### ### Fall '14 Distinguished Seminar Series in Computational Science and Engineering

September 18: Professor Andy Philpott,University of Auckland

September 25: Professor Christoph Schwab, ETH Zurich

October 16: Professor Lexing Ying, Stanford University

October 30: Professor Stephen Wright, University of Wisconsin

### Fall '14 Distinguished Seminar Series in Computational Science and Engineering

September 25: Professor Christoph Schwab, ETH Zurich

October 16: Professor Lexing Ying, Stanford University

October 30: Professor Stephen Wright, University of Wisconsin

### *Thursday September 18, 2014 | 4:00 PM | 56-114*

*Thursday September 18, 2014 | 4:00 PM | 56-114*

**Stochastic optimization in electricity systems **

*Andy Philpott *

Methods for optimization under uncertainty are becoming increasingly important in models of electricity systems. Recent interest has been driven by the growth in disruptive technologies (e.g. wind power, solar power and energy storage) which contribute to or ameliorate the volatility of demand that must be met by conventional electricity generation and transmission. In such systems, enough capacity and ramping plant must be on hand to deal with sudden increases in net demand.

On the other hand, in systems dominated by hydro power with uncertain inflows, stochastic optimization models have been studied for many years. Rather than planning capacity, these models construct generation policies to minimize some measure of total thermal fuel costs and risks of future energy shortages. Such models are indispensible in benchmarking the performance of hydro-dominated electricity markets.

We present two classes of model that show how uncertainty is incorporated in these two settings. In the first class, net demand is modeled as a time-inhomogeneous Markov chain, and we seek least-cost investments in thermal generation and transmission capacity that will cover random demand variations. We solve the investment problem using a combination of Benders and Dantzig-Wolfe decomposition. The investment solutions are contrasted with those from conventional screening-curve models.

The second class of model is a stochastic dynamic program that treats reservoir inflows as random. This is solved by DOASA, our implementation of the stochastic dual dynamic programming method of Pereira and Pinto (1991), which has been the subject of some recent interest in the stochastic programming community. We give some examples of the application of DOASA to the New Zealand electricity system by the electricity market regulator.

(Joint work with Golbon Zakeri, Geoff Pritchard, Athena Wu)

### *Thursday September 25, 2014 | 4:00 PM | 56-114*

*Thursday September 25, 2014 | 4:00 PM | 56-114*

**Infinite-Dimensional Numerical Analysis **

*Christoph Schwab *

Spurred by the emerging engineering discipline of Uncertainty Quantification and the `big-data, sparse information' issue, engineering and life-sciences have seen an explosive development in numerics of direct-, inverse- and optimization problems for (deterministic or stochastic) differential equations on high- or even infinite-dimensional state- and parameter-spaces, and for statistical inference on these spaces, conditional on given (possibly large) data.

One objective of this talk is a (biased...) survey of several emerging computational methodologies that allow efficient treatment of high- or infinite-dimensional inputs to partial differential equations in engineering, and to illustrate their performance by computational examples.

We address in particular Multilevel Monte-Carlo (MLMC) and Multilevel Quasi-Monte-Carlo (MLQMC) Methods, adaptive Smolyak and generalized polynomial chaos (gpc), of Galerkin and collocation type, and tensor compression techniques.

A second objective is to indicate elements of a mathematical basis for these methods that has emerged in recent years that has allowed to prove dimension-independent rates of convergence. The reates are shown to be limited only by the order of the method and by certain sparsity measures for the uncertain inputs' KL, gpc or ANOVA decompositions.

Examples include stochastic elliptic and parabolic PDE, their Bayesian inversion, control and optimization, reaction rate models in biological systems engineering, shape inversion in acoustic and electromagnetic scattering, and nonlinear hyperbolic conservation laws.

Despite favourable scaling, massively parallel computation is, as a rule, required for online simulations of realistic problems. Scalability and Fault Tolerance in an exascale compute environment become crucial issues in their practical deployment.

Acknowledgements:

Grant support by Swiss National Science Foundation (SNF), ETH High Performance Computing Grant, and the European Research Council (ERC).

### *Thursday October 16, 2014 | 4:00 PM | 56-114*

*Thursday October 16, 2014 | 4:00 PM | 56-114*

**Inverting high frequency wave equations **

*Lexing Ying *

Wave is ubiquitous as we see it everywhere around us. The numerical solution of high frequency wave propagation has been a longstanding challenge in computational science and engineering. This talk addresses this problem in the time-harmonic regime. We consider a sequence of examples with important applications, and for each we construct an efficient preconditioner (approximate inverse) that allows one to solve the system with a small number of iterations. From these examples emerges a new framework, where sparsity, geometry of wave phenomenon, and highly accurate discretizations are combined together to address this challenging topic.

### *Thursday October 30, 2014 | 12:00 PM | 37-212*

***SPECIAL TIME & LOCATION***

*Thursday October 30, 2014 | 12:00 PM | 37-212*

***SPECIAL TIME & LOCATION***

**Optimimization in Electrical Power Grid Monitoring and Analysis **

*Stephen Wright *

In quasi-steady state, the electrical power grid is well modeled by a system of algebraic equations that relate the supplies and demands at nodes of the grid to (complex) voltages at the nodes and currents on the lines. This "AC model" can be used to formulate nonlinear optimization problems to study various issues related to monitoring and security of the grid. We discuss three such issues here. The first is restoration of feasible operation of the grid following a disruption, with minimal shedding of demand loads. The second issue is vulnerability analysis, in which we seek the attack that causes maximum disruption to the grid, as measured by the amount of load that must be shed to return it to feasibility. The third issue is the use of streaming data from phasor measurement units (PMUs) to detect single-line outages rapidly, and optimal placement of these units to maximize reliability of detection. In each case we discuss the optimization models and algoithms that are used to formulate and solve these problems.