# Browsing by Subject "Bilevel programming"

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Item A bilevel modeling methodology to optimize the value of distributed energy resources in electric transmission and distribution systems(2023-12) Laws, Nicholas D.; Chen, Dongmei, Ph.D.; Webber, Michael E., 1971-; Beaman, Joseph; Warren, Adam; Djurdjanovic, DraganShow more The transition of electricity generation from a centralized structure to a more distributed framework in grids across the globe calls for new methods to appropriately value the services that distributed energy resources (DER) can provide. Current methods for valuing DER services account for the grid operator perspective but typically ignore DER owner objectives and constraints. The goal of this dissertation is to develop new methods for valuing distributed energy resources in electricity transmission and distribution systems, with a particular focus on accounting for multiple perspectives. This goal is achieved by developing a new linearization technique for bilevel optimization problems that allows modeling energy system optimization problems at scales that matter. The linearization technique is leveraged to develop a new framework for valuing distributed energy resources in transmission and distribution systems. The proposed framework allows for competing perspectives to be modeled. Furthermore, a new method for creating synthetic electricity price scenarios is developed and its value demonstrated in a stochastic optimization framework. The current model for valuing electricity generation in deregulated energy markets determines prices from an optimal power flow problem whose objective is to maximize the social welfare. This work develops a general framework for determining the spatiotemporal value of DER that includes DER owner objectives in concert with maximizing the social welfare. The framework is built in a bilevel program that allows for incorporation of any optimal power flow model as well as replacing the social welfare objective with any value function, such as the objective of a profit-oriented DER aggregator. Special attention is placed on linearizing bilinear products of dispatch and price variables such that the framework can scale to large network models. The general framework is leveraged to develop a method to assess the techno-economic potential of DER for distribution system upgrade deferrals. The state-of-the-art for valuing DER for distribution system upgrade deferrals is advanced by accounting for DER owner objectives and constraints in concert with system operator goals and constraints. A use-case shows how the framework can be leveraged to value DER for non-wires alternatives. Comparing life cycle costs over 20 years for the system planner, the results show that by valuing DER for non-wires alternatives the DSO can avoid upgrading most of the overloaded components as well as achieve a net present value of nearly $3M relative to the cost of the traditional upgrades. The results also show that the DSO can achieve an additional $1M in net present value when valuing privately owned DER relative to a scenario with utility owned batteries. Finally, recognizing the need for better representation of the uncertainty in electricity market prices in energy system models, a novel method for generating realistic, synthetic electricity prices is developed. Several weaknesses in the state-of-the-art for stochastic price generation methods are addressed: (1) better characterization of daily and weekly trends is achieved by replacing the mean-reversion component of the stochastic differential equation with an autoregressive integrated moving average process; (2) the conditional probability of consecutive price-spikes, or “jumps”, is captured for the first time by replacing the traditional Poisson process with a generalized point process inspired by brain neuron models; and (3) a more realistic model variance is achieved by replacing the static empirical variance with a Markov process. The new methodology allows researchers and practitioners to evaluate bidding strategies for DER in electricity markets. In addition to accurately modeling historical trends, market behavior that has not been observed can be created by tuning model parameters. The method is exercised with electricity prices from the US ERCOT market and a use-case example is provided for bidding an energy storage unit into the ERCOT market. The results show that accounting for price uncertainty via the synthetic time-series can increase market profits by as much as 47% over a bidding strategy that relies on a deterministic price forecast.Show more Item Natural gas market applications of multi-agent optimization(2022-05-09) Calci, Baturay; Leibowicz, Benjamin D.; Bard, Jonathan F.; Hasenbein, John J; Baldick, RossShow more 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.Show more Item Optimization approaches for energy infrastructure network design(2021-05-08) Geetha Jayadev, Gopika; Leibowicz, Benjamin D.; Bard, Jonathan F.; Kutanoglu, Erhan; Rai, VarunShow more This dissertation focuses on applying operations research techniques to problems arising in the energy sector. The work presented attempts to push the existing frontiers in energy optimization by adding to an existing open-source framework in electricity infrastructure optimization and applying bilevel programming to relatively unexplored applications in natural gas market modeling. This dissertation consists of five chapters. Chapter 1 provides an introduction encompassing a brief description and motivation for the dissertation’s work. The future development of the U.S. electricity sector will be shaped by technological, economic, and policy drivers whose trajectories are highly uncertain. Chapter 2 describes an optimization model for the integrated generation and transmission system in the continental U.S., which is used to explore electricity infrastructure pathways from the present through 2050. By comparing and contrasting results from numerous scenarios and sensitivity settings, we ultimately affirm five key policy-relevant insights. (1) U.S. electricity can be substantially decarbonized at a modest cost, but complete decarbonization is very costly. (2) Significant expansion of solar PV and wind to combine for at least 40% of the generation mix by 2050 is fairly certain. However, solar PV and battery storage are more affected by economic and policy assumptions than wind. (3) Investments in long-distance transmission are minimal, while investments in battery storage are much more significant under a wide range of assumptions. (4) Optimal solutions include large investments in natural gas capacity, but gas capacity utilization rates decline steadily and significantly. (5) Cost structures shift away from operating expenditures and toward capital expenditures, especially under climate policy. We conclude our article by discussing the policy implications of these findings. Chapter 3 presents a bilevel programming model to aid decision-making in natural gas markets where multiple autonomous agents interact strategically, possibly with conflicting interests. In the proposed model, a liquefied natural gas (LNG) operator is the leader, and a natural gas (NG) producer is the follower. The LNG operator attempts to optimally locate LNG export terminals, purchase gas from the NG producer, and export it as LNG. The NG producer aims to optimize production, pipeline investments, and sales to domestic consumers and the LNG operator. To solve the bilevel problem, we first reformulate it as a single-level problem by exploiting the lower-level problem’s convexity. Then, we use disjunctive reformulations of complementarity constraints and piecewise linear approximations of objective function terms to convert the problem into a convex quadratic mixed-integer program (QMIP). Computational experiments confirm that the QMIP is tractable and can be solved efficiently. We apply our bilevel framework to a case study of the Gulf-Southwest region of the United States and evaluate several decision-making scenarios. The scenario results emphasize the importance of using the bilevel methodology to anticipate the effects of new LNG export facilities on NG prices across the domestic gas network. Adding these large gas-consuming facilities at specific locations puts upward pressure on domestic gas prices, although this is somewhat mitigated by the NG producer’s optimal production response to the increased demand. Chapter 4 presents a risk-based integer bilevel programming model that considers two players in a leader-follower setting, where each tries to maximize their individual profits. The leader or manufacturer makes decisions pertaining to facility location and the amount of raw material to buy from the supplier. The supplier or follower decides how much raw material to produce. Both players face demand uncertainty in their respective markets while making investment, production, and sales decisions. We develop models for optimal decision-making under risk-neutral and risk-averse objectives and explore the effects of different risk attitudes on the problem and its optimal solution. These problems are hard to solve as the number of scenarios increase, and solving them generally involves developing customized algorithms. To find feasible solutions to the resulting stochastic bilevel problem, an algorithm is developed that iteratively solves a restricted version of the problem to obtain feasible solutions to the original problem. Extensive computational experiments are performed to evaluate algorithmic tractability and solution quality. The proposed algorithm is able to find high-quality feasible solutions to the bilevel problem in a very reasonable amount of time, and the attained solutions are found to be close to the optimal solution. The methodology is demonstrated with an example that addresses strategic issues in the natural gas market. The model considers two players, the liquefied natural gas (LNG) operator or leader and the natural gas (NG) producer or follower acting in a leader-follower setting. The LNG operator makes decisions pertaining to the locations of LNG facilities and the amount of gas to buy from the producer. The follower decides how much gas to produce. Both players face demand uncertainty in their respective markets and make investments, production, and sales decisions. The case study explores the Gulf-Southwest region of the United States and demonstrates the impact of the risk-averse decision-making approach on investment and operational decisions. Chapter 5 concludes this dissertation by summarizing the most important findings from each study and outlining valuable directions for future research.Show more