# An Integrated Energy Simulation Model for Buildings

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## Abstract

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## 1. Introduction

## 2. Methodology and Modeling Approaches

#### 2.1. The Energy Simulation Model: General Presentation of the Model, Areas of Application, Advantages, and Shortcomings

- ${q}_{\alpha sol}^{\u2033}$ is the absorbed direct and diffuse solar (short wavelength) radiation and heat flux
- ${q}_{LWR}^{\u2033}$ is the net long wavelength (thermal) radiation flux exchange with the air and surroundings
- ${q}_{conv}^{\u2033}$ is the convective flux exchange with the outside air
- ${q}_{ko}^{\u2033}$ is the conduction heat flux (q/A) into the wall

- $\u03f5$ is the long-wave emittance of the surface
- $\sigma $ is the Stefan–Boltzmann constant
- ${F}_{gnd}$ is the view factor of wall surface to ground surface temperature
- ${F}_{sky}$ is the view factor of wall surface to sky temperature
- ${F}_{air}$ is the view factor of wall surface to air temperature
- ${T}_{surf}$ is the outside surface temperature
- ${T}_{gnd}$ is the ground surface temperature
- ${T}_{sky}$ is the sky temperature
- ${T}_{air}$ is the air temperature

- ${q}_{conv}^{\u2033}$ is the rate of exterior convective heat transfer
- ${h}_{c,ext}$ is the exterior convection coefficient
- A is the surface area
- ${T}_{surf}$ is the surface temperature
- ${T}_{a}ir$ is the outdoor air temperature

- ${q}_{ko}^{\u2033}(t)$ is the conductive heat flux for the current time step
- T is temperature
- i indicates the internal element of the building
- o indicates the external element of the building
- X,Y are the response factors

- ${X}_{j}$ is the outside CTF coefficient, j = 0,1,...nz
- ${Y}_{j}$ is the cross CTF coefficient, j = 0,1,...nz
- ${Z}_{j}$ is the inside CTF coefficient, j = 0,1,...nz
- ${\varphi}_{j}$ is the flux CTF coefficient, j = 0,1,...nq
- ${T}_{i}$ is the inside surface temperature
- ${T}_{o}$ is the outside surface temperature
- ${q}_{ko}^{\u2033}$ is the conduction heat flux on the outside face
- ${q}_{ki}^{\u2033}$ is the conduction heat flux on the inside face

- ${\sum}_{i=1}^{{N}_{sl}}{\dot{Q}}_{i}$ is the sum of convective heat transfer from the zone surfaces
- ${\sum}_{i=1}^{{N}_{surfaces}}{h}_{i}{A}_{i}({T}_{si}-{T}_{z})$ is the convective heat transfer from the zone surfaces
- ${\dot{m}}_{inf}{C}_{p}({T}_{zi}-{T}_{z})$ is the heat transfer due to infiltration of outside air
- ${\sum}_{i=1}^{{N}_{surfaces}}{\dot{m}}_{i}{C}_{p}({T}_{zi}-{T}_{z})$ is the heat transfer due to interzone air mixing
- ${\dot{Q}}_{sys}$ is the air systems output
- ${C}_{z}\frac{d{T}_{z}}{dt}$ is the energy stored in zone air, and
- ${C}_{z}={\rho}_{air}{C}_{p}{C}_{T}$

- ${I}_{design}$ is the user defined infiltration value (ACH${}^{-1}$)
- ${T}_{zone}$ is the zone air temperature at current conditions (deg C)
- ${T}_{odb}$ is the outdoor air dry-bulb temperature (deg C)
- ${F}_{schedule}$ is a user defined schedule value between 0 and 1
- A is the constant term coefficient
- B is the temperature term coefficient
- C is the velocity term coefficient
- D is the velocity squared coefficient

- ${V}_{design}$ is the user defined ventilation value (ACH${}^{-1}$)
- ${T}_{zone}$ is the zone air temperature at current conditions (deg C)
- ${T}_{odb}$ is the outdoor air dry-bulb temperature (deg C)
- ${F}_{schedule}$ is a user defined schedule value between 0 and 1
- A is the constant term coefficient
- B is the temperature term coefficient
- C is the velocity term coefficient
- D is the velocity squared coefficient

#### 2.2. Shape Modeling and Systematic Inefficiencies Correction of the Prediction Model: Presentation of the Properties and Capabilities of the Shape Invariant Model and Implementation in the Current Study

#### 2.2.1. The Shape Model Approach

**Initial**

**Step**

**Step**

**1**

**Step**

**2**

**Step**

**3**

#### 2.2.2. The Weighted Shape Model Approach

#### 2.3. Postprocessing Using Kalman Filtering: The General Algorithm, Capabilities and Areas of Application, and the Filter Proposed for the Present Work

## 3. Test Cases and Results

- Prediction Bias, $Bias=\frac{1}{T}{\sum}_{t=1}^{T}({X}_{t}-{\widehat{X}}_{t})$, indicating any systematic underestimation or overestimation of the quantity of interest.
- Mean Absolute Error, $MAE=\frac{1}{T}{\sum}_{t=1}^{T}|{X}_{t}-{\widehat{X}}_{t}|$, indicating the mean absolute deviance of the model predictions from the true value.
- Root Mean Squared Error, $RMSE=\sqrt{\frac{1}{T}{\sum}_{t=1}^{T}{({X}_{t}-{\widehat{X}}_{t})}^{2}}$, indicating the mean squared deviance of the model predictions from the true value.
- Nash–Sutcliffe model efficiency coefficient, which is used to assess the predictive power of the model:$$NSE=1-\frac{{\sum}_{t=1}^{T}{({X}_{t}-{\widehat{X}}_{t})}^{2}}{{\sum}_{t=1}^{T}{({X}_{t}-{\tilde{X}}_{t})}^{2}},$$

#### 3.1. Indicative Analysis of the Initial Simulation Results: Revealing the Weak Points

#### 3.2. Diagnostic Results for the Complete Model Outputs

#### 3.2.1. Evaluating Intra-Day Energy Demand Predictions

#### 3.2.2. Evaluating Daily Summaries Energy Demand Predictions

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Example of the observed and simulated daily energy demand (per hour) and the corresponding reshape functions for the time period 22/01/2018 to 26/01/2018.

**Figure 5.**Measured total HVAC electrical energy consumption for the year 2017 versus: (

**a**) initial model (baseline) (

**left plot**) and (

**b**) parameterized model (optimized) (

**right plot**).

**Figure 6.**Measured total HVAC electrical energy consumption for the year 2018 versus: (

**a**) initial model (baseline) (

**left plot**) and (

**b**) parameterized model (optimized) (

**right plot**).

**Figure 8.**Statistical error indices for the energy prediction through the simulation model (SM) and the optimized simulation model (OSM) for the year 2017 (per month).

**Figure 9.**Statistical error indices for the energy prediction through the simulation model (SM) and the optimized simulation model (OSM) for the year 2018 (per month).

**Figure 10.**Statistical error indices for the Reshaped Simulation Model (RS) and the Weighted Reshaped Simulation Model (w-RS) for the year 2017 (per month).

**Figure 11.**Statistical error indices for the Reshaped Simulation Model (RS) and the Weighted Reshaped Simulation Model (w-RS) for the year 2018 (per month).

**Figure 12.**Prediction of the daily energy demand (summary) obtained by optimized simulation model (OSM) and Kalman filter-enhanced reshaped simulation model (KF-RS) for the year 2017.

**Figure 13.**Prediction of the daily energy demand (summary) obtained by optimized simulation model (OSM) and Kalman filter-enhanced reshaped simulation model (KF-RS) for the year 2018.

**Table 1.**Monthly measured HVAC electrical energy consumption values and the corresponding simulated ones obtained from the baseline and optimized models for 2017.

2017 | Simulated - Baseline Model (MWh) | Simulated - Optimized Model (MWh) | Measured (MWh) |
---|---|---|---|

Jan | 31.55 | 27.79 | 25.72 |

Feb | 10.26 | 19.27 | 19.61 |

Mar | 11.09 | 15.76 | 17.55 |

Apr | 6.79 | 8.92 | 9.64 |

May | 2.90 | 15.40 | 16.02 |

Jun | 21.97 | 27.10 | 26.34 |

Jul | 20.02 | 23.69 | 25.55 |

Aug | 27.19 | 30.31 | 27.27 |

Sep | 6.39 | 13.15 | 18.87 |

Oct | 7.62 | 10.56 | 14.00 |

Nov | 17.05 | 14.38 | 15.86 |

Dec | 17.70 | 15.62 | 16.24 |

**Table 2.**Monthly measured HVAC electrical energy consumption values and the corresponding simulated ones obtained from the baseline and optimized models for 2018.

2018 | Simulated - Baseline Model (MWh) | Simulated - Optimized Model (MWh) | Measured (MWh) |
---|---|---|---|

Jan | 22.60 | 27.29 | 23.02 |

Feb | 21.42 | 22.52 | 22.49 |

Mar | 20.29 | 21.07 | 20.40 |

Apr | 5.92 | 8.76 | 13.85 |

May | 3.27 | 11.76 | 17.01 |

Jun | 17.65 | 22.30 | 24.09 |

Jul | 29.32 | 29.45 | 30.90 |

Aug | 30.94 | 34.56 | 34.16 |

Sep | 9.92 | 18.99 | 20.13 |

Oct | 6.88 | 10.06 | 10.11 |

Nov | 14.29 | 18.80 | 15.75 |

Dec | 17.96 | 18.46 | 18.14 |

**Table 3.**Model diagnostic results for intra-day energy demand predictions (hourly) for the years 2017 and 2018.

Model | Bias | MAE | RMSE | NSE | Bias | MAE | RMSE | NSE |
---|---|---|---|---|---|---|---|---|

2017 | 2018 | |||||||

SM | −8.67 | 21.32 | 31.66 | 0.00 | −7.67 | 22.66 | 35.56 | 0.00 |

OSM | −1.79 | 19.39 | 28.80 | 0.17 | −0.63 | 21.77 | 32.58 | 0.16 |

RS | −0.14 | 12.92 | 20.46 | 0.58 | −0.25 | 12.91 | 22.01 | 0.62 |

w−RS | −0.51 | 9.91 | 17.03 | 0.71 | −0.18 | 9.58 | 17.65 | 0.75 |

KF−RS | 0.20 | 11.33 | 17.60 | 0.70 | −0.36 | 12.67 | 18.73 | 0.73 |

**Table 4.**Model diagnostic results for the predictions on the daily energy demand (summaries) for the years 2017 and 2018.

Model | Bias | MAE | RMSE | NSE | Bias | MAE | RMSE | NSE |
---|---|---|---|---|---|---|---|---|

2017 | 2018 | |||||||

SM | −195.00 | 344.65 | 423.71 | 0.00 | −182.59 | 306.54 | 413.80 | 0.00 |

OSM | −37.54 | 237.38 | 304.32 | 0.30 | −12.80 | 232.49 | 328.62 | 0.30 |

RS | −1.90 | 192.54 | 272.03 | 0.44 | −6.09 | 194.10 | 295.32 | 0.32 |

w−RS | −11.18 | 144.97 | 226.93 | 0.61 | −4.39 | 139.18 | 238.78 | 0.50 |

KF−RS | −0.73 | 143.46 | 207.51 | 0.66 | −1.70 | 155.74 | 247.69 | 0.51 |

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## Share and Cite

**MDPI and ACS Style**

Kampelis, N.; Papayiannis, G.I.; Kolokotsa, D.; Galanis, G.N.; Isidori, D.; Cristalli, C.; Yannacopoulos, A.N. An Integrated Energy Simulation Model for Buildings. *Energies* **2020**, *13*, 1170.
https://doi.org/10.3390/en13051170

**AMA Style**

Kampelis N, Papayiannis GI, Kolokotsa D, Galanis GN, Isidori D, Cristalli C, Yannacopoulos AN. An Integrated Energy Simulation Model for Buildings. *Energies*. 2020; 13(5):1170.
https://doi.org/10.3390/en13051170

**Chicago/Turabian Style**

Kampelis, Nikolaos, Georgios I. Papayiannis, Dionysia Kolokotsa, Georgios N. Galanis, Daniela Isidori, Cristina Cristalli, and Athanasios N. Yannacopoulos. 2020. "An Integrated Energy Simulation Model for Buildings" *Energies* 13, no. 5: 1170.
https://doi.org/10.3390/en13051170