 0.7 | [62] |

EO | Coefficients of the inertia weight equation = 2.0 | [41] |

HS | Harmony memory accepting rate = 0.85 | [63] |

SA | Initial acceptance probability = 0.4, cooling ratio = 0.95, size factor = 16, imbalance factor = 0.05 | [64] |

ABC | Number of onlooker bees = 25, number of employed bees = 25 | [65] |

ACO | Archive size = 50, locality of search = 0.1, convergence speed = 0.85 | [66] |

ALO | Self-adaptive adjustment of a single control parameter | [67] |

Algorithm | Optimised TNPC | Algorithm | Optimised TNPC |
---|---|---|---|

ABC | NZD 61,410 | HS | NZD 63,992 |

ACO | NZD 64,739 | Hybrid GA-PSO | NZD 56,120 |

ALO | NZD 63,005 | PSO | NZD 56,802 |

EO | NZD 55,175 | SA | NZD 62,790 |

GA | NZD 56,790 |

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**MDPI and ACS Style**

Mohseni, S.; Brent, A.C.
A Metaheuristic-Based Micro-Grid Sizing Model with Integrated Arbitrage-Aware Multi-Day Battery Dispatching. *Sustainability* **2022**, *14*, 12941.
https://doi.org/10.3390/su141912941

**AMA Style**

Mohseni S, Brent AC.
A Metaheuristic-Based Micro-Grid Sizing Model with Integrated Arbitrage-Aware Multi-Day Battery Dispatching. *Sustainability*. 2022; 14(19):12941.
https://doi.org/10.3390/su141912941

**Chicago/Turabian Style**

Mohseni, Soheil, and Alan C. Brent.
2022. "A Metaheuristic-Based Micro-Grid Sizing Model with Integrated Arbitrage-Aware Multi-Day Battery Dispatching" *Sustainability* 14, no. 19: 12941.
https://doi.org/10.3390/su141912941