Representing the Spatial Diffusion of Technologies in an Energy System Optimization Model

Benjamin D. Leibowicz details his YSSP project on representing spatial technology diffusion in an energy system optimization model to bring diffusion projections more into line with reality.

B. Leibowicz

B. Leibowicz


Historical experience indicates that technologies diffuse gradually, often according to S-shaped logistic growth trajectories. To ensure that new technologies diffuse in roughly this manner, energy system optimization models typically impose crude constraints on activity or capacity growth from one period to the next. This simple approach neglects important spatial aspects of diffusion, namely, the observation that technologies diffuse at different times, at different rates, and to different extents in different regions. As a result, model outputs often feature technology diffusion pathways that are inconsistent with historical experience and intuitive expectations. Schmidt's Law offers a framework for thinking about spatial technology diffusion. A technology is first developed in a core region. Rim and periphery regions adopt the technology later but benefit from the earlier experience of the core. As a result, the rate of diffusion accelerates in the rim and periphery regions. The goal of this study is to represent spatial technology diffusion in an energy system optimization model to bring diffusion projections more into line with reality.


This study uses a four-region version of the MESSAGE model implemented in GAMS. For a given electricity supply technology in a particular region, new capacity installation is constrained by the region-and-technology-specific knowledge stock. This stock reflects all prior capacity additions, with more recent additions weighted more heavily than earlier additions to capture knowledge depreciation. This soft constraint can be exceeded but at significant and marginally increasing cost. Diffusion from the core region to rim and periphery regions is controlled by a knowledge stock spillover effect. Rim and periphery regions begin with no ability to install capacity of a new technology and must rely on spillovers from the core in the early phases of adoption. Ability to add new capacity as a function of knowledge stock and the spillover magnitude are estimated using historical data on coal, gas, nuclear, and wind power.

Results and Conclusions

Relative to standard diffusion formulations, the novel representation implemented in this study generally induces smoother and more gradual diffusion trajectories featuring spatial patterns consistent with Schmidt's Law. Dependence on knowledge spillover from the core delays adoption of advanced technologies in the rest of the world. Technologies preferred by the core (e.g., coal with CCS) diffuse rapidly and persistently once they enter other regions. The spatial diffusion of technologies that are less suitable in the core (e.g., biomass with CCS) suffers significantly in the presence of the spillover requirement. It is globally optimal for the core to increase deployment of advanced technologies in light of the positive spillover externality. Developing nations should consider which technologies are likely to be deployed heavily by the innovative economies, as knowledge spillover will likely make these technologies easier to adopt than technologies that must be invented or refined domestically. 


Benjamin Leibowitz, of Stanford University, California, is a US citizen. He was funded by IIASA's National Member Organization for the USA and worked in the Energy (ENE) Program during the YSSP.

Please note these Proceedings have received limited or no review from supervisors and IIASA program directors, and the views and results expressed therein do not necessarily represent IIASA, its National Member Organizations, or other organizations supporting the work.

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Last edited: 19 August 2015


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