Investigation of off-design characteristics of an improved recompression supercritical carbon dioxide cycle for concentrated solar power application
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Received: 2 May 2020 Revised: 14 July 2020 Accepted: 15 July 2020
DOI: 10.1002/er.5857
RESEARCH ARTICLE
Investigation of off-design characteristics of an improved
recompression supercritical carbon dioxide cycle
for concentrated solar power application
Yuegeng Ma1,2 | Tatiana Morosuk2 | Ming Liu3 | Jiping Liu1
1
MOE Key Laboratory of Thermal Fluid
Science and Engineering, Xi'an Jiaotong
Summary
University, Xi'an, PR China The off-design characteristics of an improved recompression supercritical carbon
2
Institute for Energy Engineering, dioxide cycle integrated with a two-stage intercooled main compressor are inves-
Technische Universität Berlin, Berlin,
tigated with a focus on the concentrated solar power application. An off-design
Germany
3
State Key Laboratory of Multiphase Flow
model is established for each crucial component of the cycle system of
in Power Engineering, Xi'an Jiaotong 100-megawatt scale. Four cycle control schemes with different main compressor
University, Xi'an, PR China configurations or/and cycle maximum pressure modes are evaluated and com-
Correspondence
pared. A sensitivity analysis is performed on the parameters related to the cycle
Jiping Liu, MOE Key Laboratory of thermal input and ambient condition to predict the off-design characteristics
Thermal Fluid Science and Engineering, due to the plant dispatch and ambient condition change in a solar power plant.
Xi'an Jiaotong University, Xianning West
Road. 28, Xi'an 710049, PR China. The off-design results regarding the cycle thermodynamic performance and
Email: liujp@xjtu.edu.cn operational issue prevention are presented. The effect of the design-point value
Yuegeng Ma, Institute for Energy
of the main compressor inlet temperature on the off-design characteristics is
Engineering, Technische Universität
Berlin, Berlin, Germany. evaluated with the comparison among the results at three design points. The
Email: 1977497362@qq.com results reveal that the compressor surge may occur to the main compressor with
[Correction added on 16 January 2021,
basic configuration as the main compressor inlet temperature decreases to a cer-
after first online publication: Yuegeng Ma tain value beneath the corresponding design point. By contrast, the surge risk
was designated as corresponding author.] can be prevented with the modified main compressor configuration by activat-
Funding information ing the recirculation system and the cycle can thus operate normally in the
Innovation capability support program of entire off-design range of main compressor inlet temperature. The off-design
Shaanxi, Grant/Award Number: 2018TD-
change in thermal input has overall limited effects on the cycle system control.
014; China Scholarship Council, Grant/
Award Number: 201806280078; National No operational compressor issues occur for the main compressor with either
Key Research and Development Program basic or modified configuration as the thermal input deviates from the design
of China, Grant/Award Number:
points and varies in the studied ranges. The cycle maximum pressure mode has
2016YFB0600105; Science and Technology
on Thermal Energy and Power Laboratory slight effects on the cycle thermodynamic performance as the thermal input
Open Foundation of China, Grant/Award deviates from the design point. The flexible cycle maximum pressure mode has
Number: TPL2017AA001
slightly lower sensitivity to the thermal input variation in net output power due
Abbreviations: B-FP, basic configuration with fixed pressure; B-VP, basic configuration with variable pressure; CSP, concentrated solar power;
DNI, direct normal irradiance, W/m2; HTF, heat transfer media; HTR, high-temperature recuperator; ICMC, intercooled main compressor; LTR,
low-temperature recuperator; MC, main compressor; M-FP, modified configuration with fixed pressure; M-VP, modified configuration with variable
pressure; PHX, primary heat exchanger; TES, thermal energy storage.
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided
the original work is properly cited.
© 2020 The Authors. International Journal of Energy Research published by John Wiley & Sons Ltd.
1818 wileyonlinelibrary.com/journal/er Int J Energy Res. 2021;45:1818–1835.
MA ET AL. 1819
to the counteraction of mass flowrate variation. The selection of the design-point
value of the main compressor inlet temperature has significant effects on the
off-design characteristics of the cycle. A low design-point value of the main com-
pressor inlet temperature leads to less demanding control action for operational
issue prevention whereas a high design-point main compressor inlet tempera-
ture results in overall more stable thermodynamic performance under off-design
conditions. Among other schemes, the fixed maximum pressure mode with the
modified main compressor configuration is found to be the most satisfactory
one due to the consequent superior efficiency, steady net output power, and free
of hazardous operating issues despite the relatively demanding task of compres-
sor surge prevention. The developed control scheme can be further improved by
implementing parametric optimization during the off-design operation.
KEYWORDS
compressor surge prevention, concentrated solar power plant, control scheme,
off-design modeling, supercritical carbon dioxide cycle
1 | INTRODUCTION cycle with an emphasis on the CSP application. Among dif-
ferent cycle designs, the recompression with an intercooled
As a potential solution to the climate change and energy main compressor (ICMC) was considered as an competi-
shortage, concentrated solar power (CSP) is regarded as an tive option due to the outstanding cycle performance and
important renewable energy technologies in the future large temperature differential in the cycle hot end for the
energy market due to its capability of utility-scale electricity integration of the thermal storage system.10,11 Padilla
production and dispatchable power supply with the inte- et al12 carried out an exergetic comparison between several
gration of thermal energy storage.1,2 Heat transfer fluids, S-CO2 cycle configurations with the integrated exergetic
such as molten salts, synthetic oil or steam are adopted as model of the solar receiver and S-CO2 cycle system. The
the medium to transfer the solar energy into thermal authors indicated that the recompression cycle with an
energy to activate the power cycle system for power genera- ICMC was the cycle configuration with the highest overall
tion or store the thermal energy to facilitate the continuous exergetic efficiency. Ma et al13 conducted a superstructure-
operation when the desired solar power is unavailable. based optimization on the S-CO2 cycle system for CSP
Limited by the degradation temperatures of different heat application with the integrated thermo-economic model of
transfer media, the power block can operate at a maximum the entire CSP plant employing an S-CO2 cycle-based
temperature level of around 350 C-700 C.3 The commer- power block. This work also pointed out that the adoption
cialized CSP plants employ a traditional subcritical steam of the recompression cycle with an ICMC can minimize
cycle system for the power block, which requires a complex the levelized cost of electricity for the CSP plant.
system configuration and large footprint and does not An S-CO2 cycle system is expected to frequently operate
exhibit desirable limited thermal efficiency. The upgrade under off-design conditions in a CSP plant due to the varia-
of the power cycle system is an important approach to tions in ambient conditions and cycle thermal input. The
maximizing the system performance of the CSP power and studies regarding the cycle off-design characteristics and
achieving a competitive cost of the CSP power generation. operational strategy development are therefore essential
Among many other candidates, supercritical carbon diox- for the further deployment of S-CO2 cycle systems in
ide (S-CO2) cycle systems have been seen as a competitive CSP plants. Dyreby14 developed an off-design model for a
option for the CSP plant due to the superior efficiency and 10 MW recompression cycle which allows for the design
compact configuration.4,5 analysis of the cycle system. The cycle performance is
Numerous cycle designs of S-CO2 cycle were proposed predicted with the model under various design and bound-
and evaluated for applications in different power generation ary conditions. Celle15 improved Dyreby's heat exchanger
scenarios, such as nuclear power plant,6 coal-fired plant,7 model by considering the effects of variations in CO2 prop-
waste heat recovery8 and CSP plant.9 Many previous works erties and investigate the impacts of yearly variation of the
were carried out on the parametric studies of the S-CO2 ambient condition on the thermodynamic performance of
1820 MA ET AL.
the S-CO2 cycle. Wang et al16 performed a performance temperature, to simulate the cycle performance under vari-
evaluation of a solar thermal power plant employing a ous off-design conditions encountered in a real CSP plant.
direct air-cooled supercritical carbon dioxide Brayton cycle. The cycle performance and the prevention of potential haz-
The focus has been put on the design of the air-cooled heat ardous issues of the main compressor (MC) under off-
sink and the effects of it under off-design conditions. The design conditions are highlighted in the off-design study.
results revealed that the directed air-cooled system can Four operation modes featuring different MC configuration
accommodate the lower solar intensities without deteriora- and/or cycle maximum pressure control are proposed and
tion in electricity. Son et al17 developed an one-dimension compared regarding the cycle thermodynamic performance
mean-line off-design model for S-CO2 turbomachinery with and operational issue control for the MC under off-design
the assistance of Deep Neural Network. With the devel- conditions. Based on the comparison among the cycle per-
oped models, it was claimed that more accurate off-design formance with different operation modes, the optimal off-
performance prediction could be achieved in even shorter design control scheme is finally recommended.
time than that with the traditional correction model,
which would greatly facilitate the off-design performance
evaluation of the entire cycle system. Luu18 investigated 2 | MODEL ESTAB LISHMENT
the approach of flexible operation of S-CO2 cycle in a CSP
plant with the assistance of a fossil-fuel heat source. Figure 1 is the schematic of the S-CO2 recompression cycle
Two operational modes regarding the turbine inlet temper- with an ICMC and the corresponding T-S diagram. The
ature control were proposed and compared. According to detailed on-design model of this cycle was reported in our
the comparison, flexible temperature mode was reported previous work.11 In comparison to the basic recompression
to outperform constant temperature mode in terms of fossil cycle, a higher cycle efficiency (ηcyc) and a larger tempera-
fuel saving. Wright et al19 conducted an experimental study ture differential for thermal input can be achieved with the
on a small-scale Brayton cycle loop and compared the introduction of an ICMC, which can lead to more power
results with their developed models. The experimental output from the cycle and a lower capital cost of the ther-
results exhibited controllable and stable operation in the mal energy storage (TES) system.13,24 The levelized cost of
critical region, and the measured results were claimed to electricity of the entire CSP system can be reduced as a
show good coherence with their modeling data. Carsten20 result. Table 1 gives the values of cycle design parameters
developed control strategies for the dynamic operation of to initialize the off-design calculation. As shown in Table 1,
a recompression S-CO2 cycle. Several control strategies, a 100-megawatt S-CO2 power cycle system is considered in
namely, high and low-temperature control, turbine bypass this work. To accommodate this large power production
control, and inventory control, were compared under differ- scale, a split shaft configuration is applied for the turboma-
ent operating modes including part-load operation, loss-of- chinery. A synchronous generator is tied to the turbine and
load, loss of heat sink, over-power, and start-up/shut-down. variable-speed drive motors are used for the compressors
Yang et al21 carried out part-load performance analysis and for the sake of system efficiency and control flexibility.25
comparisons among various S-CO2 cycle configurations, The main compressor is a two-stage internally geared
and concluded that the modifications on the cycle configu- compressor with an intercooler in between. A CO2-Salt
ration can lead to different effects in different scenarios. counter-flow shell-and-tube heat exchanger is chosen for
The cycle configurations involved in the previous the primary heat exchanger (PHX). Counter-flow printed
off-design studies were mostly recompression S-CO2 cycle circuit heat exchangers with flow channels that are 5 mm
and simple-recuperated cycle. The results regarding the wide and 2.5 mm deep, which is deemed as a representa-
off-design characteristics of more promising S-CO2 cycle tive design for using in S-CO2 cycles,14,26 is adopted for the
designs for the CSP application, for example, the recom- high-temperature recuperator (HTR) and low-temperature
pression cycle with an ICMC, were rarely reported. Besides, recuperator (LTR). The air-cooled heat sink is applied for
very few studies focused on the effects of the potential both the precooler and intercooler. A buffer tank is inte-
hazardous operational issues and the associated control grated at the inlet of the MC to impose active control on
schemes on off-design operation. Operating in the critical the inlet pressure of the MC with inventory control.14 The
region, the variation in inlet temperature of the main com- inlet pressure of the MC is assumed to remain the on-
pressor can lead to drastic changes in CO2 density, which design value and the split ratio of the stream flowing
may cause surge or choke to the compressor.14,22,23 through the recompressor is also assumed to remain the
This article develops an off-design model for the on-design value with the active valve control.
recompression cycle with an ICMC. Sensitivity analyses are An objected-oriented approach is employed for the
conducted on the parameters related to different boundary off-design model development of each main component
conditions, namely, the thermal input and the ambient in the cycle in MATLAB 2018a. The calculation of the
MA ET AL. 1821
F I G U R E 1 Diagrams of the S-CO2 recompression cycle with an ICMC. (A) Schematic diagram, (B) T-S diagram [Colour figure can be
viewed at wileyonlinelibrary.com]
required thermal properties of the CO2 is achieved by calculation.29,30 Applying the Stodola's ellipse method, the
calling REFPROP database from MATLAB.27 The inlet following relationship between the on-design (ϕd) and off-
pressure of the MC is assumed to remain the design value design (ϕod) mass flow coefficients is obtained:
using the inventory control under off-design conditions14
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
and the split ratio of the stream flowing through the rec- 2
1 − PPout,od
ompressor is also assumed to remain the on-design value ϕod in,od
= rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2 ð1Þ
with the active valve control. The model for each compo- ϕd
nent is presented as follows. 1 − PPout,d in,d
2.1 | Turbine where ϕ is defined as
pffiffiffiffiffiffiffi
A multi-axial flow type turbine is selected for the cycle for T in
_ in
ϕ=m ð2Þ
the sake of high efficiency and steady flow considering the pin
100-megawatt power output.28 The off-design turbine inlet
pressure is calculated according to the Stodola's ellipse
method assuming the sliding mode and a fixed nozzle pin,od is then obtained as follow by substituting Equa-
area are also assumed for the turbine for the off-design tions (1) and (2) as
1822 MA ET AL.
T A B L E 1 On-design parameters
Parameter Symbol Unit Value
for the initialization of the off-design
Cycle input heat Q_ th MW 222.2 modeling of the S-CO2 recompression
Molten salt inlet temperature to the PHX TTES,hot C 565 cycle with an ICMC11
Turbine inlet temperature TT,in C 550
Main Compressor outlet pressure pMC,out MPa 25
Terminal temperature difference at ΔTC,cold-end C 15
the cooler cold ends
Isentropic efficiency of turbine ηT % 93
Isentropic efficiency of compressor ηC % 89
Pressure drop in the PHX ΔpPHX kPa 50
Pressure drop in the hot side of the HTR ΔpHTR,HT kPa 60
Pressure drop in the cold side of the HTR ΔpHTR,LT kPa 30
Pressure drop in the hot side of the LTR ΔpLTR,HT kPa 20
Pressure drop in the cold side of the LTR ΔpLTR,LT kPa 40
Pressure drop in the cooler ΔpC kPa 20
Minimal pinch point temperature difference ΔTPinch K 5
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi p2 −p2out,d where Uin is the tip velocity at the inlet as defined in
pin,od = m_ 2in,od T in,od Y d + p2out,od with Y d = in,d2
pin,d ϕ2d Equation (7) and Din is the inlet diameter of the compres-
sor. hin and hout stand for the inlet and outlet enthalpies
ð3Þ
of CO2, respectively.
The off-design isentropic efficiency of turbine (ηT,od)
is finally obtained as Din
U in = N ð7Þ
2
" 0:1 #
_ in,od ρin,od
m
ηT,od = ηT,d sin 0:5π ð4Þ Then, the nondimensionalization on the shaft speed
m_ in,d ρin,d
is done for the flow coefficient, ideal head coefficient,
and the compressor isentropic efficiency, by introducing
where ρin,d and ρin,od are the density of CO2 under on- the corresponding item relating to the shaft speed to the
design and off-design, respectively. expressions of these parameters as displayed in Equa-
tions (8) through (10). It should be noted that the modi-
fied flow coefficient should be within the range of
2.2 | Compressor 0.02-0.05 to avoid operational issues.14 The lower bound
and upper bound are deemed as the threshold to trigger
The off-design performance characterization of the com- surge and choke. Nevertheless, a more accurate perfor-
pressors in the cycle is achieved by regressing the experi- mance map is necessary for the purpose of capturing the
mental data of a prototype compressor at the Sandia abnormal operating conditions accurately. Finally, the
National Laboratory with further nondimensionalization modified ideal head coefficient (ψ C ) and modified com-
on the shaft speed (N).14 The dimensionless flow coeffi- pressor isentropic efficiency (ηC ) are characterized as the
cient (ϕC) and ideal head coefficient (ψ C) of the compres- function of modified flow coefficient ϕC with polynomial
sor are first defined as shown in Equations (5) and (6). regression as presented in Equations (11) and (12)
_
m _
m N
ϕC = ð5Þ ϕC = ½0:02,0:05 ð8Þ
ρin U in D2in ρin U in D2in N d
ðhout −hin Þ N ð20ϕC Þ
3
ðhout −hin Þ
ψC = ð6Þ ψ C = ð9Þ
U 2in U 2in Nd
MA ET AL. 1823
N ð20ϕC Þ
5 thermal property variations as shown in Equations (15)
ηC,D,0
ηC = ηC ð10Þ and (16).15
ηC,D Nd
UAod α − 1 + αh,d
−1
ηC = −0:7069 + 168:6ϕC −8089ϕC 2 + 182725ϕC 3 = −c,d _ 0:8 cnp k ð1 − nÞ μðn − 0:8Þ
1 + α − 1 with α = m
UAd αc,od h,od
−1638000ϕC 4 ð11Þ ð15Þ
ψ C = −0:4049 + 54:6ϕC −2505ϕC 2 + 53224ϕC 3
Δpod m_ d 7=4 μd 1=4 ρd − 1
= ð16Þ
− 498626ϕC 4 ð12Þ Δpd _ od
m μod ρod
where cp stands for the specific heat capacity, k stands
2.3 | Heat exchanger for the coefficient of heat conductivity. μ stands for the
dynamic coefficient of viscosity. n equals to 0.4 and 0.3
The off-design model is developed for the heat exchangers for hot and cooling fluid, respectively.
in the S-CO2 cycle system including the HTR, LTR and
PHX. For the intercooler and precooler, the off-design
models are simplified by assuming a constant cold-end 2.4 | Model validation
temperature difference of 15 K with the active control of
the cooling air flowrate. The off-design model is an one- The developed model is validated with the S-CO2 off-
dimension counter-flow heat exchanger model divided into design code developed by Dyreby.14 The results obtained
several axial nodes as commonly applied for the off-design from the developed model are compared to Dyreby's under
performance prediction of the heat exchangers in the both on-design and the off-design conditions as shown
system-level modeling in previous works.14,26 The devel- in Table 2. It is found the results of the developed model
oped off-design model considers both the heat transfer and show good coherence with the results obtained with
fluid dynamic characteristics of the heat exchanger. For Dyreby's code under both on-design and off-design condi-
the purpose of capturing the effect of fluid property varia- tions with a maximum difference of 0.14%. The accuracy
tion, the models are discretized into 20 sub-nodes. The of this model is therefore validated.
pressure loss (Δp) and the conductance of heat transfer
(UA) are calculated for each sub-node following the
method developed in Patnode's thesis31 with some custom- 3 | CONS IDERATIONS FOR THE
ized modifications. The effects of fluid property variation OFF-DESIGN CHARACTERISTIC
on the off-design performance are considered in different STUDY
way for each type of heat exchanger. For the HTR and
PHX which have insignificant thermal property variations The S-CO2 cycle system employed in a CSP plant fre-
of the CO2 fluid, the effects of thermal property variations quently operates under off-design conditions due to the
of each sub-node in the heat transfer process are neglected. implementation of CSP dispatch and variation of ambient
The conductance of heat transfer (UAod) and pressure loss conditions. The CSP dispatch leads to the variation of
(Δpod) under off-design conditions are treated as the func- thermal input to the cycle in the hot end, which may
tions of the mass flowrate as follows. change the mass flowrate (m _ salt) and inlet temperature
(Tsalt,in) of the molten salt at the inlet of the primary heat
UAod m_ − 0:8 + m − 0:8
_ h,d exchanger. This may then affect the performance of tur-
= c,d
− − 0:8 ð13Þ bine and other cycle components. The variation of ambi-
UAd m _ c,od + m
0:8
_ h,od
ent temperature causes the change of CO2 temperature at
the outlets of precooler and intercooler, which in turn
Δpod m_ d 7=4
= ð14Þ lead to the change in inlet temperature of the MC
Δpd _ od
m (TMC,in). The variations in the MC inlet temperature tend
to cause drastic changes in the density of CO2 at the inlet
The CO2 fluid flowing through the LTR displays of the main compressor, especially when the pressure of
significant and nonlinear variation in fluid properties CO2 is close to the critical pressure. Surge/choke may
relating to the heat transfer and hydraulic characteristic occur to the MC as the volume flowrate drastically fluctu-
due to the vicinity to the critical point. Therefore, ates down/up with density if no measure is taken. There-
the UAod and Δpod are calculated considering the fore, regarding the control of the potential operational
1824 MA ET AL.
TABLE 2 Validation of the developed model
On-design condition Off-design condition
Error Error
Parameter Unit Present Dyreby (%) Present Dyreby (%)
Input heat [MW] 10 10 Input 5.22 5.22 −0.04
pmin [kPa] 9000 9000 Input 9000 9000 Input
pmax [kPa] 25 000 25 000 Input 18 933.28 18 993.20 0.32
Split ratio [—] 0.3 0.3 Input 0.3 0.3 Input
effHTR [—] 0.95 0.95 Input 0.94 0.94 −0.05
effLTR [—] 0.95 0.95 Input 0.90 0.90 −0.03
Cycle efficiency [%] 44.67 44.67 0.00 40.46 40.46 0.02
Mass flowrate [kg/s] 51.76 51.76 0.00 35.90 35.90 0.00
t1 (t2,t3) [ C] 41 41 Input 50 50 Input
t4 [ C] 93.10 93.10 0.00 106.82 106.82 0.00
0
t5 [ C] 210.47 210.88 0.20 239.85 240.19 0.14
00
t5 [ C] 197.40 197.40 0.00 196.08 196.09 0.00
t5 [ C] 206.51 206.80 0.14 226.41 226.65 0.10
t6 [ C] 395.19 395.19 0.00 431.77 431.72 −0.01
t7 [ C] 550 550 Input 550 550 Input
t8 [ C] 431.12 431.12 0.00 461.20 461.20 0.00
t9 [ C] 217.67 218.03 0.17 240.91 241.24 0.14
t10 [ C] 98.35 98.36 0.00 118.82 118.87 0.04
FIGURE 2 Two configurations of the main compressor. (A) basic configuration, (B) modified configuration
issue to the MC under varied conditions of inlet tempera- additional parallel compressor for each compressor stage
ture, two configurations of the MC, namely, the basic con- besides using the shaft speed control to deal with the
figuration and the modified configuration, are evaluated potential operational issues. The prevention of the surge
and compared in the following discussion. The simplified condition is achieved by the adjustments of both shaft
diagrams of the two MC configurations are presented in speed and the recirculation flows in two stages (m_ rec,1 and
Figure 2. The shaft speed is the only control variable for m_ rec,2). The choke control is achieved by the adjustment
the MC with the basic configuration for operational issue of shaft speed and the introduction of the second parallel
prevention, whereas the MC with the modified configura- compressor configured for both stages if necessary. These
tion is further configured with an anti-surge valve and an modifications are expected to expand the applicable
MA ET AL. 1825 F I G U R E 3 Four operation schemes under off-design conditions. (A) Basic main compressor configuration with fixed cycle maximum pressure (B-FP), (B) modified main compressor configuration with fixed cycle maximum pressure (M-FP), (C) basic main compressor configuration with variable cycle maximum pressure (B-VP); (D) modified main compressor configuration with variable cycle maximum pressure (M-VP)
1826 MA ET AL.
conditions during off-design operation. Besides, two cycle 4 | RESULTS A ND DISCUSSION
maximum pressure modes, namely, fixed pressure mode
and variable pressure mode, are evaluated and compared The cycle off-design performance is evaluated with a sensi-
with each other. The main compressor outlet pressure tivity analysis in this section. Three design points of the
(pMC,out) is always controlled at 25 MPa in the fixed pres- main compressor inlet temperature (TMC,in,d), i.e., 32 C,
sure mode, whereas in the variable pressure mode, pMC,out 41 C and 50 C, are selected to investigate the effects of the
is not controlled unless it would cross the maximum bound TMC,in,d on the off-design performance. The design vari-
of 30 MPa. Four operation schemes are thereby presented ables are optimized for three design points prior to the off-
for the analysis, namely. (1) Basic main compressor config- design analysis. The values of the relevant parameters at
uration with Fixed cycle maximum Pressure mode (B-FP); the three corresponding on-design points are presented in
(2) modified main compressor configuration with Fixed Table 3. The thermodynamic states of the cycle at these
cycle maximum Pressure (M-FP); (3) basic main compres- three design points are presented in Table 4. The paramet-
sor configuration with Variable cycle maximum pressure ric analyses are performed for Tsalt,in and m_ salt to consider
(B-VP); (4) modified main compressor configuration with the off-design changes of the thermal input and for
Variable cycle maximum Pressure (M-VP). Figure 3A-D TMC,in to consider the effect of the ambient temperature.
presents the realization of these four schemes. The information regarding the off-design sensitivity
T A B L E 3 The values of the
Design value of TMC,in [ C]
relevant parameters at three optimized
Parameter Unit 32 41 50 on-design points
Inlet pressure of the MC MPa 6.63 8.06 9.82
Split ratio — 0.62 0.66 0.70
Inlet rotor diameter of the first MC stage m 0.50 0.49 0.49
Inlet rotor diameter of the second MC stage m 0.41 0.42 0.43
Shaft speed of the first MC stage rpm 2361 2562 2131
Shaft speed of the second MC stage rpm 12 000 10 329 8786
Inlet rotor diameter of the first RC stage m 0.88 0.84 0.88
Inlet rotor diameter of the second RC stage m 0.35 0.41 0.48
Shaft speed of the RC rpm 11 977 11 208 10 215
Cycle mass flow rate kg/s 859.18 986.49 1164.39
Design-point cycle efficiency % 48.00 46.44 44.81
T A B L E 4 The thermodynamic
tMC,in,d = 32 C tMC,in,d = 41 C tMC,in,d = 50 C
states of the cycle at three design points
State point t [ C] p [kPa] t [ C] p [kPa] t [ C] p [kPa]
1 32 6627.80 41 8060.06 50 9817.88
2 45.25 7909.19 54.90 9804.57 59.95 11 475.54
3 32 7889.19 41 9784.57 50 11 455.54
4 64.97 25 000 75.42 25 000 84.43041 25 000
5 201.89 24 960 196.47 24 960 191.011 24 960
50 202.05 24 960 198.96 24 960 195.672 24 960
00
5 201.62 24 960 191.72 24 960 180.6101 24 960
6 355.47 24 930 374.73 24 930 396.002 24 930
7 550 24 880 550 24 880 550 24 880
8 392.26 6727.80 413.57 8160.06 435.78 9917.88
9 211.52 6667.80 207.35 8100.06 203.08 9857.88
10 72.97 6647.80 82.62 8080.06 91.73 9837.88
MA ET AL. 1827
analysis is shown in Table 5. It should be noted that the issues occur to the MC in the entire studied range of Tsalt,in.
upper limit of Tsalt,in selected here is selected only for the The MC configuration is found to have no effects on the
sake of parametric analysis. The actual operating Tsalt,in system control. The cycle maximum pressure is slightly dif-
for the CSP using solar salt as storage media is rec- ferent in two cycle maximum pressure mode as can be
ommended to remain lower than 580 C considering the found by comparing the results of FP and VP cases. As
chemical stability of the solar salt.32 Tsalt,in rises, the cycle maximum pressure increases linearly
under the VP mode and the shaft speed decreases linearly
under the FP mode. The maximum variation of the cycle
4.1 | Analysis on thermal input maximum pressure is within ±0.15 MPa and the variation
of the shaft speed is within ±0.3% as Tsalt,in deviates the
Figure 4 presents the results of the variables relating to the design point by ±30 C. The value of TMC,in,d does not show
cycle control as the function of Tsalt,in. No operational apparent effects on the cycle control.
Figures 5 and 6 display the results of variables relating
T A B L E 5 The settings for the sensitivity analysis parameters to the cycle thermodynamic performance. As shown in
under off-design operation Figures 5 and 6, the variation of Tsalt,in has relatively mild
Design Range for effects on the cycle thermodynamic performance. The max-
point sensitivity imum variations of ηen,cycle and W _ net are both within
Parameter Unit value analysis ±5.5% as Tsalt,in deviates the design point by ±30 C. The
Tsalt,in
C 565 535-595 choice of control schemes has limited effects on the ther-
modynamic characteristics under off-design conditions
_ salt/m
m _ salt,d \ 1 0.6-1.2
of Tsalt,in as evidenced by the close variation trends of
TMC,in C 32/41/50 32-50
the four control scheme cases. The MC configuration is
F I G U R E 4 The variations of relative shaft speed (RN = N/Nd) and main compressor outlet pressure (pMC,out) with molten salt
temperature (Tsalt,in) under three design points of main compressor inlet temperature (TMC,in,d). (A) the case of TMC,in,d = 32 C, (B) the case
of TMC,in,d = 41 C, (C) the case of TMC,in,d = 50 C [Colour figure can be viewed at wileyonlinelibrary.com]1828 MA ET AL. FIGURE 5 The variations of net output power (W _ net) and cycle energetic efficiency (ηen,cycle) with molten salt temperature (Tsalt,in) under three design points of main compressor inlet temperature (TMC,in,d). (A) The case of TMC,in,d = 32 C, (B) the case of TMC,in,d = 41 C, (C) the case of TMC,in,d = 50 C [Colour figure can be viewed at wileyonlinelibrary.com] F I G U R E 6 The variations of outlet temperature of the molten salt (Tsalt,out), turbine inlet temperature (TT,in) and mass flowrate of cycle working fluid CO2 (m_ CO2 ) with molten salt temperature (Tsalt,in) under three design points of main compressor inlet temperature (TMC,in,d). (A) The case of TMC,in,d = 32 C, (B) the case of TMC,in,d = 41 C, (C) the case of TMC,in,d = 50 C [Colour figure can be viewed at wileyonlinelibrary.com]
MA ET AL. 1829
found to have no effects here according to the compari- increases under the variable pressure mode and the
son between the results of different MC configurations. shaft speed decreases linearly under the FP mode, both
The cycle maximum pressure control has slight effects on at a decreasing rate. The cycle maximum pressure is
the results, specifically, the variation rate of m _ CO2 and W _ decreased by around 0.35-0.55 MPa for the cycle with the
net with the change of Tsalt,in. The cycle with the VP mode VP mode and the shaft speed is increased by 1% -1.5% as
has slightly lower variation rate of m _ CO2 than that with the m _ salt decreases to 60% of the design value, while these
the FP mode due to the alleviation from the change of two variables only increases and decreases by less than
maximum pressure with Tsalt,in. Correspondingly, the W _ 0.04 MPa and 0.1%, respectively, as the m _ salt rises to 120%
net of the cycle with the VP mode has slightly higher vari- of the design value. The reduction in TMC,in,d slightly
ation rate than that with the FP mode. The cycle with increases the sensitivity of the control variable to the
lower TMC,in,d exhibits higher ηen,cycle and lower m _ CO2 as m_ salt variation.
expected. The effect of TMC,in,d appears to be independent Figures 8 and 9 display the sensitivity analysis results
of the variation of Tsalt,in since the studied variables have on the variables relating to the cycle thermodynamic per-
similar variation tendencies and rates as the Tsalt,in devi- formance as the functions of m _ salt,d. As shown in
_ salt/m
ates from the design point. Figures 8 and 9, the thermodynamic performance is more
Figure 7 presents the sensitivity analysis results on sensitive to the decrease in m _ salt than to its increase. The
the variables relating to the cycle control as the function ηen,cycle and W _ net decrease by 15%-22% as m _ salt decreases
of m _ salt,d. No operational compressor issues occur as
_ salt/m to 60% of the design point. The control scheme has over-
m_ salt deviates from the design point. The main compres- all limited effects on the thermodynamic characteristics
sor configuration does not affect the system control under as m _ salt deviates. The MC configuration is found to have
the off-design conditions of m _ salt. The cycle maximum no effects here according to the comparison between the
pressure is slightly different in two cycle maximum pres- results of the cases with different MC configurations.
sure modes according to the comparison between the The cycle maximum pressure mode has slight effects
results of FP and VP cases. As m _ salt changes from the 60% on the variation rate of m _ CO2 and W _ net with the change
to 120% of the design value, the cycle maximum pressure of m _ salt, especially as m_ salt decreases. The VP mode leads
F I G U R E 7 The variations of relative shaft speed (RN = N/Nd) and main compressor outlet pressure (pMC,out) with the molten salt mass
_ salt,d) under three design points of main compressor inlet temperature (TMC,in,d). (A) The case of TMC,in,d = 32 C,
_ salt/m
flow rate fraction (m
(B) the case of TMC,in,d = 41 C, (C) the case of TMC,in,d = 50 C [Colour figure can be viewed at wileyonlinelibrary.com]1830 MA ET AL.
FIGURE 8 The variations of net output power (W _ net) and cycle energetic efficiency (ηen,cycle) with the molten salt mass flow rate
fraction (m _ salt,d) under three design points of main compressor inlet temperature (TMC,in,d). (A) the case of TMC,in,d = 32 C, (B) the case
_ salt/m
of TMC,in,d = 41 C, (C) the case of TMC,in,d = 50 C [Colour figure can be viewed at wileyonlinelibrary.com]
F I G U R E 9 The variations of outlet temperature of the molten salt (Tsalt,out), turbine inlet temperature (TT,in) and mass flowrate of cycle
working fluid CO2 (m_ CO2 ) with the molten salt mass flow rate fraction (m _ salt/m
_ salt,d) under three design points of main compressor inlet
temperature (TMC,in,d). (A) the case of TMC,in,d = 32 C, (B) the case of TMC,in,d = 41 C, (C) the case of TMC,in,d = 50 C [Colour figure can be
viewed at wileyonlinelibrary.com]MA ET AL. 1831
to slightly higher W _ net than the FP mode does under the to significantly different results in the cycle maximum
low m _ salt conditions. The reason for this is also due to pressure and shaft speed. When TMC,in increases to 50 C,
the variation of the m _ CO2 as explained above in the Tsalt,in the cycle maximum pressure is reduced to around 12 MPa
cases. The cycle with a lower TMC,in,d exhibits higher in the VP mode and the shaft speed is increased by around
ηen,cycle and lower m _ CO2 as expected. It is also found that 50% in the FP mode to keep the cycle maximum pressure
the decrease of TMC,in,d leads to more drastic changes in at 25 MPa. In the cases with a TMC,in,d of 41 or 50 C, com-
the cycle variables with m _ salt, especially as the m
_ salt has a pressor surge occurs to the MC with basic configuration
significant reduction relative to the design value. when the TMC,in reduces to be lower than a certain value
as shown in Figure 10B,C. For the cycle with the modified
main compressor configuration, the recirculation system is
4.2 | Analysis on ambient temperature activated when the compressor surge is approaching. The
decrease in TMC,in entails more recirculating flow to pre-
Figure 10 presents the results of the variables relating to vent the potential surge condition. For the cycle with the
the cycle control as the function of TMC,in. In comparison FP mode, the shaft speed decreases as TMC,in decreases.
to the thermal input variation, the variation in ambient For the cycle with the VP mode, the cycle maximum pres-
temperature has more significant effects on the cycle con- sure increases as TMC,in decreases until it reaches the upper
trol. The cycle at different design points of the TMC,in,d limit of the maximum pressure, the further decrease in
exhibit different off-design characteristics. The results of TMC,in leads to the decrease in shaft speed. Besides, the
different TMC,in,d are therefore discussed separately. No cycle with the VP mode is less demanding on the preven-
operational compressor issues occur as TMC,in deviates tion of compressor surge as the cycle with the VP mode
from the design point for the cycle with a TMC,in,d of 32 C, can operate in a larger range of TMC,in without the use of
and the MC configuration does not affect the system con- recirculation system. The design under a high TMC,in,d
trol in this case. The two maximum pressure modes lead entails more demanding control actions for compressor
F I G U R E 1 0 The variations of relative shaft speed (RN = N/Nd) and main compressor outlet pressure (pMC,out) with the main
compressor inlet temperature (TMC,in) under three design points of main compressor inlet temperature (TMC,in,d). (A) The case of
TMC,in,d = 32 C, (B) the case of TMC,in,d = 41 C, (C) the case of TMC,in,d = 50 C [Colour figure can be viewed at wileyonlinelibrary.com]1832 MA ET AL. FIGURE 11 The variations of net output power (W _ net) and cycle energetic efficiency (ηen,cycle) with the main compressor inlet temperature (TMC,in) under three design points of main compressor inlet temperature (TMC,in,d). (A) the case of TMC,in,d = 32 C, (B) the case of TMC,in,d = 41 C, (C) the case of TMC,in,d = 50 C [Colour figure can be viewed at wileyonlinelibrary.com] F I G U R E 1 2 The variations of outlet temperature of the molten salt (Tsalt,out), turbine inlet temperature (TT,in) and mass flowrate of cycle working fluid CO2 (m_ CO2 ) with the main compressor inlet temperature (TMC,in) under three design points of main compressor inlet temperature (TMC,in,d). (A) The case of TMC,in,d = 32 C, (B) the case of TMC,in,d = 41 C, (C) the case of TMC,in,d = 50 C [Colour figure can be viewed at wileyonlinelibrary.com]
MA ET AL. 1833
surge prevention as can be observed by comparing the compressor issues occur when the thermal input devi-
results for the cycle with different TMC,in,d. ates from the on-design conditions in the studied ranges
Figures 11 and 12 display the results of the variables regardless of the main compressor configuration. The
relating to the cycle thermodynamic performance as the cycle maximum pressure mode has slight effects on the
functions of TMC,in. As shown in Figures 11 and 12, the cycle thermodynamic performance under off-design con-
effects of TMC,in on the cycle thermodynamic perfor- dition. The cycle in flexible maximum pressure mode
mance are significantly different for the cycle with differ- is less sensitive to the thermal input variation in W _ net
ent TMC,in,d. The W _ net reduces as TMC,in increases for all due to the counteract of m _ CO2 variation. The maximum
three TMC,in,d cases, with more significant reduction variations of ηen,cycle and W _ net are both within ±5.5% as
observed with lower TMC,in,d. The cycle maximum pres- Tsalt,in deviates the design point by ±30 C. The ηen,cycle
sure mode has significant effects on the thermodynamic and W _ net decrease by 15%-22% as m _ salt decreases to 60%
characteristics as TMC,in deviates from the design value. of the design point and increase by 1.0%-1.2% and 1.4%-
The FP mode can lead to much more stable ηen,cycle 1.9% as m _ salt increases to 120% of the design point.
and W _ net. A main reason for this is that the m
_ CO2 remains • The selection of TMC,in,d significantly affect the off-
constant for the cycle with a fixed maximum pressure. It design characteristics of the cycle under varied condi-
is found that the cycle performance exhibits lower sensi- tions of TMC,in. A low TMC,in,d leads to less demanding
tivity to the TMC,in with a higher TMC,in,d according to the control task regarding the operational issue prevention
comparison among the results of the cycle with different as no surge/choke is reported at the design point of
TMC,in,d. TMC,in,d = 32 C. The cycle with a high TMC,in,d is likely
to have stable thermodynamic performance under off-
design conditions. The maximum reductions in ηen,cycle
5 | C ON C L U S I ON and W _ net are 12.1% and 17.2% at the design point of
TMC,in,d = 50 C and 25.6% and 84.8% at the design
This article develops an off-design model for a point of TMC,in,d = 32 C.
recompression S-CO2 cycle with an ICMC with an empha- • Despite the relatively demanding control task for com-
sis on CSP application. The off-design characteristics with pressor surge prevention, M-FP appears to be the most
respect to the thermodynamic performance and opera- satisfactory control scheme for the consequent steady
tional issue prevention are highlighted. Four control ηen,cycle and W _ net as well as the effective prevention of
schemes with different cycle maximum pressure mode operational issue of the main compressor. However,
or/and main compressor configuration are evaluated and the cycle performance may be further improved when
compared. The effects of the off-design changes in cycle the real-time parametric optimization is applied for the
thermal input and ambient temperature are investigated cycle under off-design conditions.
_ salt and TMC,in.
through the sensitivity analyses on Tsalt,in, m
Three different TMC,in,d are selected to investigate the ACKNOWLEDGEMENTS
effects of the choice of TMC,in,d on the cycle off-design This work is supported by the National Key Research and
performance. The following conclusions are drawn: Development Program of China (No. 2016YFB0600105),
the Science and Technology on Thermal Energy and
• The compressor surge may occur to the main compres- Power Laboratory Open Foundation of China (No.
sor with basic configuration when the TMC,in attains a TPL2017AA001), and Innovation capability support pro-
certain value lower than the corresponding TMC,in,d. By gram of Shaanxi (No. 2018TD-014). The first author
contrast, the surge risk can be prevented with the mod- Yuegeng Ma would also like to thank China Scholarship
ified MC configuration by activating the recirculation Council (No. 201806280078) for the financial support. Open
system and can thus operate normally in the entire off- access funding enabled and organized by Projekt DEAL.
design range of TMC,in. The choke condition does not
occur to the cycle under all the off-design conditions, NOMENCLATURE
the parallel compressor is not activated for either stage
of the main compressor. This indicate that the risk of Symbol
choke appears controllable with shaft speed control. A A area of heat exchanger, m2
customized performance map is still required to pre- Cp specific heat at constant pressure, kJ kg−1 K−1
dict the abnormal conditions and exert the prevention CSP concentrated solar power
control for the main compressor with better accuracy. D diameter, m
• The off-design change in thermal input has relatively h specific enthalpy, kJ kg−1
mild effects on the cycle system control. No operational H height, m1834 MA ET AL.
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