Improving Reliability and Performance
of Electric Power Grids by Using High
Performance Computing
High Performance Computation Conference
October 22-24 2008
Eugene A. Feinberg
Department of Applied Mathematics & Statistics
Stony Brook University
Overview
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Importance of electric power systems
(EPS)
Use mathematics and computations in
EPS operations
Solutions via High Performance
Computing (HPC)
Conclusions
Importance of
Electric Power Systems (EPS)
What is EPS?
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A system dedicated to the business of electric power:
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Generation (Production)
Transmission (Transportation)
Distribution (Retailing)
A “Mission Critical System” that provides a vital
service to the society &, as such, should be operated
with the goal of achieving:
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Highest reliability standards
Minimum environmental impacts
Lowest operation costs
US National Power Grid
Data Source: FERC
EPS Functions
Although not normally owned or controlled by the power
utility, consumption devices are part of the EPS & need to be
modeled in EPS analysis.
Power Generation
Power Generation
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Takes place in geographically dispersed power plants
Power plants normally house multiple generating
units
Generating units can operate based on different:
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Energy Sources
Energy Conversion processes
Units can be at different states (on/off)
Energy Sources
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Hydrocarbons (oil, coal, natural gas, etc.)
Water
Nuclear
Wind
Solar
Tides
Chemical
etc
Energy Converters
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Conversion processes in a thermal power plant:
Burners: Chemical energy ⇒ Thermal energy
Boilers: Thermal energy ⇒ Mechanical energy
Wind Turbines: Kinetic energy (KE) ⇒ Mechanical energy
Rotating machines: KE ⇒ Electrical energy
With today’s technology, overall conversion efficiency
of a thermal power plant can approach 33%
Power Transmission
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Transmission networks
are needed to :
 Connect generating
plants to
consumption points
 Create large power
pools for increased
reliability
Power Transmission Equipment
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Transformers
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Step-up transformers
Voltage Regulators
Phase Shifters
Step-down Transformers
Transmission Lines & Cables
Circuit Breakers & Disconnects
Etc.
Power Distribution
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Receives electrical energy from the HV/MV (High
Voltage/Medium Voltage) levels at bulk power
delivery points
Supplies energy to customers:
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At standard voltage levels
Single phase and/or three-phase
Is made up of the following main equipment:
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Distribution transformers (DXF)
Feeder sections (including underground cables)
Switches, fuses, reclosures
Automatic load transfers
Etc.
Power Distribution
EPS Operation Goals
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Power Balance: Generation must remain
balanced with demand
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Generation Capacity (t)≥Total Generation (t)
Total Generation (t) = Total Demand (t)
System Security: Equipment power flows
must not exceed equipment ratings, under
normal or a single outage condition:
|Pj (t)| ≤ Pj (t)
max
Power Quality Considerations
Frequency Regulation: System frequency, must
remain within its operational range
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Voltage Regulation: Bus voltages must remain
within their operational limits
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Challenges for Power System
Operations
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Goal: meet the continually changing
load demand for both active and
reactive power while the desired system
frequency and voltage profile are
maintained. This should be done in the
cost-efficient way
From time to time blackouts happen.
Major Blackouts in the Past 30
Years
Northeast USA
Blackout
80% of
France
Blackout
1978
Sweden
Voltage
Collapse
1983
France
Voltage
Collapse
1987
Mexico
Blackout
1996
London
Blackout
Columbia
Italy
Blackout
Malaysia…
….
Moscow
Blackout
2003
2005
2007
Weather Dependence
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Electric loads fluctuate and depend on
several factors including time and
weather.
Peak load usually happen in the
afternoon during heat waves.
Equipment also depend on weather
characteristics such as ambient
temperature and winds
Complex Electricity Markets
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In the last decades, with deregulation
and introduction of competition, a new
challenge has emerged for power
market participants.
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Price volatility
Major Decision Making Processes
for EPS
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State Estimation
 Estimate the steady states condition of EPS using
online measured values
Forecasting
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Load, price, capacity, equipment states, rating, reliability
analysis, etc.
Control and Planning
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Short term, medium term, long term
Economic dispatch, optimal flow problem, energy trading,
maintenance, area planning, capital expenditure, etc.
Solutions for some of these problems are difficult and require
intensive computations
Solutions via
High Performance Computing
(HPC)
Why we need HPC?
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Challenges lead to several mathematical
problems whose exact solutions are
intractable
HPC provides tools for the solutions of
reasonable approximations in required time
HPC is important for difficult scientific and
engineering problems that can be solved by
parallel computing.
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EPS provide several such problems.
Monte Carlo simulation is one of the mathematical
methods that allows parallel algorithms.
Simulation
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Instead of simulating N scenarios on a
sequential machine, it is possible to simulate
N/M scenarios on each of M parallel
processors.
In addition to direct simulation, Monte Carlo
simulation methods are used in contemporary
optimization techniques:
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Reinforcement Learning (neuro dynamic
programming, approximate dynamic programming)
Cross-Entropy Methods
Problems of EPS using HPC:
State Estimation
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Provide reliable estimates of the quantities required
for monitoring and control of the EPS
a set of measurements obtained is centrally
processed by a state estimator
State Estimation model:
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z –measurement vector
x –true state vector
h –nonlinear vector functions
w –measurement error vector
Problems of EPS using HPC:
State Estimation
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Challenges
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Higher frequency -- shorten the time interval
between consecutive state estimations to allow a
closer monitoring of the system evolution
particularly in emergency situations in which the
system state changes rapidly
Larger size -- enlarge the supervised network by
extending state estimation to low voltage sub
networks
Problems of EPS using HPC:
Forecasting
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Load and Price Forecasting
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Solutions use optimization methods
Depend on the weather
Require HPC in real time if there are unforeseen
events (failures, sudden changes in the weather)
Require HPC for simulation-based optimization
Require weather forecasts. HPC is used for
weather forecasting. Challenging problem: wind
forecasting.
Problems of EPS using HPC:
Forecasting
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Reliability Analysis
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assess the ability of a multi-area power system
satisfy the demand
adequately satisfy the customer load requirements
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Perform a chronological hourly simulation of the system
based on the Monte Carlo simulation
Compare the hourly load demand in each area to the
total available generation in the area
Areas with excess capacity will provide emergency
assistance to those areas that are deficient, subject to
the transfer limits between the areas.
Problems of EPS using HPC:
Forecasting
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Optimization techniques in forecasting
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Non-linear programming
Dynamic programming
Difficulties: Curse of dimension
Solutions
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Decomposition techniques
Utilization of parallel computers
Problems of EPS using HPC:
Control and Planning
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Optimal Flow
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Goal: To obtain complete
voltage angle and magnitude
information for each bus in a
power system for specified
load and generator real
power and voltage conditions
Can be expressed as a
classical mathematical
program
x and u represents
respectively the states and
controls variables
Problems of EPS using HPC:
Control and Planning
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Optimal Flow
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Most of the constraints represents the operational
constraints or the automatic response of the
power system
Most of the objective functions represents
economical or security aims
These functions are nonlinear
Typical problems involve around 2000 equality
constraints and 4000 inequality constraints.
Efficient way of dealing with high dimensionality of
the problem is by Decomposition Techniques on
HPC
Problems of EPS using HPC:
Control and Planning
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Economic Dispatch
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To find a set of active power delivered by the
committed generators to satisfy the required
demand at any time subject to the unit technical
limits and at the lowest production cost.
Important to solve this problem as quickly and
accurately as possible.
Techniques
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Stochastic dynamic programming
Computational requirements are usually high
Implementation of parallel computing overcomes
this difficulty
Conclusions
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EPS are vitally important for our society
EPS are complex systems and their
efficient control, management, and
development depend on solutions of
many difficult mathematical problems
HPC is a natural tool to solve of these
problems
Thank you.