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Modelling energy systems as multi-scale systems

Modelling energy systems as multi-scale systems

Louisa Jane Di Felice

One of the main goals of the MAGIC project has been that of modelling the interactions between energy, food and water, taking a perspective that is grounded in complexity. Most systems in the world can be broken down into components: cities are made of neighbourhoods; molecules are made of atoms; societies are made of people. Nexus interactions span through systems across different scales, with each scale affecting one another. For example, a coal power plant may affect its local embedding environment by polluting a nearby water source, while also generating global greenhouse gas emissions which, in turn, alter its local environment.

Our approach to modelling nexus interactions has been to focus on this multi-scale perspective, by using different information to describe nexus patterns at different scales of analysis. These types of information cannot be reduced to a single metric, and each description may be more or less useful depending on the goal of the analysis. This is why in MAGIC we do not rely on single indicators, such as efficiency or energy intensity, to measure the performance of the energy system.

The way we have broken down the energy system across different scales has not been in purely material forms – e.g., breaking down power plants into their components. Instead, we have focused on the distinction between function and structure of the energy system, taking inspiration from biology. For the case of energy, this means considering the different functions played by energy technologies – e.g., providing heating, or fuels, or baseload electricity.


Figure 1. A multi-scale description of Spain’s energy sector (for the year 2018)


Figure 1 shows an example of this, mapping Spain’s energy sector as a multi-scale network. The main node, “Energy sector”, is split into a fuels and an electricity component (since Spain does not have a heating sector). Electricity and fuels are then split hierarchically into further sub-sectors. Additional functional layers could be added depending on the goal of the analysis. Electricity, for example, could be split into baseload, peak and intermittent electricity. Each node in the network represents a processor, i.e., each node is associated with a set of nexus inputs and outputs (water, GHG emissions, labour, land, etc.). Further information on how elements of the energy systems can be described as processors can be found in Di Felice et al. (2019) (see the link to the open-access article at the bottom of this page). While intermediate levels in the network are functional, at the lowest level these functional layers are mapped onto their structures, i.e. the technologies fulfilling different purposes.

Here, the network in Figure 1 shows a distinction between blue and red nodes. Blue nodes are local ones. They are the processes taking place within the geographic boundaries of Spain. This includes most power plants and most refineries. Red nodes, instead, are those connected to Spain’s energy system, but which take place elsewhere (what we refer to as externalised processes). These include the extraction processes tied to Spain’s direct and indirect imports, for example. Mapping the energy sector across these different functional layers, associating each node with a set of nexus inputs and outputs, and making the distinction between local and externalised processes allows us to tap into questions that are relevant to the multi-level governance of sustainability, including:

  • Which functions of the energy sector emit most greenhouse gases? How can these functions be reduced or substituted?
  • What would happen to nexus elements across different scales, if the energy sector were to be gradually electrified?
  • How would the pattern of local and global environmental effects shift, if Spain decided to produce all of its energy locally?

We are currently working on this application, providing a multi-scale network description of the energy sector of the EU as a whole, and relating it to pressing policy questions. Follow us on twitter at @MAGIC_NEXUS to find out when the article is out!



Di Felice, L. J., Ripa, M., & Giampietro, M. (2019). An alternative to market-oriented energy models: Nexus patterns across hierarchical levels. Energy Policy, 126, 431-443. https://doi.org/10.1016/j.enpol.2018.11.002



The role of human activity in the nexus structuring space

The role of human activity in the nexus structuring space

Laura Pérez-Sánchez, Raúl Velasco-Fernández, Michele Manfroni, Sandra Bukkens & Mario Giampietro

Current discussions on sustainability tend to focus principally on the shortage of natural resources and environmental degradation: water and material footprints, peak oil, greenhouse gas emissions, destruction of habitats, etc. Society is mostly pictured as a black box and its environment as a factor limiting its expansion. Constraints operating inside the society are often overlooked. Human activity or time use is one such constraint. A shortage of human time in one or more critical elements of society constrains the trajectory of economic growth, in a way like other biophysical production factors do, such as water, energy, and land. Whereas the limits to primary resource supply and sink capacity are difficult to assess, the human time yearly available both at the national and at the global level has a well-defined limit: population size × hours in a year. MuSIASEM is unique in that it analyzes sustainability from a metabolic perspective including internal societal constraints. Indeed, MuSIASEM expresses resource flows not only per unit of land but also per unit of time use (e.g. electricity per hour of human activity in the transport sector). The adopted metabolic perspective thus allows us to address the entanglement over the diverse factors (demographic, cultural, socio-economic, technical and biophysical) that affect the option space of desirable (compatibility with culture and values), viable (compatible with technology, infrastructure, and institutions) and feasible (compatible with nature’s capacity to contribute to people) profiles of human time allocation. 

Any human society simultaneously generates and requires human time for its reproduction. The demographic structure of society and the prevailing social practices define a forced dynamic equilibrium between supply and demand of time. Natural population growth does not necessarily solve a problem of shortage of time, as it does not only lead to a larger supply of human activity but also an increased requirement of working time (e.g. for child care, education, health care etc.). Post-industrial countries can (temporarily) overcome economic stagnation caused by shortage of working time through the use of technology and energy—boosting labor productivity, through immigration of adult workers—notably seasonal and temporary workers— and through the externalization of the requirement of working time in the form of imported goods and services. Indeed, the contemporary mode of socio-economic development has entailed a massive movement of workers away from the agricultural and industrial sectors to the service and government sector. This was made possible during the industrial revolution, which saw the mechanization of the primary and secondary sectors thus freeing up labor time for the service sector and, importantly, leisure time for the consumption of goods and services [1–4]. The post-industrialization process (globalization) has consolidated this trend through the use of embodied working time in the form of imported goods and services (notably in agriculture, mining, manufacturing, and waste treatment) and (seasonal/temporary) foreign migrant workers (notably for low-skilled occupations in the sectors of agriculture, mining, construction, transport and the private sector—house cleaning). Note that imported working time in the form of imported goods and services often concerns labor with lower salaries and less social protection.

Many of the applications of the Nexus Structuring Space in MAGIC have addressed the externalization of human labor. But probably the most striking ones are the comparison of the metabolic pattern of China with that of the EU and the USA [5] and the assessment of the virtual hours of labor embodied in imports in the EU [6]. These applications concern the use of the macroscope (internal end-use matrix), mesoscope (trade) and the virtual scope (embodied labor in imported goods and services). For instance, the overall amount of work required to produce the goods and services consumed by an average US, EU and Chinese citizen is respectively: 1430, 1230 and 985 hours per capita per year [6]. As for the actual hours of paid work allocated to the economy of these countries, we found that the USA and EU allocate, respectively, 790 and 730 hours per capita per year, whereas China allocates 1300 hours per capita per year (see Figure 1). China is the only country of these three presenting a positive work balance: a part of the available work hours of its internal work force goes into exports. The USA and the EU, on the other hand, almost double the internally available hours of labor to produce the goods and services they consume, thanks to embodied labor in imported goods and services. For instance, in 2011 the EU used 500 hours of embodied work per capita per year in its imports that are equivalent to more than 120 million annual work units (virtual workers; assuming a work load per unit/virtual worker of 1700 hours/year). Similar results were found for the USA. The large import of hours of embodied work in the EU is possible only because of the small size of its population compared to the world population. Given the fixed time budget at the global level, the reproduction of EU (and US) consumption levels that emerging economies such as China and India are striving for is simply implausible, given the limited size of the ‘fund’ of human activity. This raises important ethical issues and questions the EU’s commitment to the Sustainable Development Goals.


Figure 1: Time allocation in the EU and China in hours per capita per year.


The characterization of human activity patterns currently observed through the macroscope refers only to the allocation of human activity inside the paid work sector. In the future we plan to extend this analysis by characterizing the metabolic pattern associated with social practices outside the formal economy (e.g. residential/household sector). Social practices outside of the paid work sector represent the equivalent of the microscopic view of the technological process of production inside the paid work sector. 

These applications show the relevance of the MuSIASEM framework in informing sustainability discussions with regard to the viability and desirability concerns. A detailed theoretical exposition on the profile of time allocation as an emergent property of the metabolic pattern of society is forthcoming [7].



[1] G.K. Zipf, National unity and disunity: The Nation as a Bio-social Organism, Principia Press Inc., Bloomington, 1941.

[2] V. Smil, Making the Modern World : Materials and Dematerialization., Wiley, 2013. 

[3] C.M. Cipolla, The Economic History of World Population, Pelican Books, 1962.

[4] M. Giampietro, K. Mayumi, A.H. Sorman, The Metabolic pattern of societies: where economists fall short, Routledge, London, 2012.

[5] R. Velasco-Fernández, L. Pérez-Sánchez, M. Giampietro, A becoming China and the assisted maturity of the EU: assessing the factors determining their energy metabolic patterns, Energy Strateg. Rev. in press (2020).

[6] L. Pérez-Sánchez, R. Velasco-Fernández, M. Giampietro, The international division of labor and embodied working time in trade for the US, the EU and China, Ecol. Econ. (2020).

[7] M. Manfroni, R. Velasco-Fernández, M. Giampietro, The profile of allocation of human time and societal organization: the internal constraint to perpetual economic growth, Unpubl. Manuscr. (2020).