arXiv subjects

Guido Cavraro

Publications and source records attributed to Guido Cavraro.

At least 19 recordsLinked to original sources

arXiv2026

Demand Response Under Stochastic, Price-Dependent User Behavior

This paper focuses on price-based residential demand response implemented through dynamic adjustments of electricity prices during DR events. It extends existing DR models to a stochastic framework in which customer response is represented by price-dependent random variables, leveraging models and tools from the theory of stochastic optimization with decision-dependent distributions. The inherent epistemic uncertainty in the customers' responses renders open-loop, model-based DR strategies impractical. To address this challenge, the paper proposes to employ stochastic, feedback-based pricing strategies to compensate for estimation errors and uncertainty in customer response. The paper then establishes theoretical results demonstrating the stability and near-optimality of the proposed approach and validates its effectiveness through numerical simulations.

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arXiv2025

Control of Power Grids With Switching Equilibria: $Ω$-Limit Sets and Input-to-State Stability

This paper studies a power transmission system with both conventional generators (CGs) and distributed energy assets (DEAs) providing frequency control. We consider an operating condition with demand aggregating two dynamic components: one that switches between different values on a finite set, and one that varies smoothly over time. Such dynamic operating conditions may result from protection scheme activations, external cyber-attacks, or due to the integration of dynamic loads, such as data centers. Mathematically, the dynamics of the resulting system are captured by a system that switches between a finite number of vector fields -- or modes--, with each mode having a distinct equilibrium point induced by the demand aggregation. To analyze the stability properties of the resulting switching system, we leverage tools from hybrid dynamic inclusions and the concept of $Ω$-limit sets from sets. Specifically, we characterize a compact set that is semi-globally practically asymptotically stable under the assumption that the switching frequency and load variation rate are sufficiently slow. For arbitrarily fast variations of the load, we use a level-set argument with multiple Lyapunov functions to establish input-to-state stability of a larger set and with respect to the rate of change of the loads. The theoretical results are illustrated via numerical simulations on the IEEE 39-bus test system.

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arXiv2024

A Decentralized Market Mechanism for Energy Communities under Operating Envelopes

We propose an operating envelopes (OEs) aware energy community market mechanism that dynamically charges/rewards its members based on two-part pricing. The OEs are imposed exogenously by a regulated distribution system operator (DSO) on the energy community's revenue meter and is subject to a generalized net energy metering (NEM) tariff design. By formulating the interaction of the community operator and its members as a Stackelberg game, we show that the proposed two-part pricing achieves a Nash equilibrium and maximizes the community's social welfare in a decentralized fashion while ensuring that the community's operation abides by the OEs. The market mechanism conforms with the cost-causation principle and guarantees community members a surplus level no less than their maximum surplus when they autonomously face the DSO. The dynamic and uniform community price is a monotonically decreasing function of the community's aggregate renewable generation. We also analyze the impact of exogenous parameters such as NEM rates and OEs on the value of joining the community. Lastly, through numerical studies, we showcase the community's welfare, and pricing, and compare its members' surplus to customers under the DSO's regime.

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arXiv2024

Network-Aware and Welfare-Maximizing Dynamic Pricing for Energy Sharing

The proliferation of behind-the-meter (BTM) distributed energy resources (DER) within the electrical distribution network presents significant supply and demand flexibilities, but also introduces operational challenges such as voltage spikes and reverse power flows. In response, this paper proposes a network-aware dynamic pricing framework tailored for energy-sharing coalitions that aggregate small, but ubiquitous, BTM DER downstream of a distribution system operator's (DSO) revenue meter that adopts a generic net energy metering (NEM) tariff. By formulating a Stackelberg game between the energy-sharing market leader and its prosumers, we show that the dynamic pricing policy induces the prosumers toward a network-safe operation and decentrally maximizes the energy-sharing social welfare. The dynamic pricing mechanism involves a combination of a locational ex-ante dynamic price and an ex-post allocation, both of which are functions of the energy sharing's BTM DER. The ex-post allocation is proportionate to the price differential between the DSO NEM price and the energy-sharing locational price. Simulation results using real DER data and the IEEE 13-bus test systems illustrate the dynamic nature of network-aware pricing at each bus, and its impact on voltage.

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arXiv2024

Learning Provably Stable Local Volt/Var Controllers for Efficient Network Operation

This paper develops a data-driven framework to synthesize local Volt/Var control strategies for distributed energy resources (DERs) in power distribution networks (DNs). Aiming to improve DN operational efficiency, as quantified by a generic optimal reactive power flow (ORPF) problem, we propose a two-stage approach. The first stage involves learning the manifold of optimal operating points determined by an ORPF instance. To synthesize local Volt/Var controllers, the learning task is partitioned into learning local surrogates (one per DER) of the optimal manifold with voltage input and reactive power output. Since these surrogates characterize efficient DN operating points, in the second stage, we develop local control schemes that steer the DN to these operating points. We identify the conditions on the surrogates and control parameters to ensure that the locally acting controllers collectively converge, in a global asymptotic sense, to a DN operating point agreeing with the local surrogates. We use neural networks to model the surrogates and enforce the identified conditions in the training phase. AC power flow simulations on the IEEE 37-bus network empirically bolster the theoretical stability guarantees obtained under linearized power flow assumptions. The tests further highlight the optimality improvement compared to prevalent benchmark methods.

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arXiv2024

Advocating Feedback Control for Human-Earth System Applications

This paper proposes a feedback control perspective for Human-Earth Systems (HESs) which essentially are complex systems that capture the interactions between humans and nature. Recent attention in HES research has been directed towards devising strategies for climate change mitigation and adaptation, aimed at achieving environmental and societal objectives. However, existing approaches heavily rely on HES models, which inherently suffer from inaccuracies due to the complexity of the system. Moreover, overly detailed models often prove impractical for optimization tasks. We propose a framework inheriting from feedback control strategies the robustness against model errors, because inaccuracies are mitigated using measurements retrieved from the field. The framework comprises two nested control loops. The outer loop computes the optimal inputs to the HES, which are then implemented by actuators controlled in the inner loop. Potential fields of applications are also identified.

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arXiv2024

Feedback Optimization of Incentives for Distribution Grid Services

Energy prices and net power injection limitations regulate the operations in distribution grids and typically ensure that operational constraints are met. Nevertheless, unexpected or prolonged abnormal events could undermine the grid's functioning. During contingencies, customers could contribute effectively to sustaining the network by providing services. This paper proposes an incentive mechanism that promotes users' active participation by essentially altering the energy pricing rule. The incentives are modeled via a linear function whose parameters can be computed by the system operator (SO) by solving an optimization problem. Feedback-based optimization algorithms are then proposed to seek optimal incentives by leveraging measurements from the grid, even in the case when the SO does not have a full grid and customer information. Numerical simulations on a standard testbed validate the proposed approach.

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arXiv2024

Unsupervised Learning for Equitable DER Control

In the context of managing distributed energy resources (DERs) within distribution networks (DNs), this work focuses on the task of developing local controllers. We propose an unsupervised learning framework to train functions that can closely approximate optimal power flow (OPF) solutions. The primary aim is to establish specific conditions under which these learned functions can collectively guide the network towards desired configurations asymptotically, leveraging an incremental control approach. The flexibility of the proposed methodology allows to integrate fairness-driven components into the cost function associated with the OPF problem. This addition seeks to mitigate power curtailment disparities among DERs, thereby promoting equitable power injections across the network. To demonstrate the effectiveness of the proposed approach, power flow simulations are conducted using the IEEE 37-bus feeder. The findings not only showcase the guaranteed system stability but also underscore its improved overall performance.

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arXiv2023

Operating-Envelopes-Aware Decentralized Welfare Maximization for Energy Communities

We propose an operating-envelope-aware, prosumer-centric, and efficient energy community that aggregates individual and shared community distributed energy resources and transacts with a regulated distribution system operator (DSO) under a generalized net energy metering tariff design. To ensure safe network operation, the DSO imposes dynamic export and import limits, known as dynamic operating envelopes, on end-users' revenue meters. Given the operating envelopes, we propose an incentive-aligned community pricing mechanism under which the decentralized optimization of community members' benefit implies the optimization of overall community welfare. The proposed pricing mechanism satisfies the cost-causation principle and ensures the stability of the energy community in a coalition game setting. Numerical examples provide insights into the characteristics of the proposed pricing mechanism and quantitative measures of its performance.

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arXiv2023

Constraints on OPF Surrogates for Learning Stable Local Volt/Var Controllers

We consider the problem of learning local Volt/Var controllers in distribution grids (DGs). Our approach starts from learning separable surrogates that take both local voltages and reactive powers as arguments and predict the reactive power setpoints that approximate optimal power flow (OPF) solutions. We propose an incremental control algorithm and identify two different sets of slope conditions on the local surrogates such that the network is collectively steered toward desired configurations asymptotically. Our results reveal the trade-offs between each set of conditions, with coupled voltage-power slope constraints allowing an arbitrary shape of surrogate functions but risking limitations on exploiting generation capabilities, and reactive power slope constraints taking full advantage of generation capabilities but constraining the shape of surrogate functions. AC power flow simulations on the IEEE 37-bus feeder illustrate their guaranteed stability properties and respective advantages in two DG scenarios.

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arXiv2023

Learning Distribution Grid Topologies: A Tutorial

Unveiling feeder topologies from data is of paramount importance to advance situational awareness and proper utilization of smart resources in power distribution grids. This tutorial summarizes, contrasts, and establishes useful links between recent works on topology identification and detection schemes that have been proposed for power distribution grids. The primary focus is to highlight methods that overcome the limited availability of measurement devices in distribution grids, while enhancing topology estimates using conservation laws of power-flow physics and structural properties of feeders. Grid data from phasor measurement units or smart meters can be collected either passively in the traditional way, or actively, upon actuating grid resources and measuring the feeder's voltage response. Analytical claims on feeder identifiability and detectability are reviewed under disparate meter placement scenarios. Such topology learning claims can be attained exactly or approximately so via algorithmic solutions with various levels of computational complexity, ranging from least-squares fits to convex optimization problems, and from polynomial-time searches over graphs to mixed-integer programs. Although the emphasis is on radial single-phase feeders, extensions to meshed and/or multiphase circuits are sometimes possible and discussed. This tutorial aspires to provide researchers and engineers with knowledge of the current state-of-the-art in tractable distribution grid learning and insights into future directions of work.

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arXiv2022

Learning Local Volt/Var Controllers Towards Efficient Network Operation with Stability Guarantees

This paper considers the problem of voltage regulation in distribution networks. The primary motivation is to keep voltages within preassigned operating limits by commanding the reactive power output of distributed energy resources (DERs) deployed in the grid. We develop a framework for developing local Volt/Var control that comprises two main steps. In the first, by exploiting historical data and for each DER, we learn a function representing the desirable equilibrium points for the power network. These points approximate solutions of an Optimal Power Flow (OPF) problem. In the second, we propose a control scheme for steering the network towards these favorable configurations. Theoretical conditions are derived to formally guarantee the stability of the developed control scheme, and numerical simulations illustrate the effectiveness of the proposed approach.

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arXiv2022

Agent-Supervisor Coordination for Decentralized Event-Triggered Optimization

This paper proposes decentralized resource-aware coordination schemes for solving network optimization problems defined by objective functions which combine locally evaluable costs with network-wide coupling components. These methods are well suited for a group of supervised agents trying to solve an optimization problem under mild coordination requirements. Each agent has information on its local cost and coordinates with the network supervisor for information about the coupling term of the cost. The proposed approach is feedback-based and asynchronous by design, guarantees anytime feasibility, and ensures the asymptotic convergence of the network state to the desired optimizer. Numerical simulations on a power system example illustrate our results.

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arXiv2021

Online State Estimation for Time-Varying Systems

The paper investigates the problem of estimating the state of a time-varying system with a linear measurement model; in particular, the paper considers the case where the number of measurements available can be smaller than the number of states. In lieu of a batch linear least-squares (LS) approach -- well suited for static networks, where a sufficient number of measurements could be collected to obtain a full-rank design matrix -- the paper proposes an online algorithm to estimate the possibly time-varying state by processing measurements as and when available. The design of the algorithm hinges on a generalized LS cost augmented with a proximal-point-type regularization. With the solution of the regularized LS problem available in closed-form, the online algorithm is written as a linear dynamical system where the state is updated based on the previous estimate and based on the new available measurements. Conditions under which the algorithmic steps are in fact a contractive mapping are shown, and bounds on the estimation error are derived for different noise models. Numerical simulations are provided to corroborate the analytical findings.

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arXiv2021

Ripple-Type Control for Enhancing Resilience of Networked Physical Systems

Distributed control agents have been advocated as an effective means for improving the resiliency of our physical infrastructures under unexpected events. Purely local control has been shown to be insufficient, centralized optimal resource allocation approaches can be slow. In this context, we put forth a hybrid low-communication saturation-driven protocol for the coordination of control agents that are distributed over a physical system and are allowed to communicate with peers over a "hotline" communication network. According to this protocol, agents act on local readings unless their control resources have been depleted, in which case they send a beacon for assistance to peer agents. Our ripple-type scheme triggers communication locally only for the agents with saturated resources and it is proved to converge. Moreover, under a monotonicity assumption on the underlying physical law coupling control outputs to inputs, the devised control is proved to converge to a configuration satisfying safe operational constraints. The assumption is shown to hold for voltage control in electric power systems and pressure control in water distribution networks. Numerical tests corroborate the efficacy of the novel scheme.

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arXiv2020

Novel Region of Attraction Characterization for Control and Stabilization of Voltage Dynamics

In this paper, we study the monitoring and control of long-term voltage stability considering load tap-changer (LTC) dynamics. We show that under generic conditions, the LTC dynamics always admit a unique stable equilibrium. For the stable equilibrium, we characterize an explicit inner approximation of its region of attraction (ROA). Compared to existing results, the computational complexity of the ROA characterization is drastically reduced. A quadratically constrained linear program formulation for the ROA characterization problem is proposed. In addition, we formulate a second-order cone program for online voltage stability monitoring and control exploiting the proposed ROA characterization, along with an ADMM-based distributed algorithm to solve the problem. The efficacy of the proposed formulations and algorithms is demonstrated using a standard IEEE test system.

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arXiv2020

Learning to Optimize Power Distribution Grids using Sensitivity-Informed Deep Neural Networks

Deep learning for distribution grid optimization can be advocated as a promising solution for near-optimal yet timely inverter dispatch. The principle is to train a deep neural network (DNN) to predict the solutions of an optimal power flow (OPF), thus shifting the computational effort from real-time to offline. Nonetheless, before training this DNN, one has to solve a large number of OPFs to create a labeled dataset. Granted the latter step can still be prohibitive in time-critical applications, this work puts forth an original technique for improving the prediction accuracy of DNNs by taking into account the sensitivities of the OPF minimizers with respect to the OPF parameters. By expanding on multiparametric programming, it is shown that although inverter control problems may exhibit dual degeneracy, the required sensitivities do exist in general and can be computed readily using the output of any standard quadratic program (QP) solver. Numerical tests showcase that sensitivity-informed deep learning can enhance prediction accuracy in terms of mean square error (MSE) by 2-3 orders of magnitude at minimal computational overhead. Improvements are more significant in the small-data regime, where a DNN has to learn to optimize using a few examples. Beyond multiparametric QPs, the approach is currently being generalized to parametric (non)-convex optimization problems.

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arXiv2020

An MILP Approach for Distribution Grid Topology Identification using Inverter Probing

Although knowing the feeder topology and line impedances is a prerequisite for solving any grid optimization task, utilities oftentimes have limited or outdated information on their electric network assets. Given the rampant integration of smart inverters, we have previously advocated perturbing their power injections to unveil the underlying grid topology using the induced voltage responses. Under an approximate grid model, the perturbed power injections and the collected voltage deviations obey a linear regression setup, where the unknown is the vector of line resistances. Building on this model, topology processing can be performed in two steps. Given a candidate radial topology, the line resistances can be estimated via a least-squares (LS) fit on the probing data. The topology attaining the best fit can be then selected. To avoid evaluating the exponentially many candidate topologies, this two-step approach is uniquely formulated as a mixed-integer linear program (MILP) using the McCormick relaxation. If the recovered topology is not radial, a second, computationally more demanding MILP confines the search only within radial topologies. Numerical tests explain how topology recovery depends on the noise level and probing duration, and demonstrate that the first simpler MILP yields a tree topology in 90% of the cases tested.

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