Emil M. Constantinescu

A Computational Framework for Uncertainty Quantification and Stochastic Optimization in Unit Commitment With Wind Power Generation

We present a computational framework for integrating a state-of-the-art numerical weather prediction (NWP) model in stochastic unit commitment/economic dispatch formulations that account for wind power uncertainty. We first enhance the NWP model with an ensemble-based uncertainty quantification strategy implemented in a distributed-memory parallel computing architecture. We discuss computational issues arising in the implementation of the framework and validate the model using real wind-speed data obtained from a set of meteorological stations. We build a simulated power system to demonstrate the developments.

Multiphysics simulations: Challenges and opportunities

We consider multiphysics applications from algorithmic and architectural perspectives, where “algorithmic” includes both mathematical analysis and computational complexity, and “architectural” includes both software and hardware environments. Many diverse multiphysics applications can be reduced, en route to their computational simulation, to a common algebraic coupling paradigm. Mathematical analysis of multiphysics coupling in this form is not always practical for realistic applications, but model problems representative of applications discussed herein can provide insight. A variety of software frameworks for multiphysics applications have been constructed and refined within disciplinary communities and executed on leading-edge computer systems. We examine several of these, expose some commonalities among them, and attempt to extrapolate best practices to future systems. From our study, we summarize challenges and forecast opportunities.

Predicting air quality: Improvements through advanced methods to integrate models and measurements

Air quality prediction plays an important role in the management of our environment. Computational power and efficiencies have advanced to the point where chemical transport models can predict pollution in an urban air shed with spatial resolution less than a kilometer, and cover the globe with a horizontal resolution of less than 50km. Predicting air quality remains a challenge due to the complexity of the governing processes and the strong coupling across scales. While air quality prediction is closely aligned with weather prediction, there are important differences, including the role of pollution emissions and their associated large uncertainties. Improvements in air quality prediction require a close integration of observations. As more atmospheric chemical observations become available chemical data assimilation is expected to play an essential role in air quality forecasting. In this paper advances in air quality forecasting are discussed with an emphasis on data assimilation. Applications of the four-dimensional variational method (4D-Var) and the ensemble Kalman filter (EnKF) approach are presented and the computation challenges are discussed.

Multirate Timestepping Methods for Hyperbolic Conservation Laws

Abstract This paper constructs multirate time discretizations for hyperbolic conservation laws that allow different timesteps to be used in different parts of the spatial domain. The proposed family of discretizations is second order accurate in time and has conservation and linear and nonlinear stability properties under local CFL conditions. Multirate timestepping avoids the necessity to take small global timesteps (restricted by the largest value of the Courant number on the grid) and therefore results in more efficient algorithms. Numerical results obtained for the advection and Burgers’ equations confirm the theoretical findings.

Implicit-Explicit Formulations of a Three-Dimensional Nonhydrostatic Unified Model of the Atmosphere (NUMA)

We derive an implicit-explicit (IMEX) formalism for the three-dimensional (3D) Euler equations that allow a unified representation of various nonhydrostatic flow regimes, including cloud resolving and mesoscale (flow in a 3D Cartesian domain) as well as global regimes (flow in spherical geometries). This general IMEX formalism admits numerous types of methods including single-stage multistep methods (e.g., Adams methods and backward difference formulas) and multistage single-step methods (e.g., additive Runge--Kutta methods). The significance of this result is that it allows a numerical model to reuse the same machinery for all classes of time-integration methods described in this work. We also derive two classes of IMEX methods, one-dimensional and 3D, and show that they achieve their expected theoretical rates of convergence regardless of the geometry (e.g., 3D box or sphere) and introduce a new second-order IMEX Runge--Kutta method that performs better than the other second-order methods considered. We...

Time Adaptive Conditional Kernel Density Estimation for Wind Power Forecasting

This paper reports the application of a new kernel density estimation model based on the Nadaraya-Watson estimator, for the problem of wind power uncertainty forecasting. The new model is described, including the use of kernels specific to the wind power problem. A novel time-adaptive approach is presented. The quality of the new model is benchmarked against a splines quantile regression model currently in use in the industry. The case studies refer to two distinct wind farms in the United States and show that the new model produces better results, evaluated with suitable quality metrics such as calibration, sharpness, and skill score.

Flexible Operation of Batteries in Power System Scheduling With Renewable Energy

The fast growing expansion of renewable energy increases the complexities in balancing generation and demand in the power system. The energy-shifting and fast-ramping capability of energy storage has led to increasing interests in batteries to facilitate the integration of renewable resources. In this paper, we present a two-step framework to evaluate the potential value of energy storage in power systems with renewable generation. First, we formulate a stochastic unit commitment approach with wind power forecast uncertainty and energy storage. Second, the solution from the stochastic unit commitment is used to derive a flexible schedule for energy storage in economic dispatch where the look-ahead horizon is limited. Analysis is conducted on the IEEE 24-bus system to demonstrate the benefits of battery storage in systems with renewable resources and the effectiveness of the proposed battery operation strategy.

Unit commitment with wind power generation: integrating wind forecast uncertainty and stochastic programming.

We present a computational framework for integrating the state-of-the-art Weather Research and Forecasting (WRF) model in stochastic unit commitment/energy dispatch formulations that account for wind power uncertainty. We first enhance the WRF model with adjoint sensitivity analysis capabilities and a sampling technique implemented in a distributed-memory parallel computing architecture. We use these capabilities through an ensemble approach to model the uncertainty of the forecast errors. The wind power realizations are exploited through a closed-loop stochastic unit commitment/energy dispatch formulation. We discuss computational issues arising in the implementation of the framework. In addition, we validate the framework using real wind speed data obtained from a set of meteorological stations. We also build a simulated power system to demonstrate the developments.

Extrapolated Implicit-Explicit Time Stepping

This paper constructs extrapolated implicit-explicit time stepping methods that allow one to efficiently solve problems with both stiff and nonstiff components. The proposed methods are based on Euler steps and can provide very high order discretizations of ODEs, index-1 DAEs, and PDEs in the method-of-lines framework. Implicit-explicit schemes based on extrapolation are simple to construct, easy to implement, and straightforward to parallelize. This work establishes the existence of perturbed asymptotic expansions of global errors, explains the convergence orders of these methods, and studies their linear stability properties. Numerical results with stiff ODE, DAE, and PDE test problems confirm the theoretical findings and illustrate the potential of these methods to solve multiphysics multiscale problems.

Multirate Explicit Adams Methods for Time Integration of Conservation Laws

This paper constructs multirate linear multistep time discretizations based on Adams-Bashforth methods. These methods are aimed at solving conservation laws and allow different timesteps to be used in different parts of the spatial domain. The proposed family of discretizations is second order accurate in time and has conservation and linear and nonlinear stability properties under local CFL conditions. Multirate timestepping avoids the necessity to take small global timesteps—restricted by the largest value of the Courant number on the grid—and therefore results in more efficient computations. Numerical results obtained for the advection and Burgers’ equations confirm the theoretical findings.