Optimal design of renewable energy systems with flexible inputs and outputs using the P‐graph framework

Abstract

The P-graph framework introduced by Friedler et al. (Chem Eng Sci. 1992;47:1973-1988) is a general mathematical methodology based on Graph Theory which is applicable to many process design problems. We propose an extension of the P-graph framework and the associated MILP model to account for operating units and systems where the inputs and outputs are variable. This is important because the P-graph framework in its current form would otherwise apply only to systems where the ratios of inputs to outputs are fixed. Consequently, it is difficult to apply the method to many emerging systems without the new mathematical model presented here. We discuss and develop the model in detail, and we then illustrate its application with the case study of an energy system. We establish a structure with optimal cost for a baseline heat demand, and we further explore how the energy system structure and the feedstocks change as the heat demand increases.

Evaluation of the Energy Supply Options of a Manufacturing Plant by the Application of the P-Graph Framework

“…The model complicates if ratios are arbitrary, but also subject to constraints, like minimum or maximum ratios. The P-Graph framework was extended to address such case of input scenarios [18], as the underlying MILP model of the system was extended with linear constraints to obtain an appropriate model. Note that the P-Graph framework may be itself capable of modeling such operating units with several material nodes and operating unit nodes.…”

Trends in sustainable process design—from molecular to global scales

“…Recent advancements also demonstrate the benefits of incorporating spatially and temporally explicit models for the design of synthetic natural gas supply chains [36], biomass value chains with multifeedstock and multivector energy systems [37] and hydrogen networks with transport and storage [38]. Designing renewable energy supply chains has also been performed using the P-graph method considering variable inputs and outputs and processes with multiperiod operations [39] [40][41] . Biofuel and biorefinery value chains create further challenges and opportunities such as diversity of biomass feedstock and conversion technologies [42] [43].…”

Simultaneous design and operation optimization of renewable combined cooling heating and power systems

“…Ameri et al 12 proposed a novel MILP formulation to determine the optimal capacities and seasonal operations of seven CCHP systems in district cooling and heating networks; scenario analysis was performed to showcase the impacts of integrating photovoltaic with CCHP systems on the network economic performance. Szlama et al 13 developed an MILP framework based on P-graph theory for optimal design of renewable energy systems with flexible input and outputs. Li et al 14 employed MILP-based chance-constrained programming to study CCHP scheduling by minimizing generation costs.…”