(661e) Long-Term Expansion Planning of an Integrated Power and Energy Carrier Generation System: A Tailored Decomposition Algorithm

Integrating a power system with high penetration of renewables and the supply chain of liquid energy carriers (ECs) provides an appealing framework to reduce power curtailment when the supply exceeds the load demand. At the same time, an integrated design could reduce the system's requirements for battery storage and power transmission. Furthermore, the ECs can be transported from renewables' favourable sub-regions to unfavourable ones,¹ complementing the direct power transmission and the lines' expansion. Notably, technology learning curves greatly influence the economic viability of an EC supply chain, which requires long-term expansion planning.

Common formulations for the long-term expansion planning of power systems involve mix-integer linear programming (MILP) models with several millions of variables.² Integrating the supply chain of ECs into the model leads to computationally intractable problems. For instance, the MILP should capture: (i) the sub-regional hourly variability of the renewable energy sources, load demand, ramp-up/ramp-down of firm power generators, (ii) the power transmission, (iii) the daily operation of the ECs supply chain, and (iv) the sub-regional annual investment decisions. Several methods have received significant attention to circumvent the latter challenges based on relaxation and decomposition strategies, such as Benders decomposition³ and the rolling horizon method,⁴ among others.

Benders decomposition divides the original formulation into a master problem and one or several subproblems. The master problem includes the investment decisions, while the subproblem(s) consider the operating decisions. The solution strategy involves the iterative introduction of cuts to the master problem obtained from the subproblem(s), narrowing the search space until convergence is achieved. In contrast, in the rolling horizon algorithm, a given number of periods are considered to make investment decisions. The information of the investment decisions rolls ahead to investigate a new set of periods until the entire horizon is explored. Finally, other commonly adopted strategies simplify the reduction of the temporal and spatial representation, and thus, decrease the computational effort.² These include the use of representative days for the temporal dimension and the vector averaged data of aggregated sites for the renewables' availability for the spatial dimension.

Despite the advances discussed above, tailored solution strategies can further accelerate the solution process for such long-term expansion planning models. In this study, we propose a tailored decomposition algorithm that combines Benders decomposition with a tailored elastic horizon approach to address this challenge. At the same time, to demonstrate the suggested decomposition algorithm, we introduce an MILP for the long-term expansion planning of power generation coupled with a methanol supply chain. The geographical scope of the model is the State of Texas, divided into 5 sub-regions. The time horizon spans from 2020 to 2050, with a multi-scale nature, i.e., each year is modeled using representative days with hourly resolution . The hourly power load, renewables availability, and methanol demand for each sub-region are given, along with the capacities and lifetime of the existing power and methanol production facilities. Furthermore, the annual renewable generation quota and carbon tax are also given. The proposed MILP model minimizes the system's total cost, while the model's decisions comprise power generation and storage, transmission lines expansion, and methanol production, storage, and transportation. Several case studies show that the proposed scheme significantly reduces the computational cost of the solution process. Furthermore, the gains in computational time allow expanding the spatial and temporal representation and enlarging the model scope to consider additional ECs and services.

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