Search

An increasing focus on the electricity use and carbon emissions associated with computing has lead to pledges by major cloud computing companies to lower their carbon footprint. Data centers have a unique ability to shift computing load between different geographical locations, giving rise to geographic load flexibility that can be employed to reduce carbon emissions. In this paper, we present a model where data centers shift load independently of the ISOs. We first consider the impact of load shifting guided by locational marginal carbon emissions, denoted by $\lambda_{\text{CO}_2}$, a sensitivity metric that measures the impact of incremental load shifts. Relative to previous models for data center load shifting, the presented model improves accuracy and include more realistic assumptions regarding the operation of both data centers and the electricity market. Further, we introduce a new benchmark model in which data centers have access to the full information about the power system and can identify optimal shifts for the current time period. We demonstrate the efficacy of our model on the IEEE RTS GMLC system using 5 minute load and generation data for an entire year. Our results show that the proposed accuracy improvements for the shifting model based on $\lambda_{\text{CO}_2}$ are highly effective, leading to results that outperform the benchmark model., Comment: 8 pages

Recent computing needs have lead technology companies to develop large scale, highly optimized data centers. These data centers represent large loads on electric power networks which have the unique flexibility to shift load both geographically and temporally. This paper focuses on how data centers can use their geographic load flexibility to reduce carbon emissions through clever interactions with electricity markets. Because electricity market clearing accounts for congestion and power flow physics in the electric grid, the carbon emissions associated with electricity use varies between (potentially geographically close) locations. Using our knowledge about this process, we propose a new and improved metric to guide geographic load shifting, which we refer to as the locational marginal carbon emission $\lambda_{\text{CO}_2}$. We compare this and three other shifting metrics on their ability to reduce carbon emissions and generation costs throughout the course of a year. Our analysis demonstrates that $\lambda_{\text{CO}_2}$ is more effective in reducing carbon emissions than more commonly proposed metrics that do not account for the specifics of the power grid., Comment: 8 pages

We propose solving the power flow equations using monodromy. We prove the variety under consideration decomposes into trivial and nontrivial subvarieties and that the nontrivial subvariety is irreducible. We also show various symmetries in the solutions. We finish by giving numerical results comparing monodromy against polyhedral and total degree homotopy methods and giving an example of a network where we can find all solutions to the power flow equation using monodromy where other homotopy techniques fail. This work gives hope that finding all solutions to the power flow equations for networks of realistic size is possible., Comment: 5 pages

Increasing demand for computing has lead to the development of large-scale, highly optimized data centers, which represent large loads in the electric power network. Many major computing and internet companies operate multiple data centers spread geographically across the world. Thus, these companies have a unique ability to shift computing load, and thus electric load, geographically. This paper provides a "bottom-up" load shifting model which uses data centers' geographic load flexibility to lower CO$_2$ emissions. This model utilizes information about the locational marginal CO$_2$ footprint of the electricity at individual nodes, but does not require direct collaboration with the system operator. We demonstrate how to calculate marginal carbon emissions, and assess the efficacy of our approach compared to a setting where the data centers bid their flexibility into a centralized market. We find that data center load shifting can achieve substantial reductions in CO$_2$ emissions even with modest load shifting., Comment: 9 pages

In this paper we study the distributions of the number of real solutions to the power flow equations over varying electrical parameters. We introduce a new monodromy and parameter homotopy continuation method for quickly finding all solutions to the power flow equations. We apply this method to find distributions of the number of real solutions to the power flow equations and compare these distributions to those of random polynomials. It is observed that while the power flow equations tend to admit many fewer real-valued solutions than a bound on the total number of complex solutions, for low levels of load they tend to admit many more than a corresponding random polynomial. We show that for cycle graphs the number of real solutions can achieve the maximum bound for specific parameter values and for complete graphs with four or more vertices there are susceptance values that give infinitely many real solutions., Comment: 13 pages

Polyvinylidene difluoride (PVDF) is a ferroelectric polymer characterized by negative strain along the direction of the applied electric field. However, the electromechanical response mechanism of PVDF remains unclear due to the complexity of the hierarchical structure across the length scales. As described in this letter, we employ the Finsler geometry model as a new solution to the aforementioned problem and demonstrate that the deformations observed through Monte Carlo simulations on 3D tetrahedral lattices are nearly identical to those of real PVDF. Specifically, the simulated mechanical deformation and polarization are similar to those observed experimentally., Comment: 13 pages, 5 figures

The Regional Transmission Operators each have unique methods to procure frequency regulation reserves used to track real power fluctuations on the grid. Some market clearing practices result in high regulation prices with large spread compared to other markets. We present the frequency regulation market clearing formulations--as derived from operator tariffs--of the ISO New England, PJM Interconnection, and Midcontinent ISO. We offer test case examples to explain the historic market pricing behavior seen within each system operator and conclude this behavior is due to the inclusion of estimated lost opportunity costs in market clearing., Comment: 5 pages, 1 figure; This work accompanies the Review of Frequency Regulation Markets published by the authors in The Electricity Journal in December 2019, found here https://doi.org/10.1016/j.tej.2019.106668

In this paper we calculate the incremental system production cost associated with a measure of locational power injection uncertainty that can be interpreted as a locational price for tracking power fluctuations. This Locational Price of Variability (LPV) can be used to allocate charges for regulation reserves by location, and hence, can also be used to value distributed energy storage employed to mitigate such fluctuations. We consider policy changes that could enable the implementation of the LPV., Comment: 6 pages. Presented at 10th IREP Bulk Power Systems Dynamics and Control Symposium, September 2017, Espinho Portugal

We discuss preliminary results for the vector form factors $f_+^{\{\pi,K\}}$ at zero-momentum transfer for the decays $D\to\pi\ell\nu$ and $D\to K \ell\nu$ using MILC's $N_f = 2+1+1$ HISQ ensembles at four lattice spacings, $a \approx 0.042, 0.06, 0.09$, and 0.12 fm, and various HISQ quark masses down to the (degenerate) physical light quark mass. We use the kinematic constraint $f_+(q^2)= f_0(q^2)$ at $q^2 = 0$ to determine the vector form factor from our study of the scalar current, which yields $f_0(0)$. Results are extrapolated to the continuum physical point in the framework of hard pion/kaon SU(3) heavy-meson-staggered $\chi$PT and Symanzik effective theory. Our calculation improves upon the precision achieved in existing lattice-QCD calculations of the vector form factors at $q^2=0$. We show the values of the CKM matrix elements $|V_{cs}|$ and $|V_{cd}|$ that we would obtain using our preliminary results for the form factors together with recent experimental results, and discuss the implications of these values for the second row CKM unitarity., Comment: 10 pages, 3 figures, proceeding of The 36th Annual International Symposium on Lattice Field Theory

We use lattice QCD to calculate the form factors $f_+(q^2)$ and $f_0(q^2)$ for the semileptonic decay $B_s\to K\ell\nu$. Our calculation uses six MILC asqtad 2+1 flavor gauge-field ensembles with three lattice spacings. At the smallest and largest lattice spacing the light-quark sea mass is set to 1/10 the strange-quark mass. At the intermediate lattice spacing, we use four values for the light-quark sea mass ranging from 1/5 to 1/20 of the strange-quark mass. We use the asqtad improved staggered action for the light valence quarks, and the clover action with the Fermilab interpolation for the heavy valence bottom quark. We use SU(2) hard-kaon heavy-meson rooted staggered chiral perturbation theory to take the chiral-continuum limit. A functional $z$ expansion is used to extend the form factors to the full kinematic range. We present predictions for the differential decay rate for both $B_s\to K\mu\nu$ and $B_s\to K\tau\nu$. We also present results for the forward-backward asymmetry, the lepton polarization asymmetry, ratios of the scalar and vector form factors for the decays $B_s\to K\ell\nu$ and $B_s\to D_s \ell\nu$. Our results, together with future experimental measurements, can be used to determine the magnitude of the Cabibbo-Kobayashi-Maskawa matrix element $|V_{ub}|$., Comment: 57 pages, 22 figures, 13 tables

We describe a recent lattice-QCD calculation of the leptonic decay constants of heavy-light pseudoscalar mesons containing charm and bottom quarks and of the masses of the up, down, strange, charm, and bottom quarks. Results for these quantities are of the highest precision to date. Calculations use 24 isospin-symmetric ensembles of gauge-field configurations with six different lattice spacings as small as approximately 0.03 fm and several values of the light quark masses down to physical values of the average up- and down-sea-quark masses. We use the highly-improved staggered quark (HISQ) formulation for valence and sea quarks, including the bottom quark. The analysis employs heavy-quark effective theory (HQET). A novel HQET method is used in the determination of the quark masses., Comment: Talk presented CIPANP2018. 11 pages, LaTeX, 8 pdf figures

Using HISQ $N_f=2+1+1$ MILC ensembles with five different values of the lattice spacing, including four ensembles with physical quark masses, we have performed the most precise computation to date of the $K\to\pi\ell\nu$ vector form factor at zero momentum transfer, $f_+^{K^0\pi^-}(0)=0.9696(15)_\text{stat}(12)_\text{syst}$. This is the first calculation that includes the dominant finite-volume effects, as calculated in chiral perturbation theory at next-to-leading order. Our result for the form factor provides a direct determination of the Cabibbo-Kobayashi-Maskawa matrix element $|V_{us}|=0.22333(44)_{f_+(0)}(42)_\text{exp}$, with a theory error that is, for the first time, at the same level as the experimental error. The uncertainty of the semileptonic determination is now similar to that from leptonic decays and the ratio $f_{K^+}/f_{\pi^+}$, which uses $|V_{ud}|$ as input. Our value of $|V_{us}|$ is in tension at the 2--$2.6\sigma$ level both with the determinations from leptonic decays and with the unitarity of the CKM matrix. In the test of CKM unitarity in the first row, the current limiting factor is the error in $|V_{ud}|$, although a recent determination of the nucleus-independent radiative corrections to superallowed nuclear $\beta$ decays could reduce the $|V_{ud}|^2$ uncertainty nearly to that of $|V_{us}|^2$. Alternative unitarity tests using only kaon decays, for which improvements in the theory and experimental inputs are likely in the next few years, reveal similar tensions. As part of our analysis, we calculated the correction to $f_+^{K\pi}(0)$ due to nonequilibrated topological charge at leading order in chiral perturbation theory, for both the full-QCD and the partially-quenched cases. We also obtain the combination of low-energy constants in the chiral effective Lagrangian $[C_{12}^r+C_{34}^r-(L_5^r)^2](M_\rho)=(2.92\pm0.31)\cdot10^{-6}$., Comment: 42 pages and 12 figures. Expanded discussion of fit methodology. Finite volume error increased, conclusions unchanged. Version accepted by Phys. Rev. D