# Robust Optimization of Power Consumption for Public Buildings Considering Forecasting Uncertainty of Environmental Factors

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## Abstract

**:**

## 1. Introduction

- (1)
- The energy consumption of lighting systems, air-conditioning systems, and elevator systems in public buildings is analyzed. The relationship between energy consumption and the external variables of the lighting system, air-conditioning system, and elevator system are modeled, respectively.
- (2)
- Considering the forecasting uncertainty of environmental factors (outdoor illuminance, temperature, and the flow of people in buildings), the robust indexes of the lighting system, air-conditioning system, and elevator system are established, respectively, and the synthetic robust index in public buildings is established.
- (3)
- A robust optimization model for power consumption in public buildings considering the forecasting uncertainty of environmental factors is established by robust indexes, with the objective of optimizing the total electricity cost and satisfying the users’ comfort.

## 2. Modeling the Electric Energy Consumption of Public Buildings

#### 2.1. Lighting System

_{av}is average illuminance, $\varphi $ is the luminous flux, N is the number of lamps, U is the utilization coefficient, K is the maintenance coefficient of lamps, and A is the illuminated area.

_{l,t}is the power consumption at the end of the tth time slot, E

_{set}is the target illuminance, E

_{e}is the natural illuminance, P

_{l}is the power of one lamp.

#### 2.2. Air-Conditioning System

- (a)
- Heat from the roof and exterior wall$${Q}_{1}=KA\left({T}_{out}-{T}_{in}\right)$$
_{out}and T_{in}are the inside and outside temperature, respectively. - (b)
- Solar radiation heat from glass windows$${Q}_{2}={C}_{a}A{C}_{s}{C}_{i}{D}_{j\mathrm{max}}{C}_{LQ}$$
_{a}is the effective area coefficient, A is window area, C_{s}is the sun shading coefficient, C_{i}is the shading coefficient, D_{jmax}is the maximum solar radiation heat, and C_{LQ}is the cooling load coefficient of window glass. - (c)
- Heat dissipation of bodies$${Q}_{3}={q}_{s}n\psi {C}_{LQ}$$
_{s}is the sensible heat gain for male adults, n is the total number of people in the building, ψ is the cluster coefficient, and C_{LQ}is the cooling load coefficient for sensible heat gain from human bodies. - (d)
- Heat dissipation of lamps$${Q}_{4}=1000{P}_{l}{C}_{LQ}$$
_{l}is the power required for lighting, C_{LQ}is the cooling load coefficient of lamps. - (e)
- Load of fresh airIn the air-conditioning system, the inclusion of outdoor fresh air is important to guarantee indoor air quality. The load of fresh air is calculated with the following Equation (7):$${Q}_{5}=M({h}_{out}-{h}_{in})$$
_{out}is the outdoor air enthalpy, h_{in}is the indoor air enthalpy,

_{p}is the minimum fresh air per person, R

_{b}is the minimum fresh air for each square meter, n is number of people, and s is the building area.

_{a,t}is the power consumption of the air-conditioning system at the tth time slot, Q is the cooling load, and COP is the coefficient of performance.

#### 2.3. Elevator System

_{lf}is the power consumption and F

_{p,τ}and N

_{car,τ}are the flow of people and number of elevators, respectively.

_{u,τ}is the up flow, P

_{d,τ}is the down flow, ${x}_{D,u,\tau}^{in}$ is the up flow from the first floor, and ${x}_{T}^{out}$ is the down flow from the highest floor.

#### 2.4. Objective of the Power Consumption Optimization Problem of Public Building

_{t}is the electricity price at the tth time slot, x

_{t}is the whole electric power consumption of lighting system, air-conditioning system and elevator system.

#### 2.5. Constraints of the Power Consumption Optimization Problem of Public Building

## 3. Robust-Index for Electric Energy Consumption Systems

#### 3.1. Lighting System

_{l,pre}is the outdoor illuminance under deterministic prediction, E

_{l,sup}is the supposed illuminance in power consumption optimization, RI

_{l}is the robust index of the lighting system, and RI

_{l,set}is the minimum robust index value needed.

_{l,min}, E

_{l,max}], which is the range of E

_{l,sup}. The maximum and minimum value of robust index RI

_{l}are respectively calculated by the following Equations (27) and (28):

#### 3.2. Air-Conditioning System

_{a,pre}is the outdoor temperature under deterministic prediction, T

_{a.sup}is the supposed temperature in power consumption optimization, RI

_{a}is the robust index of the air-conditioning system, and RI

_{a,set}is the minimum robust index value needed.

_{a,min}, T

_{a,max}], which is the range of T

_{a,sup}. The maximum and minimum value of robust index RI

_{a}are respectively calculated by the following Equations (30) and (31):

#### 3.3. Elevator System

_{p,pre}is the flow of people under deterministic prediction, F

_{p,sup}is the supposed flow in power consumption optimization, RI

_{p}is the robust index of the elevator system, RI

_{p,set}is the minimum robust index value needed.

_{p,min}, F

_{p,max}], which is the range of F

_{p,sup}. The maximum and minimum value of robust index RI

_{p}are respectively calculated by the following Equations (33) and (34):

#### 3.4. Normalization of Robust Index

_{N}is the normalized robust index, RI

_{raw}is a raw robust index before normalization, and RI

_{max}and RI

_{min}are the maximum and minimum values of corresponding raw robust indexes.

#### 3.5. Synthetic Robust Index

_{δ}is the weighted coefficient of sub electric energy utilization system δ, and it reflects the importance of the sub electric energy utilization system, RI

_{mix}is the synthetic robust index. In addition, the synthetic robust index is less than RI

_{req}, which reflects the overall robustness level of public buildings.

## 4. Numerical Examples

#### 4.1. Initial Data

^{2}. The lighting power per unit area is 3 W with the luminous flux 100 mL/W. The lighting utilization coefficient is 0.5 and the lighting maintenance coefficient is 0.8. The total cooling area for the air-conditioning system is 17,768 m

^{2}and the total exterior wall area of the public building is 7000 m

^{2}. The average window–wall ratio is 0.38. In addition, there are 8 elevators in this building.

#### 4.2. Simulations

## 5. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

- Guan, X.; Xu, Z.; Jia, Q.S. Energy-efficient buildings facilitated by microgrid. IEEE Trans. Smart Grid
**2010**, 1, 243–252. [Google Scholar] [CrossRef] - Rahimi, F.; Ipakchi, A. Demand response as a market resource under the smart grid paradigm. IEEE Trans. Smart Grid.
**2010**, 1, 82–88. [Google Scholar] [CrossRef] - Xiao, J.; Xie, J.; Chen, X.; Yu, K.; Chen, Z.; Li, Z. Energy cost reduction robust optimization for meeting scheduling in smart commercial buildings. In Proceedings of the IEEE Conference on Energy Internet and Energy System Integration, Beijing, China, 26–28 November 2017; pp. 1–5. [Google Scholar]
- Yang, C.; Li, H.; Rezgui, Y.; Petri, I.; Yuce, B.; Chen, B. High throughput computing based distributed genetic algorithm for building energy consumption optimization. Energy Build.
**2014**, 76, 92–101. [Google Scholar] [CrossRef] - Yang, Z.; Long, K.; You, P.; Chow, M.Y. Joint scheduling of large-scale appliances and batteries via distributed mixed optimization. IEEE Trans. Power Syst.
**2015**, 30, 2031–2040. [Google Scholar] [CrossRef] - Shao, S.; Pipattanasomporn, M.; Rahman, S. Development of physical-based demand response-enabled residential load models. IEEE Trans. Power Syst.
**2013**, 28, 607–614. [Google Scholar] [CrossRef] - Shah, J.J.; Nielsen, M.C.; Shaffer, T.S.; Fittro, R.L. Cost-optimal consumption-aware electric water heating via thermal storage under time-of-use pricing. IEEE Trans. Smart Grid
**2016**, 7, 592–599. [Google Scholar] [CrossRef] - Pipattanasomporn, M.; Kuzlu, M.; Rahman, S. An algorithm for intelligent home energy management and demand response analysis. IEEE Trans. Smart Grid
**2012**, 3, 2166–2173. [Google Scholar] [CrossRef] - Nguyen, H.T.; Nguyen, D.T.; Le, L.B. Energy management for households with solar assisted thermal load considering renewable energy and price uncertainty. IEEE Trans. Smart Grid
**2015**, 6, 301–314. [Google Scholar] [CrossRef] - Diana, N.; Miguel, C.B.; Carlos, A. Impact of solar and wind forecast uncertainties on demand response of isolated microgrids. Renew. Energy
**2016**, 87, 1003–1015. [Google Scholar] - Linquan, B.; Fangxing, L.; Hantao, C.; Tao, J.; Hongbin, S.; Jinxiang, Z. Interval optimization based operating strategy for gas-electricity integrated energy systems considering demand response and wind uncertainty. Appl. Energy
**2015**, 167, 270–279. [Google Scholar] - Chen, Z.; Wu, L.; Fu, Y. Real-time price-based demand response management for residential appliances via stochastic optimization and robust optimization. IEEE Trans. Smart Grid
**2012**, 3, 1822–1831. [Google Scholar] [CrossRef] - Soroudi, A.; Siano, P.; Keane, A. Optimal DR and ESS Scheduling for Distribution Losses Payments Minimization Under Electricity Price Uncertainty. IEEE Trans. Smart Grid
**2016**, 7, 261–272. [Google Scholar] [CrossRef] - Wei, W.; Liu, F.; Mei, S. Energy pricing and dispatch for smart grid retailers under demand response and market price uncertainty. IEEE Trans. Smart Grid
**2017**, 6, 1364–1374. [Google Scholar] [CrossRef] - Linna, N.I.; Wen, F.; Liu, W.; Meng, J.; Lin, G.; Dang, S. Congestion management with demand response considering uncertainties of distributed generation outputs and market prices. J. Mod. Power Syst. Clean Energy
**2017**, 5, 66–78. [Google Scholar] - Dian-Ce, G.; Yongjun, S.; Yuehong, L. A robust demand response control of commercial buildings for smart grid under load prediction uncertainty. Energy
**2015**, 93, 275–283. [Google Scholar] - Conejo, A.J.; Morales, J.M.; Baringo, L. Real-time demand response model. IEEE Trans. Smart Grid
**2010**, 1, 236–242. [Google Scholar] [CrossRef] - Kim, S.J.; Giannakis, G.B. Scalable and robust demand response with mixed-integer constraints. IEEE Trans. Smart Grid
**2013**, 4, 2089–2099. [Google Scholar] - Wang, C.; Zhou, Y.; Wu, J.; Wang, J.; Zhang, Y.; Wang, D. Robust-index method for household load scheduling considering uncertainties of customer behavior. IEEE Trans. Smart Grid
**2017**, 6, 1806–1818. [Google Scholar] [CrossRef] - Chen, T.C.; Hsu, Y.Y.; Huang, Y.J. Optimizing the intelligent elevator group control system by using genetic algorithm. J. Comput. Theor. Nanosci.
**2012**, 9, 957–962. [Google Scholar] [CrossRef] - Hernández, J.C.; Ruiz-Rodriguez, F.J.; Jurado, F. Modelling and assessment of the combined technical impact of electric vehicles and photovoltaic generation in radial distribution systems. Energy
**2017**, 141, 316–332. [Google Scholar] [CrossRef] - Ruiz-Rodriguez, F.J.; Hernández, J.C.; Jurado, F. Voltage behaviour in radial distribution systems under the uncertainties of photovoltaic systems and electric vehicle charging loads. Int. Trans. Electr. Energy Syst.
**2017**, 28, e2490. [Google Scholar] [CrossRef] - Ruiz-Rodriguez, F.J.; Hernandez, J.C.; Jurado, F. Probabilistic load flow for radial distribution networks with photovoltaic generators. IET Renew. Power Gener.
**2012**, 6, 110–121. [Google Scholar] [CrossRef] - Cannistraro, M.; Cannistraro, G.; Restivo, R. Smart Controll of Air Climatization System in Function on the Values of the Mean Local Radiant Temperature. Smart Sci.
**2015**, 3, 157–163. [Google Scholar] [CrossRef] - Cannistraro, M.; Cannistraro, G.; Restivo, R. The Local Media Radiant Temparature for the Calculation of Comfort in areas Characterized by Radiant surfaces. Int. J. Heat Technol.
**2015**, 1, 115–122. [Google Scholar] [CrossRef] - Cannistraro, M.; Castelluccio, M.E.; Germanò, D. New Sol-Gel Deposition Technique in the Smart Windows Computation of Possible Applications of Smart Windows in Buildings. J. Build. Eng.
**2018**, 19, 295–301. [Google Scholar] [CrossRef] - Piccolo, A.; Siclari, R.; Rando, F.; Cannistraro, M. Comparative Performance of Thermoacoustic Heat Exchangers with Different Pore Geometries in Oscillatory Flow. Implementation of Experimental Techiniques. Appl. Sci.
**2017**, 7, 784. [Google Scholar]

RI_{N-set} | Cost/¥ |
---|---|

0 | 942.95 |

0.05 | 959.83 |

0.1 | 976.7 |

0.15 | 993.58 |

0.2 | 1010.46 |

0.25 | 1027.33 |

RI_{N-set} | Cost/¥ |
---|---|

0 | 2127.49 |

0.1 | 2132.75 |

0.2 | 2138 |

0.3 | 2134.81 |

0.4 | 2149.61 |

0.5 | 2155.41 |

0.6 | 2161.21 |

0.7 | 2167 |

0.8 | 2172.8 |

0.9 | 2178.6 |

1 | 2184.4 |

RI_{N-set} | Cost/¥ |
---|---|

0 | 918.02 |

0.1 | 929.11 |

0.2 | 940.2 |

0.3 | 951.29 |

0.4 | 962.38 |

0.5 | 973.47 |

0.6 | 984.56 |

0.7 | 995.65 |

0.8 | 1006.74 |

0.9 | 1017.83 |

1 | 1028.92 |

RI_{N-set} | Cost/¥ |
---|---|

0 | 756.61 |

0.1 | 791.65 |

0.2 | 826.69 |

0.3 | 861.72 |

0.4 | 896.76 |

0.5 | 931.79 |

0.6 | 966.83 |

0.7 | 1001.86 |

0.8 | 1036.9 |

0.9 | 1071.94 |

1 | 1106.97 |

Case | Weighted Coefficient | ||
---|---|---|---|

Lighting | Air-Conditioning | Elevator | |

1 | 0.3 | 0.4 | 0.3 |

2 | 0.3 | 0.4 | 0.3 |

3 | 0.6 | 0.3 | 0.1 |

Case | Robust Index Values | |||
---|---|---|---|---|

Lighting | Air-Conditioning | Elevator | Synthetic | |

1 | 0.05 | 0.43 | 0.05 | 0.2 |

2 | 0.05 | 1 | 0.28 | 0.5 |

3 | 0.325 | 1 | 0.05 | 0.5 |

Case | Cost/¥ |
---|---|

1 | 4553.26 |

2 | 4626.83 |

3 | 4681.87 |

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## Share and Cite

**MDPI and ACS Style**

Xiao, J.; Xie, J.; Chen, X.; Yu, K.; Chen, Z.; Luan, K.
Robust Optimization of Power Consumption for Public Buildings Considering Forecasting Uncertainty of Environmental Factors. *Energies* **2018**, *11*, 3075.
https://doi.org/10.3390/en11113075

**AMA Style**

Xiao J, Xie J, Chen X, Yu K, Chen Z, Luan K.
Robust Optimization of Power Consumption for Public Buildings Considering Forecasting Uncertainty of Environmental Factors. *Energies*. 2018; 11(11):3075.
https://doi.org/10.3390/en11113075

**Chicago/Turabian Style**

Xiao, Jingshu, Jun Xie, Xingying Chen, Kun Yu, Zhenyu Chen, and Kaining Luan.
2018. "Robust Optimization of Power Consumption for Public Buildings Considering Forecasting Uncertainty of Environmental Factors" *Energies* 11, no. 11: 3075.
https://doi.org/10.3390/en11113075