Distributionally Robust Chance-Constrained Approximate AC-OPF with Wasserstein Metric (1706.05538v2)

Abstract: Chance constrained optimal power flow (OPF) has been recognized as a promising framework to manage the risk from variable renewable energy (VRE). In presence of VRE uncertainties, this paper discusses a distributionally robust chance constrained approximate AC-OPF. The power flow model employed in the proposed OPF formulation combines an exact AC power flow model at the nominal operation point and an approximate linear power flow model to reflect the system response under uncertainties. The ambiguity set employed in the distributionally robust formulation is the Wasserstein ball centered at the empirical distribution. The proposed OPF model minimizes the expectation of the quadratic cost function w.r.t. the worst-case probability distribution and guarantees the chance constraints satisfied for any distribution in the ambiguity set. The whole method is data-driven in the sense that the ambiguity set is constructed from historical data without any presumption on the type of the probability distribution, and more data leads to smaller ambiguity set and less conservative strategy. Moreover, special problem structures of the proposed problem formulation are exploited to develop an efficient and scalable solution approach. Case studies are carried out on IEEE 14 and 118 bus systems to show the accuracy and necessity of the approximate AC model and the attractive features of the distributionally robust optimization approach compared with other methods to deal with uncertainties.

• The paper presents a novel distributionally robust chance-constrained AC-OPF model that integrates full AC accuracy with tractable linear approximations under VRE uncertainty.
• It employs the Wasserstein metric to build an adaptive ambiguity set for forecast errors, reducing conservativeness as more data becomes available.
• Numerical studies on IEEE 14 and 118-bus systems demonstrate enhanced operational reliability and computational efficiency, especially in voltage and reactive power predictions.

Insights into Distributionally Robust Chance-Constrained Approximate AC-OPF with Wasserstein Metric

This paper presents a novel approach to addressing uncertainties in optimal power flow (OPF) models due to variable renewable energy (VRE) sources. The authors propose a distributionally robust chance-constrained approximate AC-OPF framework leveraging the Wasserstein metric. This approach aims to maintain system security while minimizing operational costs, considering the inherent uncertainties of VRE generation.

Key Contributions and Methodology

The research addresses the limitations of traditional OPF models by formulating a tractable approximation of the AC power flow that integrates the full AC model at the nominal operating point with an approximate linear model for system response under uncertainties. This model retains the accuracy of full AC models while achieving the simplicity required for stochastic optimization.

Significantly, this work harnesses a data-driven approach using the Wasserstein metric to construct an ambiguity set for the underlying probability distribution of VRE forecast errors. This allows for robust decision-making under distributional uncertainty. The ambiguity set, a Wasserstein ball centered at the empirical distribution, adapts as more data is incorporated, reducing conservativeness.

Additionally, the authors exploit specific structural properties of the reformulated OPF problem to develop efficient solution methodologies. This includes an upper bound approximation for the worst-case expected cost and a transformation of robust chance constraints into tractably deterministic forms, enhancing scalability and computational efficiency.

Numerical Analysis and Results

Through case studies conducted on IEEE 14 and 118-bus systems, the paper demonstrates the OPF model's capability to manage different levels of wind integration effectively. The proposed model is compared against robust optimization (RO), moment-based distributionally robust optimization (MDRO), and Gauss-based stochastic programming (GSP).

The results emphasize the accuracy and necessity of incorporating voltage and reactive power constraints, showcasing their critical role in avoiding risky and impractical operations. Furthermore, the novel AC-OPF formulation delivers superior accuracy compared to DC models, especially in predicting voltage magnitudes and line flows.

On the computational front, the use of the Wasserstein metric in data-driven optimization exhibits adaptive conservatism, transitioning from approaches similar to RO when little data is available to GSP as more historical information is harnessed. Moreover, the computation time for real-time operation remains markedly efficient and independent of the amount of historical data, affirming the method's scalability.

Theoretical and Practical Implications

The paper makes substantial theoretical contributions by integrating data-driven methods with classical AC power flow models in OPF. From a practical standpoint, it offers a robust and adaptive framework for operators to manage uncertain environments induced by VREs, enhancing both operational reliability and cost-efficiency.

As power systems continue to evolve with higher VRE penetrations, future developments may include extending this robust, data-driven optimization framework to more complex and large-scale power networks. Additional research could focus on integrating other sources of uncertainty such as demand fluctuations or cyber-physical contingencies, broadening the operational reliability of modern power systems.