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Cavraro, Guido

Publications and source records attributed to Cavraro, Guido.

10 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

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 energysharing 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.

aggregates↗
DOE OSTI2024

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

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 energysharing 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.

energy communities↗
DOE OSTI2024

Dynamically Learning Incentives for Load Control

As electrical generation becomes more distributed and volatile, and loads become more uncertain, controllability of distributed energy resources (DERs), regardless of their ownership status, will be necessary for grid reliability. Grid operators lack direct control over end-users' grid interactions, such as energy usage, but incentives can influence behavior -- for example, an end-user that receives a grid-driven incentive may adjust their consumption or expose relevant control variables in response. A key challenge in studying such incentives is the lack of data about human behavior, which usually motivates strong assumptions, such as distributional assumptions on compliance or rational utility-maximization. In this paper, we propose a general incentive mechanism in the form of a constrained optimization problem -- our approach is distinguished from prior work by modeling human behavior (e.g., reactions to an incentive) as an arbitrary unknown function. We propose feedback-based optimization algorithms to solve this problem that each leverage different amounts of information and/or measurements. We show that each converges to an asymptotically stable incentive with (near)-optimality guarantees given mild assumptions on the problem. Finally, we evaluate our proposed techniques in voltage regulation simulations on standard test beds. We test a variety of settings, including those that break assumptions required for theoretical convergence (e.g., convexity, smoothness) to capture realistic settings. In this evaluation, our proposed algorithms are able to find near-optimal incentives even when the reaction to an incentive is modeled by a theoretically difficult (yet realistic) function.

demand response↗
DOE OSTI2024

A Decentralized Market Mechanism for Energy Communities under Operating Envelopes

Here, 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.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Chapter 7: Learning Stable Local Volt/Var Controllers in Distribution Grids

This chapter describes a framework to synthesize provably stable local Volt/Var controllers for distributed energy resources (DERs) in power distribution grids (DGs). The goal is to control the reactive power injections of DERs to improve the system performance as quantified by a generic optimal reactive power flow (ORPF) problem. To achieve this, we jointly design for each DER the control function, which prescribes the reactive power update rule, and the equilibrium function, which approximates the ORPF solutions from local measurements of voltages and powers. We provide conditions on the equilibrium functions and the control parameters ensuring the stability of the closed-loop system. In particular, we discuss the trade-offs between each set of conditions accounting for practical considerations, like fully exploiting the DERs' generation capabilities and reducing the optimality gap. These conditions are then translated into learning constraints on the neural networks' parameters that are enforced in the training phase. We validate our framework with numerical simulations on the IEEE 37-bus network and through a comparison with an optimized version of standard piece wise linear control rules.

closed-loop asymptotic stability↗
DOE OSTI2024

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. Herein 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.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

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 and a numerical example is provided.

biological system modeling↗
DOE OSTI2024

On the Stability of Power Transmission Systems Under Persistent Inverter Attacks: A Bi-Linear Matrix Approach

We investigate the stability and robustness properties of a power transmission system under persistent deceiving attacks on inverter-interfaced energy resources. The attacks can corrupt the damping coefficients in the inverters' controllers and measurements of the frequency at the points of coupling. Leveraging tools from hybrid dynamical systems theory, we characterize a broad family of persistent (and not necessarily periodic) attacks acting on the inverters, under which the stability properties of the transmission system can be shown to not be compromised. To address potentially conservative conditions identified through conventional bounding techniques, sufficient conditions on the average activation time of the attacks are identified via Lyapunov theory, as well as the formulation and solution of a class of bilinear matrix inequalities (BMI). The results are obtained for constant and slowly time-varying loads via input-to-state stability (ISS) tools. Numerical simulations on the IEEE 39-bus test system are also presented.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Unsupervised Learning for Equitable DER Control: Preprint

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.

asymptotic stability↗