Does Risk Aversion Affect Transmission and Generation Planning? A Western North America Case Study

Munoz, Francisco; van der Weijde, Adriaan Hendrik; Hobbs, Benjamin F.; Watson, Jean-Paul

doi:10.1016/j.eneco.2017.03.025

Title: Does Risk Aversion Affect Transmission and Generation Planning? A Western North America Case Study

Abstract

Here, we investigate the effects of risk aversion on optimal transmission and generation expansion planning in a competitive and complete market. To do so, we formulate a stochastic model that minimizes a weighted average of expected transmission and generation costs and their conditional value at risk (CVaR). We also show that the solution of this optimization problem is equivalent to the solution of a perfectly competitive risk-averse Stackelberg equilibrium, in which a risk-averse transmission planner maximizes welfare after which risk-averse generators maximize profits. Furthermore, this model is then applied to a 240-bus representation of the Western Electricity Coordinating Council, in which we examine the impact of risk aversion on levels and spatial patterns of generation and transmission investment. Although the impact of risk aversion remains small at an aggregate level, state-level impacts on generation and transmission investment can be significant, which emphasizes the importance of explicit consideration of risk aversion in planning models.

Authors:

Munoz, Francisco ^[1]; van der Weijde, Adriaan Hendrik ^[2]; Hobbs, Benjamin F. ^[3]; Watson, Jean-Paul ^[4]

Adolfo Ibanez Univ., Santiago (Chile)
Vrije Univ. Amsterdam (Netherlands)
Johns Hopkins Univ., Baltimore, MD (United States)
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Publication Date:: Fri Apr 07 00:00:00 EDT 2017

Research Org.:: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Sponsoring Org.:: USDOE Office of Electricity (OE), Advanced Grid Research & Development. Power Systems Engineering Research

OSTI Identifier:: 1356838

Alternate Identifier(s):: OSTI ID: 1419371

Report Number(s):: SAND-2017-3855J
Journal ID: ISSN 0140-9883; 652433

Grant/Contract Number:: AC04-94AL85000

Resource Type:: Accepted Manuscript

Journal Name:: Energy Economics

Additional Journal Information:: Journal Volume: 64; Journal ID: ISSN 0140-9883

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 60 APPLIED LIFE SCIENCES; Risk Aversion; Stochastic Programming; Transmission and Generation Planning; Investment

Citation Formats


                    Munoz, Francisco, van der Weijde, Adriaan Hendrik, Hobbs, Benjamin F., and Watson, Jean-Paul. Does Risk Aversion Affect Transmission and Generation Planning? A Western North America Case Study.  United States: N. p., 2017. 
Web.  doi:10.1016/j.eneco.2017.03.025.

Copy to clipboard


                    Munoz, Francisco, van der Weijde, Adriaan Hendrik, Hobbs, Benjamin F., & Watson, Jean-Paul. Does Risk Aversion Affect Transmission and Generation Planning? A Western North America Case Study.  United States.  https://doi.org/10.1016/j.eneco.2017.03.025

Copy to clipboard


                    Munoz, Francisco, van der Weijde, Adriaan Hendrik, Hobbs, Benjamin F., and Watson, Jean-Paul. Fri .  
"Does Risk Aversion Affect Transmission and Generation Planning? A Western North America Case Study".  United States.  https://doi.org/10.1016/j.eneco.2017.03.025.  https://www.osti.gov/servlets/purl/1356838.

Copy to clipboard


                    
@article{osti_1356838,

  title        = {Does Risk Aversion Affect Transmission and Generation Planning? A Western North America Case Study},

  author       = {Munoz, Francisco and van der Weijde, Adriaan Hendrik and Hobbs, Benjamin F. and Watson, Jean-Paul},

  abstractNote = {Here, we investigate the effects of risk aversion on optimal transmission and generation expansion planning in a competitive and complete market. To do so, we formulate a stochastic model that minimizes a weighted average of expected transmission and generation costs and their conditional value at risk (CVaR). We also show that the solution of this optimization problem is equivalent to the solution of a perfectly competitive risk-averse Stackelberg equilibrium, in which a risk-averse transmission planner maximizes welfare after which risk-averse generators maximize profits. Furthermore, this model is then applied to a 240-bus representation of the Western Electricity Coordinating Council, in which we examine the impact of risk aversion on levels and spatial patterns of generation and transmission investment. Although the impact of risk aversion remains small at an aggregate level, state-level impacts on generation and transmission investment can be significant, which emphasizes the importance of explicit consideration of risk aversion in planning models.},

  doi          = {10.1016/j.eneco.2017.03.025},

  journal      = {Energy Economics},

  number       = ,

  volume       = 64,

  place        = {United States},

  year         = {Fri Apr 07 00:00:00 EDT 2017},

  month        = {Fri Apr 07 00:00:00 EDT 2017}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (Publisher)

Accepted Manuscript (DOE)

Publisher's Version of Record

https://doi.org/10.1016/j.eneco.2017.03.025

Other availability

Search WorldCat to find libraries that may hold this journal

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

A Risk-Based Approach for Transmission Network Expansion Planning Under Deliberate Outages
journal, August 2010

Arroyo, José Manuel; Alguacil, Natalia; Carrión, Miguel
IEEE Transactions on Power Systems, Vol. 25, Issue 3
DOI: 10.1109/TPWRS.2010.2042310

Impact of public policy uncertainty on renewable energy investment: Wind power and the production tax credit
journal, December 2010

Barradale, Merrill Jones
Energy Policy, Vol. 38, Issue 12
DOI: 10.1016/j.enpol.2010.08.021

On the Theory of Dynamic Programming
journal, August 1952

Bellman, R.
Proceedings of the National Academy of Sciences, Vol. 38, Issue 8
DOI: 10.1073/pnas.38.8.716

Robust optimization ? methodology and applications
journal, May 2002

Ben-Tal, Aharon; Nemirovski, Arkadi
Mathematical Programming, Vol. 92, Issue 3
DOI: 10.1007/s101070100286

Robust Optimization for Transmission Expansion Planning: Minimax Cost vs. Minimax Regret
journal, November 2014

Chen, Bokan; Wang, Jianhui; Wang, Lizhi
IEEE Transactions on Power Systems, Vol. 29, Issue 6
DOI: 10.1109/TPWRS.2014.2313841

Deregulation, privatization, and competition: transmission planning under uncertainty
journal, May 1999

De la Torre, T.; Feltes, J. W.; Gomez San Roman, T.
IEEE Transactions on Power Systems, Vol. 14, Issue 2
DOI: 10.1109/59.761866

Transmission network expansion planning under demand uncertainty and risk aversion
journal, January 2013

Delgado, Daniel; Claro, João
International Journal of Electrical Power & Energy Systems, Vol. 44, Issue 1
DOI: 10.1016/j.ijepes.2012.08.033

Electricity derivatives and risk management
journal, May 2006

Deng, S.; Oren, S.
Energy, Vol. 31, Issue 6-7
DOI: 10.1016/j.energy.2005.02.015

An Overview of Value at Risk
journal, February 1997

Duffie, Darrell; Pan, Jun
The Journal of Derivatives, Vol. 4, Issue 3
DOI: 10.3905/jod.1997.407971

Generation Capacity Expansion in a Risky Environment: A Stochastic Equilibrium Analysis
journal, December 2011

Ehrenmann, Andreas; Smeers, Yves
Operations Research, Vol. 59, Issue 6
DOI: 10.1287/opre.1110.0992

Risk aversion and CO2 regulatory uncertainty in power generation investment: Policy and modeling implications
journal, November 2010

Fan, Lin; Hobbs, Benjamin F.; Norman, Catherine S.
Journal of Environmental Economics and Management, Vol. 60, Issue 3
DOI: 10.1016/j.jeem.2010.08.001

Investment under market and climate policy uncertainty
journal, August 2008

Fuss, Sabine; Szolgayova, Jana; Obersteiner, Michael
Applied Energy, Vol. 85, Issue 8
DOI: 10.1016/j.apenergy.2008.01.005

Assessing the economic value of co-optimized grid-scale energy storage investments in supporting high renewable portfolio standards
journal, December 2016

Go, Roderick S.; Munoz, Francisco D.; Watson, Jean-Paul
Applied Energy, Vol. 183
DOI: 10.1016/j.apenergy.2016.08.134

Analysis of multi-pollutant policies for the U.S. power sector under technology and policy uncertainty using MARKAL
journal, December 2010

Hu, Ming-Che; Hobbs, Benjamin F.
Energy, Vol. 35, Issue 12
DOI: 10.1016/j.energy.2010.07.001

A portfolio risk analysis on electricity supply planning
journal, February 2008

Huang, Yun-Hsun; Wu, Jung-Hua
Energy Policy, Vol. 36, Issue 2
DOI: 10.1016/j.enpol.2007.10.004

Corporate control and real investment in incomplete markets
journal, May 2007

Hugonnier, Julien; Morellec, Erwan
Journal of Economic Dynamics and Control, Vol. 31, Issue 5
DOI: 10.1016/j.jedc.2006.09.001

Robust Transmission Network Expansion Planning With Uncertain Renewable Generation and Loads
journal, November 2013

Jabr, R. A.
IEEE Transactions on Power Systems, Vol. 28, Issue 4
DOI: 10.1109/TPWRS.2013.2267058

Modeling and solving a large-scale generation expansion planning problem under uncertainty
journal, November 2011

Jin, Shan; Ryan, Sarah M.; Watson, Jean-Paul
Energy Systems, Vol. 2, Issue 3-4
DOI: 10.1007/s12667-011-0042-9

Sustainable resource planning in energy markets
journal, November 2014

Kamalinia, Saeed; Shahidehpour, Mohammad; Wu, Lei
Applied Energy, Vol. 133
DOI: 10.1016/j.apenergy.2014.07.065

Investment Propensities under Carbon Policy Uncertainty
journal, January 2011

Kettunen, Janne; Bunn, Derek W.; Blyth, William
The Energy Journal, Vol. 32, Issue 1
DOI: 10.5547/ISSN0195-6574-EJ-Vol32-No1-4

Generation and Transmission Expansion Under Risk Using Stochastic Programming
journal, August 2007

Alvarez Lopez, Juan; Ponnambalam, Kumaraswamy; Quintana, VÍctor H.
IEEE Transactions on Power Systems, Vol. 22, Issue 3
DOI: 10.1109/TPWRS.2007.901741

Risk and uncertainty in power system planning
journal, April 1991

Merrill, Hyde M.; Wood, Allen J.
International Journal of Electrical Power & Energy Systems, Vol. 13, Issue 2
DOI: 10.1016/0142-0615(91)90030-Y

Risk aversion and technology mix in an electricity market
journal, November 2013

Meunier, Guy
Energy Economics, Vol. 40
DOI: 10.1016/j.eneco.2013.10.010

An Adjustable Robust Optimization Approach for Contingency-Constrained Transmission Expansion Planning
journal, July 2015

Moreira, Alexandre; Street, Alexandre; Arroyo, Jose M.
IEEE Transactions on Power Systems, Vol. 30, Issue 4
DOI: 10.1109/TPWRS.2014.2349031

Robust Optimization of Large-Scale Systems
journal, April 1995

Mulvey, John M.; Vanderbei, Robert J.; Zenios, Stavros A.
Operations Research, Vol. 43, Issue 2
DOI: 10.1287/opre.43.2.264

An Engineering-Economic Approach to Transmission Planning Under Market and Regulatory Uncertainties: WECC Case Study
journal, January 2014

Munoz, Francisco D.; Hobbs, Benjamin F.; Ho, Jonathan L.
IEEE Transactions on Power Systems, Vol. 29, Issue 1
DOI: 10.1109/TPWRS.2013.2279654

Endogenous Assessment of the Capacity Value of Solar PV in Generation Investment Planning Studies
journal, October 2015

Munoz, Francisco D.; Mills, Andrew D.
IEEE Transactions on Sustainable Energy, Vol. 6, Issue 4
DOI: 10.1109/TSTE.2015.2456019

Approximations in power transmission planning: implications for the cost and performance of renewable portfolio standards
journal, January 2013

Munoz, Francisco D.; Sauma, Enzo E.; Hobbs, Benjamin F.
Journal of Regulatory Economics, Vol. 43, Issue 3
DOI: 10.1007/s11149-013-9209-8

Insufficient incentives for investment in electricity generations
journal, December 2004

Neuhoff, Karsten; De Vries, Laurens
Utilities Policy, Vol. 12, Issue 4
DOI: 10.1016/j.jup.2004.06.002

Economic Analysis of Transmission Expansion Planning With Price-Responsive Demand and Quadratic Losses by Successive LP
journal, March 2016

Ozdemir, Ozge; Munoz, Francisco D.; Ho, Jonathan L.
IEEE Transactions on Power Systems, Vol. 31, Issue 2
DOI: 10.1109/TPWRS.2015.2427799

The Economic Effects of Interregional Trading of Renewable Energy Certificates in the U.S. WECC
journal, October 2016

Perez, Andres P.; Sauma, Enzo E.; Munoz, Francisco D.
The Energy Journal, Vol. 37, Issue 4
DOI: 10.5547/01956574.37.4.aper

A time consistent risk averse three-stage stochastic mixed integer optimization model for power generation capacity expansion
journal, January 2016

Pisciella, P.; Vespucci, M. T.; Bertocchi, M.
Energy Economics, Vol. 53
DOI: 10.1016/j.eneco.2014.07.016

If you build it, he will come: Anticipative power transmission planning
journal, March 2013

Pozo, David; Contreras, Javier; Sauma, Enzo
Energy Economics, Vol. 36
DOI: 10.1016/j.eneco.2012.12.007

A Three-Level Static MILP Model for Generation and Transmission Expansion Planning
journal, February 2013

Pozo, David; Sauma, Enzo E.; Contreras, Javier
IEEE Transactions on Power Systems, Vol. 28, Issue 1
DOI: 10.1109/TPWRS.2012.2204073

Optimization of conditional value-at-risk
journal, January 2000

Rockafellar, R. Tyrrell; Uryasev, Stanislav
The Journal of Risk, Vol. 2, Issue 3
DOI: 10.21314/JOR.2000.038

Optimal wind power deployment in Europe—A portfolio approach
journal, July 2010

Roques, Fabien; Hiroux, Céline; Saguan, Marcelo
Energy Policy, Vol. 38, Issue 7
DOI: 10.1016/j.enpol.2009.07.048

Fuel mix diversification incentives in liberalized electricity markets: A Mean–Variance Portfolio theory approach
journal, July 2008

Roques, Fabien A.; Newbery, David M.; Nuttall, William J.
Energy Economics, Vol. 30, Issue 4
DOI: 10.1016/j.eneco.2007.11.008

Robust transmission expansion planning
journal, April 2015

Ruiz, C.; Conejo, A. J.
European Journal of Operational Research, Vol. 242, Issue 2
DOI: 10.1016/j.ejor.2014.10.030

Proactive planning and valuation of transmission investments in restructured electricity markets
journal, September 2006

Sauma, Enzo E.; Oren, Shmuel S.
Journal of Regulatory Economics, Vol. 30, Issue 3
DOI: 10.1007/s11149-006-9003-y

Short-term uncertainty in long-term energy system models — A case study of wind power in Denmark
journal, May 2015

Seljom, Pernille; Tomasgard, Asgeir
Energy Economics, Vol. 49
DOI: 10.1016/j.eneco.2015.02.004

The economics of planning electricity transmission to accommodate renewables: Using two-stage optimisation to evaluate flexibility and the cost of disregarding uncertainty
journal, November 2012

van der Weijde, Adriaan Hendrik; Hobbs, Benjamin F.
Energy Economics, Vol. 34, Issue 6
DOI: 10.1016/j.eneco.2012.02.015

Market completeness: How options affect hedging and investments in the electricity sector
journal, July 2010

Willems, Bert; Morbee, Joris
Energy Economics, Vol. 32, Issue 4
DOI: 10.1016/j.eneco.2009.10.019

Stochastic and Risk Management Models and Solution Algorithm for Natural Gas Transmission Network Expansion and LNG Terminal Location Planning
journal, June 2010

Zheng, Qipeng P.; Pardalos, Panos M.
Journal of Optimization Theory and Applications, Vol. 147, Issue 2
DOI: 10.1007/s10957-010-9725-y

Works referencing / citing this record:

Do unit commitment constraints affect generation expansion planning? A scalable stochastic model
journal, January 2019

Schwele, Anna; Kazempour, Jalal; Pinson, Pierre
Energy Systems, Vol. 11, Issue 2
DOI: 10.1007/s12667-018-00321-z

Similar Records in DOE PAGES and OSTI.GOV collections:

A Risk-Averse Approach for Distribution Grid Expansion Planning

Journal Article Moreira, Alexandre ; Heleno, Miguel ; Valenzuela, Alan - Energies

Recent episodes of natural disasters have challenged the resilience of power grids. Adequate distribution grid planning that properly captures the risk aversion of the utility system planner is a key factor to increase the flexibility of distribution networks to circumvent these events. In this paper, we propose a methodology to determine the optimal portfolio of investments in lines and storage devices in order to minimize a convex combination between expected value and CVaR of operational costs, including energy not served, while taking into account the multistage nature of the energy storage management within this context. While the expected value ofmore »« less
https://doi.org/10.3390/en14248482

Full Text Available
Risk-Averse Bi-Level Stochastic Network Interdiction Model for Cyber-Security Risk Management

Journal Article Bhuiyan, Tanveer H. ; Medal, Hugh ; Nandi, Apurba K. ; ... - International Journal of Critical Infrastructure Protection

Security of cyber networks is crucial; recent severe cyber-attacks have had a devastating effect on many large organizations. The attack graph, which maps the potential attack paths of a cyber network, is a popular tool for analyzing cyber system vulnerability. In this study, we propose a bi-level stochastic network interdiction model on an attack graph to enable a risk-averse, resource constrained cyber network defender to optimally deploy security countermeasures that protect against attackers with an uncertain budget. This risk- averse conditional-value-at-risk (CVaR) model minimizes a weighted sum of the expected maximum loss over all scenarios and the expected maximum lossmore »« less
https://doi.org/10.1016/j.ijcip.2021.100408
A Risk-Averse Conic Model for Networked Microgrids Planning With Reconfiguration and Reorganizations

Journal Article Cao, Xiaoyu ; Wang, Jianxue ; Wang, Jianhui ; ... - IEEE Transactions on Smart Grid

The advanced switching techniques enable the topology reconfiguration of microgrids (MGs) in active distribution network. Here, we enhance and generalize the traditional reconfiguration strategy resorting to the concept of “dynamic MGs” (i.e., the reorganization of MGs boundaries), to achieve a higher operational feasibility against the emergency islandings. Also, a risk-averse two-stage mixed integer conic program model is presented to support the networked MGs planning with generalized reconfiguration decisions. The MGs capacity expansion and seasonal reconfiguration decisions are made in the first stage, and validated under stochastic islanding scenarios in the second stage, where the network operations are captured by amore »« less
https://doi.org/10.1109/tsg.2019.2927833

Full Text Available
Resource Adequacy in Electricity Markets With Renewable Energy

Journal Article Kwon, Jonghwan ; Zhou, Zhi ; Levin, Todd ; ... - IEEE Transactions on Power Systems

This paper presents a market-based resource adequacy assessment framework to analyze the system generation portfolio that results in a competitive market environment. In particular, we apply the modeling framework to investigate the impact of high penetration levels of variable renewable energy resources and different market designs on achieving resource adequacy. The model captures the strategic capacity investment and retirement decision-making of profit-maximizing generation companies. In contrast to many previous studies, this paper considers markets for capacity, energy, and reserve products in detail; thus, the modeling framework allows improved analysis of generation expansion and revenue sufficiency in a competitive market environment.more »« less
Cited by 13
https://doi.org/10.1109/TPWRS.2019.2930934

Full Text Available
Electric Grid Expansion Planning with High Levels of Variable Generation

Technical Report Hadley, Stanton W. ; You, Shutang ; Shankar, Mallikarjun ; ...

Renewables are taking a large proportion of generation capacity in U.S. power grids. As their randomness has increasing influence on power system operation, it is necessary to consider their impact on system expansion planning. To this end, this project studies the generation and transmission expansion co-optimization problem of the US Eastern Interconnection (EI) power grid with a high wind power penetration rate. In this project, the generation and transmission expansion problem for the EI system is modeled as a mixed-integer programming (MIP) problem. This study analyzed a time series creation method to capture the diversity of load and wind powermore »« less
https://doi.org/10.2172/1238017

Full Text Available

Similar Records

Title: Does Risk Aversion Affect Transmission and Generation Planning? A Western North America Case Study

Abstract

Citation Formats

A Risk-Based Approach for Transmission Network Expansion Planning Under Deliberate Outages journal, August 2010

Impact of public policy uncertainty on renewable energy investment: Wind power and the production tax credit journal, December 2010

On the Theory of Dynamic Programming journal, August 1952

Robust optimization ? methodology and applications journal, May 2002

Robust Optimization for Transmission Expansion Planning: Minimax Cost vs. Minimax Regret journal, November 2014

Deregulation, privatization, and competition: transmission planning under uncertainty journal, May 1999

Transmission network expansion planning under demand uncertainty and risk aversion journal, January 2013

Electricity derivatives and risk management journal, May 2006

An Overview of Value at Risk journal, February 1997

Generation Capacity Expansion in a Risky Environment: A Stochastic Equilibrium Analysis journal, December 2011

Risk aversion and CO2 regulatory uncertainty in power generation investment: Policy and modeling implications journal, November 2010

Investment under market and climate policy uncertainty journal, August 2008

Assessing the economic value of co-optimized grid-scale energy storage investments in supporting high renewable portfolio standards journal, December 2016

Analysis of multi-pollutant policies for the U.S. power sector under technology and policy uncertainty using MARKAL journal, December 2010

A portfolio risk analysis on electricity supply planning journal, February 2008

Corporate control and real investment in incomplete markets journal, May 2007

Robust Transmission Network Expansion Planning With Uncertain Renewable Generation and Loads journal, November 2013

Modeling and solving a large-scale generation expansion planning problem under uncertainty journal, November 2011

Sustainable resource planning in energy markets journal, November 2014

Investment Propensities under Carbon Policy Uncertainty journal, January 2011

Generation and Transmission Expansion Under Risk Using Stochastic Programming journal, August 2007

Risk and uncertainty in power system planning journal, April 1991

Risk aversion and technology mix in an electricity market journal, November 2013

An Adjustable Robust Optimization Approach for Contingency-Constrained Transmission Expansion Planning journal, July 2015

Robust Optimization of Large-Scale Systems journal, April 1995

An Engineering-Economic Approach to Transmission Planning Under Market and Regulatory Uncertainties: WECC Case Study journal, January 2014

Endogenous Assessment of the Capacity Value of Solar PV in Generation Investment Planning Studies journal, October 2015

Approximations in power transmission planning: implications for the cost and performance of renewable portfolio standards journal, January 2013

Insufficient incentives for investment in electricity generations journal, December 2004

Economic Analysis of Transmission Expansion Planning With Price-Responsive Demand and Quadratic Losses by Successive LP journal, March 2016

The Economic Effects of Interregional Trading of Renewable Energy Certificates in the U.S. WECC journal, October 2016

A time consistent risk averse three-stage stochastic mixed integer optimization model for power generation capacity expansion journal, January 2016

If you build it, he will come: Anticipative power transmission planning journal, March 2013

A Three-Level Static MILP Model for Generation and Transmission Expansion Planning journal, February 2013

Optimization of conditional value-at-risk journal, January 2000

Optimal wind power deployment in Europe—A portfolio approach journal, July 2010

Fuel mix diversification incentives in liberalized electricity markets: A Mean–Variance Portfolio theory approach journal, July 2008

Robust transmission expansion planning journal, April 2015

Proactive planning and valuation of transmission investments in restructured electricity markets journal, September 2006

Short-term uncertainty in long-term energy system models — A case study of wind power in Denmark journal, May 2015

The economics of planning electricity transmission to accommodate renewables: Using two-stage optimisation to evaluate flexibility and the cost of disregarding uncertainty journal, November 2012

Market completeness: How options affect hedging and investments in the electricity sector journal, July 2010

Stochastic and Risk Management Models and Solution Algorithm for Natural Gas Transmission Network Expansion and LNG Terminal Location Planning journal, June 2010

Do unit commitment constraints affect generation expansion planning? A scalable stochastic model journal, January 2019

A Risk-Based Approach for Transmission Network Expansion Planning Under Deliberate Outages
journal, August 2010

Impact of public policy uncertainty on renewable energy investment: Wind power and the production tax credit
journal, December 2010

On the Theory of Dynamic Programming
journal, August 1952

Robust optimization ? methodology and applications
journal, May 2002

Robust Optimization for Transmission Expansion Planning: Minimax Cost vs. Minimax Regret
journal, November 2014

Deregulation, privatization, and competition: transmission planning under uncertainty
journal, May 1999

Transmission network expansion planning under demand uncertainty and risk aversion
journal, January 2013

Electricity derivatives and risk management
journal, May 2006

An Overview of Value at Risk
journal, February 1997

Generation Capacity Expansion in a Risky Environment: A Stochastic Equilibrium Analysis
journal, December 2011

Risk aversion and CO2 regulatory uncertainty in power generation investment: Policy and modeling implications
journal, November 2010

Investment under market and climate policy uncertainty
journal, August 2008

Assessing the economic value of co-optimized grid-scale energy storage investments in supporting high renewable portfolio standards
journal, December 2016

Analysis of multi-pollutant policies for the U.S. power sector under technology and policy uncertainty using MARKAL
journal, December 2010

A portfolio risk analysis on electricity supply planning
journal, February 2008

Corporate control and real investment in incomplete markets
journal, May 2007

Robust Transmission Network Expansion Planning With Uncertain Renewable Generation and Loads
journal, November 2013

Modeling and solving a large-scale generation expansion planning problem under uncertainty
journal, November 2011

Sustainable resource planning in energy markets
journal, November 2014

Investment Propensities under Carbon Policy Uncertainty
journal, January 2011

Generation and Transmission Expansion Under Risk Using Stochastic Programming
journal, August 2007

Risk and uncertainty in power system planning
journal, April 1991

Risk aversion and technology mix in an electricity market
journal, November 2013

An Adjustable Robust Optimization Approach for Contingency-Constrained Transmission Expansion Planning
journal, July 2015

Robust Optimization of Large-Scale Systems
journal, April 1995

An Engineering-Economic Approach to Transmission Planning Under Market and Regulatory Uncertainties: WECC Case Study
journal, January 2014

Endogenous Assessment of the Capacity Value of Solar PV in Generation Investment Planning Studies
journal, October 2015

Approximations in power transmission planning: implications for the cost and performance of renewable portfolio standards
journal, January 2013

Insufficient incentives for investment in electricity generations
journal, December 2004

Economic Analysis of Transmission Expansion Planning With Price-Responsive Demand and Quadratic Losses by Successive LP
journal, March 2016

The Economic Effects of Interregional Trading of Renewable Energy Certificates in the U.S. WECC
journal, October 2016

A time consistent risk averse three-stage stochastic mixed integer optimization model for power generation capacity expansion
journal, January 2016

If you build it, he will come: Anticipative power transmission planning
journal, March 2013

A Three-Level Static MILP Model for Generation and Transmission Expansion Planning
journal, February 2013

Optimization of conditional value-at-risk
journal, January 2000

Optimal wind power deployment in Europe—A portfolio approach
journal, July 2010

Fuel mix diversification incentives in liberalized electricity markets: A Mean–Variance Portfolio theory approach
journal, July 2008

Robust transmission expansion planning
journal, April 2015

Proactive planning and valuation of transmission investments in restructured electricity markets
journal, September 2006

Short-term uncertainty in long-term energy system models — A case study of wind power in Denmark
journal, May 2015

The economics of planning electricity transmission to accommodate renewables: Using two-stage optimisation to evaluate flexibility and the cost of disregarding uncertainty
journal, November 2012

Market completeness: How options affect hedging and investments in the electricity sector
journal, July 2010

Stochastic and Risk Management Models and Solution Algorithm for Natural Gas Transmission Network Expansion and LNG Terminal Location Planning
journal, June 2010

Do unit commitment constraints affect generation expansion planning? A scalable stochastic model
journal, January 2019