# Integrated Economic Optimization of Hybrid Thermosolar Concentrating System Based on Exact Mathematical Method

## Abstract

**:**

## 1. Introduction

## 2. Literature for Hybrid Thermosolar Systems and EDC Optimization

_{2}emissions is tackled in many articles in the literature [15,16]. The transition towards sustainable energy systems includes the development of new technologies for energy generation, from fossil-based to zero-carbon, which reduce CO

_{2}emissions and limit global warming effects and develop new power plants based on RES [17,18,19].

_{2}emission. The management and scheduling of electric energy consumption for controllable heating, and the amounts received from sun and wind, are studied in [26]. The aim is an efficient integration of RES, for the better energy management, to reduce the costs, and emissions. Electricity bill reduction can be realized by installing a management controller which implements the hybrid algorithms for integrating RES, scheduling the power consumption, and shifting the load demand from high to low-peak hours.

_{2}emissions, shows that under certain conditions, this installation is profitable.

## 3. Economic Dispatch and Commitment Optimization of Hybrid Thermosolar System

#### 3.1. External Data

#### 3.2. Generation Constraints

#### 3.3. The Objective Function

#### 3.4. Thermal Energy System

#### 3.5. Solar Energy System

^{2}), (Figure 1), and ${P}_{sk}(I)$ is the function of solar irradiation conversion to electric power of the SC unit $k$ from the CSP system, given by:

^{2}, ${I}_{C}$ is a cut-off irradiation level set at a maximum value of the considered SC 1500 W/m

^{2}, ${P}_{sk,\mathrm{max}}$ is the equivalent power output corresponding to ${I}_{C}$, or the available maximum active power generated by solar unit $k$, and ${P}_{sr}$ the rated equivalent power output of the SC, which depends on efficiency $\eta $, area $S$ of the considered SC, and per unit base value ${P}_{sro}$:

#### 3.6. Solution

- Fixed data for generating units: characteristics of heat rates, number and rates of thermal units, prices of fuels, power bounds constraints, solar irradiation data, and load demand data.
- Parameter for accuracy of the results is the size of increment $\Delta \lambda $.

## 4. Study Case: Thermosolar System in North-West Greece

## 5. Results, Discussion

_{2}emissions.

_{2}emissions.

## 6. Conclusions

_{2}emissions were diminished.

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

Thermal Units | ${\mathit{P}}_{\mathit{i},\mathbf{min}}$ (MW) | ${\mathit{P}}_{\mathit{i},\mathbf{max}}$ (MW) | Heat Consumption Rates | Locations | ||
---|---|---|---|---|---|---|

${\mathit{H}}_{\mathit{i},2}$ | ${\mathit{H}}_{\mathit{i},1}$ | ${\mathit{H}}_{\mathit{i},0}$ | ||||

Th1 | 28 | 70 | 0.005102 | 1.7286 | 12.80 | Ptolemaida I |

Th2 | 120 | 300 | 0.000254 | 1.6410 | 44.19 | Ptolemaida IV |

Th3 | 120 | 300 | 0.001217 | 1.3095 | 73.20 | Kardia III–IV |

Th4 | 120 | 300 | 0.000254 | 1.6410 | 44.19 | Kardia I–II |

Th5 | 170 | 300 | 0.000222 | 1.7318 | 30.99 | Agios Dimitrios I–II |

Th6 | 170 | 310 | 0.000399 | 1.6253 | 42.47 | Agios Dimitrios III–IV |

Th7 | 170 | 300 | 0.000622 | 1.5386 | 49.49 | Amidaio I–II |

Totals | 898 | 1880 |

Technology | Hybrid, Parabolic Trough |

Power Cycle | Steam Rankine |

Nominal Capacity (MW) | 22.5 |

Turbine efficiency % | 37 |

Expected Generation (GWh/year) | 44.1 |

Latitude/Longitude Location (^{o}) | 41.529/0.8 |

Solar Field Aperture Area (m^{2}) | 183120 |

Number of Solar Collector Assemblies (SCAs) | 336 |

Number of Loops | 56 |

Number of SCAs per Loop | 6 |

Number of Modules per SCA | 8 |

SCA Aperture Area (m^{2}) | 545 |

SCA Length (m) | 96 |

Total Construction Cost (2012) M EUR | 149.94 |

Total Cost (2020) M EUR | 211.67 |

Specific Cost (2020) EUR/kW | 9407.41 |

Remuneration EUR/kWh | 0.27 |

Remuneration Start Year | 2012 |

Remuneration Deflated (2020) EUR/kWh | 0.37 |

PPA or Tariff Period (Years) | 25 |

Operation and Maintenance O/M (%) (% of investment cost per year) | 1.5 |

Levelized Cost of Electricity (2020) EUR/kWh (LCOE with 5% weighted average cost of capital and 25-year payback period) | 0.41 |

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**Figure 1.**Solar Clear-sky irradiance, on a 2-axis tracking plane, in the month of July, at Ptolemaida, NW Greece, latitude/longitude: 40.463/21.762, during 24 h.

**Figure 4.**Convergence from unconstrained optimal cost to constrained optimal cost for the thermal units Th1–Th7 from northwest Greece over 24 h. The unconstrained minimal cost powers (blue o), the constrained minimal cost powers (magenta ∇), and the generated reserves of power (green*) are shown versus $\lambda $. Over 24 h, small displacements of unconstrained optimal $\lambda $, are varying from ${\lambda}_{1}$ = 176.95 to ${\lambda}_{1}$ = 176.18, and of constrained optimal ${\lambda}_{\lambda}$ are varying from ${\lambda}_{\lambda}$ = 175.95 to ${\lambda}_{\lambda}$ = 174.71.

**Figure 5.**Constrained minimal cost generated powers [${P}_{\lambda}$] by thermal units Th1–Th7 and solar power CSP unit from ${\lambda}_{\lambda}$ = 175.95 to ${\lambda}_{\lambda}$ = 174.71, over 24 h. The outputs of Th2 and Th4 are equal (shown superposed). The outputs of Th5 and Th6 are equal as well (superposed). The output of Th7 is equal to Th5 and Th6 between hours 6:45–17:45 (partly superposed).

**Figure 6.**(

**a**) Scenario 1: Total unconstrained minimal costs of seven thermal units and CSP over 24 h (CSP enabled); (

**b**) Scenario 1: Total constrained minimal costs of seven thermal units and CSP over 24 h (CSP enabled).

**Figure 7.**(

**a**) Scenario 2: Total unconstrained minimal costs of seven thermal units over 24 h (CSP disabled); (

**b**) Scenario 2: Total constrained minimal costs of seven thermal units over 24 h (CSP disabled).

**Figure 8.**Scenario 1: The balance of generated powers of optimally constrained hybrid thermosolar system, of generated reserves, with total varying electrical load, during 24 h (CSP enabled).

**Figure 9.**Balance of powers in Scenario 1 (hybrid system with CSP enabled) and Scenario 2 (thermal system with CSP disabled), during 24 h.

Thermal Units | Scenario 1 CSP Enabled | Scenario 2 CSP Disabled | Differences: Scenario 1–Scenario 2 | |||||
---|---|---|---|---|---|---|---|---|

Constraints—Boundary Values | Total Generated Energy (MWh) | Total Operational Costs (EUR) | Constraints—Boundary Values | Total Generated Energy (MWh) | Total Operational Costs (EUR) | Total Generated Energy (MWh) | Total Operational Costs (EUR) | |

${\mathit{E}}_{\mathit{i}}$ | ${\mathit{F}}_{\mathit{i}}$ | ${\mathit{E}}_{\mathit{i},\mathit{r}\mathit{e}\mathit{f}}$ | ${\mathit{F}}_{\mathit{i},\mathit{r}\mathit{e}\mathit{f}}$ | ${\mathit{E}}_{\mathit{i}}-{\mathit{E}}_{\mathit{i},\mathit{r}\mathit{e}\mathit{f}}$ | ${\mathit{F}}_{\mathit{i}}-{\mathit{F}}_{\mathit{i},\mathit{r}\mathit{e}\mathit{f}}$ | |||

Th1 | ${P}_{1}={P}_{1,\mathrm{min}}$ | 672.00 | 156,480 | ${P}_{1}={P}_{1,\mathrm{min}}$ | 672.00 | 156,480 | 0 | 0 |

Th2 | ${P}_{2,\mathrm{min}}\le {P}_{2}\le {P}_{2,\mathrm{max}}$ | 5321.77 | 1,009,361 | ${P}_{2,\mathrm{min}}\le {P}_{2}\le {P}_{2,\mathrm{max}}$ | 5606.49 | 1,059,295 | −284.73 | −49,934 |

Th3 | ${P}_{3,\mathrm{min}}\le {P}_{3}\le {P}_{3,\mathrm{max}}$ | 4378.62 | 846,277 | ${P}_{3,\mathrm{min}}\le {P}_{3}\le {P}_{3,\mathrm{max}}$ | 4437.97 | 856,686 | −59.35 | −10,409 |

Th4 | ${P}_{4,\mathrm{min}}\le {P}_{4}\le {P}_{4,\mathrm{max}}$ | 5321.77 | 1,009,361 | ${P}_{4,\mathrm{min}}\le {P}_{4}\le {P}_{4,\mathrm{max}}$ | 5606.49 | 1,059,295 | −284.73 | −49,934 |

Th5 | ${P}_{5}={P}_{5,\mathrm{min}}$ | 4080.00 | 796,330 | ${P}_{5}={P}_{5,\mathrm{min}}$ | 4080.00 | 796,330 | 0 | 0 |

Th6 | ${P}_{6}={P}_{6,\mathrm{min}}$ | 4080.00 | 792,694 | ${P}_{6}={P}_{6,\mathrm{min}}$ | 4080.00 | 792,694 | 0 | 0 |

Th7 | 0:45–6:45 and 17:45–23:45: ${P}_{7,\mathrm{min}}\le {P}_{7}\le {P}_{7,\mathrm{max}}$ 6:45–17:45: ${P}_{7}={P}_{7,\mathrm{min}}$ | 4170.17 | 805,430 | ${P}_{7,\mathrm{min}}\le {P}_{7}\le {P}_{7,\mathrm{max}}$ | 4265.17 | 822,102 | −95.00 | −16,673 |

CSP | - | 731.34 | 255,969 | - | 0 | 0 | 731.34 | 255,969 |

Totals | 28,755.67 | 5,671,901 | 28,748.13 | 5,542,882 | 7.54 | 129,019 |

Thermal Units | Scenario 1 CSP Enabled | Scenario 2 CSP Disabled | Differences Scenario 1–Scenario 2 | |||
---|---|---|---|---|---|---|

Mean Operational Costs per 1 MWh (EUR/MWh) | Mean Operational Costs per 1 MW (EUR/MW) | Mean Operational Costs per MWh (EUR/MWh) | Mean Operational Costs per 1 MW (EUR/MW) | Mean Operational Costs per MWh (EUR/MWh) | Mean Operational Costs per 1 MW (EUR/MW) | |

${\mathit{F}}_{\mathit{i}}/{\mathit{E}}_{\mathit{i}}$ | ${\mathit{F}}_{\mathit{i}}/{\mathit{E}}_{\mathit{i}}/\mathit{h}$ | ${\mathit{F}}_{\mathit{i},\mathit{r}\mathit{e}\mathit{f}}/{\mathit{E}}_{\mathit{i},\mathit{r}\mathit{e}\mathit{f}}$ | ${\mathit{F}}_{\mathit{i},\mathit{r}\mathit{e}\mathit{f}}/{\mathit{E}}_{\mathit{i},\mathit{r}\mathit{e}\mathit{f}}/\mathit{h}$ | ${\mathit{F}}_{\mathit{i}}/{\mathit{E}}_{\mathit{i}}-{\mathit{F}}_{\mathit{i},\mathit{r}\mathit{e}\mathit{f}}/{\mathit{E}}_{\mathit{i},\mathit{r}\mathit{e}\mathit{f}}$ | ${\mathit{F}}_{\mathit{i}}/{\mathit{E}}_{\mathit{i}}/\mathit{h}-{\mathit{F}}_{\mathit{i},\mathit{r}\mathit{e}\mathit{f}}/{\mathit{E}}_{\mathit{i},\mathit{r}\mathit{e}\mathit{f}}/\mathit{h}$ | |

Th1 | 232.86 | 9.70 | 232.86 | 9.70 | 0 | 0 |

Th2 | 189.67 | 7.90 | 188.94 | 7.87 | 0.73 | 0.03 |

Th3 | 193.27 | 8.05 | 193.04 | 8.04 | 0.24 | 0.01 |

Th4 | 189.67 | 7.90 | 188.94 | 7.87 | 0.73 | 0.03 |

Th5 | 195.18 | 8.13 | 195.18 | 8.13 | 0 | 0 |

Th6 | 194.29 | 8.10 | 194.29 | 8.10 | 0 | 0 |

Th7 | 193.14 | 8.05 | 192.75 | 8.03 | 0.39 | 0.02 |

CSP | 350.00 | 14.58 | 0 | 0 | 350.00 | 14.58 |

Totals | 197.24 | 8.22 | 192.81 | 8.03 | 4.44 | 0.18 |

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Papazis, S.A.
Integrated Economic Optimization of Hybrid Thermosolar Concentrating System Based on Exact Mathematical Method. *Energies* **2022**, *15*, 7019.
https://doi.org/10.3390/en15197019

**AMA Style**

Papazis SA.
Integrated Economic Optimization of Hybrid Thermosolar Concentrating System Based on Exact Mathematical Method. *Energies*. 2022; 15(19):7019.
https://doi.org/10.3390/en15197019

**Chicago/Turabian Style**

Papazis, Stylianos A.
2022. "Integrated Economic Optimization of Hybrid Thermosolar Concentrating System Based on Exact Mathematical Method" *Energies* 15, no. 19: 7019.
https://doi.org/10.3390/en15197019