arXiv subjects

Alessandro Zocca

Publications and source records attributed to Alessandro Zocca.

At least 37 records · Page 2Linked to original sources

arXiv2022

Adaptive Network Response to Line Failures in Power Systems

Transmission line failures in power systems propagate and cascade non-locally. In this work, we propose an adaptive control strategy that offers strong guarantees in both the mitigation and localization of line failures. Specifically, we leverage the properties of network bridge-block decomposition and a frequency regulation method called the unified control. If the balancing areas over which the unified control operates coincide with the bridge-blocks of the network, the proposed strategy drives the post-contingency system to a steady state where the impact of initial line outages is localized within the areas where they occurred whenever possible, stopping the cascading process. When the initial line outages cannot be localized, the proposed control strategy provides a configurable design that progressively involves and coordinates more balancing areas. We compare the proposed control strategy with the classical Automatic Generation Control (AGC) on the IEEE 118-bus and 2736-bus test networks. Simulation results show that our strategy greatly improves overall reliability in terms of the N-k security standard, and localizes the impact of initial failures in the majority of the simulated contingencies. Moreover, the proposed framework incurs significantly less load loss, if any, compared to AGC, in all our case studies.

eess.SY↗

arXiv2022

Interface Networks for Failure Localization in Power Systems

Transmission power systems usually consist of interconnected sub-grids that are operated relatively independently. When a failure happens, it is desirable to localize its impact within the sub-grid where the failure occurs. This paper introduces three interface networks to connect sub-grids, achieving better failure localization while maintaining robust network connectivity. The proposed interface networks are validated with numerical experiments on the IEEE 118-bus test network under both DC and AC power flow models.

eess.SY↗

arXiv2021

Refining bridge-block decompositions through two-stage and recursive tree partitioning

In transmission networks power flows and network topology are deeply intertwined due to power flow physics. Recent literature shows that specific network substructures named bridge-blocks prevent line failures from propagating globally. A two-stage and recursive tree partitioning approach have been proposed to create more bridge-blocks in transmission networks, improving their robustness against cascading line failures. In this paper we consider the problem of refining the bridge-block decomposition of a given power network with minimal impact on the maximum congestion. We propose two new solution methods, depending on the preferred power flow model. More specifically, (i) we introduce a novel MILP-based approach that uses the DC approximation to solve more efficiently the second-stage optimization problem of the two-stage approach and (ii) we show how the existing recursive approach can be extended to work with AC power flows, drastically improving the running times when compared to the pre-existing AC-based two-stage method.

math.OC↗

arXiv2021

A Metropolis-class sampler for targets with non-convex support

We aim to improve upon the exploration of the general-purpose random walk Metropolis algorithm when the target has non-convex support $A \subset \mathbb{R}^d$, by reusing proposals in $A^c$ which would otherwise be rejected. The algorithm is Metropolis-class and under standard conditions the chain satisfies a strong law of large numbers and central limit theorem. Theoretical and numerical evidence of improved performance relative to random walk Metropolis are provided. Issues of implementation are discussed and numerical examples, including applications to global optimisation and rare event sampling, are presented.

math.PR↗

arXiv2021

Hopping between distant basins

We present the Basin Hopping with Skipping (BH-S) algorithm for stochastic optimisation, which replaces the perturbation step of basin hopping (BH) with a so-called skipping proposal from the rare-event sampling literature. Empirical results on benchmark optimisation surfaces demonstrate that BH-S can improve performance relative to BH by encouraging non-local exploration, that is, by hopping between distant basins.

math.OC↗

arXiv2021

A Spectral Representation of Power Systems with Applications to Adaptive Grid Partitioning and Cascading Failure Localization

Transmission line failures in power systems propagate and cascade non-locally. This well-known yet counter-intuitive feature makes it even more challenging to optimally and reliably operate these complex networks. In this work we present a comprehensive framework based on spectral graph theory that fully and rigorously captures how multiple simultaneous line failures propagate, distinguishing between non-cut and cut set outages. Using this spectral representation of power systems, we identify the crucial graph sub-structure that ensures line failure localization -- the network bridge-block decomposition. Leveraging this theory, we propose an adaptive network topology reconfiguration paradigm that uses a two-stage algorithm where the first stage aims to identify optimal clusters using the notion of network modularity and the second stage refines the clusters by means of optimal line switching actions. Our proposed methodology is illustrated using extensive numerical examples on standard IEEE networks and we discussed several extensions and variants of the proposed algorithm.

math.OC↗

arXiv2021

Line Failure Localization of Power Networks Part I: Non-cut Outages

Transmission line failures in power systems propagate non-locally, making the control of the resulting outages extremely difficult. In this work, we establish a mathematical theory that characterizes the patterns of line failure propagation and localization in terms of network graph structure. It provides a novel perspective on distribution factors that precisely captures Kirchhoff's Law in terms of topological structures. Our results show that the distribution of specific collections of subtrees of the transmission network plays a critical role on the patterns of power redistribution, and motivates the block decomposition of the transmission network as a structure to understand long-distance propagation of disturbances. In Part I of this paper, we present the case when the post-contingency network remains connected after an initial set of lines are disconnected simultaneously. In Part II, we present the case when an outage separates the network into multiple islands.

eess.SY↗

arXiv2021

Line Failure Localization of Power Networks Part II: Cut Set Outages

Transmission line failure in power systems prop-agate non-locally, making the control of the resulting outages extremely difficult. In Part II of this paper, we continue the study of line failure localizability in transmission networks and characterize the impact of cut set outages. We establish a Simple Path Criterion, showing that the propagation pattern due to bridge outages, a special case of cut set failures, are fully determined by the positions in the network of the buses that participate in load balancing. We then extend our results to general cut set outages. In contrast to non-cut outages discussed in Part I whose subsequent line failures are contained within the original blocks, cut set outages typically impact the whole network, affecting the power flows on all remaining lines. We corroborate our analytical results in both parts using the IEEE 118-bus test system, in which the failure propagation patterns exhibit a clear block-diagonal structure predicted by our theory, even when using full AC power flow equations.

eess.SY↗

arXiv2020

An Integrated Approach for Failure Mitigation & Localization in Power Systems

The transmission grid is often comprised of several control areas that are connected by multiple tie lines in a mesh structure for reliability. It is also well-known that line failures can propagate non-locally and redundancy can exacerbate cascading. In this paper, we propose an integrated approach to grid reliability that (i) judiciously switches off a small number of tie lines so that the control areas are connected in a tree structure; and (ii) leverages a unified frequency control paradigm to provide congestion management in real time. Even though the proposed topology reduces redundancy, the integration of tree structure at regional level and real-time congestion management can provide stronger guarantees on failure localization and mitigation. We illustrate our approach on the IEEE 39-bus network and evaluate its performance on the IEEE 118-bus, 179-bus, 200-bus and 240-bus networks with various network congestion conditions. Simulations show that, compared with the traditional approach, our approach not only prevents load shedding in more failure scenarios, but also incurs smaller amounts of load loss in scenarios where load shedding is inevitable. Moreover, generators under our approach adjust their operations more actively and efficiently in a local manner.

eess.SY↗

arXiv2020

Large Fluctuations in Locational Marginal Prices

This paper investigates large fluctuations of Locational Marginal Prices (LMPs) in wholesale energy markets caused by volatile renewable generation profiles. Specifically, we study events of the form $\mathbb{P} \Big ( \mathbf{LMP} \notin \prod_{i=1}^n [α_i^-, α_i^+] \Big),$ where $\mathbf{LMP}$ is the vector of LMPs at the $n$ power grid nodes, and $\boldsymbolα^-,\boldsymbolα^+\in\mathbb{R}^n$ are vectors of price thresholds specifying undesirable price occurrences. By exploiting the structure of the supply-demand matching mechanism in power grids, we look at LMPs as deterministic piecewise affine, possibly discontinuous functions of the stochastic input process, modeling uncontrollable renewable generation. We utilize techniques from large deviations theory to identify the most likely ways for extreme price spikes to happen, and to rank the nodes of the power grid in terms of their likelihood of experiencing a price spike. Our results are derived in the case of Gaussian fluctuations and are validated numerically on the IEEE 14-bus test case.

math.OC↗

arXiv2020

Optimization of stochastic lossy transport networks and applications to power grids

Motivated by developments in renewable energy and smart grids, we formulate a stylized mathematical model of a transport network with stochastic load fluctuations. Using an affine control rule, we explore the trade-off between the number of controllable resources in a lossy transport network and the performance gain they yield in terms of expected power losses. Our results are explicit and reveal the interaction between the level of flexibility, the intrinsic load uncertainty and the network structure.

math.OC↗

arXiv2020

Weighted Dyck paths for nonstationary queues

We consider a model for a queue in which only a fixed number $N$ of customers can join. Each customer joins the queue independently at an exponentially distributed time. Assuming further that the service times are independent and follow an exponential distribution, this system can be described as a two-dimensional Markov process on a finite triangular region $\mathfrak S$ of the square lattice. We interpret the resulting random walk on $\mathfrak S$ as a Dyck path that is weighted according to some state-dependent transition probabilities that are constant along one axis, but are rather general otherwise. We untangle the resulting intricate combinatorial structure by introducing appropriate generating functions that exploit the recursive structure of the model. This allows us to derive a fully explicit expression for the probability density function of the number of customers served in any busy period (equivalently, of the length of any excursion of the Dyck path above the diagonal) as a weighted sum with alternating sign over a certain subclass of Dyck paths, whose study is of independent interest.

math.PR↗

arXiv2019

Less is More: Real-time Failure Localization in Power Systems

Cascading failures in power systems exhibit non-local propagation patterns which make the analysis and mitigation of failures difficult. In this work, we propose a distributed control framework inspired by the recently proposed concepts of unified controller and network tree-partition that offers strong guarantees in both the mitigation and localization of cascading failures in power systems. In this framework, the transmission network is partitioned into several control areas which are connected in a tree structure, and the unified controller is adopted by generators or controllable loads for fast timescale disturbance response. After an initial failure, the proposed strategy always prevents successive failures from happening, and regulates the system to the desired steady state where the impact of initial failures are localized as much as possible. For extreme failures that cannot be localized, the proposed framework has a configurable design, that progressively involves and coordinates more control areas for failure mitigation and, as a last resort, imposes minimal load shedding. We compare the proposed control framework with Automatic Generation Control (AGC) on the IEEE 118-bus test system. Simulation results show that our novel framework greatly improves the system robustness in terms of the N-1 security standard, and localizes the impact of initial failures in majority of the load profiles that are examined. Moreover, the proposed framework incurs significantly less load loss, if any, compared to AGC, in all of our case studies.

eess.SY↗

arXiv2018

Tunneling behavior of Ising and Potts models in the low-temperature regime

We consider the ferromagnetic $q$-state Potts model with zero external field in a finite volume and assume that the stochastic evolution of this system is described by a Glauber-type dynamics parametrized by the inverse temperature $β$. Our analysis concerns the low-temperature regime $β\to \infty$, in which this multi-spin system has $q$ stable equilibria, corresponding to the configurations where all spins are equal. Focusing on grid graphs with various boundary conditions, we study the tunneling phenomena of the $q$-state Potts model. More specifically, we describe the asymptotic behavior of the first hitting times between stable equilibria as $β\to \infty$ in probability, in expectation, and in distribution and obtain tight bounds on the mixing time as side-result. In the special case $q=2$, our results characterize the tunneling behavior of the Ising model on grid graphs.

math.PR↗

arXiv2018

Failure Localization in Power Systems via Tree Partitions

Cascading failures in power systems propagate non-locally, making the control and mitigation of outages extremely hard. In this work, we use the emerging concept of the tree partition of transmission networks to provide an analytical characterization of line failure localizability in transmission systems. Our results rigorously establish the well perceived intuition in power community that failures cannot cross bridges, and reveal a finer-grained concept that encodes more precise information on failure propagations within tree-partition regions. Specifically, when a non-bridge line is tripped, the impact of this failure only propagates within well-defined components, which we refer to as cells, of the tree partition defined by the bridges. In contrast, when a bridge line is tripped, the impact of this failure propagates globally across the network, affecting the power flow on all remaining transmission lines. This characterization suggests that it is possible to improve the system robustness by temporarily switching off certain transmission lines, so as to create more, smaller components in the tree partition; thus spatially localizing line failures and making the grid less vulnerable to large-scale outages. We illustrate this approach using the IEEE 118-bus test system and demonstrate that switching off a negligible portion of transmission lines allows the impact of line failures to be significantly more localized without substantial changes in line congestion.

eess.SY↗

arXiv2018

Temporal starvation in multi-channel CSMA networks: an analytical framework

In this paper we consider a stochastic model for a frequency-agile CSMA protocol for wireless networks where multiple orthogonal frequency channels are available. Even when the possible interference on the different channels is described by different conflict graphs, we show that the network dynamics can be equivalently described as that of a single-channel CSMA algorithm on an appropriate virtual network. Our focus is on the asymptotic regime in which the network nodes try to activate aggressively in order to achieve maximum throughput. Of particular interest is the scenario where the number of available channels is not sufficient for all nodes of the network to be simultaneously active and the well-studied temporal starvation issues of the single-channel CSMA dynamics persist. For most networks we expect that a larger number of available channels should alleviate these temporal starvation issues. However, we prove that the aggregate throughput is a non-increasing function of the number of available channels. To investigate this trade-off that emerges between aggregate throughput and temporal starvation phenomena, we propose an analytical framework to study the transient dynamics of multi-channel CSMA networks by means of first hitting times. Our analysis further reveals that the mixing time of the activity process does not always correctly characterize the temporal starvation in the multi-channel scenario and often leads to pessimistic performance estimates.

math.PR↗

arXiv2018

Tunneling of the hard-core model on finite triangular lattices

We consider the hard-core model on finite triangular lattices with Metropolis dynamics. Under suitable conditions on the triangular lattice dimensions, this interacting particle system has three maximum-occupancy configurations and we investigate its high-fugacity behavior by studying tunneling times, i.e., the first hitting times between between these maximum-occupancy configurations, and the mixing time. The proof method relies on the analysis of the corresponding state space using geometrical and combinatorial properties of the hard-core configurations on finite triangular lattices, in combination with known results for first hitting times of Metropolis Markov chains in the equivalent zero-temperature limit. In particular, we show how the order of magnitude of the expected tunneling times depends on the triangular lattice dimensions in the low-temperature regime and prove the asymptotic exponentiality of the rescaled tunneling time leveraging the intrinsic symmetry of the state space.

math.PR↗

arXiv2018

Emergent failures and cascades in power grids: a statistical physics perspective

We model power grids transporting electricity generated by intermittent renewable sources as complex networks, where line failures can emerge indirectly by noisy power input at the nodes. By combining concepts from statistical physics and the physics of power flows, and taking weather correlations into account, we rank line failures according to their likelihood and establish the most likely way such failures occur and propagate. Our insights are mathematically rigorous in a small-noise limit and are validated with data from the German transmission grid.

physics.soc-ph↗