# Financial Optimization of a Solar-Driven Organic Rankine Cycle

^{*}

## Abstract

**:**

^{2}collecting area and a 14 m

^{3}storage tank, while for the same design point the levelized cost of electricity is minimized at 0.0969 € kWh

^{−1}. The maximum net present value is 123 k€ and it is found for a 220-m

^{2}collecting area and a 14-m

^{3}storage tank volume. Moreover, the maximum system energy efficiency is found at 15.38%, and, in this case, the collecting area is 140 m

^{2}and the storage tank volume 12 m

^{3}. Lastly, a multi-objective optimization proved that the overall optimum case is for a 160-m

^{2}collecting area and a 14-m

^{3}storage tank.

## 1. Introduction

^{−1}. Bellos and Tzivanidis [11] examined the combinations of PTC with waste heat in an ORC. They found that the best working fluid is toluene and the system efficiency can range from 11.6% up to 19.7%. He et al. [12] investigated a system with PTC coupled to a regenerative ORC. They found that the system efficiency is close to 15%, and they studied the system parametrically. The main parameters of their work were the storage tank volume and the mass flow rate of the heat transfer fluid. Desai and Bandyopadhyay [13] compared the use of PTC and linear Fresnel reflectors (LFR) coupled to ORC. They studied different working fluids and they found the most suitable working fluids to be R113, isohexane, hexane, benzene and cyclohexane. They concluded that the system with PTC has higher efficiency, which is close to 20% and the LCOE is about 0.4 € kWh

^{−1}. At this point, it is important to explain that the LCOE is a critical parameter that shows how the real is the cost of the produced electricity. In the cases that the LCOE is lower than the electricity price, then the investment is viable. In cases with high LCOE, there is a need for a subsidy for creating a viable investment.

^{2}of PTC in order to feed a system with nominal power at 1 MW. The optimum ratio of the collecting area to storage tank volume was found at 80 m

^{2}/m

^{3}, and, for this case, the system efficiency is 13.46% and the payback period is at 9 years. Askari-Asli Ardeh et al. [15] examined a PTC with a V-shape cavity coupled to an ORC. They found that this unit is able to lead to a payback period lower than 9 years and to a system efficiency of about 25% in optimal design. Chacartegui et al. [16] investigated a system with PTC and ORC and they gave the emphasis in the storage system. They found that the toluene is the best working fluid which leads to an LCOE at 0.17 €·kWh

^{−1}. Casati et al. [17] performed a work about solar-driven ORC with different storage systems. They concluded that the use of storage is important and it has to be used in these systems. Moreover, their study case was for a system with 100 kW nominal power and 18% system efficiency. Bellos and Tzivanidis [18] studied the idea of using a nanofluids-based PTC in a solar-ORC. They found that toluene is the best organic fluid, while the thermal oil/CuO is the best nanofluid. The nanofluid-based system presents 20.1% system efficiency, which is 1.75% higher than the system with pure thermal oil in the solar field.

## 2. Material and Methods

#### 2.1. The Examined System

_{T}) is selected at 0.5 W m

^{−2}·K

^{−1}[21] and the specific mass flow rate in the PTC (m

_{col}/A

_{c}) is selected at 0.02 kg s

^{−1}·m

^{−2}[22]. The ORC operates with toluene as the working fluid, which is a proper selection for efficiency according to the literature [16,18,23]. The ORC is a regenerative cycle which includes a recuperator.

#### 2.1.1. Solar Field Modeling

_{th,col}) is calculated as below. This formula regards the EuroTrough module, which is assumed to be used in this work [24,25].

_{u}) is calculated as:

_{sol}) is given as:

_{th,col}) is defined as:

_{col,in}= T

_{st}) and the heat source temperature in the inlet HRS inlet is equal to the mean storage tank temperature (T

_{s,in}= T

_{st}). About the storage tank, the general energy balance is given as:

_{st}) can be expressed as:

_{loss}) are calculated as below:

#### 2.1.2. Organic Rankine Cycle Modeling

_{T}) is given as:

_{p}) is given below:

_{motor}) is selected at 80% in this work.

_{is},

_{T}) is selected at 85% [27] and its definition is given below. It has to be said that the selected value is a relatively high value and it corresponds to a well-designed expansion device in order to achieve high system efficiency.

_{el}) is given below:

_{g}) is selected at 98% and the mechanical efficiency (η

_{m}) at 99% which are reasonable values.

_{sys}) is defined as:

_{en-y}) is defined as below:

_{el}) and the yearly solar potential (E

_{sol}) are defined as:

#### 2.1.3. Financial Analysis Formulation

_{0}) is calculated as:

_{O&M}) is estimated as 1% of the capital cost:

#### 2.2. Procedure Description

_{c}) and the storage tank volume (V). Table 3 includes data about the optimization variables. The collecting area is studied from 100 up to 300 m

^{2}with a step of 20 m

^{2}, while the storage tank volume from 10 up to 30 m

^{3}with a step of 2 m

^{3}. In total, 121 cases are examined by investigating all the possible combinations of collecting areas and storage tank volumes. These 121 cases are evaluated with different criteria, and, in every case, the optimum case is selected. This is a simple optimization procedure methodology but it easy to be done due to the use of only two optimization variables and to the low computational cost of every run. The optimization goals of this work are the following: the maximization of the NPV, the minimization of the payback period, the minimization of the LCOE and the maximization of the yearly energy efficiency. In every case, only one goal is used and so this work includes single-objective optimization results.

## 3. Results and Discussion

#### 3.1. Parametric Analysis

#### 3.1.1. Energy Analysis

^{2}, the increasing trend of the curves reduces. Moreover, the curves for storage tanks between 16 and 30 m

^{3}are extremely close to each other, while for smaller tanks the electricity production is generally lower. Another interesting result is that for small collecting areas, the optimum storage tanks are smaller. More specifically, Figure 2b indicates that for collecting areas of 100 and 120 m

^{2}, the optimum storage tank is the smallest examined (10 m

^{3}), while for higher collecting areas, the optimum volume increases. The results indicate that the optimum storage tank volumes generally range from 12 up to 16 m

^{3}in order to have the maximum electricity production. The yearly production of electricity can reach up to 52.16 MWh for a 300-m

^{2}collecting area and a 30-m

^{3}storage tank volume, which indicates a system that operates about 60% of the year.

^{2}. The maximum yearly system efficiency is 15.38% and it is found for a 140-m

^{2}collecting area and a 12-m

^{3}storage tank volume.

^{3}. However, for the storage tanks of 100 and 120 m

^{2}, the tank volume is the minimum examined of 10 m

^{3}. At this point, it is critical to state that, in this work, the optimum collecting area for the smallest examined volumes is lower than 100 m

^{2}and thus some curves have different shapes in the examined range. However, this fact does not play any role in the overall optimum choice because the optimum designs are included in the examined ranges of collecting areas and storage tank volumes.

#### 3.1.2. Financial Analysis

^{2}. The overall maximum NPV is 15.71 k€ and it is found for a 220-m

^{2}collecting area and a 14-m

^{3}storage tank volume. Figure 4b indicates that the optimum storage tank volume is up to 14 m

^{3}. Generally, it has to be said that higher collecting leads to higher electricity production, but, after a limit, the gain in electricity is not so high for counterbalance the extra cost.

^{2}. For greater collecting areas, the LCOE increases and so the investment viability does not increase. The optimum storage tanks are about 12 to 14 m

^{3}. The minimum LCOE is 0.0969 € kWh

^{−1}and it is found for a 14-m

^{3}storage tank volume and a 160-m

^{2}collecting area. Higher tank volumes are not beneficial for the investments and this fact has to be taken into account when these systems are designed. Generally, the LCOE has reasonable values that are lower than the electricity price. Thus, the investment of the solar-driven ORC is viable.

^{3}storage tank volume and a 160-m

^{2}collecting area.

#### 3.2. Optimization Results

^{2}collecting area and a 12-m

^{3}storage tank volume. In this case, the yearly electricity production is 38917 kWh, the payback period is 8.58 years, the yearly solar collector efficiency 52.22%, the LCOE is 0.0989 € kWh

^{−1}and the NPV is 102.63 k€. Moreover, Table 5 proves that the overall minimum payback period is 8.37 years and it is found for a 160-m

^{2}collecting area and a 14-m

^{3}storage tank volume. In this case, the yearly electricity production is 43328 kWh, the yearly energy efficiency is 14.99%, the yearly solar collector efficiency 50.68%, the LCOE is 0.0969 € kWh

^{−1}and the NPV is 116.29 k€. Furthermore, Table 6 shows that the overall maximum net present value is 123.21 k€ and it is found for a 220-m

^{2}collecting area and a 14-m

^{3}storage tank volume. In this case, the yearly electricity production is 48275 kWh, the yearly energy efficiency is 12.14%, the yearly solar collector efficiency 40.77%, the LCOE is 0.1025 € kWh

^{−1}and the payback period 8.96 years.

^{2}collecting area and a 14-m

^{3}storage tank. This design is the one that has been found to be the best one for minimizing both the payback period and the LCOE. Thus, it can be said that this design can be adopted as the overall optimum case for the present system. At this point, it is interesting to state that the found values of the LCOE are around 0.1 €/kWh. In the literature, the reported values are generally higher and thus this work shows that the optimization is able to significantly reduce the LCOE. More specifically, Astolfi et al. [11] found the LCOE to range from 0.145 up to 0.280 € kWh

^{−1}, Desai and Bandyopadhyay [13] found the LCOE around 0.4 € kWh

^{−1}and Chacartegui et al. [16] calculated the LCOE at 0.17 € kWh

^{−1}. So, this work has to add to the literature promising results about the financial viability of the solar-driven ORC technology.

^{2}/m

^{3}in the overall optimum case. This value is different compared to another previous study of the same research team where this ratio was found 80 m

^{2}/m

^{3}[15]. There are many reasons for this difference in the found values. First of all, in the present work, the cost of the electricity price is higher than the other study due to the respective difference in the legislation. Moreover, there are different weather data between these studies. This work uses 12 typical days for simulation all the year, while the analysis of Ref. [15] used four typical days. Moreover, there are some different points in the design of the ORC and of the storage tank modeling that can lead to different results.

#### 3.3. Monthly Analysis

^{2}leads to the same electricity production because both areas are enough for operation during all the days due to the over-sizing of the system this month. However, this over-sizing is valid only for summer and not for the winter period, so, overall, the system is not oversized.

## 4. Conclusions

- The maximum system energy efficiency is found at 15.38%, and, in this case, the collecting area is 140 m
^{2}and the storage tank volume is 12 m^{3}. - The maximum net present value is 123 k€ and is found for a 220-m
^{2}collecting area and a 14-m^{3}storage tank volume. - The minimum payback period is 8.37 years and is found for a 160-m
^{2}collecting area and a 14-m^{3}storage tank, while, for the same design point, the levelized cost of electricity is minimized at 0.0969 € kWh^{−1}. - The multi-objective optimization procedure proved that the optimum design is for a 160-m
^{2}collecting area and a 14-m^{3}storage tank. Moreover, this design point is the optimum according to the payback period minimization and LCOR minimization criteria. Thus, this design is selected as the overall optimum choice. - The monthly analysis indicates that higher electricity is produced during the summer and especially in July and in August. Moreover, the use of higher collecting areas leads to significant enhancement in electricity production, mainly in the winter period.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

A_{c} | Collecting area, m^{2} |

A_{T} | Storage tank outer area, m^{3} |

c_{p} | Specific heat capacity, kJ kg^{−1} K^{−1} |

C_{0} | Capital cost, € |

CF | Hourly cash flow, € h^{−1} |

E | Yearly energy quantity, kWh |

F | Objective function of dimensionless distance, - |

G_{b} | Solar direct beam irradiation, W·m^{−2} |

i | Counter, - |

h | Specific enthalpy, kJ kg^{−1} |

K | Incident angle modifier, - |

K_{col} | Specific collector cost, € m^{−2} |

K_{el} | Electricity cost, € kWh_{el}^{−1} |

K_{orc} | Specific cost of the organic Rankine cycle, € kW_{el}^{−1} |

K_{O&M} | Yearly operating and maintenance cost, € |

K_{tank} | Specific cost of the storage tank, € m^{−3} |

LCOE | Levelized cost of electricity, € kW_{el}^{−1} |

m | Mass flow rate, kg s^{−1} |

N | Project life, years |

NPV | Net present value, k€ |

P | Pressure, bar |

P_{el} | Net electricity production, kW |

PP_{hrs} | Pinch Point, °C |

PP | Payback Period, years |

Q | Heat rate, kW |

Q_{out} | Heat rejection to the ambient, kW |

r | Discount factor, % |

R | Equivalent investment time, years |

SD | Sunny days, days |

SPP | Simple Payback Period, years |

t | Time, hours |

T | Temperature, °C |

T_{am} | Ambient temperature, °C |

U_{T} | Thermal loss coefficient of the tank, W m^{−2}·K^{−1} |

V | Storage tank volume, m^{3} |

W_{p} | Pumping work, kW |

W_{T} | Turbine work production, kW |

## Greek Symbols

ΔP | Pressure difference, bar |

ΔΤ_{sh} | Superheating degree in the turbine inlet, °C |

ΔT_{rc} | Temperature difference in the recuperator, °C |

η_{en} | Instantaneous energy efficiency, - |

η_{en-y} | Yearly energy efficiency, - |

η_{is,T} | Isentropic efficiency of the turbine, - |

η_{g} | Generator efficiency, - |

η_{m} | Mechanical efficiency, - |

η_{motor} | Motor efficiency, - |

η_{orc} | Efficiency of the power block, - |

η_{th,col} | Collector thermal efficiency, - |

θ | Incident solar angle on the collector aperture, ° |

ρ | Density, kg m^{−3} |

## Subscripts and Superscripts

col | Collector |

col,in | Collector inlet |

col,out | Collector outlet |

con | Condenser |

is | Isentropic |

in | Inlet |

hrs | Heat recovery system |

loss | Thermal losses in the tank |

max | Maximum |

min | Minimum |

opt | Optimum |

orc | Fluid in the organic Rankine cycle |

out | Outlet |

s | Heat source |

s,in | Heat source inlet |

s,out | Heat source outlet |

sat | Saturation in the heat recovery system |

sol | Solar |

st | Storage tank |

T | Turbine |

u | Useful |

## Abbreviations

CSP | Concentrating Solar Power |

EES | Engineering Equation Solver |

HRS | Heat Recovery System |

ORC | Organic Rankine Cycle |

PTC | Parabolic Trough Collector |

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**Figure 1.**The examined solar-driven organic Rankine cycle (Parabolic trough solar collector (PTC), tank, organic Rankine cycle (ORC)).

**Figure 2.**Electrical production (

**a**) for different collecting areas with the storage tank volume as the main parameter (

**b**) for different storage tank volumes with the collecting area as the main parameter.

**Figure 3.**System efficiency (

**a**) for different collecting areas with the storage tank volume as the main parameter (

**b**) for different storage tank volumes with the collecting area as the main parameter.

**Figure 4.**Net present value (

**a**) for different collecting areas with the storage tank volume as the main parameter (

**b**) for different storage tank volumes with the collecting area as the main parameter.

**Figure 5.**Levelized cost of electricity (

**a**) for different collecting areas with the storage tank volume as the main parameter (

**b**) for different storage tank volumes with the collecting area as the main parameter.

**Figure 6.**Payback period (

**a**) for different collecting areas with the storage tank volume as the main parameter (

**b**) for different storage tank volumes with the collecting area as the main parameter.

**Figure 7.**Simple payback period (

**a**) for different collecting areas with the storage tank volume as the main parameter (

**b**) for different storage tank volumes with the collecting area as the main parameter.

**Figure 8.**Pareto-front and multi-objective optimization depiction with the system efficiency and the net present value as the optimization goals. (The black points are the side points, the green point is the ideal point and the blue point is the optimum point).

**Figure 9.**Monthly electrical production for optimum cases (A

_{c}= 140 m

^{2}− V = 12 m

^{3}, A

_{c}= 160 m

^{2}− V = 14 m

^{3}, A

_{c}= 220 m

^{2}− V = 14 m

^{3}).

**Figure 10.**Monthly system efficiency for optimum cases (A

_{c}= 140 m

^{2}− V = 12 m

^{3}, A

_{c}= 160 m

^{2}− V = 14 m

^{3}, A

_{c}= 220 m

^{2}− V = 14 m

^{3}).

**Figure 11.**Monthly collector efficiency for optimum cases (A

_{c}= 140 m

^{2}− V = 12 m

^{3}, A

_{c}= 160 m

^{2}− V = 14 m

^{3}, A

_{c}= 220 m

^{2}− V = 14 m

^{3}).

Parameters | Symbols | Values |
---|---|---|

Electricity cost | (K_{el}) | 0.28485 € kWh_{el}^{−1} |

PTC specific cost | (K_{col}) | 250 € m^{−2} |

Tank specific cost | (K_{tank}) | 1000 € m^{−3} |

ORC specific cost | (K_{orc}) | 3000 € kW_{el}^{−1} |

Project life | (N) | 25 years |

Discount factor | (r) | 3% |

Equivalent project years | (R) | 17.41 |

Operation and maintenance cost | (K_{O&M}) | 1% of the capital cost |

Parameters | Symbols | Values |
---|---|---|

Nominal power production | (P_{el}) | 10 kW |

Pressure level in the turbine inlet | (P_{4}) | 37.14 bar |

Pressure level in the turbine outlet | (P_{3}) | 0.079 bar |

Superheating in the turbine inlet | (ΔT_{sh}) | 20 °C |

Condenser temperature level | (T_{con}) | 40 °C |

Saturation temperature in the HRS | (T_{sat}) | 309.7 °C |

Motor efficiency | (η_{motor}) | 80% |

Turbine isentropic efficiency | (η_{is,T}) | 85% |

Electrical generator efficiency | (η_{g}) | 98% |

Mechanical efficiency | (η_{m}) | 99% |

Recuperator temperature difference | (ΔT_{rec}) | 10 °C |

Pinch point in the HRS | (PP_{hrs}) | 5 °C |

ORC efficiency | (η_{orc}) | 32.52% |

Inlet oil temperature in the HRS | (T_{s,in}) | 334.7 °C |

Outlet oil temperature in the HRS | (T_{s,out}) | 204.6 °C |

Parameters | Symbols | Values | ||
---|---|---|---|---|

Minimum | Maximum | Step | ||

Collecting area | A_{c} (m^{2}) | 100 | 300 | 20 |

Storage tank volume | V (m^{3}) | 10 | 30 | 2 |

**Table 4.**Optimum collecting areas for different storage tank volumes for maximizing energy efficiency.

V | A_{c,opt} | E_{el} | η_{en-y} | η_{th,col} | PP | LCOE | NPV |
---|---|---|---|---|---|---|---|

(m^{3}) | (m^{2}) | (kWh) | (-) | (-) | (years) | (€ kWh^{−1}) | (k€) |

10 | 120 | 33,022 | 15.23% | 52.14% | 9.34 | 0.1060 | 81.61 |

12 | 140 | 38,917 | 15.38% | 52.22% | 8.58 | 0.0989 | 102.63 |

14 | 140 | 38,888 | 15.37% | 52.41% | 8.86 | 0.1016 | 100.14 |

16 | 140 | 38,835 | 15.35% | 52.55% | 9.15 | 0.1043 | 97.52 |

18 | 140 | 38,769 | 15.32% | 52.65% | 9.45 | 0.1070 | 94.85 |

20 | 140 | 38,694 | 15.29% | 52.74% | 9.76 | 0.1098 | 92.12 |

22 | 140 | 38,615 | 15.26% | 52.81% | 10.08 | 0.1126 | 89.39 |

24 | 140 | 38,532 | 15.23% | 52.87% | 10.40 | 0.1155 | 86.62 |

26 | 140 | 38,447 | 15.20% | 52.92% | 10.73 | 0.1183 | 83.86 |

28 | 140 | 38,365 | 15.16% | 52.96% | 11.07 | 0.1212 | 81.10 |

30 | 140 | 38,282 | 15.13% | 52.99% | 11.41 | 0.1241 | 78.34 |

**Table 5.**Optimum collecting areas for different storage tank volumes for minimizing the payback period.

V | A_{c,opt} | E_{el} | η_{en-y} | η_{th,col} | PP | LCOE | NPV |
---|---|---|---|---|---|---|---|

(m^{3}) | (m^{2}) | (kWh) | (-) | (-) | (years) | (€ kWh^{−1}) | (k€) |

10 | 140 | 37,620 | 14.87% | 50.38% | 8.66 | 0.0997 | 98.54 |

12 | 160 | 41,954 | 14.51% | 48.99% | 8.45 | 0.0977 | 111.82 |

14 | 160 | 43,328 | 14.99% | 50.68% | 8.37 | 0.0969 | 116.29 |

16 | 160 | 43,306 | 14.98% | 50.92% | 8.62 | 0.0993 | 113.83 |

18 | 160 | 43,265 | 14.96% | 51.07% | 8.87 | 0.1017 | 111.28 |

20 | 160 | 43,216 | 14.95% | 51.59% | 9.13 | 0.1041 | 108.69 |

22 | 180 | 45,537 | 14.00% | 48.02% | 9.39 | 0.1065 | 111.98 |

24 | 180 | 45,501 | 13.99% | 48.51% | 9.65 | 0.1088 | 109.45 |

26 | 180 | 45,461 | 13.98% | 48.77% | 9.90 | 0.1111 | 106.91 |

28 | 180 | 45,423 | 13.96% | 49.17% | 10.16 | 0.1134 | 104.37 |

30 | 180 | 45,386 | 13.95% | 49.67% | 10.42 | 0.1157 | 101.83 |

**Table 6.**Optimum collecting areas for different storage tank volumes for maximizing the net present value.

V | A_{c,opt} | E_{el} | η_{en-y} | η_{th,col} | PP | LCOE | NPV |
---|---|---|---|---|---|---|---|

(m^{3}) | (m^{2}) | (kWh) | (-) | (-) | (years) | (€ kWh^{−1}) | (k€) |

10 | 180 | 41,023 | 12.61% | 42.47% | 9.08 | 0.1036 | 103.68 |

12 | 200 | 45,022 | 12.46% | 41.86% | 8.92 | 0.1022 | 115.30 |

14 | 220 | 48,275 | 12.14% | 40.77% | 8.96 | 0.1025 | 123.21 |

16 | 220 | 48,653 | 12.24% | 41.23% | 9.10 | 0.1038 | 122.74 |

18 | 240 | 49,851 | 11.49% | 38.81% | 9.60 | 0.1083 | 120.46 |

20 | 240 | 49,845 | 11.49% | 38.93% | 9.82 | 0.1103 | 118.09 |

22 | 240 | 49,835 | 11.49% | 39.05% | 10.05 | 0.1123 | 115.69 |

24 | 240 | 49,822 | 11.49% | 39.15% | 10.28 | 0.1144 | 113.27 |

26 | 240 | 49,806 | 11.48% | 39.25% | 10.51 | 0.1164 | 110.85 |

28 | 240 | 49,788 | 11.48% | 39.34% | 10.75 | 0.1185 | 108.41 |

30 | 240 | 49,770 | 11.48% | 39.43% | 10.99 | 0.1205 | 105.97 |

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## Share and Cite

**MDPI and ACS Style**

Bellos, E.; Tzivanidis, C.
Financial Optimization of a Solar-Driven Organic Rankine Cycle. *Appl. Syst. Innov.* **2020**, *3*, 23.
https://doi.org/10.3390/asi3020023

**AMA Style**

Bellos E, Tzivanidis C.
Financial Optimization of a Solar-Driven Organic Rankine Cycle. *Applied System Innovation*. 2020; 3(2):23.
https://doi.org/10.3390/asi3020023

**Chicago/Turabian Style**

Bellos, Evangelos, and Christos Tzivanidis.
2020. "Financial Optimization of a Solar-Driven Organic Rankine Cycle" *Applied System Innovation* 3, no. 2: 23.
https://doi.org/10.3390/asi3020023