An exact solution method for binary equilibrium problems with compensation and the power market uplift problem

We propose a novel method to find Nash equilibria in games with binary decision variables by including compensation payments and incentive-compatibility constraints from non-cooperative game theory directly into an optimization framework in lieu of using first order conditions of a linearization, or relaxation of integrality conditions. The reformulation offers a new approach to obtain and interpret dual variables to binary constraints using the benefit or loss from deviation rather than marginal relaxations. The method endogenizes the trade-off between overall (societal) efficiency and compensation payments necessary to align incentives of individual players. We provide existence results and conditions under which this problem can be solved as a mixed-binary linear program. We apply the solution approach to a stylized nodal power-market equilibrium problem with binary on-off decisions. This illustrative example shows that our approach yields an exact solution to the binary Nash game with compensation. We compare different implementations of actual market rules within our model, in particular constraints ensuring non-negative profits (no-loss rule) and restrictions on the compensation payments to non-dispatched generators. We discuss the resulting equilibria in terms of overall welfare, efficiency, and allocational equity

SOLVING TWO-LEVEL OPTIMIZATION PROBLEMS WITH APPLICATIONS TO ROBUST DESIGN AND ENERGY MARKETS

This dissertation provides efficient techniques to solve two-level optimization problems. Three specific types of problems are considered. The first problem is robust optimization, which has direct applications to engineering design. Traditionally robust optimization problems have been solved using an inner-outer structure, which can be computationally expensive. This dissertation provides a method to decompose and solve this two-level structure using a modified Benders decomposition. This gradient-based technique is applicable to robust optimization problems with quasiconvex constraints and provides approximate solutions to problems with nonlinear constraints. The second types of two-level problems considered are mathematical and equilibrium programs with equilibrium constraints. Their two-level structure is simplified using Schur's decomposition and reformulation schemes for absolute value functions. The resulting formulations are applicable to game theory problems in operations research and economics. The third type of two-level problem studied is discretely-constrained mixed linear complementarity problems. These are first formulated into a two-level mathematical program with equilibrium constraints and then solved using the aforementioned technique for mathematical and equilibrium programs with equilibrium constraints. The techniques for all three problems help simplify the two-level structure into one level, which helps gain numerical and application insights. The computational effort for solving these problems is greatly reduced using the techniques in this dissertation. Finally, a host of numerical examples are presented to verify the approaches. Diverse applications to economics, operations research, and engineering design motivate the relevance of the novel methods developed in this dissertation

Infrastructure investments under uncertainty with the possibility of retrofit : theory and simulations

Investments in large, long-lived, energy-intensive infrastructure investments using fossil fuels increase longer-term energy use and greenhouse gas emissions, unless the plant is shut down early or undergoes costly retrofit later. These investments will depend on expectations of retrofit costs and future energy costs, including energy cost increases from tighter controls on carbon emissions. Simulation analysis shows that the retrofit option can significantly reduce anticipated future energy consumption as of the time of initial investment, and total future energy plus retrofit costs. The more uncertain are the costs, the greater the value of this option. However, the future retrofit option also induces more energy-intensive infrastructure choices, partly offsetting the direct effect of having the option on anticipated energy use. Efficient, forward-looking infrastructure investments have high potential for reducing long-term energy consumption. Particularly if energy prices are expected to rise, however, the potential for reduced energy consumption will be eroded if expectations of energy prices do not include environmental costs or future retrofit possibilities and technologies are not adequately developed.Energy Production and Transportation,Climate Change Economics,Climate Change Mitigation and Green House Gases,Environment and Energy Efficiency,Energy and Environment

Emerging Themes and Future Directions of Multi-Sector Nexus Research and Implementation

Water, energy, and food are all essential components of human societies. Collectively, their respective resource systems are interconnected in what is called the “nexus”. There is growing consensus that a holistic understanding of the interdependencies and trade-offs between these sectors and other related systems is critical to solving many of the global challenges they present. While nexus research has grown exponentially since 2011, there is no unified, overarching approach, and the implementation of concepts remains hampered by the lack of clear case studies. Here, we present the results of a collaborative thought exercise involving 75 scientists and summarize them into 10 key recommendations covering: the most critical nexus issues of today, emerging themes, and where future efforts should be directed. We conclude that a nexus community of practice to promote open communication among researchers, to maintain and share standardized datasets, and to develop applied case studies will facilitate transparent comparisons of models and encourage the adoption of nexus approaches in practice

Emerging Themes and Future Directions of Multi-Sector Nexus Research and Implementation

Water, energy, and food are all essential components of human societies. Collectively, their respective resource systems are interconnected in what is called the “nexus”. There is growing consensus that a holistic understanding of the interdependencies and trade-offs between these sectors and other related systems is critical to solving many of the global challenges they present. While nexus research has grown exponentially since 2011, there is no unified, overarching approach, and the implementation of concepts remains hampered by the lack of clear case studies. Here, we present the results of a collaborative thought exercise involving 75 scientists and summarize them into 10 key recommendations covering: the most critical nexus issues of today, emerging themes, and where future efforts should be directed. We conclude that a nexus community of practice to promote open communication among researchers, to maintain and share standardized datasets, and to develop applied case studies will facilitate transparent comparisons of models and encourage the adoption of nexus approaches in practice

Ambiguities and Nonmonotonicities under Prosumer Power

Prosumers adopt distributed energy resources (DER) to cover part of their own consumption and to sell surplus energy. Although individual prosumers are too dispersed to exert operational market power, they may collectively hold a strategic advantage over conventional generation in selecting DER capacity via aggregators. We devise a bilevel model to examine DER capacity sizing by a collective prosumer as a Stackelberg leader in an electricity industry where conventional generation may exert market power in operations. At the upper level, the prosumer chooses DER capacity in anticipation of lower-level operations by conventional generation and DER output. We demonstrate that exertion of market power in operations by conventional generation and the marginal cost of conventional generation affect DER investment by the prosumer in a nonmonotonic manner. Intuitively, in an industry where conventional generation exerts market power in operations similar to a monopoly (MO), the prosumer invests in more DER capacity than under perfectly competitive operations (PC) to take advantage of a high market-clearing price. However, if the marginal cost of conventional generation is high enough, then this intuitive result is reversed as the prosumer adopts more DER capacity under PC than under MO. This is because the high marginal cost of conventional generation prevents the market-clearing price from decreasing, thereby allowing for higher prosumer revenues. Moreover, competition relieves the chokehold on consumption under MO, which further incentivises the prosumer to expand DER capacity to capture market share. We prove the existence of a critical threshold for the marginal cost of conventional generation that leads to this counterintuitive result. Finally, we propose a countervailing regulatory mechanism that yields welfare-enhancing DER investment even in deregulated electricity industries.Peer reviewe

Multimodal Transportation Flows in Energy Networks with an Application to Crude Oil Markets

Abstract Network models of energy markets have been beneficial for analyses and decision-making to tackle challenges related to the production, distribution and consumption of energy in its various forms. Despite the growing awareness of environmental and safety impacts of fuel transfer, such as emissions, spills and other harmful effects, existing energy models for various types of networks are yet to fully capture modal distinctions which are relevant to providing pathways to limiting these impacts. To address this deficit in detailed multimodal analyses, we have built on recent work to develop a partial-equilibrium model that incorporates the representation of multimodal fuel transfer within energy networks. In a novel application to the North American crude oil market, we also demonstrate that our model is a useful tool for exploring avenues for reducing the risks of light and heavy crude oil transportation across this region. The results we obtain indicate that a combined strategy of rail loading restrictions, pipeline deployments and a discontinuation of the oil export ban is most effective in reducing the transportation of crude oil by rail and thereby mitigating the associated risks