Stochastic optimization of energy systems
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Stochastic optimization of energy systems. Cosmin Petra [email protected] 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)

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Stochastic optimization of energy systems

Stochastic optimization of energy systems

Cosmin Petra

[email protected]

Argonne National Laboratory

A project overview

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.

  • [email protected] team: MihaiAnitescu, Cosmin Petra, Miles Lubin (algorithms and implementation), Victor Zavala and Emil Constantinescu (modeling and data)

  • Funding: DOE Applied Math (2009-2012), DOE ASCR MMICC center (2012-2017)

  • DOE INCITE Award (2012-2013) - 10 mil core hours for 2012.

B science lesson

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 5-10 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

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

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

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

F) Visualization and Analysis

  • Output is small, no special analysis required

  • less

G performance

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

H) Tools

  • How do you debug your code?

    • cerr, cout

I status and scalability

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 scalability1

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

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

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