arXiv subjects

Duncan S. Callaway

Publications and source records attributed to Duncan S. Callaway.

At least 19 recordsLinked to original sources

arXiv2026

An Electricity Market with Reactive Power Trading: Incorporating Dynamic Operating Envelopes

Electricity market design that accounts for grid constraints such as voltage and thermal limits at the distribution level can increase opportunities for the grid integration of Distributed Energy Resources (DERs). In this paper, we consider rooftop solar backed by battery storage connected to a distribution grid. We design an electricity market to support customers sharing rooftop generation in excess of their energy demand, where customers earn a profit through peer-to-peer (P2P) energy trading. Our proposed electricity market also incorporates P2P reactive power trading to improve the voltage profile across a distribution feeder. We formulate the electricity market as an optimization-based problem, where voltage and thermal limits across a feeder are managed through the assignment of customer-specific dynamic operating envelopes (DOEs). The electricity market equilibrium is referred to as a competitive equilibrium, which is equivalent to a Nash equilibrium in a standard game. Our proposed market design is benchmarked using the IEEE 13-node test feeder.

eess.SY↗

arXiv2025

A Linear Pricing Mechanism for Load Management in Day-Ahead Retail Energy Markets

Regulators and utilities have been exploring hourly retail electricity pricing, with several existing programs providing day-ahead hourly pricing schedules. At the same time, customers are deploying distributed energy resources and smart energy management systems that have significant flexibility and can optimally follow price signals. In aggregate, these optimally controlled loads can create congestion management issues for distribution system operators (DSOs). In this paper, we describe a new linear pricing mechanism for day-ahead retail electricity pricing that provides a signal for customers to follow to mitigate over-consumption while still consuming energy at hours that are preferential for system performance. We show that by broadcasting a linear price designed for price-signal control of cost-optimizing loads, we can shape customer load profiles to provide congestion management without the need for bi-directional communication or customer bidding programs.

eess.SY↗

arXiv2025

Peer-to-Peer Energy Markets With Uniform Pricing: A Dynamic Operating Envelope Approach

The recent widespread adoption of rooftop solar backed by battery storage is enabling energy customers to both produce and consume electricity (i.e., prosumers of electricity). To facilitate prosumer participation in the electric grid, new market mechanisms are required. In this paper, we design peer-to-peer energy markets where prosumers trade their excess energy with peers to gain profit while satisfying the overall balance in electricity supply and demand. We first consider a market structure, considering the case where voltage and/or thermal constraints are binding. When such grid constraints are binding, market clearing prices can vary across locations. However, heterogeneous prices may be considered by regulators to lack fairness. To ensure uniform pricing, we design two peer-to-peer energy markets with dynamic operating envelopes (DOEs). DOEs enable us to decompose global voltage and thermal constraints across the power grid into local constraints for each prosumer, resulting in uniform prices across the grid. By means of numerical simulations on an IEEE 13-node feeder, we benchmark the proposed market-based approaches in the presence of binding voltage constraints.

eess.SY↗

arXiv2024

A Hardware-in-the-Loop Experimental Testbed using Air Conditioners for Grid Balancing

Driven by the need to offset the variability of renewable generation on the grid, development of load control is a highly active field of research. However, practical use of residential loads for grid balancing remains rare, in part due to the cost of communicating with large numbers of small loads and also the limited experimentation done so far to demonstrate reliable operation. To establish a basis for the safe and reliable use of fleets of compressor loads as distributed energy resources, we constructed an experimental testbed in a laboratory, so that load coordination schemes could be tested at extreme conditions. This experimental testbed was used to tune a simulation testbed to which it was then linked, thereby augmenting the effective size of the fleet. Modeling of the system was done both to demonstrate the experimental testbed's behavior and also to understand how to tune the behavior of each load. Implementing this testbed has enabled rapid turnaround of experiments on various load control algorithms, and year-round testing without the constraints and limitations arising in seasonal field tests with real houses. Experimental results show the practical feasibility of an ensemble of small loads contributing to grid balancing.

eess.SY↗

arXiv2024

PowerSimulations.jl -- A Power Systems operations simulation Library

PowerSimulations.jl is a Julia-based BSD-licensed power system operations simulation tool developed as a flexible and open source software for quasi-static power systems simulations including Production Cost Models. PowerSimulations.jl tackles the issues of developing a simulation model in a modular way providing tools for the formulation of decision models and emulation models that can be solved independently or in an interconnected fashion. This paper discusses the software implementation of PowerSimulations.jl as a template for the development and implementation of operation simulators, providing solutions to commonly encountered issues like time series read/write and results sharing between models. The paper includes a publicly-available validation of classical operations simulations as well as examples of the advanced features of the software.

eess.SY↗

arXiv2024

PowerSimulationsDynamics.jl -- An Open Source Modeling Package for Modern Power Systems with Inverter-Based Resources

In this paper we present the development of an open-source simulation toolbox, PowerSimulationsDynamics.jl, to study the dynamic response of power systems, focusing on the requirements to model systems with high penetrations of Inverter-Based Resources (IBRs). PowerSimulationsDynamics.jl is implemented in Julia and features a rich library of synchronous generator, inverter, and load models. In addition, it allows the study of quasi-static phasors and electromagnetic dq models that use a dynamic network representation. Case studies and validation exercises show that PowerSimulationsDynamics.jl results closely match other commercial and open-source simulation tools.

eess.SY↗

arXiv2024

Small-Signal Stability Impacts of Load and Network Dynamics on Grid-Forming Inverters

This paper presents several stability analyses for grid-forming inverters and synchronous generators considering the dynamics of transmission lines and different load models. Load models are usually of secondary importance compared to generation source models, but as the results show, they play a crucial role in stability studies with the introduction of inverter-based resources. Given inverter control time scales, the implications of considering or neglecting electromagnetic transients of the network are very relevant in the stability assessments. In this paper, we perform eigenvalue analyses for inverter-based resources and synchronous machines connected to a load and explore the effects of multiples models under different network representations. We explore maximum loadability of inverter-based resources and synchronous machines, while analyzing the effects of load and network dynamic models on small-signal stability. The results show that the network representation plays a fundamental role in the stability of the system of different load models. The resulting stability regions are significantly different depending on the source and load model considered.

eess.SY↗

arXiv2023

Revisiting Power Systems Time-domain Simulation Methods and Models

The changing nature of power systems dynamics is challenging present practices related to modeling and study of system-level dynamic behavior. While developing new techniques and models to handle the new modeling requirements, it is also critical to review some of the terminology used to describe existing simulation approaches and the embedded assumptions. This paper provides a first-principles review of the simplifications and transformation commonly used in the formulation of time-domain simulation models. It introduces a taxonomy and classification of time-domain simulation models depending on their frequency bandwidth, network representation, and software availability. Furthermore, it focuses on the fundamental aspects of averaging techniques, and model reduction approaches that result in modeling choices, and discusses the associated challenges and opportunities of applying these methods in systems with large shares of Inverter Based Resources (IBRs). The paper concludes with an illustrative simulation that compares the trajectories of an IBR-dominated system.

eess.SY↗

arXiv2023

Approximated Multi-Agent Fitted Q Iteration

We formulate an efficient approximation for multi-agent batch reinforcement learning, the approximated multi-agent fitted Q iteration (AMAFQI). We present a detailed derivation of our approach. We propose an iterative policy search and show that it yields a greedy policy with respect to multiple approximations of the centralized, learned Q-function. In each iteration and policy evaluation, AMAFQI requires a number of computations that scales linearly with the number of agents whereas the analogous number of computations increase exponentially for the fitted Q iteration (FQI), a commonly used approaches in batch reinforcement learning. This property of AMAFQI is fundamental for the design of a tractable multi-agent approach. We evaluate the performance of AMAFQI and compare it to FQI in numerical simulations. The simulations illustrate the significant computation time reduction when using AMAFQI instead of FQI in multi-agent problems and corroborate the similar performance of both approaches.

cs.LG↗

arXiv2022

Optimally Scheduling Public Safety Power Shutoffs

In an effort to reduce power system-caused wildfires, utilities carry out public safety power shutoffs (PSPS) in which portions of the grid are de-energized to mitigate the risk of ignition. The decision to call a PSPS must balance reducing ignition risks and the negative impact of service interruptions. In this work, we consider three PSPS scheduling scenarios, which we model as dynamic programs. In the first two scenarios, we assume that N PSPSs are budgeted as part of the investment strategy. In the first scenario, a penalty is incurred for each PSPS declared past the Nth event. In the second, we assume that some costs can be recovered if the number of PSPSs is below $N$ while still being subject to a penalty if above N. In the third, the system operator wants to minimize the number of PSPS such that the total expected cost is below a threshold. We provide optimal or asymptotically optimal policies for each case, the first two of which have closed-form expressions. Lastly, we establish the applicability of the first PSPS model's policy to critical-peak pricing, and obtain an optimal scheduling policy to reduce the peak demand based on weather observations.

math.OC↗

arXiv2022

Predicting Electricity Infrastructure Induced Wildfire Risk in California

This paper examines the use of risk models to predict the timing and location of wildfires caused by electricity infrastructure. Our data include historical ignition and wire-down points triggered by grid infrastructure collected between 2015 to 2019 in Pacific Gas & Electricity territory along with various weather, vegetation, and very high resolution data on grid infrastructure including location, age, materials. With these data we explore a range of machine learning methods and strategies to manage training data imbalance. The best area under the receiver operating characteristic we obtain is 0.776 for distribution feeder ignitions and 0.824 for transmission line wire-down events, both using the histogram-based gradient boosting tree algorithm (HGB) with under-sampling. We then use these models to identify which information provides the most predictive value. After line length, we find that weather and vegetation features dominate the list of top important features for ignition or wire-down risk. Distribution ignition models show more dependence on slow-varying vegetation variables such as burn index, energy release content, and tree height, whereas transmission wire-down models rely more on primary weather variables such as wind speed and precipitation. These results point to the importance of improved vegetation modeling for feeder ignition risk models, and improved weather forecasting for transmission wire-down models. We observe that infrastructure features make small but meaningful improvements to risk model predictive power.

eess.SY↗

arXiv2022

Stability and Robustness of a Hybrid Control Law for the Half-bridge Inverter

Hybrid systems combine both discrete and continuous state dynamics. Power electronic inverters are inherently hybrid systems: they are controlled via discrete-valued switching inputs which determine the evolution of the continuous-valued current and voltage state dynamics. Hybrid systems analysis could prove increasingly useful as large numbers of renewable energy sources are incorporated to the grid with inverters as their interface. In this work, we explore a hybrid systems approach for the stability analysis of power and power electronic systems. We provide an analytical proof showing that the use of a hybrid model for the half-bridge inverter allows the derivation of a control law that drives the system states to desired sinusoidal voltage and current references. We derive an analytical expression for a global Lyapunov function for the dynamical system in terms of the system parameters, which proves uniform, global, and asymptotic stability of the origin in error coordinates. Moreover, we demonstrate robustness to parameter changes through this Lyapunov function. We validate these results via simulation. Finally, we show empirically the incorporation of droop control with this hybrid systems approach. In the low-inertia grid community, the juxtaposition of droop control with the hybrid switching control can be considered a grid-forming control strategy using a switched inverter model.

eess.SY↗

arXiv2021

Pricing and Energy Trading in Peer-to-peer Zero Marginal-cost Microgrids

Efforts to utilize 100% renewable energy in community microgrids require new approaches to energy markets and transactions to efficiently address periods of scarce energy supply. In this paper we contribute to the promising approach of peer-to-peer (P2P) energy trading in two main ways: analysis of a centralized, welfare-maximizing economic dispatch that characterizes optimal price and allocations, and a novel P2P system for negotiating energy trades that yields physically feasible and at least weakly Pareto-optimal outcomes. Our main results are 1) that optimal pricing is insufficient to induce agents with batteries to take optimal actions, 2) a novel P2P algorithm to address this while keeping private information, 3) a formal proof that this algorithm converges to the centralized solution in the case of two agents negotiating for a single period, and 4)numerical simulations of the P2P algorithm performance with up to 10 agents and 24 periods that show it converges on average to total welfare within 0.1% of the social optimum in on the order of 10s to 100s of iterations, increasing with the number of agents, time periods, and total storage capacity.

math.OC↗

arXiv2021

Online Convex Optimization with Binary Constraints

We consider online optimization with binary decision variables and convex loss functions. We design a new algorithm, binary online gradient descent (bOGD) and bound its expected dynamic regret. We provide a regret bound that holds for any time horizon and a specialized bound for finite time horizons. First, we present the regret as the sum of the relaxed, continuous round optimum tracking error and the rounding error of our update in which the former asymptomatically decreases with time under certain conditions. Then, we derive a finite-time bound that is sublinear in time and linear in the cumulative variation of the relaxed, continuous round optima. We apply bOGD to demand response with thermostatically controlled loads, in which binary constraints model discrete on/off settings. We also model uncertainty and varying load availability, which depend on temperature deadbands, lockout of cooling units and manual overrides. We test the performance of bOGD in several simulations based on demand response. The simulations corroborate that the use of randomization in bOGD does not significantly degrade performance while making the problem more tractable.

math.OC↗

arXiv2020

Wasserstein Distributionally Robust Look-Ahead Economic Dispatch

We consider the problem of look-ahead economic dispatch (LAED) with uncertain renewable energy generation. The goal of this problem is to minimize the cost of conventional energy generation subject to uncertain operational constraints. The risk of violating these constraints must be below a given threshold for a family of probability distributions with characteristics similar to observed past data or predictions. We present two data-driven approaches based on two novel mathematical reformulations of this distributionally robust decision problem. The first one is a tractable convex program in which the uncertain constraints are defined via the distributionally robust conditional-value-at-risk. The second one is a scalable robust optimization program that yields an approximate distributionally robust chance-constrained LAED. Numerical experiments on the IEEE 39-bus system with real solar production data and forecasts illustrate the effectiveness of these approaches. We discuss how system operators should tune these techniques in order to seek the desired robustness-performance trade-off and we compare their computational scalability.

math.OC↗

arXiv2020

Grid-Coupled Dynamic Response of Battery-Driven Voltage Source Converters

With the increasing interest in converter-fed islanded microgrids, particularly for resilience, it is becoming more critical to understand the dynamical behavior of these systems. This paper takes a holistic view of grid-forming converters and considers control approaches for both modeling and regulating the DC-link voltage when the DC-source is a battery energy storage system. We are specifically interested in understanding the performance of these controllers, subject to large load changes, for decreasing values of the DC-side capacitance. We consider a fourth, second, and zero-order model of the battery; and establish that the zero-order model captures the dynamics of interest for the timescales considered for disturbances examined. Additionally, we adapt a grid search for optimizing the controller parameters of the DC/DC controller and show how the inclusion of AC side measurements into the DC/DC controller can improve its dynamic performance. This improvement in performance offers the opportunity to reduce the DC-side capacitance given an admissible DC voltage transient deviation, thereby, potentially allowing for more reliable capacitor technology to be deployed.

eess.SY↗

arXiv2020

Dynamic and Distributed Online Convex Optimization for Demand Response of Commercial Buildings

We extend the regret analysis of the online distributed weighted dual averaging (DWDA) algorithm [1] to the dynamic setting and provide the tightest dynamic regret bound known to date with respect to the time horizon for a distributed online convex optimization (OCO) algorithm. Our bound is linear in the cumulative difference between consecutive optima and does not depend explicitly on the time horizon. We use dynamic-online DWDA (D-ODWDA) and formulate a performance-guaranteed distributed online demand response approach for heating, ventilation, and air-conditioning (HVAC) systems of commercial buildings. We show the performance of our approach for fast timescale demand response in numerical simulations and obtain demand response decisions that closely reproduce the centralized optimal ones.

math.OC↗

arXiv2020

LITS.jl -- An Open-Source Julia based Simulation Toolbox for Low-Inertia Power Systems

The integration of converter-interfaced generation (CIG) from renewable energy sources poses challenges to the stability and transient behavior of electric power systems. Understanding the dynamic behavior of low-inertia power systems is critical to addressing these stability questions. However, there is a limited availability of open source tools explicitly geared towards low-inertia systems modeling. In this paper, we develop an open source simulation toolbox to study transient responses under high penetration scenarios. LITS.jl is implemented in the Julia computing language and features multi-machine modeling capability, a rich library of synchronous generators components (AVR, PSS, Governor, etc.) and inverter configurations. Several case studies are conducted and benchmarked and validated against existing toolboxes. Case studies are selected to showcase the integration of different device models' behavior in power systems.

eess.SY↗