# Performance Comparison between Two Established Microgrid Planning MILP Methodologies Tested On 13 Microgrid Projects

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## Abstract

**:**

## 1. Introduction

## 2. Model Description and Used Data Down-Sampling

#### 2.1. Peak Preserving Day-Types Representative Optimization (RO)

_{m,d}).

#### RO MILP

Indices | |

$\mathrm{c}$ | continuous generation technologies (assumed to be available in any size), $\mathrm{c}\in \mathbf{C}$ = {photovoltaic panels, solar thermal panels, and absorption chillers} |

$\mathrm{d}$ | day-types, $\mathrm{d}\in \mathbf{D}$ = {week, peak, weekend} |

$\mathrm{g}$ | discrete generation technologies (explicitly modeled in discrete sizes), internal combustion engines (ICE), micro turbines (MT), fuel cells (FC), and gas turbines (GT), with and without heat exchangers (HX), $\mathrm{g}\in \mathbf{G}$ = {ICE, ICEHX, MT, MTHX, FC, FCHX, GT, GTHX}. All discrete technologies without HX are referred to as DG, DG with HX as CHP |

$\mathrm{h}$ | hours in a day $\mathrm{h}\in \mathbf{H}=\{1,2,\dots ,24\}$ |

$\mathrm{i}$ | DER technologies, $\mathrm{i}\in \mathbf{I}=\mathbf{J}\cup \mathbf{S}$ |

$\mathrm{j}$ | generation technologies, $\mathrm{j}\in \mathbf{J}=\mathbf{G}\cup \mathbf{C}$ |

$\mathrm{m}$ | months in a year, $\mathrm{m}\in \mathbf{M}=\{1,2,\dots ,12\}$ |

$\mathrm{p}$ | utility demand periods, $\mathrm{p}\in \mathbf{P}$ = {coincident, on peak, mid peak, off peak} |

$\mathrm{s}$ | energy storage technologies, stationary storage and heat storage, $\mathrm{s}\in \mathbf{S}$ = {electric energy storage systems, heat storage} |

$\mathrm{u}$ | energy end-uses for each day-type (d), including electricity-only (eo), cooling (cl), space heating (sh), water heating (wh), and natural gas loads (ng), $\mathrm{u}\in \mathbf{U}$ = {eo, cl, sh, wh, ng} |

Parameters | |

${\mathrm{ANN}}_{\mathrm{i}}$ | annuity rate of investing in DER technology i |

ND_{m,d} | number of days of type d in month m |

${\mathrm{C}}_{\mathrm{u},\mathrm{m},\mathrm{d},\mathrm{h}}$ | volumetric electricity charges |

${\mathrm{D}}_{\mathrm{u},\mathrm{p},\mathrm{m}}$ | charges applied to peak power demand for end-use u during period p, and month m |

${\mathrm{DRC}}_{\mathrm{u},\mathrm{m},\mathrm{d},\mathrm{h}}$ | volumetric demand response costs |

${\mathrm{GENC}}_{\mathrm{j},\mathrm{u},\mathrm{m},\mathrm{d},\mathrm{h}}$ | fuel costs, maintenance costs |

${\mathrm{IFix}}_{\mathrm{i}}$ | fixed investment cost of DER technology i |

${\mathrm{IVar}}_{\mathrm{c}\cup \mathrm{s}}$ | variable investment cost of continuous energy conversion technology c, or storage technology s |

${\mathrm{LOAD}}_{\mathrm{u},\mathrm{m},\mathrm{d},\mathrm{h}}$ | Microgrid energy demand for end-use u, in month m, day-type d, and hour h |

${\mathrm{MFix}}_{\mathrm{m}}$ | fixed monthly utility charges/contract demand charges |

${\mathrm{S}}_{\mathrm{m},\mathrm{d},\mathrm{h}}$ | electricity sales price in month m, day-type d, and hour h |

η_{i} | energy conversion efficiency for i |

Decision Variables | |

$ca{p}_{\mathrm{c}\cup \mathrm{s}}$ | installed capacity of continuous generation technology c, or storage technology s |

$d{r}_{\mathrm{u},\mathrm{m},\mathrm{d},\mathrm{h}}$ | energy demand of end-use u removed by demand response measures in month m, day d, and hour h |

$ge{n}_{\mathrm{j},\mathrm{u},\mathrm{m},\mathrm{d},\mathrm{h}}$ | useful (e.g., electric output) energy provided by generation technology j for end-use u in month m, day-type d, and hour h |

$nu{m}_{\mathrm{g}}$ | number of installed units of discrete generation technology g |

$pu{r}_{\mathrm{c}\cup \mathrm{s}}$ | binary purchase decision for continuous generation technology c, or storage technology s |

$sel{l}_{\mathrm{i},\mathrm{u},\mathrm{m},\mathrm{d},\mathrm{h}}$ | energy sales from technology i that is exported in month m, day-type d, and hour h |

$si{n}_{\mathrm{s},\mathrm{m},\mathrm{d},\mathrm{h}}$ | energy input to storage technology s, in month m, day-type d, and hour h |

$sou{t}_{\mathrm{s},\mathrm{u},\mathrm{m},\mathrm{d},\mathrm{h}}$ | energy output from storage technology s for end-use u, in month m, day-type d, and hour h |

$u{\sim}_{\mathrm{u},\mathrm{m},\mathrm{d},\mathrm{h}}$ | utility purchase for end-use u, during month m, day-type d, and hour h |

#### 2.2. Full-Scale Time-Series Optimization (FSO)

_{m,d}to represent the real number of days in a month instead of the number of representative day-types. Thus, instead of e.g., using 22 representative weekdays, eight weekend days, and one peak profile for the RO, we convert ND

_{m,d}into a binary matrix containing ones to identify the real days observed in each month. In the case of January 2020, the matrix consists of ones from 1 to 31. For February 2020 it consists of ones from 1 to 29 and zeros for 30 and 31, etc. Days must be linked in time to allow energy to shift between consecutive days, creating a real seasonal model. The authors of [15] describe the changes needed to create an FSO model in detail.

## 3. Microgrid Projects

#### 3.1. General Description of Microgrid Projects

#### 3.2. Electric Load Data

_{n}) normalized by the total annual electric load to ensure that load volatilities can be compared between sites (Equation (3)).

#### 3.3. Solar Radiation Data

_{n}) and normalizing them by the total energy production (Equation (4)).

## 4. Results

#### 4.1. Representative Optimization (RO) versus Full-Scale Time-Series Optimization (FSO)

#### 4.2. Sensitivity to Electricity Sales

#### 4.3. The Influence of Optimal Dispatch Modeling—The Hybrid Optimization (HO)

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. Tariff Data

Tariff Data | |||||
---|---|---|---|---|---|

Case | Type | State | Utility Name | Tariff Name | Source Document |

Ind | Industrial/Pharmaceutical | Puerto Rico | Puerto Rico Electric Power Authority (PREPA) | LIS | [28] |

Res | Residential/Public | Connecticut | Eversource Energy | Rate 56—Intermediate Time of Day | [29] |

Man | Industrial/Materials | Puerto Rico | PREPA | GST | [28] |

Com | Commercial/Public | Washington State | Seattle City Light | MDC—Medium General Service: city | [30] |

Un1 | University | Colorado | Black Hills Energy | CO935—LPS-PTOU | [31] |

Un2 | University | Hawai’i | HECO | HECO-P | [32] |

Un3 | University | California | SDGE | AL-TOU | [33] |

Un4 | University | Vermont | CBE | Rate 08—General Service | [34] |

Mil1 | Military | Texas | Confidential | Confidential | Confidential |

Mil2 | Military | New Mexico | Confidential | Confidential | Confidential |

Mil3 | Military | Maryland | Confidential | Large Power Schedule | Confidential |

Mil4 | Military | California | Confidential | Confidential | Confidential |

Mil5 | Military | Massachusetts | Confidential | Industrial Service | Confidential |

## Appendix B. Technology Data

**Table A2.**PV technology assumptions used in the Microgrid projects. “Max. space for PV” represents the maximum available onsite space for PV generation.

Case | PV Technology Assumptions | ||||||
---|---|---|---|---|---|---|---|

PV Costs ($/kW_{DC}) | O&M Costs ($/kW and Month) | Lifetime (yrs.) | Electric Efficiency (%) | Tilt (Degrees/Confidential) | Orientation (South/North, West, East, Confidential) | Max. Space for PV (m^{2}) | |

Ind | 2150 | 0 | 30 | 16% | 20 | South | 10,000 |

Res | 2100 | 2.2 | 30 | 19% | Confidential | Confidential | 3760 |

Man | 2100 | 1.4 | 30 | 16% | 17 | South | 31,876 |

Com | 1470 | 0 | 30 | 16% | 35 | South | Unrestricted |

Un1 | 1969 | 0.8 | 25 | 19% | Confidential | Confidential | Unrestricted |

Un2 | 5000 | 0.8 | 25 | 15% | 22 | South east | 20,000 |

Un3 | 1700 | 1.4 | 30 | 16% | Confidential | Confidential | 40,000 |

Un4 | 2400 | 0 | 30 | 19% | 30 | South | 41,806 |

Mil1 | 1470 | 1.5 | 20 | 15% | Confidential | Confidential | Unrestricted |

Mil2 | 1470 | 1.5 | 20 | 15% | Confidential | Confidential | Unrestricted |

Mil3 | 1700 | 1.4 | 20 | 15% | Confidential | Confidential | Unrestricted |

Mil4 | 1700 | 1.4 | 20 | 15% | Confidential | Confidential | Unrestricted |

Mil5 | 1700 | 1.4 | 20 | 15% | Confidential | Confidential | Unrestricted |

**Table A3.**Electric Energy Storage (EES) technology assumptions. The max. allowed charging and discharging rates are constraints within the MILP. Max allowed charge and discharge rates are defined as a function of the EES power capacity.

Case | EES Technology Assumptions | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

Effective EES Costs ($/kWh) | O&M Cost ($/kW Month) | Lifetime (yrs.) | Charging/Respectively Discharge Efficiency (%) | Max. Allowed Charge Rate (-) | Max. Allowed Discharge Rate (-) | Min. SOC (-) | Max. SOC (-) | Maximum Allowed Cycles Per Year (-) | Self-Discharge Per Hour (-) | |

Ind | 250 | 0 | 5 | 90% | 0.3 | 0.3 | 0.3 | 1 | n/a | 0.001 |

Res | 350 | 0 | 15 | 90% | 0.3 | 1 | 0.1 | 1 | n/a | 0.0001 |

Man | 500 | 0 | 20 | 94% | 0.2 | 0.2 | 0.1 | 1 | n/a | 0 |

Com | 350 | 0 | 20 | 94% | 0.2 | 0.2 | 0.1 | 1 | n/a | 0.001 |

Un1 | 675 | 0.2 | 25 | 92% | 0.3 | 0.3 | 0.1 | 1 | 110 | 0 |

Un2 | 566 | 0.2 | 25 | 90% | 0.3 | 0.3 | 0.1 | 1 | n/a | 0.0001 |

Un3 | 500 | 0 | 20 | 94% | 0.2 | 0.2 | 0.1 | 1 | n/a | 0 |

Un4 | 350 | 0 | 20 | 90% | 0.5 | 0.3 | 0.1 | 1 | n/a | 0.0001 |

Mil1 | 212 | 0.3 | 18 | 87% | 0.3 | 0.3 | 0 | 1 | n/a | 0.01 |

Mil2 | 212 | 0.3 | 18 | 87% | 0.3 | 0.3 | 0 | 1 | n/a | 0.01 |

Mil3 | 212 | 0.3 | 18 | 87% | 0.3 | 0.3 | 0 | 1 | n/a | 0.01 |

Mil4 | 212 | 0.3 | 18 | 87% | 0.3 | 0.3 | 0 | 1 | n/a | 0.01 |

Mil5 | 212 | 0.3 | 18 | 87% | 0.3 | 0.3 | 0 | 1 | n/a | 0.01 |

DG/CHP Assumptions | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|

Case | Type (/) | Unit Capacity (kW) | Lifetime (yrs.) | Capacity Costs Installed ($/kW) | O&M Fixed Costs ($/kW/year) | O&M Variable Cost ($/kWh) | Efficiency (%) | Heat to Power Ratio (%) | Max. Annual Operating Hours (hrs.) | Backup Only (Yes/No) |

Ind | n/a | n/a | n/a | n/a | n/a | n/a | n/a | n/a | n/a | n/a |

Res | Microturbine | 60 | 15 | 3220 | 0.0 | 0.001 | 25% | n/a | 8760 | no |

Microturbine | 100 | 15 | 3500 | 0.0 | 0.002 | 40% | n/a | 8760 | no | |

Man | CHP | 3304 | 20 | 3281 | 0.0 | 0.009 | 24% | 175% | 8760 | no |

CHP | 3325 | 20 | 3750 | 0.0 | 0.009 | 44% | 94% | 8760 | no | |

CHP | 5670 | 20 | 3750 | 0.0 | 0.009 | 28% | 135% | 8760 | no | |

CHP | 7480 | 20 | 3705 | 0.0 | 0.009 | 45% | 33% | 8760 | no | |

Com | Microturbine CHP | 61 | 15 | 3220 | 0.0 | 0.013 | 25% | 189% | 8760 | no |

Microturbine CHP | 190 | 15 | 3150 | 0.0 | 0.016 | 28% | 133% | 8760 | no | |

Microturbine CHP | 242 | 15 | 2700 | 0.0 | 0.012 | 26% | 145% | 8760 | no | |

Microturbine CHP | 950 | 15 | 2500 | 0.0 | 0.012 | 28% | 130% | 8760 | no | |

Un1 | Distributed Generation | 250 | 25 | 2191 | 0.0 | 0.022 | 23% | n/a | 160 | no |

Distributed Generation | 250 | 25 | 2191 | 0.0 | 0.022 | 23% | n/a | 200 | no | |

Un2 | n/a | n/a | n/a | n/a | n/a | n/a | n/a | n/a | n/a | n/a |

Un3 | Internal combustion engine | 125 | 30 | 2000 | 0.0 | 0.020 | 26% | n/a | 8760 | no |

Un4 | Microturbine | 100 | 15 | 2900 | 0.0 | 0.002 | 30% | n/a | 8760 | no |

Mil1 | Diesel genset | 2000 | 20 | 600 | 10.0 | 0.000 | 32% | n/a | 8760 | yes |

Mil2 | Diesel genset | 750 | 20 | 750 | 9.3 | 0.000 | 28% | n/a | 8760 | yes |

Diesel genset | 750 | 20 | 750 | 9.3 | 0.000 | 28% | n/a | 1091 | no | |

Mil3 | Diesel genset | 750 | 20 | 750 | 9.3 | 0.000 | 28% | n/a | 8760 | yes |

Mil4 | Diesel genset | 750 | 20 | 750 | 9.3 | 0.000 | 28% | n/a | 8760 | yes |

Mil5 | Diesel genset | 750 | 20 | 750 | 9.3 | 0.000 | 28% | n/a | 8760 | yes |

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**Figure 2.**Sankey diagram for the Microgrid DER-CAM/XENDEE MILP. The five energy end-uses on the right hand side need to be supplied with energy at minimized annual energy costs or CO

_{2}emissions. The MILP analyzes the energy flows (different arrows) in each time-step and decides on the optimal investment capacities and technologies as well as energy flows in each time-step, constituting an optimal dispatch profile.

**Figure 3.**Daily demand for each day in an example March month and peak demand day profile constructed from selecting maximum hourly demand across all days.

**Figure 5.**Example time-series electric load data for Un3 (solid line, left y-axis) and Un4 (dashed line, right y-axis). Hours 120–168 are weekend days.

**Figure 6.**Summary of electric load data for all cases as a function of annual electric load (GWh) and load variability (-) expressed as the sum of the absolute values of all 1 h power changes normalized by the total annual load.

**Figure 7.**Solar production summary for all cases expressed through the annual capacity factor and the normalized annual solar variability.

**Figure 8.**OF differences (bars) and run-time savings (line) for the RO approach compared to the FSO. Negative run-time numbers represent savings.

**Figure 9.**Variations in RO technology adoption compared to the FSO. The OF difference compared to FSO is shown as a dashed line.

**Figure 10.**Scatter plot comparing the absolute value of OF deviation of each case as a function of solar variability (y-axis) and load variability (x-axis). The size of the circle represents the OF deviation of each case.

**Table 1.**Overview of considered Microgrid projects for this research. FER: Flat energy rate, FSER: Flat seasonal energy rate, FER-winter: Flat energy rate just for winter months, TOUER: Time-Of-Use energy rate, TOUER-summer: Time-Of-Use energy rate just for summer months, NCDC: Non-coincident demand charge, PDC: Peak demand charge, MPDC: Mid peak demand charge. PV: Photovoltaics, EES: Electric Energy Storage, CHP: Combined Heat and Power, DG: Distributed Generation as natural gas or diesel fired backup systems. All Microgrid projects are in the US, due to confidentiality reasons the exact locations cannot be revealed.

Case | Type | State/Territory | Techn. Modeled | Tariff Characteristics | Annual Electrical Cons. (MWh) | Annual Heating Cons. (MWh) | Electric Peak Load (MW) |
---|---|---|---|---|---|---|---|

Ind | Industrial/Pharmaceutical | Puerto Rico | PV, EES | FER, NCDC, PDC, MPDC | 22,642 | n/a | 3.96 |

Res | Residential/Public | Connecticut | PV, EES, DG | TOUER, NCDC | 1640 | n/a | 0.37 |

Man | Industrial/Materials | Puerto Rico | PV, EES, CHP | FER, NCDC | 78,400 | 41,854 | 12.48 |

Com | Commercial/Public | Washington State | PV, EES, CHP | FER, NCDC | 4263 | 667 | 0.93 |

Un1 | University | Colorado | PV, EES, DG | TOUER-summer, FER-winter, PDC | 12,076 | n/a | 2.85 |

Un2 | University | Hawai’i | PV, EES | FER, NCDC | 3338 | n/a | 0.97 |

Un3 | University | California | PV, EES, DG | TOUER, NCDC, PDC | 825 | n/a | 0.20 |

Un4 | University | Vermont | PV, EES, DG | FER, NCDC | 26,713 | 6817 | 5.00 |

Mil1 | Military | Texas | PV, EES, DG | TOUER, NCDC | 330,648 | n/a | 67.61 |

Mil2 | Military | New Mexico | PV, EES, DG | TOUER, NCDC | 78,878 | n/a | 15.99 |

Mil3 | Military | Maryland | PV, EES, DG | FSER, NCDC | 187,645 | n/a | 33.96 |

Mil4 | Military | California | PV, EES, DG | TOUER, NCDC | 86,349 | n/a | 15.00 |

Mil5 | Military | Massachusetts | PV, EES, DG | TOUER, NCDC | 16,564 | n/a | 3.41 |

**Table 2.**Overview results for the 13 modeled Microgrids. OF: Objective Function; R-time: Run-time; RO: Down-sampled representative day-types optimization.

Case | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

∆ OF (%) | R-Time RO (mins) | R-Time FSO (mins) | ∆ R-Time (%) | PV RO (kW) | PV FSO (kW) | ∆ PV Compared to FSO (%) | EES RO (kWh) | EES FSO (kWh) | ∆ EES Compared to FSO (%) | DG/CHP RO (kW) | DG/CHP FSO (kW) | ∆ DG/CHP Compared to FSO (%) | |

Ind | −0.5 | 0.2 | 1.6 | −89 | 1568 | 1568 | 0.0 | 396 | 582 | −32.0 | 0 | 0 | n/a |

Res | −0.3 | 0.3 | 121.0 | −100 | 715 | 715 | 0.0 | 1048 | 668 | 56.9 | 100 | 160 | −37.5 |

Man | 0.0 | 0.3 | 7.4 | −97 | 358 | 328 | 9.1 | 0 | 0 | n/a | 9975 | 9975 | 0 |

Com | 5.7 | 0.2 | 1.7 | −87 | 182 | 0 | 100.0 *) | 0 | 0 | n/a | 0 | 0 | n/a |

Un1 | 1.3 | 1.0 | 121.1 | −99 | 8969 | 9211 | −2.6 | 8243 | 8909 | −7.5 | 500 | 600 | −16.7 |

Un2 | −6.8 | 0.0 | 0.5 | −92 | 1627 | 1501 | 8.4 | 2242 | 2573 | −12.9 | 0 | 0 | n/a |

Un3 | −0.8 | 0.2 | 88.5 | −100 | 257 | 222 | 15.8 | 320 | 314 | 1.9 | 100 | 100 | 0 |

Un4 | 13.2 | 0.2 | 2.4 | −91 | 995 | 504 | 97.4 | 2227 | 2400 | −7.2 | 3000 | 2900 | 3.4 |

Mil1 | 0.3 | 0.2 | 1.5 | −86 | 0 | 0 | n/a | 0 | 0 | n/a | 0 | 0 | n/a |

Mil2 | 0.4 | 0.3 | 2.2 | −89 | 6107 | 4913 | 24.3 | 6600 | 8400 | −21.4 | 12,000 | 12,000 | 0 |

Mil3 | −0.1 | 0.2 | 1.4 | −85 | 0 | 0 | n/a | 0 | 0 | n/a | 0 | 0 | n/a |

Mil4 | −1.2 | 0.2 | 1.2 | −85 | 13,053 | 11,600 | 12.5 | 7800 | 8400 | −7.1 | 0 | 0 | n/a |

Mil5 | −0.2 | 0.2 | 1.1 | −85 | 0 | 0 | n/a | 0 | 0 | n/a | 0 | 0 | n/a |

**Table 3.**Overview results for the sensitivity runs considering energy sales to the utility. OF: Objective Function; R-time: Run-time; RO: Representative Optimization approach; FSO: Full Scale Time-Series Optimization.

Case | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

∆ OF (%) | R-Time RO (mins) | R-Time FSO (mins) | ∆ R-Time (%) | PV RO (kW) | PV FSO (kW) | ∆ PV Compared to FSO (%) | EES RO (kWh) | EES FSO (kWh) | ∆ EES Compared to FSO (%) | DG/CHP RO (kW) | DG/CHP 8FSO (kW) | ∆ DG/CHP Compared to FSO (%) | |

Un2 no sales | −6.8 | 0.0 | 0.5 | −92 | 1627 | 1501 | 8.4 | 2242 | 2573 | −12.9 | 0 | 0 | n/a |

Un2 sales | −2.0 | 0.0 | 0.6 | −92 | 2994 *) | 2994 *) | 0 | 1412 | 1358 | 4 | 0 | 0 | n/a |

Mil4 no sales | −1.2 | 0.2 | 1.2 | −85 | 13,053 | 11,600 | 12.5 | 7800 | 8400 | −7.1 | 0 | 0 | n/a |

Mil4 sales | −1.1 | 0.1 | 0.8 | −88 | 18,945 | 16,856 | 12.4 | 9000 | 9600 | −6.3 | 0 | 0 | n/a |

**Table 4.**Import and export balance for the energy sale sensitivity runs as well as the original runs without sales.

Case | A | B | C | D | E | F |
---|---|---|---|---|---|---|

Annual Export RO (MWh) | Annual Export FSO (MWh) | ∆ Export Compared to FSO (%) | Annual Import RO (MWh) | Annual Import FSO (MWh) | ∆ Import Compared to FSO (%) | |

Un2 no sales | 0 | 0 | n/a | 962 | 1237 | −22.2 |

Un2 sales | 2720 | 2801 | −2.9 | 1276 | 1366 | −6.6 |

Mil4 no sales | 0 | 0 | n/a | 58,694 | 61,920 | −5.2 |

Mil4 sales | 5088 | 4456 | 14.2 | 5138 | 5538 | −7.2 |

**Table 5.**Objective function as well as run-time differences between the HO and FSO. OF: Objective Function; R-time: Run-time; RO: Representative Optimization; HO: Hybrid Optimization; FSO: Full-Scale Time-Series Optimization.

Case | 1 | 1a | 2 | 2a | 3 | 4 | 4a |
---|---|---|---|---|---|---|---|

∆ OF RO Versus FSO (%) | ∆ OF HO Versus FSO (%) | R-Time RO (mins) | R-Time HO (mins) | R-Time FSO (mins) | ∆ R-Time RO Versus FSO (%) | ∆ R-Time HO Versus FSO (%) | |

Com | 5.7 | 1.4 | 0.2 | 0.9 | 1.7 | −87 | −48 |

Un4 | 13.2 | 0.6 | 0.2 | 1.0 | 2.4 | −91 | −58 |

Ind | −0.5 | 0.0 | 0.2 | 1.0 | 1.6 | −89 | −40 |

Res | −0.3 | 0.3 | 0.3 | 1.1 | 121.0 | −100 | −99 |

Man | 0.0 | 0.0 | 0.3 | 1.0 | 7.4 | −97 | −87 |

Un1 | 1.3 | 0.2 | 1.0 | 1.8 | 121.1 | −99 | −98 |

Un2 | −6.8 | 0.8 | 0.0 | 0.3 | 0.4 | −92 | −23 |

Un3 | −0.8 | 0.7 | 0.2 | 1.1 | 88.5 | −100 | −99 |

Mil1 | 0.3 | 0.0 | 0.2 | 1.2 | 1.5 | −86 | −25 |

Mil2 | 0.4 | 0.3 | 0.3 | 1.1 | 2.2 | −89 | −50 |

Mil3 | −0.1 | 0.0 | 0.2 | 0.9 | 1.4 | −85 | −34 |

Mil4 | −1.2 | 0.3 | 0.2 | 0.9 | 1.2 | −85 | −27 |

Mil5 | −0.2 | 0.0 | 0.2 | 0.9 | 1.1 | −85 | −20 |

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**MDPI and ACS Style**

Stadler, M.; Pecenak, Z.; Mathiesen, P.; Fahy, K.; Kleissl, J. Performance Comparison between Two Established Microgrid Planning MILP Methodologies Tested On 13 Microgrid Projects. *Energies* **2020**, *13*, 4460.
https://doi.org/10.3390/en13174460

**AMA Style**

Stadler M, Pecenak Z, Mathiesen P, Fahy K, Kleissl J. Performance Comparison between Two Established Microgrid Planning MILP Methodologies Tested On 13 Microgrid Projects. *Energies*. 2020; 13(17):4460.
https://doi.org/10.3390/en13174460

**Chicago/Turabian Style**

Stadler, Michael, Zack Pecenak, Patrick Mathiesen, Kelsey Fahy, and Jan Kleissl. 2020. "Performance Comparison between Two Established Microgrid Planning MILP Methodologies Tested On 13 Microgrid Projects" *Energies* 13, no. 17: 4460.
https://doi.org/10.3390/en13174460