Stochastic optimization of energy systems Cosmin Petra Argonne National Laboratory

A) Project Overview Real-time optimization (power dispatch and unit commitment) of power grid in the presence of uncertainty (renewable energy, smart grid, weather) Stochastic formulations reduce both short-term (production) and long-term (reserve) costs, stabilize prices, and increase the reliability. team: Mihai Anitescu, Cosmin Petra, Miles Lubin (algorithms and implementation), Victor Zavala and Emil Constantinescu (modeling and data) Funding: DOE Applied Math ( ), DOE ASCR MMICC center ( ) DOE INCITE Award ( ) - 10 mil core hours for 2012.

B) Science Lesson What does the application do, and how? Stochastic optimization = decisions taken now are influenced by future random conditions (multiple scenarios) Unit Commitment: Determine optimal on/off schedule of thermal (coal, natural gas, nuclear) generators. Day-ahead market prices. (solved hourly) Economic Dispatch: Set real-time market prices. (solved every min.) Scenario-based parallelization The “now” decisions cause coupling PIPS suite (PIPS-IPM, PIPS-S) - parallel implementations that exploits the stochastic structure at the linear algebra level.

C) Parallel Programming Model MPI + OpenMP –Scenario computations accelerated with OpenMP (sparse linear algebra) –Inter-scenarios communication with MPI –Distributed dense linear algebra for the coupling (done with Elemental) C++ Cmake build system Runs on “Fusion” cluster, “Intrepid” BG/P Asynchronous implementation may require new programming model (X+SMP). Yeah, I know … 99.99% X will be MPI

D) Computational Methods Standard interior-point method (PIPS-IPM) and dual simplex (PIPS-S) In-house parallel linear algebra Linear algebra kernels –Sparse: MA57, WSMP, PARDISO. –Dense: LAPACK, Elemental Next: PIPS-L – Lagrangian decomposition for integer problems –“Dual decomposition” method –Based on multi-threaded integer programming kernels (CBC,SCIP) and PIPS-IPM Asynchronous – master-worker framework to deal with load imbalance in scenarios

E) I/O Patterns and Strategy I/O requirements minimal, one file per MPI process at starting. We end up with the optimal cost (a double) and decision variables (vectors of relatively small size) Restarting done by saving the intermediate iterates (vectors) Future plans: Parallel algebraic specification of the problem –Generating the input data IN PARALLEL given an algebraic/mathematical description of the problem (AMPL-like script) –Currently done in serial

F) Visualization and Analysis Output is small, no special analysis required less

G) Performance Bottlenecks to better performance? –SMP sparse kernels (PIPS-IPM) –memory bandwidth (PIPS-S) Bottlenecks to better scaling? –Dense kernels (PIPS-IPM) –load imbalance(PIPS-S, PIPS-L) Collaboration with Olaf Schenk - PARDISO – SMP sparse rhs PIPS-L – asynchronous optimization algorithms

H) Tools How do you debug your code? –cerr, cout

I) Status and Scalability PIPS-IPM scaling Efficiency likely to decrease with faster SMP scenario computations Factors that adversely affect scalability –Serial bottlenecks: dense linear algebra for the “now” decisions –Using Elemental improves scaling for some problems

I) Status and Scalability PIPS-S scaling efficiency is –31% on Fusion from 1 to 256 cores –35% on Intrepid from 2048 to 8192 cores Factors that adversely affect scalability –Serial bottleneck (“now” decisions) –Communication ( 10 collectives per iteration, cost of 1 iteration=O(ms) ) –Load imbalance Intended to be used on up to few hundred of cores PIPS-S is the first HPC implementation of simplex

J) Roadmap 2 years from now? Solve grid optimization models with –Better resolution and larger time horizon –Larger network: continental US grid –More uncertainty –Integer variables