Temporal complementarity and value of wind-PV hybrid systems across the United States
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Harrison-Atlas, Dylan (ORCID:0000000252173355)↗
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Complementarity-based complementarity: The choice of mutually unbiased observables shapes quantum uncertainty relations
Quantum uncertainty relations impose fundamental limits on the joint knowledge that can be acquired from complementary observables: Perfect knowledge of a quantum state in one basis implies maximal indetermination in all other mutually unbiased bases (MUBs). Uncertainty relations derived from joint properties of the MUBs are generally assumed to be uniform, irrespective of the specific observables chosen within a set. In this work, we demonstrate instead that the uncertainty relations can depend on the choice of observables. Through both experimental observation and numerical methods, we show that selecting different sets of three MUBs in a five-dimensional quantum system results in distinct uncertainty bounds, i.e., in varying degrees of complementarity, in terms of both entropy and variance.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Data on temporal complementarity of hybrid renewable energy systems [SWR-23-09]
These datasets describe multiple facets of the temporal complementarity of co-located hybrid renewable energy systems throughout the United States. Several metrics characterizing the complementarity of generation profiles are provided on an annual and monthly basis (for both hourly and daily aggregations). These generation profiles are underpinned by hourly resource data (e.g., the WIND Toolkit and National Solar Radiation Database (NSRDB)) spanning the multi-year period 2007-2013. The data include complementarity results for greater than 1.76 million individual locations within the continental United States (CONUS). The data are intended to accompany two publications on the topic of temporal complementarity: 1) Harrison-Atlas, Dylan, Caitlin Murphy, Anna Schleifer, and Nicholas Grue. "Temporal complementarity and value of wind-PV hybrid systems across the United States." Renewable Energy 201 (2022): 111-123, doi:10.1016/j.renene.2022.10.060; and 2) Murphy, Caitlin, Harrison-Atlas, Dylan, Nicholas Grue, Vahan Gevorgian, Juan Gallego-Calderon, Shiloh Elliot and Thomas Mosier. “A Resource Assessment for FlexPower”. NREL Technical Report.
Harrison-Atlas, Dylan↗
Convex Relaxation of Grid-Connected Energy Storage System Models With Complementarity Constraints in DC OPF
Including complementarity constraints in energy storage system (ESS) models in optimization problems ensure an optimal solution will not produce a physically unrealizable control strategy where there is simultaneous charging and discharging. However, the current approaches to impose complementarity constraints require the use of non-convex optimization methods. Here, we propose a convex relaxation for a common ESS model that has terms for both charging and discharging based on a penalty reformulation for use in a model predictive control (MPC) based optimal power flow (DC OPF) problem. In this approach, the complementarity constraints are omitted and a penalty term is added to the optimization objective function. For the DC OPF problem, we provide analysis for the conditions under which the convex relaxation of the complementarity constraint ensures that a solution with simultaneous ESS charging and discharging operation is suboptimal. Simulation results demonstrating ESS behavior with and without the penalty reformulation are provided for an MPC-based DC OPF problem on multiple IEEE test systems.
25 ENERGY STORAGE↗
Schrödinger Cats and Quantum Complementarity
Complementarity tells us we cannot know precisely the values of all the properties of a quantum object at the same time: the precise determination of one property implies that the value of some other (complementary) property is undefined. E.g. the precise knowledge of the position of a particle implies that its momentum is undefined. Here we show that a Schrödinger cat has a well defined value of a property that is complementary to its “being dead or alive” property. Then, thanks to complementarity, it has an undefined value of the property “being dead or alive”. In other words, the cat paradox is explained through quantum complementarity: of its many complementary properties, any quantum system, such as a cat, can have a well defined value only of one at a time. Schrödinger’s cat has a definite value of a property which is complementary to “being dead or alive”, so it is neither dead nor alive. Figuratively one can say it is both dead and alive. While this interpretation only uses textbook concepts (the Copenhagen interpretation), apparently it has never explicitly appeared in the literature. We detail how to build an Arduino based simulation of Schrödinger’s experiment based on these concepts for science outreach events.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
On optimal control of hybrid dynamical systems using complementarity constraints
Optimal control for switch-based dynamical systems is a challenging problem in the process control literature. In this study, we model these systems as hybrid dynamical systems with finite number of unknown switching points and reformulate them using non-smooth and non-convex complementarity constraints as a mathematical program with complementarity constraints (MPCC). We utilize a moving finite element based strategy to discretize the differential equation system to accurately locate the unknown switching points at the finite element boundary and achieve high-order accuracy at intermediate non-collocation points. We propose a globalization approach to solve the discretized MPCC problem using a mixed NLP/MILP-based strategy to converge to a non-spurious first-order optimal solution. The method is tested on three dynamic optimization examples, including a gas–liquid tank model and an optimal control problem with a sliding mode solution.
97 MATHEMATICS AND COMPUTING↗
Optimal Complementarity Analysis of Potential Floating Solar Co-Located With Existing Hydropower Assets Across the Contiguous United States
The U.S. is expected to double its rate of renewable capacity from 2024 to 2030. However, the stochastic nature of renewable energy poses challenges to the operation and reliability of our power grid. The combined generation from renewable energy sources, with dispatchable sources (such as hydropower) operating as a hybrid energy plant, could mitigate this variability. In this paper, the complementarity analysis of selected U.S. reservoirs with existing hydropower assets (EHAs) and potential floating photovoltaics (FPVs) is conducted for the continuous U.S. (CONUS). The optimal FPV capacity for each site is determined by minimizing the variability of the combined output, while adhering to the FPV potential. Our results indicate that over 50% of the analyzed reservoirs achieve a stability coefficient exceeding 0.5, leading to a less-variable output after optimization. Finally, we analyze the complementary hydro-FPV hybrid reservoirs by considering both the Pearson correlation coefficient and the stability coefficient on daily, monthly, and yearly scales. Summaries are included of locations of theoretical FPVs co-located with hydropower plants that exhibit high complementarity based on the selected metrics.
13 - HYDRO ENERGY↗
Multi-Stage Modeling With Recourse Decisions for Solving Stochastic Complementarity Problems With an Application in Energy
This paper presents a multi-stage model with recourse decisions for solving complementarity problems in a competitive electricity market under uncertainty, while also considering renewable energy technologies and battery storage utilization. The model is based on a Nash-Cournot formulation of imperfect competition among power producers. We analyze the value of variable renewable energy (VRE) and battery storage under different uncertainties, such as demand level and VRE availability. To illustrate the proposed model, we apply it to three- bus five-player model and analyze different cases varying costs, including a user-optimal perspective (with market power) and a system-optimal perspective (with central planning). We also consider the potential for congestion in the system by restricting the transmission capacity between a single interface that connects two buses. Our findings show that increasing the battery storage capacity results in a decrease in the need for perfect information about future uncertainties. Additionally, as the model allows for more uncertainty, it becomes more apparent that the stochastic mixed complementarity problem (MCP) has an advantage over a deterministic equivalent. We propose the use of the Value of the Stochastic Equilibrium Solution (VSES) as a quality metric to compare the stochastic MCP with its deterministic equivalent. Overall, expanding battery storage capacity can lower the maximum, mean, and variance values of delivered prices, but there are diminishing returns to this approach.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Guaranteeing a Physically Realizable Battery Dispatch Without Charge-Discharge Complementarity Constraints
The non-convex complementarity constraints present a fundamental computational challenge in energy constrained optimization problems. In this work, we present a new, linear, and robust battery optimization formulation that sidesteps the need for battery complementarity constraints and integers and prove analytically that the formulation guarantees that all energy constraints are satisfied which ensures that the optimized battery dispatch is physically realizable. In addition, we bound the worst-case model mismatch and discuss conservativeness. In conclusion, simulation results further illustrate the effectiveness of this approach.
25 ENERGY STORAGE↗
Sequential Linearization Method for Bound-Constrained Mathematical Programs with Complementarity Constraints
Here, we propose an algorithm for solving bound-constrained mathematical programs with complementarity constraints on the variables. Each iteration of the algorithm involves solving a linear program with complementarity constraints in order to obtain an estimate of the active set. The algorithm enforces descent on the objective function to promote global convergence to B-stationary points. We provide a convergence analysis and preliminary numerical results on a range of test problems. We also study the effect of fixing the active constraints in a bound-constrained quadratic program that can be solved on each iteration in order to obtain fast convergence.
97 MATHEMATICS AND COMPUTING↗
A complementarity-based vapor-liquid equilibrium formulation for equation-oriented simulation and optimization
Vapor-Liquid Equilibrium (VLE) is a cornerstone of computer aided process engineering (CAPE). Embedded within process system models, VLE calculations are inherently procedural with non-smooth behavior that frequently require discrete decisions. Traditionally, these features resist the incorporation of VLE within efficient, large-scale equation-oriented (EO) process simulation and optimization strategies. On the other hand, recent reformulation of VLE models through the incorporation of complementarity constraints has broadened its scope to deal seamlessly with phase transitions and even supercritical excursions in process simulation and optimization. In this study, we extend these VLE complementarity models to EO frameworks where procedural thermodynamic property libraries are still required. Here, we develop an efficient, non-intrusive, and intuitive “square-flash” equation system that has been implemented within the IDAES Integrated Platform (IDAES-IP). Further, the effectiveness of this modular approach is demonstrated on case studies for non-ideal flash calculations and distillation optimization with disappearing phases and supercritical transitions.
97 MATHEMATICS AND COMPUTING↗
Self-complementarity of messenger RNA's of periodic proteins
It is shown that the mRNA's of three periodic proteins, collagen, keratin and freezing point depressing glycoproteins show a marked degree of self-complementarity. The possible origin of this self-complementarity is discussed.
Ycas, M.↗
Model of early self-replication based on covalent complementarity for a copolymer of glycerate-3-phosphate and glycerol-3-phosphate
Glyceraldehyde-3-phosphate acts as the substrate in a model of early self-replication of a phosphodiester copolymer of glycerate-3-phosphate and glycerol-3-phosphate. This model of self-replication is based on covalent complementarity in which information transfer is mediated by a single covalent bond, in contrast to multiple weak interactions that establish complementarity in nucleic acid replication. This replication model is connected to contemporary biochemistry through its use of glyceraldehyde-3-phosphate, a central metabolite of glycolysis and photosynthesis.
Weber, Arthur L.↗
Model of early self-replication based on covalent complementarity for a copolymer of glycerate-3-phosphate and glycerol-3-phosphate
Glyceraldehyde-3-phosphate acts as the substrate in a model of early self-replication of a phosphodiester copolymer of glycerate-3-phosphate and glycerol-3-phosphate. This model of self-replication is based on covalent complementarity in which information transfer is mediated by a single covalent bond, in contrast to multiple weak interactions that establish complementarity in nucleic acid replication. This replication model is connected to contemporary biochemistry through its use of glyceraldehyde-3-phosphate, a central metabolite of glycolysis and photosynthesis.
Weber, Arthur L.↗
Di-Higgs production in the 4b channel and gravitational wave complementarity
We present a complementarity study of gravitational waves and double Higgs production in the 4 b channel, exploring the gauge singlet scalar extension of the SM. This new physics extension serves as a simplified benchmark model that realizes a strongly first-order electroweak phase transition necessary to generate the observed baryon asymmetry in the universe. In calculating the signal-to-noise ratio of the gravitational waves, we incorporate the effect of the recently discovered significant suppression of the gravitational wave signals from sound waves for strong phase transitions, make sure that supercooled phase transitions do complete and adopt a bubble wall velocity that is consistent with a successful electroweak baryogenesis by solving the velocity profiles of the plasma. The high-luminosity LHC sensitivity to the singlet scalar extension of the SM is estimated using a shape-based analysis of the invariant 4 b mass distribution. We find that while the region of parameter space giving detectable gravitational waves is shrunk due to the new gravitational wave simulations, the qualitative complementary role of gravitational waves and collider searches remain unchanged.
79 ASTRONOMY AND ASTROPHYSICS↗
Chaos and complementarity in de Sitter space
We consider small perturbations to a static three-dimensional de Sitter geometry. For early enough perturbations that satisfy the null energy condition, the result is a shockwave geometry that leads to a time advance in the trajectory of geodesics crossing it. This brings the opposite poles of de Sitter space into causal contact with each other, much like a traversable wormhole in Anti-de Sitter space. In this background, we compute out-of-time-order correlators (OTOCs) to asses the chaotic nature of the de Sitter horizon and find that it is maximally chaotic: one of the OTOCs we study decays exponentially with a Lyapunov exponent that saturates the chaos bound. We discuss the consequences of our results for de Sitter complementarity and inflation.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Detecting new physics as novelty — Complementarity matters
Novelty detection is a task of machine learning that aims at detecting novel events without a prior knowledge. In particular, its techniques can be applied to detect unexpected signals from new phenomena at colliders. In this paper, we develop an analysis scheme that exploits the complementarity, originally studied in ref. [1], between isolation-based and clustering-based novelty evaluators. This approach can significantly improve the performance and overall applicability of novelty detection at colliders, which we demonstrate using a variety of two dimensional Gaussian samples mimicking collider events. As a further proof of principle, we subsequently apply this scheme to the detection of two significantly different signals at the LHC featuring a $t\bar{t}γγ$ final state: $t\bar{t}h$, giving a narrow resonance in the diphoton mass spectrum, and gravity-mediated supersymmetry, resulting in broad distributions at high transverse momentum. Compared to existing dedicated searches at the LHC, the sensitivities for detecting both signals are found to be encouraging.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Temporal complementarity of marine renewables with wind and solar generation: Implications for GB system benefits
Wave and tidal energy have the potential to provide benefits to power systems with high proportions of stochastic renewable generation. This is particularly applicable with wind and solar photovoltaics, as the offsetting of these renewable resources results in more reliable renewable generation. This study utilises ten metrics to quantify the temporal complementarity and supply-demand balancing requirements of the energy mix in Great Britain, to investigate the potential magnitude of these system benefits. Wave and tidal generation profiles are created using historical resource data and hydrodynamic models. The results show that the inclusion of wave and tidal generation creates a renewable energy mix which is more available under multiple conditions: throughout a year of operation; at times of peak demand; for multiple consecutive hourly time periods; and at times when wind and solar generation are not available. Three regional case studies also show that the inclusion of marine energy allows for improved regional supply-demand matching, reducing instances of energy shortage and excess and potentially relieving transmission congestion at particularly constrained locations within GB. Finally, the implications of these findings are discussed in terms of GB wholesale market operation, system balancing and system security.
16 TIDAL AND WAVE POWER↗