# Modeling, Optimization, and Analysis of a Virtual Power Plant Demand Response Mechanism for the Internal Electricity Market Considering the Uncertainty of Renewable Energy Sources

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## Abstract

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## 1. Introduction

#### 1.1. Literature Review and Research Gap

#### 1.2. Contributions and Study Layout

- The proposed strategy is designed and developed to visualize the trading of electricity within the VPP environment. This strategy encourages consumers to minimize their load at peak hours, while energy storage systems and distributed generators are also used to their full possible capacity, contributing to balancing the system’s total net load.
- The constrained OPF problem is formulated as an optimization problem, and the relevant solutions are obtained for each of the three cases in terms of cost minimization. Load curtailment of the Internal consumers has a favorable effect on the VPP’s aim of minimizing costs.
- The results obtained from the three test cases are comprehensively compared and analyzed and it was found that a DR program application has a significant impact on the VPP’s internal electricity market cost minimization as compared to the base case model and BESS model.

## 2. Aim and Approach

## 3. Uncertainty Modeling

#### 3.1. Wind Speed Modeling

_{wt}and P

_{rated}represent the WT output power and the rated power. ${\nu}_{ci}$ and ${\nu}_{co}$ represent the cut-in and cut-out speed. The rated speed of WT is represented by ${\nu}_{r}$ [15,22,25]. The wind speed power curve of WT is shown in Figure 1.

#### 3.2. Modeling of Solar Irradiance

_{STC}and P

_{PV}denote the power in (MW) under standard test conditions and the PV module output power in kilowatts, respectively. The power–temperature coefficient in (%/°C) is denoted by δ. T

_{amb}, T

_{cell}, and NOCT represent the ambient temperature in °C, the cell temperature in °C, and the nominal operating cell temperature conditions in °C. G represents solar irradiance in watt per meter square [26,27,28,29].

#### 3.3. Load Demand Uncertainty Modeling

## 4. Problem Formulation

#### 4.1. Base Case Model

#### 4.2. Demand Response Model

#### 4.3. BESS Model

## 5. VPP Electricity Market Model Description

## 6. Case Study, Simulation, and Results and Discussion

_{min}= 0.94 p. u/V

_{max}= 0.95 p. u. In this study, it is anticipated that WTs with a capacity of 660 kW, PV with a capacity of 440 kW, and a storage system with a capacity of 200 kW are installed at their assigned buses. The proposed approach is solved as a nonlinear optimization problem. All relevant data with some modifications have been taken from [14,15] to fit our purpose. Table 2 shows the results comparison of the three cases of utility cost optimization. The proposed mechanism is implemented in a GAMS environment and solved with a nonlinear model [33,34,35].

#### 6.1. Case 1

#### 6.2. Case 2

#### 6.3. Case 3

## 7. Locational Marginal Costs Comparison

## 8. Conclusions and Future Research

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

Line | Resistance (pu) | Reactance (pu) | Line Charging Susceptance (pu) | |
---|---|---|---|---|

From Bus | To Bus | |||

1 | 2 | 0.01938 | 0.05917 | 0.0528 |

1 | 5 | 0.05403 | 0.22304 | 0.0492 |

2 | 3 | 0.04699 | 0.19797 | 0.0438 |

2 | 4 | 0.05811 | 0.17632 | 0.0340 |

2 | 5 | 0.05695 | 0.17388 | 0.0346 |

3 | 4 | 0.06701 | 0.17103 | 0.0128 |

4 | 5 | 0.01335 | 0.04211 | 0 |

6 | 11 | 0.09498 | 0.19890 | 0 |

6 | 12 | 0.12291 | 0.25581 | 0 |

6 | 13 | 0.06615 | 0.13027 | 0 |

7 | 8 | 0 | 0.17615 | 0 |

7 | 9 | 0 | 0.11001 | 0 |

9 | 10 | 0.03181 | 0.08450 | 0 |

9 | 14 | 0.12711 | 0.27038 | 0 |

10 | 11 | 0.08205 | 0.19207 | 0 |

12 | 13 | 0.22092 | 0.19988 | 0 |

13 | 14 | 0.17093 | 0.34802 | 0 |

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References | RES Management | DR Model | BESS Model | Uncertainty Modeling | Power Market |
---|---|---|---|---|---|

[12] | No | No | Yes | No | Yes |

[13] | Yes | No | Yes | Yes | Yes |

[14] | Yes | No | Yes | No | Yes |

[15] | Yes | No | No | Yes | Yes |

[16] | Yes | No | Yes | Yes | Yes |

[17] | Yes | No | No | Yes | No |

[18] | Yes | Yes | No | No | No |

[19] | Yes | Yes | Yes | No | No |

[20] | Yes | No | Yes | No | Yes |

[21] | Yes | No | Yes | Yes | No |

This paper | Yes | Yes | Yes | Yes | Yes |

Cases | Total Utility Cost (USD) |
---|---|

A (base case) | 33,593,826 |

B (DR case) | 33,487,100 |

C (BESS case) | 33,589,662 |

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**MDPI and ACS Style**

Ullah, Z.; Arshad; Hassanin, H.
Modeling, Optimization, and Analysis of a Virtual Power Plant Demand Response Mechanism for the Internal Electricity Market Considering the Uncertainty of Renewable Energy Sources. *Energies* **2022**, *15*, 5296.
https://doi.org/10.3390/en15145296

**AMA Style**

Ullah Z, Arshad, Hassanin H.
Modeling, Optimization, and Analysis of a Virtual Power Plant Demand Response Mechanism for the Internal Electricity Market Considering the Uncertainty of Renewable Energy Sources. *Energies*. 2022; 15(14):5296.
https://doi.org/10.3390/en15145296

**Chicago/Turabian Style**

Ullah, Zahid, Arshad, and Hany Hassanin.
2022. "Modeling, Optimization, and Analysis of a Virtual Power Plant Demand Response Mechanism for the Internal Electricity Market Considering the Uncertainty of Renewable Energy Sources" *Energies* 15, no. 14: 5296.
https://doi.org/10.3390/en15145296