#
Thermoeconomic Modeling and Parametric Study of a Photovoltaic-Assisted 1 MW_{e} Combined Cooling, Heating, and Power System

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## Abstract

**:**

_{e}. The nominal power output of the PV subsystem is examined in a parametric study, ranging from 0 to 600 kW

_{e}, to investigate which configuration results in a minimum lifecycle cost (LCC) for a system lifetime of 20 years of service. The load profile considered is applied for a complex of households in Nicosia, Cyprus. The solar data for the PV subsystem are taken on an hourly basis for a whole year. The results suggest that apart from economic benefits, the proposed system also results in high efficiency and reduced CO

_{2}emissions. The parametric study shows that the optimum PV capacity is 300 kW

_{e}. The minimum lifecycle cost for the PV-assisted CCHP system is found to be 3.509 million €, as compared to 3.577 million € for a system without a PV subsystem. The total cost for the PV subsystem is 547,445 €, while the total cost for operating the system (fuel) is 731,814 € (compared to 952,201 € for a CCHP system without PVs). Overall, the proposed system generates a total electrical energy output of 52,433 MWh (during its whole lifetime), which translates to a unit cost of electricity of 0.067 €/kWh.

## 1. Introduction

_{2}emissions) [6]. However, rigorous design considerations have to be made to achieve high system efficiency at minimum lifecycle cost (LCC). Cogeneration can have various applications, which can typically combine the generation of power, heating and cooling. In climates which require both space heating and space cooling in different periods of the year, a promising application of cogeneration is combined cooling, heating, and power (CCHP). Therefore, CCHP systems can be considered as alternatives to large-scale, electricity-only generating power plants, to improve fuel efficiency by recovering the rejected heat from the thermal cycle for district heating and district cooling. Although such a system can be applied in various scales, configurations and capacities, an interesting application is in small-scale, decentralized, completely autonomous systems. These distributed energy systems operate with minimum losses, due to their proximity with the serviced buildings. They typically range from 1 to 10 MW

_{e}and can provide power, space heating, domestic hot water and space cooling. Heating, or cooling, can be provided with a simple district energy network connecting the consumption site with the CCHP system. Since heating and cooling loads do not generally coincide, the same district network can be used in the summer to distribute cooling, produced by thermally activated absorption chillers, also located within the CCHP system [5,7].

_{e}), to investigate the feasibility of such systems to penetrate the energy market in countries with hot climates requiring both cooling and heating energy [5,7]. In this study a PV-assisted 1 MW

_{e}CCHP system is considered for application in a hot climatic region, where the system is assumed to be located far from existing central power plants, e.g., to fulfill the energy needs of a remote community. An interesting aspect in terms of fueling could be liquefied natural gas (LNG), which is readily available in different areas of the world. However, it should be noted that the system is not restricted to the use of LNG, and most conventional hydrocarbons could be used to fuel the CCHP system. In this study, a PV subsystem is considered for operation along with the CCHP system, in the vicinity of the latter, to reduce fuel consumption when solar energy is available. The capacity of the integrated units (i.e., available heating and cooling) will vary according to the operating scheme of the gas turbine cycle. The absorption chiller unit is assumed to be of the double-effect LiBr-H

_{2}O type. Therefore, this research work investigates the above options and modifications to quantify and analyze the thermoeconomic performance of the proposed system.

## 2. System Configuration

_{2}O absorption chiller. The produced cooling energy is distributed to nearby buildings by means of a district energy network. During winter operation, the heat is recovered by HEx 3 and distributed to the buildings with the district energy network.

## 3. Modeling Methodology

- The components/subsystems for the CCHP system are modeled individually from first principles, and then they are combined to produce the total CCHP system model.
- The CCHP system is simulated at full-load and part-load to generate operating data for the nominal power output and the part-loads, i.e., 0–1 MW
_{e}. The power output of the system, along with the isentropic efficiencies for the compressor and the gas turbine of the gas turbine cycle are therefore varied, as input parameters in each simulation. Simulation data are generated for both modes of operation, i.e., summer and winter modes. The output parameters of these simulations are the following: available cooling energy in the district cooling network (DCN) or available heating energy in the district heating network (DHN) (for summer or winter operation, respectively), input fuel energy, net electrical efficiency, primary energy ratio, and mass flow rate of input fuel. - The PV subsystem is modeled and operating data are generated based on Typical Meteorological Year (TMY2) data for Nicosia, Cyprus. The area of the PV array is varied to change the nominal power output of the PV subsystem, as needed. Data are generated for the whole year on an hourly basis, i.e., 8760 time segments. The output data include: the incident solar radiation, the PV array temperature, the maximum power point efficiency of the PV array, and the PV power output.
- The generated data from the CCHP system and the PV subsystem are then combined with the load profile to calculate the number of households that can be serviced from the system, cost data and thermodynamic data.
- A parametric study is conducted to investigate how different values of nominal power output for the PV subsystem affect the cost.

#### 3.1. Gas Turbine Cycle

#### 3.2. Heat Exchangers

#### 3.3. Absorption Chiller

_{2}O type, since this is an efficient chiller with coefficient of performance (COP) values of 1.2–1.3 (double-effect) [12,13]. It is suitable for air-conditioning applications, since it generates a cooling output of 5–10 °C in the form of cold water at the evaporator output. A double-effect chiller is chosen over a single-effect one, since the heat source (steam generated in a heat recovery steam generator) is at a suitable temperature to operate a double-effect absorption chiller. The absorption chiller follows the modeling explained in detail by some of the authors in [14].

#### 3.4. District Energy Network

#### 3.5. Photovoltaic Panels

#### 3.6. Load Profile and System Balance

^{2}household in Cyprus are adjusted on an hourly basis. Since power is the most expensive energy type, no surplus power should be produced, and therefore an electricity-led operation must be followed. Since the system will be operated at both full-load and part-load, it means that power-to-heating and power-to-cooling ratios will vary accordingly. Since the available thermal energy output and, in effect, the district energy delivered to the buildings will be inadequate for certain loads, it is necessary to generate additional thermal energy (heating or cooling) with other means. Specifically, thermal energy can be generated with vapor-compression units, i.e., central electric chillers (located at the site of the CCHP system) or with electric heat pumps located inside the buildings. It is assumed in this study that the proposed CCHP system will service buildings that are already equipped with electric heat pumps, and therefore central electric chillers are not considered, as these would add an unnecessary extra cost to the system. However, for new buildings, central chiller units would be a more ideal option, since overall efficiency and performance would improve. The average COP value for the electric heat pumps is assumed to be 3.0. The cooling load is the space cooling energy, whereas the heating load is the combined space heating and domestic hot water load for the buildings. The electrical load is the load needed for lighting and appliances. The electrical energy for the operation of the heat pumps is added in the energy balance, which is shown below.

#### 3.7. Cost Model

_{e}. The cost model is integrated to the PV-assisted CCHP system model, and all the included cost functions are shown in Table 2. Table 3 includes the values for the cost factor input parameters, and Table 4 includes the values for the cost input parameters. These values are taken from [17], unless specified otherwise. The cost of LNG, ${c}_{LNG}$, is taken as 3.082 €/GJ [18], while the system lifetime is approximated at 20 years of service [17]. The specific cost for the PV subsystem is set at 1.825 €/W, based on an approximation of values found in [9].

^{3}[19]. The LNG supply times per year can be calculated as follows:

## 4. Results and Discussion

#### 4.1. Validation of the Model

#### 4.2. Simulation of the CCHP System and the PV Subsystem

_{e}. As shown in Figure 2, the useful energy output of the CCHP system depends on the selected load; at full-load the CCHP system has a heating-to-power ratio of 1.72, and a cooling-to-power ratio of 2.00; at half-load these values are 2.45 and 2.98, respectively. The increase of these ratios is due to the comparatively higher heating available from the gas turbine exhaust, since the gas turbine cycle becomes less efficient (in terms of electrical energy output) as the load decreases. This is shown more clearly in Figure 3, where the PER is shown to remain almost constant at all loads, due to the way it was defined in the previous section, since the electrical energy output decreases; at the same time, the useful heating (or cooling) energy output increases as the load decreases.

_{e}, the pattern of power generation is shown in Figure 4, with the electrical energy output (in W-h) shown on an hourly basis for a whole year as applied for the weather conditions in Nicosia, Cyprus. The average power output is 34.1 kW

_{e}.

#### 4.3. Application of the PV-assisted CCHP System to a Selected Load Profile

_{2}. The average net electrical efficiency of the system is 19.6%, while the average PER is 39.4%.

#### 4.4. Parametric Study

_{e}. Figure 6 shows the variation of useful energy output. It is obvious that less heating (or cooling) is generated as the PV capacity increases, since less natural gas is combusted in the gas turbine cycle. As the PV subsystem increases, it is also better for the overall performance of the system, as more heating (or cooling), which is available, is actually used in the load profile. This is shown more clearly in Figure 7, where the average PER increases as the PV nominal power output increases, at the expense, however, of lower average net electrical efficiency. This is inevitable, since the gas turbine cycle is forced to operate at lower loads and, in the case of a 600 kW

_{e}PV subsystem, the gas turbine basically operates either at peak loads (i.e., during daytime), or when solar energy is unavailable (i.e., during nighttime). Figure 8 shows the significant reduction in fuel consumption and CO

_{2}emissions, as the nominal power output of the PV subsystem increases. This has significant benefits in operating cost, and environmentally it can help reduce greenhouse gas emissions, especially if the system is situated in sensitive locations where this is desirable.

_{e}. After this point the LCC increases and, at 600 kW

_{e}, it reaches its maximum value for this parametric study. The reason is that at 600 kW

_{e}the useful power output of the PV subsystem is not enough to account for the higher capital cost of the PV subsystem. In other words, more electrical energy is available for consumption, but since the PV subsystem is oversized, it cannot match the requirements of the load profile. Therefore, in this case, electricity generated from the PV subsystem is wasted. The minimum, and thereby the optimum, value for the LCC is at 300 kW

_{e}of nominal power output for the PV subsystem. This pattern could change if the unit cost of PV is decreased in the future. In this case, a higher capacity for the PV subsystem could be desirable. The effect of the specific cost of the PV subsystem on the LCC of the proposed CCHP system is shown in Figure 10, where the specific cost of the PV subsystem is varied from 0.730 to 1.825 €/kW

_{e}. Specifically, a PV subsystem with a capacity of 600 kW

_{e}results in the lowest LCC in the case of a ${c}_{pv}$ at 0.730 €/kW

_{e}. In this case the LCC is 3.372 million €.

## 5. Conclusions

_{e}CCHP system, fueled by LNG, with a PV subsystem are analyzed in terms of thermoeconomic modeling and a parametric study. The study shows that the PV subsystem can significantly reduce the power generation (and thereby fuel consumption and CO

_{2}emissions) needed from the CCHP system. In the parametric study, PV capacity (nominal power output) is varied from 0 to 600 kW

_{e}, and the optimum PV capacity is found to be 300 kW

_{e}. The minimum LCC for the PV-assisted CCHP system is found to be 3.509 million €, as compared to 3.577 million € for a system without a PV subsystem. The total cost of the PV subsystem is 547,445 €, while the total cost for operating the system (fuel) is 731,814 € (compared to 952,201 € for a CCHP system without PVs). These cost savings could increase in the future as the unit PV cost decreases and the unit cost of natural gas increases.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Schematic configuration of the proposed photovoltaic (PV)-assisted 1 MW

_{e}combined cooling, heating, and power system.

**Figure 2.**Simulation of the 1 MW

_{e}combined cooling, heating, and power system at part-load and full-load: fuel input vs. useful energy output.

**Figure 3.**Simulation of the 1 MW

_{e}combined cooling, heating, and power system at part-load and full-load: variation of efficiency at full-load and part-load operation.

**Figure 5.**Annual load profile (power, heating, and cooling) for the average household considered in the study on an hourly basis.

**Figure 6.**Parametric study: annual useful energy output for different photovoltaic subsystem capacities ranging from 0 to 600 kW

_{e}.

**Figure 7.**Parametric study: annual average net electrical efficiency and average primary energy ratio (PER) for different photovoltaic subsystem capacities ranging from 0 to 600 kW

_{e}.

**Figure 8.**Parametric study: annual consumption of fuel and CO

_{2}emissions for different photovoltaic subsystem capacities ranging from 0 to 600 kW

_{e}.

**Figure 9.**Parametric study: cost analysis for different photovoltaic subsystem capacities ranging from 0 to 600 kW

_{e}.

**Figure 10.**Effect of the specific cost for the photovoltaic subsystem on the lifecycle cost of the proposed system.

Parameter Description | Value |
---|---|

Ambient temperature | 25 °C |

Ambient pressure | 1 atm |

Generator efficiency | 0.972 |

Gas turbine nominal power output | 1 MW_{e} |

Flue gas exhaust temperature (summer operation) | 145 °C |

Flue gas exhaust temperature (winter operation) | 65 °C |

Liquefied natural gas (LNG) storage temperature | −160 °C |

Natural gas temperature (after regasification) | 10 °C |

Steam supply temperature | 150 °C |

Steam return temperature | 142 °C |

Cold water supply temperature (district cooling) | 7 °C |

Cold water return temperature (district cooling) | 15 °C |

Hot water supply temperature (district heating) | 80 °C |

Hot water return temperature (district heating) | 60 °C |

Absorption chiller coefficient of performance | 1.3 |

Compressor pressure ratio | 12.6 |

Compressor isentropic efficiency | 0.741 |

Gas turbine isentropic efficiency | 0.811 |

Gas turbine exhaust temperature | 519 °C |

**Table 2.**Cost model for the proposed photovoltaic-assisted combined cooling, heating, and power system.

Variable Description (Unit) | Model Equation | |
---|---|---|

${c}_{fyy}$ | Annual cost of fuel (excl. regasification) (€/year) | ${c}_{fyy}={E}_{py}\text{\hspace{0.17em}}{c}_{LNG}$ |

${c}_{reg}$ | Annual regasification cost (€/year) | ${c}_{rgf}={E}_{py}\text{\hspace{0.17em}}{c}_{rgf}$ |

${c}_{fy}$ | Annual cost of fuel (incl. regasification) (€/year) | ${c}_{fy}={c}_{fyy}+{c}_{reg}$ |

${C}_{tr}$ | Total cost of LNG transport (€) | ${C}_{tr}={c}_{tr,km}{L}_{tr}{V}_{truck}suppl{y}_{LNG,yr}N$ |

${C}_{cc}$ | Total cost of chillers (€) | ${C}_{cc}={c}_{c}{\dot{Q}}_{c}$ |

${Q}_{fcy}$ | Annual fan-coil unit energy input (J) | ${Q}_{fcy}=\left({\dot{Q}}_{fc}\cdot 1\left[\text{yr}\right]\right)\cdot \left|\text{}3.1536\times {10}^{10}\text{}\frac{\mathrm{J}}{\text{kW}\cdot \text{yr}}\text{}\right|$ |

${Q}_{hcy}$ | Total thermal energy production from combined cooling, heating, and power (CCHP) system (J) | ${Q}_{hcy}={Q}_{hy}+{Q}_{cy}$ |

${N}_{fc}$ | Number of fan-coil units (−) | ${N}_{fc}=\frac{{Q}_{hcy}}{{Q}_{fcy}}$ |

${C}_{dn}$ | Cost of distribution network (€) | ${C}_{dn}=L{c}_{l}$ |

${C}_{pp}$ | Cost of power plant (€) | ${C}_{pp}={c}_{p}{P}_{e}$ |

${C}_{fct}$ | Total cost of fan-coil units (€) | ${C}_{fct}={c}_{fc}\text{\hspace{0.17em}}{N}_{fc}\text{\hspace{0.17em}}{\dot{Q}}_{fc}$ |

${C}_{cp}$ | Total cost of central plant (€) | ${C}_{cp}={C}_{pp}+{C}_{cc}$ |

${C}_{CHP,0}$ | Total cost of CCHP system (€) | ${C}_{CHP,0}={C}_{cp}+{C}_{dn}+{C}_{fct}$ |

${C}_{pvs}$ | Total cost of PV subsystem (€) | ${C}_{pvs}={c}_{pv}{\dot{W}}_{pv,nom}$ |

${C}_{CHP}$ | Total cost of PV-assisted CCHP system (€) | ${C}_{CHP}={C}_{CHP,0}+{C}_{pvs}$ |

${C}_{down}$ | Down payment (€) | ${C}_{down}=\left(1-{f}_{loan}\right){C}_{CHP}$ |

$A{P}_{n}$ | Capital recovery factor (−) | $A{P}_{n}=\frac{{r}_{n}}{1-{\left(1+{r}_{n}\right)}^{-N}}$ |

${r}_{1}={r}_{mL}-i\text{\hspace{1em}}{r}_{2}={r}_{mL}\text{\hspace{1em}}{r}_{3}=\frac{{r}_{2}-{r}_{1}}{0.01+{r}_{1}}\text{\hspace{1em}}{r}_{4}=\frac{{r}_{mL}-{r}_{e}}{1+{r}_{e}}$ | ||

$P{A}_{n}$ | Uniform series present worth factor (−) | $P{A}_{n}={\left(A{P}_{n}\right)}^{-1}$ |

$F{P}_{n}$ | Compound amount factor (−) | $F{P}_{n}={\left(1+{r}_{n}\right)}^{-N}$ |

$P{F}_{n}$ | Present worth factor (−) | $P{F}_{n}={\left(F{P}_{n}\right)}^{-1}$ |

${C}_{loan}$ | Cost of the loan (€) | ${C}_{loan}=\frac{A{P}_{1}}{A{P}_{2}}{f}_{loan}{C}_{CHP}$ |

${D}_{loan}$ | Tax deduction on the loan (€) | ${D}_{loan}=t\text{\hspace{0.17em}}{f}_{loan}\text{\hspace{0.17em}}{C}_{CHP}\left(\frac{A{P}_{1}}{A{P}_{2}}-\frac{A{P}_{1}-{r}_{1}}{\left(1+{r}_{1}\right)A{P}_{3}}\right)$ |

${C}_{twc}$ | Total worth of capital (€) | ${C}_{twc}={C}_{down}+{C}_{loan}-{D}_{loan}$ |

${D}_{dep}$ | Linear depreciation of capital (€) | ${D}_{dep}=\frac{{C}_{CHP}}{N}t\text{\hspace{0.17em}}P{A}_{2}$ |

${D}_{cred}$ | Tax credit (€) | ${D}_{cred}={t}_{cred}\text{\hspace{0.17em}}{C}_{CHP}$ |

${D}_{salv}$ | Salvage worth (€) | ${D}_{salv}={f}_{salv}\text{\hspace{0.17em}}{C}_{CHP}\text{\hspace{0.17em}}P{F}_{2}\left(1-{t}_{salv}\right)$ |

${C}_{prop}$ | Tax paid on property (€) | ${C}_{prop}={f}_{prop}\text{\hspace{0.17em}}{C}_{CHP}\text{\hspace{0.17em}}{t}_{prop}\left(1-t\right)$ |

${C}_{omi}$ | Operation, maintenance and insurance cost (€) | ${C}_{omi}={f}_{omi}\text{\hspace{0.17em}}{C}_{CHP}\frac{P{A}_{2}}{3}\left(1-t\right)$ |

${C}_{tcf}$ | Total cost of fuel (€) | ${C}_{tcf}={c}_{fy}\left(\frac{1-t}{A{P}_{4}}\right)$ |

$LCC$ | Lifecycle cost (€) | $LCC={C}_{tr}+{C}_{twc}+{C}_{prop}+{C}_{omi}+{C}_{tcf}-\left({D}_{dep}+{D}_{cred}+{D}_{salv}\right)$ |

Parameter | Value |
---|---|

${r}_{e}$ | 0.01 |

$i$ | 0.01 |

${r}_{m}$ | 0.06 |

${r}_{mL}$ | 0.05 |

${f}_{loan}$ | 0.08 |

$t$ | 0.40 |

${t}_{cred}$ | 0.02 |

${f}_{salv}$ | 0.10 |

${t}_{salv}$ | 0.20 |

${f}_{prop}$ | 0.50 |

${t}_{prop}$ | 0.25 |

${f}_{omi}$ | 0.01 |

Input Parameter Description | Value | |
---|---|---|

${c}_{LNG}$ | Specific cost of LNG fuel for the first year | 3.082 €/GJ |

$L$ | Length of pipe network | 2 km |

$f$ | Heat loss factor | 0.05 |

${c}_{c}$ | Specific cost of cooling plant | 365 €/kW |

${c}_{l}$ | Specific cost of distribution line | 2920 €/m |

${c}_{p}$ | Specific cost of natural gas-fired power plant | 365 €/GW |

${c}_{fc}$ | Specific cost of fan-coil unit | 73 €/kW |

$N$ | Number of years of service | 20 |

${c}_{rgf}$ | Specific cost of LNG regasification | 0.208 €/GJ |

${c}_{pv}$ | Specific cost of PV subsystem | 1.825 €/W |

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Arsalis, A.; Alexandrou, A.N.; Georghiou, G.E.
Thermoeconomic Modeling and Parametric Study of a Photovoltaic-Assisted 1 MW_{e} Combined Cooling, Heating, and Power System. *Energies* **2016**, *9*, 663.
https://doi.org/10.3390/en9080663

**AMA Style**

Arsalis A, Alexandrou AN, Georghiou GE.
Thermoeconomic Modeling and Parametric Study of a Photovoltaic-Assisted 1 MW_{e} Combined Cooling, Heating, and Power System. *Energies*. 2016; 9(8):663.
https://doi.org/10.3390/en9080663

**Chicago/Turabian Style**

Arsalis, Alexandros, Andreas N. Alexandrou, and George E. Georghiou.
2016. "Thermoeconomic Modeling and Parametric Study of a Photovoltaic-Assisted 1 MW_{e} Combined Cooling, Heating, and Power System" *Energies* 9, no. 8: 663.
https://doi.org/10.3390/en9080663