Predictive Dynamic Simulation for Large-Scale Power Systems through High-Performance Computing
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Henry Huang, Shuangshuang Jin, and Ruisheng Diao Pacific Northwest National Laboratory November 11, 2012
The 2nd SC12 Interna/onal Workshop on High Performance Compu/ng, Networking and Analy/cs for the Power Grid Salt Lake City, UT, USA, November 11, 2012
Power system is a giant dynamic machine
! Dynamic devices include: ! Generators: hydro, thermal, wind, solar ! Loads: motors ! Controllers: power electronics
! Example – Western US power grid: ~3000 generators, ~6000 loads. ! Electromechanical interactions at millisecond timeframes are of the
primary concern for system-level stability.
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Dynamic simulation is important for assessing power system stability
! Dynamic simulation finds the trajectory of a power system subject to disturbances, and thus determines power system dynamic stability.
! Primary use is off-line planning studies due to slow computation. ! Several times slower than real time for large-scale power systems.
! Objective: faster-than-real-time dynamic simulation to enable predictive capabilities.
3 t 0
x
x0
Unstable
Stable
Disturbance Occurs
real system
current simula/on target simula/on
Power system dynamics is formulated as a set of differential algebraic equations
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~ E’1∠δ
Xd1’ Pe1
Pm1 Network
~ E’2∠δ
Xd2’ Pe2
Pm2
~ E’i∠δ
Xdi’ Pei
Pmi
PL1 +jQL1
PLi +jQLi
PL2+jQL2
DAE Equa+ons Solu+on Method – Simple Euler
xi(1) = xi
(0) + f xi(0), y(0)( )!t
...
0 = g x(1), y(1)( )
dxidt
= f xi, y( )
...
!
"#
$#
0 = g x, y( )
!
"##
$##
Dynamic Devices
Network Coupling
Naturally Parallel
Coupled
Algebraic solution is the primary bottleneck
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Ini/aliza/on
Numerical Integra/on (1)
Numerical Integra/on (2)
Output
Mod
ified
Euler M
etho
d
Algebraic Solu/on (2)
Algebraic Solu/on (1)
Parallel Algorithm Design: convert coupled nonlinear equations to matrix operations
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~ E’1∠δ
Xd1’ Pe1
Pm1 Network
~ E’2∠δ
Xd2’ Pe2
Pm2
~ E’i∠δ
Xdi’ Pei
Pmi
PL1 +jQL1
PLi +jQLi
PL2+jQL2
DAE Equa+ons
dxidt
= f xi, y( )
...
!
"#
$#
0 = g x, y( )
!
"##
$## yj = yj Vbus( )
Parallel Implementation: match computing and math with the problem
! Incremental inverse – Woodbury matrix identity
! Selective computing – only need a subset of Vbus
! Sparse matrix techniques ! Memory management and data storage
! Multiple 1-dimensional arrays vs. large 2-dimensional array ! Dynamic array allocation to reduce memory size ! Matrix transpose for efficient memory access
! Parallel Implementation using OpenMP ! Currently experimenting with MPI ! Does not require special-purpose computers
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bVAUVABUAbAbUBVA 1111111 )()( −−−−−−− +−=+
Number Of Cores
Reduced Admittance Matrix
Computing (Second)
Time-Stepping Simulation (Second)
Total (Second)
1 13.26 218.87 232.14 2 8.99 111.97 120.95 4 6.46 57.49 63.96 8 5.07 29.58 34.65
16 4.58 10.64 15.22 32 4.14 6.41 10.55 64 4.16 4.88 9.04
Faster-than-real-time performance is achieved, enabling predictive capabilities
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! Achieved 26x speed-up for a WECC-size* system (16,000-bus) using 64 threads compared to the sequential version using 1 thread.
! Only took 9 seconds to run the 30 seconds WECC-size* simulation with 64 threads, which is 20 seconds ahead of the real time, and 13x faster than today’s commercial tools (which needs 120 seconds after considering the difference between CPU configurations).
0
5
10
15
20
25
30
35
40
45
50
1 2 3 4 5 6 7
Speedu
p
Number of threads
Reduced AdmiXance Matrix Compu/ng
Time-‐Stepping simula/on
Total
*WECC: Western Electricity Coordina/ng Council
Benefits of predictive dynamic simulation
! Real-time dynamic contingency analysis ! Predictive control capabilities ! “Controller-in-the-loop” simulation: e.g., PDCI modulation control
design and test ! Real-time generation reduction ! Online security assessment and decision making ! Real-time path rating for congestion management
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Real-‐Time Measurements
State Es/ma/on
Dynamic Stability Simula/on
Voltage Stability Simula/on
Real-‐Time Path Ra/ng
Dynamic Stability Ra/ng
Voltage Stability Ra/ng
Thermal Ra/ng
min
Transmission congestion – an ever increasing challenge
! Incur significant economic cost ! 2004: $1 billion cost at California ISO due to congestion and
reliability must-run requirements [1] ! 2008: >$1.5 billion congestion cost at New York ISO [2]
! Prevent wind integration ! Wind generation curtailment due to transmission congestion
! Congestion will become worse and more complicated ! Uncertainty, stochastic power flow patterns due to changing
generation and load patterns, increased renewable generation, distributed generation, demand response and the increasing complexity of energy and ancillary service markets and Balancing Authority (BA) coordination.
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[1] California Energy Commission, “Strategic Transmission Investment Plan”, November 2005 [2] NYISO, Conges/on Analysis Summary for 2008.
Building more transmission lines faces significant constraints
! Transmission build-out lags behind load growth ! 1988-98: load grew by 30%, transmission grew by only 15% [3] ! Resulting in a transmission grid that must operate closer to the maximum
limit, and this is expected to compound as demand for electricity is expected to double by 2050.
! Transmission expansion is constrained by: ! Financial and cost-recovery issues ! Right-of-way ! Environmental considerations
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[3] U.S. Department of Energy, “The Smart Grid: An Introduc/on.”
Possibility of utilizing more of what we already have
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Thermal rating 10,500 MW
Stability Rating (Transient Stability and
Voltage Stability)
4,800 MW
Example - California Oregon Intertie (COI) [4]
Path Ra/ngs
[4] Western interconnection 2006 congestion management study
U75 – % of time flow exceeds 75% of OTC (3,600 MW for COI)
U90 - % of time flow exceeds 90% of OTC (4,320 MW for COI)
U(Limit) - % of time flow reaches 100% of OTC (4,800 MW for COI)
U75, U90 and U(Limit)
% o
f Tim
e
% of OTC 75% 90% 100%
Real-time path rating
! Current Path Rating Practice and Limitations ! Offline studies – months or a year ahead of the operating season ! Worst-case scenario ! Ratings are static for the operating season è The result: conservative (most of the time) path rating, leading to artificial transmission congestion
! Real-Time Path Rating ! On-line studies ! Current operating scenarios ! Ratings are dynamic based on real-time operating conditions è The result: realistic path rating, leading to maximum use of transmission assets and relieving transmission congestion
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Real-time path rating – case studies
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5 10 15 200
500
1000
1500
2000
2500
Time, hour
Tran
sfer
lim
it of
a c
ritic
al p
ath,
MW Real-time Path Rating
Offline path rating, current practice
25.74% more energy transferusing real-time path rating
! IEEE 39-bus power system ! 26% more capacity without building new transmission lines
Benefits of real-time path rating
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! Increase transfer capability of existing power network and enable additional energy transactions ! $15M annual revenue for a 1000-MW rating increase for one
transmission path, even if only 25% of the increased margin can be used for just 25% of the year
! Reduce total generation production cost ! $28M annual production cost saving for only one path
! Avoid unnecessary flow curtailment for emergency support, e.g. wind uncertainties
! Enable dynamic transfer ! Enhance system situational awareness ! Defer building new transmission lines
Summary
! Predictive faster-than-real-time dynamic simulation is achieved via high performance computing. ! Key is to match computing and math with the problem.
! Fast dynamic simulation enables real-time path rating and improves asset utilization. ! Improved asset utilization brings financial benefits in production
cost saving and transaction revenue increase. ! Improved asset utilization also facilitates integration of renewables
(and other new technologies) by minimizing curtailment.
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Questions?
Zhenyu (Henry) Huang Pacific Northwest National Laboratory
[email protected] 509-372-6781
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