Congestion-Sensitive Grid Aggregation for DC Optimal Power Flow

TL;DR

Confronting DC-OPF scalability in large grids, the paper develops grid-aggregation methods that preserve line congestions by introducing the Network Congestion Price ($NCP$) as a congestion-sensitive distance metric. It derives $NCP = PTDF^{T}\mathrm{diag}(\bar{\boldsymbol{\varphi}} - \underline{\boldsymbol{\varphi}})$ and contrasts it with the traditional Locational Marginal Price ($LMP$) approach, evaluating five partitioning methods (combining either metric with KMeans, Spectral Clustering, or Adjacent Node Agglomerative Clustering) on adapted IEEE RTS 24-Bus and 300-Bus systems. Across two case studies, $NCP$-based methods, particularly $NCP$-KMeans, deliver lower relative objective-value errors and smaller maximum line-limit violations than $LMP$-based counterparts, while achieving faster partitioning than the ANAC approach. The results demonstrate that $NCP$ better preserves essential network physics in the aggregated DC-OPF model, enabling tractable yet accurate optimization with practical implications for planning and operation; future work includes multi-period extensions and planning-oriented distance metrics.

Abstract

The vast spatial dimension of modern interconnected electricity grids challenges the tractability of the DC optimal power flow problem. Grid aggregation methods try to overcome this challenge by reducing the number of network elements. Many existing methods use Locational Marginal Prices as a distance metric to cluster nodes. In this paper, we show that prevalent methods adopting this distance metric fail to adequately capture the impact of individual lines when there is more than one line congested. This leads to suboptimal outcomes for the optimization of the aggregated model. To overcome those issues, we propose two methods based on the novel Network Congestion Price metric, which preserves the impact of nodal power injections on individual line congestions. The proposed methods are compared to several existing aggregation methods based on Locational Marginal Prices. We demonstrate all methods on adapted versions of the IEEE RTS 24- and 300-Bus systems. We show that the proposed methods outperform existing approaches both in terms of objective function value error and maximum line limit violation, while exhibiting faster node clustering. We conclude that aggregation methods based on the novel Network Congestion Price metric are better at preserving the essential physical characteristics of the network topology in the grid aggregation process than methods based on Locational Marginal Prices.

Figures (5)

• Figure 1: Evaluation of grid aggregation methods.
• Figure 2: Illustration of the adapted IEEE RTS 24-Bus System ordoudis_updated_nodate. The colors show the optimal line loading $\boldsymbol{\bar{f}}^*$ and the LMPs.
• Figure 3: Grid partitionings of the IEEE RTS 24-Bus System resulting from the aggregation methods stated in table \ref{['tab:clustering_methods']} for $\tilde{N} = 5$ nodes in the aggregated grid. Congested lines are marked in red.
• Figure 4: Relative OFV error for different grid aggregation methods applied to the modified IEEE 300-Bus System as a function of the number of nodes $\tilde{N}=50,\dots,1$ in the AM.
• Figure 5: The maximum relative line limit violation for grid aggregations of the adapted IEEE 300-Bus system, depending on the number of nodes $\tilde{N}=50,\dots,1$ in the AM.