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At least 361 records · Page 20

Downscaling Solar Power Output to 4-Seconds for Use in Integration Studies (Presentation)

High penetration renewable integration studies require solar power data with high spatial and temporal accuracy to quantify the impact of high frequency solar power ramps on the operation of the system. Our previous work concentrated on downscaling solar power from one hour to one minute by simulation. This method used clearness classifications to categorize temporal and spatial variability, and iterative methods to simulate intra-hour clearness variability. We determined that solar power ramp correlations between sites decrease with distance and the duration of the ramp, starting at around 0.6 for 30-minute ramps between sites that are less than 20 km apart. The sub-hour irradiance algorithm we developed has a noise floor that causes the correlations to approach ~0.005. Below one minute, the majority of the correlations of solar power ramps between sites less than 20 km apart are zero, and thus a new method to simulate intra-minute variability is needed. These intra-minute solar power ramps can be simulated using several methods, three of which we evaluate: a cubic spline fit to the one-minute solar power data; projection of the power spectral density toward the higher frequency domain; and average high frequency power spectral density from measured data. Each of these methods either under- or over-estimates the variability of intra-minute solar power ramps. We show that an optimized weighted linear sum of methods, dependent on the classification of temporal variability of the segment of one-minute solar power data, yields time series and ramp distributions similar to measured high-resolution solar irradiance data.

14 SOLAR ENERGY↗

Downscaling Solar Power Output to 4-Seconds for Use in Integration Studies: Preprint

High penetration renewable integration studies require solar power data with high spatial and temporal accuracy to quantify the impact of high frequency solar power ramps on the operation of the system. Our previous work concentrated on downscaling solar power from one hour to one minute by simulation. This method used clearness classifications to categorize temporal and spatial variability, and iterative methods to simulate intra-hour clearness variability. We determined that solar power ramp correlations between sites decrease with distance and the duration of the ramp, starting at around 0.6 for 30-minute ramps between sites that are less than 20 km apart. The sub-hour irradiance algorithm we developed has a noise floor that causes the correlations to approach ~0.005. Below one minute, the majority of the correlations of solar power ramps between sites less than 20 km apart are zero, and thus a new method to simulate intra-minute variability is needed. These intra-minute solar power ramps can be simulated using several methods, three of which we evaluate: a cubic spline fit to the one-minute solar power data; projection of the power spectral density toward the higher frequency domain; and average high frequency power spectral density from measured data. Each of these methods either under- or over-estimates the variability of intra-minute solar power ramps. We show that an optimized weighted linear sum of methods, dependent on the classification of temporal variability of the segment of one-minute solar power data, yields time series and ramp distributions similar to measured high-resolution solar irradiance data.

14 SOLAR ENERGY↗

High precision beam steering using a liquid crystal spatial light modulator

Liquid crystal spatial light modulators (LCSLMs) are novel phase modulation devices. Due to the dielectric properties of the orientation layer, the orientation layer has a voltage division effect on the driving voltage. A more effective analysis of the relationship between the driving voltage and phase modulation properties of LCSLMs is needed, as well as improved beam steering accuracy. In this paper, we establish an electrical model of an LCSLM, and propose a method for quantitatively calculating the liquid crystal (LC) layer voltage. This differential iterative method based on nonlinear least squares is used to analyze the LC molecular directors. Considering the thickness of the orientation layer, we calculate the LC director distribution and the voltage division effect of the LC layer, obtaining a more accurate electro-optic characteristic curve of the LCSLM, and verify the calculations by experiment. Experimentally, the average beam pointing error of the LCSLM was 0.0098° at 532 nm, representing a significant improvement of the beam steering accuracy.

42 ENGINEERING↗

Spectral methods for flows in complex geometries

Three methods for the application of spectral methods to flows in complex geometries are discussed. They are the spectral iteration method, the spectral embedding method, and the spectral element method. Applications are given to the flow over wavy walls, past a large-eddy breakup device (LEBU), and to flow over a step.

Orszag, S. A.↗

Topics in spectral methods

After detailing the construction of spectral approximations to time-dependent mixed initial boundary value problems, a study is conducted of differential equations of the form 'partial derivative of u/partial derivative of t = Lu + f', where for each t, u(t) belongs to a Hilbert space such that u satisfies homogeneous boundary conditions. For the sake of simplicity, it is assumed that L is an unbounded, time-independent linear operator. Attention is given to Fourier methods of both Galerkin and pseudospectral method types, the Galerkin method, the pseudospectral Chebyshev and Legendre methods, the error equation, hyperbolic partial differentiation equations, and time discretization and iterative methods.

Gottlieb, D.↗

A block-corrected subdomain solution procedure for recirculating flow calculations

This paper describes a robust and efficient subdomain solution procedure for two-dimensional recirculating flows. The solution domain is divided into a number of overlapping subdomains, and a direct fully coupled solution is obtained for each subdomain using a sparse matrix form of LU decomposition. An effective parabolic block correction procedure, which calculates global corrections to the tentative solution by a marching technique similar to that used for boundary layer flows, is used to accelerate the convergence of the basic procedure. The use of effective block correction is found to be essential for the success of the subdomain approach on strongly recirculating flows. In a number of laminar two-dimensional flows, the new block-corrected method performed extremely well, rivaling the best direct methods in execution time, while requiring substantially less computer storage. The new method proved to be from two to ten times faster than conventional iterative methods, while requiring only a moderate increase in storage.

Braaten, M. E.↗

Scientific study of data analysis

We present a comparison between two numerical methods for the extrapolation of nonlinear force-free magnetic fields, the Iterative Method (IM) and the Progressive Extension Method (PEM). The advantages and disadvantages of these two methods are summarized and the accuracy and numerical instability are discussed. On the basis of this investigation, we claim that the two methods do resemble each other qualitatively.

Wu, S. T.↗

Accurate Ultrasonic Thickness Measurement for Arbitrary Time-Variant Thermal Profile

Ultrasonic thickness measurement of mechanical structures is one of the most popular and commonly used nondestructive methods for various kinds of process control and corrosion monitoring. With ultrasonic propagation speed being temperature-dependent, the thickness measurement can be performed reliably only when the thermal profile is completely known. Most conventional techniques assume the temperature of the test structure is uniform and at room temperature across its thickness. Such assumptions may lead to large errors in the thickness measurement, especially when there are significant temperature variations across the thickness. State-of-the-art techniques use external temperature measurements or implement iterative methods to compensate for the unknown thermal profiles. However, such techniques produce unsatisfactory results when the heat distribution is complex or varies rapidly with time. In this work, we propose a two-sensors technique, using both compressive and shear excitations, with a non-iterative rapid data processing method for accurate thickness measurement under arbitrary time-variant thermal profile. The independent behavior of shear and compressive waves is used to formulate a real-time thickness estimation technique. The developed technique is experimentally validated on a steel plate with fixed acoustic sensors. Test results show that the error in thickness estimation can be reduced by up to 98% compared to conventional thickness gauging methods.

36 MATERIALS SCIENCE↗

Memory-optimized shift operator alternating direction implicit finite difference time domain method for plasma

Through introducing the alternating direction implicit (ADI) technique and the memory-optimized algorithm to the shift operator (SO) finite difference time domain (FDTD) method, the memory-optimized SO-ADI FDTD for nonmagnetized collisional plasma is proposed and the corresponding formulae of the proposed method for programming are deduced. In order to further the computational efficiency, the iteration method rather than Gauss elimination method is employed to solve the equation set in the derivation of the formulae. Complicated transformations and convolutions are avoided in the proposed method compared with the Z transforms (ZT) ADI FDTD method and the piecewise linear JE recursive convolution (PLJERC) ADI FDTD method. The numerical dispersion of the SO-ADI FDTD method with different plasma frequencies and electron collision frequencies is analyzed and the appropriate ratio of grid size to the minimum wavelength is given. The accuracy of the proposed method is validated by the reflection coefficient test on a nonmagnetized collisional plasma sheet. The testing results show that the proposed method is advantageous for improving computational efficiency and saving computer memory. The reflection coefficient of a perfect electric conductor (PEC) sheet covered by multilayer plasma and the RCS of the objects coated by plasma are calculated by the proposed method and the simulation results are analyzed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

An Expectation-Maximization Method for Calibrating Synchronous Machine Models

The accuracy of a power system dynamic model is essential to its secure and efficient operation. Lower confidence in model accuracy usually leads to conservative operation and lowers asset usage. To improve model accuracy, this paper proposes an expectation-maximization (EM) method to calibrate the synchronous machine model using phasor measurement unit (PMU) data. First, an extended Kalman filter (EKF) is applied to estimate the dynamic states using measurement data. Then, the parameters are calculated based on the estimated states using maximum likelihood estimation (MLE) method. The EM method iterates over the preceding two steps to improve estimation accuracy. The proposed EM method’s performance is evaluated using a single-machine infinite bus system and compared with a method where both state and parameters are estimated using an EKF method. Sensitivity studies of the parameter calibration using EM method are also presented to show the robustness of the proposed method for different levels of measurement noise and initial parameter uncertainty.

EM Algorithms↗

Shift-and-add for astronomical imaging

Diffraction-limited astronomical images have been obtained utilizing a variant of the shift-and-add method. It is shown that the matched filter approach for extending the weighted shift-and-add method reduces specklegrams from extended objects and from an object dominated by photon noise. The method is aberration-insensitive and yields very high dynamic range results. The iterative method for arriving at the matched filter does not automatically converge in the case of photon-noisy specklegrams for objects with more than one maximum.

Ribak, Erez↗

Numerical study of vortical flow over a sideslipping delta wing

The three-dimensional vortical viscous flow past a sideslipping delta wing at a high angle of attack is numerically investigated. A computational method for calculating low-speed viscous flowfields is developed. The time-iterative method uses an implicit upwind-relaxation finite-difference algorithm with a nonsingular eigensystem to solve the preconditioned, three-dimensional, incompressible Navier-Stokes equations in curvilinear coordinates. An algebraic turbulence model is implemented to account for the eddy viscosity. The technique of local time stepping is incorporated to accelerate the rate of convergence to a steady-state solution. Computed results are compared with experimental data.

Hsu, C.-H.↗

Tool employing homotopy-based approaches in finding the controlling unstable equilibrium point in the electric power grid

The analysis tool employs a computer-implemented algorithm that uses homotopy-based approaches to map the solution from the exit point to the controlling unstable equilibrium point (UEP). The computational time is reduced significantly by using an approximate exit point rather than computing an accurate exit point as it is required in finding the controlling UEPs using traditional transient stability direct methods. In addition, this method eliminates the necessity of computing the minimum gradient point (MGP) which is a key element in using Newton methods. These properties provide an advantage to homotopy-based approaches over traditional iterative methods in terms of both speed of computation and reliability of finding solutions.

97 MATHEMATICS AND COMPUTING↗

An accelerated subspace iteration for eigenvector derivatives

An accelerated subspace iteration method for calculating eigenvector derivatives has been developed. Factors affecting the effectiveness and the reliability of the subspace iteration are identified, and effective strategies concerning these factors are presented. The method has been implemented, and the results of a demonstration problem are presented.

Ting, Tienko↗

A new method for the determination of the mixing ratio hydrogen to helium in the giant planets.

By using a numerical iterative method, it is demonstrated that the mixing ratio H2/He on the giant planets can be inferred from spectral measurements of the intensity emitted by these planets in the far infrared range. The method is successfully applied to synthetic spectra of Saturn computed from atmospheric thermal models. The effect of random and systematic measurement errors on the determination of the mixing ratio is also studied.

Gautier, D.↗

Development of a pressure based multigrid solution method for complex fluid flows

In order to reduce the computational difficulty associated with a single grid (SG) solution procedure, the multigrid (MG) technique was identified as a useful means for improving the convergence rate of iterative methods. A full MG full approximation storage (FMG/FAS) algorithm is used to solve the incompressible recirculating flow problems in complex geometries. The algorithm is implemented in conjunction with a pressure correction staggered grid type of technique using the curvilinear coordinates. In order to show the performance of the method, two flow configurations, one a square cavity and the other a channel, are used as test problems. Comparisons are made between the iterations, equivalent work units, and CPU time. Besides showing that the MG method can yield substantial speed-up with wide variations in Reynolds number, grid distributions, and geometry, issues such as the convergence characteristics of different grid levels, the choice of convection schemes, and the effectiveness of the basic iteration smoothers are studied. An adaptive grid scheme is also combined with the MG procedure to explore the effects of grid resolution on the MG convergence rate as well as the numerical accuracy.

Shyy, Wei↗

Transformation of two and three-dimensional regions by elliptic systems

Grid smoothing and orthogonalization procedures were developed and implemented in the construction of two and three dimensional grids. The procedures are based on the variational methods of grid generation. The two-dimensional examples were computed using the MSU IRIS Graphics Workstation. It was demonstrated that the elliptic grid generation equations, with arbitrary forcing functions, can be solved, in their variational formulation, using a gradient method. Since gradient methods have a global convergence property, the divergence problems often encountered when using SOR iterative methods can be avoided. It is not to be concluded, however, that SOR methods should be abandoned, since gradient methods tend to converge very slowly. In fact, slow convergence was the major problem encountered in the three-dimensional grids. Further progress was made on the continuing effort to develop conservative interpolation formulas for overlapping grids.

Mastin, C. Wayne↗