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 1 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 The Big Picture
Convex Opt. Non-Convex Opt.
ILP LP=linear LP program ILP=integer linear convex non- convex program QP QP=quadratic program
8 The Bigger Picture Complementarity Problems
KKT conditions
NLP Other non-optimization based problems convex e.g., spatial price LP equilibria, traffic QP equilibria, Nash- Cournot games
9 The Even Quasi-variational Inequality Bigger Problem (QVI) Picture
Complementarity Problems
KKT conditions
NLP Other non-optimization Variational based problems LP Inequality conve e.g., spatial price x equilibria, traffic Problem QP equilibria, Nash- Cournot games (VI)
10 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)
11
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 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 “competitiveSource: EDF (2008), EON (2008), Google fringe” Maps (2008), RWE (2008). • Need for modeling that takes this structure into account 13 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 constraints14 Fifteen-Node Network: Structure
15 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
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 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 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 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
21 Possible energy supplies for DC Water Possible biomass sources for the digester
177 dt/d
174-684 dt/d 74.1 dt/d
Maximum capacity 1,000 dt/d Flowchart for a stochastic optimization model for biogas production at the Blue Plains AWTP, DC Water
OUTSIDE SLUDGE 1st Stage Decision Variables Five possible types for construction and operational costs (50-years horizon) of digester related to biosolids capacity
Cost ($/d) Cost of five possible types of digester ($/d) 600.000
500.000 4(TH$digester)+LS Small digester 2(TH&digester)+LS 400.000 4(TH&digester)+2(TH&digester)+LS Lime stabilization 300.000 Incineration Big digester 200.000
100.000
- 0 200 400 600 800 1000 1200 Solids capacity (dt/d) The generating renewable electricity costs are calculated from a levelized cost of electricity (LCOE)
Sunlight time (hrs) 10.75 12.3 14 Capacity factor (%) 21 23 25 Net working hours (hrs) 45990 50370 54750 Capital cost1 ($/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 Electricity cost is$0.15, $0.13, $0.12 per kWh when solar panel’s is 25 years. Triangular PDF Optimize at 0.53, 0.25 and 0.22 probabilities for each price, respectively. CO2 credits RECS Scenario1
Solar electricity Triangular costs PDF Weibull Solar Electricity PDF Log normal Fossil fuel PDF costs Log normal Fertilizer prices PDF Triangular Electricity prices PDF Triangular Electricity Log normal costs PDF PDF Electricity Weibull consumptio PDF n NG prices • 59,049 (310) scenarios relate to 10 groups of uncertain data Bioisolids • 1 time period • Incineration process will be included as one of five possible cases of digester type
Scenario 59,049 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 $106.5 per ton biosolids) • Compare results of added tipping fees and solar energy with previous version (w/o tipping fees and w/o solar energy) • Multi-objective optimization Expected DC Water total value ($/d)
Max total value Min net CO2 Min Energy 0
-50.000
-85.034,2 -100.000 -99.230,0 No tipping fees + No Solar -111.399,0 -150.000 -115.454,0 $0 tipping fees + Solar
-200.000 Small digester $50 tipping fees + Solar
DC Water total value value ($/d) total DCWater $106.5 tipping fees + Solar -250.000 Big digester
-300.000 Big digester
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. Expected net CO2 emissions (tons/d)
450 Big digester
400
350 Small digester Big digester 300 251 250 No tipping fees + No solar 206,8 200 $0 tipping fees + Solar
150 $50 tipping fees + Solar
100 $106.5 tipping fees + Solar
DC Water net CO2 emissions (tons/d) net emissions CO2 DCWater 50
0 Max total value Min net CO2 Min Energy
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. Expected purchased energy (kWh/d)
1.200.000 Big digester
1.000.000 Small digester 800.000 Big digester No tipping fees + No solar 600.000 580.120,0 $0 tipping fees + Solar 392.940,0 400.000 $50 tipping fees + Solar
$106.5 tipping fees + 200.000
DC Water purchasing energy energy purchasing (kWh/d) DCWater Solar
0 Max total value Min net CO2 Min Energy
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. Future Work 1. Energy, Transportation, Renewables 2. Smart Grid Energy , Transportation, and Renewables, A Complicated Relationship
Plug-in electric vehicle, PEV (UMD) Electric power sector
Intermittent renewable power http://www.oe.energy.gov/information_center/ electricity101.htm
Renewable resources Natural gas vehicle NGV (wastewater)
Natural gas sector
http://www.ecofleetconsulting.com/ecofleet_news 33 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 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 Nexus of Energy and Transportation Natural Gas Vehicles (NGVs), http://www.altfuelprices.com
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 36 Nexus of Energy and Transportation Natural Gas Vehicles (NGVs), http://www.altfuelprices.com
37 Nexus of Energy and Transportation Plug-In Electric Vehicles (PEVs), UMD Eng. Parking Lot
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]. 38 Nexus of Energy and Transportation Wind Power Integration for Washington (Horin & Leuken) Electric Vehicles Study (Horin and Leukin, UMD)
Electricity Load: 5000 Turbines and no PHEVs 8000 7000 Peaking Plants 6000 5000 Wind System Cost = 4000 3000 $1,548,940 2000 1000 Wasted Wind Power 0 1 3 5 7 9 11 13 15 17 19 21 23 Hour
Electricity Load: 5000 System Cost 8000 7000 = 6000 PHE $1,293,808 5000 Wi
4000 3000 Savings = 2000 1000 $255,131 0 1 3 5 7 9 11 13 15 17 19 21 23 (16%) Ho PHEVs allow more efficient integration of wind power 39 Smart Grid: Need for Management of Stochastic Supply and Demand Smart Grid
Active end-users
Qualified
Facilities Generators 40 http://www.nature.com/news/2008/080730/images/454570a-6.jpg