electromagnetic transient simulation of large-scale electrical power networks...

ELECTROMAGNETIC TRANSIENT SIMULATION OF ELECTROMAGNETIC TRANSIENT SIMULATION OF LARGE-SCALE ELECTRICAL POWER NETWORKS

USING GRAPHICS PROCESSING UNITS

Presented By: Jayanta Kumar DebnathEmail: [email protected]

Advisor(s): Dr. Wai-Keung Fung&

Prof. Aniruddha M. Gole

GradCon-2011, ECE Department, University of Manitoba

OUTLINE OF THE PRESENTATION2

Introduction Introduction GPU computing and GPU architecture Electromagnetic Transient Simulation Simulation Results Simulation Results Conclusion and Future works


INTRODUCTION3

Transient is the sudden change in system state. May result in excessive current or voltage variations in the network.

Requires details model of components and Requires details model of components and complexity increases with network size.

Electromagnetic Transient (EMT) simulation is mostly used for analysis of fast transients.y y

Time domain simulation tool.


4

INTRODUCTION

Central Processing Unit (CPU) based simulation Central Processing Unit (CPU) based simulation is time consuming.

S per comp ters PC cl sters are t picall Super computers, PC-clusters are typically used.G hi P i g U it (GPU ) f EMT Graphics Processing Units (GPUs) for EMT simulation.

C t ff ti Cost effective Built in massively parallel architecture. Parallelized portions of the simulation are deployed in Parallelized portions of the simulation are deployed in

the GPUs.


OUTLINE5

Introduction GPU-computing and GPU- architecture GPU computing and GPU architecture Electromagnetic Transient Simulation Simulation Results Conclusion and Future works Conclusion and Future works


GPU-COMPUTING AND GPU- ARCHITECTURE

6

GPUs mostly handles high performance gaming and animation related applications.

Traditional application software is normally sequentialsequential.

Parallel processing techniques are applied on the GPUs.

Programming GPUs using Compute Unified Programming GPUs using Compute Unified Device Architecture (CUDA).


CPU vs GPU7


GPU ARCHITECTURE8


SCHEMATIC OF CUDA PROGRAM EXECUTION9


GPU COMPUTING10

GPU t f th i CPU GPUs acts as a co-processor for the main CPU. Perform computation in a Single Instruction

Multiple Threads (SIMT) mode. Kernel functions are used to perform Kernel functions are used to perform

computations in parallel. Launching of a Kernel function generates a grid Launching of a Kernel function generates a grid

on the GPU, which contains different blocks of threads to perform the computations in threads to perform the computations in parallel.


OUTLINE11

Introduction GPU-computing and GPU- architecture GPU computing and GPU architecture Electromagnetic Transient Simulation Simulation Results Conclusion and Future works Conclusion and Future works


ELECTROMAGNETIC TRANSIENT SIMULATION

12

Power Systems are modeled using resistances (R), capacitances (C), and inductances (L).

Mathematical model of an electrical network consists of ordinary differential equationsconsists of ordinary differential equations.

Numerical integration techniques (such as Trapezoidal rule) have been successfully employed for power systems simulation, p y p y ,Dommel (1969).


EQUIVALENT CIRCUIT FORMULATION13

Q

Inductances and Inductances and Capacitances are replaced by their replaced by their Norton equivalents.

Any electrical network Fig. Schematic equivalent circuit for (a) Inductorand (b) Capacitor following Trapezoidal Rule basedformulation of Dommel (1969) Any electrical network

is possible to solve i g d itt

formulation of Dommel (1969).

)(2

)()(

:

tvLtttILti

InductorFor

using admittance matrix based f l ti

)(2

)()(

2

ttvLtttittILand

L

formulation.

2

)(2)()(

:

C

tvtCttICti

CapacitorFor

)(2)()( ttvtCttittICand


ADMITTANCE MATRIX BASED EQUIVALENT SYSTEM FORMULATION

14

SYSTEM FORMULATION

Inductive and Capacitive branches are replaced using the above equivalents.

Admittance matrix is formed for the whole network Norton equivalent based system network. Norton equivalent based system equation becomes:

IJVY This equation is solved for nodal voltage vector, [V].

HIJVY

This equation is solved for nodal voltage vector, [V]. This equation is solved iteratively with time step, ∆t.


ELECTROMAGNETIC TRANSIENT SIMULATION

15

EMT i l ti i l t i t EMT simulation involves matrix-vector multiplication.

Admittance matrix size depends on the network size.

Drastic increase in CPU-based simulation time with network size increasewith network size increase.

Matrix-vector multiplication is one of the mostly time consuming operation in EMT simulation of time consuming operation in EMT-simulation of large networks.


PARALLELISM IN EMT SIMULATION16

This matrix-vector multiplication operation is hi hl ll lhighly parallel.

Multiplication of one row is completely indepen-p p y pdent of the other rows.

History terms related computations are highly History terms related computations are highly parallel.

Different Source related computations are also Different Source related computations are also parallel

Jobs with parallelism are most suitable to be performed on GPUs.


OUTLINE17

Introduction Background on GPU-computing and GPU- Background on GPU computing and GPU

architectureB kg d El t g ti T i t Background on Electromagnetic Transient Simulation

Simulation Results Conclusion and Future works Conclusion and Future works


18

SIMULATION PLATFORM DETAILSMain Computer (CPU) Details

TYPE Intel core 2 CPU 6420

CPU d 2 13 GHCPU speed 2.13 GHz

Total RAM 4GB

BUS speed 1.066MHzUS speed 066

GPU DETAILS

TYPE NVIDIA GeForce GTX 285

Number of multiprocessors 30

Number of cores 240

Total amo nt of global memor 2GBTotal amount of global memory 2GB

Total amount of constant memory 65 KB

Total amount of shared memory per block 16 KBy p

Total number of registers available per block

16K

W i 32Warp size 32

Maximum number of threads per block 512GradCon-2011, ECE Department, University of Manitoba

SIMULATION RESULTS19

β Speed up factor (βGPU_CPU) for GPU-computing is defined as:

timeprocessingGPU-CPUtimeprocessingonly-CPU

_ CPUGPU

Shared memory based computations are faster.

t ep ocess gG UC U

y p Efficient use of GPU-resources results in

massive performance gainmassive performance gain.



Table : Simulation results of GPU-computing

No of Nodes

Total Time (CPU only

implementation)

GPU Total Time 1(Matrix Vector multiplication

on the GPU)

GPU Total Time 2(Matrix Vector multiplication and History

terms calculations on the GPU)[Seconds] [Seconds] [Seconds]

39 14.57 19.3 33.49

78 44 52 31 63 39 2478 44.52 31.63 39.24

156 156.47 52.79 44.28

195 348.05 57.78 50.62

234 391.43 69.87 54.3

273 474.31 78.54 60.14

312 581.14 89.57 64.26

351 1016.6 100.5 70.7

390 1276 4 112 79 77 55


390 1276.4 112.79 77.55

468 2006.09 139.07 92.77


25Performance of GPU-computing

20

-GP

U

Matrix-Vector Multiplication and History related computations on the GPUMatrix-Vector Multiplication on the GPU

15

on C

PU

to C

PU

-

10

mpu

tatio

n tim

e o

5Rat

io o

f com

0 50 100 150 200 250 300 350 400 450 5000


number of nodes in the network

CONCLUSIONS22

Continuous Increase in interest for GPU-computing in general purpose applications including power system simulations.

Application of GPU computing in large electrical Application of GPU-computing in large electrical network simulation is presented in this paper.

CPU-GPU based hybrid computation showed a speed up factor of 20 for a network with only p p y468 nodes.

ECE Department, University of Manitoba

FUTURE WORKS23

F t W k Future Works: Simulation of standard electrical power

networks with: Perform all the computations on the GPU. p More nodes, Detailed models of transmission lines Detailed models of transmission lines, Detailed models of generators, transformers, and

switching phenomena including power electronic switching phenomena including power electronic equipments will be included.


24

THANK YOU FOR YOUR KIND ATTENTIONTHANK YOU FOR YOUR KIND ATTENTION


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