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

^{1}

^{2}

^{*}

## Abstract

**:**

## 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

- ENTSO-E. Continental Europe Significant Frequency Deviations January 2019. Available online: https://www.entsoe.eu (accessed on 17 February 2020).
- Kundur, P.; Paserba, J.; Ajjarapu, V.; Andersson, G.; Bose, A.; Cañizares, C.; Hatziargyriou, N.; Hill, D.; Stankovic, A.; Taylor, C.; et al. Definition and classification of power system stability IEEE/CIGRE joint task force on stability terms and definitions. IEEE Trans. Power Syst.
**2004**, 19, 1387–1401. [Google Scholar] - Kërçi, T.; Milano, F. A framework to embed the unit commitment problem into time domain simulations. In Proceedings of the 2019 IEEE International Conference on Environment and Electrical Engineering, Genova, Italy, 11–14 June 2019. [Google Scholar]
- Vorobev, P.; Greenwood, D.M.; Bell, J.H.; Bialek, J.W.; Taylor, P.C.; Turitsyn, K. Deadbands, droop, and inertia impact on power system frequency distribution. IEEE Trans. Power Syst.
**2019**, 34, 3098–3108. [Google Scholar] [CrossRef] [Green Version] - Wang, J.; Wang, J.; Liu, C.; Ruiz, J.P. Stochastic unit commitment with sub-hourly dispatch constraints. Appl. Energy
**2013**, 105, 418–422. [Google Scholar] [CrossRef] - Gangammanavar, H.; Sen, S.; Zavala, V.M. Stochastic optimization of sub-hourly economic dispatch with wind energy. IEEE Trans. Power Syst.
**2016**, 31, 949–959. [Google Scholar] [CrossRef] - Wang, B.; Hobbs, B.F. Real-time markets for flexiramp: A stochastic unit commitment-based analysis. IEEE Trans. Power Syst.
**2016**, 31, 846–860. [Google Scholar] [CrossRef] - Gu, Y.; Xie, L. Stochastic look-ahead economic dispatch with variable generation resources. IEEE Trans. Power Syst.
**2017**, 32, 17–29. [Google Scholar] [CrossRef] - Milano, F.; Dörfler, F.; Hug, G.; Hill, D.J.; Verbič, G. Foundations and challenges of low-inertia systems (invited paper). In Proceedings of the 2018 Power Systems Computation Conference (PSCC), Dublin, Ireland, 11–15 June 2018. [Google Scholar]
- Ahmadi, H.; Ghasemi, H. Security-Constrained Unit Commitment With Linearized System Frequency Limit Constraints. IEEE Trans. Power Syst.
**2014**, 29, 1536–1545. [Google Scholar] [CrossRef] - Singh Parmar, K.P.; Majhi, S.; Kothari, D.P. Load frequency control of a realistic power system with multi-source power generation. Int. J. Electr. Power Energy Syst.
**2012**, 42, 426–433. [Google Scholar] [CrossRef] - Kërçi, T.; Milano, F. Sensitivity Analysis of the Interaction between Power System Dynamics and Unit Commitment. In Proceedings of the 2019 IEEE Milan PowerTech, Milan, Italy, 23–27 June 2019. [Google Scholar]
- Kërçi, T.; Giraldo, J.; Milano, F. Analysis of the impact of sub-hourly unit commitment on power system dynamics. Int. J. Electr. Power Energy Syst.
**2020**, 119, 105819. [Google Scholar] [CrossRef] - Yuan, B.; Zhou, M.; Li, G.; Zhang, X. Stochastic Small-Signal Stability of Power Systems With Wind Power Generation. IEEE Trans. Power Syst.
**2015**, 30, 1680–1689. [Google Scholar] [CrossRef] - Wang, X.; Chiang, H.; Wang, J.; Liu, H.; Wang, T. Long-Term Stability Analysis of Power Systems With Wind Power Based on Stochastic Differential Equations: Model Development and Foundations. IEEE Trans. Power Syst.
**2015**, 30, 1534–1542. [Google Scholar] [CrossRef] [Green Version] - Milano, F.; Zárate-Miñano, R. A Systematic Method to Model Power Systems as Stochastic Differential Algebraic Equations. IEEE Trans. Power Syst.
**2013**, 28, 4537–4544. [Google Scholar] [CrossRef] - Kundur, P. Power System Stability and Control; McGraw-Hill: New York, NY, USA, 1994. [Google Scholar]
- Milano, F. Power System Modeling and Scripting; Springer: London, UK, 2010. [Google Scholar]
- IEA-WIND. Design and Operation of Power Systems with Large Amounts of Wind Power. Available online: https://community.ieawind.org (accessed on 17 February 2020).
- Morales, J.; Conejo, A.; Madsen, H.; Pinson, P.; Zugno, M. Integrating Renewables in Electricity Markets: Operational Problems; Springer: Berlin, Germany, 2013. [Google Scholar]
- Conejo, A.; Carrión, M.; Morales, J. Decision Making Under Uncertainty in Electricity Markets; Springer: Berlin, Germany, 2010. [Google Scholar]
- Blanco, I.; Morales, J.M. An Efficient Robust Solution to the Two-Stage Stochastic Unit Commitment Problem. IEEE Trans. Power Syst.
**2017**, 32, 4477–4488. [Google Scholar] [CrossRef] [Green Version] - Håberg, M. Fundamentals and recent developments in stochastic unit commitment. Int. J. Electr. Power Energy Syst.
**2019**, 109, 38–48. [Google Scholar] [CrossRef] - Zheng, Q.P.; Wang, J.; Liu, A.L. Stochastic Optimization for Unit Commitment—A Review. IEEE Trans. Power Syst.
**2015**, 30, 1913–1924. [Google Scholar] [CrossRef] - Gómez Expósito, A.; Conejo, A.; Cañizares, C. Electric Energy Systems: Analysis and Operation; CRC Press: Boca Raton, FL, USA, 2018. [Google Scholar]
- Palensky, P.; Van Der Meer, A.A.; Lopez, C.D.; Joseph, A.; Pan, K. Cosimulation of Intelligent Power Systems: Fundamentals, Software Architecture, Numerics, and Coupling. IEEE Ind. Electron. Mag.
**2017**, 11, 34–50. [Google Scholar] [CrossRef] - Milano, F. A Python-based software tool for power system analysis. In Proceedings of the IEEE PES General Meeting, Vancouver, BC, Canada, 21–25 July 2013; pp. 1–5. [Google Scholar]
- Gurobi Optimization, LLC. Gurobi Optimizer Reference Manual; Gurobi Optimization, LLC: Houston, TX, USA, 2018. [Google Scholar]
- Illinois Center for a Smarter Electric Grid (ICSEG). IEEE 39-Bus System. Available online: https://icseg.iti.illinois.edu/ieee-39-bus-system/ (accessed on 17 February 2020).
- Carrión, M.; Arroyo, J.M. A computationally efficient mixed-integer linear formulation for the thermal unit commitment problem. IEEE Trans. Power Syst.
**2006**, 21, 1371–1378. [Google Scholar] [CrossRef] - Costley, M.; Feizollahi, M.J.; Ahmed, S.; Grijalva, S. A rolling-horizon unit commitment framework with flexible periodicity. Int. J. Electr. Power Energy Syst.
**2017**, 90, 280–291. [Google Scholar] [CrossRef]

**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 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**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