Transitions from trees to cycles in adaptive flow networks

Transport networks are crucial to the functioning of natural and technological systems. Nature features transport networks that are adaptive over a vast range of parameters, thus providing an impressive level of robustness in supply. Theoretical and experimental studies have found that real-world transport networks exhibit both tree-like motifs and cycles. When the network is subject to load fluctuations, the presence of cyclic motifs may help to reduce flow fluctuations and, thus, render supply in the network more robust. While previous studies considered network topology via optimization principles, here, we take a dynamical systems approach and study a simple model of a flow network with dynamically adapting weights (conductances). We assume a spatially non-uniform distribution of rapidly fluctuating loads in the sinks and investigate what network configurations are dynamically stable. The network converges to a spatially non-uniform stable configuration composed of both cyclic and tree-like structures. Cyclic structures emerge locally in a transcritical bifurcation as the amplitude of the load fluctuations is increased. The resulting adaptive dynamics thus partitions the network into two distinct regions with cyclic and tree-like structures. The location of the boundary between these two regions is determined by the amplitude of the fluctuations. These findings may explain why natural transport networks display cyclic structures in the micro-vascular regions near terminal nodes, but tree-like features in the regions with larger veins

Distributed Stochastic Market Clearing with High-Penetration Wind Power

Integrating renewable energy into the modern power grid requires risk-cognizant dispatch of resources to account for the stochastic availability of renewables. Toward this goal, day-ahead stochastic market clearing with high-penetration wind energy is pursued in this paper based on the DC optimal power flow (OPF). The objective is to minimize the social cost which consists of conventional generation costs, end-user disutility, as well as a risk measure of the system re-dispatching cost. Capitalizing on the conditional value-at-risk (CVaR), the novel model is able to mitigate the potentially high risk of the recourse actions to compensate wind forecast errors. The resulting convex optimization task is tackled via a distribution-free sample average based approximation to bypass the prohibitively complex high-dimensional integration. Furthermore, to cope with possibly large-scale dispatchable loads, a fast distributed solver is developed with guaranteed convergence using the alternating direction method of multipliers (ADMM). Numerical results tested on a modified benchmark system are reported to corroborate the merits of the novel framework and proposed approaches.Comment: To appear in IEEE Transactions on Power Systems; 12 pages and 9 figure

Robust Matrix Completion State Estimation in Distribution Systems

Due to the insufficient measurements in the distribution system state estimation (DSSE), full observability and redundant measurements are difficult to achieve without using the pseudo measurements. The matrix completion state estimation (MCSE) combines the matrix completion and power system model to estimate voltage by exploring the low-rank characteristics of the matrix. This paper proposes a robust matrix completion state estimation (RMCSE) to estimate the voltage in a distribution system under a low-observability condition. Tradition state estimation weighted least squares (WLS) method requires full observability to calculate the states and needs redundant measurements to proceed a bad data detection. The proposed method improves the robustness of the MCSE to bad data by minimizing the rank of the matrix and measurements residual with different weights. It can estimate the system state in a low-observability system and has robust estimates without the bad data detection process in the face of multiple bad data. The method is numerically evaluated on the IEEE 33-node radial distribution system. The estimation performance and robustness of RMCSE are compared with the WLS with the largest normalized residual bad data identification (WLS-LNR), and the MCSE