# Optimal Planning of Remote Microgrids with Multi-Size Split-Diesel Generators

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Background and Motivation

#### 1.2. Literature Review

_{2}emissions of HPS was used in [14,15,16,17], where multiple smaller size DGs replaced the single large size DG. This approach is called “Split-DG”. The main idea of the Split-DG is to supply the load without excessive power generation. These studies used a tri-objective genetic algorithm to size a WT/PV/Split-DG/BES by minimizing the projects’ cost, emissions, and dump energy. The size of the DG to be used for the split-DGs is determined in such a way that the total capacity of the Split-DG supplies 120% of the load. The authors in [14,15,16] proposed a 3-Split-DG model that performed notably better than a large DG unit. In [14], it was reported that the HPS had a notable reduction of 28%, 82%, and 94% of cost, CO

_{2}emissions, and dump energy, respectively, compared to a conventional DG system. However, none of those studies considered the DG’s optimal operating region recommended by the manufacturers; instead, they assume that the DGs always operate at their rated power. Prolongated working hours out of this region would reduce the DG’s lifetime. The consideration of the operating region makes the DG’s model more realistic and accurate.

#### 1.3. Contributions

- Optimal sizing of Split-DG/FT/PV/WT/BES for a remote microgrid based on a multi-size Split-DG.
- Development of a practical and precise model based on capacity degradation of PV and BES, spinning reserve for the remote microgrid, as well as DG’s and fuel tank’s constraint.
- Development of a variable weighting particle swarm optimization algorithm for optimal sizing of remote microgrids.

## 2. System Model

#### 2.1. Model of Components

#### 2.1.1. Photovoltaic System

^{2}) and ambient temperature ${T}_{amb}$ (°C) are evaluated to calculate the output power of the PV system as follows [8]:

#### 2.1.2. Wind Turbine

#### 2.1.3. Battery Energy Storage

#### 2.1.4. Split-Diesel Generators

#### 2.1.5. Fuel Tanks (FT)

#### 2.2. Dumped Power

#### 2.3. Spinning Reserve

#### 2.4. CO_{2} Emission

_{2}) makes up the majority of greenhouse gas emissions (GHG) from the electricity sector [20], the term CO

_{2}emission has been used in this study instead of GHG. The total CO

_{2}emission (${E}_{C{O}_{2}}^{Total}$) is calculated from the total diesel consumed by the DGs during the whole year and an emission rate ($E{R}_{C{O}_{2}}$) of 2.7 kg/L [21]:

## 3. Optimization Model

- All components must operate inside their upper and lower boundaries. These boundaries have been specified in previous sections.
- Load requirement must always be supplied at each time interval.

- SOC at the end of the analyzed year cannot be less than the initial SOC. The initial SOC at the beginning of the project is predefined as 70%.

- There must always be a minimum spinning reserve of 100 kW after the load demand is supplied. This is due to the N-1 reliability index, which should consider the power rate of the largest generation unit of the system. Hence, the SR can be calculated as follows:

## 4. Optimization Algorithm

## 5. System Configurations and Input Data

#### 5.1. Configuration 1

#### 5.2. Configuration 2

#### 5.3. Configuration 3

#### 5.4. System Input Data

#### 5.4.1. Load Characteristic

#### 5.4.2. Weather

#### 5.4.3. Components’ Data

## 6. Results and Discussions

#### 6.1. Configuration 1

_{2}emission per year. The annual dumped energy is 14.65 MWh for Configuration 1.

#### 6.2. Configuration 2

#### 6.3. Configuration 3

_{2}.

#### 6.4. System Comparison

_{2}emissions decreased as well by 24 tonnes/year. The main difference between these two systems is that Split-DG has many small DGs that allows multiple configurations. This helps to follow the load variations easier as the DG1’s minimum output power is 10 kW. For instance, the minimum power delivered by the Single-DG model is 40 kW; thus, if the load in a time interval is 15 kW, then this DG will deliver an extra 25 kW that will be lost, contrary to Split-DG, where one DG1 can deliver that power without any excess. Therefore, from an economic point of view, the Split-DG system is better than the Single-DG. The reduction of diesel consumption mainly causes this difference in costs.

#### 6.5. Advantages and Disadvantages

#### 6.6. PSO Algorithm Comparison

## 7. Conclusions and Future Works

_{2}emission (433.78 tonne/year). The NPV of the Split-DG-PV-WT-BES system was obtained almost AUD 1.1 million lower than that of the Split-DG system. The PV-WT-BES system was found to be unbelievably uneconomical, as its NPV was almost two times of the Split-DG-PV-WT-BES system. It was found that the proposed variable weighting factor PSO converged to the minimum NPV faster than the fixed weighting factor one. For configuration 3, the fixed weighting factor PSO could not reach the minimum NPV in 100 generations.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

Symbol | Description |

Economic Terms | |

${C}_{cap}^{j}$ | Capital cost of component j (AUD) |

${C}_{O\&M}^{j}$ | Maintenance costs of component j (AUD) |

${C}_{rep}^{j}$ | Replacement cost of component j (AUD) |

${C}_{fuel}$ | Fuel cost for each liter of consumption by the DGs (AUD/L) |

$L{T}_{com}^{j}$ | Component’s lifetime (year) |

$L{T}_{proj}$ | Project’s lifetime (year) |

$L{T}_{rem}$ | Remaining component’s lifetime (year) |

$NP{V}_{t}$ | Total net present value (AUD) |

$P{V}_{cap}^{j}$ | Capital present value of component j (AUD) |

$P{V}_{O\&M}^{j}$ | Maintenance present value of component j (AUD) |

$P{V}_{rep}^{j}$ | Replacement present value of component j (AUD) |

$P{V}_{SV}^{j}$ | Salvation present value of component j (AUD) |

$P{V}_{fuel}$ | Total fuel present value (AUD) |

$P{V}_{LGC}$ | Total large-scale generation incentive (AUD) |

${R}_{com}^{j}$ | Number of replacements of components |

$x,u$ | Interest rate and real interest rate for fuel cost (%) |

System Terms | |

$D{G}_{Fuel}$ | Total diesel consumption (kL) |

$DG{i}_{min/max}$ | Minimum and maximum operating limits of DG (kW) |

${E}_{in}^{BB}$ | Available input energy for the battery (kWh) |

${E}_{out}^{BB}$ | Available output energy for the battery (kWh) |

${E}_{r}^{BB}$ | Battery’s rated energy (kWh) |

${E}_{C{O}_{2}}^{Total}$ | Total CO2 emissions (tonne) |

$E{R}_{C{O}_{2}}$ | Diesel emissions rate (kg/L) |

$F{R}_{DG}$ | Fuel rate consumption of diesel generators (L/kWh) |

$F{T}_{vol}$ | Fuel tank nominal capacity (kL) |

$FV$ | Fuel volume (kL) |

$F{T}_{vol}$ | Maximum fuel tank capacity (kL) |

$F{V}_{min-vol}$ | Minimum fuel tank volume (kL) |

$F{T}_{min-days}$ | Minimum number of days of diesel storage |

$g$ | Degradation rate per year (%) |

$H$ | Hub height (m) |

${H}_{0}$ | Measured wind speed’s height (m) |

${I}_{c}$ | Insolation (kW/m^{2}) |

${I}_{stc}$ | Insolation at standard test conditions (kWh/m^{2}) |

$k$ | Number of switching configuration |

$MinDG{i}_{on}$ | Minimum number of DG type i ON |

$NOCT$ | Normal operating cell temperature (°C) |

${N}_{j}$ | Number of units of component j |

${P}_{BB,r}$ | Battery’s rated power (kVA) |

${P}_{l}^{Ave}$ | Average load demand (kW) |

${P}_{in}^{BB}$ | Charging power of battery (kW) |

${P}_{out}^{BB}$ | Discharging power of battery (kW) |

${P}_{wt}$ | Wind turbine’s output power (kW) |

${P}_{WT,r}$ | Wind turbine’s rated power (kVA) |

${P}_{dump}$ | Dumped power (kW) |

${P}_{l}$ | Load demand (kW) |

${P}_{pv}$ | Solar PV’s output power (kW) |

${P}_{PV,r}$ | Solar PV’s rated power (kVA) |

${P}_{SR}$ | Spinning Reserve power (kW) |

${P}_{DGi}$ | Output power of diesel generator type i (kW) |

${P}_{rDGi}$ | Rated power of DG type i (kW) |

${P}_{DG}^{Total}$ | Total diesel generation (kW) |

${P}_{GEN}$ | Total power generated (kW) |

$SO{C}_{max/min}$ | Maximum and minimum state-of-charge of battery (%) |

$SOC$ | State-of-charge of battery (%) |

${S}_{i}$ | Switch of DG type i |

${T}_{cell}$ | Cell temperature (°C) |

${T}_{stc}$ | Cell temperature at standard test conditions (°C) |

${T}_{amb}$ | Ambient temperature (°C) |

$t$ | Time (h) |

${v}_{0}$ | Measured wind speed (m/s) |

$v$ | Wind speed (m/s) |

${v}_{c}$ | Wind speed cut-in (m/s) |

${v}_{f}$ | Wind speed cut-out (m/s) |

${v}_{r}$ | Wind speed rated (m/s) |

${\eta}_{pv}$ | Solar PV’s efficiency (%) |

${\eta}_{BB}$ | Battery’s efficiency (%) |

${\eta}_{wt}$ | Wind turbine’s efficiency (%) |

$\gamma $ | Derating temperature coefficient (%) |

$\Delta t$ | Time interval (h) |

$\alpha $ | Terrain’s friction coefficient (%) |

Algorithm Terms | |

${C}_{2}$ | Global learning coefficient |

${w}^{k}$ | Inertia weight index |

$k$ | Iteration |

${w}_{max/min}$ | Maximum and minimum inertia weight index |

${k}^{max}$ | Maximum number of iterations |

$i$ | Particle |

$Pbes{t}_{i}^{k}$ | Particle’s personal best position for iteration k |

${x}_{i}^{k}$ | Particle’s position for iterations k |

${v}_{i}^{k}$ | Particle’s velocity for iterations k |

$Gbes{t}_{i}^{k}$ | Particles’ global best position for iteration k |

${C}_{1}$ | Personal learning coefficient |

${r}_{1},{r}_{2}$ | Random numbers from 0 to 1 |

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**Figure 5.**System input data, (

**a**) daily energy demand, (

**b**) daily solar insolation, (

**c**) daily average wind speed, and (

**d**) daily average ambient temperature.

**Figure 10.**Annual operation of Configuration 2. (

**a**) Total RE generation, (

**b**) SOC, and (

**c**) power dumped.

**Figure 11.**The 48-h operation of Configuration 2: (

**a**) generation and demand and (

**b**) BES’s charge and discharge.

**Figure 13.**Annual operation of Configuration 3. (

**a**) Total RE generation, (

**b**) total DG generation, (

**c**) SOC, and (

**d**) power dumped.

**Figure 14.**The 48-h operation of Configuration 3: (

**a**) generation and demand and (

**b**) BES’s charge and discharge.

**Figure 16.**Convergence rate comparison of the PSO with variable and fixed weighting factors: (

**a**) Configuration 1, (

**b**) Configuration 2, (

**c**) Configuration 3.

**Table 1.**Summary of the characteristics of existing works on the optimal sizing of remote microgrids.

Reference | Components | Real Input Data | Spinning Reserve | Degradation of PV and BES | DG’s and FT’s Constraints | ||||
---|---|---|---|---|---|---|---|---|---|

DG | FT | PV | WT | ESS | |||||

[5] | × | × | √ | √ | √ | × | × | × | × |

[6] | × | × | √ | × | √ | √ | × | × | × |

[7] | × | × | × | √ | √ | × | × | × | × |

[8] | × | × | √ | √ | √ | √ | × | × | × |

[9] | × | × | √ | × | √ | × | × | √ | × |

[10] | × | × | √ | × | √ | √ | √ | × | × |

[11] | Single-size DG | × | √ | √ | √ | √ | × | × | × |

[12] | Single-size DG | √ | √ | √ | √ | √ | √ | × | √ |

[13] | Single-size DG | × | √ | √ | √ | × | × | × | × |

[14] | Single-size Split-DG | × | √ | √ | √ | × | × | × | × |

[15] | Single-size Split-DG | × | √ | √ | √ | × | × | × | × |

[16] | Single-size Split-DG | × | √ | √ | √ | × | × | × | × |

[17] | Single-size Split-DG | × | √ | √ | √ | √ | × | × | × |

[18] | Single-size Split-DG | × | √ | √ | √ | √ | × | × | × |

This study | Multi-size split-DG | √ | √ | √ | √ | √ | √ | √ | √ |

Combination (k) | ${\mathit{S}}_{1}$ | ${\mathit{S}}_{2}$ | ${\mathit{S}}_{3}$ |
---|---|---|---|

1 | 1 | 0 | 0 |

2 | 0 | 1 | 0 |

3 | 0 | 0 | 1 |

4 | 1 | 1 | 0 |

5 | 1 | 0 | 1 |

6 | 0 | 1 | 1 |

7 | 1 | 1 | 1 |

Parameter | Symbol | Value |
---|---|---|

Population | $nPOP$ | 500 |

Iterations | ${k}^{max}$ | 100 |

Minimum search space limit | ${x}_{min}$ | 0 |

Maximum search space limit | ${x}_{max}$ | 20,000 |

Maximum variable inertia | ${w}_{max}$ | 0.7 |

Minimum variable inertia | ${w}_{min}$ | 0.1 |

Fixed inertia | ${w}_{fixed}$ | 0.5 |

Personal and Global coefficient | ${C}_{1}and{C}_{2}$ | 2 |

Number of variables or components | $N$ | 4–7 |

Annual Average | Maximum | Minimum | |
---|---|---|---|

Wind Speed (m/s) | 4.3 | 11.5 | 0 |

Insolation (Wh/m^{2}) | 431.7 | 1015 | 0 |

Ambient Temp (°C) | 17.9 | 41.9 | 2.2 |

Specification | Symbol | Quantity | Specification | Symbol | Quantity |
---|---|---|---|---|---|

Diesel Generator 1 | Wind Turbine | ||||

Nominal power | ${P}_{\mathrm{r}DG1}$ | 25 kW | Nominal power | ${P}_{\mathrm{r}WT}$ | 10 kW |

Min. Operation | $\mathrm{DG}{1}_{\mathrm{min}}$ | 40% | Wind speed cut-in | ${v}_{c}$ | 3 m/s |

Max Operation | $\mathrm{DG}{1}_{\mathrm{max}}$ | 90% | Wind speed nominal | ${v}_{r}$ | 12 m/s |

Fuel consumption | $F{R}_{DG}$ | 0.3 L/kWh | Wind speed cut-out | ${v}_{f}$ | 25 m/s |

Lifetime | $L{T}_{DG1}$ | 10 years | Hub height | $H$ | 25 m |

Capital cost | AUD 5250 | Friction coefficient | $\mathsf{\alpha}$ | 0.4 | |

Replacement cost | AUD 5250 | Efficiency | ${\eta}_{wt}$ | 88% | |

O&M cost | AUD 525 | Lifetime | $L{T}_{WT}$ | 10 years | |

Diesel Generator 2 | Capital cost | AUD 30,000 | |||

Nominal power | ${P}_{\mathrm{r}DG2}$ | 50 kW | Replacement cost | AUD 3000 | |

Min. Operation | $\mathrm{DG}{2}_{\mathrm{min}}$ | 40% | O&M cost | AUD 100 | |

Max Operation | $\mathrm{DG}{2}_{\mathrm{max}}$ | 90% | Photovoltaic Array | ||

Fuel consumption | $F{R}_{DG}$ | 0.30 L/kWh | Nominal power | ${P}_{\mathrm{r}PV}$ | 1 kW |

Lifetime | $L{T}_{DG2}$ | 10 years | Cell temperature STC | ${T}_{stc}$ | 25 °C |

Capital cost | AUD 10,500 | Cell temperature NOCT | $NOCT$ | 45 °C | |

Replacement cost | AUD 10,500 | Temperature derating | 0.4%/°C | ||

O&M cost | AUD 1050 | Efficiency | ${\eta}_{PV}$ | 86% | |

Diesel Generator 3 | Degradation | g | 0.95%/year | ||

Nominal power | ${P}_{\mathrm{r}DG3}$ | 100 kW | Tilt angle | 30° | |

Min. Operation | $\mathrm{DG}{3}_{\mathrm{min}}$ | 40% | Azimuth | 0° | |

Max Operation | $\mathrm{DG}{3}_{\mathrm{max}}$ | 90% | Lifetime | $L{T}_{PV}$ | 10 years |

Fuel consumption | $F{R}_{DG}$ | 0.30 L/kWh | Capital cost | AUD 1500 | |

Lifetime | $L{T}_{DG3}$ | 10 years | Replacement cost | AUD 300 | |

Capital cost | AUD 21,000 | O&M cost | AUD 25 | ||

Replacement cost | AUD 21,000 | Battery Bank | |||

O&M cost | AUD 2100 | Nominal power | ${P}_{\mathrm{r}BB}$ | 0.4 kW | |

Fuel Tank | Nominal energy | ${E}_{\mathrm{r}BB}$ | 1 kWh | ||

Nominal capacity | $F{T}_{vol}$ | 10 kL | Min. SOC | ${\mathrm{SOC}}_{\mathrm{min}}$ | 20% |

Min. days of storage | $F{T}_{min-day}$ | 7 days | Max. SOC | ${\mathrm{SOC}}_{\mathrm{max}}$ | 90% |

Frequency refill | 30 days | Initial SOC | ${\mathrm{SOC}}_{\mathrm{ini}}$ | 70% | |

Lifetime | $L{T}_{FT}$ | 20 year | Efficiency | ${\eta}_{BB}$ | 91% |

Capital cost | AUD 40,000 | Lifetime | $L{T}_{BB}$ | 20 year | |

Replacement cost | AUD 30,000 | Capital cost | AUD 600 | ||

O&M cost | AUD 1000 | Replacement cost | AUD 400 | ||

O&M cost | AUD 10 |

Configuration [DG1, DG2, DG3, FT] | NPV (AUD Million) | Diesel Generation (MWh) | Fuel Consumption (kL/Year) | Dumped Energy (MWh) | CO_{2} Emissions (Tonne/Year) |
---|---|---|---|---|---|

[16, 1, 2, 6] | 6.733 | 1350.74 | 405.22 | 14.65 | 1094 |

Configuration [WT, PV, BES] | NPV (AUD Million) | Energy Generated (MWh) | PV Energy (MWh) | WT Energy (MWh) | BES Charging (MWh) | BES Discharging (MWh) | Dumped Energy (MWh) |
---|---|---|---|---|---|---|---|

[50, 1728, 10,956] | 10.03 | 2833.80 | 2243.61 | 590.18 | 766.75 | 633.01 | 1363.96 |

Configuration[DG1, DG2, DG3, FT, WT, PV, BES] | NPV(AUD Million) | Diesel Generation(MWh) | RE Energy(MWh) | RE Index(%) | Dump Energy(MWh) | Fuel(L/Year) | CO_{2}(Tonne/Year) |

[5, 4, 3, 3, 45, 498, 1372] | 5.634 | 535.54 | 1177.8 | 68.74 | 320.86 | 160.66 | 433.78 |

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## Share and Cite

**MDPI and ACS Style**

Cardenas, G.A.R.; Khezri, R.; Mahmoudi, A.; Kahourzadeh, S.
Optimal Planning of Remote Microgrids with Multi-Size Split-Diesel Generators. *Sustainability* **2022**, *14*, 2892.
https://doi.org/10.3390/su14052892

**AMA Style**

Cardenas GAR, Khezri R, Mahmoudi A, Kahourzadeh S.
Optimal Planning of Remote Microgrids with Multi-Size Split-Diesel Generators. *Sustainability*. 2022; 14(5):2892.
https://doi.org/10.3390/su14052892

**Chicago/Turabian Style**

Cardenas, Gabriel Andres Rojas, Rahmat Khezri, Amin Mahmoudi, and Solmaz Kahourzadeh.
2022. "Optimal Planning of Remote Microgrids with Multi-Size Split-Diesel Generators" *Sustainability* 14, no. 5: 2892.
https://doi.org/10.3390/su14052892