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At least 397 records · Page 22

Flexible dynamic boundary microgrid operation considering network and load unbalances

Flexible microgrids with dynamic boundaries have recently been introduced in the literature. With the ability to reconfigure the topology of the microgrids dynamically through remotely controlled switches, flexible microgrids with dynamic boundaries can further improve the resiliency and energy efficiency of microgrids with distributed energy resources (DERs). This paper focuses on the optimal operation considering one of the predominant characteristics of microgrids and distribution systems – unbalanced networks and loads. In existing literature, balanced modeling of microgrids is more common due to its attractive simplicity. The three-phase power unbalance has not been considered as a constraint on the generation units in a microgrid. Further, negative sequence constraints have also been neglected. In this article, we propose a set of constraints that is specifically related to the capabilities of inverter interfaced resources to supply unbalanced current/power when the microgrid is islanded from the main distribution grid. We incorporate the new set of constraints into two optimization formulations leveraging two convex relaxations of the three-phase power flow equations: mixed-integer linear programming (MILP) and mixed-integer semidefinite programming (MISDP) that optimize the dispatch of controllable switches and DERs in the microgrid. The algorithms are then extended to networked microgrids with grid-forming sources. We test the algorithms on a realistic community microgrid model in Puerto Rico as well as standardized IEEE distribution test feeders. The testing results demonstrate the performance of the proposed algorithms. The MILP is fast and scalable, and the MISDP enforces the negative sequence voltage constraints.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Model for current drive induced crash cycles in W7-X

In the Wendelstein 7-X (W7-X) stellarator, the vacuum rotational transform, ι, has a flat radial profile and does not cross any major rational resonance. Nevertheless, during plasma operation the ι–profile can be strongly modified by electron cyclotron current drive in such a way that the resulting ι-profile passes through low-order rational values, and this can trigger magnetohydrodynamic (MHD) events. Indeed, W7-X plasmas are sometimes subject to repetitive collapses of core confinement, which can be observed regardless of the direction in which the EC current is driven. Even though the origin of these MHD instabilities is under investigation, the crashes may be connected to the formation of magnetic islands and magnetic reconnection. In the present work, we try to shed light on the dynamics of different events happening during the course of sawtooth cycles in W7-X by proposing a model that combines a slow current diffusion with a recipe for fast relaxation that conserves the corresponding helical flux (Kadomtsev 1975 Fiz. Plazmy 1 710–15). We also propose a simple model based on Taylor relaxation (Taylor 1974 Phys. Rev. Lett. 33 1139), (Taylor 1986 Rev. Mod. Phys. 58 741) to predict the nonlinear redistribution of plasma current caused by the largest of the observed events.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Photovoltaic Analysis and Response Support (PARS) Platform for Solar Situational Awareness and Resiliency Services

The project's primary objective is to develop a digital-twin based Photovoltaic (PV) Analysis and Response Support (PARS) platform, which aims to provide real-time situational awareness and optimal response plans. This platform is designed to enhance the performance of hybrid PV systems, making them competitive with or even superior to conventional generation resources. The PARS platform enabled the project team to develop and evaluate an extensive suite of grid support functionalities for the hybrid PV systems to enhance grid performance, across key areas including visibility, dispatchability, security, resilience, and reliability. Given the global push toward achieving 100% clean energy by 2035, there is a significant increase in the integration of inverter-based resources (IBRs) throughout the energy grid. Effectively managing the inherent variability and uncertainty associated with IBRs is crucial for ensuring cost-effectiveness, reliability, and security in both the main grid and islanded microgrids. Constrained to a limited array of IEEE test systems or standard feeder models, traditional IBR modeling struggles to assimilate new field data, accurately reflect system dynamics, and adapt to the evolving energy landscape. In our project, we embraced a Digital Twin (DT) strategy for crafting the PARS platform. A digital twin acts as a precise virtual counterpart of a physical system, built on historical data and continuously honed with real-time insights. This enables the high-fidelity DT to accurately mirror current system operations and forecast future scenarios. Consequently, the PARS platform becomes an ideal environment for testing and refining monitoring, control, power, and energy management algorithms designed to boost hybrid PV system performance. The defining feature of the PARS platform, distinguishing it from other advanced simulation tools, is its exceptional adaptability. This is achieved by employing actual network topologies and utilizing real-time field data for fine-tuning and calibration, ensuring a close emulation of real-world conditions. The project deliverables include: 1) High-fidelity IBR models and tools for real-time parameterization, utilizing real-time field measurements to refine IBR models for enhanced accuracy and performance; 2) Grid-forming and Grid-following capabilities to deliver resilience services, including blackstart, voltage and frequency support, cold-load pick-up, power reserves, and three-phase load balancing across grid-connected and microgrid settings; 3) Machine learning-based forecasting tools and methods for generating synthetic data and topologies, creating diverse and realistic simulation environments for evaluating varied operational scenarios; 4) Advanced microgrid power and energy management algorithms for optimizing the integration and operation of PV, storage, and demand response resources within both feeder and community scales. The power grid data sets are provided by four utility companies in North Carolina and the New York Power Administration. Acting as industry advisors, our industry partners communicated stakeholder needs and regulatory standards to the research teams, aiding technology transfer by incorporating the developed methodologies into their daily operations. This collaboration ensures that the PARS platform, functioning as a power system digital twin, enhances our understanding of IBR dynamic behaviors and enables the development and evaluation of IBR control functions that match or exceed the capabilities of conventional synchronous generators.

14 SOLAR ENERGY↗

Control Oriented Models for Co-Design: Technical Overview of MT HVDC, MVDC, and Solid State Transformer Building Blocks

The electric power system is shifting toward a power electronics–enabled grid, where converter based “building blocks” (e.g., high voltage direct current (HVDC) links, multi terminal HVDC (MT HVDC) networks, medium voltage DC (MVDC) links, and solid state transformers (SSTs)) provide fast, precise control of power flows, voltage, and frequency. This report develops and applies publicly shareable electromagnetic transient (EMT) and phasor models to examine how such building blocks can be composed and coordinated to support offshore wind integration, inter area transfers, feeder support, and resilience. Section 2 documents a modular multilevel converter (MMC)–based MT HVDC modeling framework and two use cases: a compact WSCC/IEEE 9 bus test system and a 240 bus “mini WECC” case with five offshore wind plants (OWFs). Phasor to EMT transfer, initialization, and sanity checks are summarized, and neutral demonstrations of normal and contingency operation are reported. Section 3 frames the problem of wind plant inertial frequency response (IFR): shaping energy release and recovery to improve nadir while avoiding aerodynamic stall; representative simulations illustrate the issues without disclosing proprietary control. Section 4 develops MVDC concepts through an IEEE 16 bus loop and an Olympic Peninsula case study that compares AC vs. MVDC corridors and shows how feeder headroom can be pooled via DC couplers. Section 5 surveys SST architectures and identifies a gap: scalable, communication free coordination of multiple SSTs for islanded feeder networks. Across the report, novel methods and configurations under separate publication and IP review are not disclosed; only topic oriented, replicable setups and non proprietary results are shown. These models and use cases are intended as foundations for future publications and co design studies on architecture, control, and coordination of PE enabled grids.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Evaluating the resilience benefits of marine energy in microgrids

Marine energy resources could promote clean energy and resilience of coastal and island microgrids, and thus, these applications are a key future market for marine energy development. To demonstrate these benefits, this paper illustrates how inclusion of wave resources into energy resilience solutions can improve overall grid efficiency and sustainability, as well as maintain electricity supply during grid outages. The paper describes a case study evaluation of the potential to add wave energy to the Moloka'i grid as Hawaii strives to meet a 100% clean energy target. The Microgrid Component Optimization for Resilience tool is used to simulate operation in off-grid conditions and size different combinations of wave, solar photovoltaic (PV), wind, storage, and fuel resources required to meet resilience objectives. This research investigates how including wave resources in a microgrid contributes to reducing or eliminating biofuel generation, producing a zero-greenhouse gas emission profile in the latter case, and avoiding the over-sizing of PV and battery systems to accommodate periods of unavailability or high demand. Insight from this paper supports the value proposition of wave resources for future markets and informs the relationship between marine generators and microgrids or isolated grids.

16 TIDAL AND WAVE POWER↗

Evaluating the resilience benefits of marine energy in microgrids

Marine energy resources could promote clean energy and resilience of coastal and island microgrids, and thus, these applications are a key future market for marine energy development. To demonstrate these benefits, this paper illustrates how inclusion of wave resources into energy resilience solutions can improve overall grid efficiency and sustainability, as well as maintain electricity supply during grid outages. The paper describes a case study evaluation of the potential to add wave energy to the Moloka’i grid as Hawaii strives to meet a 100% clean energy target. The Microgrid Component Optimization for Resilience tool is used to simulate operation in off- grid conditions and size different combinations of wave, solar photovoltaic (PV), wind, storage, and fuel resources required to meet resilience objectives. This research in- vestigates how including wave resources in a microgrid contributes to reducing biofuel generation, producing a zero-greenhouse gas emission profile, and avoiding the over-sizing of PV and battery systems to accommodate periods of unavailability or high demand. Insight from this paper supports the value proposition of wave resources for future markets and informs the relationship between marine generators and microgrids or isolated grids.

Newman, Sarah F.↗

Wide Operational Windows of Edge-Localized Mode Suppression by Resonant Magnetic Perturbations in the DIII-D Tokamak

Edge-Localized-Mode (ELM) suppression by resonant magnetic perturbations (RMPs) generally occurs over very narrow ranges of the plasma current (or magnetic safety factor $q_{95}$) in the DIII-D tokamak. However, wide $q_{95}$ ranges of ELM suppression are needed for the safety and operational flexibility of ITER and future reactors. In DIII-D ITER Similar Shape (ISS) plasmas with $n$=3 RMPs, the range of $q_{95}$ for ELM suppression is found to increase with decreasing electron density. Nonlinear two-fluid MHD simulations reproduce the observed $q_{95}$ windows of ELM suppression and the dependence on plasma density, based on the conditions for resonant field penetration at the top of the pedestal. When the RMP amplitude is close to the threshold for resonant field penetration, only narrow isolated magnetic islands form near the top of the pedestal, leading to narrow $q_{95}$ windows of ELM suppression. However, as the threshold for field penetration decreases with decreasing density, resonant field penetration can take place over a wider range of $q_{95}$. For sufficiently low density (penetration threshold) multiple magnetic islands form near the top of the pedestal giving rise to continuous $q_{95}$ windows of ELM suppression. The model predicts that wide $q_{95}$ windows of ELM suppression can be achieved at substantially higher pedestal pressure in DIII-D by shifting to higher toroidal mode number ($n$=4) RMPs.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Enabling Production of Low Carbon Emissions Steel through CO 2 Capture from Blast Furnace Gases at Cleveland Cliffs’ 5 mtpa Steel Plant at Burns Harbor, Indiana

Dastur International Inc. has prepared a DOE-funded Pre-front-end engineering design (Pre-FEED) study to capture up to 2.8 mtpa of CO 2 from the available Blast Furnace (BF) gases at the Burns Harbor steel plant operated by Cleveland Cliffs in Burns Harbor, Indiana. The project consists of an amine solvent based pre-combustion carbon capture system, along with a unique BF gas conditioning process which significantly optimizes the project design and architecture in terms of higher volumes (2.8 mtpa vis-à-vis 1.6 mtpa without conditioning) & concentration (32 vol% in conditioned gas vs. 22% in raw BF gas) of CO 2 , which can be captured using a single train, resulting in reduced size and capital cost of the CO 2 capture island, and improved overall economics on a $\$$/tCO 2 captured basis.

42 ENGINEERING↗

Dynamic Load Inrush Current Mitigation in Islanded Microgrids Powered by Grid-Forming Inverters

Grid-forming inverters in a microgrid may trip due to high inrush current caused by a switched connection of an inductive load, e.g., a relatively large induction motor. The control scheme presented in this article includes virtual inertia control method superimposed on the cascaded controller. This article studies the impact of cascaded control scheme used for grid-forming inverter to mitigate the inrush current effects and enhance the inverter’s robustness for the safe connection of inductive and dynamic loads. Experimental tests are performed using the virtual inertia method for generating the reference angle for synchronous frame conversion. The experimental performance and sensitivity of the controller to different controller gain settings for a switched connection of an induction motor are discussed. The cascaded operation significantly mitigates the inrush currents while the inverters can perform a normal operation. The performance of the control method is tested in a laboratory-scale hardware setup of a 208V microgrid fed by 5kVA and 10kVA inverters, and the results are presented.

Gursoy, Mehmetcan↗

A dynamical mechanism for the Page curve from quantum chaos

If the evaporation of a black hole formed from a pure state is unitary, the entanglement entropy of the Hawking radiation should follow the Page curve, increasing from zero until near the halfway point of the evaporation, and then decreasing back to zero. The general argument for the Page curve is based on the assumption that the quantum state of the black hole plus radiation during the evaporation process is typical. In this paper, we show that the Page curve can result from a simple dynamical input in the evolution of the black hole, based on a recently proposed signature of quantum chaos, without resorting to typicality. Our argument is based on what we refer to as the “operator gas” approach, which allows one to understand the evolution of the microstate of the black hole from generic features of the Heisenberg evolution of operators. One key feature which leads to the Page curve is the possibility of dynamical processes where operators in the “gas” can “jump” outside the black hole, which we refer to as void formation processes. Such processes are initially exponentially suppressed, but dominate after a certain time scale, which can be used as a dynamical definition of the Page time. In the Hayden-Preskill protocol for young and old black holes, we show that void formation is also responsible for the transfer of information from the black hole to the radiation. We conjecture that void formation may provide a microscopic explanation for the recent semi-classical prescription of including islands in the calculation of the entanglement entropy of the radiation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Microgrid's Role in Enhancing the Security and Flexibility of City Energy Systems

Smart cities depend on flexible and secure energy systems to ensure resilient power for critical infrastructure; however, recent weather-related events and cyberattacks have highlighted weaknesses in our energy systems, with the potential for widespread economic and security impacts. As stated by the Executive Office of the President, "the resilience of the US electric grid is a key part of the nation's defense against severe weather." To address the energy delivery security challenge, microgrids are rising as a viable solution that enhances the flexibility and resilience of the distribution grid and boosts the reliability of the local supply for the end-user. Traditionally, high capital investment has been a barrier to large-scale adoption of microgrid technology. Understanding the flexibility and resilience benefits of microgrids and accounting for the associated value streams can make the microgrid's proposition economically viable. In this chapter, microgrids' utility and their potential to serve as a flexible and resilient resource for the utility grid by providing capabilities such as peak shaving, demand response, and frequency regulation is presented. Moreover, other value streams, such as (1) their ability to island during a disaster and sustain critical loads which makes them a robust resilience solution for end-users, in the event of the utility grid outage and (2) microgrids also provide a flexible platform for integrating distributed energy resources in conjunction with storage and conventional generation technologies, strengthen microgrid's role in reducing the over-arching goal of emission reduction. Given the myriad of benefits associated with microgrids, we present strategies which can be employed for making microgrid itself resilient against physical and cyberthreats by employing hardware, software, and personnel training solutions to operate the microgrid before, during, and after a potential disaster. This chapter, thus, provides a holistic study of the microgrid as a resilience resource, for the utility grid, and a self-contained end-user for the end-user.

cyber-physical system↗

Operationalizing Synchrophasors for Enhanced Grid Reliability and Asset Utilization

The report discusses the development of production-grade synchrophasor software applications. The objective is to improve system reliability and asset utilization for offline as well as real-time considerations, as per the Department of Energy (DOE) guidelines specified by Funding Opportunity Announcement (FOA) DE-FOA-0001492. On the one hand, we have developed grid management applications on how to transform synchrophasor-based monitoring into operator guidance, and commercial grade tools addressing industry needs such as NERC Reliability Standards (MOD 26, MOD 27 and MOD 33). On the other hand, with the wide industrial adoption in mind, the developed applications have been fully discussed with utility partners and installed in the utility partners site including 6 field tests. The Model Validation and Calibration software module has been integrated into GE’s PhasorAnalyticsTM. The first commercial contract has been signed even before the close date of this project. The Angle-based Grid Management (AGM), Fast Voltage Security Assessment (FastVSA), Enhanced Islanding Monitoring(EIM) and Enhanced Disturbance Management (EDM) have been integrated into GE’s Grid Stability Assessment line of applications in e-terra Suite of EMS product.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Non-intrusive reduced-order modeling for dynamical systems with spatially localized features

This work presents a non-intrusive reduced-order modeling framework for dynamical systems with spatially localized features characterized by slow singular value decay. The proposed approach builds upon two existing methodologies for reduced and full-order non-intrusive modeling, namely Operator Inference (OpInf) and sparse Full-Order Model (sFOM) inference. We decompose the domain into two complementary subdomains that exhibit fast and slow singular value decay. The dynamics of the subdomain exhibiting slow singular value decay are learned with sFOM while the dynamics with intrinsically low dimensionality on the complementary subdomain are learned with OpInf. The resulting, coupled OpInf-sFOM formulation leverages the computational efficiency of OpInf and the high resolution of sFOM, and thus enables fast non-intrusive predictions for conditions beyond those sampled in the training data set. A novel regularization technique with a closed-form solution based on the Gershgorin disk theorem is introduced to promote stable sFOM and OpInf models. We also provide a data-driven indicator for subdomain selection and ensure solution smoothness over the interface via a post-processing interpolation step. We evaluate the efficiency of the approach in terms of offline and online speedup through a quantitative, parametric computational cost analysis. We demonstrate the coupled OpInf-sFOM formulation for two test cases: a one-dimensional Burgers’ model for which accurate predictions beyond the span of the training snapshots are presented, and a two-dimensional parametric model for the Pine Island Glacier ice thickness dynamics, for which the OpInf-sFOM model achieves an average prediction error on the order of 1% with an online speedup factor of approximately 8$\times$ compared to the numerical simulation.

42 ENGINEERING↗

Unleashing the Frequency: Multi-Megawatt Demonstration of 100% Renewable Power Systems with Decentralized Communication-Less Control Scheme

Power systems, which range in size from small microgrids to island systems to large regional grids, are typically managed by a central controller that requires complex communication methods and can be unreliable and pose cyber security risks in certain applications, especially when controlling a larger number of nodes. We propose an inherently robust, scalable method of integration using multiple energy storage systems and distributed energy resources, which does not require any means of dedicated communication. This method moves beyond the paradigm of controlling grid frequency at a fixed value (e.g., 60 Hz), instead allowing the frequency to fluctuate within certain limits (e.g., 59.6-60.4 Hz). With a greater operating range, the frequency can carry necessary information from energy storage systems to highly variable distributed energy resources like photovoltaics, wind, hydro, etc.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Electric Vehicle Charging for Residential and Commercial Energy Codes: Technical Brief

Numerous studies show that sales of electric vehicles (EVs) have grown consistently over recent years in the U.S. The U.S. Energy Information Administration (EIA) estimated 3 million EVs were on the road in 2022, and the Edison Electric Institute (EEI) forecasts a total of 26.4 million EVs on the road by 2030. Based on this forecast, EEI projects the need for an additional 12.9 million EV charge ports by 2030. If EV charging infrastructure fails to keep pace with sales of EVs it could result in consumers stranded without options to power their vehicles. EVs are capable of providing substantial benefits to the consumers. EVs are less expensive to operate than conventional internal combustion engine vehicles, have lower maintenance costs, and have the convenience of fueling (charging) at home or work. Studies conducted in California show that costs associated with installing EV charging infrastructure can be substantially more expensive for retrofit scenarios compared to new construction, making inclusion of EV infrastructure in new construction codes a cost-effective policy option to increase infrastructure to meet growing demands. PNNL tracks adoption of mandatory EV provisions across the U.S. As of December 20, 2024, 12 states (California, Oregon, Washington, Colorado, New Mexico, Illinois, Maryland, Delaware, New Jersey, Rhode Island, Massachusetts and Vermont) and 53 local governments have added EV provisions to their building codes, local ordinances and zoning requirements. Originally published in 2022, this tech brief has been revised to align with recent model energy code committee discussions and published EV infrastructure code language. This technical brief summarizes market trends, costs and benefits, and provides sample code language for EV charging infrastructure for consideration to be included in model codes, such as the International Energy Conservation Code (IECC) and ANSI/ASHRAE/IES Standard 90.1, as well as directly by states and local governments in their building codes. The technical brief summarizes related efforts undertaken by states and local governments, and builds upon language considered during the 2021 and 2024 IECC development cycles.

2021 IECC↗

A Data-Driven Method for Estimating Behind-the-Meter Photovoltaic Generation in Hawaii

Due to the increasing penetration of distributed behind-the-meter photovoltaic (PV) systems and the installed utility revenue metering limited to monitoring only the net power import/export of the household, it is increasingly challenging for utilities to effectively plan and operate the grid. This paper proposes a methodology that estimates behind-the-meter PV generation using a selected subset of monitored PV systems. It is a data-driven approach, and the PV output is estimated utilizing a statistic regression model. A Minimum Redundancy Maximum Relevance (MRMR) algorithm is applied to preselect the optimal subset of the monitored PV systems. The performance of this approach is compared with a spatial interpolation method and a model-based approach. The proposed method is validated using high-resolution meter data recorded from 18 residential rooftop PV systems located on the island of Maui, Hawaii.

Data-driven modeling↗

Holistic Small-Signal Stability Analysis for Large-Scale Inverter-Intensive Power Systems with Coupled and Full-Order Dynamics from Control Systems and Power Networks

The increasing penetration of inverter-based resources (IBRs) into the existing power systems introduces tremendous benefits for enhanced sustainability but also poses inevitable challenges in terms of insufficient inertia, potential instability, and complex network dynamics, among others. However, the additional coupling introduced by the interactions among gridfollowing (GFL) and grid-forming (GFM) IBRs and the other components (i.e., synchronous generators [SGs], loads, and network, etc.) has not been clearly explored. A holistic, scalable, and quantitative stability analysis framework with the control systems and power networks is still missing. Here, in this paper, to fill in the technical gaps, a holistic small-signal model of the entire system with both rotating generation units and IBRs is established. An extended power flow model with operation dynamics from both generator control schemes and power networks is proposed to provide the varying steady-state operating points for small-signal modeling. The proposed method is compared with MATLAB solvers, and the results show that the proposed approach has a minimum calculation time, which can be less than 12 seconds for a large-scale power system with up to 2,000 buses. Furthermore, a quantitative method is developed to identify the impacts of IBRs on system performance with emphases on the potential stability issues with GFL IBRs, additional benefits of employing GFM IBRs, the feasibility of replacing SGs with GFM IBRs, and the impact of penetration level of different kinds of generation units. Finally, a field island power system is used to verify the proposed approach, and hardware-in-the-loop (HIL) tests are provided to further demonstrate the effectiveness of the proposed analysis.

14 SOLAR ENERGY↗

A Rapid Population Assessment Method for Wild Pigs Using Baited Cameras at 3 Study Sites

ABSTRACT Reliable and efficient population estimates are a critical need for effective management of invasive wild pigs ( Sus scrofa ). We evaluated the use of 10‐day camera grids for rapid population assessment (RPA) of wild pigs at 3 study sites that varied in vegetation communities and wild pig densities. Study areas included Buck Island Ranch, Florida; Tejon Ranch, California; and the Savannah River Site, South Carolina, USA, during 2016–2018. Rapid population assessments grids were composed of baited camera traps spaced approximately 500 or 750 m apart. Two RPA grids were deployed per study site and each grid was deployed twice (4–6 months apart) to assess changes in response to season or population control efforts. We assessed the ability of RPA grids to track population trends, how camera number influenced estimate precision, and how relative abundance indices related to density estimates. We detected changes in occupancy probability, detection probability, and N‐mixture estimates following removal operations and between seasons, but the ability of RPA grids to track population trends was dependent on the statistical method used and number of cameras traps. Increasing the number of cameras traps used in RPA grids increased precision, and these results can be used in determining survey design and estimate choice. We found that estimates of occupancy probability, detection probability, and N‐mixture estimates were positively correlated with spatially explicit capture–recapture density estimates. Thus, these less labor‐intensive estimates from RPA grids showed potential to index the relative abundance of wild pigs in some systems. Our evaluation of RPAs indicates that using study‐specific combinations of statistical method and number of cameras can provide a useful tool for monitoring wild pig presence, tracking population trends, and evaluating the effectiveness of management actions. © 2020 The Wildlife Society.

Schlichting, Peter E.↗