Distributionally Robust Stability-Constrained Optimization for Managing Uncertainty in Power System Dynamics

핵심 개념

The core message of this article is to propose a distributionally robust stability-constrained optimization framework that can effectively manage the uncertainty in power system dynamics, such as inaccurate modeling of system components, and ensure stable system operation.

초록

This article presents a framework for managing the uncertainty in power system dynamics through distributionally robust stability-constrained optimization. The key highlights and insights are:

1. The authors identify that the uncertainty associated with the system dynamic parameters, such as the impedances of synchronous generators and inverter-based resources, can significantly influence the system stability and operation. This uncertainty needs to be explicitly considered in the stability-constrained optimization.

2. To address this issue, the authors propose a two-step approach:
   a. Quantify the uncertainty of the stability constraint coefficients by propagating the statistical moments of the uncertain system parameters through a nonlinear and implicit function composition.
   b. Formulate a distributionally robust chance-constrained optimization problem to ensure system stability under the derived uncertainty of the constraint coefficients.

3. The authors derive the analytical expressions for the first and second-order derivatives of the stability index with respect to the uncertain system parameters, which are then used to estimate the statistical moments of the stability constraint coefficients.

4. The proposed distributionally robust stability-constrained optimization is demonstrated on a modified IEEE 39-bus system. The results show that the approach can effectively manage the system dynamic uncertainty and maintain stable system operation.

5. An alternative formulation based on distributionally robust learning is also discussed, which directly considers the uncertainty in the training process of the stability constraints. However, this formulation becomes computationally intractable due to the highly nonlinear relationship between the stability index and the uncertain system parameters.

통계

The system has a load demand of P^D ∈ [5.16, 6.24] GW and a load damping of D = 0.5%P^D/1 Hz.
The base power of the system is S_B = 100 MVA.

인용구

"With the increasing penetration of Inverter-Based Resources (IBRs) and their impact on power system stability and operation, the concept of stability-constrained optimization has drawn significant attention from researchers."
"The uncertainties in the system dynamics, however, have been less focused, which may result in unstable or over-conservative operation."

핵심 통찰 요약

Managing the Uncertainty in System Dynamics Through Distributionally Robust Stability-Constrained Optimization

by Zhongda Chu,... 게시일 arxiv.org 04-23-2024

https://arxiv.org/pdf/2309.03798.pdf

더 깊은 질문

How can the proposed distributionally robust optimization framework be extended to consider other types of uncertainties, such as renewable generation and load forecast errors, in addition to the system dynamic uncertainties

The proposed distributionally robust optimization framework can be extended to consider other types of uncertainties, such as renewable generation and load forecast errors, by incorporating these uncertainties into the optimization model. For renewable generation uncertainties, probabilistic forecasting techniques can be used to estimate the probability distribution of renewable generation outputs. This information can then be integrated into the optimization model as additional constraints or objective functions. Similarly, load forecast errors can be modeled probabilistically, and their impact on system operation can be considered in the optimization framework. By including these uncertainties in the model, the decision-making process can become more robust and adaptive to varying conditions.

What are the potential limitations of the moment-based ambiguity set used in the distributionally robust formulation, and how can alternative ambiguity sets be explored to reduce the conservativeness of the solution

The moment-based ambiguity set used in the distributionally robust formulation has certain limitations that can lead to conservativeness in the solution. One potential limitation is that the moment-based approach may not capture the full range of possible distributions, leading to overly conservative solutions. To address this, alternative ambiguity sets can be explored, such as Wasserstein ambiguity sets or distributionally robust optimization with moment constraints. These alternative sets can provide a more nuanced representation of uncertainty and reduce the conservativeness of the solution by considering a wider range of possible distributions. By incorporating these alternative ambiguity sets, the optimization model can achieve a better balance between robustness and optimality.

Given the computational complexity of the alternative formulation based on distributionally robust learning, are there any efficient reformulation techniques or approximation methods that can be developed to make this approach more tractable

Given the computational complexity of the alternative formulation based on distributionally robust learning, there are efficient reformulation techniques and approximation methods that can be developed to make this approach more tractable. One approach is to use convex relaxation techniques to approximate the non-convex optimization problem and obtain a tractable solution. Additionally, heuristic algorithms, such as genetic algorithms or simulated annealing, can be employed to find near-optimal solutions in a computationally efficient manner. By leveraging these reformulation techniques and approximation methods, the alternative formulation based on distributionally robust learning can be made more scalable and practical for real-world applications.