# The Optimal Operation Criteria for a Gas Turbine Cogeneration System

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## Abstract

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## 1. Introduction

## 2. The Criteria for the Optimal Operation of Gas Turbine Cogeneration Systems

#### 2.1. The Gas Turbine Cogeneration System Model

**Figure 1.**The energy flow of the simplified gas turbine cogeneration system with the turbine inlet air cooling.

#### 2.2. The Mathematical Formulation and the Optimal Solution

**x**and

**λ**satisfy the following conditions at the optimal solution.

#### 2.3. The Optimal Solution where the Electric Power from the Gas Turbine is less than the Capacity

Mode | Grid | Boiler | Gas Turbine | Steam Turbine | Absorption Chiller |
---|---|---|---|---|---|

a | ⊠ | ⊠ | □ | □ | □ |

b | □ | ⊠ | □ | ⊠ | □ |

c | □ | □ | ⊠ | □ | □ |

d | □ | ⊠ | ⊠ | □ | □ |

e | ⊠ | □ | ⊠ | □ | □ |

f | □ | □ | ⊠ | ⊠ | □ |

g | □ | □ | ⊠ | □ | ⊠ |

h | □ | ⊠ | ⊠ | □ | ⊠ |

i | ⊠ | □ | ⊠ | □ | ⊠ |

j | □ | □ | ⊠ | ⊠ | ⊠ |

**Figure 3.**The optimal operation cases expressed on the relative oil price-relative electricity price plane (the operational condition I).

#### 2.4. The Optimal Solution where the Electric Power from the Gas Turbine is at the Maximum

**Figure 5.**The optimal operation cases expressed on the relative oil price-relative electricity price plane (the operational condition II).

## 3. Comparison of the Optimal Operation Criteria with a Detailed Optimization Result

#### 3.1. An Example of an Existing Energy Center of a Factory

#### 3.2. The Performance Characteristics of the Equipment

#### 3.3. The Detailed Optimization of the Energy Center

#### The Detailed Optimization Method

#### The Plant Operation Obtained by the Detailed Optimization

**Figure 10.**The ratio of the heat flow rate of the steam demand to the electric power demand on a summer day and on a winter day.

#### 3.4. The Comparison of the Optimal Operation Criteria with the Detailed Optimization Results

Gas turbine electric efficiency | 25 % | (${\omega}_{\mathrm{GT}}$ = 4.0) |

Gas turbine steam to electricity ratio | 1.4 | |

Steam turbine efficiency (steam input basis) | 30 % | (${\omega}_{\mathrm{ST}}$ = 3.3) |

Absorption chiller COP | 1.2 | (${\omega}_{\mathrm{AC}}$ = 0.83) |

Boiler thermal efficiency | 85 % | (${\omega}_{\mathrm{B}}$ = 1.2) |

Gas turbine alpha number | ${\alpha}_{\mathrm{GT}}$ = 1.1 | |

Gas turbine beta number | ${\beta}_{\mathrm{GT}}$ = 0.3 |

#### The Optimal Operation Mode Selection by the Optimal Operation Criteria

**Figure 15.**The operation mode suggested by the optimal operation criteria at each hour on the summer and the winter days.

#### The Applicability of the Optimal Operation Criteria to the Energy Center

## 4. Conclusions

## Nomenclature

C | energy cost, yen | Subscripts | ||

L | Lagrangian | AC | absorption chiller | |

P | price, yen | B | boiler | |

t | time, h | e | electricity | |

x | electric power or heat ﬂow rate, kW | g | gas | |

X | capacity, kW | G | grid electricity | |

Greek symbols | GT | gas turbine | ||

α | capacity enhancement factor | o | oil or kerosene | |

β | improvement factor of the fuel consumption | s | steam | |

λ | Lagrange multiplier | ST | steam turbine | |

ρ | steam to electricity ratio | |||

ω | input to output ratio |

## References and Notes

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© 2009 by the authors; licensee Molecular Diversity Preservation International, Basel, Switzerland. This article is an open-access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

## Share and Cite

**MDPI and ACS Style**

Ishida, Y.; Bannai, M.; Miyazaki, T.; Harada, Y.; Yokoyama, R.; Akisawa, A.
The Optimal Operation Criteria for a Gas Turbine Cogeneration System. *Energies* **2009**, *2*, 202-225.
https://doi.org/10.3390/en20200202

**AMA Style**

Ishida Y, Bannai M, Miyazaki T, Harada Y, Yokoyama R, Akisawa A.
The Optimal Operation Criteria for a Gas Turbine Cogeneration System. *Energies*. 2009; 2(2):202-225.
https://doi.org/10.3390/en20200202

**Chicago/Turabian Style**

Ishida, Yasushi, Masaaki Bannai, Takahiko Miyazaki, Yasushi Harada, Ryuichi Yokoyama, and Atsushi Akisawa.
2009. "The Optimal Operation Criteria for a Gas Turbine Cogeneration System" *Energies* 2, no. 2: 202-225.
https://doi.org/10.3390/en20200202