# Experimental Analysis of a Heat Cost Allocation Method for Apartment Buildings

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## Abstract

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## 1. Introduction

_{2}emissions in the EU. As about 35% of the EU building stock is over 50 years old, the improvement of the energy efficiency of buildings could lead to a significant reduction of the total EU energy consumption and CO

_{2}emissions [1]. Space heating in apartment buildings is usually provided by outdated central heating systems, characterized by vertical hydraulic distributions with water radiators connected to the main risers. The refurbishment or the improvement of these types of heating system represents one of the main tasks towards the reduction of CO

_{2}emissions and can be pursued both by replacing older thermal-hydraulic components and devices and by optimizing their operation and control.

## 2. Thermal Power Exchanged by Water Radiators

#### 2.1. The European Standard EN 442

#### 2.2. The INRIM Central Heating System Test Facility

## 3. Characterization of the Proposed Heat Cost Allocation Method

- the correct identification of the thermal characteristics of each water radiator,
- the accurate evaluation of the temperature difference between the heat-conveying fluid flowing through each radiator and the ambient air in proximity of the radiator surface.

- the measurement of the opening time and opening degree of radiator valves,
- the identification of the characteristic coefficients of each water radiator,
- the measurements of the indoor air temperature at each living unit where the radiators are installed,
- the measurement of the hot water supply temperature at the boiler room,
- the estimation of the water flow rate circulating through each water radiator, depending on the opening degree of radiator valves, the total water flow rate flowing through the thermal-hydraulic circuit and the overall hydraulic head loss.

#### 3.1. Measurement Model

#### 3.2. Sensitivity Analysis

#### 3.3. Estimation of Water Flow Rates Circulating through the Radiators

## 4. Results of the Experimental Analysis

- Balanced hydraulic network: the thermal-hydraulic circuit of the central heating system has been preliminarily balanced, as should be recommended in real applications, in order to obtain a uniform flow rate distribution among the water radiators;
- Automatic control of the opening/closing time of radiator valves: the motorized supply valves of the 11 water radiators, which can only set on their fully-open/closed state, are preliminarily programmed in terms of opening/closing times, simulating typical daily occupancy behaviors, as shown in Figure 7;
- Constant water supply temperature and constant pump speed: the heater is set to ensure a constant hot water supply temperature of 65 °C, and the pump is set to operate at 45% of its maximum speed;
- Cooling down of radiator surfaces: the tests include the time needed for the complete natural cooling down of the heat transfer surface of radiators after either the closing of radiator valves or the shutdown of the heater; this is necessary in order to compare the heat cost allocation obtained by means of HCAs and the EN 442 model, with the one provided by reference direct heat meters;
- Long time duration of the tests: the tests are characterized by long-time recording, such that the resolution error of the 11 HCAs becomes negligible if compared to the corresponding amount of totalized units of heating consumption.

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Relative standard uncertainty associated with the thermal power measurement of a particular reference direct heat meter at the INRIM central heating system test facility.

**Figure 2.**Time evolution of: (

**a**) reference thermal power measurement obtained by direct heat metering and indirect thermal power estimation by the EN 442 model for a particular water radiator; (

**b**) corresponding relative deviation between thermal power estimation by the EN 442 model and reference direct heat metering.

**Figure 4.**Time evolution of: (

**a**) EcoThermo flow rate estimation and reference water flow rate measurement at a particular radiator; (

**b**) corresponding relative error of EcoThermo estimation with respect to reference water flow rate measurement.

**Figure 5.**Scheme of the thermal-hydraulic circuit of the INRIM test facility and selected set of water radiators.

**Figure 9.**Fractions of heating consumption associated with water radiators. HCA, Heat Cost Allocator.

**Figure 10.**Relative deviations from reference measurements of individual fractions of heating consumption.

**Figure 11.**Relative deviations from reference measurements of individual fractions of heating consumption, only for the aluminum radiators (cast iron and steel radiators have been excluded for the assessment of heat cost allocation).

**Table 1.**Uncertainties of temperature and flow rate measurement chains for a particular heat meter assembly at the INRIM central heating system test facility.

Range | Expanded Uncertainty (95% conf.int.) | |
---|---|---|

Temperature measurement chain (Pt100 sensor, 4-wire shielded cable, PLC module) | from 0 °C to 90 °C | 0.06 °C |

Electromagnetic flow meter | from 90 L/h to 1800 L/h | 0.2% (of the measured value) |

**Table 2.**Results of the sensitivity analysis and example of uncertainty budget for the proposed heat cost allocation model.

Estimate ${\mathit{x}}_{\mathit{i}}$ | Input Standard Uncertainty $\mathit{u}\left({\mathit{x}}_{\mathit{i}}\right)$ | Sensitivity Coefficient $\frac{1}{\dot{\mathit{Q}}}\frac{\partial \dot{\mathit{Q}}}{\partial {\mathit{x}}_{\mathit{i}}}$ | Output Relative Standard Uncertainty ${\mathit{u}}_{\mathit{i}}\left(\dot{\mathit{Q}}\right)/\dot{\mathit{Q}}$ | |||
---|---|---|---|---|---|---|

Water inlet temperature | 65 °C | 0.5 °C | Uniform | 2.97 | $\frac{\%}{\xb0\mathrm{C}}$ | 1.48% |

Indoor ambient temperature | 21 °C | 0.5 °C | Normal | −2.93 | $\frac{\%}{\xb0\mathrm{C}}$ | 1.47% |

Water flow rate | 80 L/h | 4 L/h | Uniform | 0.18 | $\frac{\%}{\mathrm{L}/\mathrm{h}}$ | 0.72% |

Radiator nominal thermal power (at ΔT = 50 °C) | 1400 W | 100 W | Uniform | 0.06 | $\frac{\%}{\mathrm{W}}$ | 5.95% |

Radiator exponent | 1.35 (-) | 0.1 (-) | Uniform | −21.54 | $\frac{\%}{\left(-\right)}$ | 2.15% |

Nominal Thermal Power at ΔT = 50 °C ${\dot{\mathit{Q}}}_{\mathit{N}50}$ (W) | Exponent $\mathit{n}$ | |
---|---|---|

Aluminum radiators | 1467 | 1.359 |

Cast iron radiators | 1427 | 1.3679 |

Tubular steel radiators | 1482 | 1.28 |

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**MDPI and ACS Style**

Saba, F.; Fernicola, V.; Masoero, M.C.; Abramo, S. Experimental Analysis of a Heat Cost Allocation Method for Apartment Buildings. *Buildings* **2017**, *7*, 20.
https://doi.org/10.3390/buildings7010020

**AMA Style**

Saba F, Fernicola V, Masoero MC, Abramo S. Experimental Analysis of a Heat Cost Allocation Method for Apartment Buildings. *Buildings*. 2017; 7(1):20.
https://doi.org/10.3390/buildings7010020

**Chicago/Turabian Style**

Saba, Fabio, Vito Fernicola, Marco Carlo Masoero, and Salvatore Abramo. 2017. "Experimental Analysis of a Heat Cost Allocation Method for Apartment Buildings" *Buildings* 7, no. 1: 20.
https://doi.org/10.3390/buildings7010020