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

zhenyu.huang@pnnl.gov 509-372-6781

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