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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., Comment: arXiv admin note: substantial text overlap with arXiv:2305.12607

Power grids are seeing more devices connected at the load level in the form of power electronics: e.g., data centers, electric vehicle chargers, and battery storage facilities. Therefore it is necessary to perform power system analyses with load models that capture these loads' behavior, which has historically not been done. To this end, we propose ZIP-E loads, a composite load model that has a ZIP load with a dynamic power electronic, or E, load model. We perform small signal and transient analysis of the IEEE WSCC 9 Bus test case with ZIP and ZIP-E load models. For small signals, we conclude that ZIP loads destabalize networks significantly faster than corresponding ZIP-E loads. In stable cases, transient results showed significantly larger oscillations for ZIP loads. Further, we find that a higher network loading condition is correlated with a higher sensitivity to load model choice. These results suggests that the constant power portion of the ZIP load has a large destabilizing effect and can generally overestimate instability, and that attention should be drawn to load model choice if operating near a stability boundary.

The dominant paradigm for power system dynamic simulation is to build system-level simulations by combining physics-based models of individual components. The sheer size of the system along with the rapid integration of inverter-based resources exacerbates the computational burden of running time domain simulations. In this paper, we propose a data-driven surrogate model based on implicit machine learning -- specifically deep equilibrium layers and neural ordinary differential equations -- to learn a reduced order model of a portion of the full underlying system. The data-driven surrogate achieves similar accuracy and reduction in simulation time compared to a physics-based surrogate, without the constraint of requiring detailed knowledge of the underlying dynamic models. This work also establishes key requirements needed to integrate the surrogate into existing simulation workflows; the proposed surrogate is initialized to a steady state operating point that matches the power flow solution by design., Comment: This work has been submitted to the IEEE Transactions on Energy Conversion for possible publication

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.

In a power grid with growing penetrations of renewable energy sources, inverters play a larger role in the dynamic interactions among network components. However, much is yet to be studied regarding inverter-dominated grid stability. This has initiated a re-examination of long-established assumptions made when conducting power systems studies. In this work we study the small-signal stability characteristics of a power system comprised of inverter and synchronous machine sources, and consider the effect of inverter control gains, transmission line dynamics, and network operating conditions. We utilize PowerSimulationsDynamics.jl to perform this study on the IEEE WSCC 9 Bus test system. We vary inverter parameters across reported ranges in the literature, we consider three transmission line models of varying fidelity, and compare results across different operating conditions. We find that line dynamics are generally important for correctly assessing small-signal stability in networks with large penetrations of grid-following converters, and that gain tuning in these networks should utilize high fidelity line models., Comment: Submitted to IEEE PESGM 2024. arXiv admin note: text overlap with arXiv:2310.08553

In this work, we study fast time scale dynamic interactions between inverters, synchronous machines, and transmission lines. The overlapping time scales between inverter controls and electromagnetic phenomena idfentified in recent years has necessitated a re-evaluation of assumptions made in power system dynamics studies. We utilize an open-source modeling platform to perform both small signal stability and dynamic time domain studies of networks containing inverters, machines, and loads. We use transmission line models of varying fidelity, including models with multiple segments and frequency dependence. Our results indicate that, for the cases we study, line dynamics are not important for characterizing small signal stability. However, while in many cases the high fidelity line models are unnecessary for dynamic simulations, there are some cases in which simpler models omit dynamics that could be important to the operation of inner inverter control loops.

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.

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.

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., Comment: Accepted on IEEE 2024 Conference on Innovative Smart Grid Technologies, North America (ISGT NA 2024)

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.

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.

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.

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.

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.

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.

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.

Computer simulations that demonstrate the valueof novel approaches are crucial to developing more flexibleand robust power systems operations with high penetrations ofrenewable energy at multiple geographic and temporal scales.However, optimization-based simulations that depend on forecastdata often face challenges in evaluating performance, reproducingresults, and testing under realistic simulation scenarios. In thispaper, we develop scientific computing best-practices for thevalidation and reproduction of power systems operational models.We then employ two case studies to demonstrate the proposedvalidation and reproduction framework., Comment: Accepted to 21st Power Systems Computation Conference

A rapid deployment of renewable generation has led to significant reduction in the rotational system inertia and damping, thus making frequency control in power systems more challenging. This paper proposes a novel control scheme based on Model Predictive Control (MPC) for converter-interfaced generators operating in a grid-forming mode, with the goal of exploiting their fast response capabilities to provide fast frequency control service to the system. The controller manipulates converter power injections to limit the frequency nadir and rate-of-change-of-frequency after a disturbance. Both centralized and decentralized MPC approaches are considered and compared in terms of performance and practical implementation. Special attention is given to the decentralized controller by generating an explicit MPC solution to enhance computational efficiency and reduce hardware requirements. Simulation results obtained from a high-fidelity differential-algebraic equation model of the IEEE 39-bus system demonstrate the effectiveness of the proposed control schemes.

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.

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.

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.

Implementing state estimation in low and medium voltage power distribution is still challenging given the scale of many networks and the reliance of traditional methods on a large number of measurements. This paper proposes a method to improve voltage predictions in real-time by leveraging a limited set of real-time measurements. The method relies on Bayesian estimation formulated as a linear least squares estimation problem, which resembles the classical weighted least-squares (WLS) approach for scenarios where full network observability is not available. We build on recently developed linear approximations for unbalanced three-phase power flow to construct voltage predictions as a linear mapping of load predictions constructed with Gaussian processes. The estimation step to update the voltage forecasts in real-time is a linear computation allowing fast high-resolution state estimate updates. The uncertainty in forecasts can be determined a priori and smoothed a posteriori, making the method useful for both planning, operation and post-hoc analysis. The method outperforms conventional WLS and is applied to different test feeders and validated on a real test feeder with the utility Alliander in The Netherlands., Comment: To appear in IEEE Transactions on Power Systems

The implementation of optimal power flow (OPF) methods to perform voltage and power flow regulation in electric networks is generally believed to require extensive communication. We consider distribution systems with multiple controllable Distributed Energy Resources (DERs) and present a data-driven approach to learn control policies for each DER to reconstruct and mimic the solution to a centralized OPF problem from solely locally available information. Collectively, all local controllers closely match the centralized OPF solution, providing near optimal performance and satisfaction of system constraints. A rate distortion framework enables the analysis of how well the resulting fully decentralized control policies are able to reconstruct the OPF solution. The methodology provides a natural extension to decide what nodes a DER should communicate with to improve the reconstruction of its individual policy. The method is applied on both single- and three-phase test feeder networks using data from real loads and distributed generators, focusing on DERs that do not exhibit inter-temporal dependencies. It provides a framework for Distribution System Operators to efficiently plan and operate the contributions of DERs to achieve Distributed Energy Services in distribution networks., Comment: Accepted for publication. To appear in the IEEE Transactions on Smart Grid

The central question we seek to address in this paper is: How rapidly do the operating cost benefits of grid-scale energy storage decline as installed storage capacity increases? We use a 240-bus model based on the US Western Interconnection, first optimally locating storage in the network and then dispatching it in a unit commitment model with DC load flow. The model uses storage to provide frequency regulation, load following, and arbitrage for each hour of a study year, and we investigate a range of scenarios for fuel price and renewables penetration. We find that value from long-term energy shifting is negligible at all penetrations we investigate, but also that displacing fossil-fueled generators from providing reserves is initially very valuable. However, in most scenarios the value is negligible beyond 10 GWh of storage, or the equivalent of roughly 6 minutes of average demand in the system. Above penetrations of 4-8 GWh, storage operating cost benefits are less than estimated capacity values for storage. We also show that storage has the potential to increase overall carbon emissions in the electricity sector, even when it is not providing significant amounts of arbitrage and is preferentially providing regulation and load following services.

Scalable demand response of residential electric loads has been a timely research topic in recent years. The commercial coming of age or residential demand response requires a scalable control architecture that is both efficient and practical to use. This work presents such a strategy for domestic hot water heaters and present a commercial proof-of-concept deployment. The strategy combines state of the art in aggregate-and-dispatch with a novel dispatch strategy leveraging recent developments in reinforcement learning and is tested in a hardware-in-the-loop simulation environment. The results are promising and present how model-based and model-free control strategies can be merged to obtain a mature and commercially viable control strategy for residential demand response., Comment: 8 pages, 8 figures, submitted to IEEE Transactions on Smart Grid

Electric vehicle (EV) charging can negatively impact electric distribution networks by exceeding equipment thermal ratings and causing voltages to drop below standard ranges. In this paper, we develop a decentralized EV charging control scheme to achieve "valley-filling" (i.e., flattening demand profile during overnight charging), meanwhile meeting heterogeneous individual charging requirements and satisfying distribution network constraints. The formulated problem is an optimization problem with a non-separable objective function and strongly coupled inequality constraints. We propose a novel shrunken primal-dual subgradient (SPDS) algorithm to support the decentralized control scheme, derive conditions guaranteeing its convergence, and verify its efficacy and convergence with a representative distribution network model., Comment: 16 pages, 11 figures