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ECE 530 – Analysis Techniques for Large-Scale Electrical Systems. Lecture 1: Power System Overview. Prof. Hao Zhu Dept. of Electrical and Computer Engineering University of Illinois at Urbana-Champaign Acknowledgement: Prof. Overbye (taught ECE 530 in Fall’13).

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ECE 530 – Analysis Techniques for Large-Scale Electrical Systems

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ECE 530 – Analysis Techniques for Large-Scale Electrical Systems

Lecture 1: Power System Overview

Prof. Hao Zhu

Dept. of Electrical and Computer Engineering

University of Illinois at Urbana-Champaign

Acknowledgement: Prof. Overbye (taught ECE 530 in Fall’13)

Course Overview

  • Course presents the fundamental analytic, simulation and computation techniques for the analysis of large-scale electrical systems.

  • The course stresses the importance of the structural characteristics of the systems, with an aim towards practical analysis.

Course Syllabus

  • Course mechanics and topics

    • Introduction

    • Analysis of nonlinear electrical systems, with detailed coverage of power flow and related issues

    • Data and computational issues associated with large-scale systems including sparsity and visualization

    • Nonlinear parameter estimation in electrical systems

    • Modeling for dynamic analysis including time scale separation and modal analysis

    • Dynamic performance analysis including solution of differential-algebraic systems


  • Sources of Info: Books, journals, conferences, and real-life problems

  • A. J. Wood, B. F. Wollenberg, and G. B. Sheble, “Power Generation, Operation, & Control,” 3rd ed., 2014

  • A. R. Bergen, “Power Systems Analysis,” 1986

  • M. Crow, “Computational Methods for Electric Power Systems,” 2002.

  • Y. Saad, “Iterative Methods for Sparse Linear Systems,” 1996. (Free online)

Other resources

  • IEEEXplore, Google scholar

  • Peers, networking

Simple Power System

  • Every power system has three major components

    • generation: source of power, ideally with a specified voltage and frequency

    • load: consumes power; ideally with a constant resistive value

    • transmission system: transmits power; ideally as a perfect conductor


  • No ideal voltage sources exist

  • Loads are seldom constant

  • Transmission system has resistance, inductance, capacitance and flow limitations

  • Simple system has no redundancy so power system will not work if any component fails

Notation - Power

  • Power: Instantaneous consumption of energy

  • Power Units

    Watts = voltage x current for dc (W)

    kW –1 x 103 Watt

    MW – 1 x 106 Watt

    GW–1 x 109 Watt

    TW–1 x 1012 Watt

  • Installed U.S. generation capacity is about 900 GW ( about 3 kW per person)

  • Maximum load of Champaign/Urbana about 300 MW

Notation - Energy

  • Energy: Integration of power over time; energy is what people really want from a power system

  • Energy Units

    Joule= 1 Watt-second (J)

    kWh– Kilowatthour (3.6 x 106 J)

    MWh– One MW for one hour

    TWh– One million MWh

    Btu– 1055 J; 1 MBtu=0.292 MWh

  • U.S. electric energy consumption is about 4000 TWh kWh (about 12,500 kWh per person, which means on average we each use 1.4 kW of power continuously)

Notation and Voltages

  • The IEEE standard is to write ac and dc in smaller case, but it is often written in upper case as AC and DC.

  • Three-phase is usually written with the dash, also as 3-phase.

  • In the US the standard household voltage is 120/240, +/- 5%. Edison actually started at 110V dc. Other countries have other standards, with the European Union recently standardizing at 230V. Japan’s voltage is just 100V.

Power System Examples

  • Electric utility: can range from quite small, such as an island, to one covering half the continent

    • there are four major interconnected ac power systems in North American, each operating at 60 Hz ac; 50 Hz is used in some other countries.

  • Airplanes and Spaceships: reduction in weight is primary consideration; frequency is 400 Hz.

  • Ships and submarines

  • Automobiles: dc with 12 volts standard

  • Battery operated portable systems

North America Interconnections

Electric Systems in Energy Context

  • Class focuses on electric power systems, but we first need to put the electric system in context of the total energy delivery system

  • Electricity is used primarily as a means for energy transportation

    • Use other sources of energy to create it, and it is usually converted into another form of energy when used

  • About 40% of US energy is transported in electric form

  • Concerns about need to reduce CO2 emissions and fossil fuel depletion are becoming main drivers for change in world energy infrastructure

Sources of Energy - US

About 40% of our energy is consumed in the formof electricity, a percentagethat is gradually increasing.The vast majority of the non-fossil fuel energy is electric!

In 2012 we got about 1.4% of our energy from wind and 0.04% from solar (PV andsolar thermal)

About 84% Fossil Fuels

1 Quad = 293 billion kWh (actual), 1 Quad = 98 billion kWh (used, taking into account efficiency)

Source: EIA Annual Energy Outlook 2013, Electric Power Monthly, July 2013

US Historical and Projected Energy Usage

Projections say we will still be 79% fossil in 2040!

Source: EIA Annual Energy Outlook 2014

Worldwide Energy Usage

Source: EIA International Energy Outlook, 2013

1980-2011 Energy by Region

million toe

Latin America

North America

Former Soviet Union


Middle East



Variation In Electricity Sources

Electric Energy Economics

  • Electric generating technologies involve a tradeoff between fixed costs (costs to build them) and operating costs

    • Nuclear and solar high fixed costs, but low operating costs

    • Natural gas/oil have low fixed costs but high operating costs (dependent upon fuel prices)

    • Coal, wind, hydro are in between

  • Also the units capacity factor is important to determining ultimate cost of electricity

  • Potential carbon “tax” seen as unlikely soon

Ball park Energy Costs




Hydro:varies but usually water constrained

Solar:$120 to 180/MWh

Natural Gas:8 to 10 times fuel cost in $/Mbtu (3-12)

Note, to get price in cents/kWh take price in $/MWh and divide by 10.

Natural Gas Prices 1990’s to 2013

Marginal cost for natural gas fired electricity price

in $/MWh is about 7-10 times gas price

Key Driver for Renewables: Concerns about Global Warming

Value wasabout 280ppm in 1800; in 2013 it is 396 ppm


Worldwide Temperature Graph

Baseline is 1961 to 1990 mean


Looking Back a Little Further

With lots more uncertainty!


Going Back Further it Was Mostly Cold!

natural forcing only

anthropogenic forcing only

natural +anthropogenic forcing

Compelling Evidence?

natural (solar + volcanic) forcing alone does not account for warming in the past50 years

  • "With four parameters I can fit an elephant and with five I can make him wiggle his trunk." — John von Neumann

adding human influences (greenhouse

gases + sulfate aerosols) brings the models and observations into pretty close agreement

Source: Prof. Gross Fall 2013 ECE 333 Notes

And Where Might Temps Go?

The modelsshow rate of increase valuesof between0.18 to 0.4 C per decade.The rate from1975 to 2005was about 0.2 C per decade.


Brief History of Electric Power

  • Early 1880’s – Edison introduced Pearl Street dc system in Manhattan supplying 59 customers within a one mile radius

  • 1884 – Sprague produces practical dc motor

  • 1885 – invention of transformer

  • Mid 1880’s – Westinghouse/Tesla introduce rival ac system

  • Late 1880’s – Tesla invents ac induction motor

  • 1893 – First 3-phase transmission line operating at 2.3 kV, 12 km in Southern California

History, cont’d

  • 1896 – ac lines deliver electricity from hydro generation at Niagara Falls to Buffalo, 20 miles away

  • Early 1900’s – Private utilities supply all customers in area (city); recognized as a natural monopoly; states step in to begin regulation

  • By 1920’s – Large interstate holding companies control most electricity systems; highest voltages were 200 kV

History, cont’d

  • 1935 – Congress passes Public Utility Holding Company Act to establish national regulation, breaking up large interstate utilities (repealed 2005)

  • 1935/6 – Rural Electrification Act brought electricity to rural areas

  • 1930’s – Electric utilities established as vertical monopolies

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