# Dynamic Approach to Evaluate the Effect of Reducing District Heating Temperature on Indoor Thermal Comfort

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Calculation Framework

- A text general input file, in which the main settings and input parameters are listed, and
- Database spreadsheet files for buildings and primary heat exchangers

#### 2.2. Energy Calculation Model

#### 2.3. Heating System Model

- Plate heat exchanger (HE) to transfer heat from the primary (DH) side to the secondary (user, U) side; it is modeled based on the technical information provided by the manufacturer, as explained below.
- Primary control valve (V1), to modulate the primary flow rate in order to obtain the desired supply temperature on the secondary side; it is assumed as an ideal component that instantaneously performs the required action.
- Thermostatic radiator valve (TRV), a proportional controller that modulates the secondary flow rate according to the difference between room temperature and average radiator temperature.
- Radiator (RAD) with a given nominal power referred to the design temperatures typical of the period of installation; due to the single-zone assumption, all the heating emitters are lumped into a single component, whose installed power is calculated in a preliminary simulation run based on the peak load of the building.

**Power released to the room.**The equation describing the heat release $\mathsf{\Phi}$ from a radiator with thermostatic control to the room is

**Return temperature.**In their paper, Lundström et al. [37] include an empirical correlation for the return temperature from the radiator which has also been used in the present work:

**Secondary supply temperature control.**The secondary supply temperature is controlled through the modulation of the primary flow rate according to a certain logic. In case of fixed-point option, the control system acts to keep the secondary supply temperature at the set value, ${\overline{\theta}}_{\mathrm{u},\mathrm{s}}$:

**Radiator energy balance.**Neglecting the thermal inertia of the radiator, the heating power transferred from the water flowing through the radiator is given by

**Power supplied by DH.**Neglecting the thermal inertia of the water circulating on the user side, the heating power transferred from the DH to the secondary side of the heat exchanger is

**DH heat exchanger model.**To close the system, a set of equations must be derived that represents the heat transfer behavior of the interface heat exchanger. This model is fully described in the next Subsection.

#### 2.4. Heat Exchanger Model

#### 2.5. Evaluation of Indoor Comfort

- metabolic rate M, expressing a typical level of activity of the occupants;
- thermal insulation for clothing, ${I}_{\mathrm{cl}}$;
- internal air temperature, ${\theta}_{\mathrm{air}}$;
- mean radiant temperature of the internal surfaces, ${\theta}_{\mathrm{mr}}$;
- air velocity, ${v}_{\mathrm{air}}$;
- relative humidity, RH.

## 3. Application

#### 3.1. Presentation of the Case

#### 3.2. Heating System Information

- Full definition of the building.
- Calculation of heating load according to EN ISO 52016-1:2017, clause 6.5.5.2.
- Definition of user supply/return temperatures based on period of construction, which are set as the outlet and inlet flow temperatures on the secondary side of the heat exchanger.
- Calculation of design user flow rate from the calculated load and temperature difference: the secondary side of the heat exchanger is fully characterized.
- Sizing of the heat exchanger with the complete information on the secondary side and the DH supply temperature on the primary side: the DH return temperature and the primary flow rate are outputs of the calculation, together with the heat exchanger model. Here, this step is entirely performed by means of the proprietary software made available by the heat exchanger manufacturer.
- Collection of the heat exchanger parameters necessary for the model described in Section 2.4, including number of plates, heat transfer area, channel areas and so on. Parameters $c1$, $c2$ and $c3$ in Equation (12) are derived by fitting the equation on the results of simulations performed with the manufacturer software.

#### 3.3. Building Typology Matrix and Additional Data

- single family house (SFH)
- terraced house (TH)
- multifamily house (MFH)
- apartment block (AB)

- ≤1900
- 1901–1920
- 1921–1945
- 1946–1960
- 1961–1975
- 1976–1990
- 1991–2005
- ≥2006

- mass distribution of opaque and ground floor elements (Table 2). The reference is Table 1 in Lundström et al. [37], where five possible arrangements of the three layers are outlined: mass on interior side (I), mass on exterior side (E), mass divided on interior and exterior side (IE), equally distributed mass (D) and inside/centered mass (M);
- specific heat capacities of opaque and ground floor elements (Table 2). The reference is Table A.14 of EN ISO 52016-1:2017 standard, where five classes are identified: very light (VL), light (L), medium (M), heavy (H), very heavy (VH). The assigment has been made based on the detailed layer structure description given in the TABULA/EPISCOPE project;
- exposition fractions (Table 3);
- nominal supply and return temperature of the user heating system (Table 2); assuming a design internal set-point, the calculation of the nominal LMTD is straightforward;
- nominal (installed) power, referred to the nominal conditions assumed at the previous point (Table 2).

#### 3.4. Climate-Related Input Data

- outdoor air temperature;
- wind speed at 10 m height;
- beam normal and diffuse horizontal solar irradiance;
- ground temperature;
- surface infrared thermal irradiance on horizontal plane.

#### 3.5. Comfort Indicators

- Operative temperature, defined according to EN ISO 52016-1:2017 as:$${\theta}_{\mathrm{op}}=\frac{{\theta}_{\mathrm{air}}+{\theta}_{\mathrm{mr}}}{2}$$
- Minimum PMV calculated in the reference period T:$${PMV}_{\mathrm{min}}=\underset{\forall \mathit{t}\in \mathit{T}}{min}\left\{PMV\left(t\right)\right\}.$$
- Percentage of time steps in the reference period in which the PMV is below the minimum threshold for the selected IEQ class, ${PMV}_{\mathrm{IEQ},\mathrm{l}}$, which is a modified version of the “percentage of outside the range” parameter:$$POR=\frac{{\sum}_{\forall \mathit{t}\in \mathit{T}}\left(PMV\left(t\right)\le {PMV}_{\mathrm{IEQ},\mathrm{l}}\right)}{{N}_{\mathit{T}}}\xb7100,$$

## 4. Results and Discussion

#### 4.1. Baseline and Pre-Retrofitting

- original building with design DH supply temperature;
- original building with reduced DH supply temperature;
- renovated building with reduced DH supply temperature,

#### 4.2. Three Retrofitting Scenarios

- Building in the original state
- Building with replaced windows
- Building with replaced windows and state-of-the-art insulation applied to the opaque elements

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

AB | Apartment Block |

DH | District Heating |

GIS | Geographical Information System |

HE | Heat Exchanger |

HVAC | Heating, Ventilation, and Air Conditioning |

LMTD | Logarithmic Mean Temperature Difference |

LTDH | Low Temperature District Heating |

MFH | Multi-Family House |

PB | Proportional Band |

PMV | Predicted Mean Vote |

POR | Percentage Outside Range |

PPD | Predicted Percentage of Dissatisfied |

RC | Resistor-Capacitor |

RES | Renewable Energy Source |

RH | Relative Humidity |

SFH | Single Family House |

TES | Thermal Energy Storage |

TH | Terraced House |

TRV | Thermostatic Radiator Valve |

air | internal air |

c | cold fluid |

cl | clothing |

DH | district heating |

e | external, outdoors |

ew | external walls |

foul | fouling |

gf | ground floor |

gl | glazing |

h | hot fluid |

int | internal |

max | maximum |

min | minimum |

nom | nominal |

op | operative |

p | plate |

r | return |

rad | radiator |

rf | roof |

rm | mean radiant |

s | supply |

set | set-point |

u | user |

w | water |

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**Figure 3.**Variation of percentage outside range (POR) parameter with decreased district heating (DH) temperature (115 ${}^{\circ}$C to 95 ${}^{\circ}$C and 115 ${}^{\circ}$C to 88 ${}^{\circ}$C).

**Figure 4.**Top: user supply/return temperatures in a winter period in a single family house built before 1900 (

**left**) and a single family house built after 2006 (

**right**) after decreasing the DH temperature from 115 ${}^{\circ}$C to 88 ${}^{\circ}$C. Bottom: corresponding PMVs. Discomfort periods are indicated by the gray areas.

**Figure 5.**Ratio between actual and design LMTD for an old single family house built before 1900 (solid line) and a new single family house built after 2006 (dashed line), for the same period of the year as in Figure 4. Discomfort periods are indicated by the hatched area (old building) and the gray area (new building).

**Figure 6.**Minimum predicted mean vote (PMV) recorded in the heating season for the different types of buildings as a function of construction period. Gray area: standard deviation of the PMVs for the different building types.

**Figure 7.**Distribution of predicted percentage of dissatisfied (PPD) over the heating season for single family house built between 1961–1975 (

**left**) and built after 2006 (

**right**), and decreasing DH supply temperatures.

**Figure 8.**Indoor operative temperature in a winter period for a single family house built between 1961 and 1975 at different DH supply temperatures. Original design temperature: ${\theta}_{\mathrm{DH}}=115$${}^{\circ}$C. Operative temperature set-point: 20.5 ${}^{\circ}$C.

**Figure 9.**Ratio between the secondary flow rate need with decreased DH temperature (${\theta}_{\mathrm{DH}}=88$${}^{\circ}$C) and the original design flow rate (${\theta}_{\mathrm{DH}}=115$${}^{\circ}$C) for the different types of buildings as a function of construction period.

**Figure 10.**Radiator oversizing factor, ${k}_{\mathrm{rad}}$, for the different types of buildings as a function of construction period.

**Figure 11.**Variation of POR parameter with decreased DH temperature (115 ${}^{\circ}$C to 88 ${}^{\circ}$C) for different retrofit measures on the buildings: original building with no renovation (lightest shade); building with original opaque elements and state-of-the-art windows (intermediate shade); fully renovated building (darkest shade).

**Figure 12.**Indoor operative temperature in a winter period for a single family house built between 1961 and 1975. Operative temperature set-point: 20.5 ${}^{\circ}$C.

**Table 1.**Indoor environmental quality classes and relative index limits (${v}_{\mathrm{air}}<0.1$ m/s; RH ≈ 50%; ${I}_{\mathrm{cl}}\approx 1$ clo).

Category | Level of Expectation | Accepted PMV | Accepted PPD | Minimum ${\mathit{\theta}}_{\mathbf{op}}$ (Heating) |
---|---|---|---|---|

I | High | <6 | $-0.2<$ PMV $<+0.2$ | $21.0$ |

II | Medium | <10 | $-0.5<$ PMV $<+0.5$ | $20.0$ |

III | Moderate | <15 | $-0.7<$ PMV $<+0.7$ | $18.0$ |

IV | Low | <25 | $-1.0<$ PMV $<+1.0$ | $16.0$ |

**Table 2.**Additional information for the Italian building typology matrix (MDc: mass distribution class, according to Reference [37], Table 1; SHCc: specific heat capacity class, according to Reference [34], Table A.14). Subscripts “rf”, “ew” and “gf” indicate roof, external walls and ground floor elements, respectively.

Quantity | Unit | SFH.01 | SFH.02 | SFH.03 | SFH.04 | SFH.05 | SFH.06 | SFH.07 | SFH.08 |

SHCc${}_{\mathrm{rf}}$ | - | VL | VL | VL | H | H | H | VH | VH |

MDc${}_{\mathrm{rf}}$ | - | E | E | E | M | M | M | D | IE |

SHCc${}_{\mathrm{ew}}$ | - | VH | VH | VH | VH | VH | VH | VH | VH |

MDc${}_{\mathrm{ew}}$ | - | D | D | D | D | D | IE | M | I |

SHCc${}_{\mathrm{gf}}$ | - | VH | VH | VH | VH | VH | VH | VH | VH |

MDc${}_{\mathrm{gf}}$ | - | D | D | D | D | D | D | D | E |

${\theta}_{\mathrm{u},\mathrm{s},\mathrm{nom}}$ | ${}^{\circ}$C | 85 | 85 | 85 | 85 | 85 | 75 | 70 | 60 |

${\theta}_{\mathrm{u},\mathrm{r},\mathrm{nom}}$ | ${}^{\circ}$C | 75 | 75 | 75 | 75 | 75 | 65 | 55 | 40 |

${\mathsf{\Phi}}_{\mathrm{nom}}$ | W | 20,280 | 18,120 | 16,630 | 20,710 | 22,280 | 11,870 | 7000 | 4480 |

Quantity | Unit | TH.01 | TH.02 | TH.03 | TH.04 | TH.05 | TH.06 | TH.07 | TH.08 |

SHCc${}_{\mathrm{rf}}$ | - | VL | VL | VH | H | VH | VL | VH | VH |

MDc${}_{\mathrm{rf}}$ | - | E | E | E | M | D | E | IE | IE |

SHCc${}_{\mathrm{ew}}$ | - | VH | VH | VH | H | VH | H | VH | VH |

MDc${}_{\mathrm{ew}}$ | - | D | D | D | IE | D | IE | M | I |

SHCc${}_{\mathrm{gf}}$ | - | H | VH | VH | VH | VH | VH | VH | VH |

MDc${}_{\mathrm{gf}}$ | - | D | D | D | D | D | D | IE | E |

${\theta}_{\mathrm{u},\mathrm{s},\mathrm{nom}}$ | ${}^{\circ}$C | 85 | 85 | 85 | 85 | 85 | 75 | 70 | 60 |

${\theta}_{\mathrm{u},\mathrm{r},\mathrm{nom}}$ | ${}^{\circ}$C | 75 | 75 | 75 | 75 | 75 | 65 | 55 | 40 |

${\mathsf{\Phi}}_{\mathrm{nom}}$ | W | 12,310 | 11,400 | 9400 | 9960 | 7830 | 6690 | 4510 | 3500 |

Quantity | Unit | MFH.01 | MFH.02 | MFH.03 | MFH.04 | MFH.05 | MFH.06 | MFH.07 | MFH.08 |

SHCc${}_{\mathrm{rf}}$ | - | H | VL | VH | VH | VH | VH | VH | VH |

MDc${}_{\mathrm{rf}}$ | - | D | D | D | D | D | D | IE | IE |

SHCc${}_{\mathrm{ew}}$ | - | VH | VH | VH | VH | H | H | H | VH |

MDc${}_{\mathrm{ew}}$ | - | D | D | D | D | IE | M | IE | M |

SHCc${}_{\mathrm{gf}}$ | - | H | VH | VH | VH | VH | VH | VH | VH |

MDc${}_{\mathrm{gf}}$ | - | D | D | D | D | D | D | IE | IE |

${\theta}_{\mathrm{u},\mathrm{s},\mathrm{nom}}$ | ${}^{\circ}$C | 85 | 85 | 85 | 85 | 85 | 75 | 70 | 60 |

${\theta}_{\mathrm{u},\mathrm{r},\mathrm{nom}}$ | ${}^{\circ}$C | 75 | 75 | 75 | 75 | 75 | 65 | 55 | 40 |

${\mathsf{\Phi}}_{\mathrm{nom}}$ | W | 51,000 | 70,090 | 94,330 | 63,200 | 61,620 | 46,150 | 34,660 | 18,750 |

Quantity | Unit | AB.01 | AB.02 | AB.03 | AB.04 | AB.05 | AB.06 | AB.07 | AB.08 |

SHCc${}_{\mathrm{rf}}$ | - | VL | VH | VH | VH | VH | VH | VH | VH |

MDc${}_{\mathrm{rf}}$ | - | D | D | E | D | D | D | IE | IE |

SHCc${}_{\mathrm{ew}}$ | - | VH | VH | VH | H | H | H | VH | VH |

MDc${}_{\mathrm{ew}}$ | - | D | D | D | IE | IE | IE | M | M |

SHCc${}_{\mathrm{gf}}$ | - | VH | VH | VH | VH | VH | VH | VH | VH |

MDc${}_{\mathrm{gf}}$ | - | D | D | I | D | D | D | IE | IE |

${\theta}_{\mathrm{u},\mathrm{s},\mathrm{nom}}$ | ${}^{\circ}$C | 85 | 85 | 85 | 85 | 85 | 75 | 70 | 60 |

${\theta}_{\mathrm{u},\mathrm{r},\mathrm{nom}}$ | ${}^{\circ}$C | 75 | 75 | 75 | 75 | 75 | 65 | 55 | 40 |

${\mathsf{\Phi}}_{\mathrm{nom}}$ | W | 52,550 | 224,740 | 139,630 | 116,810 | 164,000 | 123,030 | 93,170 | 46,160 |

Element | South | West | East | North |
---|---|---|---|---|

External walls | 0.3 | 0.2 | 0.2 | 0.3 |

Glazing (SFH, MFH, AB) | 0.4 | 0.3 | 0.3 | 0 |

Glazing (TH) | 0.6 | 0 | 0 | 0.4 |

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Grassi, B.; Piana, E.A.; Beretta, G.P.; Pilotelli, M.
Dynamic Approach to Evaluate the Effect of Reducing District Heating Temperature on Indoor Thermal Comfort. *Energies* **2021**, *14*, 25.
https://doi.org/10.3390/en14010025

**AMA Style**

Grassi B, Piana EA, Beretta GP, Pilotelli M.
Dynamic Approach to Evaluate the Effect of Reducing District Heating Temperature on Indoor Thermal Comfort. *Energies*. 2021; 14(1):25.
https://doi.org/10.3390/en14010025

**Chicago/Turabian Style**

Grassi, Benedetta, Edoardo Alessio Piana, Gian Paolo Beretta, and Mariagrazia Pilotelli.
2021. "Dynamic Approach to Evaluate the Effect of Reducing District Heating Temperature on Indoor Thermal Comfort" *Energies* 14, no. 1: 25.
https://doi.org/10.3390/en14010025