# Energy Turnover for Stages of a Generic Energy System

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As before defined by the author (in Goldsmith et al., 2009), “Energy Turnover” (ET) is the relation between energy and the underlying immobilized assets used to produce or move this energy from one level of the production chain to the next. Formally, it is the ratio of energy (E) to its underlying assets (A) in the form of joules to monetary units of underlying immobilized assets (A), as represented by equation (4.1). (4.1) Where: [Joules per Assets] Energy Turn - the relation between energy and the underlying immobilized assets used to produce or move this energy from one level of the production chain to the next; [tons ∙ day-1] Total Energy that is captured, produced or that flows throughout the system; [monetary units] Total Immobilized assets. 3.3 Energy Turnover for Stages of a Generic Energy System (biomass) As aforementioned, the study of an energy-production system can be broken down into its multiple composing stages to ease its exploration (please refer to Figure 1 “General Stages that Compose Biomass-Based Energy Systems”, page 66, for a graphical visualization of the stages adopted by this paper). In order to mathematically define such stages, let “s” denote the set of s* components, of our studied energy system. Then, for each production stage we can calculate its respective Energy Turn using of equation (4.2): (4.2) Where: [Joules per Assets] Energy Turn at the production stage [tons ∙ day-1] Total Energy that flows throughout stage [tons ∙ day-1] Immobilized assets within stage From (4.2), the Overall-System Energy Turnover (OET) of the system can be expressed as: (4.3) 3.4 Modeling Energy Flow for Each Production Stage A chicken-or-egg problem arises when ch... ... middle of paper ... ...licated step, called photosynthesis, leads to the production of the raw energy-material (biomass) used by the processing unit for conversion into other more desirable forms of energy. As aforementioned, the effects of many environmental variables come into play, influencing renewable energy systems. Within the context of energy capture, for biomass-based energy systems, such variables affect the amount of energy that is available to be harvested. The stochastic behavior of these environmental variables causes a coherent mathematical attempt of modeling REPs to benefit from the modeling of each raw-material supplier. Therefore, the number of suppliers must be calculated. For each biomass conversion technology available at the Processing Unit, the number of independent-suppliers that are associated with the delivery of raw materials (biomass) can be calculated as: