Large-scale integration of inverter-based resources (IBRs) challenges primary frequency control because IBRs don’t typically respond to frequency fluctuations, which is partially due to a lack of financial incentives. To address this, we consider four ancillary service products for primary frequency control: Primary Frequency Response (PFR) reserve, which accommodates droop control, Fast Frequency Response (FFR) reserve, Virtual Inertia (VI) reserve, and synchronous inertia. The available frequency response reserve requirement is proposed, which ensures sufficient available PFR and FFR reserve to cover the largest contingency. To ensure that PFR reserve is available fast enough to contribute to primary frequency control, we propose enforcing novel rate-based PFR reserve limits that vary with inertia and FFR reserve and are constructed by a simulation-based heuristic. The proposed requirements are incorporated into the unit-commitment problem and are compatible with the equivalency ratio requirement used by the Electric Reliability Council of Texas (ERCOT). Results are provided using an ERCOT test case. We illustrate that PFR reserve limits currently used by ERCOT may be insufficient due to generator ramping limitations, while the addition of our rate-based limits would not significantly increase cost. We also illustrate that including VI reserve allows storage devices to fully utilize their power and energy capacities.

Microgrids have emerged as a leading solution offering resilience to distribution grid operation. In the event of a power outage, microgrids can form while leveraging clean energy resources, dynamically morph boundaries, to energize the distribution system in an autonomous manner enabling self-assembly of the energized network pockets. This paper presents the concept implementation using advanced optimization techniques, validation through co- simulation, integration into a commercial DERMS platform, and a field pilot at a campus site.

We propose a three-stage stochastic programming model to inform risk-averse investment in power system resilience to winter storms. The first stage pertains to long-term investment in generator winterization and mobile battery energy storage system (MBESS) resources, the second stage to MBESS deployment prior to an imminent storm, and the third stage to operational response. Serving as a forecast update, an imminent winter storm’s severity is assumed to be known at the time the deployment decisions are made. We incorporate conditional value-at-risk (CVaR) as the risk measure in the objective function to target loss, represented in our model by unserved energy, experienced during high-impact, low-frequency events. We apply the model to a Texas-focused case study based on the ACTIVS 2000-bus synthetic grid with winter storm scenarios generated using historical Winter Storm Uri data. Results demonstrate how the optimal investments are affected by parameters like cost and risk aversion, and also how effectively using CVaR as a risk measure mitigates the outcomes in the tail of the loss distribution over the winter storm impact uncertainty.

The article introduces the stochastic N-k interdiction problem for power grid operations and planning that aims to identify a subset of k components (out of N components) that maximizes the expected damage, measured in terms of load shed. Uncertainty is modeled through a fixed set of outage scenarios, where each scenario represents a subset of components removed from the grid. We formulate the stochastic N-k interdiction problem as a bi-level optimization problem and propose two algorithmic solutions. The first approach reformulates the bi-level stochastic optimization problem to a single level, mixed-integer linear program (MILP) by dualizing the inner problem and solving the resulting problem directly using a MILP solver to global optimality. The second is a heuristic cutting-plane approach, which is exact under certain assumptions. We compare these approaches in terms of computation time and solution quality using the IEEE-Reliability Test System and present avenues for future research.

Unit Commitment (UC) problems that consider the Alternating Current (AC) model of the transmission network have long been considered intractable to solve at scale by the power system community. Recently, the Grid-Optimization (GO) Competition held by the Advanced Research Project Agency-Energy (ARPA-E) has facilitated the development of the first algorithms to solve large-scale ACUC problems. This new capability opens a path towards the explicit consideration of the AC transmission network model in UC problems used to clear day-ahead electricity markets. This calls for the analysis of electricity market structures that accommodate both the continuous non-linearity of the AC transmission network and the discrete non-linearity of the UC problem simultaneously. This paper serves as an initial effort to do so by proposing an Average Incremental Cost (AIC) pricing structure that is designed around the ACUC problem. In particular, an AIC one-pass pricing problem is proposed that represents a continuously constrained variant of the ACUC problem and allows for the computation of Locational Incremental Prices (LIPs) for both real and reactive power as the local optimal Lagrange multipliers of the power balance constraints. To avoid degeneracy, the pricing problem includes a small parameter ϵ > 0. Under certain assumptions market participants are shown to realize profit that converges to a non-negative value as ϵ approaches zero, practically ensuring profitability for small values of ϵ. We additionally provide many simple and important examples that provide intuition and insights into the proposed prices. Examples illustrate the basic concept of AIC pricing, the derived profitability results, the existence of multiple LIPs, the importance of including reactive power in the dispatch and pricing problems, the need for reactive power prices, and the improved incentives exhibited by LIPs as compared to traditional Locational Marginal Prices (LMPs). We additionally indicate many directions for future work including analysis of larger test cases.

We develop two-stage stochastic programming models for generator winterization that enhance power grid resilience while incorporating social equity. The first stage in our models captures the investment decisions for generator winterization, and the second stage captures the operation of a degraded power grid, with the objective of minimizing load shed and social inequity. To incorporate equity into our models, we propose a concept called adverse effect probability that captures the disproportionate effects of power outages on communities with varying vulnerability levels. Grid operations are modeled using DC power flow, and equity is captured through mean or maximum adverse effects experienced by communities. We apply our models to a synthetic Texas power grid, using winter storm scenarios created from the generator outage data from the 2021 Texas winter storm. Our extensive numerical experiments show that more equitable outcomes, in the sense of reducing adverse effects experienced by vulnerable communities during power outages, are achievable with no impact on total load shed through investing in winterization of generators in different locations and capacities.

a commercially available tools to simulate the interaction of these two responses has limited the energy industry's understanding of when the depletion of primary control reserve will impact the performance of secondary conrol response or vice versa. To investigate this issue, in this paper we develop a multi-area frequency response integration model with combined primary and secondary frequency control capabilities.

requires explicit descriptions of market participants’ convex hulls -or the Lagrangian dual of the corresponding non-convex scheduling problem. Here, we propose a computationally feasible and industrially scalable Benders decomposition approach to computing convex hull prices at least an order of magnitude faster than the current state-of-the-art while leveraging recent advances in convex hull formulations for thermal generating units.

Here, the novelty of the approach lies in decoupling the production cost estimation from the unit commitment and economic dispatch optimization problems under uncertainty without compromising on the fidelity of the solutions. A data-driven machine learning model is first developed to predict the mean optimal production cost. A physics-based inverse problem is then solved to get the stochastic UC and ED profiles from the expected cost. The presented approach considers, for the first time, solar uncertainty in UC/ED determination and enables efficient and accurate propagation of wind and solar uncertainty to estimate the statistics of the production cost. The effectiveness of the developed approach is demonstrated systematically on a stylized RTS-GMLC single-node system. The overall framework predicts the expected cost 62.5% more accurately than the existing state-of-the-art, on unforeseen days during the entire year, and yields, for the first time, the associated physically consistent UC and ED profiles. The solutions are also shown to be flexible in providing adequate daily reserves to address any statistical deviations from probabilistic power forecasts. The computational time associated with the presented method is only about 10 s compared to over 24 h needed for a conventional stochastic UC/ED determination under uncertainty on an Intel Core i9 processor with 32 GB of RAM.

This paper proposes a Dynamic Regulation Market Mechanism (DRMM) that results in improved financial settlements for wholesale electricity markets. The DRMM dispatches control signals at the Tertiary Control (TC) level based on a co-optimization problem that jointly optimizes energy production and reserve capacity. At the Secondary Control (SC) level the DRMM dispatches control signals using an iterative algorithm that effectively eliminates steady state error in the system frequency. In addition to the overall DRMM remaining stable, the conditions under which it leads to improved financial settlements are described. Using a three area example, where each area corresponds to a modified IEEE-300 bus system, the control performance and the financial settlements are compared to standard SC. It is shown that the frequency response is nearly identical and that the make-whole payments, a performance metric associated with financial settlements, are smaller with the proposed DRMM.

Power system operators rely critically on state estimation for verification, fault detection and localization, and re-dispatch under contingency operations. In current practice, power system data within a control area such as voltages, phases, real and reactive power flows and injections, are relayed to the operator using SCADA systems. State estimation is formulated as an over-determined weighted nonlinear least squares problem and the solver of choice is the Newton-Raphson method. Two critical issues are: (a) estimate quality, due to data latency or convergence to false local minima, and (b) computation time, due to the large number of state variables involved. In this paper, we explore techniques to accelerate state estimation by computing state estimates at a small subset of buses using limited measurements from the power subsystem of interest. These could be operator selected “important” buses which connect to “important” lines with significant real power transfer. Our techniques are inspired by uncertainty quantification methods. The influence of power flows from exogenous buses is treated as uncertainty which defines a feasible set of state variables consistent with available measurements. The state estimation problem can be cast as a non-convex optimization problem. We use a surrogate model relaxation and Shor's rank relaxation to obtain state estimates and associated error bounds at user-defined confidence levels.

We develop and analyze real-time scheduling algorithms for coordinated aggregation of deferrable loads and storage. These distributed resources offer flexibility that can enable the integration of renewable generation by reducing reserve costs. We present three scheduling policies: earliest deadline first (EDF), least laxity first (LLF), and receding horizon control (RHC). We offer a novel cost metric for RHC-based scheduling that explicitly accounts for reserve costs. We study the performance of these algorithms in the metrics of reserve energy and capacity through simulation studies. We conclude that the benefits of coordinated aggregation can be realized from modest levels of both deferrable load participation and flexibility.

We consider a collection of distributed energy resources [DERs] such as electric vehicles and thermostatically controlled loads. These resources are flexible: they require delivery of a certain total energy over a specified service interval. This flexibility can facilitate the integration of renewable generation by absorbing variability, and reducing the reserve capacity and reserve energy requirements. We first model the energy needs of these resources as tasks, parameterized by arrival time, departure time, energy requirement, and maximum allowable servicing power. We consider the problem of servicing these resources by allocating available power using real-time scheduling policies. The available generation consists of a mix of renewable energy [from utility-scale wind-farms or distributed rooftop photovoltaics], and load-following reserves. Reserve capacity is purchased in advance, but reserve energy use must be scheduled in real-time to meet the energy requirements of the resources. We show that there does not exist a causal optimal scheduling policy that respects servicing power constraints. We then present three heuristic causal scheduling policies: Earliest Deadline First [EDF], Least Laxity First [LLF], and Receding Horizon Control [RHC]. We show that EDF is optimal in the absence of power constraints. We explore, via simulation studies, the performance of these three scheduling policies in the metrics of required reserve energy and reserve capacity.

Coordinated cyberattacks of power meter readings can be arranged to be undetectable by any bad data detection algorithm in the power system state estimation process. These unobservable attacks present a potentially serious threat to grid operations. Of particular interest are sparse attacks that involve the compromise of a modest number of meter readings. An efficient algorithm to find all unobservable attacks [under standard DC load flow approximations] involving the compromise of exactly two power injection meters and an arbitrary number of line power meters is presented. This requires O (n(2) m) flops for a power system with n buses and m line meters. If all lines are metered, there exist canonical forms that characterize all 3, 4, and 5-sparse unobservable attacks. These can be quickly detected in power systems using standard graph algorithms. Known-secure phasor measurement units [PMUs] can be used as countermeasures against an arbitrary collection of cyberattacks. Finding the minimum number of necessary PMUs is NP-hard. It is shown that p + 1 PMUs at carefully chosen buses are sufficient to neutralize a collection of p cyberattacks.

Polycarbonate (PC), a critical component in ballistic laminates (BLs), is known to degrade upon exposure to ultraviolet (UV) light. For the purpose of reducing the photodegradation, a UV blocking chemical has been added to the adhesives used to join the layers of the BL. This report describes the development of a spectroscopic method for monitoring surface photodegradation of PC and the method's use in demonstrating the effectiveness of the UV blocker. Reports in the literature demonstrate that photodegradation in thin PC films may be detected by transmission infrared (IR) spectroscopy. The present work extends this approach to thick films, where small surface changes are detected by reflectance IR spectroscopy. We show that UV photodegradation of the PC surface produces a characteristic shift in the carbonyl absorption band at about 1775 cm−1. This shift is consistently observed in PC samples that have been subjected to direct artificial exposure and in PC samples that have been subjected through the outboard layers of the BL to both natural and artificial exposure. When a UV blocker is incorporated into the adhesive layers of the laminate, no peak shift is observed in the carbonyl band after the equivalent of 10 years of exposure.