Carnegie Mellon Optimized Parallel Distribution Load Flow Solver on Commodity Multi-core CPU Tao Cui (Presenter) Franz Franchetti Dept. of ECE. Carnegie Mellon University Pittsburgh PA This work is supported by NSF &

Carnegie Mellon Smart Grids 2 Image by Dr. M.Sanchez

Carnegie Mellon Smart Grids New players in the grid Challenges  Undispatchable, large variances, great impact on grid  Large population exhibits stochastic properties 3 Images from wikipedia Source: LBNL-3884eSource: ORNL/TM2004/291 Source: Pantos 2011

Carnegie Mellon 4 Conventional Distribution System  Passively receiving power  Few realtime monitoring or controls Challenges in Distribution System  Solar, wind, stochastic  Large variance and impact Smart Distribution System  New Sensors: Smart Meters  High Performance Deskside Supercomputer A Computational Tool for Probabilistic Grid Monitoring Motivation Image from: Wikipedia ~Tflop/s $1000 1kW power Image from: Dell

Carnegie Mellon Outline Motivation Distribution System Load Flow Analysis Code Optimization Real Time Implementation Conclusion 5

Carnegie Mellon 6 Core: Distribution Load Flow Distribution System:  Radial, high R/X ratio, varying Z, unbalanced  NOT suitable for transmission load flow  Forward / Backward Sweep (FBS)  Implicit Z-matrix, detail model, convergence Generalized Component Model [Kersting2006]  One Terminal Node Model: Constant PQ:  Two Terminal Link Model: Source: IEEE PES Distribution System Analysis Subcommittee IEEE 37 NodeTest Feeder: Based on an actual feeder in California Backward: Forward:

Carnegie Mellon 7 Core: Distribution Load Flow Forward / Backward Sweep [Kersting2006]  Branch current based  Input: substation voltage, load; output: all node voltages  Steps:  1: Initial current = 0, Initial voltage V = V 0 ;  2: Compute node current I n using Node model;  3: Backward: Compute branch current I b using Link model & KCL;  4: Forward: Update V k+1 = V k based on I b over Link model;  5: Check convergence (|dS|<Error Limit) stop or go to step 2. Forward Backward IEEE 4 Node Test Feeder Example

Carnegie Mellon 8 Core: Distribution Load Flow 3-Phase Voltage on IEEE 37 Nodes Test Feeder Phase APhase B Phase C ANSI C84.1: Nominal: 115, Range A:110~126V Range B:107~127V Nominal

Carnegie Mellon 9 Our Approach Random Number Generator  Basic Uniform RNG + Transformation for different PDFs  Parallel strategy for multi-thread implementation Optimized Parallel Distribution Load Flow Solver  Code optimizations  Highly parallel implementation for Monte Carlo applications Density Estimation & Visualization  Kernel density estimation Random Variable Sampling Parallel High Performance Power Flow Solver

Carnegie Mellon Outline Motivation Distribution System Load Flow Analysis Code Optimization Real Time Implementation Conclusion 10

Carnegie Mellon 11 Optimization: Data Structures Data Structure Optimization  Baseline: C++ object oriented, a tree object  Translate to array access, exploit spatial/temporal locality  Other techniques: unroll innermost loops, scalar replacement, pre- compute as much as possible (C++) (C Array) GridLab-D: the Smart Grid Simulator opensource since 2009

Carnegie Mellon Optimization: Pattern Based Syntehsis 12 Algorithm-level Optimization  Pattern based matrix-vector multiplication For A,B,c,d matrices:  Multi-grounded Cable: diagonal matrix  Ignore shunt & coupling: c = 0, d = I, A = I Reduce unnecessary operations Reduce unnecessary storage for better memory access Similar to [Belgin2009] case 1:case 2:case N: … code 1code 2code N (C Pattern) switch (mat_type){ case real_diag_equal_mat: output[0] = *constant * input[0];... output[5] = *constant * input[5]; break; case imag_diag_equal_mat: output[0] = -*constant * input[3]; output[1] = -*constant * input[4]; output[2] = -*constant * input[5]; output[3] = *constant * input[0]; output[4] = *constant * input[1]; output[5] = *constant * input[2]; break;... }

Carnegie Mellon 13 Data Parallelism (SIMD) SIMD parallelization  SIMD: Single Instruction Multiple Data SSE: Streaming SIMD Extensions  128bit, 4 floats in one register  eg. 4 “fadd” at cost of 1 “addps” AVX: Advanced Vector eXtensions (256bit, 8 floats), Larrabee (512bit, 16 floats)  Vectorized solver on SIMD level for MCS:  Assumptions & Limitations: converge at same step vector register xmm1 vector operation addps xmm0, xmm1 xmm0 4-way SSE example (SIMD)

Carnegie Mellon Variant Synthesis with SPIRAL 14 Symbolic process [Puschel2005] :  pattern based matrix vector product code case 1:case 2:case N: … SPL Compiler

Carnegie Mellon Multithreading, Run across All CPUs  Vectorized load flow solver in each thread  Each thread pinned to a physical core exclusively  Fully utilize computation power of Multi-core CPUs  Double buffer (automatic load balancing for MCS application) 15 (Multi-Core) Multithreading

Carnegie Mellon 16 Performance Results: Across Sizes Performance of Optimized Code, Mass Amount Load Flow Pseudo flop/s: >60 % peak Flop/s: 50% Peak

Carnegie Mellon Details: Performance Gains 17 >20x >50x

Carnegie Mellon Performance Results: Across Machines 18 Problem Size (IEEE Test Feeders) Approx. flops Approx. Time / Core2 Extreme Approx. Time / Core i7 Baseline. C++ ICC –o3 (~300x faster then pure Matlab scripts) Comments IEEE37: one iteration12 K~ 0.3 us IEEE37: one load flow (5 Iter)60 K~ 1.5 us 0.01 kVA error IEEE37: 1 million load flow60 G~ < 2 s~ < 1 s~ 60 s (>5 hrs Matlab)SCADA Interval: 4 seconds IEEE123: 1 million load flow200 G~ < 10 s~ < 3.5 s~ 200 s (>15 hrs Matlab)

Carnegie Mellon 19 Accuracy Convergence of Monte Carlo  Very crude. MCG59+ICDF, 50 trials with “time(NULL)” seeds Out: Voltage on Node 738 In: Active Power P~ u=0,std=100kw on Phase A of Node 738,711,741

Carnegie Mellon Outline Motivation Distribution System Load Flow Analysis Code Optimization Real Time Implementation Conclusion 20

Carnegie Mellon 21 System Implementation Distribution System Probabilistic Monitoring System (DSPMS)  System Structure:  MCS solver running on Multi-core Desktop Server (Code optimization)  Results published via ECE Web Server (TCP/IP socket)  Web based dynamic User Interface by client side scripts (JavaScript)  Smart meters in campus building (MODBUS/TCP)

Carnegie Mellon 22 System Implementation Distribution System Probabilistic Monitoring System (DSPMS)  Web Server and User Interface  Link:

Carnegie Mellon 23 Conclusion Smart Distribution Network: Impact of renewable and stochastic Commodity HPC & code optimization: Millions of cases /sec on $1K class machine Distribution System Probabilistic Monitor: A prove of concept real time application source: LBNL-3884e

Carnegie Mellon References [LBNL-3884E]. Mills, A. Implications of Wide-Area Geographic Diversity for Short-Term Variability of Solar Power, LBNL-3884E. Lawrence Berkeley National Laboratory, Berkeley, [ORNL/TM2004/291]. B. Kirby, "Frequency Regulation Basics and Trends," ORNL/TM 2004/291, Oak Ridge National Laboratory, December [Pantos2011]. Miloš Pantoš Stochastic optimal charging of electric-drive vehicles with renewable energy Energy, Volume 36, Issue 11, November 2011 [Ghosh97]. A.K. Ghosh, D. L. Lubkeman, M. J. Downey, R. H. Jones “Distribution Circuit State Estimation Using a Probabilistic Approach,” IEEE Transactions on Power Systems, vol. 12, no. 1, pp , 1997 [Belgin2009]. M. Belgin, G. Back, and C. J. Ribbens, “Pattern-based sparse matrix representation for memory-efficient smvm kernels,” in Proceedings of the 23rd international conference on Supercomputing, ser. ICS ’09. New York, NY, USA: ACM, 2009, pp. 100–109. [Puschel2005]. M. Puschel, J. M. F. Moura, J. Johnson, D. Padua, M. Veloso, B. Singer, J. Xiong, F. Franchetti, A. Gacic, Y. Voronenko, K. Chen, R. W. Johnson, and N. Rizzolo, “SPIRAL: Code generation for DSP transforms,” Proceedings of the IEEE, special issue on “Program Generation, Optimization, and Adaptation”, vol. 93, no. 2, pp. 232– 275, [Kersting2006]. W. Kersting, Distribution system modeling and analysis. CRC,

Carnegie Mellon The End Thank You! Q&A 25