Future Technology Transformations in the Power Sector (FTT:Power)
FTT:Power and its theoretical grounding
It has been known for many years that technology diffusion follows S-shaped function, for instance the logistic function, when entering a market, where initial diffusion is slow, then progresses fast, before saturating at high levels of market penetration. This property is an empiricalfinding, but can also be explained with simple arguments, which concern consumer/investor behaviour when they make their choices.
Technology diffusion can be viewed as a replacement of existing technology by a new one, and therefore the S-shaped behaviour is one of technology substitution. If consumers decide to replace old systems by a new innovation (e.g. replacing horses by cars, natural for synthetic fibres in fabrics, wood for steel in construction, etc), the replacement generally follows this trend. When, however, consumers/investors have a choice between several new technologies, the result is not necessarily an S-shaped curve, but can take many forms. It becomes more complex, but can still be described.
The S-shape trend of technology diffusion can be explained in terms of the replacement of existing technology at rates that depend on technology lifetime. In other words, the replacement is often done when the existing technology comes to the end of its working life due to wear (e.g. every 15 years for cars?). The rate of requirement for replacement provides a rate of opportunities to change technology, and constrains the overall rate of technological change.
Using S as a variable for the market share, for 2 technologies, this is described by:
For an arbitrary number of technologies, exchanges between technology i and j can be written as:
where the matrix Aij contains technology transition time constants (between every possible pair of technologies), while the matrix Fij expresses investor/consumer preferences (e.g. the choice may be 60% of the time for i, 40% for j, in which case Fij = 60% and Fji = 40%) This is described in reference .
When several options exist for consumers/investors, the complexity of the exchanges (left in the image above) can be reduced by considering individual exchanges between technology categories. If one can evaluate the exchanges between one technology and all the others (right in the image above), its diffusion or decline can be followed by adding up all exchanges with all other technologies. Thus total changes for a particular technology are
This equation drives the simulation of technology substitution in the model. From there, given a demand for electricity in a particular region of the world, the total capacity for each technology is straightforward to determine, as well as electricity generation and GHG emissions. This is described in reference [2-3].
This theory of technological change expresses the competition for market space by several existing technologies, or options for consumers/investors. This turns out to be a very similar problem to the population growth of species in ecosystems, in the field of mathematical ecology. These equations were derived years ago for ecosystems, by Lotka and Volterra [4-5]. Thus, given that the two problems map to each other, we benefit from a large body of literature on the mathematics involved.
Use for policy
This model is designed for use in policy advising. The goal is to attempt to foresee the impacts of chosen policy. As opposed to many other models of energy systems, the FTT family of models is not a normative model (finding the optimal technology pathway), it is a descriptive model (predicting its likely evolution). Therefore, in order to find an optimal technology pathway, one would be required to run the FTT family of models many times. While this might appear inconvenient, one must emphasise that the role of policy is to incentivise actors and their choices towards particular directions, and rarely does policy intervene directly. Therefore, even when knowing which technology pathways would be optimal to follow, it is unlikely that policy-makers succeed to actually make the energy sector follow such pathways, particularly when some sectors are dominated by market diffusion (e.g. transport). We therefore expect that, through an important methodological and conceptual contrast to the numerous contemporary normative (optimisation) models of energy systems, the FTT family will generate a useful contribution to current debates.
 J.-F. Mercure, FTT:Power : A global model of the power sector with induced technological change and natural resource depletion, Energy Policy 48, 799-811 (2012)
Free text available on ArXiv arXiv:1205.4868
 J.-F. Mercure, An age structured demographic theory of technological change. 4th International Conference on Sustainability Transitions, Zurich, 2013 (2013).
Preprint available on ArXiv: arxiv:1304.3602
 J.-F. Mercure, On the changeover timescales of technology transitions and induced efficiency changes: an overarching theory, Preprint available on ArXiv arXiv:1209.0424 [math.DS]
 A. J. Lotka, Elements of Physical Biology, Wiliams and Wilkins Company, 1925.
 V. Volterra, The general equations of biological strife in the case of historical actions, Proceedings of the Edinburgh Mathematical Society, 6 (1) (1939) 4.