# Sensitivity Analysis of the Impact of the Sub- Hourly Stochastic Unit Commitment on Power System Dynamics

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## Abstract

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## 1. Introduction

#### 1.1. Motivation

#### 1.2. Literature Review

#### 1.3. Contributions

- A cosimulation framework that allows to assess the effect that different subhourly SUC models have on the long-term dynamic behaviour of power systems.
- A thorough sensitivity analysis with respect to the interaction between different subhourly SUC models, different frequency control/machine parameters and power system dynamics.
- Show through the aforementioned analysis that synchronous machine inertia has little effect on the standard deviation of the frequency. This result is in accordance with the discussion provided in [4].
- Show that the gain of automatic generation control (AGC) is (most of the time) the main parameter affecting the standard deviation of the frequency.

#### 1.4. Organization

## 2. Modeling

#### 2.1. Stochastic Long-Term Power System Model

#### 2.2. Wind Power Modeling

#### 2.3. Primary and Secondary Frequency Controllers of Conventional Power Plants

#### 2.4. Stochastic Unit Commitment

#### 2.5. Simplified SUC Formulation

#### 2.6. Alternative SUC Formulation

#### 2.7. Cosimulation Framework

## 3. Case Study

#### 3.1. Sensitivity Analysis of the Impact of Different Frequency Controllers/Machine Parameters

#### 3.1.1. SUC with 15-min Time Period

#### 3.1.2. DUC with 15-min Time Period

#### 3.1.3. Sensitivity Analysis Using the Simplified and Alternative SUC, and 15-min Time Period

#### 3.1.4. SUC with 5-min Time Period

#### 3.1.5. DUC with 5-min Time Period

#### 3.2. Comparison of Different SUC Models

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**Structure of the interaction between the discrete model of the stochastic unit commitment (SUC) and dynamic model of SDAEs.

**Figure 4.**15-min time period—${\sigma}_{\mathrm{COI}}$ as a function of different frequency controllers/machine parameters using the complete SUC and DUC models.

**Figure 5.**15-min time period—${\sigma}_{\mathrm{COI}}$ as a function of different frequency controllers/machine parameters using the simplified and alternative SUC models.

**Figure 6.**5-min time period—${\sigma}_{\mathrm{COI}}$ as a function of different frequency controllers/machine parameters.

**Figure 9.**Mechanical power of synchronous generators 1, 2 and 4, for 15-min time period and complete SUC model.

**Figure 10.**Mechanical power of synchronous generators 1, 2 and 4, for 15-min time period and simplified SUC model.

**Figure 11.**Trajectories of ${\omega}_{\mathrm{COI}}$ for 15-min time period and alternative SUC model.

**Figure 12.**Mechanical power synchronous generators 1, 2 and 4, for 15-min time period and alternative SUC model.

Model | Total Operation Cost ($) |
---|---|

SUC (Complete) | 412,000 |

SUC (Simplified) | 398,000 |

SUC (Alternative) | 339,470 |

DUC | 411,580 |

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**MDPI and ACS Style**

Kërçi, T.; Giraldo, J.S.; Milano, F.
Sensitivity Analysis of the Impact of the Sub- Hourly Stochastic Unit Commitment on Power System Dynamics. *Energies* **2020**, *13*, 1468.
https://doi.org/10.3390/en13061468

**AMA Style**

Kërçi T, Giraldo JS, Milano F.
Sensitivity Analysis of the Impact of the Sub- Hourly Stochastic Unit Commitment on Power System Dynamics. *Energies*. 2020; 13(6):1468.
https://doi.org/10.3390/en13061468

**Chicago/Turabian Style**

Kërçi, Taulant, Juan S. Giraldo, and Federico Milano.
2020. "Sensitivity Analysis of the Impact of the Sub- Hourly Stochastic Unit Commitment on Power System Dynamics" *Energies* 13, no. 6: 1468.
https://doi.org/10.3390/en13061468