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Off-Grid Multi-Carrier Microgrid Design Optimisation: The Case of Rakiura–Stewart Island, Aotearoa–New Zealand^{ †}

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## Abstract

**:**

## 1. Introduction

#### 1.1. Literature Review and Knowledge Gaps

- A narrow focus on state-of-the-art meta-heuristic-based optimisation algorithms applied to the MECM equipment capacity planning problem;
- General absence of configurations addressing the electricity, space heating, water heating, and e-mobility demands simultaneously, and more particularly, paucity of MECM systems tailored to off-grid applications;
- Negligence of transient power supplies necessary for the stability of MECMs; and
- Lack of multi-energy schemes where the hydrogen energy vector is directly used as a transportation fuel.

#### 1.2. Objective and Novel Contributions

- Developing a general, meta-heuristic-based solution algorithm for MECMs considering separate reliability indicators for different end-use energy carriers with associated specifically devised rule-based dispatch strategies;
- Conceptualising a fundamentally new off-grid MECM configuration driven by non-dispatchable RESs, and backed by a three-timescale energy storage system to cost-optimally meet nearly all the energy needs of remote and peripheral communities;
- Cost-optimal integration of electric double-layer super-capacitors (SCs) into MECMs, which are associated with high power densities and fast transient response, to serve the transient power load requirements and ensure the stability of such systems; and
- Cost-optimal system integration of a hydrogen refuelling station, where locally-produced green hydrogen is used as an alternative transportation fuel to power fuel cells in various zero-emission vehicles, which benefit from the fast filling time.

#### 1.3. Organisation

## 2. Methodology

#### 2.1. Objective Function

#### 2.2. Constraints

- Non-strict equality of the initial and terminal states of energy stored (terminal energy in-store greater than or equal to the initial energy in-store) in the battery bank, the SC bank, and the hydrogen reservoir over an entire representative operational horizon (8760 h); the storage devices are assumed to be half-full-charged at the beginning of simulations to avoid oversizing due to the peaks occurring early in the net load time-series data;
- The demand–supply balance of energy at each time-step of operating the MECM;
- Enforcing the states of energy stored in the SC bank, battery bank, and the hydrogen tank to lie within their pre-defined allowable limits (in percentages) at each time-step of operating the MECM;
- Enforcing the operating points of all the components to lie between zero and the associated rated capacities; and
- Adhering to the pre-specified upper bounds of the design variables (capacity of the MECM’s equipment), in compliance with the target site’s real-world, physical limitations, such as land access.

#### 2.3. Meta-Heuristic Optimisation Algorithm

#### 2.4. Overview of the Method

## 3. Test-Case Off-Grid MECM System

#### 3.1. Wind Turbines

#### 3.2. Solar PV Panels

^{2}) represent the global solar irradiance on the horizontal surface and the solar irradiance at the STC, respectively; and $NMOT$(43 °C) and $DF$ (85%) denote the nominal module operating temperature and derating factor, respectively. The tilt angle is assumed as 30°. The numeric values 20 and 0.8 represent the ambient temperature (°C) and solar irradiance (kW/m

^{2}), respectively, at which the $NMOT$ is defined.

#### 3.3. Hybrid SC/Battery System

#### 3.4. Fuel Cell

#### 3.5. Other Components

#### 3.6. Dispatch Strategy

_{4}lithium-ion battery bank, and the stationary hydrogen-based energy storage system—are considered to compensate for the mismatches in supply and demand and meet the net loads (loads minus onsite variable generation). The rationale behind the use of these components lies in their different characteristics in terms of energy and power densities [56]. Specifically, fuel cells and SCs are associated with high energy/power densities, but low power/energy densities; thus, they are best suited to address the mid-to-long-term/instantaneous mismatches in renewable power supply and electricity demand. In addition, batteries bridge the gap between the SCs and fuel cells; they are fit for the purpose of compensating for the daily to weekly fluctuations in supply–demand owing to the intermediary level of both their energy and power densities.

^{−4}Hz), $K$ represents the DC gain (1.586), and $Q=1/2\xi $ identifies the filter quality, with $\xi $ indicating the damping factor (0.707).

^{−5}Hz and 8.3331 × 10

^{−4}Hz, respectively. Expectedly, the second filter’s cut-off frequency is greater than that of the first one, as it is geared towards decomposing renewable excess/shortage signals on a finer scale.

#### 3.7. Data: Techno-Economic Specifications of the Components

#### 3.8. Case Study Site: Rakiura–Stewart Island, Aotearoa–New Zealand

#### 3.8.1. Background

_{2}. Advantageously, local residents believe that reducing the consumption of diesel and developing a renewables-based energy generation system is one of the island’s highest priorities. Collectively, these statistics and facts suggest that using renewable energy rather than fossil fuels to serve the energy needs of the community residing on the ecologically sensitive Rakiura–Stewart Island is of utmost importance [62,63,64].

#### 3.8.2. Data: Meteorological and Load Demand Forecasts

^{2}), ambient temperature (°C), and wind speed (m/s) are shown in Figure 4, Figure 5 and Figure 6, respectively.

_{2}/h) imposed on the conceptualised isolated MECM model—populated for the case of Rakiura–Stewart Island with the goal of decarbonising the transportation sector—is shown in Figure 9. The following assumptions were made in deriving the daily hydrogen load profile:

- One HFC-powered ferry, five HFC-powered heavy-freight trucks, and five HFC-powered heavy-duty tractors, which can store 208 kg, 32.9 kg, and 8.2 kg of hydrogen, respectively, in their purpose-built carbon composite tanks are considered for integration into the system. The 100-seater marine vessel serves the purpose of transporting the passengers between Rakiura–Stewart Island (at the port of Oban) and the port of Bluff (six crossings per day in summer, and four in winter, and hence, an annual average of five crossings per day), while the trucks and tractors effectively contribute towards achieving the objectives of agricultural sustainability;
- A fleet of thirty 8.5 kW HFC-powered light-duty passenger vehicles also utilise the hydrogen station to refill their 1.5 kg hydrogen tanks;
- A valley-filling energy management scheme that refuels the vessel, heavy-duty tractors, and heavy-freight trucks in the early morning hours (by uniformly distributing their hydrogen loads over the hours 1 a.m. to 6 a.m.) is adopted, while the light-duty passenger vehicles utilise the station randomly during day-time hours (from 9 a.m. to 8 p.m.), following a specifically derived normal distribution; and
- The hydrogen tanks of the light-duty passenger vehicles, heavy-duty tractors, and heavy-freight trucks need to be refuelled from 5% to 100% of their rated capacities every 3, 4, and 5 days, respectively, while the hydrogen tank of the ferry is refuelled from 23% to 100% of its nominal capacity every 2 days [68,69].

## 4. Numerical Simulation Results and Discussion

^{®}software. The optimum combination of the capacity of the MECM’s equipment yielded by solving the formulated problem using the MFOA-based solution algorithm subject to the imposed constraints is presented in Table 4. The minimised total NPC of the MECM system is found to be NZD 7,940,348.

#### 4.1. Benchmarking the MFOA

- In the context of off-grid MECM designing and equipment capacity planning optimisation, the performance of the MFOA is superior to the other six meta-heuristics investigated in terms of yielding the least-cost solution. Notably, it outperforms the second-best algorithm (the hybrid GA-PSO) by a significant ~8% (equating to a saving of ~NZD 714,255). The following rank order is achieved for the evaluated algorithms: the MFOA > the hybrid GA-PSO > the GA > the PSO > the hybrid ABC-ACO > the ABC > the ACO.
- Although no significant dependence of the optimal resource portfolio—in terms of the overall configuration and the selected components from the candidate pool—on the chosen meta-heuristic was observed (or in other words, none of the components were rejected and were not even downsized with increases in optimised total system cost due to the sub-optimality of the solutions yielded by the benchmarking meta-heuristics)—to illustrate, in some cases, sub-optimality results in lower than optimum sizes for some of the components at the cost of increases in the size of other components, but this has not occurred here—similar patterns of stagnation in local optima were found in the solution sets returned by the algorithms that have been hybridised. More specifically, although the performance of the hybrid version is slightly better, the GA, the PSO, and the hybrid GA-PSO return practically the same equipment mix (and in turn, practically the same total discounted system cost values), which is also the case for the ABC, the ACO, and the hybrid ABC-ACO. This provides further evidence to support the argument that the hybridisation of meta-heuristics does not necessarily result in improved solution quality in any application.
- The practically unaltered optimal resource mix yielded by the seven meta-heuristics of interest in terms of system configuration indicates that the superiority of the MFOA to the well-established algorithms in off-grid MECM sizing applications stems largely from its well-balanced exploration and exploitation phases, rather than accessing the regions that are invisible to the well-established algorithms. More specifically, the global superiority of the MFOA can be attributed to its unique feature of systematically rebalancing exploration—the early stages of the optimisation process that mimics the long-range movement of individuals—for improved exploitation—the local search around promising regions—of the search space for potential solutions.

#### 4.2. Total Discounted Cost Breakdown

#### 4.3. Energy Balance Analyses

#### 4.4. Capital Budgeting

_{2}, respectively.

_{2}and 8.91 NZD/kg-H

_{2}for small- and large-scale hydrogen production schemes, respectively [76,77]. Moreover, in general, depending on the availability of RESs, scale of the system, and technologies utilised to heat the water renewably, a litre of hot water is expected to cost between NZD 0.0077 and NZD 0.028 [78].

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**The 2 °C scenario for electricity generation, REmap case, 2015–2050 [4].

**Figure 5.**Monthly mean daily ambient temperature (°C) (data source: [66]).

**Figure 6.**Monthly mean daily wind speed (m/s) (data source: [66]).

**Figure 7.**Monthly mean 24-h electric load (kW) (data source: [67]).

**Figure 8.**Monthly mean 24-h heat load (kW) (data source: [54]).

Reference | MECM Configuration; Components in the Candidate Pool | Energy Carriers | Consideration of Water Heating | Consideration of Electrified Transportation | Optimisation Algorithm |
---|---|---|---|---|---|

Ding et al. [26] | Grid-connected; WTs, boilers, a CHP unit, BESS, TESS | Electricity, natural gas, heating, cooling | ✗ | ✓ | MILP |

Ghanbari et al. [27] | Grid-connected; WTs, solar PV, boilers, a CHP unit, BESS, TESS, hydrogen storage | Electricity, natural gas, hydrogen, heating, cooling | ✗ | ✗ | MINLP |

Mansour-Saatloo et al. [28] | Grid-connected; WTs, boilers, a CHP unit, BESS, TESS, hydrogen storage, ice storage | Electricity, natural gas, heating, cooling | ✗ | ✗ | MILP |

Mashayekh et al. [29] | Grid-connected; solar PV, solar thermal, electric chillers, boilers, micro-turbines, absorption chillers, BESS, TESS, cold storage | Electricity, heating, cooling, natural gas | ✓ | ✗ | MILP |

Mashayekh et al. [30] | Off-grid; solar PV, solar thermal, electric chillers, boilers, micro-turbines, absorption chillers, BESS, TESS, cold storage | Electricity, heating, cooling, natural gas | ✓ | ✗ | MILP |

Ge et al. [31] | Grid-connected; solar PV, CHP, BESS, TESS | Electricity, heating, cooling | ✓ | ✗ | MINLP |

Lekvan et al. [32] | Grid-connected; WTs, batteries, a CHP unit, boiler, hydrogen storage | Electricity, natural gas, heating | ✗ | ✓ | MILP |

Wang et al. [33] | Grid-connected; solar PV, CHP, boilers, electric chillers, absorption chillers, BESS, TESS, cold storage | Electricity, natural gas, heating, cooling | ✓ | ✗ | MILP |

Lorestani et al. [34] | Off-grid; WTs, solar PV thermal, micro-turbines, boilers, BESS, TESS | Electricity, heating, natural gas | ✗ | ✗ | Evolutionary particle swarm optimisation |

Lorestani and Ardehali [35] | Grid-connected; WTs, solar PV thermal, BESS, TESS, electric heaters, electric chillers, absorption chillers | Electricity, heating, cooling, natural gas | ✗ | ✗ | Evolutionary particle swarm optimisation |

Azimian et al. [36] | Grid-connected; WTs, solar PV, CHP, auxiliary boiler, BESS, TESS | Electricity, natural gas | ✗ | ✗ | MINLP |

Sanjareh et al. [37] | Grid-connected; WTs, solar PV, fuel cell, micro-turbine, BESS | Electricity, heating, cooling | ✗ | ✗ | A specifically developed enumerative method |

Swaminathan et al. [38] | Islanded; solar PV, micro-turbine, BESS | Electricity, heating, cooling | ✗ | ✗ | Particle swarm optimisation |

Li et al. [39] | Grid-connected; WTs, solar PV, electric heater, TESS | Electricity, heating | ✗ | ✗ | Improved differential evolution algorithm |

Dakir et al. [40] | Islanded; solar PV, diesel generators, BESS, cold storage system, TESS | Electricity, heating, cooling | ✗ | ✗ | MILP |

This study | Off-grid; solar PV, WTs, hydrogen storage, hybrid super-capacitor/battery energy storage, a hot water storage tank, a heat exchanger, an inline electric heater, a hydrogen refuelling station | Electricity, heating, hydrogen | ✓ | ✓ | Moth-flame optimisation algorithm |

Component | Rated Capacity/Capacity Step-Size | $\mathit{C}\mathit{C}$^{1} (NZD)
| $\mathit{R}\mathit{C}$^{1} (NZD)
| $\mathit{O}\&\mathit{M}$ Cost ^{1} (NZD)
| Efficiency ^{2} (%) | Lifetime |
---|---|---|---|---|---|---|

PV panels | 280 W | 437/unit | 350/unit | 1.9/unit/year | 17 | 20 years |

WTs | 100 kW | 120 k/unit | 100 k/unit | 4.6 k/unit/year | N/A ^{3} | 20 years |

SC modules | 166 F, 48 V ≡ 0.054 kWh | 1.3 k/module | 0.7 k/module | 5/module/year | 95 | 10 years |

Battery packs | 1 kWh | 910/kWh | 620/kWh | 2.2/kWh/year | 90 | 12 years |

Electrolyser | 1 kW | 1 k/kW | 1 k/kW | 20/kW/year | 60 | 15 years |

Hydrogen reservoir | 1 kg | 470/kg | 470/kg | 9/kg/year | 98 | 20 years |

Fuel cell | 1 kW | 1.1 k/kW | 900/kW | 0.02/kW/hour | 50 ^{4} | 10 k hours |

Heat exchanger | 1 kW | 100/kW | 90/kW | 2/kW/year | 90 | 15 years |

Hot water tank ^{5} | 1 L | 0.5/L | 0.3/L | 0.001/L/year | 96 | 15 years |

Inline electric heater | 1 kW | 1 k/kW | 1 k/kW | 8/kW/year | 97 | 15 years |

Hydrogen refilling station | 1 kg-H_{2} | 6 k/kg-H_{2}/h | 5 k/kg-H_{2}/h | 180/kg-H_{2}/h/year | 95 | 20 years |

Electric loads’ inverter | 1 kW | 350/kW | 300/kW | 7/kW/year | 95 | 15 years |

^{1}The capital, replacement, and O&M costs include the costs associated with the converters shown inside the dashed lines in Figure 3.

^{2}The equipment efficiency is reported excluding the efficiencies associated with the converters shown inside the dashed lines in Figure 3. All the power electronics devices are associated with an efficiency of 95%.

^{3}The WT plant is modelled using Equations (4) and (5), which model the relationship between its output power and the hub height wind speed.

^{4}The value represents the fuel cell’s electric efficiency.

^{5}The hot water tank’s specifications include the techno-economic specifications associated with the water pump shown in Figure 3.

Scalar | Value | Source | Scalar | Value | Source |
---|---|---|---|---|---|

${c}_{p}$ | 4.19 kJ/kg-°C | [54] | ${v}_{r}$ | 13 m/s | [47] |

$DF$ | 85% | [52] | $\gamma $ | 0.25 | [51] |

$HH{V}_{{H}_{2}}$ | 39.7 kWh/kg | [45] | ${\eta}_{B}$ | 90% | [25] |

${I}_{STC}$ | 1 kW/m^{2} | [52] | ${\eta}_{E}$ | 60% | [45] |

${K}_{p}$ | –0.40%/°C | [52] | ${\eta}_{FC}$ | 50% | [45] |

$NMOT$ | 43 °C | [52] | ${\eta}_{H}$ | 97% | [45] |

${P}_{PV,r}$ | 280 W | [52] | ${\eta}_{HE}$ | 90% | [54] |

${P}_{WT,r}$ | 100 kW | [47] | ${\eta}_{HW}$ | 96% | [54] |

${r}_{FC}^{h}$ | 0.8 | [54] | ${\eta}_{I}$ | 95% | [45] |

${T}_{in}$ | 12 °C | [54] | ${\eta}_{S}$ | 95% | [25] |

${T}_{STC}$ | 25 °C | [52] | ${\eta}_{SC}$ | 95% | [25] |

${v}_{ci}^{}$ | 2.5 m/s | [47] | ${\eta}_{tank}$ | 98% | [45] |

${v}_{co}^{}$ | 25 m/s | [47] |

Component | Optimal Size |
---|---|

PV panels (no.) | 796 |

WTs (no.) | 31 |

SC modules (no.) | 329 |

Battery packs (no.) | 18 |

Electrolyser (kW) | 964 |

Hydrogen reservoir (kg) | 619 |

Fuel cell (kW) | 261 |

Heat exchanger (kW) | 213 |

Hot water tank (L) | 283,301 |

Inline heater (kW) | 97 |

Hydrogen station (kg-H_{2}/h) | 17.2 |

Inverter (kW) | 741 |

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

MFOA | The constant that defines the shape of the logarithmic spiral = 1 | [43] |

GA | Mutation rate = 0.05, crossover probability = 0.1, mutation probability = 0.9 | [70] |

PSO | Acceleration coefficients = 2, inertia weight = 0.7 | [71] |

Hybrid GA-PSO | Mutation rate = 0.05, crossover probability = 0.1, mutation probability = 0.9, acceleration coefficients = 2, inertia weight = 0.7 | [72] |

ABC | Number of onlooker beers = 25, number of employed bees = 25 | [73] |

ACO | Archive size = 50, locality of search = 0.1, convergence speed = 0.85 | [74] |

Hybrid ABC-ACO | Number of onlooker beers = 25, number of employed bees = 25, archive size = 50, locality of search = 0.1, convergence speed = 0.85 | [75] |

**Table 6.**Comparative total discounted system cost returned by the evaluated meta-heuristics and the associated CPU usage times.

Algorithm | Total NPC (NZD) | CPU Time (s) |
---|---|---|

MFOA | 7,940,348 | 181,749 |

GA-PSO | 8,654,603 | 178,325 |

GA | 8,771,219 | 161,088 |

PSO | 8,924,580 | 159,957 |

ABC-ACO | 9,541,309 | 164,412 |

ABC | 9,621,367 | 183,560 |

ACO | 9,849,651 | 188,217 |

Algorithm | MFOA | GA-PSO | GA | PSO | ABC-ACO | ABC | ACO |
---|---|---|---|---|---|---|---|

PV panels (no.) | 796 | 971 | 974 | 982 | 1021 | 1028 | 1091 |

WTs (no.) | 31 | 34 | 35 | 35 | 38 | 38 | 39 |

SC modules (no.) | 329 | 381 | 382 | 397 | 425 | 431 | 439 |

Battery packs (no.) | 18 | 48 | 48 | 57 | 79 | 85 | 85 |

Electrolyser (kW) | 964 | 1015 | 1020 | 1055 | 1104 | 1122 | 1127 |

Hydrogen reservoir (kg) | 619 | 731 | 732 | 762 | 788 | 793 | 795 |

Fuel cell (kW) | 261 | 279 | 280 | 294 | 329 | 336 | 351 |

Heat exchanger (kW) | 213 | 285 | 285 | 298 | 331 | 332 | 359 |

Hot water tank (L) | 283,301 | 370,214 | 376,097 | 380,017 | 401,257 | 411,104 | 419,185 |

Inline heater (kW) | 97 | 148 | 152 | 155 | 191 | 199 | 219 |

Hydrogen station (kg-H_{2}/h) | 17.2 | 19.4 | 20.1 | 20.3 | 20.9 | 20.9 | 21.0 |

Inverter (kW) | 741 | 741 | 741 | 741 | 741 | 741 | 741 |

DPP (years) | PI (%) | IRR (%) |
---|---|---|

8.79 | 2.45 | 13.68 |

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**MDPI and ACS Style**

Mohseni, S.; Brent, A.C.; Burmester, D.
Off-Grid Multi-Carrier Microgrid Design Optimisation: The Case of Rakiura–Stewart Island, Aotearoa–New Zealand. *Energies* **2021**, *14*, 6522.
https://doi.org/10.3390/en14206522

**AMA Style**

Mohseni S, Brent AC, Burmester D.
Off-Grid Multi-Carrier Microgrid Design Optimisation: The Case of Rakiura–Stewart Island, Aotearoa–New Zealand. *Energies*. 2021; 14(20):6522.
https://doi.org/10.3390/en14206522

**Chicago/Turabian Style**

Mohseni, Soheil, Alan C. Brent, and Daniel Burmester.
2021. "Off-Grid Multi-Carrier Microgrid Design Optimisation: The Case of Rakiura–Stewart Island, Aotearoa–New Zealand" *Energies* 14, no. 20: 6522.
https://doi.org/10.3390/en14206522