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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

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

Overview of Complementarity Modeling in Energy Markets

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

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

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

Some Illustrative Modeling Examples

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The Big Picture

LP

Non-Convex Opt. Convex Opt.

QP

ILP

convex non-convex

LP=linear

program ILP=integer

linear program

QP=quadratic program

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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

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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

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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)

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.

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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).

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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

Fifteen-Node Network: Structure

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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

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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)

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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…)

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Some Examples of Renewable Energy Integration-Current or Previous Work

(Gabriel et al.)

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

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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

Possible energy supplies for DC Water

177 dt/d

74.1 dt/d 174-684 dt/d

Maximum capacity 1,000 dt/d

Possible biomass sources for the digester

Flowchart for a stochastic optimization model for biogas production at the Blue Plains AWTP, DC Water

OUTSIDE SLUDGE

-

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

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

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

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

-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

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

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

Future Work 1. Energy, Transportation, Renewables

2. Smart Grid

Energy , Transportation, and Renewables, A Complicated Relationship

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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

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/

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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

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Nexus of Energy and Transportation Natural Gas Vehicles (NGVs), http://www.altfuelprices.com

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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

Nexus of Energy and Transportation Natural Gas Vehicles (NGVs), http://www.altfuelprices.com

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Nexus of Energy and Transportation Plug-In Electric Vehicles (PEVs), UMD Eng. Parking Lot

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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].

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

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Nexus of Energy and Transportation Electric Vehicles Study (Horin and Leukin, UMD)

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

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Smart Grid