Energy. Transcritical or supercritical CO 2 cycles using both low- and high-temperature. heat sources. Y.M. Kim a, *, C.G. Kim a,d.favrat b.

Energy 43 (2012) 402e415 Contents lists available at SciVerse ScienceDirect Energy journal homepage: www.elsevier.com/locate/energy Transcritical or supercritical CO 2 cycles using both low- and high-temperature heat sources Y.M. Kim a, *, C.G. Kim a,d.favrat b a ECO Machinery Division, Korea Institute of Machinery and Materials, 171 Jang-dong, Yuseong-gu, Daejeon 305-343, Republic of Korea b Industrial Energy System Laboratory, Swiss Federal Institute of Technology of Lausanne (EPFL), Station 9, CH1015 Lausanne, Switzerland article info abstract Article history: Received 17 November 2011 Received in revised form 26 February 2012 Accepted 31 March 2012 Available online 4 May 2012 Keywords: Transcritical CO 2 Supercritical CO 2 Rankine cycle Brayton cycle Thermal energy storage (TES) Exergy In CO 2 cycles with high-temperature heat sources that are used in applications such as nuclear power, concentrated solar power, and combustion, partial condensation transcritical CO 2 (T-CO 2 ) cycles or recompression supercritical CO 2 (S-CO 2 ) cycles are considered to be promising cycles; this is because these cycles cause a reduction in the large internal irreversibility in the recuperator owing to the higher specific heat of the high-pressure side than that of the low-pressure side. However, if heat is available in the low-temperature range, the T-CO 2 Rankine cycles (or fully-cooled S-CO 2 cycles) will be more effective than the T-CO 2 Brayton cycles (or less-cooled S-CO 2 cycles) and even than the partial condensation T-CO 2 cycles (or recompression S-CO 2 cycles). This is because the compression work is reduced while achieving the same temperature rise by heat recovery through the recuperator before the high-temperature heater. The proposed T-CO 2 Rankine cycles or fully-cooled S-CO 2 cycles using both the low- and hightemperature heat sources can maximize the power output of the CO 2 power cycle with the given high-temperature heat sources. Moreover, the proposed CO 2 cycles combined with the low-temperature thermal energy storage offer the advantage of load leveling over other CO 2 cycles, with the given hightemperature heat sources. Ó 2012 Elsevier Ltd. All rights reserved. 1. Introduction Recently, interest in a supercritical CO 2 power cycle has increased in conjunction with its application in nuclear reactors owing to its simplicity, compactness, sustainability, enhanced safety, and superior economy [1e5]. The supercritical CO 2 cycle is expected to benefit fossil, renewable, and advanced nuclear power plants because CO 2 is an extremely effective working fluid in its supercritical state. In the case of CO 2 cycles with high-temperature (HT) heat sources such as nuclear power, concentrated solar power, and combustion, the working fluid goes through both subcritical and supercritical states (transcritical cycle), or is used entirely above its critical pressure (supercritical cycle). Further, the CO 2 cycles can be gas cycles (Brayton cycles) or condensation cycles (Rankine cycles). Feher [6] proposed a supercritical CO 2 (S-CO 2 ) power cycle that operates entirely above the critical pressure of CO 2, is regenerative, and ensures the compression in the liquid phase to * Corresponding author. Tel.: þ82 42 868 7377; fax: þ82 42 868 7305. E-mail addresses: ymkim@kimm.re.kr (Y.M. Kim), cgkim@kimm.re.kr (C.G. Kim), daniel.favrat@epfl.ch (D. Favrat). minimize pump work [1]. Angelino [7] conducted one of the most detailed investigations on transcritical CO 2 (T-CO 2 ) cycles and primarily focused on condensation cycles [1]. However, it was found that the T-CO 2 Rankine cycles exhibited a large internal irreversibility in the recuperator owing to heat transfer from the turbine exhaust stream with a low specific heat to the pump exit stream with a high specific heat [1]. Feher [6] first revealed the same problem associated with irreversibility in the recuperator used in the S-CO 2 cycles. A recompression cycle was proposed to avoid the problem; the recuperator was divided into low- and high-temperature parts, each having different flow rates to cope with a large variation in the heat capacity of the fluid. Thus, only a fraction of the CO 2 fluid flow is bypassed to the recompressing compressor before pre-cooling and is merged with the rest of the fluid flow, heated through the low-temperature (LT) recuperator, from the main pump (or compressor) before it enters the HT recuperator. The recompression cycle can be applied to both the S- CO 2 and the T-CO 2 cycles, and it has been studied as the most promising CO 2 cycle for HT heat conversion [1e9]. Sarkar et al. [10] studied the effects of various operating conditions and performance of components on the optimization of the S-CO 2 recompression cycle. Meanwhile, the T-CO 2 Rankine cycles (fully condensation cycles) have been mostly studied for low-grade heat 0360-5442/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2012.03.076

Y.M. Kim et al. / Energy 43 (2012) 402e415 403 Nomenclature B Brayton c p isobaric specific heat [kj/(kg K)] e specific exergy (kj/kg) E exergy (kj) _E rate of exergy (kw) ε heat exchanger effectiveness h specific enthalpy (kj/kg) H, HT high-temperature L, LT low-temperature L exergy loss (kj) _L rate of exergy loss (kw) LH both low- and high-temperature heat sources m mass (kg) _m mass flow rate (kg/s) max maximum P pressure (kpa) Q heat (kj) _Q rate of heat (kw) R Rankine R Dc p;h L ðtþ ratio of specific heat difference at T s specific entropy [kj/(kg K)] S-CO 2 supercritical CO 2 T temperature (K) T-CO 2 transcritical CO 2 TES thermal energy storage TEES thermo-electric energy storage W work (kj) _W rate of work (kw) y split ratio h h th h * th h II isentropic efficiency thermal efficiency increased thermal efficiency second law efficiency Subscripts a atmospheric (environmental) state C compressor, condenser CO 2 carbon dioxide E expander H heater H, C heat source, cooling water (heat sink) H1, H2 LT heat source, HT heat source H, L high-pressure, low-pressure i state point in inlet L cool down to lowest temperature net net output out outlet P pump R recuperator R1, R2 LT recuperator, HT recuperator s isentropic T turbine tot total W waste heat w water Supercripts þ input output conversion such as geothermal energy, waste heat, and LT solar collectors [11e19]. In the case of the T-CO 2 Rankine cycle for HT heat conversion, although the compression work is significantly reduced, the outlet temperature of CO 2 heated through the recuperator is much lower than that in the T-CO 2 Brayton cycle. This is because at temperatures below 150 C, especially below 120 C, the isobaric specific heat of CO 2 in the high-pressure side is considerably higher than that in the low-pressure side. The operation of the T-CO 2 Brayton cycle can escape from this temperature range, and therefore, the outlet temperature of CO 2 heated through the recuperator in this cycle is much higher than that in the T-CO 2 Rankine cycle. However, if heat, which is used to compensate for the difference in the specific heats of CO 2 between the two sides, is available in this LT range, the T-CO 2 Rankine cycle will be more effective than the T-CO 2 Brayton cycle and even than the recompression T-CO 2 cycle. This is because less compression work is required while obtaining the same outlet temperature of CO 2 heated through the recuperator before it enters the HT heater as observed in the T-CO 2 Brayton cycle. The concept of the T-CO 2 cycle using both the LT and the HT heat sources can also be applied to the S-CO 2 cycle. Minimizing the irreversibilities while heating up the working fluid particularly in the lower temperature is a well known challenge with respect to efficiency and specific work. As an example, the integrated solar combined cycle system (ISCCS) is a steam Rankine cycle using both low- and hightemperature heat sources to improve the cycle efficiency and system cost [20]. In this paper, for obtaining the maximum power output with the given HT heat sources, a novel concept of a T-CO 2 (or S-CO 2 ) cycle using both the LT and the HT heat sources and its applications are presented in comparison with the basic T-CO 2 Rankine and Brayton cycles and the partial condensation T-CO 2 (or recompression S-CO 2 ) cycle by energy and exergy analyses. 2. Transcritical CO 2 cycle using both low- and hightemperature heat sources (LH T-CO 2 cycle) 2.1. Energy analysis The configurations and T-s diagrams of the basic T-CO 2 Rankine and Brayton cycles studied here are shown in Figs. 1 and 2 and in Figs. 3 and 4, respectively. The following general assumptions are used in this analysis: the kinetic and potential energies as well as the heat and friction losses are negligible, isentropic efficiencies of the pump or compressor and the turbine are both 90%, effectiveness of the recuperator is 0.95, condensation temperature for CO 2 is 20 C, and saturated liquid exits the condenser. For the power range of 300e500 MWe considered in this study, the assumed isentropic efficiencies of 90% are reasonable and are based on the values of conservative turbomachinery deign [2]. In the case of the T-CO 2 Brayton cycle, saturated vapor, which is about to condense, exits the cooler. The properties of CO 2 are obtained from REFPROP-NIST [21]. The equations for the different components of the cycle are as follows. For the pump or compressor, h PðCÞ ¼ h 1;s h o h 1 h 0 ; (1) _W PðCÞ ¼ _m CO2 ðh 1 h 0 Þ: (2)

404 Y.M. Kim et al. / Energy 43 (2012) 402e415 2 1 Q R HT (T H ) Heat Source Q H Recuperator 5 3 T 4 W T Q L Heat Sink (T 0 ) Condenser Pump 0 W P Turbine Fig. 1. Schematic of T-CO 2 Rankine cycle with HT heat source. For the turbine, h T ¼ h 3 h 4 h 3;s h 4 ; (3) _W T ¼ _m CO2 ðh 3 h 4 Þ: (4) _Q C ¼ _m CO2 ðh 6 h 0 Þ (10) h th ¼ For the thermal efficiency of the cycle, _W T _ W PðCÞ _Q H : (11) The efficiency of the recuperator, ε R, is expressed as ε R ¼ _m CO 2 ðh 4 h 5 Þ _Q max ¼ _m CO 2 ðh 2 h 1 Þ _Q max : (5) The rate of maximum heat exchange, _ Q max, is given as follows: _Q max ¼ _m CO2 ðh 4 h 5 Þ assuming T 5 ¼ T 1 : (6) For the heater, _Q H ¼ _m CO2 ðh 3 h 2 Þ: (7) For the condenser or cooler, _Q W ¼ _m CO2 ðh 5 h 0 Þ: (8) The rate of heat wasted to the heat sink, _ Q W, can be split into the rate of heat to cool down, _ Q L, and the rate of heat to condense, _ Q C, as follows: _Q L ¼ _m CO2 ðh 5 h 6 Þ; (9) where state 6 is the saturated gas state. 2.2. Exergy analysis The purpose of the idea proposed in this paper is to find a novel CO 2 cycle that maximizes the power output of the CO 2 cycle with the given HT heat sources by using available LT heat sources. Exergy analysis is very helpful in understanding the advantages of the novel CO 2 cycle over other CO 2 cycles. Although increasing the maximum cycle temperature can increase the cycle efficiency, the maximum cycle temperature is assumed to be 600 C considering the cost and lifetime of materials under the high-pressure conditions of CO 2 cycles. In this study, the ideal cycle is assumed to be a Carnot cycle operating between an HT (T H ¼ 600 C) heat source and an LT (T C ¼ 15 C) heat sink with water cooling. Therefore, the maximum work from the Carnot engine can be written as W max ¼ 1 T C Q T H : (12) H This work can be assumed to be the exergy input from the HT heat source, E þ H, and the exergy losses in the components are investigated. The exergy of a CO 2 stream can be expressed as _E CO2 ¼ _m CO2 e ¼ _m CO2 ½h h a T a ðs s a ÞŠ; (13) where e, h, and s are the specific exergy, enthalpy, and entropy, respectively, and the subscript a indicates that the properties are taken at ambient temperature and pressure (T a,p a ). The ambient temperature T a is assumed to be the temperature of the heat sink, T C, and the ambient pressure P a is assumed to be the atmospheric pressure. The general exergy balance can be expressed as a rate equation [22]: _E þ _ E ¼ _ L; (14) Fig. 2. T-s diagram of T-CO 2 Rankine cycle with HT heat source. where _ E þ is the rate of exergy transfer to the system by heat, work, and mass; _ E is the rate of exergy transfer from the system; and _ L is the rate of exergy loss.

Y.M. Kim et al. / Energy 43 (2012) 402e415 405 Fig. 3. Schematic of T-CO 2 Brayton cycle with HT heat source. The exergy loss of compression (pumping) is given by _L CðPÞ ¼ E _ þ CðPÞ _m CO 2 ðe 1 e 0 Þ: (15) The exergy loss of the turbine is given by _L T ¼ _m CO2 ðe 3 e 4 Þ E _ T : (16) The exergy loss of the recuperator is given by _L R ¼ _m CO2 ðe 4 e 5 Þ _m CO2 ðe 2 e 1 Þ: (17) The exergy loss of the heater is given by _L H ¼ _ E þ H _m CO 2 ðe 3 e 2 Þ: (18) The exergy loss of waste heat to the condenser or cooler is given as _L W ¼ _m CO2 ðe 5 e 0 Þ: (19) The second law (exergy) efficiency of the overall system with transcritical or supercritical cycles can be defined as Fig. 6. Reference cycle of T-CO 2 Brayton cycle with HT heat source. Fig. 4. T-s diagram of T-CO 2 Brayton cycle with HT heat source. Fig. 5. Reference cycle of T-CO 2 Rankine cycle with HT heat source. Fig. 7. Isobaric specific heats of CO 2 in high- and low-pressure sides over temperature range of heat recovery.

406 Y.M. Kim et al. / Energy 43 (2012) 402e415 Table 1 Exergy analysis of transcritical CO 2 Rankine cycle with HT heat source. State (i) T ( C) P (bar) e i e 0 Q(E), W (kj/kg) L (kj/kg) (kj/kg) 0 20.0 57.3 0.0 QW ¼ 222.7 (E W ¼ 7.0) L W ¼ 7.0 (7.0%) 1 39.2 200.0 17.6 W þ P ¼ 19.4 (Eþ P ¼ 19.4) L P ¼ 1.8 (1.8%) 2 297.5 200.0 180.7 Q þ R ¼ 449.0 (Eþ R ¼ 163.1) L R ¼ 25.2 (25.3%) 3 600.0 200.0 372.8 Q þ H ¼ 373.1 (Eþ H ¼ 245.0) L H ¼ 57.9 (58.2%) 4 449.0 57.3 195.3 WT ¼ 169.9 (E T ¼ 169.9) L T ¼ 7.6 (7.6%) 5 54.3 57.3 7.0 QR ¼ 449.0 (E R ¼ 188.3) (L R ¼ 25.2) h II ¼ E T Eþ P E þ H ¼ 0.614 E þ H ¼ 245.0 L tot ¼ 99.5 (100%) Table 2 Exergy analysis of transcritical CO 2 Brayton cycle with HT heat source. State (i) T ( C) P (bar) e i e 0 Q(E), W(E) (kj/kg) L (kj/kg) (kj/kg) 0 20.0 57.3 0.0 QW ¼ 164.2 (E W ¼ 23.6) L W ¼ 23.6 (33.4%) 1 114.6 200.0 46.7 W þ C ¼ 50.4 (Eþ C ¼ 50.4) L C ¼ 3.8 (5.4%) 2 370.0 200.0 195.2 Q þ R ¼ 355.5 (Eþ R ¼ 148.5) L R ¼ 20.6 (29.2%) 3 600.0 200.0 370.2 Q þ H ¼ 283.6 (Eþ H ¼ 190.0) L H ¼ 15.0 (21.2%) 4 449.0 57.3 192.7 WT ¼ 169.9 (E T ¼ 169.9) L T ¼ 7.6 (10.8%) 5 131.1 57.3 23.6 QR ¼ 355.5 (E R ¼ 169.1) (L R ¼ 20.6) h II ¼ E T Eþ C E þ H _E T h II ¼ E _ þ CðPÞ : (20) _E þ H ¼ 0.629 E þ H ¼ 190.0 L tot ¼ 70.6 (100%) 2.3. Comparison between T-CO 2 Rankine cycle and T-CO 2 Brayton cycle To compare the basic two cycles (i.e., the T-CO 2 Rankine and Brayton cycles), we assume the following conditions: high-pressure of 200 bar, low-pressure of 57.3 bar (condensation temperature 20 C), and turbine inlet temperature of 600 C. These conditions are similar to those in other literature that discuss the use of S-CO 2 cycles for next-generation nuclear reactors [1e3]. Figs. 5 and 6 show the energy flow per unit mass of the working fluid on temperature versus entropy (T-s) diagrams of the T-CO 2 Rankine and Brayton cycles, respectively. The exergy analyses of the Fig. 9. Reference cycle of LH T-CO 2 cycle using both LT and HT heat sources. T-CO 2 Rankine and Brayton cycles, expressed on unit mass basis, are summarized in Tables 1 and 2, respectively. The efficiency of the T-CO 2 Rankine cycle is lower than that of the T-CO 2 Brayton cycle. Although the compression work of the T-CO 2 Rankine cycle is significantly reduced, the outlet temperature of CO 2 heated through the recuperator in this cycle is much lower than that of the T-CO 2 Brayton cycle. This is because below 150 C and especially below 120 C, the isobaric specific heat, c p,ofco 2 in the high-pressure side is much higher than that in the low-pressure side, as shown in Fig. 7. The operation of T-CO 2 Brayton cycle can escape from this temperature range, and therefore, the outlet temperature of CO 2 heated through the recuperator is much higher in the T-CO 2 Brayton cycle than in the T-CO 2 Rankine cycle. The accumulated difference in the isobaric specific heat between the high-pressure side (c p,h ) and the low-pressure side (c p,l ) below a temperature T that is over the temperature range for heat recovery in the T-CO 2 Rankine cycle (from T 1 to T 4 ) can be defined as Z T cp;h c p;l dt R Dc p;h L ðtþh T1 Z T4 T1 cp;h c p;l dt : (21) LT (T H1 ) Heat Source Q H1 3 2 1 Q R2 Q R1 HT (T H2 ) Heat Source HT Recuperator 6 LT Recuperator Q H2 4 5 Q L +Q C Heat Sink (T 0 ) T 0 W T Condenser Pump W P Turbine Fig. 8. Schematic of LH T-CO 2 cycle using both LT and HT heat sources.

Y.M. Kim et al. / Energy 43 (2012) 402e415 407 Table 3 Comparison of performances of different T-CO 2 cycles (H: High-temperature of T H2, L: Low-temperature of T H1, R: Rankine, B: Brayton). Cycle T H1 ( C) Q H1 (kj/kg) T H2 ( C) Q H2 (kj/kg) T R ( C) W P(C) (kj/kg) W T (kj/kg) W net (kj/kg) h th h * th H-R (1) e e 600 373.1 298 19.4 169.9 150.4 0.403 e H-B (2) e e 600 283.6 370 50.4 169.9 119.4 0.421 e L-R (3) 112 178.0 e e e 19.4 40.9 21.4 0.120 e LH-R (4) 112 87.0 600 286.1 368 19.4 169.9 150.4 0.403 0.526 L-R (3) þ H-B (2) 112 87.0 600 286.1 370 9.5 þ 50.9 20.0 þ 171.3 10.5 þ 120.5 0.351 e m = w 0.310 m w mco2 LT (T H1 ) Heat Source T w,in = 117.0 T w,in T w,out T w,out = 50.1 P H T 2 = 112.2 2 ΔT H1 ΔT R1 Q H1 Q R1 T 1 = 39.2 1 P L 6 T 6 = 128.8 LT Recuperator 7 T 7 = 54.3 Fig. 10. Mass flow rate and inlet/outlet temperature of hot water required in LT recuperator. As shown in Fig. 7, R Dc p;h L ðtþ is approximately 0.5 at 112 C and approximately 0.68 at 150 C. This indicates that the outlet temperature of CO 2 heated through the recuperator is low owing to the large difference in the specific heat between the high- and lowpressure sides in this LT range. The exergy analyses of both cycles, expressed on a unit mass basis, are summarized in Tables 1 and 2. The exergy loss of the heater, L H, is larger in the T-CO 2 Rankine cycle than in the T-CO 2 Brayton cycle because of the lower temperature, T R (T 2 ), through the recuperator on the high-pressure side. On the other hand, the exergy loss of waste heat, L W, is larger in the T-CO 2 Brayton cycle than in the T-CO 2 Rankine cycle because of the higher temperature, T 5, through the recuperator on the low-pressure side. The overall exergy efficiency of the T-CO 2 Brayton cycle is higher than that of the T-CO 2 Rankine cycle. T R ( o C) 460 440 420 400 380 360 340 320 300 280 0.85 0.80 0.75 0.70 T R η * th 0.65 0.60 0.55 0.50 0.45 0.40 0.35 50 100 150 200 250 300 350 400 450 Temperature of LT heat source (T H1 ( o C)) η th * 1.6 1.5 ΔC ( T) C ( P, T) C ( P, T + ΔT ) p p H p L Fig. 12. Temperature T R and thermal efficiency h * according to temperature of LT heat th source (T H1 ). Isobaric specific heat (kj/kg-k) 1.4 1.3 1.2 1.1 1.0 0.9 ΔC p S- S+ 0.8 40 50 60 70 80 90 100 110 Temperature ( o C) Fig. 11. Isobaric specific heat of LT heat source required to make up for difference in isobaric specific heats between two CO 2 streams. Fig. 13. Reference cycle of T-CO 2 cycle with LT heat source.

408 Y.M. Kim et al. / Energy 43 (2012) 402e415 Table 4 Exergy analysis of transcritical CO 2 cycle using both LT and HT heat sources. State (i) T ( C) P (bar) e i e 0 (kj/kg) Q(E), W(E) (kj/kg) L (kj/kg) 0 20.0 57.3 0.0 QW ¼ 222.7 (E W ¼ 7.0) L W ¼ 7.0 (12.1%) 1 39.2 200.0 17.6 W þ P ¼ 19.4 (Eþ P ¼ 19.4) L P ¼ 1.8 (3.1%) L ¼ 4.8 (8.3%) 2 112.2 200.0 48.0 Q þ R1 ¼ 91.0 (Eþ R1 ¼ 18.6) Q þ H1 ¼ 87.0 (Eþ H1 ¼ 16.6) 3 368.0 200.0 196.4 Q þ R2 ¼ 358.1 (Eþ R ¼ 148.4) L R2 ¼ 21.4 (37.0%) 4 600.0 200.0 372.8 Q þ H2 ¼ 286.1 (Eþ H2 ¼ 191.7) L H2 ¼ 15.3 (26.4%) 5 449.0 57.3 195.3 WT ¼ 169.9 (E T ¼ 169.9) L T ¼ 7.6 (13.1%) 6 128.8 57.3 25.5 QR2 ¼ 358.1 (E R ¼ 169.8) (L R2 ¼ 21.4) 7 54.3 57.3 7.0 QR1 ¼ 91.0 (E R ¼ 18.6) (L R1 ¼ 3.5) h II ¼ E T Eþ E þ P H1 E þ H1 þ ¼ 0.723 L tot ¼ 57.9 (100%) Eþ E þ H2 H2 ¼ 191.7 the LT range. Therefore, the thermal efficiency of the T-CO 2 Rankine cycle is lower than that of the T-CO 2 Brayton cycle. However, if heat is available from other heat sources in this LT range, it is possible to make up for the difference in the isobaric specific heat of CO 2 between the high- and low-pressure sides and rectify this imbalance in specific heats. Therefore, a T-CO 2 cycle using both the LT and the HT heat sources (named an LH T-CO 2 cycle) is proposed. The configuration of the LH T-CO 2 cycle system is shown in Fig. 8. The recuperator is divided into two parts: a lowtemperature (LT) recuperator and a high-temperature (HT) recuperator. In the LT recuperator, the supplemental heat is supplied by an LT (T H1 ) heat source. Fig. 9 shows the energy flow per unit mass of the working fluid on the T-s diagram of the system for the previous T-CO 2 Rankine cycle with an additional LT heat source to heat CO 2 up to 112 C. Table 3 compares the performances, expressed on a unit mass basis, of different CO 2 cycles. Hot water is used as an example of an LT heat source, and the mass flow rate and inlet/outlet temperature of the hot water are shown in Fig. 10. The mass flow rate and inlet/outlet temperature of hot water required in the LT recuperator can be calculated from the thermal match of three flows as follows. As shown in Fig. 11, Dc p ðtþ is the isobaric specific heat of an LT heat source required to make up for the difference in the isobaric specific heats between the high-pressure (P H ) side and the low-pressure (P L ) side. Considering the temperature difference, DT, for the heat transfer from the low-pressure side to the high-pressure side, Dc p (T) can be defined as Dc p ðtþhc p ðp H ; TÞ c p ðp L ; T þ DTÞ: (22) Fig. 14. Schematic of partial pre-cooling S-CO 2 cycle. 2.4. T-CO 2 cycle using both low- and high-temperature heat sources As mentioned before, in the case of the T-CO 2 Rankine cycle with HT heat sources, although the compression work and exergy loss of waste heat are significantly reduced, the outlet temperature of CO 2 heated through the recuperator is much lower than that of the T-CO 2 Brayton cycle owing to the large difference in the isobaric specific heat of CO 2 between the high- and low-pressure sides in Because the isobaric specific heat of water as an LT heat source is almost constant, the average isobaric specific heat, Dc p ðtþ, to make up for Dc p (T) over the temperature range of the LT recuperator can be obtained as shown in Fig. 11, where the area marked Sþ is equal to the area marked S. The mass flow rate of hot water can be calculated from the obtained Dc p ðtþ as _m w ~c p;w ¼ _m CO2 Dc p ; (23) where _m w and ~ C p;w are the mass flow rate and average isobaric specific heat of water flowing through the LT recuperator, respectively. Fig. 15. Schematic of LH T-CO 2 cycle combined with T-CO 2 Brayton cycle and TES, T-CO 2 Brayton mode (night).

Y.M. Kim et al. / Energy 43 (2012) 402e415 409 Fig. 16. Schematic of LH T-CO 2 cycle combined with T-CO 2 Brayton cycle and TES, LH T-CO 2 mode (day). If the minimum temperature difference for heat transfer from the hot water to the side with CO 2 at high-pressure is assumed to 5 C, the outlet temperature of water can be calculated from a heat balance equation as _Q H1 ¼ _m w ~c p;w Tw;in T w;out ; (24) h th ¼ h * th ¼ _ W T _ W P _Q H1 þ _ Q H2 ; (25) _ W T _ W P _Q H2 : (26) where T w,in and T w,out are the inlet and outlet temperatures of water flowing through the LT recuperator, respectively. With additional heat, Q H1 ¼ 87.0 kj/kg, provided by the LT heat source, the temperature after the HT recuperator, T R, can be increased significantly, and therefore, it is possible to reduce the heat input, Q H2, from the HT (T H2 ) heat source in the T-CO 2 Rankine cycle. As compared to the previous T-CO 2 Rankine cycle, the LH T- CO 2 cycle can achieve the same thermal efficiency using 23.3% of the total heat input from the LT heat source, not from the HT heat source. In order to compare the LH T-CO 2 cycle with other CO 2 cycles, two different thermal efficiencies are defined: Isobaric specific heat (kj/kg-k) 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 2 c ( P 57.3 bar) p L = c ( P 200 bar) p H = c ( P 57.3 bar) p L = h th represents general thermal efficiency; however, h * th represents the increased thermal efficiency with the given heat input from the HT heat source by using the heat available from the LT heat source. As compared to the previous T-CO 2 Brayton cycle with the same heat input Q H2 from the HT heat source, the LH T-CO 2 cycle can produce approximately 25% more power by reducing the compression work and achieve an increased thermal efficiency of h * ¼ 0:526. Fig. 12 shows the temperature after the HT recuperator, T R, and the increased efficiency, h *, as functions of the th th temperature (T H1 ) of the LT heat source. It can be seen that the LT heat source below 150 C aids in increasing T R and h * th of the T-CO 2 Rankine cycle with the given heat input Q H2 from the HT heat source, despite the low-grade of the heat source. The LH T-CO 2 cycle operates synergistically with the sum of the two separate cycles (i.e., a T-CO 2 Rankine cycle with the LT (T H1 ) heat source, as shown in Fig. 13, and a T-CO 2 Brayton cycle with the HT (T H2 ) heat source, as shown in Fig. 6). The LH T-CO 2 cycle can eliminate both exergy losses from the turbine in the LT cycle and 0.0 40 50 60 70 80 90 100 110 120 Temperature ( o C) Fig. 17. Thermal match over low-temperature range in LH T-CO 2 cycle combined with T-CO 2 Brayton cycle and TES. Fig. 18. Reference cycle of partial condensation T-CO 2 cycle.

410 Y.M. Kim et al. / Energy 43 (2012) 402e415 Fig. 19. Reference cycle of fully-cooled S-CO 2 cycle. the compressor in the HT cycle by combining them; moreover, the LH T-CO 2 cycle can utilize the waste heat from the HT cycle for the LT cycle. As shown in Table 3, the LH T-CO 2 cycle can produce approximately 15% more power than the sum of the separate two cycles with the same heat inputs by these synergistic effects. The exergy analysis of the LH T-CO 2 cycle, expressed on a unit mass basis, is summarized in Table 4. The exergy loss of the heater, which is the main exergy loss in the previous T-CO 2 Rankine cycle, is reduced in the LH T-CO 2 cycle and the exergy loss of the waste heat, which is the main exergy loss in the previous T-CO 2 Brayton cycle, is also reduced in the LH T-CO 2 cycle. The LH T-CO 2 cycle has an exergy efficiency of 72%, approximately over 10% higher than those of the T-CO 2 Rankine and Brayton cycles. Chen et al. studied transcritical Rankine cycles using CO 2 and R32 as the working fluids for converting low-grade heat to power [11] and found that the exergy efficiencies of these cycles are in the range of 50%w60% at the cycle high-temperature of 160 C. In their analysis, the isentropic efficiencies of the compressor and turbine were fixed at 85% and the condensation temperature for the working fluids was fixed at 24 C. Zhao et al. [23] investigated the multiple reheat helium Brayton cycles for sodium-cooled fast reactors. In their analysis, the isentropic efficiencies of the compressor and turbine were fixed at 88% and 93%, respectively, and the effectiveness of the recuperator was fixed at 0.95. At turbine inlet temperature of 600 C and compressor inlet temperature of 20 C, the thermal efficiency of the cycle with three expansion stages and six compression stages was approximately 47%, which is equivalent to an exergy efficiency of 71% in this study. The exergy efficiency of 72% of the proposed LH T-CO 2 cycle in this study is a significant achievement considering the simplicity of the cycle. Fig. 21. Reference cycle of recompression S-CO 2 cycle. 3. Applications of LH T-CO 2 cycle 3.1. Nuclear power plant As mentioned previously, interest in the S-CO 2 cycle has recently been revived in conjunction with its application to Generation IV nuclear reactors at the Massachusetts Institute of Technology (MIT) and the Tokyo Institute of Technology (TIT) [1e5]. At the TIT, a partial pre-cooling (or a partial condensation) T-CO 2 cycle was Isobaric specific heat (kj/kg-k) 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 1.7 c ( P 77bar) p L = c ( P 200bar) p H = c ( P 77 bar) p L = 0.0 60 70 80 90 100 110 120 130 140 150 Temperature ( o C) Fig. 22. Thermal match over low-temperature range in recompression S-CO 2 cycle. Fig. 20. Reference cycle of less-cooled S-CO 2 cycle. Fig. 23. Reference cycle of LH S-CO 2 cycle using both LT and HT heat sources.

Y.M. Kim et al. / Energy 43 (2012) 402e415 411 studied to eliminate the temperature mismatch in the CO 2 cycles between the high- and low-pressure sides. As shown in Fig. 14 [1e5], if the CO 2 flow is bypassed to the compressor before precooling, this temperature mismatch will be avoided. However, the bypassed flow reduces the heat rejected to the cooling water through the pre-cooler and increases the required compressor work. Despite the opposing effect on the cycle efficiency owing to the bypassed flow of CO 2, the cycle efficiency is enhanced by approximately 4% at 800 C [1]. The MIT is developing the recompression S-CO 2 cycle recommended by Feher [6]. However, the condensation of CO 2 was eliminated, and the pump was replaced by a compressor because condensing CO 2 cycles require year-round supply of very cold cooling water (10e15 C), which is not available in all regions worldwide [1]. The LH T-CO 2 cycle can also be used to avoid the temperature mismatch in the CO 2 cycles and improve the cycle efficiency with Fig. 24. Schematic of thermo-electric energy storage (TEES) system with transcritical CO 2 cycles, charging (top) and discharging (bottom) modes.

412 Y.M. Kim et al. / Energy 43 (2012) 402e415 Fig. 25. Reference cycle of TEES system with transcritical CO 2 cycles. the given heat input from the nuclear reactor. If heat is available from the LT heat source below 120 C, then our results, which were discussed previously, suggest that the cycle efficiency can be enhanced by slightly over 10% at 600 C from the basic T-CO 2 Rankine and Brayton cycles. However, if no heat is available from the LT heat source, the LH T-CO 2 cycle combined with the T-CO 2 Brayton cycle and an LT thermal energy storage (TES) can be used. A schematic of the cycle is shown in Fig. 15 (night) and Fig. 16 (day). During the night, when the demand for electricity is low, the system is operated as the T-CO 2 Brayton cycle (Fig. 6) and the waste heat (Q L ) is stored in the LT TES using the water flowing from the cold tank to the hot tank. During the day, when the demand for electricity is high, the system is operated as the LH T-CO 2 cycle (Fig. 9) and the supplemental heat needed in the LT range (Q H1 )is supplied by the LT TES using the water flowing from the hot tank to the cold tank. The amount of waste heat (Q L ) from the T-CO 2 Brayton cycle is larger than the supplemental heat needed in the LT range (Q H1 ) for the LH T-CO 2 cycle. Moreover, as shown in Fig. 17, Fig. 26. Schematic of TEES LH T-CO 2 cycles, charging mode (top) and discharging and generation mode (bottom).

Y.M. Kim et al. / Energy 43 (2012) 402e415 413 twice (current þ stored) the isobaric specific heat of CO 2 in the lowpressure side is well matched to that in the high-pressure, and given the unused waste heat from the HT recuperator, it is possible to supply Q H1 for the LH T-CO 2 cycle by using Q L stored from the previous T-CO 2 Brayton cycle. As shown in our previous results, during the day with high demand for electricity, the LH T-CO 2 cycle can produce approximately 25% more power than during the night by reducing the compression work and by enhancing the cycle efficiency from 42.1% to 52.6% at 600 C with the same heat input from the nuclear reactor. The thermal energy storage used is very similar to that of a new type of thermo-electric energy storage (TEES) system with transcritical CO 2 cycles using hot water storage, recently proposed by the ABB Corporate Research Center [19]. Water tanks (289MWt, thermal energy storage) similar to that of the 50 MWe TEES system are needed for the nuclear power plant operating from 400 MWe (night) to 500 MWe (day) using the proposed LH T-CO 2 cycle. As shown in Fig. 18, the partial condensation T-CO 2 cycle in a study at the TIT is similar to a compound cycle of the T-CO 2 Rankine and Brayton cycles in this study. The configuration of the system is similar to that of the previously combined LH T-CO 2 cycle as shown in Figs. 15 and 16; however, no thermal energy is stored, and half a fraction of the fluid flow is bypassed to the compressor before it enters the condenser. If the mass flow in the high-pressure side is half of that in the low-pressure side in the LT recuperator, the temperature mismatch problem in the LT recuperator can be avoided in the same way as shown in Fig. 17. As shown in Fig. 18, the compression work and the power output of the partial condensation T-CO 2 cycle are the mean values of those in the T-CO 2 Brayton cycle (night) and the LH T-CO 2 cycle with LT TES (day), indicating a nuclear power plant with a constant power output of 450 MWe. However, the proposed LH T-CO 2 cycle combined with the T-CO 2 Brayton cycle and the LT TES offers the advantage of load leveling from 400 MWe to 500 MWe by regulating the split ratio for the bypass CO 2 flow and the direction and the quantity of water flow of the LT TES. Traditionally, reactor power control has been used in base-load operating conditions. With the increasing share of power plant, it seems that the load-follow operating of nuclear reactors will be inevitable in the future. But, it is hard to get the satisfying performance with classic control strategy to control nuclear reactor power [24,25]. The concept of the LH T-CO 2 cycle can also be applied to the S- CO 2 cycle. The turbine inlet temperature and pressure in the S-CO 2 cycle are maintained constant (600 C and 200 bar); however, the compressor inlet temperature and pressure are slightly higher than those in the T-CO 2 cycle (32 C and 77 bar), which is very close to the optimal recompression S-CO 2 cycle in other literature [1e3]. Similar to the previous LH T-CO 2 cycle, two S-CO 2 cyclesdfullycooled and less-cooled S-CO 2 cycles e can be considered as shown in Figs. 19 and Fig. 20, respectively. The recompression S-CO 2 cycle is similar to a compound cycle of the two S-CO 2 cycles, as shown in Fig. 21. If 41% of the fluid flow at point 0A is bypassed to the compressor before the final cooler (0A-0B), temperature mismatch in the LT recuperator can be avoided in the same way, as that shown in Fig. 22, and the cycle efficiency can be increased up to 46.4% from the two basic S-CO 2 cycles. The present numerical model was verified using the same data and operating conditions as those used by Dostal [2]; these conditions are as follows: maximum cycle temperature of 550 C, maximum cycle pressure of 200 bar, pressure ratio of 2.6, recompressed mass flow ratio of 0.41, ε R of 96.3%, and turbine and compressor isentropic efficiencies of 90% and 89%, respectively. The calculated cycle efficiency (45.8%) is slightly higher than that of the reference case (45.3%), considering the assumption of zero pressure drop in the primary system in this study. Fig. 27. Reference cycle of TEES LH T-CO 2 cycle, discharging and generation mode. On the other way, the LH S-CO 2 cycle combined with the LT TES can be used. The system is operated as a less-cooled S-CO 2 cycle (Fig. 20), and the waste heat (Q L ) is stored in the LT TES using the water flowing from the cold tank to the hot tank. During the day, when the demand for electricity is high, the system is operated as Heat (kj/kg) Work (kj/kg) 300 250 200 150 100 50 0 220 200 180 160 140 120 100 80 60 40 20 0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 W net W T W E W P Split Ratio (y) Q H1 Q H2 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Split Ratio (y) Fig. 28. Heat input (top) and work input/output (bottom) as a function of split ratio y in TEES LH T-CO 2 cycle.

414 Y.M. Kim et al. / Energy 43 (2012) 402e415 Table 5 Comparison of performances of different T-CO 2 cycles with TEES (H: High-temperature of T H2, L: Low-temperature of T H1, R: Rankine, B: Brayton). Cycle T H1 ( C) Q H1 (kj/kg) T H2 ( C) Q H2 (kj/kg) T R ( C) W P(C) (kj/kg) W T (kj/kg) W net (kj/kg) h th h * th H-R (1) e e 600 456.8 225 14.7 201.5 186.8 0.409 e H-B (2) e e 600 292.6 360 72.8 201.5 128.7 0.440 e L-R (3) 122 281.7 e e e 14.7 59.0 44.3 0.157 e LH-R (4) 122 161.1 600 295.7 357 14.7 201.5 186.8 0.409 0.632 L-R (3) þ H-B (2) 122 161.1 600 295.7 360 8.4 þ 73.6 33.7 þ 203.7 25.3 þ 130.1 0.340 e an LH S-CO 2 cycle (Fig. 23) and the supplemental heat needed in the LT range (Q H1 ) is supplied by the LT TES using the water flowing from the hot tank to the cold tank. As shown in Fig. 22, 1.7 times (current þ stored) the isobaric specific heat of CO 2 in the lowpressure side is well matched to that in the high-pressure side. For thermal matching, the system is operated as a less-cooled S-CO 2 cycle (Fig. 20) for 10 h and an LH S-CO 2 cycle (Fig. 23) for 14 h. During the day, when there is a high demand for electricity, the LH S-CO 2 cycle can produce approximately 40% more power than during the night by reducing the compression work and enhancing the cycle efficiency from 37.6% to 52.5% at 600 C with the same heat input from the nuclear reactor. The proposed LH S-CO 2 cycle combined with the LT TES offers the advantages of load leveling from 358 MWe to 500 MWe with the constant nuclear reactor by regulating the split ratio for the bypass CO 2 flow and the direction and the quantity of water flow of the LT TES. 3.2. Hybrid system of LH transcritical CO 2 cycle combined with TEES As mentioned before, a new type of TEES system with reversible T-CO 2 cycles was recently proposed by the ABB Corporate Research Center [19]. The system layout is shown in Fig. 24, and the energy flow per unit mass of working fluid on T-s diagram of the base reference (reversible) cycle is shown in Fig. 25. The concept is based on heat pump and heat engine (reverse cycle) technologies utilizing T-CO 2 cycles, storage of pumped heat in hot water, and ice generation and melting at the cold end of the cycles. Figs. 24 and 25 are based on the preferred realization of the transcritical cycle with CO 2 as the working fluid and hot water and ice as the storage materials. Liquid water has a very high heat capacity, which provides a high energy density for energy storage. The potential advantages of using ice for energy storage are increased site-independence with minimum interaction with the ambient, reduction of back-work, and an increased temperature potential and therefore an increased storage utilization factor [19]. TEES systems with transcritical CO 2 cycles can be used as a hybrid system combined with an LH T-CO 2 cycle (we refer to this as an LH T-CO 2 cycle with TEES). The schematic and reference cycle of this system are shown in Figs. 26 and 27, respectively. The charging mode of the system is the same as the TEES system. However, in the discharging mode of the system, the high-pressure CO 2 gas heated by the LT source (thermal energy storage) is divided by two parts by a split ratio y, which is controlled according to the demand for electricity. One portion, y, of the CO 2 gas is sent to the HT heater and the other portion, 1 y, is sent to the LT expander. The expanded hot CO 2 gas from the HT turbine transfers its heat to the compressed CO 2 gas through the HT recuperator, where it is cooled down and combined with the expanded CO 2 gas from the LT expander. The combined, expanded CO 2 gas transfers its heat to the compressed CO 2 gas through the LT recuperator. Fig. 28 shows the heat input and the work input/output according to the split ratio, expressed on a unit mass basis. Table 5 compares the performances, expressed on a unit mass basis, of different CO 2 cycles based on the reference cycle in Fig. 27 to show the synergistic effects of the hybrid system that combines the TEES system with the LH T-CO 2 cycle. During the day with high demand for electricity, in comparison with the T-CO 2 Brayton cycle, the LH T-CO 2 cycle can produce approximately 45% more power by reducing the compression work and improve the cycle efficiency, h * th, by approximately 19% at 600 C with the same heat input from the HT heat source. 4. Conclusions In this paper, a novel transcritical CO 2 Rankine cycle using both the LT and the HT heat sources (LH T-CO 2 cycle) is proposed to maximize the power output of the CO 2 power cycle with the given HT heat sources for use in applications such as nuclear power, concentrated solar power, and combustion. Although the compression work and exergy loss of waste heat are significantly reduced in the T-CO 2 Rankine cycle with HT heat sources as compared to the T-CO 2 Brayton cycle, the outlet temperature of CO 2 heated through the recuperator is considerably lower than that in the T-CO 2 Brayton cycle. Therefore, the thermal efficiency of the T- CO 2 Rankine cycle is lower than that of the T-CO 2 Brayton cycle. This is because below 150 C, particularly below 120 C, the isobaric specific heat of CO 2 in the high-pressure side is considerably higher than that in the low-pressure side. However, if heat is available in this LT range to compensate for the difference in the specific heat of CO 2 between the high- and the low-pressure sides, the T-CO 2 Rankine cycle will be more effective than the T-CO 2 Brayton cycle. Further, the T-CO 2 is more effective than the partial condensation T- CO 2 cycle, which is a compound cycle of the T-CO 2 Rankine and Brayton cycles, because low compression work is required while obtaining the same outlet temperature of CO 2 heated through the recuperator before it enters the HT heater. As compared to the T-CO 2 Brayton cycle with an HT heat source, the proposed LH T-CO 2 cycle can produce approximately 25% more power by reducing the compression work and enhancing the cycle efficiency by approximately 10% at 600 C with the same heat input from the HT heat source by utilizing an LT heat source. The exergy efficiency of the LH T-CO 2 cycle using both the LT and the HT heat sources is approximately 10% higher than that of the T-CO 2 Brayton cycle with an HT heat source. For the application of this novel concept to nuclear power plants, during the night, when the demand for electricity is low, the system is operated as a T-CO 2 Brayton cycle, and the waste heat is stored in an LT TES. Further, during the day, when the demand for electricity is high, the system is operated as an LH T-CO 2 cycle using the LT TES. During the day, the LH T-CO 2 cycle can produce approximately 25% more power than during the night by reducing the compression work and enhancing the cycle efficiency from 42.1% to 52.6% at 600 C with the same heat input from the nuclear reactor. The proposed LH T-CO 2 cycle combined with the T-CO 2 Brayton cycle and LT TES offers the advantage of load leveling from 400 MWe to 500 MWe over the partial condensation T-CO 2 cycle with a constant power output of 450 MWe. The concept of the LH T- CO 2 cycle can also be applied to the S-CO 2 cycle, and the LH S-CO 2 cycle combined with the LT TES offers the advantage of load leveling from 358 MWe for 10 h to 500 MWe for 14 h over the

Y.M. Kim et al. / Energy 43 (2012) 402e415 415 recompression S-CO 2 cycle with a constant power output of 442 MWe. Moreover, a new type of thermo-electric energy storage (TEES) system with reversible transcritical CO 2 cycles can be used as a hybrid system combined with the LH T-CO 2 cycle. References [1] Hejzlar P, Dostal V, Driscoll MJ, Dumaz P, Poullennec G, Alpy N. Assessment of gas cooled fast reactor with indirect supercritical CO 2 cycle. Nuclear Engineering and Technology 2006;38:109e18. [2] Dostal V. A supercritical carbon dioxide cycle for next-generation nuclear reactors. Ph.D. thesis, Department of Nuclear Engineering, MIT, USA; 2004. [3] Dostal V, Hejzlar P, Driscoll MJ. The supercritical carbon dioxide power cycle: comparison to other advanced power cycles. Nuclear Technology 2006;154: 283e301. [4] Sarkar J. Second law analysis of supercritical CO 2 recompression Brayton cycle. Energy 2009;34:1172e8. [5] Kato Y, Nitawaki T, Muto Y. Medium temperature carbon dioxide gas turbine reactor. Nuclear Engineering and Design 2004;230:195e207. [6] Feher EG. The supercritical thermodynamic power cycle. Energy Conversion 1968;8:85e90. [7] Angelino G. Carbon dioxide condensation cycles for power production; 1968 [ASME paper no. 68-CT-23]. [8] Jeong WS, Lee JI, Jeong YH. Potential improvements of supercritical recompression CO 2 Brayton cycle by mixing other gases for power conversion system of a SFR. Nuclear Engineering and Design 2011;241:2128e37. [9] Kulhanek M, Dostal V. Supercritical carbon dioxide cycles thermodynamic analysis and comparison. In: Student s Conference 2009 at Faculty of Mechanical Engineering of Czech Technical University; Prague, Czech. [10] Sarkar J, Bhattacharyya. Optimization of recompression S-CO 2 power cycle with reheating. Energy Conversion and Management 2009;50:1939e45. [11] Chen H, Goswami DY, Rahman MM, Stefanakos EK. Energetic and exergetic analysis of CO 2 - and R32-based transcritical Rankine cycles for low-grade heat conversion. Applied Energy 2011;88:2802e8. [12] Li X, Zhang X. Component exergy analysis of solar powered transcritical CO 2 Rankine cycle system. Journal of Thermal Science 2011;20:195e200. [13] Galanis N, Cayer E, Roy P, Denis ES, Desilets M. Electricity generation from low temperature sources. Journal of Applied Fluid Mechanics 2009;2:55e67. [14] Cayer E, Galanis N, Desilets M, Nesreddine H, Roy P. Analysis of a carbon dioxide transcritical power cycle using a low temperature source. Applied Energy 2009;86:1055e63. [15] Yamaguchi H, Zhang XR, Fujima K, Sawada N. Solar energy powered Rankine cycle using supercritical CO 2. Applied Thermal Engineering 2006;26:2345e54. [16] Chen Y. Novel cycles using carbon dioxide as working fluid. Licentiate thesis, School of Industrial Engineering and Management, KTH, Sweden; 2006. [17] Chen Y, Lundqvist P, Johansson A, Platell P. A comparative study of the carbon dioxide transcritical power cycle compared with an organic Rankine cycle with R123 as working fluid in waste heat recovery. Applied Thermal Engineering 2006;26:2142e7. [18] Zhang S, Wang H, Guo T. Performance comparison and parametric optimization of subcritical Organic Rankine Cycle (ORC) and transcritical power cycle system for low-temperature geothermal power generation. Applied Energy 2011;88:2740e54. [19] Mercangoez M, Hemrle J, Kaufmann L, Buchter F, Ohler C. Thermoelectric energy storage with transcritical CO 2 cycles. In: ECOS 2011: Proceedings of the 23rd International Conference on Efficiency, Cost, Optimization, Simulation, and Environmental Impact of Energy Systems; 2011 Jul 4e7; Novi Sad, Serbia. [20] Baghernejad A, Yaghoubi M. Exergy analysis of an integrated solar combined cycle system. Renewable Energy 2010;35:2157e64. [21] Lemmon EW, Mclinden MO, Huber ML. Reference fluid thermodynamic and transport properties (REFPROP). NIST standard reference database 23, version 7.0; 2002. [22] Borel L, Favrat D. Thermodynamics and energy systems analysis. Lausanne: Presses Poly-techniques Universitaires Romandes; 2010. 399e490. [23] Zhao H, Peterson PF. Multiple reheat helium Brayton cycles for sodium cooled fast reactors. Nuclear Engineering and Design 2008;238:1535e46. [24] Liu C, Peng JF, Zhao FY, Li C. Design and optimization of fuzzy-pid controller for the nuclear reactor power control. Nuclear Engineering and Design 2009; 239:2311e6. [25] Sohn SW, Lee KJ. Development of a boron concentration prediction model using multi-cell simulation of the automatic load follow operation. Annals of Nuclear Energy 2011;38:463e73.