CHEMICAL ENGINEERING TRANSACTIONS  
 

VOL. 81, 2020 

A publication of 

 

The Italian Association 
of Chemical Engineering 
Online at www.cetjournal.it 

Guest Editors: Petar S. Varbanov, Qiuwang Wang, Min Zeng, Panos Seferlis, Ting Ma, Jiří J. Klemeš 

Copyright © 2020, AIDIC Servizi S.r.l. 

ISBN 978-88-95608-79-2; ISSN 2283-9216 

Optimal Design and Sizing of Solar-assisted CHP System 

Based on Thermodynamic and Economic Analysis  

Fengyuan Wang, Yao Sheng, Linlin Liu*, Lei Zhang, Yu Zhuang, Jian Du 

Institute of Chemical Process Systems Engineering, School of Chemical Engineering, Dalian University of Technology,  

Dalian 116024, Liaoning, China 

liulinlin@dlut.edu.cn 

This work develops a method for the optimal design of a solar-assisted combined heat and power (CHP) system, 

in which the solar thermal central receiver subsystem and the steam power cycle subsystem are integrated to 

meet the real-time requirements of steam and power from production process. A mathematical model with the 

objectives of minimum total annual cost (TAC) and environmental impact (EI) is formulated to optimize the 

configuration and the size of the major equipment units, and schedule the dynamic operation of entire system. 

This model accounts for the hourly variability of Direct Normal Irradiance (DNI) and the electricity load in a typical 

day, as well as the power losses caused by the partial load operation of steam turbines. Based on the presented 

model, the optimum level of solar capacity is determined through a comprehensive analysis considering the 

trade-off between TAC and EI of the system. At last, a case study is illustrated and the results are elaborated to 

demonstrate that the desired system configuration can be obtained by application of the proposed model. 

1. Introduction 

With the increasing depletion of fossil fuels and the deterioration of environment, various clean energy sources 

as alternatives to fossil fuels are developed, in which solar energy, as an abundant and widely distributed 

renewable energy source, has attracted more and more attention (Abikoye et al., 2019). Sorgulu et al. (2018) 

proposed a solar tower–based energy system to produce electricity and fresh water, where the thermal energy 

storage tanks were considered to ensure power output in cloudy situations and at night, and the performance 

of the system has been discussed through energy analysis. Besagni et al. (2018) conducted an experimental 

test on an existing solar-assisted dual-source multifunctional heat pump to obtain the seasonal performances; 

in particular, energy and exergy analyses have been formulated based on experimental observations. 

Compared to the systems driven solely by solar energy, the synergy of solar energy and fossil fuels can not only 

improve the thermal efficiency of the entire system, but also improve the ability to resist the output fluctuations 

caused by the intermittent nature of solar energy. Ocon et al. (2018) proposed a novel multi-criteria decision-

making methodology for the selection of the most appropriate energy system for the off-grid electrification. Eight 

technology combination options were evaluated using six criteria covering socio-economic, environmental, and 

technical aspects. Results indicate that the fuel saver (diesel-solar PV hybrid) and diesel-solar PV-Li-ion hybrid 

systems yield the highest performance scores among the eight alternatives. Gutiérrez-Arriaga et al.(2013) 

presented a unified framework that combines process simulation with multi-objective optimization involving 

trade-off between annual profit and environmental impact (EI), while the types and amounts of primary energy 

sources as well as the optimal values of the operating conditions of the plant were optimized at the same time. 

Ponce-Ortega et al.(2011) presented a methodology for the energy integration of a system containing absorption 

refrigeration, which is driven by solar energy and other different types of heat sources. 

The utility systems in chemical industry consume large amounts of fossil fuels every year. In previous studies, 

most of the researches on utility systems coupled with renewable energy and fossil fuels have focused on the 

analysis and evaluation for system with given structure, but few studies considered design problem for such 

system with variable heat and electricity demands and variable solar energy supply simultaneously. This study 

aims to launch the structure design and operating strategy optimization of a solar-assisted combined heat and 

power (CHP) system considering economic and environmental objectives. Typical structures of a solar-assisted 

 
 
 
 
 
 
 
 
 
 
                                                                                                                                                                 DOI: 10.3303/CET2081008 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Paper Received: 30/04/2020; Revised: 01/06/2020; Accepted: 09/06/2020 
Please cite this article as: Wang F., Sheng Y., Liu L., Zhang L., Zhuang Y., Du J., 2020, Optimal Design and Sizing of Solar-assisted CHP 
System Based on Thermodynamic and Economic Analysis, Chemical Engineering Transactions, 81, 43-48  DOI:10.3303/CET2081008 
  

43



CHP system with and without energy storage unit are designed and optimized, which has also taken energy 

loss caused by variable energy demand and solar energy supply into account. In the CHP system, power and 

steam with defined pressure and temperature are generated through boiler and a set of turbines. Besides, solar 

energy is selected as a supplement to partially replace fossil fuel to drive utility systems, which effectively 

reduces EI. However, as the capital cost of the solar system is much higher than the utility system driven solely 

by fossil fuel, and the trade-off between total annual cost (TAC) and EI with different ratio of solar energy 

utilization is performed and a compromising system can be obtained to ensure the economic feasibility of the 

system on the premise that the EI meets the criterion. Corresponding mixed integer nonlinear programming 

(MINLP) mathematical model is formulated for optimal design purpose, and the case study is performed to 

illustrate the proposed method. 

2. Superstructure 

The integration of solar thermal central receiver subsystem and steam power cycle subsystem based on the 

superstructure is presented in Figure1. In steam power cycle subsystem, the boiler consumes natural gas to 

generate the highest-level steam (VHP), part of which is used to directly meet the steam load, and the rest goes 

to multi-stage steam turbine expansion to generate power and lower-level steams including high-, middle- and 

low-pressure steams. In solar thermal central receiver subsystem, solar energy captured by cavity receiver fixed 

on the solar tower is used to heat the molten salt and thermal energy storage (TES) system consisting of high 

and low temperature molten salt storage tanks is considered (Sorgulu et al., 2018). In the steam generator, a 

part of the high temperature molten salt is used to generate VHP to reduce the load on boiler, and the rest is 

used to generate lower-level steams selectively along with turbine extraction to meet the remaining steam load. 

There are many factors related to the efficiency of multi-stage steam turbines. In order to reduce the difficulty in 

modelling, this study refers to the practice in Sun et al. (2015), which split a multi-stage turbine into a set of 

single-stage turbines which contains six back-pressure turbines and two condensing turbines. Binary variables 

are used to determine the existence of each single-stage turbine. 

Make-up Water

Make-up Water

Molten Salt

Steam Generator

    Solar 
Collector

VHP

HP

MP

LP

Boiler
G

G

G

G

G

G

G G

CON

Natural Gas

 

Figure 1: Superstructure for the solar-assisted CHP system with energy storage unit 

3. Mathematical model 

According to the superstructure proposed above, an MINLP mathematical model is formulated to assist the 

optimal design purpose of the study. The entire model consists of the both portions of central solar system and 

utility system, as well as the objective functions. Solver Baron in GAMS (Rosenthal, 2012) is employed to solve 

the model and obtain needed configuration. Then, ε-constraint method is introduced to launch the multi-objective 

optimization, where EI is set as constraint and TAC is set as objective function. 

3.1 Model for central solar system 

The total energy balance for the molten salt cavity receiver is given by Eq(1). Average receiver surface 

temperature is calculated by Eq(2) (Tehrani et al., 2016), which has an effect on the amount of energy loss on 

the receiver surface. Eq(3)-(6) denote energy loss caused by various mechanisms including radiation, reflection 

and convection (Li et al., 2010). The energy balance during the steam generation of molten salt is shown in 

Eq(7). 

44



Qin,t=Qabs,t+Qloss,t=Aheliostat×Ih,t×ηopt×HURt 
(1) 

Qin,t

Are
=(Tre,t-Taverage)/(

douter

dinner×hMS,t
+
douter

2×λtube
×ln

douter

dinner
) (2) 

Qloss,t=Qemission,t+Qreflection,t+Qconvection,t  
(3) 

Qemission,t=εaverage×σ×(Tre,t
4

-Tambient
4

)×Aaperture 
(4) 

Qreflection,t=ρ×Qin,t×VF 
(5) 

Qconvection,t=hforce×(Tre,t-Tambient)×Aaperture+hnature,t×(Tre,t-Tambient)×Areceiver (6) 

Qabs,t=mMS,t×CpMS×(TH-TL)= ∑ ṁsteami,t
solar

i

×∆Hi 
(7) 

Where λtube denotes the thermal conductivity of receiver tube, which takes a value of 23.9 W/(m∙K); Taverage and 

Tambient are average temperature of molten salt in the receiver tube and ambient temperature; dinner and douter are 

the inner and outer diameter of receiver tube; hMS, hforce and hnature denote the convection heat transfer coefficient 

of molten salt, forced convection and natural convection (Tehrani et al., 2016); subscripts i,t denote the steam 

level for utility system and hours in a day ; heat conduction loss is ignored in Eq(3) because of its small proportion 

(Li et al., 2010). 

3.2 Model for utility system design 

Energy balance in boiler is given by Eq(8). Eq(9)-(10) denote the mass balance of steam. Eq(11) represents a 

linear formulation to determine performance of single-stage turbines (Aguilar et al., 2007). 

QFt×LHV×EFFboiler=ṁsteamt
boiler

×ΔHVHP (8) 

∑ ṁsteami,t
solar

i

+ṁsteamt
boiler

= ∑ ṁsteamloadi
i

+ṁcondensatet 
(9) 

∑ ṁturbinei,ip,t
i

×zi.ip+ṁsteamip,t
solar

= ∑ ṁturbinei,ip,t
ip

×zi,ip+ṁsteamloadip 
(10) 

Wturbinei,ip,t=∆Hi,ip×
(Lsti,ip+1)

Bsti,ip
×ṁturbinei,ip,t-Lsti,ip×WEDi,ip-(Lsti,ip+1)×

Asti,ip

Bsti,ip
 (11) 

Where Wturbinei,ip,t and denotes power generated via turbines; ṁturbinei,ip,t  denotes steam mass flow in 

turbines; ṁsteami,t
solar

 and ṁsteamt
boiler

 denote the steam generated via steam generator and boiler; Ast, Bst and 

Lst are regression coefficients; WEDi,ip denotes the rated power of a single-stage steam turbine. 

3.3 Objective function 

In this study, the TAC and the EI of the solar-assisted CHP system are simultaneously minimized to guide the 

system design. As indicated in Eq(12)-(14), the TAC is composed of capital cost (CAPC) and operating cost 

(OPEC). The operating cost is the sum of fuel cost and solar field maintain cost. 

minTAC=CAPC+OPEC (12) 

CAPC=Cheliostat×Aheliostat+FCsolar+CSG×(Qabs,t)MAX+CAPCU (13) 

OPEC= ∑ CNG×QFt
t

+C𝑀× ∑ Qabs,t
t

 (14) 

EI is measured by Greenhouse gas (GHG) emissions, which is related to the extraction and combustion of 

natural gas (Gutiérrez-Arriaga et al., 2013). 

minEI=GENG×LHV× ∑ QFt
t

×ECclimate+ ∑ QFt
t

×ECresource (15) 

Where Cheliostat and CSG are the unit capital cost of heliostat and steam generator; CAPCU is the capital cost of 

main equipment units of the steam power cycle; FCsolar is the fixed capital cost of solar tower and receiver; CNG 

and CM are the units operating costs for natural gas and heliostat field maintenance; GENG denotes GHG 

45



emission; Ecclimate and Ecresource denote the eco-indicator related to damage caused by GHG emissions and 

extraction of natural gas. 

3.4 Model for the solar-assisted CHP system considering energy storage 

When energy storage system is considered, the energy storage cost should be added into the CAPC. Eq(17) is 

used to determine the corresponding molten salt storage tank capacity under a specified heliostat field area. 

CAPC=Cheliostat×Aheliostat+FCsolar+CSG×(Qabs,t)MAX+CAPCstorage+CAPCU (16) 

VH=max [(mH,in,1-mH,out,1), ∑(mH,in,h-mH,out,h),

2

h=1

∑(mH,in,h-mH,out,h),…, ∑(mH,in,h-mH,out,h)

24

h=1

3

h=1

] /ρ
ms
×φ (17) 

4. Case study 

A case study is presented in this section to illustrate the proposed method. Irradiation on an hourly basis is 

considered for a specific day in a typical summer month (Abikoye et al., 2019). The steam mains and demands 

are given in Table 1 and the hourly power demands are given in Table 2. Other parameters used in this study 

include: the price and heating value of natural gas are 0.8552 $/kg and 54.0 MJ/kg (Gutiérrez-Arriaga et al., 

2013); the temperatures of the molten salt at the inlet and outlet of the cavity receiver are 559 K and 838 K 

(Tehrani et al., 2016); Cheliostat CSG and CM are specified with 126 $/m2, 300 $/kWe and 0.012 $/kWh (Li et al., 

2019); the optical efficiency of heliostat field and burn efficiency of the boiler are set as 0.6 and 0.98. 

Table 1: Steam mains and demands data 

Steam main VHP HP MP LP 

Pressure(MPa) 10.1 2.06 0.41 0.27 

Temperature(℃) 539 333 186 150 

Demands(t/h) 30 60 40 50 

Table 2: Power demands data 

Time(h) 0 1 2 3 4 5 6 7 8 9 10 11 

Power 

demand (kW) 
15,075 15,237 15,412 15,745 15,970 15,969 16,370 15,172 12,360 11,615 12,974 14,060 

Time(h) 12 13 14 15 16 17 18 19 20 21 22 23 

Power 

demand(kW) 
14,554 15019 14,003 13,287 13,047 13,540 10,298 8,640 10,638 13,164 14,411 14,427 

For the solar thermal central receiver subsystem studied in this paper, two situations are investigated for 

comparative analysis. Energy storage is not considered in the first situation (Structure 1), so molten salt absorbs 

solar energy as heat transfer fluid and directly enters the steam generator as heat sources to produce steam in 

real time; the other structure contains an energy storage unit (Structure 2), and the molten salt is heated to the 

specified temperature in the cavity receiver and sent to the high-temperature storage tank firstly, then the stored 

molten salt can be assigned to the steam generator for steam generation according to the real-time fluctuating 

energy demand. Both structures are presented into MINLP models and solved using BARON in GAMS with 

near-optimal solutions obtained. 

Figure 2 shows the economic-environment multi-objective curves corresponding to the two structures. The left 

and right endpoints in the curve are calculated using the EI and TAC as the single objective function (the left 

endpoint of Structure 2 is omitted for reason of rationality). The intermediate points are obtained by taking equal 

step EI value as the upper boundary constraint and minimizing the TAC. It can be seen from Figure 2 that the 

two curves on the right side almost overlap with environmental constraints increasing. At this area, the energy 

storage unit in Structure 2 does not exist, and there is no obvious difference between Structure 1 and 2. The 

reason is that solar energy in this area can be fully utilized at any time of the day, so the energy storage unit 

has no extra contribution to the improvement of economic performance. With the decrease of EI constraints, the 

economic advantage of Structure 2 grows greater. 

Points with the same EI in both structures are selected (EI=1.17×106 Ec) to analyse the performance of the two 

systems within one day. Table 3 shows the economic comparison of these two structures, including TAC, CAPC, 

Aheliostat, CAPCstorage and OPEC. As it can be seen, the heliostat field area required for Structure 2 to achieve 

the same EI is greatly reduced, which leads to a significant reduction in capital cost. At the same time, the 

additional cost of energy storage is negligible, so the TAC of Structure 2 has been significantly reduced. Figure 

46



3a shows the hourly steam generation at the specified EI. Correspondingly, Figure 3b shows hourly steam 

generation for Structure 2 under the same EI. As indicated, in Structure 2, solar energy not only drives the utility 

system during periods of sufficient irradiation, but also generates low pressure steam by releasing energy stored 

in the energy storage unit during low irradiation periods to partially meet the steam demand. 

 

Figure 2: Pareto curves for structure 1 and Structure 2 

With the decrease of EI constraint, the scale of solar subsystem in Structure 1 must increase greatly to absorb 

sufficient solar energy during periods of low irradiation to meet the environmental constraints, however, the 

utilization of solar energy at noon is insufficient, leading a waste. This part of energy can be effectively stored 

and released when needed in Structure 2, which can effectively reduce the scale of solar thermal central receiver 

subsystem under the same EI, accordingly, the initial investment cost of equipment is reduced as well. 

Finally, the optimal design point is obtained on the multi-objective curve corresponding to Structure 2 (EI = 

5.98×106 Ec). Both TAC and EI take reasonable values at this point. The heliostat field area is 61.9 ha, and the 

required molten salt quality is 524.8 t. 

0 2 4 6 8 10 12 14 16 18 20 22 24
0

10

20

30

40

50

60

S
te

a
m

 G
e
n
e
ra

ti
o
n
(k

g
/s

)

Time（h）

 SolarLP
 SolarMP
 SolarVHP
 BoilerVHP

 
0 2 4 6 8 10 12 14 16 18 20 22 24

0

10

20

30

40

50

60

S
te

a
m

 G
e
n
e
ra

ti
o
n
(k

g
/s

)

Time（h）

 SolarLP
 SolarVHP
 BoilerVHP

 
 (a) Structure 1  (b) Structure 2 

Figure 3: Steam generation 

 

0.0 2.0E+06 4.0E+06 6.0E+06 8.0E+06 1.0E+07 1.2E+07
0.0

5.0E+07

1.0E+08

1.5E+08

2.0E+08

2.5E+08

3.0E+08

3.5E+08

4.0E+08

T
O

T
A

L
 A

N
N

U
A

L
 C

O
S

T
($

/y
e
a

r)

 STRUCTURE 1

(7.17E+06, 2.91E+08)

(5.98E+06, 2.36E+08)

ENVIRONMENTAL IMPACT(Ec)

 STRUCTURE 2

(7.17E+06, 2.05E+08)

   0             2×106         4×106        6×106         8×106        1×107      1.2×107 

(5.98×106, 2.36×108 ) 

(7.17×106, 2.05×108 ) 

(7.17×106, 2.91×108 ) 

4.0×108         

3.5×108     

3.0×108 

2.5×108  

2.0×108    

1.5×108 

1.0×108 

5.0×107 

0 

47



Table 3: Economic comparison between Structure 1 and Structure 2 

 TAC($/y) CAPC($) Aheliostat (ha) CAPstorage ($) OPEC($/y) 

Structure1 2.91 × 108 2.38 × 108 128.60 0 5.30 × 107 

Structure2 2.05 × 108 1.52 × 108 49.40 4.40 × 106 5.28 × 107 

5. Conclusions 

This paper has developed a multi-objective optimization method for a solar-assisted CHP system to realize the 

trade-off between the TAC and EI. Optimal structure of CHP system is designed considering the energy loss 

caused by fluctuation of energy demands and solar energy supply. The systems with and without energy storage 

units are both studied based on the method, with the operating strategy determined simultaneously according 

to the variation of solar irradiation and power demands. The multi-objective optimization is launched to 

investigate the influence of solar subsystem scale on TAC and EI of the overall system. Results show that 

energy storage units are necessary when there is greater demand for EI reduction, because they will help to 

reduce the cost of the system. But if the solar subsystem is in smaller scale, the two systems have almost the 

same performance in economic and environmental aspects. The optimal point is obtained by making a trade-

off between TAC and EI, where the values of TAC and EI are 2.36 × 108 $/y and 5.98 × 106 Ec. In the future, 

works will be aimed at optimal designs of the obtained system under uncertainty. 

Acknowledgements 

The authors gratefully acknowledge the financial support from “Natural Science Foundation of China” (No. 

21878034) and the Fundamental Research Funds for Central Universities of China (DUT18LAB11). 

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