a stochastic, mixed-integer optimization model with - diw berlin
TRANSCRIPT
![Page 1: A Stochastic, Mixed-Integer Optimization Model with - DIW Berlin](https://reader031.vdocuments.us/reader031/viewer/2022021307/62074ba749d709492c2ffde5/html5/thumbnails/1.jpg)
1
Models for the Energy Sector with a Focus on the Renewables Integration
„Modellgestützte Analysen für die Strommarktgestaltung zur Integration erneuerbarer Energien im Rahmen der Energiewende (MASMIE)“
Stiftung Mercator
Steven A. Gabriel1
(for wastewater-to-energy work: Chalida U-tapao1, Christopher Peot2 and Mark Ramirez2)
1 University of Maryland, College Park, Maryland
2District of Columbia Water and Sewer Authority, Washington DC
Berlin, Germany 12 October 2012
![Page 2: A Stochastic, Mixed-Integer Optimization Model with - DIW Berlin](https://reader031.vdocuments.us/reader031/viewer/2022021307/62074ba749d709492c2ffde5/html5/thumbnails/2.jpg)
Outline • Complementarity Modeling in Energy Markets, Springer July
2012 (S.A. Gabriel, A.J. Conejo, J.D. Fuller, B.F. Hobbs, C. Ruiz)
• Overview
• Illustrative modeling examples
• Some examples of renewable energy integration
• Current work
• Wastewater-to-energy, DC Water and Sewer Authority (new results as of Fall 2012)
• Possible future work
• Energy, transportation and renewables
• Smart Grid and renewables
![Page 3: A Stochastic, Mixed-Integer Optimization Model with - DIW Berlin](https://reader031.vdocuments.us/reader031/viewer/2022021307/62074ba749d709492c2ffde5/html5/thumbnails/3.jpg)
Overview of Complementarity Modeling in Energy Markets
![Page 4: A Stochastic, Mixed-Integer Optimization Model with - DIW Berlin](https://reader031.vdocuments.us/reader031/viewer/2022021307/62074ba749d709492c2ffde5/html5/thumbnails/4.jpg)
Complementarity Modeling in Energy Markets
• Main goals:
• Clear presentation of market equilibrium models for the energy sector
• Accessible by non-mathematicians
• Comprehensive in modeling formats and illustrative in examples
• Consideration of models for:
• Perfect competition (optimization)
• Imperfect competition (optimization, complementarity problems,variational inequalities (VI), quasi-VI two-level models (MPEC, EPEC))
• Engineering details for energy networks
• Other interesting energy market aspects and algorithmic aspects of solving equilibrium problems
![Page 5: A Stochastic, Mixed-Integer Optimization Model with - DIW Berlin](https://reader031.vdocuments.us/reader031/viewer/2022021307/62074ba749d709492c2ffde5/html5/thumbnails/5.jpg)
Complementarity Modeling in Energy Markets
• Chapter 1: Friendly introduction to complementarity and other equilibrium models
• Chapter 2: Quick mathematical introduction to optimization and equilibrium models
• Chapter 3: Microeconomic theory
• Chapter 4: Correspondence between optimization and equilibrium problems
• Chapter 5: Variational inequality problems
• Chapter 6: Two-level problems: MPECs
• Chapter 7: Two-level problems: EPECs
![Page 6: A Stochastic, Mixed-Integer Optimization Model with - DIW Berlin](https://reader031.vdocuments.us/reader031/viewer/2022021307/62074ba749d709492c2ffde5/html5/thumbnails/6.jpg)
Complementarity Modeling in Energy Markets
• Chapters 8&9: Basic and advanced algorithms for solving equilibrium problems
• Chapter 10: Natural gas market equilibria
• Chapter 11: Models for electricity and environmental issues
• Chapter 12: Multi-Commodity models
• Appendix A: Convex sets and functions
• Appendix B: GAMS codes for selected problems
• Appendix C: Electrical engineering details for power flows
• Appendix D: Engineering details for natural gas flows
![Page 7: A Stochastic, Mixed-Integer Optimization Model with - DIW Berlin](https://reader031.vdocuments.us/reader031/viewer/2022021307/62074ba749d709492c2ffde5/html5/thumbnails/7.jpg)
Some Illustrative Modeling Examples
![Page 8: A Stochastic, Mixed-Integer Optimization Model with - DIW Berlin](https://reader031.vdocuments.us/reader031/viewer/2022021307/62074ba749d709492c2ffde5/html5/thumbnails/8.jpg)
8
The Big Picture
LP
Non-Convex Opt. Convex Opt.
QP
ILP
convex non-convex
LP=linear
program ILP=integer
linear program
QP=quadratic program
![Page 9: A Stochastic, Mixed-Integer Optimization Model with - DIW Berlin](https://reader031.vdocuments.us/reader031/viewer/2022021307/62074ba749d709492c2ffde5/html5/thumbnails/9.jpg)
9
NLP
QP
convex
The Bigger Picture
LP
Complementarity Problems
Other non-optimization based problems
e.g., spatial price equilibria, traffic equilibria, Nash-Cournot games
KKT conditions
![Page 10: A Stochastic, Mixed-Integer Optimization Model with - DIW Berlin](https://reader031.vdocuments.us/reader031/viewer/2022021307/62074ba749d709492c2ffde5/html5/thumbnails/10.jpg)
10
Complementarity Problems
Other non-optimization based problems
e.g., spatial price equilibria, traffic equilibria, Nash-Cournot games
NLP
QP
convex
LP
KKT conditions
Variational Inequality Problem (VI)
Quasi-variational Inequality Problem (QVI)
The Even Bigger Picture
![Page 11: A Stochastic, Mixed-Integer Optimization Model with - DIW Berlin](https://reader031.vdocuments.us/reader031/viewer/2022021307/62074ba749d709492c2ffde5/html5/thumbnails/11.jpg)
11
Generalized Nash Equilibria Duopoly Example from Chapter 4, Gabriel et al. (2013)
• Two energy producers, i=1,2, maximizing profit
subject to nonnegative production and joint constraints (e.g., drilling rigs)
![Page 12: A Stochastic, Mixed-Integer Optimization Model with - DIW Berlin](https://reader031.vdocuments.us/reader031/viewer/2022021307/62074ba749d709492c2ffde5/html5/thumbnails/12.jpg)
More Complicated MPEC Example
Formulation and Solution of a Discretely-Constrained Energy MPEC as
an MIP S.A. Gabriel, F.U. Leuthold , 2010. "Solving Discretely-
Constrained MPEC Problems with Applications in Electric Power Markets," Energy Economics, 32, 3-14.
12
![Page 13: A Stochastic, Mixed-Integer Optimization Model with - DIW Berlin](https://reader031.vdocuments.us/reader031/viewer/2022021307/62074ba749d709492c2ffde5/html5/thumbnails/13.jpg)
Motivation: Market Structures in Europe
• France: EDF has a market share of 80%
• Germany: EON+RWE 55% market share; +Vattenfall+EnBW 85% market share
• Liberalization of vertical integrated companies proceeds sluggish
• Former integrated companies have information advantages in terms of geographical specifics and network knowledge
• This gives rise potentially to one (or more) dominant players in the market, rest can be considered as “competitive fringe”
• Need for modeling that takes this structure into account
Source: EDF (2008), EON (2008), Google Maps (2008), RWE (2008).
13
![Page 14: A Stochastic, Mixed-Integer Optimization Model with - DIW Berlin](https://reader031.vdocuments.us/reader031/viewer/2022021307/62074ba749d709492c2ffde5/html5/thumbnails/14.jpg)
Electricity Market Model I: Fundamental Idea
• Assumption: Stackelberg competition
• Leader makes output decision
• Follower decides taking the leaders decision as given
• Leader: Strategic production company
• Maximizes individual profit under maximum generation constraints and non-negative production (upper-level problem)
• Takes into account followers’ decisions (lower-level problem)
• Follower: ISO
• Maximizes social welfare
• Decides over the output decision of the competitive fringe
• Takes into account technical constraints such as maximum fringe generation, line flow, and energy balance constraints 14
![Page 15: A Stochastic, Mixed-Integer Optimization Model with - DIW Berlin](https://reader031.vdocuments.us/reader031/viewer/2022021307/62074ba749d709492c2ffde5/html5/thumbnails/15.jpg)
Fifteen-Node Network: Structure
15
![Page 16: A Stochastic, Mixed-Integer Optimization Model with - DIW Berlin](https://reader031.vdocuments.us/reader031/viewer/2022021307/62074ba749d709492c2ffde5/html5/thumbnails/16.jpg)
Fifteen-Node Network: Results Generation (MWh)
• We compare perfect competition (comp) to an imperfect competition (strat) run
• It can be shown that under strategic behavior, the player produces in total less than in the competitive
• Why? Next slide
16
![Page 17: A Stochastic, Mixed-Integer Optimization Model with - DIW Berlin](https://reader031.vdocuments.us/reader031/viewer/2022021307/62074ba749d709492c2ffde5/html5/thumbnails/17.jpg)
Fifteen-Node Network: Results II
• Because the player can influence the prices at nodes where it is profitable for him, in order to maximize individual profits
• Also, a player can use network constraints in order to game (price differences)
17
![Page 18: A Stochastic, Mixed-Integer Optimization Model with - DIW Berlin](https://reader031.vdocuments.us/reader031/viewer/2022021307/62074ba749d709492c2ffde5/html5/thumbnails/18.jpg)
Fifteen-Node Network: Results
• Problem size increases dramatically for strategic behavior runs
• The size depends on the number of discrete production choice possibilities
• The computation times is long but varies depending on the possible discrete choices (but has been greatly speeded by Daniel Huppmann…)
18
![Page 19: A Stochastic, Mixed-Integer Optimization Model with - DIW Berlin](https://reader031.vdocuments.us/reader031/viewer/2022021307/62074ba749d709492c2ffde5/html5/thumbnails/19.jpg)
Some Examples of Renewable Energy Integration-Current or Previous Work
(Gabriel et al.)
![Page 20: A Stochastic, Mixed-Integer Optimization Model with - DIW Berlin](https://reader031.vdocuments.us/reader031/viewer/2022021307/62074ba749d709492c2ffde5/html5/thumbnails/20.jpg)
Driving Forces for Integration of Renewables
• Environmental initiatives related to climate change mitigation
•Power generation (e.g., 20-20-20 in Europe, state-level renewable portfolio standards in the U.S.) •Alternative vehicles that emit less CO2 (e.g., electric vehicles, natural gas vehicles)
•Advent of smart grid and need for better coordination of intermittent energy sources
![Page 21: A Stochastic, Mixed-Integer Optimization Model with - DIW Berlin](https://reader031.vdocuments.us/reader031/viewer/2022021307/62074ba749d709492c2ffde5/html5/thumbnails/21.jpg)
21
Example of Renewables Integration: A Stochastic, Multi-Objective, Mixed-Integer
Optimization Model for Management of Wastewater Derived energy at the Blue Plains AWTP, DC Water
Steven A. Gabriel, Chalida U-tapao University of Maryland
PRELIMINARY RESULTS
![Page 22: A Stochastic, Mixed-Integer Optimization Model with - DIW Berlin](https://reader031.vdocuments.us/reader031/viewer/2022021307/62074ba749d709492c2ffde5/html5/thumbnails/22.jpg)
Possible energy supplies for DC Water
![Page 23: A Stochastic, Mixed-Integer Optimization Model with - DIW Berlin](https://reader031.vdocuments.us/reader031/viewer/2022021307/62074ba749d709492c2ffde5/html5/thumbnails/23.jpg)
177 dt/d
74.1 dt/d 174-684 dt/d
Maximum capacity 1,000 dt/d
Possible biomass sources for the digester
![Page 24: A Stochastic, Mixed-Integer Optimization Model with - DIW Berlin](https://reader031.vdocuments.us/reader031/viewer/2022021307/62074ba749d709492c2ffde5/html5/thumbnails/24.jpg)
Flowchart for a stochastic optimization model for biogas production at the Blue Plains AWTP, DC Water
OUTSIDE SLUDGE
![Page 25: A Stochastic, Mixed-Integer Optimization Model with - DIW Berlin](https://reader031.vdocuments.us/reader031/viewer/2022021307/62074ba749d709492c2ffde5/html5/thumbnails/25.jpg)
-
100.000
200.000
300.000
400.000
500.000
600.000
0 200 400 600 800 1000 1200
Cost ($/d)
Solids capacity (dt/d)
Cost of five possible types of digester ($/d)
4(TH$digester)+LS
2(TH&digester)+LS
4(TH&digester)+2(TH&digester)+LS
Lime stabilization
Incineration
1st Stage Decision Variables Five possible types for construction and operational costs (50-years horizon) of digester related to biosolids capacity
Small digester
Big digester
![Page 26: A Stochastic, Mixed-Integer Optimization Model with - DIW Berlin](https://reader031.vdocuments.us/reader031/viewer/2022021307/62074ba749d709492c2ffde5/html5/thumbnails/26.jpg)
The generating renewable electricity costs are calculated from a levelized cost of electricity (LCOE)
Sunlight time (hrs) 10.75 12.3 14
Capacity factor (%) 21 23 25
Net working hours (hrs) 45990 50370 54750
Capital cost1 ($/kW) 6000 6000 6000
O&M2 ($/kW) 15 15 15
Lifetime2 (yrs) 25 25 25
Solar energy cost ($/kWh) 0.15 0.13 0.12
Probability 0.530 0.250 0.220
Costs ($/kWh) = [Fuel cost ($/kWh) + capital cost($/capacity) + non-fuel operating costs ($/capacity)] /output (kWh/capacity)
Source: 1 = EPA 2005, 2 = Zweibel, 2010
![Page 27: A Stochastic, Mixed-Integer Optimization Model with - DIW Berlin](https://reader031.vdocuments.us/reader031/viewer/2022021307/62074ba749d709492c2ffde5/html5/thumbnails/27.jpg)
Bioisolids
NG prices
Electricity consumptio
n
Electricity costs
Electricity prices
Fertilizer prices
Fossil fuel costs
Solar Electricity
Solar electricity costs
CO2 credits RECS Scenario1
Scenario 59,049
Electricity cost is$0.15, $0.13, $0.12 per kWh when solar panel’s is 25 years. Optimize at 0.53, 0.25 and 0.22 probabilities for each price, respectively.
• 59,049 (310) scenarios relate to 10 groups of uncertain data
• 1 time period • Incineration process will be
included as one of five possible cases of digester type
Weibull PDF
Log normal PDF
Triangular PDF
Weibull PDF
Triangular PDF
Log normal PDF
Log normal PDF
Triangular PDF
Triangular PDF
![Page 28: A Stochastic, Mixed-Integer Optimization Model with - DIW Berlin](https://reader031.vdocuments.us/reader031/viewer/2022021307/62074ba749d709492c2ffde5/html5/thumbnails/28.jpg)
Preliminary results and discussion
• Expected solutions under three objectives
• Expected DC Water total value
• Expected net CO2 e emissions
• Expected purchased energy
• Compare expected total value with different tipping fees ($0, $50 and $106.5 per ton biosolids)
• Compare results of added tipping fees and solar energy with previous version (w/o tipping fees and w/o solar energy)
• Multi-objective optimization
![Page 29: A Stochastic, Mixed-Integer Optimization Model with - DIW Berlin](https://reader031.vdocuments.us/reader031/viewer/2022021307/62074ba749d709492c2ffde5/html5/thumbnails/29.jpg)
-115.454,0 -111.399,0
-99.230,0 -85.034,2
-300.000
-250.000
-200.000
-150.000
-100.000
-50.000
0Max total value Min net CO2 Min Energy
DC
Wat
er to
tal v
alue
($/d
)
Expected DC Water total value ($/d)
No tipping fees + No Solar
$0 tipping fees + Solar
$50 tipping fees + Solar
$106.5 tipping fees + Solar
Digester cost is the most influential variable for operations costs. Therefore DC Water should use a small digester in order to reduce digester cost, then generate
electricity from biogas. Also, tipping fees increase DC Water revenue.
Small digester Big digester
Big digester
![Page 30: A Stochastic, Mixed-Integer Optimization Model with - DIW Berlin](https://reader031.vdocuments.us/reader031/viewer/2022021307/62074ba749d709492c2ffde5/html5/thumbnails/30.jpg)
251
206,8
0
50
100
150
200
250
300
350
400
450
Max total value Min net CO2 Min Energy
DC
Wat
er n
et C
O2
emis
sion
s (t
ons/
d)
Expected net CO2 emissions (tons/d)
No tipping fees + No solar
$0 tipping fees + Solar
$50 tipping fees + Solar
$106.5 tipping fees + Solar
Small digester
Generate electricity from renewable energy (biogas and solar) and use for the Blue Plains facility to decrease CO2 e emissions. Therefore DC Water should use a big
digester and install solar panels.
Big digester
Big digester
![Page 31: A Stochastic, Mixed-Integer Optimization Model with - DIW Berlin](https://reader031.vdocuments.us/reader031/viewer/2022021307/62074ba749d709492c2ffde5/html5/thumbnails/31.jpg)
580.120,0
392.940,0
0
200.000
400.000
600.000
800.000
1.000.000
1.200.000
Max total value Min net CO2 Min Energy
DC
Wat
er p
urch
asin
g en
ergy
(kW
h/d)
Expected purchased energy (kWh/d)
No tipping fees + No solar
$0 tipping fees + Solar
$50 tipping fees + Solar
$106.5 tipping fees +Solar
Big digester
Big digester
Generate electricity from renewable energy (biogas and solar) and use for the Blue Plains facility to decrease energy purchase costs from outside sources. Therefore DC
Water should use a big digester and install solar panels.
Small digester
![Page 32: A Stochastic, Mixed-Integer Optimization Model with - DIW Berlin](https://reader031.vdocuments.us/reader031/viewer/2022021307/62074ba749d709492c2ffde5/html5/thumbnails/32.jpg)
Future Work 1. Energy, Transportation, Renewables
2. Smart Grid
![Page 33: A Stochastic, Mixed-Integer Optimization Model with - DIW Berlin](https://reader031.vdocuments.us/reader031/viewer/2022021307/62074ba749d709492c2ffde5/html5/thumbnails/33.jpg)
Energy , Transportation, and Renewables, A Complicated Relationship
33
Natural gas vehicle NGV
Plug-in electric vehicle, PEV (UMD)
http://www.oe.energy.gov/information_center/electricity101.htm
Electric power sector
Natural gas sector
Renewable resources (wastewater)
Intermittent renewable power
http://www.ecofleetconsulting.com/ecofleet_news
![Page 34: A Stochastic, Mixed-Integer Optimization Model with - DIW Berlin](https://reader031.vdocuments.us/reader031/viewer/2022021307/62074ba749d709492c2ffde5/html5/thumbnails/34.jpg)
Nexus of Energy , Transportation, and Renewables Wind Power and Natural Gas Vehicles
Pickens Plan (U.S.*) – Wind power in the center of the country
(N. Texas to Canadian border) – Need to increase transmission lines to
transport the electricity – Use natural gas for vehicles (range issue) – Decreasing U.S. reliance on petroleum – How to incentivize transmission grid
investments? – How to incentivize natural gas
transportation infrastructure investments?
– What will be the effects on emissions goals?
*http://www.pickensplan.com/theplan/
34
![Page 35: A Stochastic, Mixed-Integer Optimization Model with - DIW Berlin](https://reader031.vdocuments.us/reader031/viewer/2022021307/62074ba749d709492c2ffde5/html5/thumbnails/35.jpg)
Nexus of Energy and Transportation Natural Gas Vehicles (NGVs)
•Natural gas vehicles (NGVs) have already gained some popularity in certain areas in the U.S. •California energy company PG& E has used light-duty natural gas vehicles within their fleet of over 1,100 natural gas vehicles due to economic, maintenance and other advantages •Washington, DC has also starting using compressed natural gas (CNG) for its buses (164 out of 1433) •In a study by the U.S. Department of Energy’s FreedomCAR and Vehicle Technologies (FCVT) Program, such vehicles showed distinct environmental advantages as compared to conventional diesel
35
![Page 36: A Stochastic, Mixed-Integer Optimization Model with - DIW Berlin](https://reader031.vdocuments.us/reader031/viewer/2022021307/62074ba749d709492c2ffde5/html5/thumbnails/36.jpg)
Nexus of Energy and Transportation Natural Gas Vehicles (NGVs), http://www.altfuelprices.com
36
CNG: $2.04/GGE=$2.04/3.79 L=$0.538/L=0.414 EUR/L Gasoline: $3.65/G=$3.65/3.79=$0.963/L=0.741 EUR/L Berlin, Germany: 1.56 EUR/L
![Page 37: A Stochastic, Mixed-Integer Optimization Model with - DIW Berlin](https://reader031.vdocuments.us/reader031/viewer/2022021307/62074ba749d709492c2ffde5/html5/thumbnails/37.jpg)
Nexus of Energy and Transportation Natural Gas Vehicles (NGVs), http://www.altfuelprices.com
37
![Page 38: A Stochastic, Mixed-Integer Optimization Model with - DIW Berlin](https://reader031.vdocuments.us/reader031/viewer/2022021307/62074ba749d709492c2ffde5/html5/thumbnails/38.jpg)
Nexus of Energy and Transportation Plug-In Electric Vehicles (PEVs), UMD Eng. Parking Lot
38
Plug-In Electric Vehicles (PEVs), UMD Eng. Parking Lot
•Assuming an average CO2 emissions of 1.341 lb/kWh based on EPA data, the emissions per plug-in hybrid electric vehicle (PHEV) is almost 60% (7.6 kg) of the emissions from a conventional car, assuming the entire energy to fully charge the battery comes from fossil fueled power plant (Raghavan and Khaligh, 2011). •Technical aspects: The battery number of cycles to failure versus DoD [Shaltz et al., 2009].
![Page 39: A Stochastic, Mixed-Integer Optimization Model with - DIW Berlin](https://reader031.vdocuments.us/reader031/viewer/2022021307/62074ba749d709492c2ffde5/html5/thumbnails/39.jpg)
Wind Power Integration for Washington (Horin & Leuken)
E l e c t r i c i t y L o a d : 5 0 0 0
W iP H E
0
1 0 0 0
2 0 0 0
3 0 0 0
4 0 0 0
5 0 0 0
6 0 0 0
7 0 0 0
8 0 0 0
1 3 5 7 9 1 1 1 3 1 5 1 7 1 9 2 1 2 3
H o
PHEVs allow more efficient integration of wind power
Electricity Load: 5000 Turbines and no PHEVs
Wind
0
1000
2000
3000
4000
5000
6000
7000
8000
1 3 5 7 9 11 13 15 17 19 21 23Hour
System Cost = $1,293,808 Savings = $255,131 (16%)
System Cost = $1,548,940
Wasted Wind Power
Peaking Plants
39
Nexus of Energy and Transportation Electric Vehicles Study (Horin and Leukin, UMD)
![Page 40: A Stochastic, Mixed-Integer Optimization Model with - DIW Berlin](https://reader031.vdocuments.us/reader031/viewer/2022021307/62074ba749d709492c2ffde5/html5/thumbnails/40.jpg)
Smart Grid: Need for Management of Stochastic Supply and Demand
http://www.nature.com/news/2008/080730/images/454570a-6.jpg
Active end-users
Generators
Qualified Facilities
40
Smart Grid