# Multi-Criteria Evaluation of Energy Systems with Sustainability Considerations

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## Abstract

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## 1. Introduction

## 2. From Sustainability Indicators to Composite Sustainability Index

#### 2.1. Selection and Grouping of Indicators

- Technical indicators (energetic efficiency, exergetic efficiency, power density, fuel consumption, reliability, availability, etc.)
- Environmental indicators (quantities of emitted pollutants, effect on health, effect on flora and fauna, etc.)
- Economic indicators (life cycle cost, internal rate of return, payback period, etc.)
- Social indicators (job creation, general welfare, etc.).

**Figure 1.**Steps for calculation of composite sustainability index (adapted from [6]).

#### 2.2. Judging the Indicators

#### 2.3. Normalizing the Indicators

#### 2.4. Weighting the Indicators and Calculating the Sub-Indices

#### 2.5. The Composite Sustainability Index

## 3. Case Study: Assessment of Alternative Energy Systems Related to An Industrial Unit

#### 3.1. Selection of Indicators

i | Symbol | Units | Description |
---|---|---|---|

1 | ${\eta}_{e}$ | – | Energetic electric efficiency |

2 | ${\eta}_{tot}$ | – | Energetic total efficiency |

3 | ${\zeta}_{e}$ | – | Exergetic electric efficiency |

4 | ${\zeta}_{tot}$ | – | Exergetic total efficiency |

5 | ${m}_{N{O}_{x}}$ | kg/a | Annual emission of NO_{x} |

6 | ${m}_{CO}$ | kg/a | Annual emission of CO |

7 | ${m}_{UHC}$ | kg/a | Annual emission of UHC (unburned hydrocarbons) |

8 | ${m}_{P{M}_{10}}$ | kg/a | Annual emission of PM_{10} (particular mater of a diameter up to 10 μm) |

9 | ${m}_{C{O}_{2}}$ | kg/a | Annual emission of CO_{2} |

10 | ${m}_{S{O}_{x}}$ | kg/a | Annual emission of SO_{x} |

11 | NPC | € | Net Present Cost (conventional analysis) |

12 | NPC_{env} | € | Net Present Cost including environmental externalities |

#### 3.2. Energy Needs of the Industrial Unit and Alternative Energy Systems

Electric power: | $\dot{W}=30000$ kW |

Mass flow rate of saturated steam: | ${\dot{m}}_{s}=14$ kg/s |

Steam pressure: | $p=20$ bar |

Feed water properties: | $p=20$ bar, T = 25 °C |

Annual operation: | $\tau =7480$ h (11 months/a × 680 h/month) |

- System A:
- Electricity from the local network and steam from a boiler operating with natural gas and located in the industrial unit.
- System B:
- System C:
- Cogeneration system with dual fuel reciprocating internal combustion engine.

Lower heating value of natural gas: | ${H}_{uNG}=36400$ kJ/Nm^{3} |

Temperature of the environment: | T_{0} = 25 °C (298.15 K) |

Exergy to energy ratio of natural gas: | ${\varphi}_{NG}=1.04$ |

Technical life of the system: | $N=20$ years |

Salvage value at the end of N years: | ${V}_{sN}=0$ |

Cost of natural gas: | ${c}_{NG}=0.2$ €/Nm^{3} |

Market interest rate: | i = 0.10 |

General inflation rate: | f = 0.03 |

Fuel inflation rate: | f_{f} = 0.04 |

Annual insurance rate: | ${\Delta}_{ins}=0.5\%$ of investment |

_{0}is given in Table 3. The results are as follows:

**Table 4.**Specific emissions (in grams per kWh of useful energy production) and external environmental cost due to pollution.

Pollutant | Specific emissions (g/kWh) | External environmental cost (€/kg) | |||
---|---|---|---|---|---|

Electric network | Boiler | Gas turbine | Dual Fuel Engine | ||

NO_{x} | 0.5 | 0.3466 | 1.4225 | 2 | 3.4384 |

CO | 0.3 | 0.0266 | 0.0864 | 5 | 1.1600 |

UHC | 0 | 0 | 0.0665 | 3 | 0.1608 |

PM_{10} | 0.04 | 0.0177 | 0.04653 | 0.0299 | 15.1114 |

CO_{2} | 531.68 | 224.488 | 537.198 | 429 | 0.0190 |

SO_{x} | 0 | 0 | 0 | 0.067 | 1.0000 |

#### 3.3. Additional Information about System A

Technical Data | |
---|---|

Efficiency of the electricity generation and supply by the local network: | ${\eta}_{en}=0.38$ |

Contribution of fuels to the electricity production (small contribution from other sources is neglected) Lignite: Natural gas: Petroleum products: | 61.6% 21.4% 17.0% |

Exergy to energy ratio of fuels used for electricity generation by the network (weighted average): | ${\varphi}_{en}=1.07$ |

Efficiency of the boiler: | ${\eta}_{b}=0.90$ |

Economic Data | |

Installed cost of boiler: | ${C}_{b}=941700$ € |

Construction period of boiler: | 1 year |

Electricity tariff system. Power charge: | XZ = 2.1581 €/kW/month |

Energy charge: | ${c}_{e}=0.10039$€/kWh |

Operation and maintenance cost of boiler (excluding fuel): | ${c}_{mb}=2$ €/MWh_{th} |

- Total energetic efficienc:$${\eta}_{tot,A}=\frac{\dot{W}+\dot{Q}}{\dot{W}/{\eta}_{en}+\dot{Q}/{\eta}_{b}}$$
- Exergetic efficiency of the electricity network:$${\zeta}_{en}=\frac{\dot{W}}{{\dot{E}}_{f,en}}=\frac{{\eta}_{en}{H}_{u,en}}{{\dot{E}}_{f,en}}=\frac{{\eta}_{en}}{{\varphi}_{en}}$$
- Volumetric flow rate of fuel consumed by the boiler:$${\dot{V}}_{fb,A}=\frac{\dot{Q}}{{\eta}_{b}{H}_{uNG}}$$
- Exergy flow rate of fuel consumed by the boile$${\dot{E}}_{fb,A}={\dot{V}}_{fb,A}{H}_{uNG}{\varphi}_{NG}$$
- Total exergetic efficiency of System A:$${\zeta}_{tot,A}=\frac{\dot{W}+{\dot{E}}_{s}^{Q}}{\dot{W}/{\zeta}_{en}+{\dot{E}}_{fb,A}}$$

#### 3.4. Additional Information about System B

Technical Data | |
---|---|

Electric energetic efficiency: | ${\eta}_{e,B}=0.3761$ |

Thermal energetic efficiency: | ${\eta}_{h,B}=0.4722$ |

Total energetic efficiency: | ${\eta}_{tot,B}=0.8483$ |

Electric exergetic efficiency: | ${\zeta}_{e,B}=0.36$ |

Thermal exergetic efficiency: | ${\zeta}_{h,B}=0.153$ |

Total exergetic efficiency: | ${\zeta}_{tot,B}=0.513$ |

Economic Data | |

Installed cost of the system: | ${C}_{B}=30\cdot {10}^{6}$ € |

Construction period: | 2 years |

Operation and maintenance cost (excluding fuel): | ${c}_{mB}=6$ €/MWh_{e} |

#### 3.5. Additional Information about System C

Technical Data | |
---|---|

Thermal power of the dual fuel engine: | ${\dot{Q}}_{DF}=24255$ kW_{th} |

Thermal power of the boiler ($\dot{Q}-{\dot{Q}}_{DF}$): | ${\dot{Q}}_{b,C}=13413$ kW_{th} |

Electric energetic efficiency of the engine: | ${\eta}_{e,DF}=0.47$ |

Thermal energetic efficiency of the engine: | ${\eta}_{h,DF}=0.38$ |

Total energetic efficiency of the engine: | ${\eta}_{tot,DF}=0.85$ |

Efficiency of the boiler: | ${\eta}_{b}=0.90$ |

Lower heating value of Diesel oil: | ${H}_{uDO}=42700$ kJ/kg |

Exergy to energy ratio of Diesel oil: | ${\varphi}_{DO}=1.06$ |

Density of Diesel oil: | ${\rho}_{DO}=0.83$ kg/lt |

Economic Data | |

Installed cost of the cogeneration system: | ${C}_{DF}=27\cdot {10}^{6}$ € |

Installed cost of the boiler: | ${C}_{b,C}=335325$ € |

Construction period: | 2 years |

Cost of Diesel oil: | ${c}_{DO}=1$ €/lt |

Operation and maintenance cost of the cogeneration system: | ${c}_{mDF}=10$ €/MWh_{e} |

Operation and maintenance cost of the boiler: | ${c}_{mB}=2$ €/MWh_{th} |

- Volumetric flow rate of natural gas consumed by the dual fuel engine:$${\dot{V}}_{NG,DF}=0.9\cdot \frac{\dot{W}}{{\eta}_{e,DF}{H}_{uNG}}$$
- Mass flow rate of Diesel oil consumed by the dual fuel engine:$${\dot{m}}_{DO,DF}=0.1\cdot \frac{\dot{W}}{{\eta}_{e,DF}{H}_{uDF}}$$
- Total energetic efficiency of System C:$${\eta}_{tot,C}=\frac{\dot{W}+\dot{Q}}{{\dot{W}}_{DF}/{\eta}_{e,DF}+{\dot{Q}}_{b,C}/{\eta}_{b}}$$
- Exergy flow rate of fuels in the dual fuel engine$${\dot{E}}_{DF}={\dot{V}}_{NG,DF}{H}_{uNG}{\varphi}_{NG}+{\dot{m}}_{DO,DF}{H}_{uDO}{\varphi}_{DO}$$
- Exergy flow rate of steam produced by the cogeneration system$${\dot{E}}_{DF}^{Q}={\dot{E}}_{s}^{Q}{\dot{Q}}_{DF}/\dot{Q}$$
- Exergy flow rate of steam produced by the boiler$${\dot{E}}_{b,C}^{Q}={\dot{E}}_{s}^{Q}-{\dot{E}}_{DF}^{Q}$$
- Volumetric flow rate of fuel consumed by the boiler:$${\dot{V}}_{fb,C}=\frac{{\dot{Q}}_{b,C}}{{\eta}_{b}{H}_{uNG}}$$
- Exergy flow rate of fuel consumed by the boile$${\dot{E}}_{fb,C}={\dot{V}}_{fb,C}{H}_{uNG}{\varphi}_{NG}$$
- Total exergetic efficiency of System C:$${\zeta}_{tot,C}=\frac{\dot{W}+{\dot{E}}_{s}^{Q}}{{\dot{E}}_{DF}+{\dot{E}}_{fb,C}}$$

## 4. Results and Discussion

#### 4.1. Calculation of Indicators, Sub-Indices and the Composite Sustainability Index

_{0}is the cost of investment (installed cost of each system) and C

_{t}, t = 1-N, is the total operation and maintenance cost (in other words the total cost for covering the energy needs) in year t. The C

_{t}for the net present cost including environmental externalities, NPC

_{env}, has one additional term corresponding to the environmental cost due to the pollutants:

_{k}is the annual emissions of pollutant k and c

_{env,k}is the unit environmental cost due to pollutant k, as given in Table 4. The values of the indicators are given in Table 8.

i | Symbol | Units | System A | System B | System C |
---|---|---|---|---|---|

1 | ${\eta}_{e}$ | – | 0.38 | 0.3761 | 0.47 |

2 | ${\eta}_{tot}$ | – | 0.56 | 0.8483 | 0.86 |

3 | ${\zeta}_{e}$ | – | 0.36 | 0.36 | 0.451 |

4 | ${\zeta}_{tot}$ | – | 0.337 | 0.513 | 0.522 |

5 | ${m}_{N{O}_{x}}$ | kg/a | 209,856.8 | 319,209 | 483,574.1 |

6 | ${m}_{CO}$ | kg/a | 74,814.7 | 19,388 | 1,124,668.8 |

7 | ${m}_{UHC}$ | kg/a | 0 | 14,923 | 673,199 |

8 | ${m}_{P{M}_{10}}$ | kg/a | 13,963 | 10,441 | 8,485.8 |

9 | ${m}_{C{O}_{2}}$ | kg/a | 182,559,976.6 | 120,547,231 | 118,790,310 |

10 | ${m}_{S{O}_{x}}$ | kg/a | 0 | 0 | 15,035 |

11 | NPC | € | 319,384,905.1 | 181,429,678 | 232,009,565.8 |

12 | NPC_{env} | € | 357,593,745 | 211,828,489.5 | 278,628,728.5 |

i | Symbol | Units | Lower threshold | Upper threshold |
---|---|---|---|---|

1 | ${\eta}_{e}$ | – | 0 | 0.80 |

2 | ${\eta}_{tot}$ | – | 0 | 1 |

3 | ${\zeta}_{e}$ | – | 0 | 1 |

4 | ${\zeta}_{tot}$ | – | 0 | 1 |

5 | ${m}_{N{O}_{x}}$ | kg/a | 209,856.8 | 483,574.1 |

6 | ${m}_{CO}$ | kg/a | 19,388 | 1,124,668.8 |

7 | ${m}_{UHC}$ | kg/a | 0 | 673,199 |

8 | ${m}_{P{M}_{10}}$ | kg/a | 8,485.8 | 13,963 |

9 | ${m}_{C{O}_{2}}$ | kg/a | 118,790,310 | 182,559,976.6 |

10 | ${m}_{S{O}_{x}}$ | kg/a | 0 | 15,035 |

11 | NPC | € | 181,429,678 | 319,384,905.1 |

12 | NPC_{env} | € | 211,828,489.5 | 357,593,745 |

No. | Indicator ${\overline{\mathit{I}}}_{\mathit{i}\mathit{j}}$ | Physical Symbol | System A | System B | System C |
---|---|---|---|---|---|

1 | ${\overline{I}}_{1,1}$ | ${\eta}_{e}$ | 0.475 | 0.4701 | 0.5875 |

2 | ${\overline{I}}_{2,1}$ | ${\eta}_{tot}$ | 0.56 | 0.8483 | 0.86 |

3 | ${\overline{I}}_{3,1}$ | ${\zeta}_{e}$ | 0.36 | 0.36 | 0.451 |

4 | ${\overline{I}}_{4,1}$ | ${\zeta}_{tot}$ | 0.337 | 0.513 | 0.522 |

5 | ${\overline{I}}_{1,2}$ | ${m}_{N{O}_{x}}$ | 1 | 0.6005 | 0 |

6 | ${\overline{I}}_{2,2}$ | ${m}_{CO}$ | 0.9498 | 1 | 0 |

7 | ${\overline{I}}_{3,2}$ | ${m}_{UHC}$ | 1 | 0.9778 | 0 |

8 | ${\overline{I}}_{4,2}$ | ${m}_{P{M}_{10}}$ | 0 | 0.6430 | 1 |

9 | ${\overline{I}}_{5,2}$ | ${m}_{C{O}_{2}}$ | 0 | 0.9724 | 1 |

10 | ${\overline{I}}_{6,2}$ | ${m}_{S{O}_{x}}$ | 1 | 1 | 0 |

11 | ${\overline{I}}_{1,3}$ | NPC | 0 | 1 | 0.6327 |

12 | ${\overline{I}}_{2,3}$ | NPC_{env} | 0 | 1 | 0.5417 |

${\overline{I}}_{ave}$ | – | 0.474 | 0.782 | 0.466 |

Index | System A | System B | System C |
---|---|---|---|

${\overline{I}}_{S1}$ | 0.433 | 0.548 | 0.605 |

${\overline{I}}_{S2}$ | 0.658 | 0.866 | 0.333 |

${\overline{I}}_{S3}$ | 0 | 1 | 0.587 |

${I}_{CS}$ | 0.364 | 0.805 | 0.508 |

#### 4.2. Graphical Presentation of the Results

_{I}is the total number of indicators. Furthermore, since the maximum surface area of the plot is equal to the surface area of the circle with radius equal to 1, i.e. ${A}_{\mathrm{max}}=\pi $, a normalized value of A can be defined:

#### 4.3. Comments on the Results

_{x}, CO and UHC emissions (according to the source of related information used in this work).

## 4. Conclusions and Recommendations

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**MDPI and ACS Style**

Frangopoulos, C.A.; Keramioti, D.E.
Multi-Criteria Evaluation of Energy Systems with Sustainability Considerations. *Entropy* **2010**, *12*, 1006-1020.
https://doi.org/10.3390/e12051006

**AMA Style**

Frangopoulos CA, Keramioti DE.
Multi-Criteria Evaluation of Energy Systems with Sustainability Considerations. *Entropy*. 2010; 12(5):1006-1020.
https://doi.org/10.3390/e12051006

**Chicago/Turabian Style**

Frangopoulos, Christos A., and Despoina E. Keramioti.
2010. "Multi-Criteria Evaluation of Energy Systems with Sustainability Considerations" *Entropy* 12, no. 5: 1006-1020.
https://doi.org/10.3390/e12051006