Improving Reliability and Performance Improving Reliability and Performance of Electric Power Grids by Using High of Electric Power Grids by Using High

Performance ComputingPerformance Computing

Eugene A. Feinberg Department of Applied Mathematics &

StatisticsStony Brook University

High Performance Computation Conference

October 22-24 2008

Overview 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? A system dedicated to the business of electric

power: 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:

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 powerutility, consumption devices are part of the EPS & need to bemodeled in EPS analysis.

Power Generation

Power Generation Takes place in geographically dispersed power

plants Power plants normally house multiple generating

units Generating units can operate based on different:

Energy Sources Energy Conversion processes Units can be at different states (on/off)

Energy Sources Hydrocarbons (oil, coal, natural gas, etc.) Water Nuclear Wind Solar Tides Chemical etc

Energy Converters 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 Transmission

networks are needed to : Connect

generating plants to consumption points

Create large power pools for increased reliability

Power Transmission Equipment

Transformers Step-up transformers Voltage Regulators Phase Shifters Step-down Transformers

Transmission Lines & Cables Circuit Breakers & Disconnects Etc.

Power Distribution Receives electrical energy from the HV/MV

(High Voltage/Medium Voltage) levels at bulk power delivery points

Supplies energy to customers: At standard voltage levels Single phase and/or three-phase

Is made up of the following main equipment: Distribution transformers (DXF) Feeder sections (including underground cables) Switches, fuses, reclosures Automatic load transfers Etc.

Power Distribution

EPS Operation Goals

Power Balance: Generation must remain balanced with demand 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, mustremain within its operational range

Voltage Regulation: Bus voltages must remainwithin their operational limits

Challenges for Power System Operations

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

1978

80% of France

Blackout

1983

Sweden Voltage Collapse

1987

FranceVoltage Collapse

1996

MexicoBlackout

2003 2005

LondonBlackout

Northeast USABlackout

ItalyMalaysia…

….MoscowBlackout

2007

ColumbiaBlackout

Weather Dependence 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

In the last decades, with deregulation and introduction of competition, a new challenge has emerged for power market participants. Price volatility

Major Decision Making Processes for EPS

State Estimation Estimate the steady states condition of EPS

using online measured values Forecasting

Load, price, capacity, equipment states, rating, reliability analysis, etc.

Control and Planning 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? 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. EPS provide several such problems. Monte Carlo simulation is one of the

mathematical methods that allows parallel algorithms.

Simulation 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: Reinforcement Learning (neuro dynamic

programming, approximate dynamic programming)

Cross-Entropy Methods

Problems of EPS using HPC: State Estimation

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:

z –measurement vector x –true state vector h –nonlinear vector functions w –measurement error vector

Problems of EPS using HPC: State Estimation

Challenges 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 Load and Price Forecasting

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 Reliability Analysis

assess the ability of a multi-area power system satisfy the demand

adequately satisfy the customer load requirements

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

Optimization techniques in forecasting Non-linear programming Dynamic programming

Difficulties: Curse of dimension Solutions

Decomposition techniques Utilization of parallel computers

Problems of EPS using HPC:Control and Planning

Optimal Flow 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 Optimal Flow

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 Economic Dispatch

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 Stochastic dynamic programming

Computational requirements are usually high Implementation of parallel computing

overcomes this difficulty

Conclusions

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.