Stochastic Small Signal Stability of a Power System with Uncertainties
Abstract
:1. Introduction
- (1)
- First, the probability of the state deviations falling within an interval is provided in an analytical way, so it is easier than the existing methods by solving a partial differential equation;
- (2)
- Secondly, only some algebraic conditions need to be examined for identifying stochastic stability and this can be carried out efficiently compared with the Monte Carlo based approaches for practical applications;
- (3)
- Thirdly, since the proposed system stability index explicitly takes the uncertainty magnitudes into consideration, the dynamic process of the system states with uncertainties can be theoretically explained.
2. Mathematical Background
3. Noise-to-State Stability Based Probabilistic Stability Analysis
3.1. The Stochastic Model of a Power System
3.2. Stochastic Small Signal Stability Analysis
3.3. Application of Noise-to-State Stability Based Probabilistic Stability Analysis
3.4. Algorithm of Noise-to-State Stability Based Probabilistic Stability Analysis
4. Case Studies
4.1. A Stochastic Single-Machine Infinite-Bus System
4.2. The 145-Bus Test System
5. Conclusions
- (a)
- The NSS based probabilistic stability index is proposed for the stochastic stability analysis of a power system;
- (b)
- The impact of power stochastic variation magnitudes is explicitly presented in the proposed NSS based probabilistic stability index;
- (c)
- The NSS based probabilistic stability analysis for the power system is obtained by using the NSS-LF;
- (d)
- The algorithm for the stability probability computation is given for power system small signal stability analysis;
- (e)
- The algebraic relation between the magnitude of uncertainty and the probabilistic stability of the system responses is found.
Author Contributions
Funding
Conflicts of Interest
Nomenclatures
δi | The rotor angle of the ith generator (rad) |
ωi | The rotor speed of the ith generator (rad/s) |
ωN | The synchronous machine speed 2πf (rad/s) |
Hi | The inertia coefficient of the ith generator (seconds) |
Pmi | The mechanical power of the ith generator (p.u.) |
Ei | The internal voltage of the ith generator (p.u.) |
Di | The damping constant of the ith generator (p.u.) |
Bij | The element in the ith row and jth column of Kron-reduced susceptance matrix (p.u.) |
Σi | The magnitude of stochastic power fluctuation (p.u.) |
Appendix A
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State Variables | Estimated Interval | Stability Probability |
---|---|---|
|δ| | ≤1.8524 | ≥0.9 |
|δ| | ≤1.3099 | ≥0.8 |
State variables of G1, G6, and G37 | Estimated Interval | Stability Probability |
---|---|---|
|δ| | ≤3.5174 | ≥0.9 |
|δ| | ≤2.4871 | ≥0.8 |
|δ| | ≤2.0307 | ≥0.7 |
Test System | Proposed Method | Monte Carlo Simulation |
---|---|---|
New England test system | 0.019 | 99.92 |
145-bus test system | 0.022 | 195.47 |
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Xu, Y.; Wen, F.; Zhao, H.; Chen, M.; Yang, Z.; Shang, H. Stochastic Small Signal Stability of a Power System with Uncertainties. Energies 2018, 11, 2980. https://doi.org/10.3390/en11112980
Xu Y, Wen F, Zhao H, Chen M, Yang Z, Shang H. Stochastic Small Signal Stability of a Power System with Uncertainties. Energies. 2018; 11(11):2980. https://doi.org/10.3390/en11112980
Chicago/Turabian StyleXu, Yan, Fushuan Wen, Hongwei Zhao, Minghui Chen, Zeng Yang, and Huiyu Shang. 2018. "Stochastic Small Signal Stability of a Power System with Uncertainties" Energies 11, no. 11: 2980. https://doi.org/10.3390/en11112980
APA StyleXu, Y., Wen, F., Zhao, H., Chen, M., Yang, Z., & Shang, H. (2018). Stochastic Small Signal Stability of a Power System with Uncertainties. Energies, 11(11), 2980. https://doi.org/10.3390/en11112980