In this paper, we first proceed to develop the mathematical tools for the calculation of CO2 emissions abatement (annual and total) due to the installation of concentrating solar power (CSP) plants.

In this paper, we first proceed to develop the mathematical tools for the calculation of CO emissions abatement (annual and total) due to the installation of concentrating solar power (CSP) plants instead of the traditional systems. For this, we take into account the targets for the CSP cumulative installed capacity from several scenarios elaborated by the International Energy Agency. We have also developed in this paper mathematical closed-form expressions for the evaluation of the extra-costs of implementing these scenarios, and calculated the unit costs of the CO emissions avoided by the new CSP systems. The obtained results are shown both graphically and numerically, and their applications to energy planning policies are discussed. From the results exposed in this paper, it is possible to evaluate the economic advantages of installing the new CSP plants in those geographical areas with higher pollutant electricity mixes, as well as the planning of the most convenient calendar for CSP systems implementation.

Due to the continuous global growth in total energy demand, most scenarios contemplate a permanent increase in greenhouse gas (GHG) emissions, but partly tempered, among other factors, by improvements in energy efficiency and the introduction of additional renewable resources. Even taking these factors into account, most studies predict that global CO emissions in 2030 will show an increase of 20%–25% over the present levels. 1 In effect, according to the recent report of the International Panel on Climate Change (IPCC), 1 in order to avoid by 2050 an increase in the global temperature above 2 °C, the amount of CO emissions should peak in about one or two decades, and from there on start to diminish. To achieve this objective implies that the CO atmospheric concentration is maintained in the 450–500 parts per million (ppm) range.

Under the most stringent scenarios elaborated by the International Energy Agency (IEA), 2 the power-generating sector is the one that can contribute the most (around 40%) to CO emission reductions, followed by industry, transport, and buildings with about 20% each. Therefore, it will be desirable within the power-generating sector, the continuous implementation of renewable resources at sufficiently high growth rates. For instance, at present wind and solar technologies are growing at the tremendous annual rates of 27% and 42%, respectively, during the last decade. 2,3 In the case of photovoltaics (PVs) this remarkable growth has been mainly possible due to the large reduction of solar modules costs during the last 4–5 yr.

It is at present recognized that for the next decades renewables will be one of the main players in reducing carbon emissions, especially those corresponding to power generation. According to the Blue Map and Roadmap IEA Scenarios, 4,5 in 2050, concentrating solar power (CSP) generation might represent 5%–11% of all the electricity produced in the world. The main advantages of CSP are: 6–8 (a) Hybridization, usually with gas, when there is not enough solar irradiation. (b) Thermal energy storage. (c) Electricity costs approaching grid parity in locations with high direct solar radiation or in relatively isolated regions (islands). (d) CSP shows the lowest life-cycle emissions of all renewables. 9

There are several publications on the contribution of renewable solar technologies to CO abatement. However, most of them are related to PV solar technologies due to its higher degree of development. 10–13 In fact, we have only found one publication addressing the whole life-cycle CO emissions in relation to CSP electricity production. 14 Therefore, in this paper, we intent to fill this gap by calculating first the CSP contribution to the mitigation of CO emissions, and second the extra-costs (ECs) incurred in the implementation of this technology. Evidently, for this, we have to previously estimate the present and the future Levelized Costs of Energy (LCOE) for CSP, for what we have followed a method previously established by us. 15,16

A.  Past and present status of CSP

Figure 1 represents the cumulative installed capacity and the annual electricity production of CSP systems between 2003 and 2012. 17–20 It can be observed from this figure that the cumulative installed power has increased considerably during the last years, from 1.08 GW in 2010 to 1.58 GW in 2011 and reaching 2.5 GW at the end of 2012, when 3.7 TW h/yr of CSP electricity was produced. Notice also that during the period 2006–2012, the CSP market has experienced a considerably annual growth rate of 40% in the cumulative installed capacity, mostly in Spain and the United States. Besides, in the short term, the growth for CSP is assured, due to the large number of projects under construction or in the development stage, especially in countries with very high direct normal irradiance (DNI), which would add up to 12 GW in 2018. 21,22 This estimation takes into account the reconversion of some projects from CSP to PV, as well as the possible influence of the lowering of the feed-in tariffs in countries like Spain.

B.  CSP technology roadmaps and scenarios from the IEA

We have considered in this work three different scenarios published by the IEA in order to compare the effect of CSP implementation on each of them, in terms of CO saved emissions costs incurred in the process. These scenarios justify their importance in terms of urgency to slow down global warming. In effect, it has been estimated by the last IPCC report 1 that if the trends in emissions would continue at the present rate, the average atmospheric temperature could reach an increase of as much as 4–6 °C by the end of this century.

The objectives for the cumulative installed power and the annual electricity production for each of the three IEA scenarios considered (New Policies, Blue Map, and Roadmap) have been summarized in Tables I and II , respectively. As one can derive from Tables I and II and Sec. II A , there is a large increase of the outputs of CSP plants per unit of installed capacity between 2013 and their future values (2020–2035). This is due to several factors. First, we have assumed that most of the future plants will incorporate a substantial amount of thermal storage, as a consequence of its proven better economic and technical performance. In addition, we have assumed that future CSP plants will be mainly installed in locations with higher DNI, since at present many plants are located in places with DNI very close to the lowest values to achieve a reasonable economic performance, i.e., 2000 kW h/m 2/yr (case of Southern Spain). Finally, we have also considered that the thermal and optical efficiencies of the plants will improve as a consequence of learning and R&D advances.

The most moderate scenario of the three considered in this work is the New Policies Scenario, 17 which reflects pledges by countries to cut emissions and boast energy efficiency. This scenario aims to mitigate global warming by stabilizing the annual CO emissions around 40 Gt/yr before 2035. In order to reach this objective it would be necessary to triple the renewable electricity production in 2035 with respect to 2010, so that renewable energy sources would represent 31% of the world electricity mix in 2035. 17 CSP systems would be a relevant contributor in order to achieve those emissions reductions, but we would like also to remark that we have used this scenario as a baseline for comparison with the other two more ambitious IEA scenarios.

In our opinion, the most relevant scenario of the three considered is the Blue Map, 4 published in 2008, and renamed in 2012 as the 2DS Scenario. 2 This scenario pretends to cut down CO emissions in 2050 to half their level of 2009, what would result in a stabilization of the CO atmospheric concentration around 450 ppm, and a global warming of just 2 °C. For this purpose, annual CO emissions should reach their maximum level in 2020, with 32 Gt/yr, and thereafter start reducing up to 23 Gt/yr in 2035 and 16 Gt/yr in 2050. The contribution of CSP in this scenario would be of around 5% of the world electricity mix in 2050. 4

Finally, the third scenario considered in this work is the Roadmap Scenario 5 published in 2010, which forecasts that in 2050 CSP systems would provide about 11% of the world electricity production. This is the most ambitious scenario of the three and would harmonize with the optimistic predictions of the CSP industry.

C.  Analytical expressions for the evolution of CSP installed power and electricity generation

In this section we assign, for each of the three IEA scenarios, an analytical equation for the future evolution of the cumulative installed power Q(t) and the annual electricity production E(t), for a year t between 2013 and 2035, which is the period that we have considered in our study. We would like to remark the importance of assigning analytical closed-form expressions to Q(t) and E(t), since this will allow us to directly calculate and plot our results (Sec. IV ) in a continuous (year by year) and accurate way, that is, without applying mathematical approximation techniques. Obtaining analytical expressions has other additional advantages since they allow the calculation of the sensitivity factors simply by differentiating.

We have taken as the reference year in our studies the beginning of 2013, when the values of Q(t) and E(t) were 2.5 GW and 3.7 TW h/yr, respectively (see Figure 1 ). With these values and the intermediate and final objectives of the three scenarios, summarized in Tables I and II , we next assign the analytical equations that best fit those objectives. Although the period considered is just 2013–2035, we have also taken into account the objectives until 2050 in order to estimate the trends of the fitted analytical curves at the end of the period considered.

One of the most frequently used equations for the analytical simulation for Q(t) and E(t) is based on the well-known logistic function (“S shaped curve”), whose expression for the cumulative installed power for a year t, after 2013, would be 23

Q(t)=er(t2013)(1/Q(0))(1/M)+(er(t2013)/M),

(1)

where Q(0) is the initial value, i.e., the cumulative installed capacity at the beginning of 2013, M the maximum value of Q, and r the so called growth factor. Evidently, the equation for E(t) would be analogous to Eq. (1) .

In Table III , we have listed the functions, and the values of the parameters, for the specific analytic equations of Q(t) and E(t) assigned to each scenario. In all cases, except in the Roadmap Scenario for which we have assigned a second grade polynomial, the function that best fits the specified targets is the logistic curve. In Figure 2 , the specific curves proposed in Table III for the annual electricity production E(t) between 2013 and 2035 have been represented, together with the objectives for each scenario. The representation of Q(t) is very similar to the evolution of E(t) shown in Figure 2 and therefore has been omitted.

In this section, we will first derive in Subsection III A the expressions for the calculation of the CSP curtailment of CO emissions, both annually and total, in the period 2013–2035. Subsequently in Sec. III B we will develop the expressions for the calculation of the extra-costs that have to be incurred in this operation, which finally will allow us in Sec. III C to establish the unit emission costs per tonne of CO avoided. Once these expressions are obtained, in Sec. IV we will represent and discuss the numerical results derived in this section.

A.  CO emissions curtailment by implementing CSP plants

For the calculation of the avoided emissions, we first assign specific values to the CO emissions per kW h produced for each technology considered, including both CSP and also the conventional energy sources, mainly based in fossil fuels, which will be replaced. Due to their preponderance in the whole world, and for simplicity reasons, we have considered the electricity generated from the major conventional fuels like coal, natural gas and nuclear power, as the reference sources to be substituted for the following reasons. Coal is the fuel most used in the world for electric power generation since it is cheap and widely available, whilst the use of natural gas is continuously increasing due to its higher flexibility and lower CO emissions. Last, nuclear power reduces the energy dependence of countries and has a modest CO footprint.

Although CSP systems do not emit , all the emissions caused during their whole life-cycle, mainly due to the construction and operation of the plants, will be taken into account in this work. CSP systems have, at present, associated emissions that range between 14 and 32 gCO /kW h, 1,24 and therefore we have considered the average value recommended by the IPCC 1 of 22 gCO /kW h. We have also considered that these emissions will diminish linearly in the future, reaching 11 gCO /kW h in 2050. 24 We have summarized in Table IV , besides the values previously considered for CSP systems, the carbon emissions associated with coal, natural gas, and nuclear power plants, both, currently in 2013 1,25,26 and the expected values in 2050. 27 By using a linear approximation, we have also included in Table IV the analytical equations that determine the annual evolution of the associated emissions Y(t) for each technology. In these expressions, Y is given in gCO /kW h units and t varies from 2013 to 2035. As the reader can easily check, by substituting in the equation Y(t) = at + b, the constants a and b by the values given in Table IV , one gets the proper values for 2013 and 2050. Note that the large reduction in the coal emission factor from 2013 to 2050 is partly due to the assumption that in 2050 a relevant share of the coal power plants will be equipped with carbon capture and storage (CCS) systems. Another important fact that contributes to this emission factor reduction is that at present many inefficient old plants are still in operation; however, these plants will supposedly be reconverted or decommissioned in the near future.

We next develop the equations to estimate the savings in CO emissions due to the installation of CSP systems in the period 2013–2035 for each scenario considered for CSP implementation, and in relation to the conventional electricity sources to be replaced by CSP. As a way of illustrating the replacement procedure, we have considered two different reference electricity mixes constituted just by conventional energy sources. Evidently this could be performed for any specific region and electricity mix, but in this work we only pretend to set the basis for the calculation of CO emissions avoided while replacing conventional energy sources (for instance coal, natural gas, nuclear power, etc.) by CSP generation systems. Accordingly, in Table V , we have defined two reference mixes to illustrate the procedure: mix A is composed of coal and natural gas power plants equally, i.e., 50% each, whilst mix B also includes nuclear power as a third component, i.e., 33.3% each technology. In addition, and for comparison purposes, we have also considered in our work the electricity mix corresponding to the whole world, whose associated emissions are at present around 536 gCO /kW h. 25 For simplicity reasons we have assumed this value as constant during the 2013–2035 period due to the foreseeable increase of electricity production in developing countries, like China or India, whose electricity mixes are considerably more pollutant than those corresponding to developed countries.

The fact that the mixes A and B are quite simple in comparison to other model-based projections does not mean that the corresponding results would be very different of those obtained from more realistic or heterogeneous mixes (for instance, the one corresponding to the world average), as we will show in Sec. IV . This is due to the fact that the most important factors of the conventional technologies that we use in our analysis are the emissions factors and the levelized cost of energy, to which we have assigned values which are consistent with other many climate scenarios (see Ref. 28 ), and future energy and emission projections elaborated by the IEA. 2,4,5,17,25,29 In addition, mix A could be representative of those regions with electricity mixes mostly dependent on fossil fuels, whilst mix B closely resembles the world average, for which approximately 2/3 of the mix corresponds to fossil fuels and the remaining 1/3 to non-emitting sources (nuclear, hydro, renewables, etc.). In fact, close to 70% of the World’s electricity was generated from fossil fuels in the period 1990–2012. 30

In Table V , we have summarized the equations that determine the CO emissions avoided by CSP systems, F(t) in gCO /kW h units, during the 2013–2035 period, for the mixes A, B and the World average. Notice that the functions F(t) are estimated as the difference between the emissions associated with conventional energy sources, properly weighted with the corresponding electricity mix, and the corresponding to CSP systems (see functions Y(t) in Table IV ).

According to our previous definitions, the annual CO saved emissions, for a year t between 2013 and 2035, for each scenario considered, would be

CO2(t)=F(t)E(t),

(2)

where F(t) are the emissions saved per kW h for each mix in the period 2013–2035, summarized in Table V , and E(t) is the annual CSP electricity production for each scenario considered (see Table III and Figure 2 ).

The total savings in terms of CO emissions during the period 2013–2035 for each scenario, would therefore be

CO2=20352013CO2(t)dt.

(3)

The results obtained for the annual and total CO avoided by the implementation of the CSP technology will be represented in Sec. IV A in Figures 4 and 5 , respectively.

B.  Total extra-costs to accomplish the scenarios considered

In this section, we establish the expressions for the LCOE and its future evolution for the electricity produced by the CSP systems between 2013 and 2035 for each scenario considered. The assignment of LCOEs is the method most frequently used when comparing electricity generation technologies and evaluating the economic feasibility of an electric generation project. The calculation of the LCOE is based on the equivalence of the so-called present value of the sum of the discounted revenues and the present value of the sum of discounted expenditures. 31 The discount rate used in LCOE calculations reflects the return on the capital for an investor in the absence of specific market or technology risks. 29 In order to determine the future evolution of the LCOE for CSP systems in the period 2013–2035, we use a model previously proposed by us. 16 This relatively simple model is based on the discounted cash flow (DCF) economic techniques and the experience curves approach, and estimates the cost during the whole lifetime of the system. In the following, all costs are given in 2013 US Dollars, so that they are not distorted by inflation rates. According to this model, the LCOE for the new systems installed in a future year t is given by 16

LCOE(t)=C(t)+L+Nn=1((O&M+I)C(t)/(1+r)n)Nn=1(STFη(1d)n/(1+r)n).

(4)

In this equation, the cost of the CSP system for a year t, C(t), is given by

C(t)=C(0)(Q(t)/Q(0))log(1LR)/log(2),

(5)

where C(0) is the initial cost of the system, i.e., in 2013, taken as 7.2 $/W for a plant with 6 h of storage. 32 Q(t) is the cumulative installed capacity evolution (see Table III ), and Q(0) is the value of Q(t) in 2013, i.e., 2.5 GW. LR is the learning rate, which according to the learning curve approach indicates the cost reduction per cumulative doubling of installed capacity, taken as 10% for CSP systems. 4,5 L is the land costs, and O&M and I are the operation and management costs and the insurance costs, respectively, expressed as a percentage of the cost of the system. N is the expected lifetime of the system, considered as 30 yr, 5 and r is the discount rate, taken as 10% for CSP systems. 29 S represents the solar resource, which for CSP systems is the DNI 33 taken in this work as 2400 kW h/m 2/yr. This value has been obtained from the average between the minimum DNI value to achieve a reasonable economic performance, which is around 2000 kW h/m 2/yr corresponding to some places in Spain, 5,34 and 2800 kW h/m 2/yr of some of the best locations in the southwest of the US. 6,35,36 TF is the tracking factor, 37 and d the annual output degradation rate. Finally, the performance factor η has been estimated as 1.452 m 2/kW. 32,38 The factors of Eq. (4) , which values have not been specified, have been explained before in previous works. 15,16 In Figure 3 , we have represented the future evolution 2013–2035, of the LCOE for CSP systems for the three scenarios considered, i.e., the New Policies, the Blue Map, and the Roadmap Scenarios (recall Sec. II C and Table III ). Additionally, we also represent in Figure 3 the LCOE for the electricity generated by coal, natural gas and nuclear power plants, whose average values have been taken as 7.25, 8.85, and 7.85 c$/kW h, respectively. 39 We have considered the cost of conventional electricity to stay constant in real terms, i.e., to increase its nominal value just at the same rate that inflation, taken as 2% in the US, 40 although this can be easily changed in case is necessary. This simplifying assumption can be partially justified due to the opposite tendencies in costs related to CCS incorporation to coal-power plants (Sec. III A ) and the expected lowering of costs due to learning and technological advancements.

We can observe in Figure 3 that the present LCOEs taken for the conventional energy sources (coal, natural gas, and nuclear power) are considerably lower than our calculation for CSP systems, more specifically, around three times lower. However, these differences will reduce substantially in the future, as CSP technology would progress according to its learning curve.

At this stage, we proceed with the calculation of the extra-costs, in relation to the electricity mixes considered (see Table V ), to accomplish the three CSP scenarios. In addition to “t,” that represents the year between 2013 and 2035 in which the CSP system is installed, we now introduce another temporary variation “x,” defined as a given year within the lifetime of the system, which obviously should be equal or greater than “t,” i.e.,

t
[2013,2035],

(6)

x[2013,2035],

(7)

xt.

(8)

To proceed further, we now determine the function of two variables E(t, x), that represents the electricity produced by all the CSP systems which were installed a year “t” during a certain year “x” of the lifetime of the system, i.e.,

E(t,x)=(E(t)(E(t1)(1d)))(1d)xt,

(9)

where E(t) and E(t-1) are the annual electricity production for a year “t” and “t-1,” respectively (see Table III ), and d is the annual output degradation rate, whose effect on E(t,x) increase as the years, “x-t,” pass in relation to the installation of the systems.

At this stage, we are prepared to calculate the EC for all the new CSP systems installed a year “t” during a certain year “x” of their lifetimes, which should be given by

EC(t,x)=(LCOE(t)LCOEMIX)E(t,x),

(10)

where LCOE(t) is the LCOE for the CSP systems installed in a year “t” (see Eq. (4) ) and LCOEMIX is the average electricity cost of the reference mix considered. Taking into account the composition of each mix stated in Table V and the LCOE for conventional energy sources used in Figure 3 , the LCOEMIX values are 8.05 and 7.98 US cents/kW h for the mixes A and B, respectively. In addition to the mixes A and B, the LCOE corresponding to the world electricity mix has been estimated as the average wholesale electricity price of the EU-27, 41 USA, 41 and China, 42 whose values are around 9, 7, and 7.8 c$/kW h, respectively. Consequently, we have estimated an average LCOE of the world electricity mix of 7.93 c$/kW h. The reason for choosing these specific regions is due to their importance and representativeness in the whole world, and also because of the difficulties to accurately estimate an average LCOE for the whole world since even the average LCOEs for the same regions fluctuate depending on the reference sources (see, for example, Refs. 41–45 ).

The total extra-costs incurred during a certain year “x” between 2013 and 2035, taking into account all the systems installed during the previous years, i.e., in the period from 2013 to x, is therefore given by

EC(x)=x2013EC(t,x)dt.

(11)

Now we can finally estimate the total extra-cost during the period 2013–2035 to accomplish the three scenarios that we have analyzed. These total extra-costs should be given by

EC=20352013EC(x)dx=2035x=2013xt=2013(LCOE(t)LCOEMIX)E(t,x)dtdx,

(12)

where LCOE(t) is determined by Eq. (4) and E(t,x) by Eq. (9) .

C.  Cost per tonne of CO saved

In order to compare the emissions saved due to CSP systems, with the corresponding to the replaced conventional technologies or with the carbon emission market price, we need to know the unit costs of the tonne of avoided CO . To estimate these unit EC (UEC), we just have to divide the total extra-costs to accomplish the scenarios considered (EC), given by Eq. (12) , by the total emissions of CO saved in the period 2013–2035 from Eq. (3) . Therefore, we have

UEC=EC/CO2=20352013EC(x)dx/20352013CO2(t)dt.

(13)

As we will see in Sec. IV , the concept of unit emission costs will be very useful for comparing the cost of the different technologies for emissions abatement in the power sector, including renewables, substitution of polluting fuels by cleaner ones, CCS, etc.

A.  Annual and total avoided emissions (2013–2035)

Based on the calculations from Eq. (2) , Figure 4 represents the annual CO emissions saved for each scenario, in gigatonnes per year (Gt/yr), in relation to mixes A and B (Table V ), for the period 2013–2035. As it can be observed, the path followed by the annual CO avoided emissions, represented in Figure 4 , is very different for each scenario, leading to quite diverse total amounts of CO saved in the period 2013–2035. In addition, by integration of these curves, as shown in Eq. (3) , we can get the total savings of CO emissions during the same period, whose results are shown in the legends of Figure 4 and separately in Figure 5 together with the results of the world average electricity mix. We would like also to highlight the large influence of the electricity mix considered in our estimations, which is mainly caused by the larger effectiveness of CSP for carbon abatement when the systems are installed in locations where the original installations emitted higher relative levels of CO .

The Roadmap Scenario, which is the one contemplating the highest CSP share in the energy mix of the three scenarios considered, presents a continuous and steady growth of the annual CO emissions avoided (see Figure 4 ), being quite remarkable the initial growth during the first decade. Consequently, the total emissions avoided in the period 2013–2035 are quite substantial, 9.6, 6.39, and 8.13 Gt, in the case of the mixes A, B, and the World average, respectively.

As it can be appreciated in Figure 4 , the Blue Map Scenario yields in 2035 an amount of annual avoided emissions, which is very similar to that of the Roadmap Scenario. However, the paths corresponding to how these values are reached are quite different. In the case of the Blue Map Scenario, most of the avoided emissions occur during the last decade of the study (2025–2035), and therefore the total CO saved in the period 2013–2035 is around 30% lower than in the case of the Roadmap Scenario, being 6.58, 4.38 Gt and 5.69 for the mix A, B, and the World average, respectively (see Figure 5 ).

Finally, the New Policies Scenario presents similar annual CO savings than the Blue Map until 2020, but from there on they increase progressively but at a much slower pace. Although annual emissions avoided in 2035 are around six times lower than for the Blue Map and Roadmap Scenarios (see Figure 4 ), the total emissions avoided between 2013 and 2035 are just three times lower than in the Blue Map Scenario, being 1.97, 1.31, and 1.67 Gt for the mixes A, B, and the World average, respectively (see Figure 5 ).

As far as we know, there are not detailed published results on emissions abatement caused by CSP deployment and therefore we are very limited to make comparisons to other results. The only data reported by the IEA 5 for the Roadmap Scenario is that annual CO emissions avoided by CSP systems would be around 2.5 Gt/yr in 2050, what is consistent with our estimations if we take into account the uptrend slope of the curves corresponding to the Roadmap Scenario in 2035 (Figure 4 ). In the case of the Blue Map Scenario, the IEA 4 only gives an estimation for 2050 that the annual emissions avoided would be of around 1.2 Gt/yr in 2050, a value that is consistent with our results for 2035, since in this year the slope of the curve reduces considerably (see Figure 4 ).

B.  Additional costs for CSP scenarios implementation (2013–2035)

In Figure 6 , we represent, according to Eq. (11) , the annual extra-costs to accomplish the three scenarios considered in the period 2013–2035 in relation to mix A (see Table V ). We have not represented those corresponding to mix B and the World average since the evolution of the curves would be analogous. Evidently, the shapes of these curves are influenced by both, the annual electricity production and the LCOE costs, represented in Figures 2 and 3 , respectively. Hence, for the case of the Roadmap Scenario (Figure 6 ) the extra-costs follow an almost linear progression, while for the Blue Map Scenario they grow very slowly during the first decade, until they start growing substantially and overtake the values corresponding to the Roadmap Scenario in 2029, reaching a considerable value in 2035. This pronounced uprising observed in the case of the Blue Map Scenario could be attributed to its higher LCOE, in relation to the Roadmap Scenario, as it can be observed in Figure 3 .

The total extra-costs (2013–2035) for the three scenarios represented in Figure 7 were obtained from Eq. (12) , by integrating the curves represented in Figure 6 . Their values are around 894, 861, and 322 USD billion for the Roadmap, Blue Map, and New Policies Scenarios, respectively, in the case of mix A, and a bit higher in the case of the mix B and the World average, due to its lower average LCOE. These results point out that the Roadmap and Blue Map Scenarios present practically the same total extra-costs, even though the Roadmap Scenario avoids a considerably higher (about 45%) amount of CO . This is due to a higher cost reduction in the Roadmap Scenario, as a consequence of a faster technology learning process, according to the learning curve approach. Finally, the less ambitious New Policies Scenario shows total extra-costs around three times lower than the Roadmap and Blue Map Scenarios.

We can next compare the results obtained in Figures 6 and 7 with the data provided by the IEA on the scenarios considered. First, for the Roadmap Scenario 5 there is no data available about the total extra-costs, and consequently our appraisals could be very useful for energy planning actions. The Blue Map Scenario 4 states that total additional investment in the power sector should amount to 3.6 USD trillion (1000 × 10 9) until 2050. More specifically, it also recommends an annual investment for solar power (including photovoltaics contribution) of around 61 and 124 USD billion/yr for the periods 2010–2020 and 2020–2030, respectively. Our calculations, represented in Figure 6 , agree relatively well with these appreciations. Finally, for the New Policies Scenario, the IEA 17 estimates that the total investment in CSP electricity for the period 2013–2035 should be of around 300 USD billion, which agrees fairly well with our estimations presented in Figure 7 , of 322 USD billion.

C.  Unit costs of avoided CO

In Figure 8 , we present the results of our calculations derived from Eq. (13) for the unit cost per tonne of avoided CO , for the three scenarios, and in relation to each electricity mix considered. It is interesting to observe that, even though the Roadmap Scenario is the most ambitious and costly to accomplish of the three scenarios considered, it yields the lowest costs per tonne of CO saved, of 93.1, 141.6, and 112.4 $/tCO for mixes A, B, and the World average, respectively. This can be interpreted as due to its higher initial growth, and consequently faster technology learning, which shows the convenience of an early and intensive investment. It is also for this reason that in the Blue Map Scenario the unit cost of saved CO is around 50% higher than for the Roadmap (130.8, 198, and 153.6$/tCO for mixes A, B, and the World average, respectively), in spite of the fact that in 2035 their predicted annual electricity production is practically the same. Finally, the more moderate New Policies Scenario, although it presents the lowest total extra-costs, is the one with the highest unit cost of CO saved, around 163.7, 247.8, and 195.3 $/tCO for mixes A, B, and the World average, respectively. We would like to remark that the economic results obtained in this work are quite dependent on the learning rate considered, what implies some degree of uncertainty. 46 Next, we try to position our results in the context of the data provided by the three Scenarios considered in this work. It is interesting to observe that, according to the IEA Blue Map Scenario, the marginal costs per tonne of CO avoided reach a value of 200$/tCO , 4 which is higher than the units costs calculated by us of 130, 198, and 153 $/tCO (depending on the electricity mix). As a first attempt, we can compare our estimations for CSP abatement costs with the corresponding to PV systems, which have been estimated by the IEA as 50$/tCO for the Roadmap Scenario. 47 Despite the fact that the methods and scenarios considered are partly different, we can generally appreciate that PV unit emissions costs are lower than those corresponding to CSP. However, since CSP systems normally include thermal storage, this could compensate for their higher costs.

In this article, we have developed various mathematical tools for the calculation of CO emissions abatement (annual and total) according to the targets proposed by several IEA scenarios (Blue Map, Roadmap, and New Policies) for CSP implementation. In addition, we have calculated the corresponding financial extra-costs. We would like to remark that in all of the above calculations, we have taken into account the often ignored degradation of the CSP plants over their lifetime (30 yr), as well as their life-cycle CO emissions, inherent to any electrical power technology, including renewable.

From the results presented in this paper, we can reach the following conclusions: (i) Following the calculation of the unit extra-costs for avoiding C-emissions by implementing CSP systems during the period 2013–2035, we have also evaluated how much more economically efficient is for the new plants to be installed in those specific geographical areas where, at present, the electricity generated produces the highest amount of emissions; in addition, we have estimated how much lower the unit extra-costs are, per ton of avoided CO , the earlier the investments in CSP plants are made. (ii) From the study of the IEA Scenarios, it can be concluded that the unit extra-costs strongly diminish as the targets for CSP deployment get larger. (iii) From our results, it is clear that the values of the European Union on carbon emissions trading (at most 20 $/tCO ) are insufficient to compensate for the extra-costs derived from CSP implementation, which we estimate should range between 50 and 80$/tCO . (iv) The analytical method developed in this work allows to complement the scarce CSP data on avoided emissions and corresponding costs supplied by the IEA with the values derived from our proposed analytic curves specified on a year-to-year basis. (v) Finally, the results of this paper can be of interest in energy planning policies, like those related to the design of future scenarios for reducing CO emissions by means of renewable systems for power generation.

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1,2,a)

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a) Author to whom correspondence should be addressed. Electronic mail: martinez.duart@uam.es.

J. Renewable Sustainable Energy 6, 053134 (2014); http://dx.doi.org/10.1063/1.4899191