Natural gas market applications of multi-agent optimization




Calci, Baturay

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In today's energy climate in the United States (U.S.), it is hard to overestimate the importance of understanding the natural gas markets and how they interact with other energy systems in the light of the facts that more electricity is generated from natural gas than any other source¹, natural gas is used by the most households for residential heating², and current natural gas production levels in the U.S. are at an all time high³. There has been a lively discussion both in the academic literature and in the energy industry as to what the role of natural gas will be in our energy climate going forward, or whether it would be a bridge fuel to a carbon neutral future. To this end, many researchers have developed various models to understand natural gas systems where multiple agents such as natural gas producers, pipeline operators, and liquefied natural gas (LNG) exporters interact, sometimes with conflicting objectives. Models have also been developed to represent how natural gas players interact with the electricity markets to assess the implications of various scenarios. Two of the many approaches used in these contexts are mixed complementarity problem-based modeling and bilevel programming. The former represents a system where all players are in an equilibrium, simultaneously maximizing their profits. In the latter, players interact in a sequential manner where a follower optimizes based on the actions of the leader, and the leader optimizes knowing its actions will affect the follower's decisions, which in turn affect the leader's own objective. This dissertation focuses on natural gas market modeling applications between different players using these two modeling paradigms. It also presents novel approaches to such models by rigorously working on incorporation of these approaches into optimization problems, and conducts insightful analyses on the future of natural gas and electricity markets and infrastructure under various scenarios. Chapter 2 of this dissertation builds a natural gas mixed complementarity model for North American markets that incorporates endogenous capacity decisions of six strategically interacting players in nine regions that also trade with two LNG demand markets. This model is solved by coupling Karush-Kuhn-Tucker (KKT) conditions of all underlying optimization problems with market clearing constraints, which collectively represent the equilibrium of the system. After parameterizing this model using publicly available sources, we run scenarios to assess how North American natural gas markets and infrastructure evolve under different levels of LNG demand, and restrictions on where new LNG infrastructure can be built. Our findings in this chapter are as follows. West coast of North America is well-positioned to supply the rising LNG demand by Asia/Pacific region with the help of scaled up natural gas production. When such infrastructure is not allowed on this coast, North American LNG exports largely shift to other regions rather than suffering an overall decline, making the total export volume robust to such infrastructure restrictions. We also find that high LNG demand puts upward pressure on regional prices in North America. In Chapter 3, the focus is on adding a learning-by-doing (LBD) component to mixed complementarity problems (MCPs) to represent endogenous technological change that allows the unit cost of production to decrease as a function of cumulative experience up until that point. As this component is known to introduce non-convexity in the formulation, we first develop a way of incorporating LBD into an optimization model so that convexity is preserved. Accordingly, corresponding KKT conditions remain necessary and sufficient for optimality. This allows us to incorporate LBD into larger MCP model. We show that under a monopolistic or oligopolistic market assumption, incorporating LBD into the cost of the revenue-generating activity along with a representation of a high enough initial knowledge stock results in a convex optimization problem. We provide closed-form expressions for the convexity-ensuring initial knowledge stock for two-period problems, and provide numerical approaches for ensuring convexity in generalized T-period problems. We then apply this formulation to the liquefier's problem in a simplified version of the natural gas market model presented in Chapter 2. Our results demonstrate that learning in liquefaction leads to increased LNG exports and puts an upward pressure on regional prices in North America. We also show that this effect gets stronger in the presence of higher learning rates and learning spillovers. Chapter 4 presents a bilevel model to represent the interaction between a profit maximizing natural gas producer in the upper-level and an aggregated electric utility solving a capacity expansion problem in the lower-level. We replace the lower-level problem with its KKT conditions to obtain a single-level problem in the form of a mathematical program with complementarity constraints (MPCC). We then convert this MPCC to a mixed integer linear program by replacing these KKT conditions with their disjunctive reformulations and linearizing the bilinear terms in the objective function by exploiting the strong duality condition of the lower-level problem. We analyze three groups of different scenarios, two regarding carbon policies, and one on the effects of strategic upper-level pricing. Our results show that carbon tax and carbon capture credits can result in non-monotonic effects in producer revenues and natural gas prices in this particular market context. We also observe that the effects of carbon capture credits can spill over to technologies without carbon capture due to strategically lowered gas prices, which enables the producer to induce investments in natural gas power plants with carbon capture and storage in the lower-level. Finally, we find that upper-level strategic pricing can lead to vastly different results in the decisions of the lower-level player, while the omission of strategic pricing from the model leads to both lower revenue for the producer and higher costs for the utility. Lastly, Chapter 5 concludes the dissertation by summarizing research contributions, key research findings, and presenting future research directions.


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