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SUPPLEMENTARY INFORMATIONDOI: 10.1038/NCLIMATE2717

NATURE CLIMATE CHANGE | www.nature.com/natureclimatechange 1

Supplementary Information

of 26

Solar Thermal Technologies As A Bridge from Fossil Fuels to Renewables

Name: Vishwanath Haily Dalvi

Email: [email protected]; [email protected]

Postal Address: Institute of Chemical Technology, Nathalal Parekh Marg, Matunga, Mumbai – 400019, INDIA

Tel: +91 99 8725 0603

Name: Sudhir V. Panse

Email: [email protected]


Tel: +91 22 3361 2661

Name: Jyeshtharaj B. Joshi

Email: [email protected]


Tel: +91 22 2559 7625 Fax: +91 22 3361 1020

© 2015 Macmillan Publishers Limited. All rights reserved

http://dx.doi.org/10.1038/nclimate2704

2 NATURE CLIMATE CHANGE | www.nature.com/natureclimatechange

SUPPLEMENTARY INFORMATION DOI: 10.1038/NCLIMATE2717Supplementary Information

of 26

Supplementary Discussion: 1. Introduction

The need to cut greenhouse-gas emissions drastically is well recognized. However, thermal power plants burning fossil fuels, which are the largest single source of global greenhouse gas emissions1,2, supply the overwhelming majority (~70%) of the world’s power3–5. Although some renewable technologies for power-production, notably wind and solar-photovoltaic can reasonably claim to have reached “grid-parity”6,7, this is only true intermittently: as long as the sun is shining or the wind is blowing. The cost of electric storage (e.g. battery8 or pumped-hydostorage9) and the significant changes to power distribution infrastructure required, make intermittent energy technologies still uneconomical for providing base-load or dispatchable power; as the German experience will warrant10,11. Hence, notwithstanding the forceful arguments in favour of mothballing coal-fired power plants12,13, this is not a feasible medium-term solution even in the developed world11. On top of this, it now appears that the renewables renaissance is under pressure from a new era of cheap hydrocarbons14. Although an excellent case can be made for pricing/taxing carbon-dioxide emissions13,15 as a means to encourage greater adoption of renewables, the design of such instruments is non-trivial16 and any step towards enforcement is likely to encounter stiff resistance from a wide swath of the socio-political spectrum in the developed world15,17 and find practically no traction in the developing world18. The current thermal power infrastructure is fully depreciated, has decades of operational life left and hence the immediate effect of applying carbon pricing will merely be an increase in electricity/fuel prices which will disproportionately burden the poor i.e. it could easily become a regressive tax which will need complex instruments (“green cheques” etc) to offset. The problem is severe19 enough that the founders of Google’s ambitious RE<C program have despaired of finding a solution with current technology20.

This paper presents a strategy by which the existing fossil fuel power plant infrastructure can be co-opted to progressively mitigate greenhouse gas emissions in an economical and sustainable manner.

Solar thermal electricity generation, accompanied by cost-effective thermal storage, is widely held to be the renewable resource utilization strategy that promises to deliver base-load and/or dispatchable electricity in the medium term21,22, pending development of radically cheaper electricity storage devices or perhaps massive deployment of wind-power23. Notwithstanding the fossil-fuel “backup” (used to tide over periods of lower solar intensity and/or extend operation beyond sunlit hours), these plants are conceived as primarily solar powered and thought of as replacements for conventional fossil-fuel fired thermal power plants22. However, as things stand, solar-thermal power production is on the back-foot especially in comparison to solar-photovoltaics24, with several solar-plant developers having shifted from the former to the latter in the recent past25.

A major reason for this poor show is the strategy of conventionally deploying solar-thermal power plants a la the SEGS systems of the Californian desert26 or the numerous solar thermal projects implemented in Spain27; which constitute the overwhelming majority of solar-thermal power producers28. The alternative is to integrate solar-thermal technology into the heat cycle of a conventional fossil-fuel fired power plant; a straightforward implementation since the power block of both is essentially the same. The idea of such synergetic solar aided/assisted/augmented/boosted/repowered fossil-fuel power plants has been investigated for


Page 3 of 26

some time29. However, this strategy has not drawn the attention it deserves from the stakeholders in the field. As a result, these plants constitute less than a tenth of the total installed solar-thermal power capacity* around the world28 and find no mention in comprehensive renewable energy roadmaps by Pacala and Socolow (2004)34, Shinnar and Citro (2006)35 and only a passing mention in the solar-thermal roadmap of the International Energy Agency (IEA) in 201022. A separate report by the National Renewable Energy Laboratory (NREL) in 201136 argues that the solar-augment potential of American thermal power plants is less than 5%.

A possible explanation for this neglect of a promising strategy could be a “one-plant-one-fuel” paradigm in the area of power production. We must point out that this neglect is not benign. Solar-thermal subsidies (e.g. in Spain and the United States) are designed to reward conventionally deployed solar-thermal power producers with an upper limit set to fossil-fuel co-firing. Such a policy clearly precludes solar-aided fossil fuel power plants, with minority solar-fractions, from its rewards.

This paper presents a comprehensive analysis of the benefits of injecting solar-thermal heat, harvested by various technologies, into the Rankine cycle of a coal-fired power plant. We have shown that there is no thermodynamic barrier to reaching as high as 50% (details given later) fossil fuel offset using existing line-concentrating technologies and with solar-to-electricity conversion efficiencies several percentage points better than those obtained by conventionally deployed solar thermal power plants. We also bring out several other subtle synergies of such integration.

It is therefore the contention of this paper that solar-thermal technology should not be treated on par with intermittent power production systems like photovoltaics or wind-turbines but treated as an independent category in itself for policy purposes. An example of the result of such a policy change would be to relax the requirement for large solar fractions in solar thermal power plants for attracting government assistance; but rather the solar thermal contribution to solar-aided power plants should be monitored for extending support to this technology. Policy recommendations in this direction are already made while keeping in mind the fossil-fuel backup of conventionally deployed solar thermal power plants22 but their scope needs to be extended to the solar-fraction of solar-aided thermal power plants.

An additional, and vitally important, advantage of such plants is modularity i.e. that the solar thermal component can be applied incrementally depending upon available financial resource, or available land or DNI, facilitating project planning, execution and maintenance and greatly lowering project risk.

We have explored the benefit of integrating several common, ready-to-deploy, solar-thermal technologies into a coal-fired thermal power plant operating on the Rankine Cycle in a simple, transparent manner that also generalizes the analyses already presented29. We have shown thereby that optimum solar thermal radiation harvesting calls for a portfolio of technologies, each optimized

* Notable plants executing this strategy are the Martin-Next-Generation-Solar-Energy-Centre in South Florida (with installed solar capacity corresponding to 2% of the 3.8 GW plant), Kogan Creek Solar Boost in Australia (6% of 750 MW), ISCC Kuryamat in Egypt (15% of 140 MW) and ISCC Hassi R’Mel in Algeria (17% of 150 MW). None of these plants have thermal storage i.e. their fuel offsets are a quarter of their fractional capacities. The 100 MW Shams-I plant in the UAE, with natural gas fired steam superheaters following solar-thermal boilers, may also be considered an example, though it would have been more efficient to pass the natural gas through a Brayton cycle first.




SUPPLEMENTARY INFORMATIONDOI: 10.1038/NCLIMATE2717Supplementary Information

Page 2 of 26

Supplementary Discussion: 1. Introduction

The need to cut greenhouse-gas emissions drastically is well recognized. However, thermal power plants burning fossil fuels, which are the largest single source of global greenhouse gas emissions1,2, supply the overwhelming majority (~70%) of the world’s power3–5. Although some renewable technologies for power-production, notably wind and solar-photovoltaic can reasonably claim to have reached “grid-parity”6,7, this is only true intermittently: as long as the sun is shining or the wind is blowing. The cost of electric storage (e.g. battery8 or pumped-hydostorage9) and the significant changes to power distribution infrastructure required, make intermittent energy technologies still uneconomical for providing base-load or dispatchable power; as the German experience will warrant10,11. Hence, notwithstanding the forceful arguments in favour of mothballing coal-fired power plants12,13, this is not a feasible medium-term solution even in the developed world11. On top of this, it now appears that the renewables renaissance is under pressure from a new era of cheap hydrocarbons14. Although an excellent case can be made for pricing/taxing carbon-dioxide emissions13,15 as a means to encourage greater adoption of renewables, the design of such instruments is non-trivial16 and any step towards enforcement is likely to encounter stiff resistance from a wide swath of the socio-political spectrum in the developed world15,17 and find practically no traction in the developing world18. The current thermal power infrastructure is fully depreciated, has decades of operational life left and hence the immediate effect of applying carbon pricing will merely be an increase in electricity/fuel prices which will disproportionately burden the poor i.e. it could easily become a regressive tax which will need complex instruments (“green cheques” etc) to offset. The problem is severe19 enough that the founders of Google’s ambitious RE<C program have despaired of finding a solution with current technology20.

This paper presents a strategy by which the existing fossil fuel power plant infrastructure can be co-opted to progressively mitigate greenhouse gas emissions in an economical and sustainable manner.

Solar thermal electricity generation, accompanied by cost-effective thermal storage, is widely held to be the renewable resource utilization strategy that promises to deliver base-load and/or dispatchable electricity in the medium term21,22, pending development of radically cheaper electricity storage devices or perhaps massive deployment of wind-power23. Notwithstanding the fossil-fuel “backup” (used to tide over periods of lower solar intensity and/or extend operation beyond sunlit hours), these plants are conceived as primarily solar powered and thought of as replacements for conventional fossil-fuel fired thermal power plants22. However, as things stand, solar-thermal power production is on the back-foot especially in comparison to solar-photovoltaics24, with several solar-plant developers having shifted from the former to the latter in the recent past25.

A major reason for this poor show is the strategy of conventionally deploying solar-thermal power plants a la the SEGS systems of the Californian desert26 or the numerous solar thermal projects implemented in Spain27; which constitute the overwhelming majority of solar-thermal power producers28. The alternative is to integrate solar-thermal technology into the heat cycle of a conventional fossil-fuel fired power plant; a straightforward implementation since the power block of both is essentially the same. The idea of such synergetic solar aided/assisted/augmented/boosted/repowered fossil-fuel power plants has been investigated for


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some time29. However, this strategy has not drawn the attention it deserves from the stakeholders in the field. As a result, these plants constitute less than a tenth of the total installed solar-thermal power capacity* around the world28 and find no mention in comprehensive renewable energy roadmaps by Pacala and Socolow (2004)34, Shinnar and Citro (2006)35 and only a passing mention in the solar-thermal roadmap of the International Energy Agency (IEA) in 201022. A separate report by the National Renewable Energy Laboratory (NREL) in 201136 argues that the solar-augment potential of American thermal power plants is less than 5%.

A possible explanation for this neglect of a promising strategy could be a “one-plant-one-fuel” paradigm in the area of power production. We must point out that this neglect is not benign. Solar-thermal subsidies (e.g. in Spain and the United States) are designed to reward conventionally deployed solar-thermal power producers with an upper limit set to fossil-fuel co-firing. Such a policy clearly precludes solar-aided fossil fuel power plants, with minority solar-fractions, from its rewards.

This paper presents a comprehensive analysis of the benefits of injecting solar-thermal heat, harvested by various technologies, into the Rankine cycle of a coal-fired power plant. We have shown that there is no thermodynamic barrier to reaching as high as 50% (details given later) fossil fuel offset using existing line-concentrating technologies and with solar-to-electricity conversion efficiencies several percentage points better than those obtained by conventionally deployed solar thermal power plants. We also bring out several other subtle synergies of such integration.

It is therefore the contention of this paper that solar-thermal technology should not be treated on par with intermittent power production systems like photovoltaics or wind-turbines but treated as an independent category in itself for policy purposes. An example of the result of such a policy change would be to relax the requirement for large solar fractions in solar thermal power plants for attracting government assistance; but rather the solar thermal contribution to solar-aided power plants should be monitored for extending support to this technology. Policy recommendations in this direction are already made while keeping in mind the fossil-fuel backup of conventionally deployed solar thermal power plants22 but their scope needs to be extended to the solar-fraction of solar-aided thermal power plants.

An additional, and vitally important, advantage of such plants is modularity i.e. that the solar thermal component can be applied incrementally depending upon available financial resource, or available land or DNI, facilitating project planning, execution and maintenance and greatly lowering project risk.

We have explored the benefit of integrating several common, ready-to-deploy, solar-thermal technologies into a coal-fired thermal power plant operating on the Rankine Cycle in a simple, transparent manner that also generalizes the analyses already presented29. We have shown thereby that optimum solar thermal radiation harvesting calls for a portfolio of technologies, each optimized

* Notable plants executing this strategy are the Martin-Next-Generation-Solar-Energy-Centre in South Florida (with installed solar capacity corresponding to 2% of the 3.8 GW plant), Kogan Creek Solar Boost in Australia (6% of 750 MW), ISCC Kuryamat in Egypt (15% of 140 MW) and ISCC Hassi R’Mel in Algeria (17% of 150 MW). None of these plants have thermal storage i.e. their fuel offsets are a quarter of their fractional capacities. The 100 MW Shams-I plant in the UAE, with natural gas fired steam superheaters following solar-thermal boilers, may also be considered an example, though it would have been more efficient to pass the natural gas through a Brayton cycle first.




SUPPLEMENTARY INFORMATION DOI: 10.1038/NCLIMATE2717


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for a certain temperature range. We have further shown that retrofitting existing thermal power plants with solar-thermal technology is more profitable than installing and operating carbon capture and compression equipment for mitigating equivalent greenhouse gas emissions.

2. Results and Discussion Figure 2 of the main article is a summary of our results for a sub-critical and a super-critical Rankine cycle. If the enthalpy to the SEGS type solar-thermal plant of Table 1 of the main article were gathered by 𝐶𝐶𝐶𝐶50, the solar-collection efficiency would be 47% i.e. with thermal-to-electric efficiency of 34.6%, the solar-to-electricity efficiency would be ~16%, consistent with the values reported from installed solar-thermal power producers. The observation most pertinent to this paper is that HTF heated to 400oC (the limit of state-of-the-art HTF DowthermA) can be used to offset as much as 57% and 28% of fossil fuel combustion in a sub-critical and super-critical (respectively) Rankine cycle plant with solar-to-electric efficiencies in excess of 16% (the value for a conventionally-deployed solar-thermal plant with CR50). If a temperature of 500oC is permitted (necessitating an HTF other than DowthermA e.g. eutectic mixtures of nitrate salts), these numbers rise to 80% and 54% respectively with solar-to-electric efficiencies in the range of 18-22% (with CR50). If a temperature of 600oC and 700oC is permitted then all of the sub-critical and super-critical Rankine cycles respectively can be run by solar-thermal radiation alone. Note that these numbers are for the standard configuration which does not affect the steam cycle in the plant and would necessitate, at most, a reconfiguration of the plant’s heat exchangers. This is, of course, contingent on the (a) availability of solar resource and (b) availability of sufficient thermal storage without which the fuel-offset numbers would drop by a factor of 4†.

Another, perhaps counterintuitive, result is the poor correlation between concentration ratio and solar-to-electric efficiency. For HTF temperatures upto 200oC i.e. fuel offsets of 6-7% with feedwater heating, the CR1 is the most efficient solar-harvester: mainly due to its ability to use diffuse solar radiation in addition to DNI. Similarly, CR1000 is a consistently poorer harverster than CR50 and even CR20 for most cases. This is primarily because at temperatures far (>200oC) from the stagnation temperature, the solar-capture efficiency is practically independent of temperature, and other considerations e.g. area-cosine factor, dominate. This is particularly pertinent since the central receiver tower technology (the best candidate for CR1000), which is considerably more expensive and less mature than the parabolic trough technology (C20 and C50), is also less optimum (thermodynamically) for running a Rankine cycle power plant; though it could be superior for offsetting natural gas combustion in the Brayton Cycle of a combined-cycle plant.

In light of these results, it would make sense to operate different solar-thermal harvester technologies for different temperature regions i.e. the cheaper low concentration ratio harvesters may be deployed for lower temperatures (where the performance differentials are small or reversed) with the more expensive harvesters brought in for higher temperatures. This also suggests a strategy for the incremental introduction of solar-fraction into power plants: begin with the low-cost collectors and gradually move up the technology ladder.

Feedwater preheating alone has the potential to offset about 20% of fossil fuel combustion; a fact that has been commented on30,31,37. However, feed-water preheating has an upper limit set by the

† For 6 sunny hours out of 24 productive hours in a day.


Page 5 of 26

quantum of additional steam that the turbines can take which is about 10-20% above rated capacity. This constraint forces preheating to remain at about 200oC; achieving the far lower fossil-fuel offsets of about 6%. On the other hand, it can be accomplished by relatively cheap and easy-to-operate solar-harvesters like vacuum tube collectors and may constitute “low-hanging fruit” for power plants seeking to meet emission norms e.g. China, which operates a large fraction of coal-fired power plants, is also the largest manufacturer of vacuum tube solar collectors. A second, perhaps more subtle, advantage of feedwater preheating is that it can avoid the efficiency penalty that accompanies suppressing a steam-bleed to meet a temporary spike in demand; thereby making a base-load coal fired power plant dispatchable to the tune of 6% of its operating capacity. This fraction can be higher if there is a spare turbine (e.g. the “spinning reserve”) to accept the excess steam. Alternatively, the excess steam could be used to drive the regenerator of an absorption based carbon-capture unit.

A point that needs to be addressed is the report that solar-augment potential of U.S. power plants is in the single digits36: which appears to be in stark contrast to our analysis. The resolution lies in the fact that the report was examining the potential for increased electricity generation (solar-boosting) by injecting solar heat into existing power plants. This will have a definite upper limit due to the capacity of the existing equipment. Since plants normally have less than 20% excess capacity, and since the report does not account for thermal-storage, the solar-augment potential they found is around 5%‡ with variations on either side. We suggest instead that power-plants be operated in the “fuel-saving” mode with incremental addition of solar-thermal capacity with the express purpose of reducing greenhouse-gas emissions as a prelude to an eventual solar-thermal takeover.

For a quick feel of the numbers, consider a 500 MW sub-critical Rankine cycle power plant (coal fired) which would circulate about 275 kg/s of condensate (rising to 392 kg/s in the boiler with addition of bled-steam). The enthalpy of combustion necessary would be about 1.35 GW of which 0.2 GW (~15%) would be lost through the stack. If it were being augmented (standard configuration) with HTF heated to 400oC, the enthalpy of combustion necessary would be 0.58 GW of which only ~13% would leave through the stack. The HTF (Dowtherm A) flow would be 866 kg/s (0.13 GW between 270-330oC at 48% collector efficiency with C50) for the economizer and 2700 kg/s (0.5 GW between 330-400oC at 47% collector efficiency with C50) in the boiler. The solar collector area (C50) would be 670 hectares on 1340 hectares of land. If heat were stored in a material of specific heat capacity equal to that of the HTF, the quantity of material stored (for 18§ hours of storage at 400oC) would be 175 MTons i.e. about 257000 m3**.

3. Simple Economic Analysis We now present a simple economic analysis to show that solar thermal integration into existing power plants can be profitable under certain conditions. We have deliberately chosen solar

‡ A quarter of 20% (6 sunny hours in a 24 hour period). § 18 hours of storage is necessary to provide base-load power. For a conventionally a storage capacity of 6-8 hours, enough to tide over dips in solar intensity, increase capacity factor of the turbine and to supply electricity during peak demand periods (normally right after sunset) is sufficient for most purposes. Large deployment of wind power could further reduce the thermal storage necessary23. ** Density of DowthermA at 400oC is 680 kg/m3. The quantity of hot stored fluid can be held in two tanks, each with 50 m diameter and height.




SUPPLEMENTARY INFORMATIONDOI: 10.1038/NCLIMATE2717


Page 4 of 26

for a certain temperature range. We have further shown that retrofitting existing thermal power plants with solar-thermal technology is more profitable than installing and operating carbon capture and compression equipment for mitigating equivalent greenhouse gas emissions.

2. Results and Discussion Figure 2 of the main article is a summary of our results for a sub-critical and a super-critical Rankine cycle. If the enthalpy to the SEGS type solar-thermal plant of Table 1 of the main article were gathered by 𝐶𝐶𝐶𝐶50, the solar-collection efficiency would be 47% i.e. with thermal-to-electric efficiency of 34.6%, the solar-to-electricity efficiency would be ~16%, consistent with the values reported from installed solar-thermal power producers. The observation most pertinent to this paper is that HTF heated to 400oC (the limit of state-of-the-art HTF DowthermA) can be used to offset as much as 57% and 28% of fossil fuel combustion in a sub-critical and super-critical (respectively) Rankine cycle plant with solar-to-electric efficiencies in excess of 16% (the value for a conventionally-deployed solar-thermal plant with CR50). If a temperature of 500oC is permitted (necessitating an HTF other than DowthermA e.g. eutectic mixtures of nitrate salts), these numbers rise to 80% and 54% respectively with solar-to-electric efficiencies in the range of 18-22% (with CR50). If a temperature of 600oC and 700oC is permitted then all of the sub-critical and super-critical Rankine cycles respectively can be run by solar-thermal radiation alone. Note that these numbers are for the standard configuration which does not affect the steam cycle in the plant and would necessitate, at most, a reconfiguration of the plant’s heat exchangers. This is, of course, contingent on the (a) availability of solar resource and (b) availability of sufficient thermal storage without which the fuel-offset numbers would drop by a factor of 4†.

Another, perhaps counterintuitive, result is the poor correlation between concentration ratio and solar-to-electric efficiency. For HTF temperatures upto 200oC i.e. fuel offsets of 6-7% with feedwater heating, the CR1 is the most efficient solar-harvester: mainly due to its ability to use diffuse solar radiation in addition to DNI. Similarly, CR1000 is a consistently poorer harverster than CR50 and even CR20 for most cases. This is primarily because at temperatures far (>200oC) from the stagnation temperature, the solar-capture efficiency is practically independent of temperature, and other considerations e.g. area-cosine factor, dominate. This is particularly pertinent since the central receiver tower technology (the best candidate for CR1000), which is considerably more expensive and less mature than the parabolic trough technology (C20 and C50), is also less optimum (thermodynamically) for running a Rankine cycle power plant; though it could be superior for offsetting natural gas combustion in the Brayton Cycle of a combined-cycle plant.

In light of these results, it would make sense to operate different solar-thermal harvester technologies for different temperature regions i.e. the cheaper low concentration ratio harvesters may be deployed for lower temperatures (where the performance differentials are small or reversed) with the more expensive harvesters brought in for higher temperatures. This also suggests a strategy for the incremental introduction of solar-fraction into power plants: begin with the low-cost collectors and gradually move up the technology ladder.

Feedwater preheating alone has the potential to offset about 20% of fossil fuel combustion; a fact that has been commented on30,31,37. However, feed-water preheating has an upper limit set by the

† For 6 sunny hours out of 24 productive hours in a day.


of 26

quantum of additional steam that the turbines can take which is about 10-20% above rated capacity. This constraint forces preheating to remain at about 200oC; achieving the far lower fossil-fuel offsets of about 6%. On the other hand, it can be accomplished by relatively cheap and easy-to-operate solar-harvesters like vacuum tube collectors and may constitute “low-hanging fruit” for power plants seeking to meet emission norms e.g. China, which operates a large fraction of coal-fired power plants, is also the largest manufacturer of vacuum tube solar collectors. A second, perhaps more subtle, advantage of feedwater preheating is that it can avoid the efficiency penalty that accompanies suppressing a steam-bleed to meet a temporary spike in demand; thereby making a base-load coal fired power plant dispatchable to the tune of 6% of its operating capacity. This fraction can be higher if there is a spare turbine (e.g. the “spinning reserve”) to accept the excess steam. Alternatively, the excess steam could be used to drive the regenerator of an absorption based carbon-capture unit.

A point that needs to be addressed is the report that solar-augment potential of U.S. power plants is in the single digits36: which appears to be in stark contrast to our analysis. The resolution lies in the fact that the report was examining the potential for increased electricity generation (solar-boosting) by injecting solar heat into existing power plants. This will have a definite upper limit due to the capacity of the existing equipment. Since plants normally have less than 20% excess capacity, and since the report does not account for thermal-storage, the solar-augment potential they found is around 5%‡ with variations on either side. We suggest instead that power-plants be operated in the “fuel-saving” mode with incremental addition of solar-thermal capacity with the express purpose of reducing greenhouse-gas emissions as a prelude to an eventual solar-thermal takeover.

For a quick feel of the numbers, consider a 500 MW sub-critical Rankine cycle power plant (coal fired) which would circulate about 275 kg/s of condensate (rising to 392 kg/s in the boiler with addition of bled-steam). The enthalpy of combustion necessary would be about 1.35 GW of which 0.2 GW (~15%) would be lost through the stack. If it were being augmented (standard configuration) with HTF heated to 400oC, the enthalpy of combustion necessary would be 0.58 GW of which only ~13% would leave through the stack. The HTF (Dowtherm A) flow would be 866 kg/s (0.13 GW between 270-330oC at 48% collector efficiency with C50) for the economizer and 2700 kg/s (0.5 GW between 330-400oC at 47% collector efficiency with C50) in the boiler. The solar collector area (C50) would be 670 hectares on 1340 hectares of land. If heat were stored in a material of specific heat capacity equal to that of the HTF, the quantity of material stored (for 18§ hours of storage at 400oC) would be 175 MTons i.e. about 257000 m3**.

3. Simple Economic Analysis We now present a simple economic analysis to show that solar thermal integration into existing power plants can be profitable under certain conditions. We have deliberately chosen solar

‡ A quarter of 20% (6 sunny hours in a 24 hour period). § 18 hours of storage is necessary to provide base-load power. For a conventionally a storage capacity of 6-8 hours, enough to tide over dips in solar intensity, increase capacity factor of the turbine and to supply electricity during peak demand periods (normally right after sunset) is sufficient for most purposes. Large deployment of wind power could further reduce the thermal storage necessary23. ** Density of DowthermA at 400oC is 680 kg/m3. The quantity of hot stored fluid can be held in two tanks, each with 50 m diameter and height.





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performance values far lower than our calculations indicate (and higher fossil fuel performance values) to emphasize the potential of this approach.

Conventional Thermal Power Plant: Let 𝑝𝑝𝑒𝑒 be the cost of a power plant per unit of power produced, 𝐸𝐸 be the capacity of the plant, 𝑌𝑌 be the yearly on-line time (in hours), 𝜂𝜂𝑇𝑇 be the overall thermal-to-electric efficiency, ℎ𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 be the heating value of coal by weight (kWhth/kg-coal), 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 be the price of coal by weight ($/kg-coal) and 𝑠𝑠𝑒𝑒 be the selling price of electricity ($/kWh).

Hence the return on investment based on cash-flow for the conventional power plant is

𝑟𝑟𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 = 𝑌𝑌𝑝𝑝𝑒𝑒(𝑠𝑠𝑒𝑒 −

1𝜂𝜂𝑇𝑇

𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐ℎ𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐

)

For: 𝑌𝑌 = 8000 ℎ𝑟𝑟𝑠𝑠, 𝑝𝑝𝑒𝑒 = 1000 $/𝑘𝑘𝑘𝑘, 𝑠𝑠𝑒𝑒 = 0.05 $𝑘𝑘𝑘𝑘ℎ, ℎ𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 = 5.8 𝑘𝑘𝑘𝑘ℎ𝑇𝑇ℎ

𝑘𝑘𝑘𝑘 , 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 = 0.09 $𝑘𝑘𝑘𝑘, 𝜂𝜂𝑇𝑇 = 0.4

(high value), 𝑟𝑟𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 = 9.0%

Solar-Aided Plant: Now let 𝑝𝑝𝑠𝑠 be the cost of a solar collector field per unit collector area ($/m2) and 𝑝𝑝𝑐𝑐 be the cost of land per unit area ($/m2). Let 𝜙𝜙𝑐𝑐 be the fraction of land utilized by solar collectors, 𝜂𝜂𝑐𝑐𝑐𝑐𝑐𝑐 be the fraction of solar radiation captured by the collectors and 𝜂𝜂𝑇𝑇𝑠𝑠 be the fraction of captured radiation converted to electricity. Let 𝑓𝑓𝑠𝑠 be the fraction of the electricity obtained from the solar component and 𝐼𝐼 be the solar insolation per unit area (Wm-2) and let 𝑌𝑌𝑠𝑠 be the sunny time (in hours) of the year.

If selling price of solar electricity is 𝑠𝑠𝑒𝑒𝑠𝑠 ($/kWh), then the return on investment is:

𝑟𝑟𝑠𝑠𝑐𝑐𝑐𝑐−𝑐𝑐𝑎𝑎𝑎𝑎 =𝑌𝑌 ((1− 𝑓𝑓𝑠𝑠) (𝑠𝑠𝑒𝑒 −

1𝜂𝜂𝑇𝑇


) + 𝑓𝑓𝑠𝑠𝑠𝑠𝑒𝑒𝑠𝑠 )

𝑝𝑝𝑒𝑒 + 𝑓𝑓𝑠𝑠𝐼𝐼𝑔𝑔𝑐𝑐𝑐𝑐𝑔𝑔𝑐𝑐𝑐𝑐𝜂𝜂𝑇𝑇𝑠𝑠𝜂𝜂𝑐𝑐𝑐𝑐𝑐𝑐

𝑌𝑌𝑌𝑌𝑠𝑠

(𝑝𝑝𝑠𝑠 + 𝑐𝑐𝑐𝑐𝜙𝜙𝑐𝑐)

The solar-aided power plant will be more profitable than the conventional power plant when: 𝑟𝑟𝑠𝑠𝑐𝑐𝑐𝑐−𝑐𝑐𝑎𝑎𝑎𝑎 > 𝑟𝑟𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 i.e.

𝑠𝑠𝑒𝑒𝑠𝑠𝑠𝑠𝑒𝑒

> (1 − 1𝜂𝜂𝑇𝑇ℎ𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐

𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑠𝑠𝑒𝑒

)(1 + 1𝑝𝑝𝑒𝑒(𝐼𝐼𝜂𝜂𝑇𝑇𝑠𝑠𝜂𝜂𝑐𝑐𝑐𝑐𝑐𝑐)


(𝑝𝑝𝑠𝑠 + 𝑝𝑝𝑐𝑐𝜙𝜙𝑐𝑐))

For our calculations, 𝜂𝜂𝑇𝑇𝑠𝑠 = 0.3 (low value), 𝜂𝜂𝐶𝐶𝑐𝑐𝑐𝑐 = 0.4 (low value for C20 and higher), 𝐼𝐼 =0.8 𝑘𝑘𝑘𝑘/𝑚𝑚2, 𝑌𝑌𝑌𝑌𝑠𝑠 = 4, 𝑝𝑝𝑠𝑠 = 300 $/𝑚𝑚2, 𝑝𝑝𝑐𝑐 = 0.3 $/𝑚𝑚2, 𝜙𝜙𝑐𝑐 = 0.25. An illustrative set of numbers is

presented in Table 2 of the main article which show that a solar-fuel plant can become competitive with a thermal power plant if 𝑝𝑝𝑠𝑠 drops to $150/𝑚𝑚2 and can greatly exceed the profitability of a power plant if the feed-in tariff of three times the electricity cost is applied to its solar fraction.

Solar Retrofit as an alternative to Carbon Capture: Consider a requirement that a fraction 𝑓𝑓𝑠𝑠 of carbon dioxide generated by a power plant be captured and compressed. Let 𝑞𝑞𝐶𝐶𝑂𝑂2 be the quantity of carbon dioxide emitted per unit of coal burnt and let 𝑒𝑒𝐶𝐶𝑂𝑂2 be the quantity of electricity required to capture and compress each unit of CO2. Let 𝑝𝑝𝐶𝐶𝑂𝑂2 be


Page 7 of 26

the capital cost of the equipment required to capture and compress this carbon-dioxide per unit capacity. Let 𝑐𝑐𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 be the cost of transport and geological storage per unit CO2. Hence the capital

cost of carbon capture would be: 𝐸𝐸𝑓𝑓𝑠𝑠𝑝𝑝𝐶𝐶𝑂𝑂2𝑇𝑇𝐶𝐶𝑂𝑂2

𝜂𝜂𝑇𝑇ℎ𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 and the yearly operating cost would be

𝐸𝐸𝐸𝐸𝑓𝑓𝑠𝑠𝑇𝑇𝐶𝐶𝑂𝑂2

𝜂𝜂𝑇𝑇ℎ𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐(𝑒𝑒𝐶𝐶𝑂𝑂2𝑠𝑠𝑒𝑒 + cTrSq). Here 𝐸𝐸 is the plant’s capacity in kW.

By operating a solar retrofit, both the capital and operating cost of the carbon capture are saved.

Hence the effective cost of the collector field becomes: 𝐸𝐸𝑓𝑓𝑠𝑠 (1

𝐼𝐼𝜂𝜂𝑇𝑇𝑇𝑇𝜂𝜂𝑐𝑐𝑐𝑐𝑐𝑐𝑌𝑌𝑌𝑌𝑇𝑇

(𝑝𝑝𝑠𝑠 + 𝑝𝑝𝑐𝑐𝜙𝜙𝑐𝑐) − 𝑝𝑝𝐶𝐶𝑂𝑂2

𝑇𝑇𝐶𝐶𝑂𝑂2𝜂𝜂𝑇𝑇ℎ𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐

)

while the revenue is effectively increased to: 𝐸𝐸𝐸𝐸𝑓𝑓𝑠𝑠 (𝑠𝑠𝑒𝑒𝑠𝑠 + 𝑇𝑇𝐶𝐶𝑂𝑂2𝜂𝜂𝑇𝑇ℎ𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐

(𝑒𝑒𝐶𝐶𝑂𝑂2𝑠𝑠𝑒𝑒 + cTrSq)).

The return on investment of a solar-thermal retrofit as an alternative to carbon capture is therefore:

𝑟𝑟𝑠𝑠𝑠𝑠𝑠𝑠−𝑓𝑓𝑓𝑓𝑒𝑒𝑠𝑠 𝑇𝑇𝑒𝑒𝑟𝑟𝑇𝑇𝑠𝑠𝑓𝑓𝑟𝑟𝑟𝑟 =

𝐸𝐸 (𝑠𝑠𝑒𝑒𝑠𝑠 + 𝑇𝑇𝐶𝐶𝑂𝑂2𝜂𝜂𝑇𝑇ℎ𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐

(𝑒𝑒𝐶𝐶𝑂𝑂2𝑠𝑠𝑒𝑒 + cTrSq) )1


(𝑝𝑝𝑠𝑠 + 𝑝𝑝𝑐𝑐𝜙𝜙𝑐𝑐) − 𝑇𝑇𝐶𝐶𝑂𝑂2

𝜂𝜂𝑇𝑇ℎ𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑝𝑝𝐶𝐶𝑂𝑂2

For a pulverized coal power plant we have the following representative values38: 𝑇𝑇𝐶𝐶𝑂𝑂2𝜂𝜂𝑇𝑇ℎ𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐

=

0.762 𝑘𝑘𝑘𝑘−𝐶𝐶𝑂𝑂2𝑘𝑘𝑘𝑘ℎ , 𝑒𝑒𝐶𝐶𝑂𝑂2 = 0.35 𝑘𝑘𝑘𝑘ℎ

𝑘𝑘𝑘𝑘−𝐶𝐶𝑂𝑂2, 𝑐𝑐𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 = 0.005 $

𝑘𝑘𝑘𝑘−𝐶𝐶𝑂𝑂2 ,𝑝𝑝𝐶𝐶𝑂𝑂2 = 914 $

𝑘𝑘𝑘𝑘𝐶𝐶𝑂𝑂2 𝑝𝑝𝑒𝑒𝑇𝑇 ℎ𝑠𝑠𝑓𝑓𝑇𝑇.

A set of illustrative numbers appears in Table 3 of the main article which show that solar thermal retrofitting is a preferable option to carbon-capture and compression for sequestration especially if the solar thermal fraction would attract the same subsidy as solar-power generated by a conventionally deployed plant. It has other obvious advantages besides, not least of which is that the problem of transport and long-term storage of CO2 is entirely avoided.

4. Another Look at Solar Energy Policy The experience of solar thermal developers the world over25,39 has been that solar thermal power plants are significantly more difficult and risky to setup and operate compared to photovoltaic power plants of similar peak power capacities.

The barriers to development of solar-thermal power project as identified by developers from the United States25 and India39 (two countries with abundant solar resources but at practically opposite ends of the development spectrum) are listed below along with how solar-aided thermal power paradigm can substantially overcome them.

1. Flexibility: Whereas photovoltaic modules can be added incrementally, as finance becomes available, say, conventionally deployed solar-thermal power plants have to be installed in blocks of several hundred megawatts: enough to sustain an economically sized Rankine cycle power plant. However, a solar-aided power plant allows incremental addition of solar-thermal capacity to an existing, operational power plant since any temporary lack of heat can be readily compensated by fossil fuel in the plant.

2. Stymied Innovation: Unlike photovoltaics, where innovations are mostly on the level of the semiconductor materials which can be tested on small units and then rapidly scaled up, innovations in solar thermal are mostly on the side of system integration; which have a much higher probability of failure due to unforeseen pitfalls. The nature of the solar thermal





Page 6 of 26

performance values far lower than our calculations indicate (and higher fossil fuel performance values) to emphasize the potential of this approach.

Conventional Thermal Power Plant: Let 𝑝𝑝𝑒𝑒 be the cost of a power plant per unit of power produced, 𝐸𝐸 be the capacity of the plant, 𝑌𝑌 be the yearly on-line time (in hours), 𝜂𝜂𝑇𝑇 be the overall thermal-to-electric efficiency, ℎ𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 be the heating value of coal by weight (kWhth/kg-coal), 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 be the price of coal by weight ($/kg-coal) and 𝑠𝑠𝑒𝑒 be the selling price of electricity ($/kWh).

Hence the return on investment based on cash-flow for the conventional power plant is

𝑟𝑟𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 = 𝑌𝑌𝑝𝑝𝑒𝑒(𝑠𝑠𝑒𝑒 −

1𝜂𝜂𝑇𝑇


)

For: 𝑌𝑌 = 8000 ℎ𝑟𝑟𝑠𝑠, 𝑝𝑝𝑒𝑒 = 1000 $/𝑘𝑘𝑘𝑘, 𝑠𝑠𝑒𝑒 = 0.05 $𝑘𝑘𝑘𝑘ℎ, ℎ𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 = 5.8 𝑘𝑘𝑘𝑘ℎ𝑇𝑇ℎ

𝑘𝑘𝑘𝑘 , 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 = 0.09 $𝑘𝑘𝑘𝑘, 𝜂𝜂𝑇𝑇 = 0.4

(high value), 𝑟𝑟𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 = 9.0%

Solar-Aided Plant: Now let 𝑝𝑝𝑠𝑠 be the cost of a solar collector field per unit collector area ($/m2) and 𝑝𝑝𝑐𝑐 be the cost of land per unit area ($/m2). Let 𝜙𝜙𝑐𝑐 be the fraction of land utilized by solar collectors, 𝜂𝜂𝑐𝑐𝑐𝑐𝑐𝑐 be the fraction of solar radiation captured by the collectors and 𝜂𝜂𝑇𝑇𝑠𝑠 be the fraction of captured radiation converted to electricity. Let 𝑓𝑓𝑠𝑠 be the fraction of the electricity obtained from the solar component and 𝐼𝐼 be the solar insolation per unit area (Wm-2) and let 𝑌𝑌𝑠𝑠 be the sunny time (in hours) of the year.

If selling price of solar electricity is 𝑠𝑠𝑒𝑒𝑠𝑠 ($/kWh), then the return on investment is:

𝑟𝑟𝑠𝑠𝑐𝑐𝑐𝑐−𝑐𝑐𝑎𝑎𝑎𝑎 =𝑌𝑌 ((1− 𝑓𝑓𝑠𝑠) (𝑠𝑠𝑒𝑒 −

1𝜂𝜂𝑇𝑇


) + 𝑓𝑓𝑠𝑠𝑠𝑠𝑒𝑒𝑠𝑠 )

𝑝𝑝𝑒𝑒 + 𝑓𝑓𝑠𝑠𝐼𝐼𝑔𝑔𝑐𝑐𝑐𝑐𝑔𝑔𝑐𝑐𝑐𝑐𝜂𝜂𝑇𝑇𝑠𝑠𝜂𝜂𝑐𝑐𝑐𝑐𝑐𝑐


(𝑝𝑝𝑠𝑠 + 𝑐𝑐𝑐𝑐𝜙𝜙𝑐𝑐)

The solar-aided power plant will be more profitable than the conventional power plant when: 𝑟𝑟𝑠𝑠𝑐𝑐𝑐𝑐−𝑐𝑐𝑎𝑎𝑎𝑎 > 𝑟𝑟𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 i.e.

𝑠𝑠𝑒𝑒𝑠𝑠𝑠𝑠𝑒𝑒

> (1 − 1𝜂𝜂𝑇𝑇ℎ𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐

𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑠𝑠𝑒𝑒

)(1 + 1𝑝𝑝𝑒𝑒(𝐼𝐼𝜂𝜂𝑇𝑇𝑠𝑠𝜂𝜂𝑐𝑐𝑐𝑐𝑐𝑐)


(𝑝𝑝𝑠𝑠 + 𝑝𝑝𝑐𝑐𝜙𝜙𝑐𝑐))

For our calculations, 𝜂𝜂𝑇𝑇𝑠𝑠 = 0.3 (low value), 𝜂𝜂𝐶𝐶𝑐𝑐𝑐𝑐 = 0.4 (low value for C20 and higher), 𝐼𝐼 =0.8 𝑘𝑘𝑘𝑘/𝑚𝑚2, 𝑌𝑌𝑌𝑌𝑠𝑠 = 4, 𝑝𝑝𝑠𝑠 = 300 $/𝑚𝑚2, 𝑝𝑝𝑐𝑐 = 0.3 $/𝑚𝑚2, 𝜙𝜙𝑐𝑐 = 0.25. An illustrative set of numbers is

presented in Table 2 of the main article which show that a solar-fuel plant can become competitive with a thermal power plant if 𝑝𝑝𝑠𝑠 drops to $150/𝑚𝑚2 and can greatly exceed the profitability of a power plant if the feed-in tariff of three times the electricity cost is applied to its solar fraction.

Solar Retrofit as an alternative to Carbon Capture: Consider a requirement that a fraction 𝑓𝑓𝑠𝑠 of carbon dioxide generated by a power plant be captured and compressed. Let 𝑞𝑞𝐶𝐶𝑂𝑂2 be the quantity of carbon dioxide emitted per unit of coal burnt and let 𝑒𝑒𝐶𝐶𝑂𝑂2 be the quantity of electricity required to capture and compress each unit of CO2. Let 𝑝𝑝𝐶𝐶𝑂𝑂2 be


of 26

the capital cost of the equipment required to capture and compress this carbon-dioxide per unit capacity. Let 𝑐𝑐𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 be the cost of transport and geological storage per unit CO2. Hence the capital

cost of carbon capture would be: 𝐸𝐸𝑓𝑓𝑠𝑠𝑝𝑝𝐶𝐶𝑂𝑂2𝑇𝑇𝐶𝐶𝑂𝑂2

𝜂𝜂𝑇𝑇ℎ𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 and the yearly operating cost would be

𝐸𝐸𝐸𝐸𝑓𝑓𝑠𝑠𝑇𝑇𝐶𝐶𝑂𝑂2

𝜂𝜂𝑇𝑇ℎ𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐(𝑒𝑒𝐶𝐶𝑂𝑂2𝑠𝑠𝑒𝑒 + cTrSq). Here 𝐸𝐸 is the plant’s capacity in kW.

By operating a solar retrofit, both the capital and operating cost of the carbon capture are saved.

Hence the effective cost of the collector field becomes: 𝐸𝐸𝑓𝑓𝑠𝑠 (1


(𝑝𝑝𝑠𝑠 + 𝑝𝑝𝑐𝑐𝜙𝜙𝑐𝑐) − 𝑝𝑝𝐶𝐶𝑂𝑂2

𝑇𝑇𝐶𝐶𝑂𝑂2𝜂𝜂𝑇𝑇ℎ𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐

)

while the revenue is effectively increased to: 𝐸𝐸𝐸𝐸𝑓𝑓𝑠𝑠 (𝑠𝑠𝑒𝑒𝑠𝑠 + 𝑇𝑇𝐶𝐶𝑂𝑂2𝜂𝜂𝑇𝑇ℎ𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐

(𝑒𝑒𝐶𝐶𝑂𝑂2𝑠𝑠𝑒𝑒 + cTrSq)).

The return on investment of a solar-thermal retrofit as an alternative to carbon capture is therefore:

𝑟𝑟𝑠𝑠𝑠𝑠𝑠𝑠−𝑓𝑓𝑓𝑓𝑒𝑒𝑠𝑠 𝑇𝑇𝑒𝑒𝑟𝑟𝑇𝑇𝑠𝑠𝑓𝑓𝑟𝑟𝑟𝑟 =

𝐸𝐸 (𝑠𝑠𝑒𝑒𝑠𝑠 + 𝑇𝑇𝐶𝐶𝑂𝑂2𝜂𝜂𝑇𝑇ℎ𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐

(𝑒𝑒𝐶𝐶𝑂𝑂2𝑠𝑠𝑒𝑒 + cTrSq) )1


(𝑝𝑝𝑠𝑠 + 𝑝𝑝𝑐𝑐𝜙𝜙𝑐𝑐) − 𝑇𝑇𝐶𝐶𝑂𝑂2

𝜂𝜂𝑇𝑇ℎ𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑝𝑝𝐶𝐶𝑂𝑂2

For a pulverized coal power plant we have the following representative values38: 𝑇𝑇𝐶𝐶𝑂𝑂2𝜂𝜂𝑇𝑇ℎ𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐

=

0.762 𝑘𝑘𝑘𝑘−𝐶𝐶𝑂𝑂2𝑘𝑘𝑘𝑘ℎ , 𝑒𝑒𝐶𝐶𝑂𝑂2 = 0.35 𝑘𝑘𝑘𝑘ℎ

𝑘𝑘𝑘𝑘−𝐶𝐶𝑂𝑂2, 𝑐𝑐𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 = 0.005 $

𝑘𝑘𝑘𝑘−𝐶𝐶𝑂𝑂2 ,𝑝𝑝𝐶𝐶𝑂𝑂2 = 914 $

𝑘𝑘𝑘𝑘𝐶𝐶𝑂𝑂2 𝑝𝑝𝑒𝑒𝑇𝑇 ℎ𝑠𝑠𝑓𝑓𝑇𝑇.

A set of illustrative numbers appears in Table 3 of the main article which show that solar thermal retrofitting is a preferable option to carbon-capture and compression for sequestration especially if the solar thermal fraction would attract the same subsidy as solar-power generated by a conventionally deployed plant. It has other obvious advantages besides, not least of which is that the problem of transport and long-term storage of CO2 is entirely avoided.

4. Another Look at Solar Energy Policy The experience of solar thermal developers the world over25,39 has been that solar thermal power plants are significantly more difficult and risky to setup and operate compared to photovoltaic power plants of similar peak power capacities.

The barriers to development of solar-thermal power project as identified by developers from the United States25 and India39 (two countries with abundant solar resources but at practically opposite ends of the development spectrum) are listed below along with how solar-aided thermal power paradigm can substantially overcome them.

1. Flexibility: Whereas photovoltaic modules can be added incrementally, as finance becomes available, say, conventionally deployed solar-thermal power plants have to be installed in blocks of several hundred megawatts: enough to sustain an economically sized Rankine cycle power plant. However, a solar-aided power plant allows incremental addition of solar-thermal capacity to an existing, operational power plant since any temporary lack of heat can be readily compensated by fossil fuel in the plant.

2. Stymied Innovation: Unlike photovoltaics, where innovations are mostly on the level of the semiconductor materials which can be tested on small units and then rapidly scaled up, innovations in solar thermal are mostly on the side of system integration; which have a much higher probability of failure due to unforeseen pitfalls. The nature of the solar thermal





of 26

power production paradigm makes it difficult for developers to recover from such setbacks. However, for a solar-aided plant, there already exists a full thermal power plant ready to compensate any lack from the solar thermal side and experimentation becomes much less costly. It now becomes possible to completely shut down entire sections of the solar thermal collector field without default on contract obligations. This alone should greatly improve developers’ appetite for experimentation and innovation. A large number of problems associated with thermal storage should yield in face of such innovation.

3. Familiarity and Reliability: As a result of the difficulties involved in setting up solar thermal power plants, developers have not had time to develop the familiarity that is necessary to ensure reliable set-up and operation. Even thermal storage technology, the trump card of solar thermal power production, appears to have stagnated††. However, Rankine/Brayton/Combined Cycle power plants are one of the most familiar technological systems in operation. Integration of solar-thermal systems into them greatly reduces the cost of failure/mis-calculation and allows the experimentation necessary to familiarize operators and investors with a technology. With the fossil fuel plant ready to compensate for any shortcoming, reliability of this system is perhaps much higher than an equivalent photovoltaic system.

4. Access to Finance: An outcome of fewer solar thermal installations is also that banks are unwilling to finance solar thermal projects with the same readiness as they would finance photovoltaic power projects. However, bankers are even more familiar with fossil-fuel fired power plants. Hence access to finance for a ‘solar-aided’ plant should be definitely much easier than for a conventionally deployed solar thermal plant; perhaps even easier than for a photovoltaics plant.

5. Deployment in Resource Restricted Environments: Conventional solar thermal technologies for power production cannot be deployed in regions with low-DNI or with limited land area. This is not barrier for solar-aided plants where even a few square meters of collector area, even without concentration, can be used to generate power.

Advantages of ‘Solar-Aided’ over other Renewables

The ‘solar-aided’ paradigm will not only lower the identified barriers but will have certain advantages that other renewable power sources (including wind and photovoltaics) lack.

1. Gradual Transition from Conventional to Renewable: Solar-aided power plants present an evolutionary mechanism for businesses traditionally involved with coal/gas power to move to renewables in a way that leverages their expertise, capital and connections.

2. Leveraging Existing Power Plant Infrastructure: According to a study of the Australian renewables sector40: “Grid connection costs are a significant barrier to the development of the renewable energy industry and can substantially increase the capital expenditure required for a project.” National grids are not set up for the large fluctuations in production that would be the result of operating with a significant fraction of intermittents. This barrier

†† Although 50% of solar-thermal capacity has thermal storage of about 7 hours, 99.5% of this is a single technology: the “2-Tank Indirect” variety where the HTF exchanges heat with molten salt from a cold-salt tank and the heated molten salt is stored in a separate hot-salt tank. Thermal storage is considered an added project risk great enough to offset the lower risk from solar-augmented plants36.


Page 9 of 26

does not exist for a solar-aided plant which can leverage existing, and fully depreciated, thermal power plant infrastructure to greatly mitigate set-up costs.

3. Uninterrupted Power Suppy: With access to a full thermal power plant running hot, solar-aided plants can considerably reduce the risk of failure due to problems in the solar-thermal circuit. In certain cases, the solar heat may be used to boost the output of the plant to supply spikes in demand making this strategy suitable for supplying base-load as well as dispatchable power.

4. Better Use of Fossil Fuels: With a solar-aided plant the fossil fuel which is capable of sustaining a high temperature flame is spared from having to heat working fluid at lower temperatures. This is a much more efficient and effectual use of the potential of fossil-fuels.

5. Making Carbon Emission Reduction Palatable: Retrofitting solar thermal solutions to existing power plants is more economically attractive than installing a carbon capture system for capturing and sequestering CO2 equivalent to that mitigated by the solar contribution. This approach has the additional benefit of not requiring a secure geological reservoir to hold the concentrated and pressurized CO2. The solar fraction, in certain configurations, can even supply the steam for driving the regenerator of an absorption based carbon-capture unit.

Policy Change Recommended

A major thrust of the policy change that we recommend is to break away from the ‘one-plant-one-fuel’ paradigm. This paradigm is implicit in practically every nation’s renewables policy‡‡. Our argument is that, with the solar-aided power plant paradigm, the conventional power infrastructure can actually prepare the way for development and deployment of renewable power.

Our policy recommendation is therefore quite simple: that policy makers should drop the insistence on majority-solar-fractions in solar power plants and instead offer the same incentives to the solar-thermal fraction of solar-aided power plants that would be offered to the corresponding conventionally deployed solar-thermal power plant: including the favourable feed-in tariffs (a point echoed in the IEA Solar Thermal Roadmap 201022 but not made forcefully enough).

There is therefore no need to call for moth-balling of coal-fired power plants12,13: a strategy that has proved unworkable in Germany10, let alone the developing world. The strategy of carbon-pricing is at once politically untenable and stands a real chance of becoming a regressive tax. Instead, we propose incentivizing renewable power irrespective of its source using funds raised by a progressive taxation regime. Not only will this, as a subsidy rather than a penalty, be politically palatable, it will give power plants the breathing room needed to familiarize themselves with solar-thermal technologies. A further course of action in this direction would be to develop protocols for estimating the fraction of power output that can be attributed to the solar-thermal section41. This will facilitate the solar-takeover of thermal power plants.

Solar-thermal power production is indispensable for a renewable future but has not seen the support from policymakers, entrepreneurs or researchers that solar-photovoltaics has enjoyed. The

‡‡ The policies of the United States and Spain actually prescribe an upper limit to the fossil-fuel co-firing permissible in a solar-thermal power plant and reward the entire output of the plant – a policy that excludes the minority solar-thermal fraction in a solar-augmented fossil-fuel power plant.





Page 8 of 26

power production paradigm makes it difficult for developers to recover from such setbacks. However, for a solar-aided plant, there already exists a full thermal power plant ready to compensate any lack from the solar thermal side and experimentation becomes much less costly. It now becomes possible to completely shut down entire sections of the solar thermal collector field without default on contract obligations. This alone should greatly improve developers’ appetite for experimentation and innovation. A large number of problems associated with thermal storage should yield in face of such innovation.

3. Familiarity and Reliability: As a result of the difficulties involved in setting up solar thermal power plants, developers have not had time to develop the familiarity that is necessary to ensure reliable set-up and operation. Even thermal storage technology, the trump card of solar thermal power production, appears to have stagnated††. However, Rankine/Brayton/Combined Cycle power plants are one of the most familiar technological systems in operation. Integration of solar-thermal systems into them greatly reduces the cost of failure/mis-calculation and allows the experimentation necessary to familiarize operators and investors with a technology. With the fossil fuel plant ready to compensate for any shortcoming, reliability of this system is perhaps much higher than an equivalent photovoltaic system.

4. Access to Finance: An outcome of fewer solar thermal installations is also that banks are unwilling to finance solar thermal projects with the same readiness as they would finance photovoltaic power projects. However, bankers are even more familiar with fossil-fuel fired power plants. Hence access to finance for a ‘solar-aided’ plant should be definitely much easier than for a conventionally deployed solar thermal plant; perhaps even easier than for a photovoltaics plant.

5. Deployment in Resource Restricted Environments: Conventional solar thermal technologies for power production cannot be deployed in regions with low-DNI or with limited land area. This is not barrier for solar-aided plants where even a few square meters of collector area, even without concentration, can be used to generate power.

Advantages of ‘Solar-Aided’ over other Renewables

The ‘solar-aided’ paradigm will not only lower the identified barriers but will have certain advantages that other renewable power sources (including wind and photovoltaics) lack.

1. Gradual Transition from Conventional to Renewable: Solar-aided power plants present an evolutionary mechanism for businesses traditionally involved with coal/gas power to move to renewables in a way that leverages their expertise, capital and connections.

2. Leveraging Existing Power Plant Infrastructure: According to a study of the Australian renewables sector40: “Grid connection costs are a significant barrier to the development of the renewable energy industry and can substantially increase the capital expenditure required for a project.” National grids are not set up for the large fluctuations in production that would be the result of operating with a significant fraction of intermittents. This barrier

†† Although 50% of solar-thermal capacity has thermal storage of about 7 hours, 99.5% of this is a single technology: the “2-Tank Indirect” variety where the HTF exchanges heat with molten salt from a cold-salt tank and the heated molten salt is stored in a separate hot-salt tank. Thermal storage is considered an added project risk great enough to offset the lower risk from solar-augmented plants36.


of 26

does not exist for a solar-aided plant which can leverage existing, and fully depreciated, thermal power plant infrastructure to greatly mitigate set-up costs.

3. Uninterrupted Power Suppy: With access to a full thermal power plant running hot, solar-aided plants can considerably reduce the risk of failure due to problems in the solar-thermal circuit. In certain cases, the solar heat may be used to boost the output of the plant to supply spikes in demand making this strategy suitable for supplying base-load as well as dispatchable power.

4. Better Use of Fossil Fuels: With a solar-aided plant the fossil fuel which is capable of sustaining a high temperature flame is spared from having to heat working fluid at lower temperatures. This is a much more efficient and effectual use of the potential of fossil-fuels.

5. Making Carbon Emission Reduction Palatable: Retrofitting solar thermal solutions to existing power plants is more economically attractive than installing a carbon capture system for capturing and sequestering CO2 equivalent to that mitigated by the solar contribution. This approach has the additional benefit of not requiring a secure geological reservoir to hold the concentrated and pressurized CO2. The solar fraction, in certain configurations, can even supply the steam for driving the regenerator of an absorption based carbon-capture unit.

Policy Change Recommended

A major thrust of the policy change that we recommend is to break away from the ‘one-plant-one-fuel’ paradigm. This paradigm is implicit in practically every nation’s renewables policy‡‡. Our argument is that, with the solar-aided power plant paradigm, the conventional power infrastructure can actually prepare the way for development and deployment of renewable power.

Our policy recommendation is therefore quite simple: that policy makers should drop the insistence on majority-solar-fractions in solar power plants and instead offer the same incentives to the solar-thermal fraction of solar-aided power plants that would be offered to the corresponding conventionally deployed solar-thermal power plant: including the favourable feed-in tariffs (a point echoed in the IEA Solar Thermal Roadmap 201022 but not made forcefully enough).

There is therefore no need to call for moth-balling of coal-fired power plants12,13: a strategy that has proved unworkable in Germany10, let alone the developing world. The strategy of carbon-pricing is at once politically untenable and stands a real chance of becoming a regressive tax. Instead, we propose incentivizing renewable power irrespective of its source using funds raised by a progressive taxation regime. Not only will this, as a subsidy rather than a penalty, be politically palatable, it will give power plants the breathing room needed to familiarize themselves with solar-thermal technologies. A further course of action in this direction would be to develop protocols for estimating the fraction of power output that can be attributed to the solar-thermal section41. This will facilitate the solar-takeover of thermal power plants.

Solar-thermal power production is indispensable for a renewable future but has not seen the support from policymakers, entrepreneurs or researchers that solar-photovoltaics has enjoyed. The

‡‡ The policies of the United States and Spain actually prescribe an upper limit to the fossil-fuel co-firing permissible in a solar-thermal power plant and reward the entire output of the plant – a policy that excludes the minority solar-thermal fraction in a solar-augmented fossil-fuel power plant.





of 26

time is ripe for a revolution in the field of solar-thermal power production a la that which led to Swanson’s law6 for photovoltaics. Perhaps this small policy change will help kickstart that revolution.

Supplementary Bibliography

1. Boden, T. A., Marland, G. & Andres, R. J. GLOBAL, REGIONAL, AND NATIONAL FOSSIL-FUEL CO2

EMISSIONS. (2010). at <http://www.epa.gov/climatechange/ghgemissions/global.html#two>

2. World Energy Outlook 2014 Factsheet. (International Energy Agency, 2014). at

<http://www.worldenergyoutlook.org/media/weowebsite/2014/141112_WEO_FactSheets.pdf>

3. U. S. Energy Information Administration. Electric Power Annual 2012. Table 1.1 (U.S. Department

of Energy, 2013). at <http://www.eia.gov/electricity/annual/pdf/epa.pdf>

4. Purohit, I. & Purohit, P. Techno-economic evaluation of concentrating solar power generation in

India. Energy Policy 38, 3015–3029 (2010).

5. The World Bank. World Development Indicators: Electricity production, sources, and access.

World Development Indicators (2014). at <http://wdi.worldbank.org/table/3.7#>

6. Carr, G. Sunny uplands. The Economist (2012). at <http://www.economist.com/news/21566414-

alternative-energy-will-no-longer-be-alternative-sunny-uplands>

7. Bullard, N. Renewable energy now cheaper than new fossil fuels in Australia. Bloomberg New

Energy Finance at <http://about.bnef.com/press-releases/renewable-energy-now-cheaper-than-

new-fossil-fuels-in-australia/>

8. Crowe, R. Energy Storage Industry Grows To Integrate Wind, Solar. Renewable Energy World at

<http://www.renewableenergyworld.com/rea/news/article/2011/08/energy-storage-industry-

grows-to-integrate-wind-solar>

9. Mandel, J. DOE Promotes Pumped Hydro as Option for Renewable Power Storage. The New York

Times (2010). at <http://www.nytimes.com/gwire/2010/10/15/15greenwire-doe-promotes-

pumped-hydro-as-option-for-renewa-51805.html>


Page 11 of 26

10. Germany’s Tenuous Transition to Renewable Energy. Stratfor at

<http://www.stratfor.com/sample/analysis/germanys-tenuous-transition-renewable-energy>

11. Gabriel: Beim Klimaschutz ist das Ziel nicht zu halten. Spiegel Online (2014). at

<http://www.spiegel.de/politik/deutschland/gabriel-beim-klimaschutz-ist-das-ziel-nicht-zu-

halten-a-1003183.html>

12. Hansen, J. E. Storms of my grandchildren: the truth about the coming climate catastrophe

and our last chance to save humanity. (Bloomsbury, 2009).

13. Parry, I., Veung, C. & Heine, D. How Much Carbon Pricing is in Countries’ Own Interests? The

Critical Role of Co-Benefits. (2014). at

<http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2512804>

14. Bawden, T. Why cheap oil is a really bad thing... The Independent (2014). at

<http://www.independent.co.uk/environment/new-era-of-cheap-oil-will-destroy-green-

revolution-9922217.html>

15. Climate, C. for & 2013, E. S. F. Options and Considerations for a Federal Carbon Tax | Center

for Climate and Energy Solutions. at <http://www.c2es.org/publications/options-considerations-

federal-carbon-tax>

16. Sumner, J., Bird, L. & Smith, H. Carbon Taxes: A Review of Experience and Policy Design

Considerations. (National Renewable Energy Laboratory, 2009). at

<http://www.nrel.gov/docs/fy10osti/47312.pdf>

17. Krugman, P. Could Fighting Global Warming Be Cheap and Free? The New York Times (2014).

at <http://www.nytimes.com/2014/09/19/opinion/paul-krugman-could-fighting-global-warming-

be-cheap-and-free.html>

18. Shah, A. Climate justice and equity. Global issues: Social, political, economic and

environmental issues that affect us all (2011). at

<http://www.globalissues.org/article/231/climate-justice-and-equity>

19. Hoffert, M. I. Farewell to Fossil Fuels? Science 329, 1292–1294 (2010).





Page 10 of 26

time is ripe for a revolution in the field of solar-thermal power production a la that which led to Swanson’s law6 for photovoltaics. Perhaps this small policy change will help kickstart that revolution.

Supplementary Bibliography

1. Boden, T. A., Marland, G. & Andres, R. J. GLOBAL, REGIONAL, AND NATIONAL FOSSIL-FUEL CO2

EMISSIONS. (2010). at <http://www.epa.gov/climatechange/ghgemissions/global.html#two>

2. World Energy Outlook 2014 Factsheet. (International Energy Agency, 2014). at

<http://www.worldenergyoutlook.org/media/weowebsite/2014/141112_WEO_FactSheets.pdf>

3. U. S. Energy Information Administration. Electric Power Annual 2012. Table 1.1 (U.S. Department

of Energy, 2013). at <http://www.eia.gov/electricity/annual/pdf/epa.pdf>

4. Purohit, I. & Purohit, P. Techno-economic evaluation of concentrating solar power generation in

India. Energy Policy 38, 3015–3029 (2010).

5. The World Bank. World Development Indicators: Electricity production, sources, and access.

World Development Indicators (2014). at <http://wdi.worldbank.org/table/3.7#>

6. Carr, G. Sunny uplands. The Economist (2012). at <http://www.economist.com/news/21566414-

alternative-energy-will-no-longer-be-alternative-sunny-uplands>

7. Bullard, N. Renewable energy now cheaper than new fossil fuels in Australia. Bloomberg New

Energy Finance at <http://about.bnef.com/press-releases/renewable-energy-now-cheaper-than-

new-fossil-fuels-in-australia/>

8. Crowe, R. Energy Storage Industry Grows To Integrate Wind, Solar. Renewable Energy World at

<http://www.renewableenergyworld.com/rea/news/article/2011/08/energy-storage-industry-

grows-to-integrate-wind-solar>

9. Mandel, J. DOE Promotes Pumped Hydro as Option for Renewable Power Storage. The New York

Times (2010). at <http://www.nytimes.com/gwire/2010/10/15/15greenwire-doe-promotes-

pumped-hydro-as-option-for-renewa-51805.html>


of 26

10. Germany’s Tenuous Transition to Renewable Energy. Stratfor at

<http://www.stratfor.com/sample/analysis/germanys-tenuous-transition-renewable-energy>

11. Gabriel: Beim Klimaschutz ist das Ziel nicht zu halten. Spiegel Online (2014). at

<http://www.spiegel.de/politik/deutschland/gabriel-beim-klimaschutz-ist-das-ziel-nicht-zu-

halten-a-1003183.html>

12. Hansen, J. E. Storms of my grandchildren: the truth about the coming climate catastrophe

and our last chance to save humanity. (Bloomsbury, 2009).

13. Parry, I., Veung, C. & Heine, D. How Much Carbon Pricing is in Countries’ Own Interests? The

Critical Role of Co-Benefits. (2014). at

<http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2512804>

14. Bawden, T. Why cheap oil is a really bad thing... The Independent (2014). at

<http://www.independent.co.uk/environment/new-era-of-cheap-oil-will-destroy-green-

revolution-9922217.html>

15. Climate, C. for & 2013, E. S. F. Options and Considerations for a Federal Carbon Tax | Center

for Climate and Energy Solutions. at <http://www.c2es.org/publications/options-considerations-

federal-carbon-tax>

16. Sumner, J., Bird, L. & Smith, H. Carbon Taxes: A Review of Experience and Policy Design

Considerations. (National Renewable Energy Laboratory, 2009). at

<http://www.nrel.gov/docs/fy10osti/47312.pdf>

17. Krugman, P. Could Fighting Global Warming Be Cheap and Free? The New York Times (2014).

at <http://www.nytimes.com/2014/09/19/opinion/paul-krugman-could-fighting-global-warming-

be-cheap-and-free.html>

18. Shah, A. Climate justice and equity. Global issues: Social, political, economic and

environmental issues that affect us all (2011). at

<http://www.globalissues.org/article/231/climate-justice-and-equity>

19. Hoffert, M. I. Farewell to Fossil Fuels? Science 329, 1292–1294 (2010).





of 26

20. Koningstein, R. & Fork, D. What It Would Really Take to Reverse Climate Change. IEEE Spectr.

(2014). at <http://spectrum.ieee.org/energy/renewables/what-it-would-really-take-to-reverse-

climate-change>

21. Pfenninger, S. et al. Potential for concentrating solar power to provide baseload and

dispatchable power. Nat. Clim. Change advance online publication, (2014).

22. Philibert, C. et al. Technology Roadmap. (2010). at

<http://www.iea.org/publications/freepublications/publication/csp_roadmap.pdf>

23. Sinden, G. Characteristics of the UK wind resource: Long-term patterns and relationship to

electricity demand. Energy Policy 35, 112–127 (2007).

24. How Solar PV is Winning Over CSP. Renewable Energy World at

<http://www.renewableenergyworld.com/rea/blog/post/2013/03/how-solar-pv-is-winning-over-

csp>

25. Reuters. Solar thermal plants scrap steam for photovoltaic. CNET at

<http://www.cnet.com/news/solar-thermal-plants-scrap-steam-for-photovoltaic/>

26. Price, H. et al. Advances in Parabolic Trough Solar Power Technology. J. Sol. Energy Eng. 124,

109 (2002).

27. Arninghoff, R. et al. AndaSol-50MW Solar Plants with 9 hour storage for Southern Spain. in

Proceedings of 11th SolarPACES International Symposium 37–42 (2002).

28. CSP Projects Around the World. SolarPACES at <http://www.solarpaces.org/csp-

technology/csp-projects-around-the-world>

29. Petrov, M. P., Salomon Popa, M. & Fransson, T. H. Solar augmentation of conventional steam

plants: from system studies to reality. in World Renewable Energy Forum, WREF 2012, Including

World Renewable Energy Congress XII and Colorado Renewable Energy Society (CRES) Annual

Conference 2682–2689 (American Solar Energy Society, 2012). at <http://www.diva-

portal.org/smash/record.jsf?pid=diva2:600916>


Page 13 of 26

30. Gupta, M. K. & Kaushik, S. C. Exergetic utilization of solar energy for feed water preheating in

a conventional thermal power plant. Int. J. Energy Res. 33, 593–604 (2009).

31. Pierce, W., Gauché, P., von Backström, T., Brent, A. C. & Tadros, A. A comparison of solar

aided power generation (SAPG) and stand-alone concentrating solar power (CSP): A South African

case study. Appl. Therm. Eng. 61, 657–662 (2013).

32. Mouawad, J. The Newest Hybrid Model. The New York Times (2010). at

<http://www.nytimes.com/2010/03/05/business/05solar.html>

33. Siros, F., Le Moullec, P. Y., Tussea, M. & Bonnelle, D. The value of hybridizing CSP. in

Proceedings of SolarPACES (SolarPACES, 2012).

34. Pacala, S. & Socolow, R. Stabilization Wedges: Solving the Climate Problem for the Next 50

Years with Current Technologies. Science 305, 968–972 (2004).

35. Shinnar, R. & Citro, F. A Road Map to U.S. Decarbonization. Science 313, 1243–1244 (2006).

36. Turchi, C. S., Langle, N., Bedilion, R. & Libby, C. Solar-augment potential of US fossil-fired

power plants. (National Renewable Energy Laboratory, 2011). at <http://www.osti.gov/bridge>

37. Suresh, M. V. J. J., Reddy, K. S. & Kolar, A. K. 4-E (Energy, Exergy, Environment, and

Economic) analysis of solar thermal aided coal-fired power plants. Energy Sustain. Dev. 14, 267–

279 (2010).

38. Rubin, E., Meyer, L. & de Coninck, H. IPCC Special Report: Carbon Dioxide Capture and

Storage (Technical Summary). (Cambridge University Press, 2005). at

<http://www.ipcc.ch/pdf/special-reports/srccs/srccs_technicalsummary.pdf>

39. Ghosh, A. et al. Concentrated Solar Power: Heating Up India’s Solar Thermal Market Under

National Solar Mission. (Council on Energy, Environment and Water AND Natural Resources

Defence Council, 2012). at <http://ceew.in/pdf/CEEW-NRDC-

Concentrated%20Solar%20Power_Sep12.pdf>

40. Byrnes, L., Brown, C., Foster, J. & Wagner, L. D. Australian renewable energy policy: Barriers

and challenges. Renew. Energy 60, 711–721 (2013).





Page 12 of 26

20. Koningstein, R. & Fork, D. What It Would Really Take to Reverse Climate Change. IEEE Spectr.

(2014). at <http://spectrum.ieee.org/energy/renewables/what-it-would-really-take-to-reverse-

climate-change>

21. Pfenninger, S. et al. Potential for concentrating solar power to provide baseload and

dispatchable power. Nat. Clim. Change advance online publication, (2014).

22. Philibert, C. et al. Technology Roadmap. (2010). at

<http://www.iea.org/publications/freepublications/publication/csp_roadmap.pdf>

23. Sinden, G. Characteristics of the UK wind resource: Long-term patterns and relationship to

electricity demand. Energy Policy 35, 112–127 (2007).

24. How Solar PV is Winning Over CSP. Renewable Energy World at

<http://www.renewableenergyworld.com/rea/blog/post/2013/03/how-solar-pv-is-winning-over-

csp>

25. Reuters. Solar thermal plants scrap steam for photovoltaic. CNET at

<http://www.cnet.com/news/solar-thermal-plants-scrap-steam-for-photovoltaic/>

26. Price, H. et al. Advances in Parabolic Trough Solar Power Technology. J. Sol. Energy Eng. 124,

109 (2002).

27. Arninghoff, R. et al. AndaSol-50MW Solar Plants with 9 hour storage for Southern Spain. in

Proceedings of 11th SolarPACES International Symposium 37–42 (2002).

28. CSP Projects Around the World. SolarPACES at <http://www.solarpaces.org/csp-

technology/csp-projects-around-the-world>

29. Petrov, M. P., Salomon Popa, M. & Fransson, T. H. Solar augmentation of conventional steam

plants: from system studies to reality. in World Renewable Energy Forum, WREF 2012, Including

World Renewable Energy Congress XII and Colorado Renewable Energy Society (CRES) Annual

Conference 2682–2689 (American Solar Energy Society, 2012). at <http://www.diva-

portal.org/smash/record.jsf?pid=diva2:600916>


of 26

30. Gupta, M. K. & Kaushik, S. C. Exergetic utilization of solar energy for feed water preheating in

a conventional thermal power plant. Int. J. Energy Res. 33, 593–604 (2009).

31. Pierce, W., Gauché, P., von Backström, T., Brent, A. C. & Tadros, A. A comparison of solar

aided power generation (SAPG) and stand-alone concentrating solar power (CSP): A South African

case study. Appl. Therm. Eng. 61, 657–662 (2013).

32. Mouawad, J. The Newest Hybrid Model. The New York Times (2010). at

<http://www.nytimes.com/2010/03/05/business/05solar.html>

33. Siros, F., Le Moullec, P. Y., Tussea, M. & Bonnelle, D. The value of hybridizing CSP. in

Proceedings of SolarPACES (SolarPACES, 2012).

34. Pacala, S. & Socolow, R. Stabilization Wedges: Solving the Climate Problem for the Next 50

Years with Current Technologies. Science 305, 968–972 (2004).

35. Shinnar, R. & Citro, F. A Road Map to U.S. Decarbonization. Science 313, 1243–1244 (2006).

36. Turchi, C. S., Langle, N., Bedilion, R. & Libby, C. Solar-augment potential of US fossil-fired

power plants. (National Renewable Energy Laboratory, 2011). at <http://www.osti.gov/bridge>

37. Suresh, M. V. J. J., Reddy, K. S. & Kolar, A. K. 4-E (Energy, Exergy, Environment, and

Economic) analysis of solar thermal aided coal-fired power plants. Energy Sustain. Dev. 14, 267–

279 (2010).

38. Rubin, E., Meyer, L. & de Coninck, H. IPCC Special Report: Carbon Dioxide Capture and

Storage (Technical Summary). (Cambridge University Press, 2005). at

<http://www.ipcc.ch/pdf/special-reports/srccs/srccs_technicalsummary.pdf>

39. Ghosh, A. et al. Concentrated Solar Power: Heating Up India’s Solar Thermal Market Under

National Solar Mission. (Council on Energy, Environment and Water AND Natural Resources

Defence Council, 2012). at <http://ceew.in/pdf/CEEW-NRDC-

Concentrated%20Solar%20Power_Sep12.pdf>

40. Byrnes, L., Brown, C., Foster, J. & Wagner, L. D. Australian renewable energy policy: Barriers

and challenges. Renew. Energy 60, 711–721 (2013).





of 26

41. Zhai, R., Yang, Y., Zhu, Y. & Chen, D. The Evaluation of Solar Contribution in Solar Aided Coal-

Fired Power Plant. Int. J. Photoenergy 2013, e197913 (2013).


Page 15 of 26

Supplementary Methodology:

Sub-Critical Rankine Cycle Power Plant Here we present details of our calculations whose results we have reported in our main article. The sub-critical Rankine cycle is described in great detail to lay out the protocol; which is also used for the solar-thermal and supercritical Rankine cycle. The details are shown for an ideal cycle with two preheat stages while our main paper extends it to six preheat stages and a non-ideal cycle where all turbines have the same pressure ratio and the bleed pressures are approximately equispaced between the condenser pressure and the boiler pressure in the logarithmic scale.

For the purposes of this exercise, we have chosen a typical coal fired thermal power plant operating on a Rankine Cycle: more particularly, the regenerative Rankine cycle with reheat. The numbers used are for the purposes of illustrating our point. The Cycle raises high pressure steam in a boiler which is depressurized via one or more steam turbines and the exhaust steam condensed in a condensor and the condensate reheated to raise steam. A schematic diagram of the power plant appears in Figure 1 and the corresponding temperature-entropy diagram in Figure 2.

For the calculations, the properties of steam at various conditions of temperature and pressure have been taken from IF-97 steam tables via the MS-Excel Macro written by Magnus Holmgren (www.x-eng.com).

The power plant and our calculation methodology can be described very briefly using Figure 1 and Figure 2. The condensate (1) from the condensor is at a temperature Tcond = 50°C. It is pumped up to a pressure P1

preheat = 6 bar and mixed with an appropriate quantity (m1bleed) of steam (10) bled

from the medium pressure turbine in the first preheater. The combined flow of condensate and condensed bled steam (2) is a saturated liquid at temperature T1

preheat = 159°C. This is pumped up

to P2preheat = 50 bar and mixed with an appropriate quantity (m2

bleed) of steam (7) from the high pressure turbine. The combined flow of condensate and condensed bled steam (3) is a saturated liquid at T2

preheat = 264°C. This is pumped up to the pressure of the boiler Pboiler = 98.7 bar and sent to the boiler. In the boiler, the liquid is heated indirectly by flue-gases, first to its saturation temperature Tboiler = 310°C and then to supply latent heat of vapourization to produce saturated steam (5). This steam is further superheated by indirect heat-exchange with flue gases to Tsup =540°C by supplying enthalpy Hsuperheat

HP = 750.4 kJkg and this superheated steam (6) is injected into

the high-pressure turbine. The steam is expanded isentropically (to first order approximation) in the

high pressure turbine and work (WHP = 631 kJkg) is extracted from it. The entropy of the steam is

sHP = 6.74 kJkg−K. A part of this steam (7) is bled from the turbine to use in the second (higher

temperature) preheater to generate stream (3), while the remainder is exhausted. This high-pressure-turbine exhaust (8) is at a pressure PoutHP = 10 bar which is the same as the pressure of steam (PinMP) entering the medium pressure turbine. This exhaust steam is heated back to Tsup = 540°C by

supplying enthalpy HsuperheatMP = 718.9 kJ

kg and this hot steam (9) is sent to the medium pressure

turbine where it is isentropically depressurized to PoutMP = 1 bar. The entropy of this steam is sMP =





Page 14 of 26

41. Zhai, R., Yang, Y., Zhu, Y. & Chen, D. The Evaluation of Solar Contribution in Solar Aided Coal-

Fired Power Plant. Int. J. Photoenergy 2013, e197913 (2013).


of 26

Supplementary Methodology:

Sub-Critical Rankine Cycle Power Plant Here we present details of our calculations whose results we have reported in our main article. The sub-critical Rankine cycle is described in great detail to lay out the protocol; which is also used for the solar-thermal and supercritical Rankine cycle. The details are shown for an ideal cycle with two preheat stages while our main paper extends it to six preheat stages and a non-ideal cycle where all turbines have the same pressure ratio and the bleed pressures are approximately equispaced between the condenser pressure and the boiler pressure in the logarithmic scale.

For the purposes of this exercise, we have chosen a typical coal fired thermal power plant operating on a Rankine Cycle: more particularly, the regenerative Rankine cycle with reheat. The numbers used are for the purposes of illustrating our point. The Cycle raises high pressure steam in a boiler which is depressurized via one or more steam turbines and the exhaust steam condensed in a condensor and the condensate reheated to raise steam. A schematic diagram of the power plant appears in Figure 1 and the corresponding temperature-entropy diagram in Figure 2.

For the calculations, the properties of steam at various conditions of temperature and pressure have been taken from IF-97 steam tables via the MS-Excel Macro written by Magnus Holmgren (www.x-eng.com).

The power plant and our calculation methodology can be described very briefly using Figure 1 and Figure 2. The condensate (1) from the condensor is at a temperature Tcond = 50°C. It is pumped up to a pressure P1

preheat = 6 bar and mixed with an appropriate quantity (m1bleed) of steam (10) bled

from the medium pressure turbine in the first preheater. The combined flow of condensate and condensed bled steam (2) is a saturated liquid at temperature T1

preheat = 159°C. This is pumped up

to P2preheat = 50 bar and mixed with an appropriate quantity (m2

bleed) of steam (7) from the high pressure turbine. The combined flow of condensate and condensed bled steam (3) is a saturated liquid at T2

preheat = 264°C. This is pumped up to the pressure of the boiler Pboiler = 98.7 bar and sent to the boiler. In the boiler, the liquid is heated indirectly by flue-gases, first to its saturation temperature Tboiler = 310°C and then to supply latent heat of vapourization to produce saturated steam (5). This steam is further superheated by indirect heat-exchange with flue gases to Tsup =540°C by supplying enthalpy Hsuperheat

HP = 750.4 kJkg and this superheated steam (6) is injected into

the high-pressure turbine. The steam is expanded isentropically (to first order approximation) in the

high pressure turbine and work (WHP = 631 kJkg) is extracted from it. The entropy of the steam is

sHP = 6.74 kJkg−K. A part of this steam (7) is bled from the turbine to use in the second (higher

temperature) preheater to generate stream (3), while the remainder is exhausted. This high-pressure-turbine exhaust (8) is at a pressure PoutHP = 10 bar which is the same as the pressure of steam (PinMP) entering the medium pressure turbine. This exhaust steam is heated back to Tsup = 540°C by

supplying enthalpy HsuperheatMP = 718.9 kJ

kg and this hot steam (9) is sent to the medium pressure

turbine where it is isentropically depressurized to PoutMP = 1 bar. The entropy of this steam is sMP =





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7.87 kJkg−K and additional work (WMP = 672.4 kJ

kg) is extracted from it. Part of this steam (10) at

pressure P1preheat = 6 bar is bled for use in the first (lower temperature) preheater to generate

stream (2). The remainder is exhausted as exhaust medium pressure steam (11). This steam is

reheated to a temperature TinLP = 261°C by supplying HsuperheatLP = 102.7 kJ

kg and this reheated steam

(12) is sent to the low-pressure turbine for isentropic expansion. The entropy of this steam is sLP =8.08 kJ

kg−K. The steam is exhausted as saturated vapour (13) at ToutLP = Tcond = 50°C and pressure

PoutLP = Pcond = 0.12 bar which is condensed in the condensor by rejecting heat equal to Hreject =2382 kJ

kg to give back the condensate (1). The work extracted is WLP = 404.8 kJ/kg.

The work done to pump the condensate from condensor pressure at point (1) to pressure of the first

preheater at point (2) is w1pump = 0.6194 kJ

kg. From the first preheater at point (2) to the second at

point (3) it is w2pump = 4.947 kJ

kg and from there to boiler pressure at point (4) is w3pump = 6.113 kJ

kg.

The quantity of steam bled from medium pressure steam turbine is given by

m1bleed = H(P1

preheat ,sMP)−HT1,preheatsat

HT1,preheatsat −Hcondensor

mcondensate.

The flow rate is increased to mcondensate + m1bleed. Here H(P1

preheat, sMP) is the enthalpy of steam at P1

preheatwith entropy sMPwhich is the entropy of steam in the medium pressure turbine. Hence

m1bleed = 0.1696 kg

kg−condensate.

Similarly, m2bleed = H(P2

preheat,sHP)−HT2,preheatsat

HT2,preheatsat −HT1,preheat

sat (mcondensate + m1bleed) = 0.2666 kg

kg−condensate .

Hence the quantity of liquid entering the boiler is 1.436 kJkg−condensate which requires Hboiler =

1567 kJkg of heat to convert to saturated steam.

The process is depicted graphically in Figure 3 which shows three circuits: (a) the condenstate circuit through all heat exchangers and turbines, (b) the HP bleed circuit which bypasses the condenser, part of the HP turbine and both the MP and LP turbines and (c) the MP bleed circuit which bypasses the condenser, part of the MP turbine and the LP turbine. Hence 1 kg of condensate:

1. (See Figure 3a) Receives 1567kJ of heat from the boiler, 750.4 kJ of heat from the first superheater, 718.9 kJ from the second and 102.7 kJ from the third superheater making 3139 kJ of heat. The HP turbine yields 631 kJ of work, the MP turbine yields 672.3 kJ and the LP turbine yields 404.8 kJ making 1708 kJ of work. Work equal to 0.6194 kJ is expended in the first preheat pump, 4.947 kJ in the second and 6.113 kJ in the third pump making 11.68 kJ of pump work expended per kg of condensate the completes a full circuit.

2. (see Figure 4c) Generates m1bleed = 0.1696kg of MP steam bleed. This is heated from

T1preheat to saturated steam at the expenditure of 1567 × 0.1696 = 265.8 kJ of heat. It also

takes 127.3 kJ and 121.9 kJ of heat from the first and second superheaters respectively


Page 17 of 26

making 515.0 kJ of heat in all. It travels through the HP turbine doing 107 kJ of work but is bled from the MP turbine so that it can only do 30.59 kJ of work there i.e. 137.6 kJ of work are extracted from it. Pumping work done on it is 1.876 kJ.

3. (see Figure 4b) Generates m2bleed = 0.2666 kg of HP steam bleed which is heated from

T2preheat to saturated steam at the expenditure of 0.2666 × 1567 = 417.8 kJ of heat. It also

takes 200 kJ of heat from the first superheater and does 59.15 kJ of work in the HP turbine before it is bled out. 1.63 kJ of pump work is done on it.

Hence 1 kg condensate corresponds to 4272 kJ of heat supplied to the working fluid and 2382 kJ of heat rejected to the surroundings in the condendsor: corresponding to 4272 − 2382 = 1890 kJ of work extracted. Alternatively, 1905 kJ of work is extracted from the turbines and 15.19 kJ of work supplied via the pumps i.e. 1890 kJ of net work extracted per kg of working fluid circulated: which number agrees exactly with the number obtained from overall energy balances. This is an efficiency of 44.2% for an ideal Rankine cycle.

Non-Idealities:

In reality, however, the pumps and the turbines are not isentropic and a significant amount of work is lost e.g. as frictional or viscous dissipation; this loss is converted to heat and is added to the enthalpy of the system. The Figure 3 shows the temperature entropy diagram of the non-ideal Rankine cycle with the same imposed pressures and temperatures as for the ideal-cycle of Figure 2 (also superimposed on the diagram). The key difference between the two is that the (a) the lines corresponding to the isentropic expansion in the HP turbine (point (6) to point (8)) and in the MP turbine (point (9) to point (11)) now have a finite slope (b) there is no need to reheat the MP steam exhaust and hence the points (11) and (12), which are distinct in the ideal cycle, are coincident here and (c) the exhaust of the LP turbine is not saturated, but a superheated vapour i.e. point (13) of the non-ideal cycle does not lie on the saturation envelope but above it and (d) the HP and MP bleeds (depicted by points (7) and (10) respectively) are now at a higher temperature than those of the ideal cycle. For example, with an 80% mechanical efficiency of the pumps and turbines, the overall thermal-to-electrical efficiency of this system is 37.8% i.e. 85.5% of the value of the ideal Rankine cycle. The overall thermal-to-electrical efficiency is higher than the mechanical efficiency because the work lost in the turbines and pumps (20% of the work that could have been extracted from lossless machines) is put back into the working fluid as heat; the quantity of energy remains the same, but the quality is degraded.

Flue Gas:

There is a constant temperature of gas in the furnace where superheat occurs. This is an approximation to cross flow contacting. Hence if 𝑇𝑇𝑓𝑓,𝑖𝑖𝑖𝑖

𝑔𝑔𝑔𝑔𝑔𝑔 is the inlet temperature of the gas into the furnace and 𝑇𝑇𝑓𝑓,𝑜𝑜𝑜𝑜𝑜𝑜

𝑔𝑔𝑔𝑔𝑔𝑔 is the exit temperature, then

𝐹𝐹𝑤𝑤1(ℎ𝑔𝑔𝑜𝑜𝑠𝑠1 − ℎ𝑏𝑏𝑜𝑜𝑖𝑖𝑏𝑏𝑏𝑏𝑏𝑏) + 𝐹𝐹𝑤𝑤2(ℎ𝑔𝑔𝑜𝑜𝑠𝑠2 − ℎ𝐻𝐻𝐻𝐻𝑏𝑏𝑖𝑖𝑔𝑔𝐻𝐻ℎ𝑔𝑔𝑎𝑎𝑔𝑔𝑏𝑏) = 𝐹𝐹𝑔𝑔𝑔𝑔𝑔𝑔(ℎ𝑓𝑓,𝑖𝑖𝑖𝑖𝑔𝑔𝑔𝑔𝑔𝑔 − ℎ𝑓𝑓,𝑜𝑜𝑜𝑜𝑜𝑜

𝑔𝑔𝑔𝑔𝑔𝑔 )

Where 𝐹𝐹𝑤𝑤1 and 𝐹𝐹𝑤𝑤2 are the flow rates of steam into the first and second superheater respectively, ℎ𝑔𝑔𝑜𝑜𝑠𝑠1,ℎ𝑏𝑏𝑜𝑜𝑖𝑖𝑏𝑏𝑏𝑏𝑏𝑏 are the specific enthalpies of steam at the exit and entrance (respectively) of the first superheater and ℎ𝑔𝑔𝑜𝑜𝑠𝑠2,ℎ𝐻𝐻𝐻𝐻𝑏𝑏𝑖𝑖𝑔𝑔𝐻𝐻ℎ𝑔𝑔𝑎𝑎𝑔𝑔𝑏𝑏 are the corresponding terms for the second superheater. 𝐹𝐹𝑔𝑔𝑔𝑔𝑔𝑔





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making 515.0 kJ of heat in all. It travels through the HP turbine doing 107 kJ of work but is bled from the MP turbine so that it can only do 30.59 kJ of work there i.e. 137.6 kJ of work are extracted from it. Pumping work done on it is 1.876 kJ.

3. (see Figure 4b) Generates m2bleed = 0.2666 kg of HP steam bleed which is heated from

T2preheat to saturated steam at the expenditure of 0.2666 × 1567 = 417.8 kJ of heat. It also

takes 200 kJ of heat from the first superheater and does 59.15 kJ of work in the HP turbine before it is bled out. 1.63 kJ of pump work is done on it.

Hence 1 kg condensate corresponds to 4272 kJ of heat supplied to the working fluid and 2382 kJ of heat rejected to the surroundings in the condendsor: corresponding to 4272 − 2382 = 1890 kJ of work extracted. Alternatively, 1905 kJ of work is extracted from the turbines and 15.19 kJ of work supplied via the pumps i.e. 1890 kJ of net work extracted per kg of working fluid circulated: which number agrees exactly with the number obtained from overall energy balances. This is an efficiency of 44.2% for an ideal Rankine cycle.

Non-Idealities:

In reality, however, the pumps and the turbines are not isentropic and a significant amount of work is lost e.g. as frictional or viscous dissipation; this loss is converted to heat and is added to the enthalpy of the system. The Figure 3 shows the temperature entropy diagram of the non-ideal Rankine cycle with the same imposed pressures and temperatures as for the ideal-cycle of Figure 2 (also superimposed on the diagram). The key difference between the two is that the (a) the lines corresponding to the isentropic expansion in the HP turbine (point (6) to point (8)) and in the MP turbine (point (9) to point (11)) now have a finite slope (b) there is no need to reheat the MP steam exhaust and hence the points (11) and (12), which are distinct in the ideal cycle, are coincident here and (c) the exhaust of the LP turbine is not saturated, but a superheated vapour i.e. point (13) of the non-ideal cycle does not lie on the saturation envelope but above it and (d) the HP and MP bleeds (depicted by points (7) and (10) respectively) are now at a higher temperature than those of the ideal cycle. For example, with an 80% mechanical efficiency of the pumps and turbines, the overall thermal-to-electrical efficiency of this system is 37.8% i.e. 85.5% of the value of the ideal Rankine cycle. The overall thermal-to-electrical efficiency is higher than the mechanical efficiency because the work lost in the turbines and pumps (20% of the work that could have been extracted from lossless machines) is put back into the working fluid as heat; the quantity of energy remains the same, but the quality is degraded.

Flue Gas:

There is a constant temperature of gas in the furnace where superheat occurs. This is an approximation to cross flow contacting. Hence if 𝑇𝑇𝑓𝑓,𝑖𝑖𝑖𝑖

𝑔𝑔𝑔𝑔𝑔𝑔 is the inlet temperature of the gas into the furnace and 𝑇𝑇𝑓𝑓,𝑜𝑜𝑜𝑜𝑜𝑜

𝑔𝑔𝑔𝑔𝑔𝑔 is the exit temperature, then

𝐹𝐹𝑤𝑤1(ℎ𝑔𝑔𝑜𝑜𝑠𝑠1 − ℎ𝑏𝑏𝑜𝑜𝑖𝑖𝑏𝑏𝑏𝑏𝑏𝑏) + 𝐹𝐹𝑤𝑤2(ℎ𝑔𝑔𝑜𝑜𝑠𝑠2 − ℎ𝐻𝐻𝐻𝐻𝑏𝑏𝑖𝑖𝑔𝑔𝐻𝐻ℎ𝑔𝑔𝑎𝑎𝑔𝑔𝑏𝑏) = 𝐹𝐹𝑔𝑔𝑔𝑔𝑔𝑔(ℎ𝑓𝑓,𝑖𝑖𝑖𝑖𝑔𝑔𝑔𝑔𝑔𝑔 − ℎ𝑓𝑓,𝑜𝑜𝑜𝑜𝑜𝑜


Where 𝐹𝐹𝑤𝑤1 and 𝐹𝐹𝑤𝑤2 are the flow rates of steam into the first and second superheater respectively, ℎ𝑔𝑔𝑜𝑜𝑠𝑠1,ℎ𝑏𝑏𝑜𝑜𝑖𝑖𝑏𝑏𝑏𝑏𝑏𝑏 are the specific enthalpies of steam at the exit and entrance (respectively) of the first superheater and ℎ𝑔𝑔𝑜𝑜𝑠𝑠2,ℎ𝐻𝐻𝐻𝐻𝑏𝑏𝑖𝑖𝑔𝑔𝐻𝐻ℎ𝑔𝑔𝑎𝑎𝑔𝑔𝑏𝑏 are the corresponding terms for the second superheater. 𝐹𝐹𝑔𝑔𝑔𝑔𝑔𝑔





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is the flow rate of gas and ℎ𝑓𝑓,𝑖𝑖𝑖𝑖𝑔𝑔𝑔𝑔𝑔𝑔,ℎ𝑓𝑓,𝑜𝑜𝑜𝑜𝑜𝑜

𝑔𝑔𝑔𝑔𝑔𝑔 are the specific enthalpies of the gas at the exit of the combustor and the inlet of the furnace respectively.

Also, if the point of entry into the boiler is the pinch point, then

𝑇𝑇𝑏𝑏𝑜𝑜𝑖𝑖𝑖𝑖,𝑜𝑜𝑜𝑜𝑜𝑜𝑔𝑔𝑔𝑔𝑔𝑔 = 𝑇𝑇𝑏𝑏𝑜𝑜𝑖𝑖𝑖𝑖 + Δ𝑇𝑇𝑔𝑔𝑎𝑎𝑎𝑎

Where 𝑇𝑇𝑏𝑏𝑜𝑜𝑖𝑖𝑖𝑖.𝑜𝑜𝑜𝑜𝑜𝑜𝑔𝑔𝑔𝑔𝑔𝑔 is the temperature of the flue gas leaving the boiler which is at 𝑇𝑇𝑏𝑏𝑜𝑜𝑖𝑖𝑖𝑖 with Δ𝑇𝑇𝑔𝑔𝑎𝑎𝑎𝑎.

The corresponding enthalpy is ℎ𝑏𝑏𝑜𝑜𝑖𝑖𝑖𝑖,𝑜𝑜𝑜𝑜𝑜𝑜𝑔𝑔𝑔𝑔𝑔𝑔 . The enthalpy of water entering the boiler is ℎ𝑏𝑏𝑜𝑜𝑖𝑖𝑖𝑖𝑏𝑏𝑏𝑏 and its

flowrate is 𝐹𝐹𝑤𝑤1 Hence,

𝐹𝐹𝑤𝑤1(ℎ𝑏𝑏𝑜𝑜𝑖𝑖𝑖𝑖𝑏𝑏𝑏𝑏 − ℎ𝑏𝑏𝑜𝑜𝑖𝑖𝑖𝑖𝑏𝑏𝑏𝑏) = 𝐹𝐹𝑔𝑔𝑔𝑔𝑔𝑔(ℎ𝑓𝑓,𝑜𝑜𝑜𝑜𝑜𝑜𝑔𝑔𝑔𝑔𝑔𝑔 − ℎ𝑏𝑏𝑜𝑜𝑖𝑖𝑖𝑖,𝑜𝑜𝑜𝑜𝑜𝑜


Hence,

𝐹𝐹𝑤𝑤1(ℎ𝑔𝑔𝑜𝑜𝑎𝑎1 − ℎ𝑏𝑏𝑜𝑜𝑖𝑖𝑖𝑖𝑏𝑏𝑏𝑏) + 𝐹𝐹𝑤𝑤2(ℎ𝑔𝑔𝑜𝑜𝑎𝑎2 − ℎ𝐻𝐻𝐻𝐻𝑏𝑏𝑖𝑖𝑔𝑔𝐻𝐻ℎ𝑔𝑔𝑏𝑏𝑔𝑔𝑏𝑏)𝐹𝐹𝑤𝑤1(ℎ𝑏𝑏𝑜𝑜𝑖𝑖𝑖𝑖𝑏𝑏𝑏𝑏 − ℎ𝑏𝑏𝑜𝑜𝑖𝑖𝑖𝑖𝑏𝑏𝑏𝑏) =

ℎ𝑓𝑓,𝑖𝑖𝑖𝑖𝑔𝑔𝑔𝑔𝑔𝑔 − ℎ𝑓𝑓,𝑜𝑜𝑜𝑜𝑜𝑜

𝑔𝑔𝑔𝑔𝑔𝑔

ℎ𝑓𝑓,𝑜𝑜𝑜𝑜𝑜𝑜𝑔𝑔𝑔𝑔𝑔𝑔 − ℎ𝑏𝑏𝑜𝑜𝑖𝑖𝑖𝑖,𝑜𝑜𝑜𝑜𝑜𝑜


Hence,

𝐹𝐹𝑤𝑤1(ℎ𝑔𝑔𝑜𝑜𝑎𝑎1 − ℎ𝑏𝑏𝑜𝑜𝑖𝑖𝑖𝑖𝑏𝑏𝑏𝑏) + 𝐹𝐹𝑤𝑤2(ℎ𝑔𝑔𝑜𝑜𝑎𝑎2 − ℎ𝐻𝐻𝐻𝐻𝑏𝑏𝑖𝑖𝑔𝑔𝐻𝐻ℎ𝑔𝑔𝑏𝑏𝑔𝑔𝑏𝑏)𝐹𝐹𝑤𝑤1(ℎ𝑏𝑏𝑜𝑜𝑖𝑖𝑖𝑖𝑏𝑏𝑏𝑏 − ℎ𝑏𝑏𝑜𝑜𝑖𝑖𝑖𝑖𝑏𝑏𝑏𝑏) (ℎ𝑓𝑓,𝑜𝑜𝑜𝑜𝑜𝑜

𝑔𝑔𝑔𝑔𝑔𝑔 − ℎ𝑏𝑏𝑜𝑜𝑖𝑖𝑖𝑖,𝑜𝑜𝑜𝑜𝑜𝑜𝑔𝑔𝑔𝑔𝑔𝑔 ) + ℎ𝑓𝑓,𝑜𝑜𝑜𝑜𝑜𝑜

𝑔𝑔𝑔𝑔𝑔𝑔 = ℎ𝑓𝑓,𝑖𝑖𝑖𝑖𝑔𝑔𝑔𝑔𝑔𝑔

Hence 𝐹𝐹𝑔𝑔𝑔𝑔𝑔𝑔 can be determined.

If preheat extends all the way to superheat, then we keep ℎ𝑓𝑓,𝑖𝑖𝑖𝑖𝑔𝑔𝑔𝑔𝑔𝑔 the same as for when it was

supplying all preheat upto boiler and reduce 𝐹𝐹𝑔𝑔𝑔𝑔𝑔𝑔.

At the point where preheat just supplies everything short of the superheater i.e. ℎ𝑏𝑏𝑜𝑜𝑖𝑖𝑖𝑖𝑏𝑏𝑏𝑏 − ℎ𝑖𝑖𝑎𝑎 → 0 then ℎ𝑓𝑓,𝑜𝑜𝑜𝑜𝑜𝑜

𝑔𝑔𝑔𝑔𝑔𝑔 − ℎ𝑖𝑖𝑎𝑎,𝑜𝑜𝑜𝑜𝑜𝑜𝑔𝑔𝑔𝑔𝑔𝑔 → 0. Hence,

𝐹𝐹𝑤𝑤1(ℎ𝑔𝑔𝑜𝑜𝑎𝑎1 − ℎ𝑏𝑏𝑜𝑜𝑖𝑖𝑖𝑖𝑏𝑏𝑏𝑏) + 𝐹𝐹𝑤𝑤2(ℎ𝑔𝑔𝑜𝑜𝑎𝑎2 − ℎ𝐻𝐻𝐻𝐻𝑏𝑏𝑖𝑖𝑔𝑔𝐻𝐻ℎ𝑔𝑔𝑏𝑏𝑔𝑔𝑏𝑏)𝐹𝐹𝑤𝑤1

= ℎ𝑓𝑓,𝑖𝑖𝑖𝑖𝑔𝑔𝑔𝑔𝑔𝑔 − ℎ𝑓𝑓,𝑜𝑜𝑜𝑜𝑜𝑜


If 𝑇𝑇𝑓𝑓,𝑖𝑖𝑖𝑖𝑔𝑔𝑔𝑔𝑔𝑔 > 1200oC then 𝑇𝑇𝑓𝑓,𝑖𝑖𝑖𝑖

𝑔𝑔𝑔𝑔𝑔𝑔 is set to 1200oC and hence ℎ𝑓𝑓,𝑖𝑖𝑖𝑖𝑔𝑔𝑔𝑔𝑔𝑔 is obtained which is used to calculate 𝐹𝐹𝑔𝑔𝑔𝑔𝑔𝑔.

For the subcritical Rankine cycle, 𝑇𝑇𝑓𝑓,𝑔𝑔𝑔𝑔𝑔𝑔𝑜𝑜𝑜𝑜𝑜𝑜 = 600°𝐶𝐶 i.e. ℎ𝑓𝑓,𝑔𝑔𝑔𝑔𝑔𝑔

𝑜𝑜𝑜𝑜𝑜𝑜 = 904.5 𝑘𝑘𝑘𝑘𝑘𝑘𝑔𝑔−𝑔𝑔𝑔𝑔𝑔𝑔. The properties of the gas

are those of Air at 1 bar pressure (taken from Perry’s Chemical Engineer’s Handbook Edition VII).

For a sub-critical Rankine cycle, 𝐹𝐹𝑤𝑤1(ℎ𝑔𝑔𝑜𝑜𝑎𝑎1 − ℎ𝑏𝑏𝑜𝑜𝑖𝑖𝑖𝑖𝑏𝑏𝑏𝑏) = 750.4 + 127.3 + 200 = 1078 kJkg−condensate

and 𝐹𝐹𝑤𝑤2(ℎ𝑔𝑔𝑜𝑜𝑎𝑎2 − ℎ𝐻𝐻𝐻𝐻𝑏𝑏𝑖𝑖𝑔𝑔𝐻𝐻ℎ𝑔𝑔𝑏𝑏𝑔𝑔𝑏𝑏) = 718.9 + 121.9 + 59.15 = 900.0 kJkg−condensate . Since the

temperature driving force between gas and liquid is 50K, hence 𝑇𝑇𝑏𝑏𝑜𝑜𝑖𝑖𝑖𝑖,𝑜𝑜𝑜𝑜𝑜𝑜𝑔𝑔𝑔𝑔𝑔𝑔 = 310 + 50 = 360°𝐶𝐶 i.e.

ℎ𝑏𝑏𝑜𝑜𝑖𝑖𝑖𝑖,𝑜𝑜𝑜𝑜𝑜𝑜𝑔𝑔𝑔𝑔𝑔𝑔 = 643.1 𝑘𝑘𝑘𝑘

𝑘𝑘𝑔𝑔−𝑔𝑔𝑔𝑔𝑔𝑔 . Also 𝐹𝐹𝑤𝑤1(ℎ𝑏𝑏𝑜𝑜𝑖𝑖𝑖𝑖𝑏𝑏𝑏𝑏 − ℎ𝑏𝑏𝑜𝑜𝑖𝑖𝑖𝑖𝑏𝑏𝑏𝑏) = (1567 + 265.8 + 417.8)− 1.463 ×

(h310°C − h264°C) = 2251 − 362.8 = 1888 kJkg (here the economizer enthalpy is subtracted). Hence


Page 19 of 26

ℎ𝑓𝑓,𝑖𝑖𝑖𝑖𝑔𝑔𝑔𝑔𝑔𝑔 = 1078+900

1888 (904.5 − 643.1) + 904.5 = 1178.0 𝑘𝑘𝑘𝑘𝑘𝑘𝑔𝑔−𝑔𝑔𝑔𝑔𝑔𝑔 which corresponds to a temperature

𝑇𝑇𝑓𝑓,𝑖𝑖𝑖𝑖𝑔𝑔𝑔𝑔𝑔𝑔 = 840°𝐶𝐶.

Hence 𝐹𝐹𝑔𝑔𝑔𝑔𝑔𝑔 = Η𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠ℎ𝑠𝑠𝑒𝑒𝑒𝑒𝑀𝑀𝑀𝑀 +Η𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠ℎ𝑠𝑠𝑒𝑒𝑒𝑒𝐻𝐻𝑀𝑀

ℎ𝑓𝑓,𝑖𝑖𝑖𝑖𝑔𝑔𝑒𝑒𝑠𝑠−ℎ𝑓𝑓,𝑜𝑜𝑠𝑠𝑒𝑒

𝑔𝑔𝑒𝑒𝑠𝑠 = 1078+9001178−904.5 = 7.23 𝑘𝑘𝑔𝑔

𝑘𝑘𝑔𝑔−𝑐𝑐𝑐𝑐𝑖𝑖𝑐𝑐𝑐𝑐𝑖𝑖𝑔𝑔𝑔𝑔𝑐𝑐𝑐𝑐.

Enthalpy of gas leaving the economizer is given by 𝐹𝐹𝑔𝑔𝑔𝑔𝑔𝑔(ℎ𝑓𝑓,𝑐𝑐𝑜𝑜𝑐𝑐𝑔𝑔𝑔𝑔𝑔𝑔 − ℎ𝑐𝑐𝑐𝑐𝑐𝑐𝑖𝑖,𝑐𝑐𝑜𝑜𝑐𝑐

𝑔𝑔𝑔𝑔𝑔𝑔 ) = 𝐹𝐹𝑤𝑤1 × Η𝑏𝑏𝑐𝑐𝑖𝑖𝑏𝑏𝑐𝑐𝑏𝑏 =1.463 × 1567 = 2292.5 . Hence ℎ𝑐𝑐𝑐𝑐𝑐𝑐𝑖𝑖,𝑐𝑐𝑜𝑜𝑐𝑐

𝑔𝑔𝑔𝑔𝑔𝑔 = 904.5− 2292.57.23 = 587.4 𝑘𝑘𝑘𝑘

𝑘𝑘𝑔𝑔 i.e. 𝑇𝑇𝑐𝑐𝑐𝑐𝑐𝑐𝑖𝑖,𝑐𝑐𝑜𝑜𝑐𝑐𝑔𝑔𝑔𝑔𝑔𝑔 = 307.5°𝐶𝐶 .

This gas is countercurrently contacted with ambient air at 30°𝐶𝐶 (enthalpy 303.5 kJ/kg) in the air preheater and leaves at its acid-dew point of 130°𝐶𝐶 i.e. a specific enthalpy of 404.4 𝑘𝑘𝑘𝑘

𝑘𝑘𝑔𝑔. The enthalpy

of the preheated air is therefore: 303.5 + (587.4 − 404.4) = 486.6 𝑘𝑘𝑘𝑘/𝑘𝑘𝑘𝑘 i.e. a preheated temperature of 210°𝐶𝐶 . The additional enthalpy required for it to reach 840°𝐶𝐶 is 7.23 ×(1178 − 486.6) = 4998 𝑘𝑘𝑘𝑘


Hence the actual efficiency of the process is 1890×0.854998 × 100 = 32%. If we assume 90% mechanical

efficiency (95% isentropic efficiency), this number becomes 36%.

Heat Transfer Fluid:

The procedure is a straightforward countercurrent heat-exchange calculation for each region in the working fluid heating cycle. Unlike for Fgas the flowrates of HTF in each region need not be correlated to the other. The flowrates in each region (preheating+economizer, boiler, superheater1 and superheater2) are calculated independently with a temperature approach of 20K. For liquid-liquid heat exchange, temperature driving force is generally 10K. However, heat is generally stored in another fluid in the “2-tank indirect scheme” that is probably the only thermal storage technology deployed on a utility scale: necessitating the additional 10K. The flow rates in the boiler for the subcritical rankine cycle are calculated assuming a temperature swing in the HTF between 330oC and 400oC. In the superheater, the swing is between 400°𝐶𝐶 and 590°𝐶𝐶 while in the economizer the temperature is between 330°𝐶𝐶(max) and a minimum ranging from 70°𝐶𝐶 to a 20K excess over the last preheater temperature.

Supercritical Rankine Cycle Power Plant Many power plants operate the supercritical Rankine Cycle where the “boiler” raises steam at temperatures exceeding the critical temperature of water. The highest pressure in the plant is 300 bar and the highest temperature of steam is 620°𝐶𝐶. For the supercritical Rankine cycle, 𝑇𝑇𝑓𝑓,𝑔𝑔𝑔𝑔𝑔𝑔

𝑐𝑐𝑜𝑜𝑐𝑐 =680°𝐶𝐶. Also the “boiler” does not operate at a single temperature (there is no phase-change in this cycle) but is taken to be the heat-exchanger for the temperatures between 380°𝐶𝐶 and 460°𝐶𝐶 where the fluid has a higher heat capacity. The pinch point is taken to be the entrance of the superheater rather than the entrance of the boiler.

Solar Thermal Power Plant Figure 5 shows a solar thermal power plant of the SEGS type where electricity is generated entirely from solar heat. The plant is identical to that shown in Figure 1 except for the method of heat supply. Whereas the conventional power plant gets heat from flue gases generated by burning coal, the solar





Page 18 of 26

is the flow rate of gas and ℎ𝑓𝑓,𝑖𝑖𝑖𝑖𝑔𝑔𝑔𝑔𝑔𝑔,ℎ𝑓𝑓,𝑜𝑜𝑜𝑜𝑜𝑜

𝑔𝑔𝑔𝑔𝑔𝑔 are the specific enthalpies of the gas at the exit of the combustor and the inlet of the furnace respectively.

Also, if the point of entry into the boiler is the pinch point, then

𝑇𝑇𝑏𝑏𝑜𝑜𝑖𝑖𝑖𝑖,𝑜𝑜𝑜𝑜𝑜𝑜𝑔𝑔𝑔𝑔𝑔𝑔 = 𝑇𝑇𝑏𝑏𝑜𝑜𝑖𝑖𝑖𝑖 + Δ𝑇𝑇𝑔𝑔𝑎𝑎𝑎𝑎

Where 𝑇𝑇𝑏𝑏𝑜𝑜𝑖𝑖𝑖𝑖.𝑜𝑜𝑜𝑜𝑜𝑜𝑔𝑔𝑔𝑔𝑔𝑔 is the temperature of the flue gas leaving the boiler which is at 𝑇𝑇𝑏𝑏𝑜𝑜𝑖𝑖𝑖𝑖 with Δ𝑇𝑇𝑔𝑔𝑎𝑎𝑎𝑎.

The corresponding enthalpy is ℎ𝑏𝑏𝑜𝑜𝑖𝑖𝑖𝑖,𝑜𝑜𝑜𝑜𝑜𝑜𝑔𝑔𝑔𝑔𝑔𝑔 . The enthalpy of water entering the boiler is ℎ𝑏𝑏𝑜𝑜𝑖𝑖𝑖𝑖𝑏𝑏𝑏𝑏 and its

flowrate is 𝐹𝐹𝑤𝑤1 Hence,

𝐹𝐹𝑤𝑤1(ℎ𝑏𝑏𝑜𝑜𝑖𝑖𝑖𝑖𝑏𝑏𝑏𝑏 − ℎ𝑏𝑏𝑜𝑜𝑖𝑖𝑖𝑖𝑏𝑏𝑏𝑏) = 𝐹𝐹𝑔𝑔𝑔𝑔𝑔𝑔(ℎ𝑓𝑓,𝑜𝑜𝑜𝑜𝑜𝑜𝑔𝑔𝑔𝑔𝑔𝑔 − ℎ𝑏𝑏𝑜𝑜𝑖𝑖𝑖𝑖,𝑜𝑜𝑜𝑜𝑜𝑜


Hence,

𝐹𝐹𝑤𝑤1(ℎ𝑔𝑔𝑜𝑜𝑎𝑎1 − ℎ𝑏𝑏𝑜𝑜𝑖𝑖𝑖𝑖𝑏𝑏𝑏𝑏) + 𝐹𝐹𝑤𝑤2(ℎ𝑔𝑔𝑜𝑜𝑎𝑎2 − ℎ𝐻𝐻𝐻𝐻𝑏𝑏𝑖𝑖𝑔𝑔𝐻𝐻ℎ𝑔𝑔𝑏𝑏𝑔𝑔𝑏𝑏)𝐹𝐹𝑤𝑤1(ℎ𝑏𝑏𝑜𝑜𝑖𝑖𝑖𝑖𝑏𝑏𝑏𝑏 − ℎ𝑏𝑏𝑜𝑜𝑖𝑖𝑖𝑖𝑏𝑏𝑏𝑏) =

ℎ𝑓𝑓,𝑖𝑖𝑖𝑖𝑔𝑔𝑔𝑔𝑔𝑔 − ℎ𝑓𝑓,𝑜𝑜𝑜𝑜𝑜𝑜


ℎ𝑓𝑓,𝑜𝑜𝑜𝑜𝑜𝑜𝑔𝑔𝑔𝑔𝑔𝑔 − ℎ𝑏𝑏𝑜𝑜𝑖𝑖𝑖𝑖,𝑜𝑜𝑜𝑜𝑜𝑜


Hence,

𝐹𝐹𝑤𝑤1(ℎ𝑔𝑔𝑜𝑜𝑎𝑎1 − ℎ𝑏𝑏𝑜𝑜𝑖𝑖𝑖𝑖𝑏𝑏𝑏𝑏) + 𝐹𝐹𝑤𝑤2(ℎ𝑔𝑔𝑜𝑜𝑎𝑎2 − ℎ𝐻𝐻𝐻𝐻𝑏𝑏𝑖𝑖𝑔𝑔𝐻𝐻ℎ𝑔𝑔𝑏𝑏𝑔𝑔𝑏𝑏)𝐹𝐹𝑤𝑤1(ℎ𝑏𝑏𝑜𝑜𝑖𝑖𝑖𝑖𝑏𝑏𝑏𝑏 − ℎ𝑏𝑏𝑜𝑜𝑖𝑖𝑖𝑖𝑏𝑏𝑏𝑏) (ℎ𝑓𝑓,𝑜𝑜𝑜𝑜𝑜𝑜

𝑔𝑔𝑔𝑔𝑔𝑔 − ℎ𝑏𝑏𝑜𝑜𝑖𝑖𝑖𝑖,𝑜𝑜𝑜𝑜𝑜𝑜𝑔𝑔𝑔𝑔𝑔𝑔 ) + ℎ𝑓𝑓,𝑜𝑜𝑜𝑜𝑜𝑜

𝑔𝑔𝑔𝑔𝑔𝑔 = ℎ𝑓𝑓,𝑖𝑖𝑖𝑖𝑔𝑔𝑔𝑔𝑔𝑔

Hence 𝐹𝐹𝑔𝑔𝑔𝑔𝑔𝑔 can be determined.

If preheat extends all the way to superheat, then we keep ℎ𝑓𝑓,𝑖𝑖𝑖𝑖𝑔𝑔𝑔𝑔𝑔𝑔 the same as for when it was

supplying all preheat upto boiler and reduce 𝐹𝐹𝑔𝑔𝑔𝑔𝑔𝑔.

At the point where preheat just supplies everything short of the superheater i.e. ℎ𝑏𝑏𝑜𝑜𝑖𝑖𝑖𝑖𝑏𝑏𝑏𝑏 − ℎ𝑖𝑖𝑎𝑎 → 0 then ℎ𝑓𝑓,𝑜𝑜𝑜𝑜𝑜𝑜

𝑔𝑔𝑔𝑔𝑔𝑔 − ℎ𝑖𝑖𝑎𝑎,𝑜𝑜𝑜𝑜𝑜𝑜𝑔𝑔𝑔𝑔𝑔𝑔 → 0. Hence,

𝐹𝐹𝑤𝑤1(ℎ𝑔𝑔𝑜𝑜𝑎𝑎1 − ℎ𝑏𝑏𝑜𝑜𝑖𝑖𝑖𝑖𝑏𝑏𝑏𝑏) + 𝐹𝐹𝑤𝑤2(ℎ𝑔𝑔𝑜𝑜𝑎𝑎2 − ℎ𝐻𝐻𝐻𝐻𝑏𝑏𝑖𝑖𝑔𝑔𝐻𝐻ℎ𝑔𝑔𝑏𝑏𝑔𝑔𝑏𝑏)𝐹𝐹𝑤𝑤1

= ℎ𝑓𝑓,𝑖𝑖𝑖𝑖𝑔𝑔𝑔𝑔𝑔𝑔 − ℎ𝑓𝑓,𝑜𝑜𝑜𝑜𝑜𝑜


If 𝑇𝑇𝑓𝑓,𝑖𝑖𝑖𝑖𝑔𝑔𝑔𝑔𝑔𝑔 > 1200oC then 𝑇𝑇𝑓𝑓,𝑖𝑖𝑖𝑖

𝑔𝑔𝑔𝑔𝑔𝑔 is set to 1200oC and hence ℎ𝑓𝑓,𝑖𝑖𝑖𝑖𝑔𝑔𝑔𝑔𝑔𝑔 is obtained which is used to calculate 𝐹𝐹𝑔𝑔𝑔𝑔𝑔𝑔.

For the subcritical Rankine cycle, 𝑇𝑇𝑓𝑓,𝑔𝑔𝑔𝑔𝑔𝑔𝑜𝑜𝑜𝑜𝑜𝑜 = 600°𝐶𝐶 i.e. ℎ𝑓𝑓,𝑔𝑔𝑔𝑔𝑔𝑔

𝑜𝑜𝑜𝑜𝑜𝑜 = 904.5 𝑘𝑘𝑘𝑘𝑘𝑘𝑔𝑔−𝑔𝑔𝑔𝑔𝑔𝑔. The properties of the gas

are those of Air at 1 bar pressure (taken from Perry’s Chemical Engineer’s Handbook Edition VII).

For a sub-critical Rankine cycle, 𝐹𝐹𝑤𝑤1(ℎ𝑔𝑔𝑜𝑜𝑎𝑎1 − ℎ𝑏𝑏𝑜𝑜𝑖𝑖𝑖𝑖𝑏𝑏𝑏𝑏) = 750.4 + 127.3 + 200 = 1078 kJkg−condensate

and 𝐹𝐹𝑤𝑤2(ℎ𝑔𝑔𝑜𝑜𝑎𝑎2 − ℎ𝐻𝐻𝐻𝐻𝑏𝑏𝑖𝑖𝑔𝑔𝐻𝐻ℎ𝑔𝑔𝑏𝑏𝑔𝑔𝑏𝑏) = 718.9 + 121.9 + 59.15 = 900.0 kJkg−condensate . Since the

temperature driving force between gas and liquid is 50K, hence 𝑇𝑇𝑏𝑏𝑜𝑜𝑖𝑖𝑖𝑖,𝑜𝑜𝑜𝑜𝑜𝑜𝑔𝑔𝑔𝑔𝑔𝑔 = 310 + 50 = 360°𝐶𝐶 i.e.

ℎ𝑏𝑏𝑜𝑜𝑖𝑖𝑖𝑖,𝑜𝑜𝑜𝑜𝑜𝑜𝑔𝑔𝑔𝑔𝑔𝑔 = 643.1 𝑘𝑘𝑘𝑘

𝑘𝑘𝑔𝑔−𝑔𝑔𝑔𝑔𝑔𝑔 . Also 𝐹𝐹𝑤𝑤1(ℎ𝑏𝑏𝑜𝑜𝑖𝑖𝑖𝑖𝑏𝑏𝑏𝑏 − ℎ𝑏𝑏𝑜𝑜𝑖𝑖𝑖𝑖𝑏𝑏𝑏𝑏) = (1567 + 265.8 + 417.8)− 1.463 ×

(h310°C − h264°C) = 2251 − 362.8 = 1888 kJkg (here the economizer enthalpy is subtracted). Hence


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ℎ𝑓𝑓,𝑖𝑖𝑖𝑖𝑔𝑔𝑔𝑔𝑔𝑔 = 1078+900

1888 (904.5 − 643.1) + 904.5 = 1178.0 𝑘𝑘𝑘𝑘𝑘𝑘𝑔𝑔−𝑔𝑔𝑔𝑔𝑔𝑔 which corresponds to a temperature

𝑇𝑇𝑓𝑓,𝑖𝑖𝑖𝑖𝑔𝑔𝑔𝑔𝑔𝑔 = 840°𝐶𝐶.

Hence 𝐹𝐹𝑔𝑔𝑔𝑔𝑔𝑔 = Η𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠ℎ𝑠𝑠𝑒𝑒𝑒𝑒𝑀𝑀𝑀𝑀 +Η𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠ℎ𝑠𝑠𝑒𝑒𝑒𝑒𝐻𝐻𝑀𝑀

ℎ𝑓𝑓,𝑖𝑖𝑖𝑖𝑔𝑔𝑒𝑒𝑠𝑠−ℎ𝑓𝑓,𝑜𝑜𝑠𝑠𝑒𝑒

𝑔𝑔𝑒𝑒𝑠𝑠 = 1078+9001178−904.5 = 7.23 𝑘𝑘𝑔𝑔


Enthalpy of gas leaving the economizer is given by 𝐹𝐹𝑔𝑔𝑔𝑔𝑔𝑔(ℎ𝑓𝑓,𝑐𝑐𝑜𝑜𝑐𝑐𝑔𝑔𝑔𝑔𝑔𝑔 − ℎ𝑐𝑐𝑐𝑐𝑐𝑐𝑖𝑖,𝑐𝑐𝑜𝑜𝑐𝑐

𝑔𝑔𝑔𝑔𝑔𝑔 ) = 𝐹𝐹𝑤𝑤1 × Η𝑏𝑏𝑐𝑐𝑖𝑖𝑏𝑏𝑐𝑐𝑏𝑏 =1.463 × 1567 = 2292.5 . Hence ℎ𝑐𝑐𝑐𝑐𝑐𝑐𝑖𝑖,𝑐𝑐𝑜𝑜𝑐𝑐

𝑔𝑔𝑔𝑔𝑔𝑔 = 904.5− 2292.57.23 = 587.4 𝑘𝑘𝑘𝑘

𝑘𝑘𝑔𝑔 i.e. 𝑇𝑇𝑐𝑐𝑐𝑐𝑐𝑐𝑖𝑖,𝑐𝑐𝑜𝑜𝑐𝑐𝑔𝑔𝑔𝑔𝑔𝑔 = 307.5°𝐶𝐶 .

This gas is countercurrently contacted with ambient air at 30°𝐶𝐶 (enthalpy 303.5 kJ/kg) in the air preheater and leaves at its acid-dew point of 130°𝐶𝐶 i.e. a specific enthalpy of 404.4 𝑘𝑘𝑘𝑘

𝑘𝑘𝑔𝑔. The enthalpy

of the preheated air is therefore: 303.5 + (587.4 − 404.4) = 486.6 𝑘𝑘𝑘𝑘/𝑘𝑘𝑘𝑘 i.e. a preheated temperature of 210°𝐶𝐶 . The additional enthalpy required for it to reach 840°𝐶𝐶 is 7.23 ×(1178 − 486.6) = 4998 𝑘𝑘𝑘𝑘


Hence the actual efficiency of the process is 1890×0.854998 × 100 = 32%. If we assume 90% mechanical

efficiency (95% isentropic efficiency), this number becomes 36%.

Heat Transfer Fluid:

The procedure is a straightforward countercurrent heat-exchange calculation for each region in the working fluid heating cycle. Unlike for Fgas the flowrates of HTF in each region need not be correlated to the other. The flowrates in each region (preheating+economizer, boiler, superheater1 and superheater2) are calculated independently with a temperature approach of 20K. For liquid-liquid heat exchange, temperature driving force is generally 10K. However, heat is generally stored in another fluid in the “2-tank indirect scheme” that is probably the only thermal storage technology deployed on a utility scale: necessitating the additional 10K. The flow rates in the boiler for the subcritical rankine cycle are calculated assuming a temperature swing in the HTF between 330oC and 400oC. In the superheater, the swing is between 400°𝐶𝐶 and 590°𝐶𝐶 while in the economizer the temperature is between 330°𝐶𝐶(max) and a minimum ranging from 70°𝐶𝐶 to a 20K excess over the last preheater temperature.

Supercritical Rankine Cycle Power Plant Many power plants operate the supercritical Rankine Cycle where the “boiler” raises steam at temperatures exceeding the critical temperature of water. The highest pressure in the plant is 300 bar and the highest temperature of steam is 620°𝐶𝐶. For the supercritical Rankine cycle, 𝑇𝑇𝑓𝑓,𝑔𝑔𝑔𝑔𝑔𝑔

𝑐𝑐𝑜𝑜𝑐𝑐 =680°𝐶𝐶. Also the “boiler” does not operate at a single temperature (there is no phase-change in this cycle) but is taken to be the heat-exchanger for the temperatures between 380°𝐶𝐶 and 460°𝐶𝐶 where the fluid has a higher heat capacity. The pinch point is taken to be the entrance of the superheater rather than the entrance of the boiler.

Solar Thermal Power Plant Figure 5 shows a solar thermal power plant of the SEGS type where electricity is generated entirely from solar heat. The plant is identical to that shown in Figure 1 except for the method of heat supply. Whereas the conventional power plant gets heat from flue gases generated by burning coal, the solar





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thermal power plant gets heat from a heat transfer fluid (generally a eutectic mixture of diphenyl/biphenyl oxide) that is heated in tubes irradiated by solar radiation concentrated by arrays of mirrors in a solar field.

Solar Capture Efficiency Let 𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟 be the concentration ratio. Hence the incident radiative flux on the receiver is given by:

𝐼𝐼𝑖𝑖𝑖𝑖𝑖𝑖 = 𝛼𝛼𝑟𝑟𝑎𝑎𝑎𝑎𝛼𝛼𝑖𝑖𝑐𝑐𝑎𝑎𝑖𝑖𝑖𝑖𝑐𝑐𝐼𝐼 (1 + 𝛼𝛼𝑟𝑟𝑐𝑐𝑟𝑟𝛼𝛼𝐷𝐷𝐷𝐷𝐷𝐷(𝐶𝐶𝑅𝑅𝑟𝑟𝑟𝑟 − 1))

Where 𝛼𝛼𝑟𝑟𝑎𝑎𝑎𝑎 is the solar averaged absorptivity of the receiver, 𝛼𝛼𝑖𝑖𝑐𝑐𝑎𝑎𝑖𝑖𝑖𝑖𝑐𝑐 is the area-cosine factor of the reflector, 𝐼𝐼 is the total solar insolation, 𝛼𝛼𝐷𝐷𝐷𝐷𝐷𝐷 is the fraction of solar insolation that is direct normal insolation and 𝛼𝛼𝑟𝑟𝑐𝑐𝑟𝑟 is the solar averaged reflectivity of the reflector. If 𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟 = 1, there is no reflector and all solar insolation falls, unconcentrated, onto the receiver. For an introduction to these terms, the reader is referred to standard textbooks (e.g. Solar Energy: Principles of Thermal Collection and Storage by Sukhatme (Tata McGraw-Hill 2008)) or the excellent on line resources at www.powerfromthesun.net .

Assuming well evacuated receivers, where losses due to convection are negligible, the only losses will be due to re-radiation from the surface of the receiver. Neglecting the difference between the temperature of the heat transfer fluid and the receiver surface, the net flux absorbed is given by:

𝐼𝐼𝑟𝑟𝑎𝑎𝑎𝑎 = 𝐼𝐼𝑖𝑖𝑖𝑖𝑖𝑖 − 𝜖𝜖𝜖𝜖(𝑇𝑇𝐻𝐻𝐻𝐻𝐻𝐻4 − 𝑇𝑇𝑐𝑐4)

Where 𝜖𝜖 is the averaged emissivity and 𝜖𝜖 is Stefan’s Constant. 𝑇𝑇𝐻𝐻𝐻𝐻𝐻𝐻 and 𝑇𝑇𝑐𝑐 are the temperature of the heat transfer fluid and of the ambient respectively, both in K. Hence the flux lost is:

𝐼𝐼𝑙𝑙𝑐𝑐𝑎𝑎𝑟𝑟 = 𝐶𝐶𝑅𝑅𝑟𝑟𝑟𝑟𝐼𝐼 − 𝐼𝐼𝑟𝑟𝑎𝑎𝑎𝑎

And the stagnation temperature (𝑇𝑇𝑎𝑎𝑟𝑟𝑠𝑠) is the temperature of the heat transfer fluid when 𝐼𝐼𝑟𝑟𝑎𝑎𝑎𝑎 = 0.

𝑇𝑇𝑎𝑎𝑟𝑟𝑠𝑠4 = 𝑇𝑇𝑐𝑐4 + 𝐼𝐼𝑖𝑖𝑖𝑖𝑖𝑖𝜖𝜖𝜖𝜖

Differential heat balance across a receiver tube (the HTF is assumed DowthermA here).

𝑑𝑑𝑑𝑑 = 𝐼𝐼𝑟𝑟𝑎𝑎𝑎𝑎𝑃𝑃𝑑𝑑𝑃𝑃 = �̇�𝑚𝐻𝐻𝐻𝐻𝐻𝐻𝐶𝐶𝑝𝑝,𝐻𝐻𝐻𝐻𝐻𝐻𝑑𝑑𝑇𝑇𝐻𝐻𝐻𝐻𝐻𝐻 = �̇�𝑚𝐻𝐻𝐻𝐻𝐻𝐻𝑑𝑑ℎ𝐻𝐻𝐻𝐻𝐻𝐻

where 𝑃𝑃 is the perimeter of the receiver cross-section (which receives and re-radiates heat), 𝑃𝑃 is the length. �̇�𝑚𝐻𝐻𝐻𝐻𝐻𝐻 is the mass rate of flow.

Hence:

𝐼𝐼𝑟𝑟𝑎𝑎𝑎𝑎𝑑𝑑(𝑃𝑃𝑃𝑃) = �̇�𝑚𝐻𝐻𝐻𝐻𝐻𝐻𝑑𝑑ℎ𝐻𝐻𝐻𝐻𝐻𝐻

i.e.

(𝐼𝐼𝑖𝑖𝑖𝑖𝑖𝑖 − 𝜖𝜖𝜖𝜖(𝑇𝑇𝐻𝐻𝐻𝐻𝐻𝐻4 − 𝑇𝑇𝑐𝑐4))𝑑𝑑 ( 𝑃𝑃𝑃𝑃�̇�𝑚𝐻𝐻𝐻𝐻𝐻𝐻

) = 𝐶𝐶𝑝𝑝,𝐻𝐻𝐻𝐻𝐻𝐻𝑑𝑑𝑇𝑇𝐻𝐻𝐻𝐻𝐻𝐻

Hence:


Page 21 of 26

𝑑𝑑 ( 𝑃𝑃𝑃𝑃�̇�𝑚𝐻𝐻𝐻𝐻𝐻𝐻

) =𝐶𝐶𝑝𝑝,𝐻𝐻𝐻𝐻𝐻𝐻𝑑𝑑𝑇𝑇𝐻𝐻𝐻𝐻𝐻𝐻

𝐼𝐼𝑖𝑖𝑖𝑖𝑖𝑖 − 𝜖𝜖𝜖𝜖(𝑇𝑇𝐻𝐻𝐻𝐻𝐻𝐻4 − 𝑇𝑇𝑜𝑜4)

Hence:

𝑃𝑃𝑃𝑃�̇�𝑚𝐻𝐻𝐻𝐻𝐻𝐻

= ∫𝐶𝐶𝑝𝑝,𝐻𝐻𝐻𝐻𝐻𝐻𝑑𝑑𝑇𝑇𝐻𝐻𝐻𝐻𝐻𝐻

𝐼𝐼𝑖𝑖𝑖𝑖𝑖𝑖 − 𝜖𝜖𝜖𝜖(𝑇𝑇𝐻𝐻𝐻𝐻𝐻𝐻4 − 𝑇𝑇𝑜𝑜4)𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻,max

𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻,𝑚𝑚𝑚𝑚𝑚𝑚

Heat incident is: 𝑃𝑃𝑃𝑃𝐼𝐼𝑔𝑔𝑔𝑔𝑜𝑜𝑔𝑔𝑔𝑔𝑔𝑔𝐶𝐶𝑅𝑅𝑔𝑔𝑅𝑅. Using the notation that ℎ𝐻𝐻𝐻𝐻𝐻𝐻(𝑇𝑇) is the specific enthalpy of the HTF

at temperature 𝑇𝑇, heat captured is given by �̇�𝑚𝐻𝐻𝐻𝐻𝐻𝐻 (ℎ𝐻𝐻𝐻𝐻𝐻𝐻(𝑇𝑇𝐻𝐻𝐻𝐻𝐻𝐻𝑚𝑚𝑔𝑔𝑚𝑚) − ℎ𝐻𝐻𝐻𝐻𝐻𝐻(𝑇𝑇𝐻𝐻𝐻𝐻𝐻𝐻𝑚𝑚𝑖𝑖𝑖𝑖)). Hence, efficiency

of capture is:

𝜂𝜂𝑖𝑖𝑔𝑔𝑝𝑝 =�̇�𝑚𝐻𝐻𝐻𝐻𝐻𝐻 (ℎ𝐻𝐻𝐻𝐻𝐻𝐻(𝑇𝑇𝐻𝐻𝐻𝐻𝐻𝐻𝑚𝑚𝑔𝑔𝑚𝑚)− ℎ𝐻𝐻𝐻𝐻𝐻𝐻(𝑇𝑇𝐻𝐻𝐻𝐻𝐻𝐻𝑚𝑚𝑖𝑖𝑖𝑖))

𝑃𝑃𝑃𝑃𝐼𝐼𝐶𝐶𝑅𝑅𝑔𝑔𝑅𝑅

i.e.

𝜂𝜂𝑖𝑖𝑔𝑔𝑝𝑝 =�̇�𝑚𝐻𝐻𝐻𝐻𝐻𝐻 (ℎ𝐻𝐻𝐻𝐻𝐻𝐻(𝑇𝑇𝐻𝐻𝐻𝐻𝐻𝐻𝑚𝑚𝑔𝑔𝑚𝑚)− ℎ𝑑𝑑𝑜𝑜𝑑𝑑(𝑇𝑇𝐻𝐻𝐻𝐻𝐻𝐻𝑚𝑚𝑖𝑖𝑖𝑖))

�̇�𝑚𝐻𝐻𝐻𝐻𝐻𝐻𝐼𝐼𝐶𝐶𝑅𝑅𝑔𝑔𝑅𝑅 ∫𝐶𝐶𝑝𝑝,𝐻𝐻𝐻𝐻𝐻𝐻𝑑𝑑𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻

𝐼𝐼𝑚𝑚𝑚𝑚𝑖𝑖−𝜖𝜖𝜖𝜖(𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻4 −𝐻𝐻𝑜𝑜4)𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻,max𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻,𝑚𝑚𝑚𝑚𝑚𝑚

i.e.

𝜂𝜂𝑖𝑖𝑔𝑔𝑝𝑝 = ℎ𝐻𝐻𝐻𝐻𝐻𝐻(𝑇𝑇𝐻𝐻𝐻𝐻𝐻𝐻𝑚𝑚𝑔𝑔𝑚𝑚)− ℎ𝐻𝐻𝐻𝐻𝐻𝐻(𝑇𝑇𝐻𝐻𝐻𝐻𝐻𝐻𝑚𝑚𝑖𝑖𝑖𝑖)𝐼𝐼𝐶𝐶𝑅𝑅𝑔𝑔𝑅𝑅 ∫

𝐶𝐶𝑝𝑝,𝐻𝐻𝐻𝐻𝐻𝐻𝑑𝑑𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐼𝐼𝑚𝑚𝑚𝑚𝑖𝑖−𝜖𝜖𝜖𝜖(𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻4 −𝐻𝐻𝑜𝑜4)

𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻,max𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻,𝑚𝑚𝑚𝑚𝑚𝑚





Page 20 of 26

thermal power plant gets heat from a heat transfer fluid (generally a eutectic mixture of diphenyl/biphenyl oxide) that is heated in tubes irradiated by solar radiation concentrated by arrays of mirrors in a solar field.

Solar Capture Efficiency Let 𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟 be the concentration ratio. Hence the incident radiative flux on the receiver is given by:

𝐼𝐼𝑖𝑖𝑖𝑖𝑖𝑖 = 𝛼𝛼𝑟𝑟𝑎𝑎𝑎𝑎𝛼𝛼𝑖𝑖𝑐𝑐𝑎𝑎𝑖𝑖𝑖𝑖𝑐𝑐𝐼𝐼 (1 + 𝛼𝛼𝑟𝑟𝑐𝑐𝑟𝑟𝛼𝛼𝐷𝐷𝐷𝐷𝐷𝐷(𝐶𝐶𝑅𝑅𝑟𝑟𝑟𝑟 − 1))

Where 𝛼𝛼𝑟𝑟𝑎𝑎𝑎𝑎 is the solar averaged absorptivity of the receiver, 𝛼𝛼𝑖𝑖𝑐𝑐𝑎𝑎𝑖𝑖𝑖𝑖𝑐𝑐 is the area-cosine factor of the reflector, 𝐼𝐼 is the total solar insolation, 𝛼𝛼𝐷𝐷𝐷𝐷𝐷𝐷 is the fraction of solar insolation that is direct normal insolation and 𝛼𝛼𝑟𝑟𝑐𝑐𝑟𝑟 is the solar averaged reflectivity of the reflector. If 𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟 = 1, there is no reflector and all solar insolation falls, unconcentrated, onto the receiver. For an introduction to these terms, the reader is referred to standard textbooks (e.g. Solar Energy: Principles of Thermal Collection and Storage by Sukhatme (Tata McGraw-Hill 2008)) or the excellent on line resources at www.powerfromthesun.net .

Assuming well evacuated receivers, where losses due to convection are negligible, the only losses will be due to re-radiation from the surface of the receiver. Neglecting the difference between the temperature of the heat transfer fluid and the receiver surface, the net flux absorbed is given by:

𝐼𝐼𝑟𝑟𝑎𝑎𝑎𝑎 = 𝐼𝐼𝑖𝑖𝑖𝑖𝑖𝑖 − 𝜖𝜖𝜖𝜖(𝑇𝑇𝐻𝐻𝐻𝐻𝐻𝐻4 − 𝑇𝑇𝑐𝑐4)

Where 𝜖𝜖 is the averaged emissivity and 𝜖𝜖 is Stefan’s Constant. 𝑇𝑇𝐻𝐻𝐻𝐻𝐻𝐻 and 𝑇𝑇𝑐𝑐 are the temperature of the heat transfer fluid and of the ambient respectively, both in K. Hence the flux lost is:

𝐼𝐼𝑙𝑙𝑐𝑐𝑎𝑎𝑟𝑟 = 𝐶𝐶𝑅𝑅𝑟𝑟𝑟𝑟𝐼𝐼 − 𝐼𝐼𝑟𝑟𝑎𝑎𝑎𝑎

And the stagnation temperature (𝑇𝑇𝑎𝑎𝑟𝑟𝑠𝑠) is the temperature of the heat transfer fluid when 𝐼𝐼𝑟𝑟𝑎𝑎𝑎𝑎 = 0.

𝑇𝑇𝑎𝑎𝑟𝑟𝑠𝑠4 = 𝑇𝑇𝑐𝑐4 + 𝐼𝐼𝑖𝑖𝑖𝑖𝑖𝑖𝜖𝜖𝜖𝜖

Differential heat balance across a receiver tube (the HTF is assumed DowthermA here).

𝑑𝑑𝑑𝑑 = 𝐼𝐼𝑟𝑟𝑎𝑎𝑎𝑎𝑃𝑃𝑑𝑑𝑃𝑃 = �̇�𝑚𝐻𝐻𝐻𝐻𝐻𝐻𝐶𝐶𝑝𝑝,𝐻𝐻𝐻𝐻𝐻𝐻𝑑𝑑𝑇𝑇𝐻𝐻𝐻𝐻𝐻𝐻 = �̇�𝑚𝐻𝐻𝐻𝐻𝐻𝐻𝑑𝑑ℎ𝐻𝐻𝐻𝐻𝐻𝐻

where 𝑃𝑃 is the perimeter of the receiver cross-section (which receives and re-radiates heat), 𝑃𝑃 is the length. �̇�𝑚𝐻𝐻𝐻𝐻𝐻𝐻 is the mass rate of flow.

Hence:

𝐼𝐼𝑟𝑟𝑎𝑎𝑎𝑎𝑑𝑑(𝑃𝑃𝑃𝑃) = �̇�𝑚𝐻𝐻𝐻𝐻𝐻𝐻𝑑𝑑ℎ𝐻𝐻𝐻𝐻𝐻𝐻

i.e.

(𝐼𝐼𝑖𝑖𝑖𝑖𝑖𝑖 − 𝜖𝜖𝜖𝜖(𝑇𝑇𝐻𝐻𝐻𝐻𝐻𝐻4 − 𝑇𝑇𝑐𝑐4))𝑑𝑑 ( 𝑃𝑃𝑃𝑃�̇�𝑚𝐻𝐻𝐻𝐻𝐻𝐻

) = 𝐶𝐶𝑝𝑝,𝐻𝐻𝐻𝐻𝐻𝐻𝑑𝑑𝑇𝑇𝐻𝐻𝐻𝐻𝐻𝐻

Hence:


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𝑑𝑑 ( 𝑃𝑃𝑃𝑃�̇�𝑚𝐻𝐻𝐻𝐻𝐻𝐻

) =𝐶𝐶𝑝𝑝,𝐻𝐻𝐻𝐻𝐻𝐻𝑑𝑑𝑇𝑇𝐻𝐻𝐻𝐻𝐻𝐻

𝐼𝐼𝑖𝑖𝑖𝑖𝑖𝑖 − 𝜖𝜖𝜖𝜖(𝑇𝑇𝐻𝐻𝐻𝐻𝐻𝐻4 − 𝑇𝑇𝑜𝑜4)

Hence:

𝑃𝑃𝑃𝑃�̇�𝑚𝐻𝐻𝐻𝐻𝐻𝐻

= ∫𝐶𝐶𝑝𝑝,𝐻𝐻𝐻𝐻𝐻𝐻𝑑𝑑𝑇𝑇𝐻𝐻𝐻𝐻𝐻𝐻

𝐼𝐼𝑖𝑖𝑖𝑖𝑖𝑖 − 𝜖𝜖𝜖𝜖(𝑇𝑇𝐻𝐻𝐻𝐻𝐻𝐻4 − 𝑇𝑇𝑜𝑜4)𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻,max

𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻,𝑚𝑚𝑚𝑚𝑚𝑚

Heat incident is: 𝑃𝑃𝑃𝑃𝐼𝐼𝑔𝑔𝑔𝑔𝑜𝑜𝑔𝑔𝑔𝑔𝑔𝑔𝐶𝐶𝑅𝑅𝑔𝑔𝑅𝑅. Using the notation that ℎ𝐻𝐻𝐻𝐻𝐻𝐻(𝑇𝑇) is the specific enthalpy of the HTF

at temperature 𝑇𝑇, heat captured is given by �̇�𝑚𝐻𝐻𝐻𝐻𝐻𝐻 (ℎ𝐻𝐻𝐻𝐻𝐻𝐻(𝑇𝑇𝐻𝐻𝐻𝐻𝐻𝐻𝑚𝑚𝑔𝑔𝑚𝑚) − ℎ𝐻𝐻𝐻𝐻𝐻𝐻(𝑇𝑇𝐻𝐻𝐻𝐻𝐻𝐻𝑚𝑚𝑖𝑖𝑖𝑖)). Hence, efficiency

of capture is:

𝜂𝜂𝑖𝑖𝑔𝑔𝑝𝑝 =�̇�𝑚𝐻𝐻𝐻𝐻𝐻𝐻 (ℎ𝐻𝐻𝐻𝐻𝐻𝐻(𝑇𝑇𝐻𝐻𝐻𝐻𝐻𝐻𝑚𝑚𝑔𝑔𝑚𝑚)− ℎ𝐻𝐻𝐻𝐻𝐻𝐻(𝑇𝑇𝐻𝐻𝐻𝐻𝐻𝐻𝑚𝑚𝑖𝑖𝑖𝑖))

𝑃𝑃𝑃𝑃𝐼𝐼𝐶𝐶𝑅𝑅𝑔𝑔𝑅𝑅

i.e.

𝜂𝜂𝑖𝑖𝑔𝑔𝑝𝑝 =�̇�𝑚𝐻𝐻𝐻𝐻𝐻𝐻 (ℎ𝐻𝐻𝐻𝐻𝐻𝐻(𝑇𝑇𝐻𝐻𝐻𝐻𝐻𝐻𝑚𝑚𝑔𝑔𝑚𝑚)− ℎ𝑑𝑑𝑜𝑜𝑑𝑑(𝑇𝑇𝐻𝐻𝐻𝐻𝐻𝐻𝑚𝑚𝑖𝑖𝑖𝑖))

�̇�𝑚𝐻𝐻𝐻𝐻𝐻𝐻𝐼𝐼𝐶𝐶𝑅𝑅𝑔𝑔𝑅𝑅 ∫𝐶𝐶𝑝𝑝,𝐻𝐻𝐻𝐻𝐻𝐻𝑑𝑑𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻

𝐼𝐼𝑚𝑚𝑚𝑚𝑖𝑖−𝜖𝜖𝜖𝜖(𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻4 −𝐻𝐻𝑜𝑜4)𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻,max𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻,𝑚𝑚𝑚𝑚𝑚𝑚

i.e.

𝜂𝜂𝑖𝑖𝑔𝑔𝑝𝑝 = ℎ𝐻𝐻𝐻𝐻𝐻𝐻(𝑇𝑇𝐻𝐻𝐻𝐻𝐻𝐻𝑚𝑚𝑔𝑔𝑚𝑚)− ℎ𝐻𝐻𝐻𝐻𝐻𝐻(𝑇𝑇𝐻𝐻𝐻𝐻𝐻𝐻𝑚𝑚𝑖𝑖𝑖𝑖)𝐼𝐼𝐶𝐶𝑅𝑅𝑔𝑔𝑅𝑅 ∫

𝐶𝐶𝑝𝑝,𝐻𝐻𝐻𝐻𝐻𝐻𝑑𝑑𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐼𝐼𝑚𝑚𝑚𝑚𝑖𝑖−𝜖𝜖𝜖𝜖(𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻4 −𝐻𝐻𝑜𝑜4)

𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻,max𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻,𝑚𝑚𝑚𝑚𝑚𝑚





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Supplementary Figures

Figure 1: Schematic of a conventional regenerative Rankine Cycle with reheat power plant. Flue gas from combustor supplies heat for boiling water as well as superheating steam. Steam raised in the boiler is superheated in the superheater. Steam is passed through three turbines at successively lower pressure with reheating (via superheater) between turbines. The condenser condenses the exhaust steam of the LP turbine and the condensate is pumped back up to boiler pressure via three pumps. The outlet of each of the first two pumps is preheated to its saturation temperature by direct contact with steam bled from the turbines (see text for details). The parts indicated by the numbered callouts are shown on the Temperature Entropy diagram (Figure 2).

HP MP LP

Condensor

Preheater-1 Preheater-2

Boiler+ Economizer

Superheater

Flue gas from Combustor

Flue gas to Air-Preheater

1 2 3

4

5

6 7

8 9

10

11 12

13


Page 23 of 26

Figure 2: Temperature entropy diagram of the Ideal Rankine Cycle of a power plant. The two-phase envelope is the faint dome shaped curve. The solid line traces the path of a packet of working fluid through the cycle. The two dotted lines are the paths of the bled steam. The numbered callouts correspond to the sections marked in the schematic diagram of the power plant in Figure 1. The ideal thermal-to-electric efficiency of this plant is 45%: however, due to various non-idealities, the turbines are not isentropic (see Figure 4) and its actual efficiency is 80% of this value i.e. 36%.

0

200

400

600

0 2 4 6 8 10

Tem

pera

ture

oC

Entropy (kJ/kg-K)

Temperature Entropy Diagram for Power Plant

1

23

4

5

6

7

8

9

10

11

12

13





Page 22 of 26

Supplementary Figures

Figure 1: Schematic of a conventional regenerative Rankine Cycle with reheat power plant. Flue gas from combustor supplies heat for boiling water as well as superheating steam. Steam raised in the boiler is superheated in the superheater. Steam is passed through three turbines at successively lower pressure with reheating (via superheater) between turbines. The condenser condenses the exhaust steam of the LP turbine and the condensate is pumped back up to boiler pressure via three pumps. The outlet of each of the first two pumps is preheated to its saturation temperature by direct contact with steam bled from the turbines (see text for details). The parts indicated by the numbered callouts are shown on the Temperature Entropy diagram (Figure 2).

HP MP LP

Condensor


Boiler+ Economizer

Superheater

Flue gas from Combustor

Flue gas to Air-Preheater

1 2 3

4

5

6 7

8 9

10

11 12

13


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Figure 2: Temperature entropy diagram of the Ideal Rankine Cycle of a power plant. The two-phase envelope is the faint dome shaped curve. The solid line traces the path of a packet of working fluid through the cycle. The two dotted lines are the paths of the bled steam. The numbered callouts correspond to the sections marked in the schematic diagram of the power plant in Figure 1. The ideal thermal-to-electric efficiency of this plant is 45%: however, due to various non-idealities, the turbines are not isentropic (see Figure 4) and its actual efficiency is 80% of this value i.e. 36%.

0

200

400

600

0 2 4 6 8 10

Tem

pera

ture

oC

Entropy (kJ/kg-K)

Temperature Entropy Diagram for Power Plant

1

23

4

5

6

7

8

9

10

11

12

13





of 26

Figure 3: Block diagram illustrating the Subcritical Rankine Cycle. Three loops are shown: (a) the top most loop represents the working fluid that completes a circuit of the power plant (b) the middle loop shows the circuit of the HP steam bleed and (c) the lower most loop shows the circuit of the MP steam bleed. Each bleed transfers heat to the condensate for preheating: depicted by the broken lines capped by arrowheads. Working fluid flow is depicted by solid lines capped by arrowheads. Heat supplied is depicted by a thick solid arrow, work extracted is depicted by a polka-dotted thick arrow while heat rejected is depicted by a brick-pattern thick arrow.

1567 kJ

750.4 kJ 718.9 kJ 102.7 kJ

631 kJ 672.3 kJ 404.8 kJ

1659 kJ

417.8 kJ 59.2 kJ

1 kg condensate 50oC, 0.12 bar

200.0 kJ

0.2666 kg HP bleed 424oC, 50 bar

265.8 kJ

127.3 kJ 121.9 kJ

107 kJ 30.6 kJ

0.1696 kg MP bleed 454oC, 6 bar

159oC 6 bar

264oC 50 bar

310oC 98 bar 540oC

98 bar

208oC 10 bar 540oC

10 bar

209oC 1 bar

261oC 1 bar

50oC 0.12 bar

159oC 6 bar

264oC 50 bar

264oC 50 bar

310oC 98 bar

310oC 98 bar

540oC 98 bar

540oC 98 bar

208oC 10 bar 540oC

10 bar

(a)

(b)

(c)


Page 25 of 26

Figure 4: Temperature entropy diagram of a Rankine Cycle with non-isentropic turbines and pumps (heavy solid lines) is superimposed on the temperature entropy diagram of the ideal Rankine Cycle (heavy dotted lines, also shown in Figure 2) corresponding to the base case. The imposed pressures and temperatures are the same for both cycles. See the “Non-Idealities” sub-section of the section on Sub-Critical Rankine Cycle Power Plant for more details. .

0

200

400

600

0 2 4 6 8 10

Tem

pera

ture

oC

Entropy (kJ/kg-K)

Temperature Entropy Diagram for Non-Ideal Power Plant

1

23

4

5

6

7

8

9

10

11

12

13





Page 24 of 26

Figure 3: Block diagram illustrating the Subcritical Rankine Cycle. Three loops are shown: (a) the top most loop represents the working fluid that completes a circuit of the power plant (b) the middle loop shows the circuit of the HP steam bleed and (c) the lower most loop shows the circuit of the MP steam bleed. Each bleed transfers heat to the condensate for preheating: depicted by the broken lines capped by arrowheads. Working fluid flow is depicted by solid lines capped by arrowheads. Heat supplied is depicted by a thick solid arrow, work extracted is depicted by a polka-dotted thick arrow while heat rejected is depicted by a brick-pattern thick arrow.

1567 kJ

750.4 kJ 718.9 kJ 102.7 kJ

631 kJ 672.3 kJ 404.8 kJ

1659 kJ

417.8 kJ 59.2 kJ

1 kg condensate 50oC, 0.12 bar

200.0 kJ

0.2666 kg HP bleed 424oC, 50 bar

265.8 kJ

127.3 kJ 121.9 kJ

107 kJ 30.6 kJ

0.1696 kg MP bleed 454oC, 6 bar

159oC 6 bar

264oC 50 bar

310oC 98 bar 540oC

98 bar

208oC 10 bar 540oC

10 bar

209oC 1 bar

261oC 1 bar

50oC 0.12 bar

159oC 6 bar

264oC 50 bar

264oC 50 bar

310oC 98 bar

310oC 98 bar

540oC 98 bar

540oC 98 bar

208oC 10 bar 540oC

10 bar

(a)

(b)

(c)


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Figure 4: Temperature entropy diagram of a Rankine Cycle with non-isentropic turbines and pumps (heavy solid lines) is superimposed on the temperature entropy diagram of the ideal Rankine Cycle (heavy dotted lines, also shown in Figure 2) corresponding to the base case. The imposed pressures and temperatures are the same for both cycles. See the “Non-Idealities” sub-section of the section on Sub-Critical Rankine Cycle Power Plant for more details. .

0

200

400

600

0 2 4 6 8 10

Tem

pera

ture

oC

Entropy (kJ/kg-K)

Temperature Entropy Diagram for Non-Ideal Power Plant

1

23

4

5

6

7

8

9

10

11

12

13




SUPPLEMENTARY INFORMATION DOI: 10.1038/NCLIMATE2717


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Figure 5: A solar thermal power plant of the SEGS type. The only difference between this and the conventional power plant shown in Figure 1 is that instead of combustion flue gas for the heating, a heat transfer fluid (e.g. a eutectic mixture of biphenyl/diphenyl oxide) is used. The heat transfer fluid is heated in the solar field by concentrated solar radiation. The temperature-entropy diagram for this process is therefore identical Figure 2.

HP MP LP

Condensor


Boiler+ Economizer

Superheater

1 2 3

4

5

6 7

8 9

10

11 12

13

Solar Field

Heat Transfer Fluid From Solar Field

Heat Transfer Fluid To Solar Field



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