# Multicriteria Assessment of Combined Heat and Power Systems

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Performance Evaluation of CHPS

_{x}, SO

_{2}, PM

_{10}, and CO

_{2}, from burning natural gas and the default emission factor. Alanne et al. [18] believe that financial and environmental performances are critical in evaluating the performance of CHPS. Aussant et al. [19] state that environmental characteristics should both be considered, whilst evaluating the performance of CHPS. Meanwhile, Ren and Gao [20] consider environmental factors to assess fuel cell and gas engine CHPS alternatives. Earlier studies suggest that electricity generation leads to carbon emissions. Wang et al. [21] believe that emission of the energy system is certainly a criterion to be considered in the performance evaluation process. Jannelli et al. [11] point out that by reducing the primary energy sector consumption and using the appropriate CHPS, this will have a positive impact on the environment. Wang et al. [22] point out the monetary values of damage to the environment and health, resulting from atmospheric emissions created by the CHPS. Thus, the assessment of environmental factors, in terms of the benefits to end users, will support the goal of minimizing carbon emissions [23].

_{1}), gas turbine (A

_{2}), and micro turbine (A

_{3}) technology alternatives were considered for evaluation.

## 3. The Multicriteria Assessment Model

_{i}(i = 1, 2, …, m), with respect to all available criteria from the decision makers D

_{k}(k = 1, 2, …, s). The interval-valued intuitionistic fuzzy decision matrix for each decision maker is represented as ${R}^{(k)}={\left({r}_{ij}^{(k)}\right)}_{m\times n}$, where k = 1, 2, …, s and $\left({r}_{ij}^{(k)}\right)=\{({\mu}_{ij}^{L(k)},{\mu}_{ij}^{U(k)}),({\nu}_{ij}^{L(k)},{\nu}_{ij}^{U(k)})\}$ is an interval-valued intuitionistic fuzzy number, which represents the performance rating of alternatives with respect to all available criteria. $({\mu}_{ij}^{L(k)},{\mu}_{ij}^{U(k)})$ indicates the degree to which alternative A

_{i}satisfies criterion C

_{j}, whilst $({\nu}_{ij}^{L(k)},{\nu}_{ij}^{U(k)})$ indicates the degree to which alternative A

_{i}dissatisfies criterion C

_{j}. $w={({w}_{1},{w}_{2},\dots ,{w}_{m})}^{T}$ is the weight of each decision maker where $\sum _{j=1}^{n}{w}_{j}}=1\text{\hspace{0.17em}}\mathrm{and}\text{\hspace{0.17em}}{w}_{j}\in \left[0,\text{\hspace{0.17em}}1\right].$

_{i}and the positive ideal solution and the negative solution can be respectively calculated as

_{i}across all the criteria can be determined by

_{i}values obtained as in Equation (6), the ranking order of each alternative A

_{i}can be determined. The larger the performance index P

_{i}, the better the performance of the alternative A

_{i}.

- Step 1:
- Obtain the performance ratings, with respect to all available criteria from the decision makers.
- Step 2:
- Aggregate individual fuzzy decision matrices into a collective interval-valued intuitionistic fuzzy decision matrix by using Equation (1).
- Step 3:
- Determine the interval-valued intuitionistic fuzzy positive ideal solution ${\alpha}^{*}$, and the interval-valued intuitionistic fuzzy negative ideal solution ${\alpha}^{-}$, as in Equations (2) and (3), respectively.
- Step 4:
- Calculate the weighted separation measures by using Equations (4) and (5).
- Step 5:
- Calculate the performance index P
_{i}by using Equation (6). - Step 6:
- Determine the ranking order of each alternative A
_{i}, based on the performance index P_{i}.

## 4. Application of the Model to a Case Study

_{1}), (b) technology (C

_{2}), (c) environment (C

_{3}), and (d) economy (C

_{4}), were used to evaluate the performance of three CHPS, consisting of the steam turbine (A

_{1}), gas turbine (A

_{2}), and micro turbine (A

_{3}).

_{i}values, for each CHPS across all the criteria, can then be calculated using Equation (6). Table 5 shows the calculated results.

_{2}, is the best alternative, as it has the highest performance index value of 0.709.

_{2}, which is the gas turbine alternative, was found to be the most suitable CHPS alternative for implementation at the sugar company, compared to the steam turbine (A

_{1}) and micro turbine (A

_{3}).

## 5. Conclusions

_{2}) was found to be the most suitable alternative for selection. Thus, the proposed multicriteria assessment model was able to help organizations understand the performance of CHPS, and provide opportunities for these organizations to improve the overall performance of available CHPS.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**The Hierarchical Structure for combined heat and power systems (CHPS) Performance Evaluation.

Criteria | |||||
---|---|---|---|---|---|

C_{1} | C_{2} | C_{3} | C_{4} | ||

A_{1} | D_{1} | ([0.3,0.6], [0.1,0.2]) | ([0.3,0.6], [0.2,0.4]) | ([0.4,0.6], [0.3,0.5]) | ([0.3,0.5], [0.2,0.4]) |

D_{2} | ([0.2,0.3], [0.3,0.5]) | ([0.4,0.5], [0.3,0.4]) | ([0.5,0.7], [0.4,0.5]) | ([0.4,0.6], [0.3,0.4]) | |

D_{3} | ([0.5,0.7], [0.3,0.4]) | ([0.3,0.6], [0.2,0.3]) | ([0.4,0.6], [0.1,0.4]) | ([0.5,0.4], [0.2,0.5]) | |

A_{2} | D_{1} | ([0.3,0.4], [0.2,0.3]) | ([0.4,0.7], [0.4,0.5]) | ([0.3,0.5], [0.1,0.3]) | ([0.3,0.5], [0.1,0.2]) |

D_{2} | ([0.4,0.7], [0.3,0.4]) | ([0.5,0.6], [0.3,0.4]) | ([0.4,0.7], [0.3,0.4]) | ([0.3,0.6], [0.2,0.3]) | |

D_{3} | ([0.3,0.5], [0.1,0.2]) | ([0.3,0.5], [0.2,0.3]) | ([0.3,0.6], [0.3,0.5]) | ([0.5,0.8], [0.3,0.6]) | |

A_{3} | D_{1} | ([0.2,0.6], [0.1,0.3]) | ([0.3,0.6], [0.1,0.2]) | ([0.5,0.7], [0.2,0.4]) | ([0.6,0.8], [0.4,0.5]) |

D_{2} | ([0.4,0.6], [0.3,0.4]) | ([0.1,0.3], [0.2,0.4]) | ([0.6,0.8], [0.1,0.5]) | ([0.2,0.3], [0.1,0.2]) | |

D_{3} | ([0.5,0.7], [0.3,0.5]) | ([0.2,0.3], [0.1,0.3]) | ([0.3,0.7], [0.1,0.3]) | ([0.4,0.6], [0.3,0.5]) |

Criteria | ||||
---|---|---|---|---|

C_{1} | C_{2} | C_{3} | C_{4} | |

A_{1} | ([0.136,0.194], [0.255,0.371]) | ([0.073,0.316], [0.237,0.468]) | ([0.086,0.328], [0.557,0.726]) | ([0.134,0.216], [0.317,0.437]) |

A_{2} | ([0.157,0.438], [0.479,0.731]) | ([0.258,0.517], [0.462,0.703]) | ([0.159,0.347], [0.432,0.558]) | ([0.142,0.327], [0.564,0.831]) |

A_{3} | ([0.169,0.264], [0.417,0.596]) | ([0.214,0.385], [0.336,0.568]) | ([0.168,0.283], [0.325,0.489]) | ([0.138,0.315], [0.537,0.641]) |

${\alpha}^{*}$ | ${\alpha}^{-}$ |

([0.216, 0.372], [0.461, 0.639]) | ([0.218, 0.438], [0.342, 0.572]) |

([0.237, 0.358], [0.427, 0.624]) | ([0.246, 0.437], [0.536, 0.836]) |

([0.361, 0.614], [0.335, 0.482]) | ([0.184, 0.328], [0.326, 0.524]) |

([0.156, 0.524], [0.626, 0.723]) | ([0.235, 0.448], [0.481, 0.684]) |

([0.128, 0.372], [0.456, 0.627]) | ([0.159, 0.335], [0.158, 0.319]) |

${S}_{i}^{+}$ | ${S}_{i}^{-}$ |

0.144 | 0.201 |

0.179 | 0.436 |

0.147 | 0.284 |

Alternative | Performance Index | Ranking |
---|---|---|

A_{1} | 0.583 | 3 |

A_{2} | 0.709 | 1 |

A_{3} | 0.659 | 2 |

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**MDPI and ACS Style**

Wibowo, S.; Grandhi, S.
Multicriteria Assessment of Combined Heat and Power Systems. *Sustainability* **2018**, *10*, 3240.
https://doi.org/10.3390/su10093240

**AMA Style**

Wibowo S, Grandhi S.
Multicriteria Assessment of Combined Heat and Power Systems. *Sustainability*. 2018; 10(9):3240.
https://doi.org/10.3390/su10093240

**Chicago/Turabian Style**

Wibowo, Santoso, and Srimannarayana Grandhi.
2018. "Multicriteria Assessment of Combined Heat and Power Systems" *Sustainability* 10, no. 9: 3240.
https://doi.org/10.3390/su10093240