# Optimal Operation of Sustainable Virtual Power Plant Considering the Amount of Emission in the Presence of Renewable Energy Sources and Demand Response

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## Abstract

**:**

## 1. Introduction

#### 1.1. Background

#### 1.2. Literature Review

- (1)
- Considering a new stochastic multi-objective system for SVPP management to minimize the operational costs and emissions.
- (2)
- Proposing a multi-energy SVPP that includes electrical, natural gas, heating, and cooling sectors to meet the type of user demand and balance supply and demand at all times.
- (3)
- Investigating the effect of cost-effective and environment-friendly sources such as PVs, WTs, and ESS on the operation and scheduling of an SVPP.

## 2. System Model

#### 2.1. Multi-Energy Sustainable Virtual Power Plant (SVPP) Architecture

#### 2.2. SVPP Operation Model

## 3. The Mathematical Model

#### 3.1. Wind Turbine (WT)

#### 3.2. Photovoltaic (PV)

#### 3.3. Diesel Generator (DG)

#### 3.3.1. Costs of DG

#### 3.3.2. DG Generation Constraints

#### 3.4. Energy Storage System (ESS)

#### 3.5. Heating and Cooling Loads

#### 3.6. Objective Function

#### 3.6.1. Costs of SVPP’s Operator

#### 3.6.2. Emission

#### 3.7. Problem Constraints

#### 3.8. Modeling of Demand Response Program (DRP)

#### 3.9. Uncertainty Modeling

## 4. Simulations and Discussion

#### 4.1. Basic Data

#### 4.2. Case Studies (CSs)

#### 4.3. Simulation Results and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

List of acronyms. | |

Symbol | Meaning |

2PEM | Two-Point Estimate Method |

CHP | Combined Heat and Power |

DER | Distributed Energy Resource |

DG | Diesel Generator |

DRP DSO | Demand Response Program Distributed System Operator |

EMS | Energy Management System |

ESS | Energy Storage System |

GA | Genetic Algorithm |

ISO MINLP | Independent System Operator Mixed-Integer Non-linear Programming |

PSO | Particle Swarm Optimization |

PV | Photovoltaic |

RES | Renewable Energy Source |

SVPP | Sustainable Virtual Power Plant |

TOU | Time of Use |

VPP | Virtual Power Plant |

WT | Wind Turbine |

List of symbols. | |

Abbreviation | Meaning |

$i,I$ | Index for WT |

$j,J$ | Index for PV |

$m,M$ | Index for DG |

$n,N$ | Index for ESS |

$t,c,T$ | Index for time (hour) |

$un$ | Index for uncertainty parameters |

${a}_{k},{b}_{k},{c}_{k}$ | Coefficients of DG cost function |

${C}_{{ES}_{n}}\left(t\right),{C}_{{MESS}_{n}}\left(t\right)$ | Operational ($/MWh) and maintenance costs of ESS ($) |

${C}_{{OPV}_{j}}\left(t\right),{C}_{{CPV}_{j}}\left(t\right)$ | Operational ($/MWh) and constant costs of PV ($) |

${C}_{{OWT}_{i}}\left(t\right),{C}_{{CWT}_{i}}\left(t\right)$ | Operational ($/MWh) and constant costs of WT ($) |

${C}_{NG}\left(t\right),{C}_{eNG}\left(t\right)$ | Total ($) and operational costs of natural gas ($/MWh) |

${CO}_{2}^{{DG}_{m}},{SO}_{2}^{{DG}_{m}},{NO}_{X}^{{DG}_{m}}$ | Emission factor of DG (kg/MWh) |

${CO}_{2}^{buy},{SO}_{2}^{buy},{NO}_{X}^{buy}$ | Emission factor of main grid (kg/MWh) |

${COST}_{em}^{buy},{COST}_{em}^{{DG}_{m}}$ | Cost of emission main grid and DG ($/kg) |

${C}_{ebuy}\left(t\right),{C}_{esell}\left(t\right)$ | Cost of buying/selling power from/to the main grid ($/MWh) |

${D}_{h}\left(t\right),{D}_{c}\left(t\right)$ | Heating and cooling loads (MW) |

${DT}_{{DG}_{m}},{UT}_{{DG}_{m}}$ | The minimum up/minimum down-time of DG (hour) |

${ES}_{{e}_{n}}\left(0\right)$ | Initial state of charge of ESS (MWh) |

${ES}_{{e}_{n}}^{min},{ES}_{{e}_{n}}^{max}$ | Minimum and maximum energy of ESS (MWh) |

${G}_{std}$ | Solar radiation in standard test condition (W/m^{2}) |

$G\left(t\right)$ | Solar radiation for normal operating cell temperature (W/m^{2}) |

${D}_{e}\left(t\right)$ | Amount of load (MW) |

${P}^{\mathrm{max}line}$ | Maximum capacity of transmission line (MW) |

${P}_{{ES}_{n}-ch}^{max},{P}_{{ES}_{n}-dch}^{max}$ | Maximum charge and discharge rates of ESS (MW) |

${P}_{{rated}_{i}}$ | Rated power of WT (MW) |

${P}_{{sn}_{j}}$ | Rated power of PV (MW) |

${P}_{{DG}_{m}}^{min},{P}_{{DG}_{m}}^{max}$ | Minimum and maximum power in operating of DG (MW) |

${R}_{c}$ | Certain radiation point for PV (W/m^{2}) |

${v}_{ci},{v}_{co}$ | Minimum and maximum wind speed (m/s) |

${v}_{r}$ | Rated wind speed (m/s) |

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

$\vartheta $ | Elasticity |

${\eta}_{hc},{\eta}_{gh}^{f}$ | Efficiency of chiller boiler and furnace (%) |

${\eta}_{ch}^{{ES}_{n}},{\eta}_{dch}^{{ES}_{n}}$ | Efficiency of charge and discharge (%) |

${\eta}_{ee}$ | Efficiency of the transformer (%) |

${\rho}_{1}\left(t\right)$, ${\rho}_{2}\left(t\right)$ | Electricity prices before and after DRP |

$\theta $ | Interval of operation |

${Co}_{{DG}_{m}}\left(t\right)$ | Cost function of DG $m$ ($) |

${C}_{DG}\left(t\right)$ | Cost of all DGs ($) |

${C}_{ESS}\left(t\right)$ | Cost of all ESSs ($) |

${C}_{PV}\left(t\right)$ | Cost of all PVs ($) |

${C}_{WT}\left(t\right)$ | Cost of all WTs ($) |

${C}_{buy}\left(t\right)$ | Cost of buying energy ($) |

$EM\left(t\right)$ | Total emissions (kg) |

${ES}_{{e}_{n}}\left(t\right)$ | Energy of ESS |

${G}_{NG}\left(t\right)$ | Amount of energy for cooling and heating sector (MW) |

${H}_{1}\left(t\right),{H}_{2}\left(t\right)$ | Amount of produced natural gas (MW) |

${I}_{{DG}_{m}}\left(t\right)$ | Binary variable for on/off state DG $m$ |

${y}_{{DG}_{m}}\left(t\right)$ | Binary variable for start-up state DG $m$ |

${z}_{{DG}_{m}}\left(t\right)$ | Binary variable for shut-down state DG $m$ |

${P}_{{DG}_{m}}\left(t\right)$ | Amount produced power of DG $m$ (MW) |

${P}_{{PV}_{j}}\left(t\right)$ | Amount produced power of PV $j$ (MW) |

${P}_{{WT}_{i}}\left(t\right)$ | Amount produced power of WT $i$ (MW) |

${R}_{sell}\left(t\right)$ | Total costs of sold energy ($) |

${ch}_{{ES}_{n}}\left(t\right),{dis}_{{ES}_{n}}\left(t\right)$ | Binary variable of charge and discharge modes |

$Cost\left(t\right)$ | Total costs of SVPP ($) |

$DR\left(t\right)$ | Power demand after implementation DRP (MW) |

${{E1}_{WT}}_{i}\left(t\right),{{E2}_{PV}}_{j}\left(t\right),{{E3}_{DG}}_{m}\left(t\right)$ | Power of WT, PV, and DG considering efficiency transformer (MW) |

$OF$ | Objective Function |

$Cem\left(t\right)$ | Total costs of emissions ($) |

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**Figure 3.**The flowchart of the two-point estimate method (2PEM) [41].

**Figure 5.**(

**a**): Data for buying/selling prices of power from/to the main grid. (

**b**): Electricity prices before and after implementing TOU based DRP. (

**c**): The heating and cooling demand curve for the 24 h.

**Figure 8.**The amount of exchange power between SVPP and the main grid in time horizon planning in CS#1.

**Figure 15.**The amount of charged/discharged power of ESS and imported/exported power from/to the main grid in CS#4.

**Figure 17.**The value of purchased power from the main grid and production power of DGs in various CSs.

**Table 1.**DG parameters [42].

DGs | Start-Up Cost ($) | Minimum-Up/Down Time (h) | Maximum Ramp-Up/Down Rate (MW/h) | ${\mathit{P}}^{\mathit{m}\mathit{a}\mathit{x}}$ | ${\mathit{P}}^{\mathit{m}\mathit{i}\mathit{n}}$ |
---|---|---|---|---|---|

DG1 | 15 | 2 | 1.8 | 3.5 | 1 |

DG2 | 25 | 1 | 1.5 | 3 | 0.75 |

DG3 | 28 | 1 | 1.5 | 3 | 0.75 |

DG4 | 26 | 2 | 1.5 | 4.1 | 1 |

**Table 2.**Operational cost coefficients of DGs [42].

DGs | ${\mathit{a}}_{\mathit{i}}(\frac{\mathbf{\$}}{\mathit{M}\mathit{W}{\mathit{h}}^{\mathbf{2}}})$ | ${\mathit{b}}_{\mathit{i}}(\frac{\mathbf{\$}}{\mathit{M}\mathit{W}\mathit{h}})$ | ${\mathit{c}}_{\mathit{i}}\left(\mathbf{\$}\right)$ |
---|---|---|---|

DG 1 | 0.0025 | 87 | 27 |

DG 2 | 0.0035 | 87 | 25 |

DG 3 | 0.0035 | 92 | 28 |

DG 4 | 0.184 | 81 | 26 |

Wind Turbine [45] | PV [36] | ||||
---|---|---|---|---|---|

Parameters | Amount | Unit | Parameters | Amount | Unit |

${\mathbf{P}}_{\mathbf{r}}$ | 2.05 | MW | ${P}_{sn}$ | 1.1 | MW |

${\mathbf{V}}_{\mathbf{c}\mathbf{i}}$ | 2 | m/s | ${G}_{std}$ | 1000 | W/m^{2} |

${\mathbf{V}}_{\mathbf{r}}$ | 14 | m/s | ${R}_{c}$ | 150 | W/m^{2} |

${\mathbf{V}}_{\mathbf{c}\mathbf{o}}$ | 25 | m/s |

**Table 4.**Technical parameters, maintenance and operational costs of ESS [45].

Parameters | Amount | Unit |
---|---|---|

${\mathbf{E}\mathbf{S}}_{\mathbf{e}}^{\mathbf{m}\mathbf{i}\mathbf{n}}$ | 0.2 | MW |

${\mathbf{E}\mathbf{S}}_{\mathbf{e}}^{\mathbf{m}\mathbf{a}\mathbf{x}}$ | 2 | MW |

${\mathbf{P}}_{\mathbf{E}\mathbf{S}-\mathbf{d}\mathbf{c}\mathbf{h}}^{\mathbf{m}\mathbf{a}\mathbf{x}}$ | 0.5 | MW |

${\mathbf{P}}_{\mathbf{E}\mathbf{S}-\mathbf{c}\mathbf{h}}^{\mathbf{m}\mathbf{a}\mathbf{x}}$ | 0.5 | MW |

${\mathbf{E}\mathbf{S}}_{\mathbf{e}}\left(\mathbf{0}\right)$ | 0.2 | MW |

${\mathrm{\eta}}_{\mathbf{c}\mathbf{h}}^{\mathbf{E}\mathbf{S}}$ | 90 | % |

${\mathrm{\eta}}_{\mathbf{d}\mathbf{c}\mathbf{h}}^{\mathbf{E}\mathbf{S}}$ | 80 | % |

${\mathbf{C}}_{\mathbf{M}\mathbf{E}\mathbf{S}\mathbf{S}}$ | 0.001 | $/h |

${\mathbf{C}}_{\mathbf{O}\mathbf{E}\mathbf{S}\mathbf{S}}$ | 15 | $/MWh |

Emission Factor | DG [46] | Main-Grid [47] |
---|---|---|

${\mathbf{C}\mathbf{O}}_{\mathbf{2}}$ | 73.98 | 921.25 |

${\mathbf{S}\mathbf{O}}_{\mathbf{2}}$ | 1.02 | 3.583 |

${\mathbf{N}\mathbf{O}}_{\mathbf{X}}$ | 0.09 | 2.295 |

CS | Cost | Variation * (%) | Emission | Variation * (%) |
---|---|---|---|---|

CS#1 | 238,077.95 $ | - | 74,580.2 kg | - |

CS#2 | 236,937.56 $ | 0.47 | 67,359.99 kg | 9.68 |

CS#3 | 237,801.2 $ | 0.11 | 61,717.98 kg | 17.24 |

CS#4 | 235,473.46 $ | 1.10 | 52,354.95 kg | 29.80 |

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## Share and Cite

**MDPI and ACS Style**

Darvishi, M.; Tahmasebi, M.; Shokouhmand, E.; Pasupuleti, J.; Bokoro, P.; Raafat, J.S.
Optimal Operation of Sustainable Virtual Power Plant Considering the Amount of Emission in the Presence of Renewable Energy Sources and Demand Response. *Sustainability* **2023**, *15*, 11012.
https://doi.org/10.3390/su151411012

**AMA Style**

Darvishi M, Tahmasebi M, Shokouhmand E, Pasupuleti J, Bokoro P, Raafat JS.
Optimal Operation of Sustainable Virtual Power Plant Considering the Amount of Emission in the Presence of Renewable Energy Sources and Demand Response. *Sustainability*. 2023; 15(14):11012.
https://doi.org/10.3390/su151411012

**Chicago/Turabian Style**

Darvishi, Mostafa, Mehrdad Tahmasebi, Ehsan Shokouhmand, Jagadeesh Pasupuleti, Pitshou Bokoro, and Jwan Satei Raafat.
2023. "Optimal Operation of Sustainable Virtual Power Plant Considering the Amount of Emission in the Presence of Renewable Energy Sources and Demand Response" *Sustainability* 15, no. 14: 11012.
https://doi.org/10.3390/su151411012