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Challenges and Opportunities of Optimization for Smart Gird
Yigang Wang, Ph.D.
Corporate Research & Technology
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To be a power management leader,
it helps to have a 100 year head start
• Founded in 1911 by J.O. Eaton 伊顿由 J. O. Eaton先生始创于1911年
• Headquarters in Cleveland, Ohio 伊顿公司全球总部设于美国俄亥俄州克里夫兰市
• Regional Headquarters in Shanghai; Morges, Switzerland; Mexico City
• Innovation Centers in the USA, China and India
• $13.7 billion revenue in 2010 2010年的全球销售额达137亿美元
• Customers in 150 countries 客户遍及全球150多个国家
• 70,000 employees worldwide 全球现有员工7万多名
• 55% of sales outside the U.S.
3 © 2016 Eaton. All Rights Reserved.
We have transformed our company …
Helping Customers Use Power Efficiently, Effectively and Safely
Eaton’s Past
A Vehicle Component
Manufacturer…
Eaton Today
A Leader in
Power Management!
Eaton’s Past
A Vehicle Component
Manufacturer…
Eaton Today
A Leader in
Power Management!
4 © 2016 Eaton. All Rights Reserved.
CRT: We are about …
People
Solutions
Technology
Global
Research
Technology
“Innovation excellence
with the right people in the
right place”
“Valuable customer
solutions enabling
Eaton’s & our customer’s
growth”
“Research and
technologies
with
cross-business impact”
… being “world class” at innovating
power management solutions globally
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Controls, Systems and Solutions
CSS System Modeling & Controls
• Dynamical modeling
• Control & Automation
• Sensors & Actuators
Machine Learning & PHM
• Inferential Sensing
• Health Monitoring/Management
• Complex Data Analytics
Safety & Fault Tolerance
• Functional safety methodology
• Cyber Security Framework
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Emerging Industrial Applications: Smart Grid and Micro-grid
• Our current electric grid was built in the 1890s and has slowly been improved upon as
technology advances through each decade. We are stretching the current grid to its
capacity and addressing new technologies in a patchwork and piecemeal manner.
• With the help of computerized equipment and communication, smart grid that can
automate and manage the increasing complexity and needs of electricity.
• Control related topics
• Large scale power and energy management -> power flow analysis
• Smart grid power system stability
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Inflection Point Driving Changes in Distribution
• Decreasing by 30%/year • Driven by off-shore manufacturing (China)
• Initially driven by mandates and subsidies
Note: Data for solar only http://www.seco.cpa.state.tx.us/publications/renewenergy/
2020: 15%
2025: 25%
2020: 33%
2025: 25% 2020:
30%
2030: 40%
2015: 29%
ME - 2020: 30%
VT - 2025: 24.8%
NH - 2017: 20%
MA - 2020: 22.1%
RI - 2020: 16%
CT - 2020: 27%
NJ - 2021: 20.4%
DE - 2026: 25%
MD - 2022: 20%
2015: 15%
2015: 10%
2015: 10%
2020: 20% 2025:
20%
2025: 15% 2020:
20%
2015: 15%
2021: 15%
2021: 18%
105 MW
2015: 5880 MW
< 10%
10% - 20%
> 20%
Legislated Renewable Standards Policies and Goals IREC North Carolina Energy Center
“inflection point” • Economic / social benefits prevail (< $0.10/kWh) • Renewable penetration exceeds 5% (point of
stability problems)
PV Price & Penetration Texas Renewable Energy Resource Assessment
• Penetration of PV at inflection point
• Other intermittent sources and loads continue to drive complexity in distribution grid
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Bi-Directional Power Flow by Renewables
IEEE 34-Bus Test Feeder with PV integration
Voltage rise
introduced by
reverse power
flow introduced
by PV integration
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Intermittency of Renewables
• Intermittency is one of major challenges of renewables
Data source: NREL
PV Power Output “Ideal” Insulation
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Impacts of Renewable Intermittency
PV Power
Voltage at PCC
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Economic Dispatch and Power Flow Analysis
• Objective: minimize the cost of generation
• Constraints
• Equality constraint: load generation balance
• Inequality constraints: upper and lower limits on generating units output
• Generating units and loads are not all connected to the same bus
• The economic dispatch may result in unacceptable flows or voltages
in the network
A B C L
© 2011 D. Kirschen and the University of Washington
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Optimal Power Flow (OPF) - Overview
• Optimization problem
• Classical objective function
• Minimize the cost of generation
• Equality constraints
• Power balance at each node - power flow
equations
• Inequality constraints
• Network operating limits (line flows, voltages)
• Limits on control variables
© 2011 D. Kirschen and the University of Washington
13 © 2016 Eaton. All Rights Reserved.
General Power Flow Solution Methods
• Newton-Raphson: ∆𝑉 = (𝜕𝑃/𝜕𝑉)−1∆𝑃 • Iterative linear approximation (Jacobian matrix)
• Main computational cost: (𝐽−1𝑝 = 𝑏)
• Quadratic convergence
• Small region of attraction
• Gauss-Seidel: 𝑉 = −𝑌𝐿𝐿−1𝑌𝐿𝐸𝐸 + 𝑌𝐿𝐿
−1(𝑆
𝑉)∗
• Fixed-point iteration (𝑥 = 𝑓(𝑥))
• Main computation cost:
Admittance matrix inversion
• Linear convergence
• Small region of convergence
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PF Solution Method in Distribution Network
• Gauss-Seidel more popular • Ideal loading condition: light loading
• Operating condition within convergence region
• Ideal topological structure: Radial or weakly
meshed
• Admittance matrix inversion not needed
• Impedance matrix (𝑍𝐿𝐿 = (𝑌𝐿𝐿)−1) can be formed
analytically
• Variations of GS • Forward-backward sweeping
• DistFlow
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Approximate Power Flow Solution (𝑉 = 𝐾𝐸 − 𝑍𝐼)
• Gauss-Seidel Iteration:
𝑉(𝑖) = −𝑌𝐿𝐿−1𝑌𝐿𝐸𝐸 + 𝑌𝐿𝐿
−1(
𝑆
𝑉(𝑖−1))∗
• DC approximation:
𝑉 = −𝑌𝐿𝐿−1𝑌𝐿𝐸𝐸 + 𝑌𝐿𝐿
−1(𝑆
𝐸)∗
• Can we combine the two to approximate PF
solution by performing only one iteration or
first-order approximation of it?
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Optimization Challenges for OPF
• Power flow equations are quadratic and hence OPF
can be formulated as a quadratically constrained
quadratic program (QCQP). It is generally nonconvex
and hence NP-hard.
• Renewable Integration makes optimization even more
challenging: from “static” power flow to more
“dynamic” power flow
• Some researches working on convex relaxations with
reasonable assumptions, such as Steven Low from
Cal-tech.
• More work needs to be done before industries can
take it.
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