Determinants of energy futures—a scenario discovery method applied to cost and carbon emission futures for South American electricity infrastructure

The energy system is both strategic and capital intensive. Policies and development support therefore need to be easy to audit and review. Because energy infrastructure outlast any electoral or administrative cycle, such transparent information is critical for stakeholders including the public, that is, taxpayers and voters, and support organisations, like development banks. To this end, the analysis uses the Open Source Energy MOdelling SYStem (OSeMOSYS) which is an open source energy model generator that uses linear optimization techniques, and has global application (Fattori et al 2016, Löffler et al 2017, Niet et al 2017, Pfenninger et al 2018, Taliotis et al 2016, UN DESA 2016). It determines the cost-optimal long-term investment and operation required to satisfy an exogenously defined energy demand (Howells et al 2011). It overcomes recent criticism levelled at similar energy systems models that are not open. Pfenninger (2017) argues that lack of transparency, stemming from lack of open source methods leads to lack of trust in analysis. Yet trust and transparency will be needed to address future long-term low-carbon investment trajectories.

For the same reasons, this paper uses the OSeMOSYS-generated South AMerica Model BAse (SAMBA): an open-source, open-access, long-term, integrated electricity sector model. It explicitly represents eleven South American countries: Argentina, Brazil, Bolivia, Chile, Colombia, Ecuador, Guyana, Paraguay, Peru, Uruguay and Venezuela. Each country is included as an individual region except for Brazil, which is represented using four sub-systems (ONS 2015). The final model has fourteen regions and a time horizon spanning 2013–2063 in one-year time-steps.

SAMBA includes a wide range of technologies, which are represented on a national level. These comprise renewable, nuclear and fossil-fuelled technologies. Hydropower storage is included in the four sub-regions of Brazil and in Venezuela; a detailed list is included in appendix A—table A1. An early application of SAMBA can be found in (de Moura et al 2017 and de Moura et al 2018). Changes as implemented for this project can be found in appendix A—table A2.

Electricity trade between countries relies on the 21 existing international interconnection lines (CIER 2013). It also accounts for a 700 MW connection between Argentina and Bolivia that will come online in 2019 (Power Engineering International 2016). Further trade expansions are not considered in this formulation of the model.

Recent and announced power plant projects are 'hard-wired' into the model as 'committed'. On the one hand, these include large hydropower additions of 48.8 GW expected between 2013 and 2022. This represents a capacity increase of 21% from 234 GW installed capacity in the region. Major projects such as e.g. Belo Monte, Madeira or Teles Pires dams in Brazil as well as large hydropower expansions in Argentina, Chile, Colombia, Ecuador, Peru and Venezuela are represented. On the other hand, they cover 2.4 GW of planned wind and solar capacity (Brazil, Argentina, Chile, Ecuador, Peru, Uruguay and Venezuela) as well as smaller installations of thermal power plants including 1.4 GW of nuclear power in Brazil.

This capacity data is kept constant between model runs. New investment beyond 2022 may change flexibly in the model. All other scenario data is described below.

This work goes beyond the selection of a limited number of cases and instead explores different uncertainty combinations by developing 324 scenarios. These explore changes in six key model inputs: (1) electricity demand, (2) fossil fuel price, (3) renewable technology learning curves, (4) discount rate (cost of capital), (5) CO₂-emission cap and (6) the effects of climate change on hydropower (see table 1). Each of these a discrete number of settings are considered. Each setting in the range is termed a lever⁷ . This parameterisation is described below.

• Electricity demand is modelled using three levers (low, medium and high). Each level is linked to assumptions of GDP, population, urbanization rates and the penetration of electric vehicles (see next section 'Demand and climate change') that are loosely based on views of the future described by the Shared Socio Economic Pathways (SSPs) commonly employed in global modelling efforts (O'Neill et al 2017).
• Fossil fuel prices are defined using two levers (low and high). Values are based on the World Bank Commodities Price forecast (World Bank 2016 July), for the short term, and the World Energy Outlook (IEA 2015) low oil price scenario and current policies scenario, for the long term.
• RET cost and performance outlooks are defined using three levers (low, medium and high). These are based on the projected learning rates from (NREL 2016).
• The discount rate is represented using three levers at 3%, 6% and 12% and is a proxy for the cost of capital (as referred to hereafter).
• CO₂ levers were set as targets for 2050. They include zero emissions, 50% reduction compared to 2013, and no target.
• Finally, climate change impacts are modelled using changes in hydro-generation. Two levers cover 'reference'—no change in anticipated output—and 'low' water availabilities. The latter rely on downscaled precipitation, and resulting river runoff analysis, from (Alfieri et al 2017) calibrated using outputs from a climate model of Representative Concentration Pathway 8.5 (RCP 8.5, see section 'Demand and climate change').

Appendix B contains full details for each input parameter along with the documentation of corresponding model adjustments.

The purpose of this analysis is to generate country-level electricity demand projections that represent a range of plausible future pathways. For narrative consistency across countries, these projections are, where possible, linked to the five SSPs (O'Neill et al 2017). Note however that this does not necessarily imply that demand projections for the region are identical to those found in the SSPs.

Future GDP, population and urbanization rates are calculated at the country level for each of the SSPs. These form the basis for the projected demand to which electric vehicle electricity consumption projections is then added. The latter are not based on SSP narratives. (See appendix B, figure B3). The resulting maximum, medium and minimum demand trends for the region are then chosen.

Effects of climate change on hydropower in South America are projected following an econometric Vector auto regression (VAR) modelling approach. VAR models are widely used for multi-variate analysis and use predictors for projecting data series (Lütkepohl 2005). This work calculates the potential for hydropower electricity generation using projected discharge for RCP 8.5 from Alfieri et al (2017) as a predictor. Details of this projected change in hydro-power generation can be found in appendix B.

Crossing all levers for the chosen determinants results in a total of 324 scenarios. These are analysed across two cost dimensions (capital and variable⁸ costs) and clustered into groups using a Gaussian mixture model (GMM) (Sugiyama 2016). Clustering highlights common determinants to groups of results in the solution space. A data-mining algorithm then 'discovers' what key determinants best explain the cost parameters of each groups. The Patient Rule Induction Method (PRIM) (Friedman and Fisher 1999) algorithm for 'scenario discovery' through statistical data-mining searches for combinations of input parameters (determinants) that best explain the group of interest. The best combination of parameters is chosen through a trade-off between interpretability, 'density' and 'coverage' of different combinations of determinants. Coverage measures the share of scenarios as described by the combination of input conditions relative to all scenarios in the group of interest. Density measures the share of the scenarios in the group of interest relative to all scenarios that meet the combination of conditions. The quasi-p-value test (qp-value) estimates the likelihood that PRIM constrains some parameter purely by chance (Friedman and Fisher 1999, Bryant and Lempert 2010)⁹ .

Cumulative total system cost (2013–2050, discounted at 6%¹⁰ ) across the 324 scenarios is spread between 900 billion USD and 1.7 trillion USD. To unpack the full scenario ensemble, we use the clustering and PRIM analysis for capital versus fixed and variable cost (including fuel cost). Four scenario clusters with different characteristics are identified (figure 1).

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All the clusters in figure 1 are driven by a combination of cost of capital, demand and CO₂ constraint. A high cost of capital promotes technologies that have low upfront capital costs, which most often leads to investment in fossil-fuelled power plants. These tend to have a high variable cost associate with fuel purchases. However, these investment strategies are only adopted by the model, if there is no constraint on CO₂ emissions. This is the case of cluster 2 (orange crosses in figure 1) in which the high cost of capital and absence, or medium level, of CO₂ constraint leads to investments in fossil fuel technologies, and thus low capital costs but relatively high variable costs.

Cluster 3 (blue triangles in figure 1) is on the opposite side of the spectrum compared to Cluster 2: its outcome characteristics are only driven by a strong CO₂ constraint. Cluster investments are characterised by RET deployment at a high cost (table 2).

Cluster 4 (pink squares) is characterised by high capital and high variable costs. These scenarios are driven by high demand levels; combined with medium to high cost of capital; in futures with a medium CO₂ constraint. The high demand leads to higher costs, but this is exacerbated by the combination of a high cost of capital (which favours fossil fuel technologies) and a medium CO₂ constraint (which favours renewables). The result is a trajectory in which there are high investments in fossil-fuel generation at the beginning of the period (by 2030), followed by stranded fossil fuel capacity and high renewable penetration towards the end of the period (by 2050). Note that the CO₂ cap peaks in 2040.

At the opposite end of the spectrum, the first cluster (green circles) has limited capital and variable costs. It is characterized by low to medium levels of both demand and cost of capital combined with either an absence, or a medium level, of CO₂ constraint (table 2).

To better compare scenario results with past investments, we report total investment cost as percentage value of projected GDP (figure 2). Most scenarios have a total discounted system cost below 1.4% of the projected GDP associated with its respective scenario. (For context, the region spent 1.4% of GDP on energy investments before investments declined in the years 2000s (Fay et al 2017)).

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A PRIM analysis is carried out on the 20% most expensive scenarios (these spend 1.34% of GDP on electricity investments). The analysis shows that they are characterized by a high demand and a medium or strong CO₂-emission cap. Additionally, 60% represent a future characterised by a high cost of renewables. This combination of factors causes initial investment to focus on low capital intensity technologies (fossil fuels) which are then stranded by a switch to renewables occurring toward the end of the period. This is when the CO₂ constraint becomes more stringent. While cost-optimal given the range of determinants, the strategy is expensive. This suggests that policies should be prepared to either recover the value of stranded assets, or invest in adequate retrofit schemes with e.g. carbon capture storage (CCS).

Given that a continent wide-CO₂ scheme may be difficult to impose, we focus here on scenarios without any emission caps (108 futures). Looking at determinants that lead to low/high carbon emission reveals three scenario clusters (figure 3, table 3). Cases with low-carbon emission futures are in Cluster 2 (orange crosses). They are characterised by low to medium demand and low to medium cost of capital. Conversely, the cluster with high emissions (green circles) is characterized by high demand and high cost of capital (12%). These are the futures in which fossil fuel power plants are optimal investments. Interestingly there is little impact on costs and emission levels when fuel prices change. This reflects the critical role that financial incentives (e.g. low interest loans) and demand reduction can have, highlighting that—for CO₂ emissions reduction—both can be more important than the use of an emission cap.

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Demand is identified as a determinant for overall system cost, both in absolute and relative terms (percent of GDP). That is because additional electricity demand leads to additional capacity and/or additional fuel consumption. Both result in increased average total cost of electricity¹¹ with values ranging from 123 USD/MWh in low demand cases to 154 USD/MWh in high demand futures. None of the low demand scenarios exceeds a total cost of 1.12 trillion USD, whereas the high demand scenarios consistently stay above 1.11 trillion USD. There is also a strong correlation between demand, overall system cost and emission levels.

The cost of capital is a determinant of whole system cost and CO₂-emissions. The technology changes under different costs of capital have similar characteristics. High cost of capital will favour technologies with low upfront investment costs to minimize depreciation or interest during construction. These technologies include Gas, Biogas, Coal, and Photovoltaic (figure 4). A higher cost of capital will favour biogas over biomass. This is due to the seasonality of the biomass compared to the year round availability of biogas.

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RET learning rates—or rather the lack thereof—have a lower impact than might be expected. They are found to be the third most significant factor for explaining high total system costs, when combined with a high demand and a CO₂ target. There is however a noticeable shift away from wind and PV panels in scenarios with higher RET costs (figure 5). The capital cost for PV (in 2050) varies between 422 USD/kW and 1897 USD/kW across RET learning rate futures. These are modest values when compared to hydropower, coal and nuclear per unit capacity costs, yet the latter however favoured under low RET learning rates. Nuclear has both higher per kW carbon free power output than either PV or wind. Further, the variability of wind and solar input requires intermittency contingency capacity either in the form or storage or of production capacity for wind-still or cloudy days and nights.

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The CO₂-emission cap is a significant determinant for both capital and operational system costs. The 'no emission limit' scenarios never exceed 1.3 trillion USD. Conversely, the zero emissions scenarios can have costs of up to 1.7 trillion USD. Importantly, there are trajectories that can meet zero emission scenarios at a low cost (below 1 trillion USD). The common characteristics for such trajectories are low demand and a low cost of capital.

Looking at stranded assets, figure 6 illustrates fossil-fuel power plant capacity under zero emissions scenarios. These still have operating life after 2050 with a range of installed capacity of between 50–85 GW for the whole region. Similar to the PRIM analysis for capital and operational cost, demand and discount rate are main determinants of stranded asset levels in the zero emissions scenarios (table 4). Further, looking at Cluster 4 (pink squares) shows that low to medium renewable technology capital costs decrease total system cost without necessarily decreasing overall stranded asset capacity.

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Removing the CO₂-emission limit has distinct impacts in terms of installed capacity with mixes shifting from low-carbon technologies such as Nuclear, Biogas and Wind to e.g. Gas and Coal. Some technologies prove to be competitive regardless of the CO₂-emission cap: PV is also favoured in the high emissions scenarios. This implies that nuclear energy ambitions are likely to be a function of government support.

Fossil fuel price and climate change impact scenarios were not identified as significant determinants in the PRIM analysis. The first is linked the changes in fossil fuel price impacting mainly the price of oil, which is not widespread for electricity generation in South America (for details see appendix B, figure B7). Natural gas, much more widely used in the region, has a variation in price of 0.39 USD/GJ (IEA 2015). Similarly, climate change impacts across the continent are reflected by changes in hydropower capacity factor changes for South America of −0.5% from 2013–2050. Additionally, planned hydropower projects (48.8 GW) are included in the base model which and are therefore installed across all possible futures. The change of −0.5% in the capacity factor will not be a determining factor for further investments for hydropower.

Low-carbon pathways are generally correlated with perceptions of low investment risk. As results show, fossil fuel prices are not a significant driver of either whole system cost or low-carbon futures for South America and would not, at modelled levels, have enough impact to turn the system towards a low-carbon future. The cost of capital however is found to be a key determinant throughout our analyses with low cost of capital favouring more capital-intensive, often low-carbon, technologies. Higher levels of perceived risk, conversely, increase the cost of capital and hamper the introduction of these same technologies (Schmidt 2014, Iyer et al 2015b).

Both financial and political measures can be introduced to help de-risk these investments. Examples of 'financial' interventions might include subsidizing the interest rate or offering tax breaks for low-carbon technologies. Political 'interventions' could include the removal of barriers in the associated investment environment - such as streamlining the construction process (Carbon Pricing Leadership Coalition 2017).

Demand reduction has an important effect on both emissions and relative scenario costs. Contingent on them being cost effective, energy efficiency measures could decrease electricity demand without affecting major economic processes or decreasing living standards. As they would lower supply-side investment requirements, such measures would not need to mobilise higher levels of funding. By mapping the cost of energy efficiency measures under a US utility's efficiency program, Hoffman et al (2017) found the 'savings-weighted average cost' of efficiency measure to be 46 USD/MWh¹² across all sectors. The residential sector cost averaged at 30 USD/MWh whereas for the non-residential sectors cost savings averaged at 53 USD/MWh. Residential sector measures included the deployment of energy efficient lighting and appliances. Non-residential sector measures were mainly prescriptive and custom rebate program based.

These results indicate that efficiency measures are cheaper to implement compared to expanding power capacity. While US and South American conditions are different, the energy efficiency costs from Hoffman et al of 46 USD/MWh compare to the cost of increasing the demand in South America which ranges from 123 USD/MWh to 154 USD/MWh. In addition to energy efficiency measures, demand-side management systems (DSM) also offers peak shaving and can thus reduce the need for peaking or backup power plants. DSM (including demand response) systems also provide opportunities to utilize the energy from intermittent capacity such as wind and solar (IRENA 2015).

These findings suggest that energy efficiency and DSM should be the focus of future refinements of the OSeMOSYS based scenario discovery approach presented in this paper.

South America has significant natural resources along with large inter-connection and trade capacity. Together, these can protect the region from expensive generation options that are higher up the supply curve. Note however that this may change under cases with limited trade where countries with lower hydropower resources, unable to rely on their neighbours, may need to resort to more expensive options that drive up the cost to consumers. Further analysis may include the 'degree of inter-connectedness' as an additional scenario matrix dimension.

The CO₂ cap is set to the same target over all the countries, which provides information about the implications of the CO₂ cap in the region. As the countries are interconnected and have different NDC targets, analysis into the possible carbon leakages would also represent interesting future work.

With a high cost of capital, it is optimal to keep investing in gas generation ahead of the net zero-emissions cap in 2050 after which phasing out of fossil-fuelled power leaves idle capacity which remains unused (between 50–85 GW). In order for the system to have zero emissions, the reserve margin for the zero-emission scenarios has to be supplied by low-carbon technologies. These scenarios therefore lead to additional low-carbon capacity installation. This is consistent with other work (Lecuyer and Vogt-Schilb 2014), that notes that stranded assets increase the cost of the transition, and might be politically unacceptable (Rozenberg et al 2014b). There are several ways of mitigating this issue. One would be to use the idle fossil capacity to supply the reserve margin while investing in negative emissions options including e.g. CCS of the forestry sector. Another way is to lower capital costs by offering financial incentives for stakeholders to invest today in larger renewable capacity (see for instance the chapter on Finance in (Fay et al 2015)). Appropriate concessionary finance, with low interest rates on borrowing, may be an important key to unlocking clean growth.

Forecasting the electricity consumption using econometric approaches have been widely used e.g. (Mohamed and Bodger 2005, Bianco et al 2009), using economic and demographic variables as predictors. The demand projections for SAMBA are divided into three steps. First, the electricity consumption is forecasted using econometric forecasting Vector Auto-Regression (VAR) or Vector Error Correction Model (VECM). The predictors used in the analysis are GDP and population forecasts for the 10 countries (except for Guyana as data was unavailable, where respective growth rate was applied) as seen in table B1.

As illustrated in figure B1, the evaluation process for the VAR and VECM follows three steps.

• 1.  
  To avoid spurious regression analysis a unit root test is preformed to determine whether the variables are stationary or not. For the test, the Augmented Dickey-Fuller (ADF) test is used for both intercept and time trend (for results, see table B2).

  • a.  
    If all variables are stationary at first difference I(1), a Johansen co-integration test is performed. If there are co-integrated equations, then Vector error correction model (VECM) is performed (for results see table B3).
  • b.  
    For the mixed integration degrees an unrestricted VAR model is developed where the variables are differentiated if non-stationary.

• 1.  
  For all residuals a heteroskedasity test, serial correlation test and normality test are performed to see if the residuals are white noise (for results see table B4).

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Step 2.

Urbanization rates are based on SSP1-SSP5 and connected to respectively forecasted SSP. The rates stay the same for SSP1, SSP4 and SSP5, thus the change in urbanization is accounted for only in SSP2 and SSP3 as seen in equation B.

$$\begin{eqnarray*}\begin{array}{lll}Electricity\,demand & = & F(pop,GDP)+Durbanisation\\ & = & F(pop,GDP)+(urbSSP1\mbox{--}urbSSP2/SSP3)\\ & & * \,PopSSP2/SSP3\,* \,(UrbKWh/cap\mbox{--}RurKWh/cap)\end{array}\end{eqnarray*}$$

The delta between urban demand compared to rural demand is estimated for Bolivia in (Peña et al 2017) at 349 kWh/capita in 2035. Bolivia is a country in the region with a high urbanization rate. Its delta is assumed representative for the other South American countries. The data was extrapolated to 2060 with a difference between urban and rural consumption of 510 kWh/capita.

Step 3.

The electric vehicle (EV) electricity consumption from (Guivarch and Fisch 2016) is defined for Latin America based on the EMF-450 scenario from Assessment Report 5 (AR5) scenarios. There are 6 scenarios developed for the transport sector, which follow the narrative of the AR5 scenarios. The assumed corresponding SSPs with the transport scenarios from AR5 scenarios are illustrated in figure B2. The data were disaggregated in two steps. First, the total electricity demand was divided by the projected population for EMF-450 scenario. Second, the electricity demand per capita was multiplied by each SSP projected population per country.

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The electricity demand from transportation was assumed to be an additional demand which was not included in any of the previous steps. Thus the EV demand/capita was added to the total demand.

The results did not reach satisfactory levels in the VAR/VECM analysis for Colombia. Colombia and Guyana was therefore assumed to have the average growth rate of South America for each SSP scenario. The final results for the region can are illustrated in figure B3.

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Renewable technology learning curves were based on the National Renewable Laboratories (NREL) projections (NREL 2016). The RET technologies with learning potential considered in the analysis are: On-shore Wind, Offshore Wind, Solar Utility PV, CSP and Geothermal. Two parameters are considered for the learning curves: Efficiency and cost. As shown in figure B4 the highest capital cost reductions are for CSP, Off-shore Wind and PV.

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Regarding capacity factors, seen in figure B5, learning curves are related to wind power while other technologies are expected to stay the same throughout the modelling period. (Therein efficiency and cost improvements are assumed to fully account for the learning).

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The discount rate was set to 3%, 6% and 12% to represent a spread of plausible pathways. For all power plant technologies, the discount rate was similarly used to represent interest rate during construction (IDC)—thus capturing the cost of borrowing capital and not simply the overnight cost. The modelled costs for the three discount rates are illustrated for 2013 and 2050 in table B5 (renewable technologies are based on medium cost). For the renewable technologies the capital cost is dynamic, meaning that depending on the combination of discount rate and renewable technology (with its respective learning) the capital cost varies with both the discount rate and the technology cost profile.

The life span, fixed and variable cost of each technology was obtained from the Energy Technology Systems Analysis Program (ETSAP) Technology Brief reports (IEA ETSAP 2010a, 2010b, 2010c, 2010d, 2010e, IEA ETSAP 2010a, 2010b, 2010c, 2010d, 2010e, IEA ETSAP 2010a, 2010b, 2010c, 2010d, 2010e, IEA ETSAP 2010a, 2010b, 2010c, 2010d, 2010e, IEA ETSAP 2010a, 2010b, 2010c, 2010d, 2010e, IEA ETSAP 2013a, 2013b, IEA ETSAP 2013a, 2013b, IEA ETSAP 2014). For fossil fuel technologies, the thermal efficiency and its corresponding future improvements was obtained from the Energy Technologies Perspectives report (IEA ETP 2012, IEA ETP 2014, IEA ETP 2015).

The CO₂-emission cap was set to three levers:

• (1)  
  No limit
• (2)  
  50% reduction of 2013 emissions by 2050, with a peak in 2040.
• (3)  
  0% emissions by 2050 with a peak in 2020.

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The capacity changes with changes (as a function of demand, but also) in technology investment—in particular as variable renewable energies are added. This reflects the power system reliability needs—and the requirement to maintain an invoke-able reserve margin. The reserve margin is the difference between the effective installed capacity and the system peak load, expressed in percentage value. A functional power system usually operates with 15%–18% reserve margin (Rochlin 2004). These vary as a function of system specifics, reliability requirements, risk perception and other factors. For SAMBA, a 15% reserve margin was set for all countries. To account for variability, and yet maintain a reserve margin, 'capacity credits' are assigned. These represent the amount of capacity for which can be accounted for the reserve margin. For the SAMBA model the chosen capacity credits are shown in table B6 where solar and wind power would have a lower capacity credit as the timing of the peak demand might not coincide with the availability of solar and wind.

Because the energy system in the 0% emissions scenario has no carbon emissions, the reserve margin contributions from fossil fuelled technologies are from 2040 gradually phased out. By 2050 only carbon free technologies are allowed to satisfy the capacity reserve constraint. With their associated capacity credit, total investment numbers increase.

The fossil fuel price development is based on two reports: World Bank Commodities Price Forecast (constant US dollars) July 2016 and World Energy Outlook (2015) (World Bank 2016, July) (IEA 2017). For the years 2013–2025 all scenarios are based on the same forecasted price from World Bank Commodities Price Forecast (figure B7). From 2025–2040 the two projected scenarios: Current policies scenario (high) and Low oil price scenario (low) is applied. From 2040 and onwards the Compound Annual Growth Rate (CAGR) from 2013–2040 is applied.

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Many of the South American countries have large reserves of fossil fuels and the domestic price of fuels are assumed to be 5% cheaper than the international price due to reduced costs for logistics. Trade between the interlinked countries such as Argentina and Bolivia the international price is assumed for the consuming country.

The climate change scenario has two levers: one with a static future climate and the other with a climatic change following the Representative Concentration Pathway (RCP) 8.5. The RCP 8.5 is the scenario with the highest emissions and temperature changes for AR5 (IPCC 2007, 19–21 September). The data which was used were from two data sets:

• (1)  
  Discharge projection (Alfieri et al 2017) 2006–2057. The monthly average discharge was identified for locations with existing hydro power plants (Geofabrik 2016) (as seen in figure B8). This was identified based on changes in the geographically closest location. Discharge data was aggregated to the level at which generation data is available.

• (1)  
  Monthly generation data for all hydro technologies are considered in SAMBA. For power plants in Brazil and Venezuela with hydro storage, the Affluent Natural Energy (ANE) was modelled instead of generation as this is more closely connected to the discharge compared to the generation collected from the national databases: (CONELEC 2010, Goberno de Bolivariano de Venezuela 2012, Autoridad de Fiscalización y Control Social de Electricidad 2013, COES 2013, ADME 2013, Comisión Nacional de Energía Atómica 2013, ONS 2013, SIEL 2014, CNE 2015).

In the case of Guyana and Tele Pires, generation data was not available and were instead based on discharge change from 2013 (average of 2006–2013) to 2050 (average 2045–2055). Bel Monte Dam, Paraguay Large hydro, Tapajos, Madeira did not have available discharge data nor generation data and the closest regional change was assumed for these.

To be able to use the discharge as a predictor, a vector auto regression (VAR) with seasonal adjustment with dummy variables was applied. The following steps for the VAR for each hydro technology in SAMBA were executed.

• 1.  
  Unit root test (Augmented Dicker Fuller) to assess if the process (both generation and discharge) is stationary.
• 2.  
  Unrestricted VAR with generation as dependent variable, discharge as endogenous and dummy variables as exogenous.
• 3.  
  Lag-length criteria is assessed from Akaike Information Criterion (AIC) and Schwarz Information Criterion (SC) to find the optimal lag length.
• 4.  
  Evaluation of the quality of the forecast is based on R-squared, Durbin-Watson, AIC, Root Mean Square Error (RMSE), Covariance Proportion and Thiel Inequality coefficient.
• 5.  
  The process is reiterated from step 2 to find the best fit with different seasonal division (6 months, 12 months and no season).

To keep the model from having any changes from the 'no climate change' scenario in the starting years the percentage change from the VAR was applied to existing capacity factors to keep consistency between scenarios. All percentage changes were calculated on a monthly basis to capture the seasonal changes of generation with climate change.

The results are shown in figure B9 for both the discharge changes (average of 2006–2013 to average of 2045–2055) and forecasted generation changes (2013 to average of 2045–2055). In general, the discharge changes are higher than the generation changes.

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A study by (Schaeffer et al 2008) analysed the impact of climate change in hydrology for Brazil. Schaeffer et al based their analysis on the Special Report on Emissions Scenarios (SRES) A2 scenario, which in Assessment Report 4 (AR4) was the high emissions scenario. They found a hydrology generation impact of −1% for Brazil for the period 2071–2100. The results from this study found an overall generation impact for Brazil of −1.5% for the RCP 8.5 for the period 2045–2055. Comparing the RCP 8.5 to SRES the scenario it is comparable to the A1F1 scenario which has higher emissions than A2 (IPCC 2000, SEI 2016). The higher impact in this study can be explained by the difference in scenario projections.