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Javad Lavaei
Electrical Engineering
Columbia University
ELEN E4511: Power Systems Analysis
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What’s the course about?
The course is about energy:
Power Grid
Transportation Systems
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What’s the course about?
Fossil fuel energy:
Sustainable energy
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What’s important about energy?
Many years ago, we learned how to generate power:
We happily designed electric devices:
How to provide power to loads: Assign a (or a few) generator to
every group of loads.
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What’s important about energy?
There were several issues:
A single fault would lead to blackout.
Every area needs a dedicated source of energy.
Dedicated generators make energy more expensive .
Remedy:
Have a group of generators
Have a group of loads
Connect them to each other via a
physical network (transmission lines)
Generators Loads
Power Network
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What’s important about energy?
This seems really cool!
Reliability: A fault may not cause blackout
Efficiency: Shared generators reduce costs
Less capital cost (infrastructure)
This is not the end of the story!
Reliability: A fault may propagate (from a state to another)
Efficiency:
There are an infinite number of operation strategies.
Bad coordination between areas breaks the network down
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What’s important about energy?
Emerging challenges:
We are running out of gray energy.
Traditional power generation leads to global warming.
We can’t tolerate power outages given our needs.
Generation can’t keep up with ever-growing demand.
Possible solution:
Replace fossil fuel energy with renewable energy
Optimize reliability
Optimize efficiency
The modernized grid is called Smart grid.
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What’s the course about?
Researchers from EE, CE, CS, ME, OR, Econ, Law, Phy,… work on
Smart Grid all together.
If you’re interested in energy, this course is right for
you.
Topics to be covered: Modeling of power systems (transmission
lines, transformers, etc.) Architecture of power networks Operation
of power systems (study of both steady state and transient
behavior) Control of power networks Optimization for power networks
Electricity market Smart Grid
Theories to be covered:
Circuit Control Optimization
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What’s the course about?
References: "Power Systems Analysis" by Arthur R. Bergen and
Vijay Vittal "Fundamentals of Power System Economics" by Daniel S.
Kirschen and Goran Strbac "Applied Optimization: Formulation and
Algorithms for Engineering Systems" by Ross
Baldick "Convex Optimization" by Stephen Boyd and Lieven
Vandenberghe Research papers
What do I expect from you? Active participation (10 %) Do ~6
homework sets (30%) Do a course project (60%)
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Outline
Modeling of power systems (transmission lines, transformers,
etc.)
Architecture of power networks
Operation of power systems (study of both steady state and
transient behavior)
Control of power networks
Optimization for power networks
Electricity market
Smart Grid
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Modeling of Power Systems
Transmission line
Capacitor bank
Transformer
Load
Generator
FACTS
Circuit, multi-phase modeling,..
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Outline
Modeling of power systems (transmission lines, transformers,
etc.)
Architecture of power networks
Operation of power systems (study of both steady state and
transient behavior)
Control of power networks
Optimization for power networks
Electricity market
Smart Grid
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Architecture of Power Networks
Transmission and distribution networks (and their features)
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Outline
Modeling of power systems (transmission lines, transformers,
etc.)
Architecture of power networks
Operation of power systems (study of both steady state and
transient behavior)
Control of power networks
Optimization for power networks
Electricity market
Smart Grid
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Operation of Power Systems (Steady State)
Forecast loads
How to find an operating point (PF)?
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Operation of Power Systems (Transient)
We have dynamics.
How to study the real-time behavior of the network?
Need tools from control theory.
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Outline
Modeling of power systems (transmission lines, transformers,
etc.)
Architecture of power networks
Operation of power systems (study of both steady state and
transient behavior)
Control of power networks
Optimization for power networks
Electricity market
Smart Grid
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Control of Power Systems
Various signals (e.g., frequency, voltage,…) must be kept at
very narrow bands.
Given a small disturbance in the system, the error must
attenuate to zero.
Design stabilizing controller (we’ll talk about centralized
versus decentralized).
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Outline
Modeling of power systems (transmission lines, transformers,
etc.)
Architecture of power networks
Operation of power systems (study of both steady state and
transient behavior)
Control of power networks
Optimization for power networks
Electricity market
Smart Grid
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Optimization for Power Systems
We want to optimize efficiency, minimize cost, maximize
robustness,…
Interesting problems: OPF, SCOPF, UC, transmission
planning,…
Tools from optimization (e.g., convex optimization) will be
taught.
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Outline
Modeling of power systems (transmission lines, transformers,
etc.)
Architecture of power networks
Operation of power systems (study of both steady state and
transient behavior)
Control of power networks
Optimization for power networks
Electricity market
Smart Grid
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Electricity Market
Government is not in charge of generation.
Consumers buy energy.
Producers sell energy.
We need a market for this (PJM).
We will discuss the following:
Various pricing signals
Pool-based market
Decentralized market
Equilibrium
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Outline
Modeling of power systems (transmission lines, transformers,
etc.)
Architecture of power networks
Operation of power systems (study of both steady state and
transient behavior)
Control of power networks
Optimization for power networks
Electricity market
Smart Grid
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Smart Grid
Replace bulk generators with distributed generating units
Integrate renewable energy, e.g. solar and wind
Integrate electric vehicles
Introduce a demand response strategy
Enhance efficiency and reliability
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Questions?
��Javad Lavaei��Electrical Engineering ��Columbia
UniversityWhat’s the course about?What’s the course about?What’s
important about energy?What’s important about energy?What’s
important about energy?What’s important about energy?What’s the
course about?What’s the course about?OutlineModeling of Power
SystemsOutlineArchitecture of Power NetworksOutlineOperation of
Power Systems (Steady State)Operation of Power Systems
(Transient)OutlineControl of Power SystemsOutlineOptimization for
Power SystemsOutlineElectricity MarketOutlineSmart
GridQuestions?
