arXiv subjects

Andrey Bernstein

Publications and source records attributed to Andrey Bernstein.

At least 19 recordsLinked to original sources

arXiv2026

Unlocking Deep Demand Flexibility via Dynamic Signals

The rapid proliferation of distributed energy resources (DERs) and the electrification of residential loads offer significant potential for grid flexibility but pose stability challenges under static pricing regimes. Specifically, high levels of automation under static Time-of-Use (TOU) tariffs often induce ``device synchronization,'' where simultaneous responses from home energy management systems (HEMS) create artificial demand peaks that threaten grid stability. This paper proposes a privacy-preserving, one-way dynamic signaling framework to unlock deep demand flexibility from HEMS. We utilize a feedback-based learning algorithm that updates day-ahead price profiles based on aggregate substation demand and environmental contexts, effectively closing the loop between utility objectives and aggregated edge behaviors. The framework is rigorously validated using high-fidelity simulations on an 84-bus distribution network populated with hundreds of HEMS controlling diverse devices, including HVAC, PV, batteries, and flexible loads. Results demonstrate that the proposed mechanism achieves substantial reductions in both peak demand and total load variation. Extensive analyses across diverse climates and scalable deployments confirm the framework's robustness, indicating that dynamic pricing acts as a force multiplier for DERs, with peak shaving potential increasing significantly under high renewable penetration scenarios.

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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

Stochastic Online Feedback Optimization for Networks of Non-Compliant Agents

In several applications of online optimization to networked systems such as power grids and robotic networks, information about the system model and its disturbances is not generally available. Within the optimization community, increasing interest has been devoted to the framework of online feedback optimization (OFO), which aims to address these challenges by leveraging real-time input-output measurements to empower online optimization. We extend the OFO framework to a stochastic setting, allowing the subsystems comprising the network (the $\textit{agents}$) to be $\textit{non-compliant}$. This means that the actual control input implemented by the agents is a random variable depending upon the control setpoint generated by the OFO algorithm. Mean-square error bounds are obtained for the general algorithm and the theory is illustrated in application to power systems.

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arXiv2025

Generation Expansion Planning with Upstream Supply Chain Constraints on Materials, Manufacturing, and Deployment

Rising electricity demand underscores the need for secure and reliable generation expansion planning that accounts for upstream supply chain constraints. Traditional models often overlook limitations in materials, manufacturing capacity, lead times for deployment, and field availability, which can delay availability of planned resources and thus to threaten system reliability. This paper introduces a multi-stage supply chain-constrained generation expansion planning (SC-GEP) model that optimizes long-term investments while capturing material availability, production limits, spatial and temporal constraints, and material reuse from retired assets. A decomposition algorithm efficiently solves the resulting MILP. A Maryland case study shows that supply chain constraints shift technology choices, amplify deployment delays caused by lead times, and prompt earlier investment in shorter lead-time, low-material-intensity options. In the low-demand scenario, supply chain constraints raise investment costs by $1.2 billion. Under high demand, persistent generation and reserve shortfalls emerge, underscoring the need to integrate upstream constraints into long-term planning.

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arXiv2025

Reconfiguration and Real-Time Operation of Networked Microgrids Under Load Uncertainty

Distribution networks are increasingly exposed to threats such as extreme weather, aging infrastructure, and cyber risks--resulting in more frequent contingencies and outages, a trend likely to persist. Microgrids, particularly dynamic networked microgrids (DNMGs), offer a promising solution to mitigate the impacts of such contingencies and enhance resiliency. However, distribution networks present unique challenges due to their unbalanced nature and the inherent uncertainty in both loads and generation. This paper builds upon our prior work on the two-stage mixed-integer robust optimization problem for configuring DNMGs, improving the solve time and scalability. Furthermore, we present a model-free, real-time optimal power flow algorithm to manage DNMG operations in the time between reconfigurations. A case study on a realistic network based on part of the San Francisco Bay Area demonstrates the scalability of both approaches. The case study also illustrates the ability to maintain power flow feasibility as loads vary and operating conditions change when the methods are used in tandem.

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arXiv2024

Optimizing Individualized Incentives from Grid Measurements and Limited Knowledge of Agent Behavior

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.

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arXiv2024

Learning with Adaptive Conservativeness for Distributionally Robust Optimization: Incentive Design for Voltage Regulation

Information asymmetry between the Distribution System Operator (DSO) and Distributed Energy Resource Aggregators (DERAs) obstructs designing effective incentives for voltage regulation. To capture this effect, we employ a Stackelberg game-theoretic framework, where the DSO seeks to overcome the information asymmetry and refine its incentive strategies by learning from DERA behavior over multiple iterations. We introduce a model-based online learning algorithm for the DSO, aimed at inferring the relationship between incentives and DERA responses. Given the uncertain nature of these responses, we also propose a distributionally robust incentive design model to control the probability of voltage regulation failure and then reformulate it into a convex problem. This model allows the DSO to periodically revise distribution assumptions on uncertain parameters in the decision model of the DERA. Finally, we present a gradient-based method that permits the DSO to adaptively modify its conservativeness level, measured by the size of a Wasserstein metric-based ambiguity set, according to historical voltage regulation performance. The effectiveness of our proposed method is demonstrated through numerical experiments.

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arXiv2024

Revealing Decision Conservativeness Through Inverse Distributionally Robust Optimization

This paper introduces Inverse Distributionally Robust Optimization (I-DRO) as a method to infer the conservativeness level of a decision-maker, represented by the size of a Wasserstein metric-based ambiguity set, from the optimal decisions made using Forward Distributionally Robust Optimization (F-DRO). By leveraging the Karush-Kuhn-Tucker (KKT) conditions of the convex F-DRO model, we formulate I-DRO as a bi-linear program, which can be solved using off-the-shelf optimization solvers. Additionally, this formulation exhibits several advantageous properties. We demonstrate that I-DRO not only guarantees the existence and uniqueness of an optimal solution but also establishes the necessary and sufficient conditions for this optimal solution to accurately match the actual conservativeness level in F-DRO. Furthermore, we identify three extreme scenarios that may impact I-DRO effectiveness. Our case study applies F-DRO for power system scheduling under uncertainty and employs I-DRO to recover the conservativeness level of system operators. Numerical experiments based on an IEEE 5-bus system and a realistic NYISO 11-zone system demonstrate I-DRO performance in both normal and extreme scenarios.

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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

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

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

Equitable Networked Microgrid Topology Reconfiguration for Wildfire Risk Mitigation

The increasing number of wildfires in recent years consistently challenges the safe and reliable operations of power systems. To prevent power lines and other electrical components from causing wildfires under extreme conditions, electric utilities often deploy public safety power shutoffs (PSPS) to mitigate the wildfire risks therein. Although PSPS are effective countermeasures against wildfires, uncoordinated strategies can cause disruptions in electricity supply and even lead to cascading failures. Meanwhile, it is important to consider mitigating biased decisions on different communities and populations during the implementation of shutoff actions. In this work, we primarily focus on the dynamic reconfiguration problem of networked microgrids with distributed energy resources. In particular, we formulate a rolling horizon optimization problem allowing for flexible network reconfiguration at each time interval to mitigate wildfire risks. To promote equity and fairness during the span of shutoffs, we further enforce a range of constraints associated with load shedding to discourage disproportionate impact on individual load blocks. Numerical studies on a modified IEEE 13-bus system and a larger-sized Smart-DS system demonstrate the performance of the proposed algorithm towards more equitable power shutoff operations.

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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

Time-Varying Feedback Optimization for Quadratic Programs with Heterogeneous Gradient Step Sizes

Online feedback-based optimization has become a promising framework for real-time optimization and control of complex engineering systems. This tutorial paper surveys the recent advances in the field as well as provides novel convergence results for primal-dual online algorithms with heterogeneous step sizes for different elements of the gradient. The analysis is performed for quadratic programs and the approach is illustrated on applications for adaptive step-size and model-free online algorithms, in the context of optimal control of modern power systems.

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arXiv2023

Evaluation of Communication Issues in Primal-Dual-Based Distributed Energy Resource Management Systems (DERMS)

With the increasing adoption of distributed energy resources (DERs) in distribution networks, distributed energy resource management systems (DERMS) are becoming an attractive option to coordinate the control of DERs, especially primal-dual-based DERMS, which is a well-developed class. To help reduce the uncertainty in commercializing DERMS, we evaluate and find the upper limits of severity for some common issues that can occur within the communication systems upon which a primal-dual-based DERMS relies; these issues include packet losses, link failures, and delays. This information can help a DERMS operator decide on the specifications for the communication infrastructure it will invest in for the DERMS. Our evaluation is based on numerical simulations of a real-world feeder with approximately 2,000 nodes and a DERMS that controls 163 photovoltaic generators and 140 energy storage batteries. In general, we find that the DERMS becomes less resistant to communication issues as the information flows closer to the DERs implementing the controllable power injections.

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arXiv2023

Adaptive Primal-Dual Control for Distributed Energy Resource Management

With the increased adoption of distributed energy resources (DERs) in distribution networks, their coordinated control with a DER management system (DERMS) that provides grid services (e.g., voltage regulation, virtual power plant) is becoming more necessary. One particular type of DERMS using primal-dual control has recently been found to be very effective at providing multiple grid services among an aggregation of DERs; however, the main parameter, the primal-dual step size, must be manually tuned for the DERMS to be effective, which can take a considerable amount of engineering time and labor. To this end, we design a simple method that self-tunes the step size(s) and adapts it to changing system conditions. Additionally, it gives the DER management operator the ability to prioritize among possibly competing grid services. We evaluate the automatic tuning method on a simulation model of a real-world feeder in Colorado with data obtained from an electric utility. Through a variety of scenarios, we demonstrate that the DERMS with automatically and adaptively tuned step sizes provides higher-quality grid services than a DERMS with a manually tuned step size.

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arXiv2022

Frequency shaping control for weakly-coupled grid-forming IBRs

We consider the problem of controlling the frequency of low-inertia power systems via inverter-based resources (IBRs) that are weakly connected to the grid. We propose a novel grid-forming control strategy, the so-called frequency shaping control, that aims to shape the frequency response of synchronous generators (SGs) to load perturbations so as to efficiently arrest sudden frequency drops. Our solution relaxes several existing assumptions in the literature and is able to navigate tradeoffs between peak power requirements and maximum frequency deviations. Finally, we analyze the robustness to imperfect knowledge of network parameters, while particularly highlighting the importance of accurate estimation of these parameters.

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arXiv2022

Enabling Grid-Aware Market Participation of Aggregate Flexible Resources

Increasing integration of distributed energy resources (DERs) within distribution feeders provides unprecedented flexibility at the distribution-transmission interconnection. With the new FERC 2222 order, DER aggregations are allowed to participate in energy market. To enable market participation, these virtual power plants need to provide their generation cost curves. This paper proposes efficient optimization formulations and solution approaches for the characterization of hourly as well as multi-time-step generation cost curves for a distribution system with high penetration of DERs. Network and DER constraints are taken into account when deriving these cost curves, and they enable active distribution systems to bid into the electricity market. The problems of deriving linear and quadratic cost curves are formulated as robust optimization problems and tractable reformulation/solution algorithm are developed to facilitate efficient calculations. The proposed formulations and solution algorithm are validated on a realistic test feeder with high penetration of flexible resources.

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