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Electric vehicle managed charging can benefit all consumers by supporting grid planning, operation, and reliability – especially complementing high-renewable systems.

Major technological advancements and recent policy support are improving the outlook for heavy-duty truck electrification in the United States. In particular, short-haul operations (≤200 miles (≤322 km)) are prevalent and early candidates for plug-in electric vehicles (EVs) given their short, predictable routes and return-to-base applications, which allows vehicles to recharge when off shift at their depots. Although previous studies investigated the impacts of added electrical loads on distribution systems, which included light-duty EVs, the implications for heavy-duty EV charging are underexplored. Here we summarize the causes, costs and lead times of distribution system upgrades anticipated for depot charging. We also developed synthetic depot charging load profiles for heavy-duty trucks from real-world operating schedules, and found that charging requirements are met at common light-duty EV charging rates (≤100 kW per vehicle). Finally, we applied depot charging load profiles to 36 distribution real-world substations, which showed that most can accommodate high levels of heavy-duty EV charging without upgrades. Increasing attention is being paid to the electrification of trucks, in particular for short-haul operations. Borlaug et al. simulate depot charging load profiles based on real-world operating schedules to explore future charging requirements and assess the likely distribution substation upgrades needed to support them.

Multicarrier energy systems (MCESs) are characterized by strong coordination in operation and planning across multiple energy vectors and/or sectors to deliver reliable, cost-effective energy services to end users/customers with minimal impact on the environment. They have efficiency and flexibility benefits and are deployed in large and small scales on the supply and demand sides and at the network level but are more complex to control and manage. In this article, MCESs are reviewed in the context of future low carbon energy systems based on electrification and very high variable renewable energy penetrations. Fully exploiting these systems requires some cost reductions, more sophisticated operations enabled by standardized communications and control capabilities detailed planning paradigms, and addressing their corresponding economic challenges. All these point toward the direction of analysis, markets, and technology research and development coupled with better policy and regulatory frameworks. One futuristic vision of a very low carbon energy system is proposed that illustrates potential pathways to an MCES-dominated energy future.

Summary The cost to charge an electric vehicle (EV) varies depending on the price of electricity at different charging sites (home, workplace, public), vehicle use, region, and time of day, and for different charging power levels and equipment and installation costs. This paper provides a detailed assessment of the current (2019) levelized cost of light-duty EV charging in the United States, considering the purchase and installation costs of charging equipment and electricity prices from real-world utility tariffs. We find national averages of $0.15/kWh for battery EVs and $0.14/kWh for plug-in hybrid EVs in the United States. Costs, however, vary considerably (e.g., $0.08/kWh to $0.27/kWh for battery EVs) for different charging behaviors and equipment costs, corresponding to a total projected fuel cost savings between $3,000 and $10,500 compared with gasoline vehicles (over a 15-year time horizon). Regional heterogeneities and uncertainty on lifetime vehicle use and future fuel prices produce even greater variations.

In this survey paper we discuss a series of recent results concerning nonnegative solutions to nonlinear diffusion equations of porous-medium type on Cartan–Hadamard manifolds, a special class of negatively-curved Riemannian manifolds that generalize the Euclidean space. We focus on sharp barrier estimates, asymptotic convergence and smoothing effects, describing quantitatively how the curvature behavior at infinity affects the way solutions depart from having a Euclidean-like structure.

Given a complete, connected Riemannian manifold $ \mathbb{M}^n $ with Ricci curvature bounded from below, we discuss the stability of the solutions of a porous medium-type equation with respect to the 2-Wasserstein distance. We produce (sharp) stability estimates under negative curvature bounds, which to some extent generalize well-known results by Sturm and Otto-Westdickenberg. The strategy of the proof mainly relies on a quantitative $L^1-L^\infty$ smoothing property of the equation considered, combined with the Hamiltonian approach developed by Ambrosio, Mondino and Savar\'e in a metric-measure setting., Comment: 41 pages. We have corrected the definition of the nondegenerate nonlinearity. Fixed some typos. Final version, to appear in "Journal of Functional Analysis"

We investigate the problem of the equivalence of $L^q$-Sobolev norms in Malliavin spaces for $q\in [1,\infty)$, focusing on the graph norm of the $k$-th Malliavin derivative operator and the full Sobolev norm involving all derivatives up to order $k$, where $k$ is any positive integer. The case $q=1$ in the infinite-dimensional setting is challenging, since at such extreme the standard approach involving Meyer's inequalities fails. In this direction, we are able to establish the mentioned equivalence for $q=1$ and $k=2$ relying on a vector-valued Poincar�� inequality that we prove independently and that turns out to be new at this level of generality, while for $q=1$ and $k>2$ the equivalence issue remains open, even if we obtain some functional estimates of independent interest. With our argument (that also resorts to the Wiener chaos) we are able to recover the case $q\in (1,\infty)$ in the infinite-dimensional setting; the latter is known since the eighties, however our proof is more direct than those existing in the literature, and allows to give explicit bounds on all the multiplying constants involved in the functional inequalities. Finally, we also deal with the finite-dimensional case for all $q\in [1,\infty)$ (where the equivalence, without explicit constants, follows from standard compactness arguments): our proof in such setting is much simpler, relying on Gaussian integration-by-parts formulas and an adaptation of Sobolev inequalities in Euclidean spaces, and it provides again quantitative bounds on the multiplying constants, which however blow up when the dimension diverges to $\infty$ (whence the need for a different approach in the infinite-dimensional setting).

The electrification of transportation and the integration of electric vehicles (EVs) with buildings connected to clean grids has been touted as one of the key solutions to the global decarbonization challenge. Cities are on the frontlines of current and future electrification, as they depend on and drive electricity generation, distribution, and use. City actors also occupy a central role in the actions to enable electrification to support energy transitions in efficient, equitable, environmentally sound, and resilient ways. Currently, however, research and development on the interactions between actors, cities and energy systems is predominantly conducted in disciplinary siloes. This topical review analyzes the transformational potential of urban electrification. It focuses on efforts to electrify transportation and integrate EVs with buildings connected to a clean grid. We find that actions in these area are driving change; they are adopted by wealthier populations and on an experimental basis by specific communities. Their larger-scale growth is constrained by institutional, behavioral, and infrastructural factors. We also find that existing siloed disciplinary approaches are often incompatible with advancing holistic research. To achieve that, divergent communities of scholars need to come together to integrate their research and create broader perspectives. Through incorporation of the social sciences, these perspectives need to consider the societal limits and potentials brought to bear by human behavior and decision making. Only then can urban electrification be understood as the empirically rich and socially complex topic that it is. And only with this understanding will innovations and smart policy actions be able to tap into the transformational potential of urban electrification.

Widespread adoption of alternative fuel vehicles is being hindered by high vehicle costs and refueling or range limitations. For plug-in electric vehicles, direct-current fast charging (DCFC) is proposed as a solution to support long-distance travel and relieve range anxiety. However, DCFC has also been shown to be potentially more expensive compared to residential or workplace charging. In particular, electricity demand charges can significantly impact electricity cost for fast charging applications. Here we explore technological solutions that can help reduce the electricity cost for electric vehicle fast charging. In particular, we consider thousands of electricity rates available in the United States and real-world vehicle charging load scenarios to assess opportunities to reduce the cost of DCFC by deploying solar photovoltaics (PV) panels and energy storage (battery), and implementing a co-location configuration where a DCFC station is connected to an existing meter within a commercial building. Results show that while the median electricity cost across more than 7000 commercial retail rates remains less than $0.20/kWh for all charging load scenarios considered, cost varies greatly, and some locations do experience significantly higher electricity cost. Co-location is almost always economically viable to mitigate fixed cost and demand charges, but the relative benefit of co-locating diminishes as station size and utilization increase. Energy storage alone can help mitigate demand charges and is more effective at reducing costs for “peaky” or low-utilization loads. On the other hand, PV systems primarily help mitigate energy charges, and are more effective for loads that are more correlated with solar production, even in areas with lower solar resource. PV and energy storage can deploy synergistically to provide cost reductions for DCFC, leveraging their ability to mitigate demand and energy charges.

The Cartan-Hadamard conjecture states that, on every $n$-dimensional Cartan-Hadamard manifold $ \mathbb{M}^n $, the isoperimetric inequality holds with Euclidean optimal constant, and any set attaining equality is necessarily isometric to a Euclidean ball. This conjecture was settled, with positive answer, for $n \le 4$. It was also shown that its validity in dimension $n$ ensures that every $p$-Sobolev inequality ($ 1 < p < n $) holds on $ \mathbb{M}^n $ with Euclidean optimal constant. In this paper we address the problem of classifying all Cartan-Hadamard manifolds supporting an optimal function for the Sobolev inequality. We prove that, under the validity of the $n$-dimensional Cartan-Hadamard conjecture, the only such manifold is $ \mathbb{R}^n $, and therefore any optimizer is an Aubin-Talenti profile (up to isometries). In particular, this is the case in dimension $n \le 4$. Optimal functions for the Sobolev inequality are weak solutions to the critical $p$-Laplace equation. Thus, in the second part of the paper, we address the classification of radial solutions (not necessarily optimizers) to such a PDE. Actually, we consider the more general critical or supercritical equation \[ -��_p u = u^q \, , \quad u>0 \, , \qquad \text{on } \mathbb{M}^n \, , \] where $q \ge p^*-1$. We show that if there exists a radial finite-energy solution, then $\mathbb{M}^n$ is necessarily isometric to $\mathbb{R}^n$, $q=p^*-1$ and $u$ is an Aubin-Talenti profile. Furthermore, on model manifolds, we describe the asymptotic behavior of radial solutions not lying in the energy space $\dot{W}^{1,p}(\mathbb{M}^n)$, studying separately the $p$-stochastically complete and incomplete cases., Accepted for publication on Annali della Scuola Normale Superiore di Pisa, Classe di Scienze

Non-technical summaryWe summarize some of the past year's most important findings within climate change-related research. New research has improved our understanding of Earth's sensitivity to carbon dioxide, finds that permafrost thaw could release more carbon emissions than expected and that the uptake of carbon in tropical ecosystems is weakening. Adverse impacts on human society include increasing water shortages and impacts on mental health. Options for solutions emerge from rethinking economic models, rights-based litigation, strengthened governance systems and a new social contract. The disruption caused by COVID-19 could be seized as an opportunity for positive change, directing economic stimulus towards sustainable investments.Technical summaryA synthesis is made of ten fields within climate science where there have been significant advances since mid-2019, through an expert elicitation process with broad disciplinary scope. Findings include: (1) a better understanding of equilibrium climate sensitivity; (2) abrupt thaw as an accelerator of carbon release from permafrost; (3) changes to global and regional land carbon sinks; (4) impacts of climate change on water crises, including equity perspectives; (5) adverse effects on mental health from climate change; (6) immediate effects on climate of the COVID-19 pandemic and requirements for recovery packages to deliver on the Paris Agreement; (7) suggested long-term changes to governance and a social contract to address climate change, learning from the current pandemic, (8) updated positive cost–benefit ratio and new perspectives on the potential for green growth in the short- and long-term perspective; (9) urban electrification as a strategy to move towards low-carbon energy systems and (10) rights-based litigation as an increasingly important method to address climate change, with recent clarifications on the legal standing and representation of future generations.Social media summaryStronger permafrost thaw, COVID-19 effects and growing mental health impacts among highlights of latest climate science.

It is well known that the Euclidean Sobolev inequality holds on any Cartan-Hadamard manifold of dimension n ≥ 3, i.e. any complete, simply connected Riemannian manifold with nonpositive sectional curvature. Moreover, in the very special case of the Euclidean space itself, the optimal constant is achieved by the Aubin-Talenti functions. On a generic Cartan-Hadamard manifold \( \mathbb {M}^n \), one may ask whether there exist at all optimal functions. Here we prove, with ad hoc arguments that do not take advantage of the validity of the so-called Cartan-Hadamard conjecture (claiming that such optimal constant is always Euclidean), that this is false at least for functions that are radially symmetric with respect to the geodesic distance from a fixed pole. More precisely, we show that if the optimum in the Sobolev inequality is achieved by some radial function, then \(\mathbb {M}^n \) must be isometric to \( \mathbb {R}^n \).

Bioenergy is expected to play an important role in long-run climate change mitigation strategies as highlighted by many integrated assessment model (IAM) scenarios. These scenarios, however, also show a very wide range of results, with uncertainty about bioenergy conversion technology deployment and biomass feedstock supply. To date, the underlying differences in model assumptions and parameters for the range of results have not been conveyed. Here we explore the models and results of the 33rd study of the Stanford Energy Modeling Forum to elucidate and explore bioenergy technology specifications and constraints that underlie projected bioenergy outcomes. We first develop and report consistent bioenergy technology characterizations and modeling details. We evaluate the bioenergy technology specifications through a series of analyses—comparison with the literature, model intercomparison, and an assessment of bioenergy technology projected deployments. We find that bioenergy technology coverage and characterization varies substantially across models, spanning different conversion routes, carbon capture and storage opportunities, and technology deployment constraints. Still, the range of technology specification assumptions is largely in line with bottom-up engineering estimates. We then find that variation in bioenergy deployment across models cannot be understood from technology costs alone. Important additional determinants include biomass feedstock costs, the availability and costs of alternative mitigation options in and across end-uses, the availability of carbon dioxide removal possibilities, the speed with which large scale changes in the makeup of energy conversion facilities and integration can take place, and the relative demand for different energy services.

We investigate the well-posedness of the fast diffusion equation (FDE) on noncompact Riemannian manifolds. Existence and uniqueness of solutions for L 1 L^1 initial data was established in Bonforte, Grillo, and Vázquez [J. Evol. Equ. 8 (2008), pp. 99–128]. However, in the Euclidean space, it is known from Herrero and Pierre [Trans. Amer. Math. Soc. 291 (1985), pp. 145–158] that the Cauchy problem associated with the FDE is well posed for initial data that are merely in L l o c 1 L^1_{\mathrm {loc}} . We establish here that such data still give rise to global solutions on general manifolds. If, moreover, the radial Ricci curvature satisfies a suitable pointwise bound from below (possibly diverging to − ∞ -\infty at spatial infinity), we prove that also uniqueness holds, for the same type of data, in the class of strong solutions. Besides, assuming in addition that the initial datum is in L l o c 2 L^2_{\mathrm {loc}} and nonnegative, a minimal solution is shown to exist, and we establish uniqueness of purely (nonnegative) distributional solutions, a fact that to our knowledge was not known before even in the Euclidean space. The required curvature bound is sharp, since on model manifolds it is equivalent to stochastic completeness, and it was shown in Grillo, Ishige, and Muratori [J. Math. Pures Appl. (9) 139 (2020), pp. 63–82] that uniqueness for the FDE fails even in the class of bounded solutions when stochastic completeness does not hold. A crucial ingredient of the uniqueness result is the proof of nonexistence of nonnegative, nontrivial distributional subsolutions to certain semilinear elliptic equations with power nonlinearities, of independent interest.

We prove that conservation of probability for the free heat semigroup on a Riemannian manifold $M$ (namely stochastic completeness), hence a linear property, is equivalent to uniqueness of positive, bounded solutions to nonlinear evolution equations of fast diffusion type on $M$ of the form $u_t=\Delta \phi(u)$, $\phi$ being an arbitrary concave, increasing positive function, regular outside the origin and with $\phi(0)=0$. Either property is also shown to be equivalent to nonexistence of nontrivial, nonnegative bounded solutions to the elliptic equation $\Delta W=\phi^{-1}(W)$ with $\phi$ as above. As a consequence, explicit criteria for uniqueness or nonuniqueness of bounded solutions to fast diffusion-type equations on manifolds, and on existence or nonexistence of bounded solutions to the mentioned elliptic equations on $M$ are given, these being the first results on such issues., Comment: Final version. To appear in J. Math. Pures Appl

This paper explores the potential role of bioenergy coupled to carbon dioxide (CO2) capture and storage (BECCS) in long-term global scenarios. We first validate past insights regarding the potential use of BECCS in achieving climate goals based on results from 11 integrated assessment models (IAMs) that participated in the 33rd study of the Stanford Energy Modeling Forum (EMF-33). As found in previous studies, our results consistently project large-scale cost-effective BECCS deployment. However, we also find a strong synergistic nexus between CCS and biomass, with bioenergy the preferred fuel for CCS as the climate constraint increases. Specifically, the share of bioenergy that is coupled to CCS technologies increases since CCS effectively enhances the emissions mitigation capacity of bioenergy. For the models that include BECCS technologies across multiple sectors, there is significant deployment in conjunction with liquid fuel or hydrogen production to decarbonize the transportation sector. Using a wide set of scenarios, we find carbon removal to be crucial to achieving goals consistent with 1.5 °C warming. However, we find earlier BECCS deployment but not necessarily greater use in the long-term since ultimately deployment is limited by economic competition with other carbon-free technologies, especially in the electricity sector, by land-use competition (especially with food) affecting biomass feedstock availability and price, and by carbon storage limitations. The extent of BECCS deployment varies based on model assumptions, with BECCS deployment competitive in some models below carbon prices of 100 US$/tCO2. Without carbon removal, 2 °C is infeasible in some models, while those that solve find similar levels of bioenergy use but substantially greater mitigation costs. Overall, the paper provides needed transparency regarding BECCS’ role, and results highlight a strong nexus between bioenergy and CCS, and a large reliance on not-yet-commercial BECCS technologies for achieving climate goals.

Hydrogen is a flexible energy carrier that can be produced in various ways and support a variety of applications including industrial processes, energy storage and electricity production, and can serve as an alternative transportation fuel. Hydrogen can be integrated in multiple energy sectors and has the potential to increase overall energy system flexibility, improve energy security, and reduce environmental impact. In this paper, the interactions between fuel cell electric vehicles (FCEVs), hydrogen production facilities, and the electric power grid are explored. The flexibility of hydrogen production systems can create synergistic opportunities to better integrate renewable sources into the electricity system. To quantify this potential, we project the hourly system-wide balancing challenges in California out to 2025 as more renewables are deployed and electricity demand continues to grow. Passenger FCEV adoption and refueling behavior are modeled in detail to spatially and temporally resolve the hydrogen demand. We then quantify the system-wide balancing benefits of controlling hydrogen production from water electrolysis to mitigate renewable intermittency, without compromising the mobility needs of FCEV drivers. Finally, a control algorithm that can achieve different objectives, including peak shaving, valley filling, and ramping mitigation is proposed. Our results show that oversizing electrolyzers can provide considerable benefits to mitigate renewable intermittency, while also supporting the deployment of hydrogen vehicles to help decarbonize the transportation sector.

The U.S. transportation sector is expected to meet numerous goals in differing applications. These goals address security, safety, fuel source, emissions reductions, advanced mobility models, and improvements in quality and accessibility. Solutions to meeting these goals include a variety of alternative-fuel technologies, including batteries, fuel cells, synthetic fuels, and biofuels, as well as modifying how current transportation systems are used and integrating new systems, such as storing renewable energy. Overall, there are many combinations of problems, objectives, and solutions.

We investigate existence and uniqueness of solutions of the Cauchy problem for the porous medium equation on a class of Cartan-Hadamard manifolds. We suppose that the radial Ricci curvature, which is everywhere nonpositive as well as sectional curvatures, can diverge negatively at infinity with an at most quadratic rate: in this sense it is referred to as critical. The main novelty with respect to previous results is that, under such hypotheses, we are able to deal with unbounded initial data and solutions. Moreover, by requiring a matching bound from above on sectional curvatures, we can also prove a blow-up theorem in a suitable weighted space, for initial data that grow sufficiently fast at infinity.

Electrification of transport offers opportunities to increase energy security, reduce carbon emissions, and improve local air quality. Plug-in electric vehicles (PEVs) are creating new connections between the transportation and electric sectors, and PEV charging will create opportunities and challenges in a system of growing complexity. Here, I use highly resolved models of residential power demand and PEV use to assess the impact of uncoordinated in-home PEV charging on residential power demand. While the increase in aggregate demand might be minimal even for high levels of PEV adoption, uncoordinated PEV charging could significantly change the shape of the aggregate residential demand, with impacts for electricity infrastructure, even at low adoption levels. Clustering effects in vehicle adoption at the local level might lead to high PEV concentrations even if overall adoption remains low, significantly increasing peak demand and requiring upgrades to the electricity distribution infrastructure. This effect is exacerbated when adopting higher in-home power charging. Electrification of transport offers many benefits for the energy transition but introduces a number of complexities around the electric system. This study undertakes modelling of residential power demand and electric vehicle use to understand the impact of uncoordinated vehicle charging on the electricity load.

This paper documents the approaches and methods used in the Transportation Energy & Mobility Pathway Options™ (TEMPO) model to evaluate passenger and freight demand for transportation and mobility services, project vehicle ownership and technology adoption decisions, and determine transport mode choices to derive scenarios of future energy use and emissions. TEMPO is an all-inclusive transportation demand model that covers the entire United States, with an implicit spatial resolution and an hourly temporal resolution that allows for generating time-resolved energy use profiles to assess multisectoral integration aspects. Key features of the TEMPO model include the ability to perform endogenous out-of-sample forecasting to extrapolate recent emerging trends and analyze impacts of disruptive technological breakthroughs and behavioral changes. TEMPO employs an innovative representation of passenger mobility demand stemming from household-level decisions that determine vehicle adoption, ownership, and use based on sociodemographics (e.g., income, household composition), technology attributes (e.g., travel cost, time), geography (e.g., urban, suburban, rural) and population-specific multiday mobility and travel requirements. This representation enables a more forward-looking perspective on the use of new mobility options and the adoption of alternative fuel vehicles, as well as a more accurate representation of their energy usage profiles than previous modeling approaches. A comparison with the U.S. Energy Information Administration’s Annual Energy Outlook showcases the ability of TEMPO to accurately replicate widely accepted projections by representing the key elements of the entire transportation sector at the appropriate level of resolution. TEMPO is intended to generate future scenarios of technology adoption, energy use, and emissions in the transportation sector to compare alternatives, inform decision makers, and assess integration with energy infrastructure and supply systems at an appropriate spatiotemporal resolution.