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
GradCon-2011, ECE Department, University of Manitoba
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.
GradCon-2011, ECE Department, University of Manitoba
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.
GradCon-2011, ECE Department, University of Manitoba
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
GradCon-2011, ECE Department, University of Manitoba
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).
GradCon-2011, ECE Department, University of Manitoba
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.
GradCon-2011, ECE Department, University of Manitoba
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
GradCon-2011, ECE Department, University of Manitoba
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).
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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
GradCon-2011, ECE Department, University of Manitoba
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.
GradCon-2011, ECE Department, University of Manitoba
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.
GradCon-2011, ECE Department, University of Manitoba
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.
GradCon-2011, ECE Department, University of Manitoba
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
GradCon-2011, ECE Department, University of Manitoba
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.
GradCon-2011, ECE Department, University of Manitoba
SIMULATION RESULTS20
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
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390 1276.4 112.79 77.55
468 2006.09 139.07 92.77
SIMULATION RESULTS21
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
GradCon-2011, ECE Department, University of Manitoba
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.
ECE Department, University of Manitoba