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 & StatisticsStony Brook University
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 power utility, consumption devices are part of the EPS & need to be modeled in EPS analysis.
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.
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, must remain within its operational range • Voltage Regulation: Bus voltages must remain within 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.
80% of France Blackout 1978 Major Blackouts in the Past 30 Years Northeast USA Blackout Sweden Voltage Collapse London Blackout France Voltage Collapse Columbia Blackout Mexico Blackout Italy Malaysia… …. Moscow Blackout 1996 1983 1987 2003 2005 2007
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