# Environmentally Constrained Optimal Dispatch Method for Combined Cooling, Heating, and Power Systems Using Two-Stage Optimization

^{*}

## Abstract

**:**

## 1. Introduction

_{2}prevalence, which increases acid rain, gradually increased in China in the period 2001–2015. Consequently, China implemented a five-year plan to reduce SO

_{2}emissions by 8% during 2011–2015 with a subsequent 15% reduction in the period 2016–2020 [2]. NO

_{x}emissions have also increased 3–6-fold worldwide due to anthropogenic activity [3], and greenhouse gas (GHG) concentrations have increased due to reckless development plans that were formulated without regard for the environmental impact [4]. The New Zealand (NZ) Clean Air Act (1990) highlighted how to dramatically reduce SO

_{2}emissions generated by electricity generation [5], with the New Zealand government implementing a plan in 2007 to replace 90% of the electricity sector with renewable energy by 2025 for national energy power production [6]. Moreover, research on European regions presents pollutant emissions (e.g., SO

_{2}and NO

_{x}) as a result of generation through mean-varying models and argues for the importance of using natural gas over conventional fossil fuels [7].

_{2}emissions, life cycle cost, and dump energy using distributed generation rather than large diesel generators and implemented the genetic algorithm (GA) for grid-embedded PV, wind, split diesel, and battery hybrid energy systems for residential buildings. Bernal-Agustín et al. [11] considered costs and emissions simultaneously, applying the Pareto evolutionary algorithm to a multi-objective design with isolated hybrid systems (e.g., PV, wind, and diesel). CCHPs were preferred as efficient systems for this desired power combination. Other studies have considered the improved energy efficiency and minimized emissions and costs associated with CCHP systems. Ren et al. [12] proposed a mixed-integer nonlinear programming model and examined the optimal storage tank size and the key components for residential CHP systems while minimizing annual costs and CO

_{2}emissions to meet energy policies. Kim et al. [13] considered the energy efficiency and economic sensitivity for CCHP systems used in residential, commercial, and industrial buildings using HOMER software, and analyzed the effects of the CCHP system on economic efficiency, and environmental aspects. Ren et al. [14] proposed a hybrid combined cooling heating and power system integrated with solar and geothermal energies and obtained the Pareto-optimal solutions for the configurations of a hybrid system. Wang et al. [15] defined the flexibility of hybrid CCHP systems and constructed a multi-objective optimization model considering flexibility while analyzing the influence of flexibility on system performance.

_{2}emissions while satisfying electric power demand, but they rarely considered NO

_{x}, another GHG, or SO

_{2}, which causes acid rain. Moreover, water is another resource that ought to be reduced. Hence, no previous study has considered dispatch models for CHP systems that have simultaneously considered (CO

_{2}, SO

_{2}, NO

_{x}) and water usage, and ABC usage. CCHP systems usually have a relatively small capacity compared with conventional power generation units and have a limited reliability in relation to the provision of sufficient power for the total load required for a region since they are not normally used for centralized power generation. Therefore, residential communities with CCHP systems commonly purchase electric energy from the power grid. For example, the Georgia Power company produced power for USD 24.70/MWh and purchased energy at USD 43.3/MWh (175% increase) in 2015 [16]. Therefore, the energy required from the power grid should be minimized or optimized when designing CHP systems. However, it is difficult to determine the exact quantities if the source state or national-wide grid cannot be properly modeled.

_{2}, SO

_{2}, and NO

_{x}emissions and water usage within the proposed objective function. Thus, this study not only optimized the weighting coefficients for the objective function but also the optimal energy mix. We considered a case study to examine the reduced emissions using the objective function with weight coefficients. Generation units with reduced CO

_{2}emissions often also reduce SO

_{2}and NO

_{x}emissions, but these can sometimes be increased. Thus, it is essential to add weighting factors for reducing SO

_{2}and NO

_{x}(e.g., where soil pollution is severe due to acid rain).

_{2}, SO

_{2}, and NO

_{x}emissions and water consumption for a specific reason using equal or adjusted weights, but also verified the proposed CCHP optimization algorithm validity based on the achieved emission reductions. Stage One calculated the optimal energy mix using the Lagrange multiplier implemented in MATLAB for state-wide grids (specifically, Georgia USA). Stage Two used the Atlanta, Georgia energy mix as an input and then optimized the CCHP systems in the area every hour through a complete year (8760 h).

_{2}, SO

_{2}, and NO

_{x}emissions, and water consumption. Section 5 discusses a case study and the simulations for the Georgia, USA grid and the Atlanta area, obtaining the optimal energy mix using the proposed two-stage optimization. Finally, Section 6 summarizes and concludes the paper.

## 2. Problem Statement

- (1)
- MTs used in CCHP systems can operate at their highest capacity for the primary power load;
- (2)
- MTs can operate at optimal efficiency for the simulation period to minimize the proposed objective function.

_{1}to G

_{4}(corresponding to hydroelectric, nuclear, coal, and gas generation) were calculated from their known generating costs or using the optimal generation dispatch algorithm. MTs provide electrical and useful heat energy, and their waste heat energy can also act as input energy to ABCs, i.e., waste heat energy can be recovered using ABCs to cool air and water, which is subsequently used for cooling and heating loads. The proposed two-stage optimization shows that the effect of the recovered cooled air on cooling demand, mostly generated at the highest prices, can dramatically reduce peak demand during summer. The heat energy that MTs cannot supply during winter is provided by gas facilities.

## 3. Combined Heat and Power and Emission Output

#### 3.1. Combined Heat and Power System

#### 3.1.1. Microturbines

_{i}is MT power output (kW), and F

_{natural gas, i}is fuel consumption (L/h).

#### 3.1.2. Absorption Chillers

_{ABC}has a loss coefficient = 0.75 and a pipe loss coefficient = 0.9 [20]. Using the chilled water to supplement the cooling load reduces the required electrical power purchased from the grid for the cooling load. Let P

_{Total}be total power required from the load, and P

_{ABC}the cooling load offset from ABCs. Then, the power required from the grid is:

#### 3.2. Generator and Emission Modeling to Develop Optimization Algorithms

#### 3.2.1. Steam Turbine Generation

- F
_{i}= the fuel input of generating unit i in MBtu/h - P
_{Gi}= the net power output of generating unit i in MW - C
_{i}= total operating costs in USD/h - fp
_{i}= the equivalent fuel price of generating unit i in USD/MBtu

#### 3.2.2. Hydroelectric Unit

- q
_{i}= the water discharge of unit i or during interval i in acre-ft/h - P
_{Hi}= the hydroelectricity generation of unit i in MW

#### 3.2.3. Emissions Output

_{2}, NO

_{x}, and CO

_{2}and water evaporation can be estimated as cubics [23], respectively:

_{i}, ef

_{i}, F

_{i}, and WO

_{i}are the emission outputs (kg/h), the emission factors (kg/MBtu or gallons/MBtu), fuel input (MBtu/h), and water output (gallons/h) for unit i, respectively.

#### 3.3. Objective Function

_{2}, SO

_{2}, NO

_{x}, or water) with the weighting factors [24]. Users can perform various optimization simulations according to the target by resetting the weighted factor.

- W
_{cost}= weighting factors of grid generation units - W
_{i}= weighting factors of objective function i from 0 to 1

_{T}is the total cost to supply the indicated load, P

_{i}is the electrical power generated by unit I, P

_{loss}is the transmission network loss, and Ø is the energy balance, including losses.

#### 3.4. Typically Generation Allocation Algorithms with Lagrange Multiplier

## 4. Proposed Two-Stage Optimization

#### 4.1. First Stage Optimization

#### 4.2. Second Stage Optimization

## 5. Case Study

#### 5.1. Case Study A: First Stage Optimization in Georgia

#### 5.1.1. Electric and Thermal Load Profile

#### 5.1.2. Daily Generation Profiles

#### 5.1.3. Weekly Generation Profiles

#### 5.2. Case Study B: Second Stage Optimization in Atlanta

#### 5.2.1. Generation Profile

#### 5.2.2. Electric and Thermal Energy Savings

#### 5.2.3. Emissions Savings

_{2}reductions = 33.1%, 0.6%, and 55.1% compared to conditions without a CHP system. Although CO

_{2}decreased in all conditions, to minimize emissions, optimal-blast conditions show the most significant reduction, as expected. Figure 17b shows SO

_{2}reduction = 57.2% and 40.5% reductions for full and optimal-blast (minimize emissions) cases. However, the optimal-blast (to minimize costs) case (green bar) exhibited a 1.8% increase. Thus, optimal-blast (minimize costs) cannot reduce SO

_{2}. Figure 17c,d shows NO

_{x}and water reductions follow the same pattern as for SO

_{2}. Thus, we verified the proposed algorithm’s effectiveness from annual energy and emissions savings results as shown in Figure 16 and Figure 17.

## 6. Conclusions

_{2}, SO

_{2}, and NO

_{x}, emissions and water usage.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

ABC | absorption chiller |

CHP | combined heat and power |

CCHP | combined cooling heat and power |

GA | genetic algorithm |

GHG | greenhouse gas |

MT | microturbine |

p.u. | per unit |

PV | photovoltaic |

## Appendix A

_{2}, SO

_{2}, NO

_{x}, and water emissions, respectively.

**Table A1.**Parameters associated with C65 MTs [19].

Rating | 65 kW |
---|---|

Electrical efficiency (lower heating value) | 29% |

Combined heat and power efficiency | Up to 90% |

Exhaust temperature | 309 °C (599 °F) |

Compatible fuels | Natural gas, liquid fuels, sour gas, etc. |

Coal | Gas | Nuclear | Hydro | CHP | |
---|---|---|---|---|---|

CO_{2} (kg/kWh) | 8.8800 × 10^{−1} | 4.9900 × 10^{−1} | 2.9000 × 10^{−2} | 0 | 3.0255 × 10^{−1} |

SO_{2} (kg/kWh) | 6.0781 × 10^{−3} | 2.3133 × 10^{−6} | 0 | 0 | 3.0391 × 10^{−6} |

NO_{x} (kg/kWh) | 2.5401 × 10^{−3} | 9.0718 × 10^{−6} | 0 | 0 | 5.8967 × 10^{−5} |

Water (gallon/kWh) | 6.7000 × 10^{−1} | 2.7500 × 10^{−1} | 6.2000 × 10^{−1} | 18 | 0 |

Water (L/kWh) | 2.536225 | 1.040988 | 2.346954 | 68 | 0 |

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**Figure 3.**Typical fuel–cost curve for steam generation [13].

**Figure 13.**Original electric demand for peak day in Atlanta area [13].

Type for Electricity | Cost (USD/MWh) |
---|---|

Coal | 45.5 |

Nuclear | 7.8 |

Gas | 24.7 |

Purchased (imported) | 43.3 |

Microturbine | 39.11 |

Solar (community) | 40.14 |

Type for thermal | [USD/MWh] |

Thermal gas price | 48.11 |

Min Only CO_{2} | Min All Emissions | |
---|---|---|

Operation time per year (hour) | 23 | 8125 |

Utilization rate (%) | 0.26% | 92.75% |

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**MDPI and ACS Style**

Jo, H.; Park, J.; Kim, I.
Environmentally Constrained Optimal Dispatch Method for Combined Cooling, Heating, and Power Systems Using Two-Stage Optimization. *Energies* **2021**, *14*, 4135.
https://doi.org/10.3390/en14144135

**AMA Style**

Jo H, Park J, Kim I.
Environmentally Constrained Optimal Dispatch Method for Combined Cooling, Heating, and Power Systems Using Two-Stage Optimization. *Energies*. 2021; 14(14):4135.
https://doi.org/10.3390/en14144135

**Chicago/Turabian Style**

Jo, Haesung, Jaemin Park, and Insu Kim.
2021. "Environmentally Constrained Optimal Dispatch Method for Combined Cooling, Heating, and Power Systems Using Two-Stage Optimization" *Energies* 14, no. 14: 4135.
https://doi.org/10.3390/en14144135