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Modelling the Evolutionary Paths of Multiple Carbon-Free Energy Technologies with Policy Incentives

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Abstract

In this paper, we establish an economy-energy-environment integrated model by introducing a new technical mechanism, that is, the revised logistic model, to be the technical core of the energy module. This gives the conventional top-down modes more bottom-up features and allows us to model the evolutionary pathways of multiple non-carbon technologies. The model’s simulations indicate that the mixed policy of both carbon tax and subsidy plays a significant part in promoting the development of new energy technologies. The shares in total primary energy usage for PV solar, geothermal power and wind energy, for example, will have increased to 24.9, 9.7 and 6.12 %, respectively. Meanwhile, technological progress can be significantly enhanced by introducing research and development (R&D) investment. As a result, the percentages of usage of the above three technologies are likely to increase to 26.2, 12.1 and 7.2 %, respectively, in that case. Besides, energy supply market will be locked up by non-fossil energy as early as 2035, or thereabouts, under the current R&D investment regime. Thus, the expansion of R&D may significantly improve the carbon-reducing potential of the mixed policy and perform well in easing the tax burden on businesses and consumers in the long run.

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Notes

  1. Gerlagh and van der Zwaan [9] give sensitivity analysis of substitution elasticities between fossil fuels and zero-carbon energy based on their DEMETER model. When the value of elasticity is set to be 2.0, 3.0 and 4.0 respectively, the carbon emissions in 2020 will range from 7.6 to 7.8 GtC, and the reductions will be in the interval 36–73 %; shares of non-fossil energy demand will change from 9 to 16 %.

  2. Top-down models focus on macroeconomy, in which output is given by a production function, with capital, labour to be the inputs. Sometimes, energy or electricity is also input to be the complemented production factor, leaving energy technology advancement exogenized by automatic energy efficiency improvement (AEEI). Bottom-up models always get relatively rich set of specific energy technologies, making technological progress an exogenous process of cost and efficiency improvements. That is why the bottom-up models are often called “energy-system model” [8, 36].

  3. Arrow [3] is regarded as the first to discuss learning curves to which he refers as “learning-by-doing” (LBD), while the R&D-driven learning curve is often called “learning-by searching” (LBS) process. More information about learning curves can be attributed to Ibenholt [15] and Mattsson [25].

  4. Kouvaritakis et al. [20] and Barreto and Kypreos [4] have done some research on the two-factor learning method, but they did not discuss it in the scope of E3 models, and their study intention is different from ours as well.

  5. Debates on discount rate have never ceased; for more details on how to set depreciation rates appropriately in environmental problems, see [38]. In this paper, we give the value by referring to Nordhaus [32].

  6. Rubin et al. [39] did much research on the learning rates of multiple energy technologies, suggesting that the costs of the technologies are declining in the past few decades, with learning rates ranging from 10 to 12 %.

  7. We replace C i (t) with C i (t − 1) − C imin after taking some simple derivative and difference operations to Eq. 12, then we get C i (t) → C imin, as t → ∞, and the learning effect tends to zero, which fits in with the reality (see Appendix 2).

  8. In the one-dimension case, the relationship between parameter χ and the standard deviation can be described as χ 2 = π 2/3σ 2 ≈ 1.81π 2/σ 2, when turning to the multi-dimension case, the relationship becomes more complex [2]. Overall, the dynamics of logistic curve is sensitive to the parameter value χ, for the formulation, S t  = αS t − 1(1 − S t − 1), if α ≥ 3.57, the long run solution starts to become chaotic; if α ≥ 3.83, there will be unaccountable number of asymptotically α-periodic trajectories, as well as cycles for every integer period [26].

  9. The monetary figures in this paper are in 1990 USD.

  10. Data for R&D are only available for IEA countries (http://www. iea.org/stats/index.asp), data for the rest of world is not given in detail. Then we adopt the estimation of total public R&D expenditures for the entire world in 2000, and the share the R&D relates to energy is set to be 2 %, referring to Popp [36].

  11. The learning ratio is the rate at which the specific cost declines each time the cumulative capacity doubles, the relationship between the learning rate and the learning index is described by Eq. 7 [4].

  12. The CO2 emission in this model in 2100 is much lower than in the RICE model (38 GtC) while approaches to the projection in the DICE model (21 GtC), but the carbon projections in both E3METL and DICE model are in the IPCC’s projection interval of 5 to 35 GtC [33, 42]. The comparisons of the main results in this work to that of the existing models are listed in Table 4 in Appendix 1.

  13. The results here are in line with that of most of the relevant studies; for example, Gerlagh and van der Zwaan [10] believed that at least half of the world’s energy supply would be provided by alternative technologies at the end of the century.

  14. Data resources: Dams and Development, the report of the World Commission on Dams, Nov. 2000, Earthscan Publications Ltd.

  15. The “lock-up” points define the first time when the share of non-carbon technologies surpasses that of fossil fuels.

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Acknowledgments

This work was supported financially by the National Natural Science Foundation of China under Grant Nos. 71210005, 71273253 and 71133005. We are grateful to the anonymous referees for their helpful comments and suggestions. And, special thanks go to Reyer Gerlagh and Socrates Kypreos for their comments on the early work of this research.

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Authors and Affiliations

  1. Center for Energy & Environmental Policy Research (CEEP), Institute of Policy and Management (IPM), Chinese Academy of Sciences (CAS), 100190, Beijing, China

    Hong-Bo Duan, Lei Zhu & Ying Fan

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Correspondence to Ying Fan.

Appendices

Appendix 1

The following table compares the GWP, CO2 emissions, energy demand and CO2 concentration for various models by the end of 21st century.

Table 4 Comparisons of key results among various E3 models by 2100
Full size table

Appendix 2

The differential Eq. 12 is equivalent to the difference Eq. 13, and the derivation is as follows:

$$ \begin{array}{l}\varDelta {C}_i\left(t+1\right)=\frac{\partial {C}_i\left(t+1\right)}{\partial K{D}_i}\varDelta K{D}_i\left(t+1\right)+\frac{\partial {C}_i\left(t+1\right)}{\partial K{S}_i}\varDelta K{S}_i\left(t+1\right)\\ {}\kern3.75em ={C}_i(0)\cdot \frac{-{b}_i}{{\left(K{D}_i(0)\right)}^{-{b}_i}}\cdot {\left(K{D}_i\left(t+1\right)\right)}^{-{b}_i-1}\cdot \varDelta K{D}_i\left(t+1\right)\\ {}\kern4.75em +{C}_i(0)\cdot \frac{-{c}_i}{{\left(K{S}_i(0)\right)}^{-{c}_i}}\cdot {\left(K{S}_i\left(t+1\right)\right)}^{-{c}_i-1}\cdot \varDelta K{S}_i\left(t+1\right)\\ {}\kern3.75em ={C}_i(0)\cdot \frac{-{b}_i}{K{D}_i\left(t+1\right)}\cdot {\left(\frac{K{D}_i\left(t+1\right)}{K{D}_i(0)}\right)}^{-{b}_i}\cdot \varDelta K{D}_i\left(t+1\right)\\ {}\kern4.75em +{C}_i(0)\cdot \frac{-{c}_i}{K{S}_i\left(t+1\right)}\cdot {\left(\frac{K{S}_i\left(t+1\right)}{K{S}_i(0)}\right)}^{-{c}_i}\cdot \varDelta K{S}_i\left(t+1\right)\\ {}\kern3.75em =-{b}_i\cdot {C}_i\left(t+1\right)\cdot \left(\frac{K{D}_i\left(t+1\right)-K{D}_i(t)}{K{D}_i\left(t+1\right)}\right)\\ {}\kern4.5em -{c}_i\cdot {C}_i\left(t+1\right)\cdot \left(\frac{K{S}_i\left(t+1\right)-K{S}_i(t)}{K{S}_i\left(t+1\right)}\right)\\ {}\kern3.75em =-{b}_i\cdot \left({C}_i(t)-{C}_{i \min}\right)\cdot \left(\frac{K{D}_i\left(t+1\right)-K{D}_i(t)}{K{D}_i\left(t+1\right)}\right)\\ {}\kern4.5em -{c}_i\cdot \left({C}_i(t)-{C}_{i \min}\right)\cdot \left(\frac{K{S}_i\left(t+1\right)-K{S}_i(t)}{K{S}_i\left(t+1\right)}\right)\\ {}\Rightarrow \kern1em {C}_i\left(t+1\right)={C}_i(t)-\left({C}_i(t)-{C}_{i \min}\right)\left({b}_i\cdot \left(\frac{K{D}_i\left(t+1\right)-K{D}_i(t)}{K{D}_i\left(t+1\right)}\right)+{c}_i\cdot \left(\frac{K{S}_i\left(t+1\right)-K{S}_i(t)}{K{S}_i\left(t+1\right)}\right)\right)\end{array} $$

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Duan, HB., Zhu, L. & Fan, Y. Modelling the Evolutionary Paths of Multiple Carbon-Free Energy Technologies with Policy Incentives. Environ Model Assess 20, 55–69 (2015). https://doi.org/10.1007/s10666-014-9415-5

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