# A Framework for Defining Sustainable Energy Transitions: Principles, Dynamics, and Implications

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## Abstract

**:**

## 1. Introduction

#### 1.1. Theories of Energy Transitions

- (1)
- Energy end-use capacity, as a rule, is much larger than generation capacity. This means that transitions in energy services are able to lead the energy supply transitions. It also means that the energy using equipment stock may create lock-in for the energy supply.
- (2)
- Energy transition rates vary across nations—they are usually slower in large, developed economies but faster in smaller ones—which by implication have a smaller, less extensive infrastructure.
- (3)
- The patterns of energy transitions are similar to generic s-curve technology diffusion processes (cf. [4,5]): a long experimentation phase with limited uptake, emergence of dominant design(s) that slowly move upward from niche to general adoption, a parallel move down the cost curve through standardization, scale and network economies, and eventual spreading from the lead innovation adopter countries to the periphery countries.

#### 1.2. Energy Transition Cases

#### 1.3. Approach and Outline of the Paper

## 2. Framework and Terminology for Energy Transitions: A Broad View of the Energy Economy System

#### 2.1. Fossil Energy Sub-System

_{M}the year of the peak production. The net primary power (PF

_{net}) of the resource has a net declining average EROEI R

_{f}(t) through a combination of the increase in technological efficiency and the decrease in the quality of the remaining resource [30]. Net primary power can be written in relation to EROEI as:

#### 2.2. Renewable Energy Sub-System

_{0}) minus the capacity that has been decommissioned at the end of its lifetime L (Equation (3))—i.e., the existing stock of renewable energy generating capacity. Every period t approximately 1/L of capacity is decommissioned [31], The renewable energy EROEI (R

_{r}) is a composite subject to a reinforcing feedback due to economies of scale and learning and a balancing feedback due to the installation of renewable resources in the prime locations first. Since the absolute maximum renewable energy potential (PR

_{max}) is several orders of magnitude larger than the installed capacity on a global scale (e.g., [32]) we ignore the renewable saturation loop and assume an increasing EROEI (R

_{r}) due to a learning curve with elasticity to installation volume γ (Equation (3)). The two parts of Equation (3) can be combined to form Equation (4) which calculates the amount of renewable power available on average in year t.

_{r}(0) · c in Equation (4) with R

_{r}(ñ).

#### 2.3. Energy Economy Sub-system

_{gross}). It is equal to the total production by both renewable energy and fossil resources. This energy though is not fully available to society as a portion must be reinvested in further energy recovery—i.e., building renewable (I) and non-renewable new energy generation infrastructure, with the remainder being available for societal needs—e.g., agriculture, non-energy manufacturing, and services (net social surplus—PS

_{net}). Surplus energy is the key flow that allows a civilization to thrive—it is what permits recreation, experimentation, development and entrepreneurship. In an energy economy representation, we can also identify the portion of PSnet that is invested in building or replacing energy-consuming capital—the infrastructure and equipment that transforms secondary energy into desirable energy services (a flow that we represent as Ib). In equation form, the net social power is captured in Equation (5).

_{net}(t) = PF

_{net}(t) + PR(t) − I(t)

- the renewable energy investment ratio (ε)—i.e., the ratio of energy invested in renewable energy generation I(t) over the total primary available energy as shown in Equation (6), and
- the energy cost ratio (k)—which is the marginal energy investment cost weighted by energy output. It combines the energy cost of finite energy resources (summarily represented by the ratio of energy invested in fossil extraction to net available) that exhibits the desired non-linearity as R
_{f}(t) tends to 1 plus the ratio of the available energy that is directed to renewable energy investment (ε(t)) as shown in Equation (7).

_{net}(t) = PD(t)u[p(k,t)]

## 3. Definition of and Propositions for Sustainable Energy Transitions

- (1)
- The rate of pollution emissions is less than the ecosystem assimilative capacity.
- (2)
- Renewable energy generation does not exceed the long-run ecosystem carrying capacity nor irreparably compromises it.
- (3)
- Per capita available energy remains above the minimum level required to satisfy societal needs at any point during SET and without disruptive discontinuity in its rate of change.
- (4)
- The investment rate for the installation of renewable generation and consumption capital stock is sufficient to create a sustainable long-term renewable energy supply basis before the non-renewable safely recoverable resource is exhausted.
- (5)
- Future consumption commitment (i.e., debt issuance) is coupled to and limited by future energy availability.

#### 3.1. Environmental Sustainability of SET

#### ● Proposition I: The rate of pollution emissions is less than the ecosystem assimilative capacity.

_{i}) may not be the ultimately recoverable resources (URR) but instead the safely recoverable resources (SRR). In other words, even if extraction can continue beyond the SRR towards the URR it would be unsafe, entailing unwarranted risk of intolerable climate change and environmental impacts. In SRR we include the reserves burned without pollution control (ER), plus the amount that can be economically used in systems that capture the pollutants (CS). The existence of CS technology with efficiency (e

_{CS}) allows the SRR to be higher but at a cost, as the final available energy is further reduced by the parasitic losses of the CS process. In constraint form, PI is shown in Equation (11).

_{i}ER

_{i}· c

_{i}< C

_{max}

#### ● Proposition II: Renewable energy generation should not exceed the long-run ecosystem carrying capacity nor irreparably compromise it.

_{max}) can be assumed, as shown in Equation (12).

_{j}(t) < PR

_{j_max}

#### 3.2. Societal Sustainability of SET

#### ● Proposition III. Per capita energy consumption remains above the minimum level required to satisfy societal needs at any point during SET and its rate of change is free of disruptive discontinuities.

#### 3.3. Energetic and Economic Sustainability of SET

#### ● Proposition IV: The investment rate for the installation of renewable generation and consumption capital stock is sufficient to create a sustainable long-term renewable energy supply basis before the non-renewable safely recoverable resource is exhausted.

_{0}) that allows sufficient net societally available energy PSnet as fossil fuel production winds down. The actual desired limit can vary and will depend on the conversion efficiency of the energy consuming capital stock in a dynamic interaction with Equation (13) (cf. Principle III). PIV creates a constraint on the energy supply side and is applied on Equation (8).

#### ● Proposition V: Future consumption commitments (i.e., debt issuance) is coupled to and limited by future energy availability.

_{0}FD(t) as shown in Equation (15) utilizing Equation (4) for the renewable energy generation stream.

## 4. Application of SET Propositions in the Global Energy Transition: Dynamics and Observations

_{2}eq but in either case, long-term stabilization implies reaching a near-zero net rate of anthropogenic emissions (cf. [43]). The fifth IPCC assessment report [44] estimated the upper threshold of anthropogenic carbon emissions should be 4440 Gt CO

_{2}for a fifty percent chance of remaining below 2 °C. This translates into 3010 Gt CO

_{2}when accounting for non-carbon forcings. With estimated cumulative emissions of 1890 Gt CO

_{2}by 2011, a safe emissions budget for the remaining 21st century is 1120 Gt CO

_{2}, assuming that the SET is completed by the end of the century.

_{f}) curve based on Gupta and Hall [50] and Gagnon et al. [51] was created for the cases of the uncapped and capped carbon emissions. The analysis extends for one hundred fifty years starting in 1950. Using a similar time-horizon (1940–2100), as a starting point, we estimate the global equivalent renewable energy investment additions (availability adjusted) at 34.3 GW in 2010, while the global fossil power output was 13.4 TW and total power output ~15.8 TW giving a current value for ε of approximately 0.22% [52] (based on data from [53]). As a crosscheck, the same order of magnitude value for ε (0.32%) can be confirmed by using the ratio of renewable energy investment as a proxy ($227 billion USD in 2010) over global GDP ($71 trillion USD in 2010) [54].

_{2}total anthropogenic) in Figure 4. The possibility of capture and storage technologies (CCS) could provide additional breathing space between the two options but would be closer to the capped scenario than the uncapped [55] and as a result is not discussed in this first exposition. Three renewable energy investment ratios (ε) targets are evaluated: near BAU (0.375%), S1 (1.5% = 4 × BAU), S2: (3% = 8 × BAU). Average renewable EROEI in the beginning of the SET policy is set to 20, which is pn the higher end of the current portfolio of resources [50], lifetime (L) is set at 25 years, and the learning effect (γ) at 0.07.

**Figure 3.**Primary Energy Supply (Gross, Net, and Energy Cost Ratio) and Carbon Dynamics for Uncapped Carbon Emissions and Variable Renewable Energy Investment Ratios.

**Figure 4.**Primary Energy Supply (Gross, Net, and Energy Cost Ratio) and Carbon Dynamics for Capped Carbon Emissions and Variable Renewable Energy Investment Ratios.

**Figure 5.**Primary Energy Supply (Gross, Net, and Energy Cost Ratio) for Capped Carbon Emissions and: (a) EROEI Rr = 15; (b) postponing of ε acceleration until 2050.

## 5. Conclusions

_{2}total—which implies a 50% chance of avoiding 2 °C average global temperature increase) while current debt obligations exceed the energy capacity of the energy-economy system to service them without partial default. Dynamic modeling of the energy economy system and disaggregation of the renewable energy sources will be able to further illuminate the possible pathways of the SET evolution.

## Acknowledgments

## Author Contributions

## Supplementary Materials

## Conflicts of Interest

## References and Notes

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Sgouridis, S.; Csala, D. A Framework for Defining Sustainable Energy Transitions: Principles, Dynamics, and Implications. *Sustainability* **2014**, *6*, 2601-2622.
https://doi.org/10.3390/su6052601

**AMA Style**

Sgouridis S, Csala D. A Framework for Defining Sustainable Energy Transitions: Principles, Dynamics, and Implications. *Sustainability*. 2014; 6(5):2601-2622.
https://doi.org/10.3390/su6052601

**Chicago/Turabian Style**

Sgouridis, Sgouris, and Denes Csala. 2014. "A Framework for Defining Sustainable Energy Transitions: Principles, Dynamics, and Implications" *Sustainability* 6, no. 5: 2601-2622.
https://doi.org/10.3390/su6052601