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Register a new userMultistability in lossy power grids and oscillator networks
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The stable operation of the electric power grid relies on a precisely synchronized state of all generators and machines. All machines rotate at exactly the same frequency with fixed phase differences, leading to steady power flows throughout the grid. Whether such a steady state exists for a given network is of eminent practical importance. The loss of a steady state typically leads to power outages up to a complete blackout. But also the existence of multiple steady states is undesirable, as it can lead to sudden transitions, circulating flows and eventually also to power outages. Steady states are typically calculated numerically, but this approach gives only limited insight into the existence and (non-)uniqueness of steady states. Analytic results are available only for special network configuration, in particular for grids with negligible Ohmic losses or radial networks without any loops. In this article, we introduce a method to systematically construct the solutions of the real power load-flow equations in the presence of Ohmic losses. We calculate the steady states explicitly for elementary networks demonstrating different mechanisms leading to multistability. Our results also apply to models of coupled oscillators which are widely used in theoretical physics and mathematical biology.
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Modern societies crucially depend on the robust supply with electric energy. Blackouts of power grids can thus have far reaching consequences. During a blackout, often the failure of a single infrastructure, such as a critical transmission line, results in several subsequent failures that spread across large parts of the network. Preventing such large-scale outages is thus key for assuring a reliable power supply. Here we present a non-local curing strategy for oscillatory power grid networks based on the global collective redistribution of loads. We first identify critical links and compute residual capacities on alternative paths on the remaining network from the original flows. For each critical link, we upgrade lines that constitute bottlenecks on such paths. We demonstrate the viability of this strategy for random ensembles of network topologies as well as topologies derived from real transmission grids and compare the nonlocal strategy against local back-ups of critical links. These strategies are independent of the detailed grid dynamics and combined may serve as an effective guideline to reduce outages in power grid networks by intentionally strengthen optimally selected links.
Behavioral homogeneity is often critical for the functioning of network systems of interacting entities. In power grids, whose stable operation requires generator frequencies to be synchronized--and thus homogeneous--across the network, previous work suggests that the stability of synchronous states can be improved by making the generators homogeneous. Here, we show that a substantial additional improvement is possible by instead making the generators suitably heterogeneous. We develop a general method for attributing this counterintuitive effect to converse symmetry breaking, a recently established phenomenon in which the system must be asymmetric to maintain a stable symmetric state. These findings constitute the first demonstration of converse symmetry breaking in real-world systems, and our method promises to enable identification of this phenomenon in other networks whose functions rely on behavioral homogeneity.
A scenario has recently been reported in which in order to stabilize complete synchronization of an oscillator network---a symmetric state---the symmetry of the system itself has to be broken by making the oscillators nonidentical. But how often does such behavior---which we term asymmetry-induced synchronization (AISync)---occur in oscillator networks? Here we present the first general scheme for constructing AISync systems and demonstrate that this behavior is the norm rather than the exception in a wide class of physical systems that can be seen as multilayer networks. Since a symmetric network in complete synchrony is the basic building block of cluster synchronization in more general networks, AISync should be common also in facilitating cluster synchronization by breaking the symmetry of the cluster subnetworks.
We show that amplitude chimeras in ring networks of Stuart-Landau oscillators with symmetry-breaking nonlocal coupling represent saddle-states in the underlying phase space of the network. Chimera states are composed of coexisting spatial domains of coherent and of incoherent oscillations. We calculate the Floquet exponents and the corresponding eigenvectors in dependence upon the coupling strength and range, and discuss the implications for the phase space structure. The existence of at least one positive real part of the Floquet exponents indicates an unstable manifold in phase space, which explains the nature of these states as long-living transients. Additionally, we find a Stuart-Landau network of minimum size $N=12$ exhibiting amplitude chimeras
We study the strategy to optimally maximize the dynamic range of excitable networks by removing the minimal number of links. A network of excitable elements can distinguish a broad range of stimulus intensities and has its dynamic range maximized at criticality. In this study, we formulate the activation propagation in excitable networks as a message passing process in which the critical state is reached when the largest eigenvalue of the weighted non-backtracking (WNB) matrix is exactly one. By considering the impact of single link removal on the largest eigenvalue, we develop an efficient algorithm that aims to identify the optimal set of links whose removal will drive the system to the critical state. Comparisons with other competing heuristics on both synthetic and real-world networks indicate that the proposed method can maximize the dynamic range by removing the smallest number of links, and at the same time maintain the largest size of the giant connected component.
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