4. Actual dynamic model corrected by using open-loop test

#### 4.1. The purposes of OLT

The return water temperature from the end-user (radiator and radiant floor heating) is addressed in Eqs. (9)–(11). The net heat stored in the terminal equals to the heat difference

dt <sup>¼</sup> cwð Þ <sup>u</sup>21G21<sup>d</sup> � <sup>0</sup>:5Gmk<sup>21</sup> ð Þþ Ts21<sup>z</sup> � Tr<sup>21</sup> qsolsFs<sup>1</sup> <sup>þ</sup> <sup>q</sup>intF<sup>1</sup> � Uen1ð Þ Tz<sup>1</sup> � To (12)

dt <sup>¼</sup> cwð Þ <sup>u</sup>22G22<sup>d</sup> � <sup>0</sup>:5Gmk<sup>22</sup> ð Þþ Ts22<sup>z</sup> � Tr<sup>22</sup> qsolsFs<sup>2</sup> <sup>þ</sup> <sup>q</sup>intF<sup>2</sup> � Uen2ð Þ Tz<sup>2</sup> � To (13)

Zone air temperature dynamic responses can be represented in Eqs. (12)–(14). The net heat stored is related to the heat obtained from the circulation water in the secondary system, the solar radiation from south side windows, the internal heat gains and the heat transferred to the outside environment. Note that the thermal capacity in the terminal of floor heating is consid-

The schematic diagram of a pipe segment is shown in Figure 2. The makeup water and the heat loss from the pipe insulation are considered to gather the water temperature left from the pipe segment. The supply water temperature from the pipe segment is related to the heat loss from the pipe segment, while the return water temperature has been considered in the heat losses from pipe insulation and makeup water. In Eq. (15), the net heat stored in the pipe segment equals to the heat received from the entrance minus the heat outlet from the exit and the heat losses from both makeup water leakage and pipe segment. Note that supply pipe segments do not consider the water leakage by the assumption. Letter j represents each pipe segment.

In summary, 29 dynamic equations are used to address the overall DHS mathematical model. The developed model is utilized to obtain system properties, simulate various dynamic

responses of control strategies and compare with system energy consumption.

ered by accumulating the influence of the concrete structure.

3.3.5. Pipe segment in the primary and secondary systems

dTsegoutj

dt <sup>¼</sup> cwð Þ <sup>u</sup>23G23<sup>d</sup> � <sup>0</sup>:5Gmk<sup>23</sup> ð Þþ Ts23<sup>z</sup> � Tr<sup>23</sup> qsolsFs<sup>3</sup> <sup>þ</sup> <sup>q</sup>intF<sup>3</sup> � Uen3ð Þ Tz<sup>3</sup> � To (14)

dt <sup>¼</sup> cwGseginjTseginj � cwGsegoutjTsegoutj � Qmksegj � Qhlsegj (15)

between the heat gathered from the circulation water and emitted to the indoor air.

98 Sustainable Buildings - Interaction Between a Holistic Conceptual Act and Materials Properties

3.3.4. Indoor air model

dTz3

Csegj

Figure 2. Schematic diagram of a pipe segment.

Cz<sup>1</sup> dTz1

Cz<sup>2</sup> dTz2

ð Þ Cz<sup>3</sup> þ Cc

The purposes of doing OLT based on the developed dynamic model are stated hereby. Firstly, the mathematical model should be checked out with ideal condition to ensure the accuracy. Then, by applying the experience and operational data, the ideal dynamic model could be corrected to seek the characteristics of the DHS and various simulations.

#### 4.2. Ideal model of the DHS

The ideal conditions represent that outside and indoor air temperature and water mass flow rate in primary and secondary system are same as their design values. The affluent factors of both heat transfer area of each substation and terminal equal to 1. No solar radiation and internal heat gains exist in the ideal dynamic system. The heat losses from both water leakage and pipe network are ignored.

With these situations, the dynamic responses of the ideal model with the fuel control signal by 0.798 are shown in Figure 3. In addition to the zone air temperature in Substation #3, which is equal to 17.9C due to the huge thermal capacity of the floor heating structure, the supply and return temperatures from the heat source and substations are identical to the design conditions. Steady-state time of the water temperatures and zone air temperatures except for the zone air temperature in Substation #3 (48 h) reaches 15 h similarly.

Figure 3. Dynamic responses of ideal model (a) Time(h), (b) Time(h), (c) Time(h), (d) Time(h).

#### 4.3. Actual model of the DHS

In practice, the affluent factors of both heat transfer area of each substation and terminal are greater than 1 because of the safety consideration from designers. The circulation water flow rate could be adjusted rather than design values. With these situations, the ideal dynamic model should be modified to simulate the real DHS, which is entitled as actual dynamic model. Regarding the experience and operational data of typical DHSs in China, the affluent factors of each heat transfer area and terminal in Substations #1–#3 are provided as [1.4, 1.4, 1.4, 1.5, 1.35, 1.4], respectively.

5. Advanced control strategies and simulations

respectively, for all simulations of the cases.

points for related parameters used in control strategies.

5.4. Case study based on dynamic simulation

Table 2. Set points used in control strategies.

Usually, the disturbances taking place in DHSs include outdoor air temperature, solar radiation and internal heat gains, while outdoor air temperature plays the biggest rule in system operation. On the other hand, when the comprehensive heat transfer coefficient (Uen value) of the buildings is getting smaller and smaller, the additional heat gains (solar radiation and internal gains) should be considered in the simulation and in real system operation. In this chapter, outdoor air temperature, solar radiation and internal heat gains are drawn into actual model with the range from 8.2 to 13.1C, from 0 to 45 W/m<sup>2</sup> and from 0.9 to 6.8 W/m<sup>2</sup>

Advanced Control Strategies with Simulations for a Typical District Heating System to Approaching Energy…

In many circumstances, DHSs are operated with experience; likely, the supply water temperature from the heat source has been controlled depending on the experience of operators. Nevertheless, the disturbances described above change based on time. It means that the heating supply from the heat source and the heat consumption (heating load) should be tracked and balanced. Thus, the DHS must be regulated accordingly. Otherwise, the zone air temperature could fluctuate in larger range, which influences thermal comfort of end-user. By simulating the dynamic responses of actual model with different conditions (change outdoor air temperature, indoor air temperature as similar as design value, design water mass flow rate in the pipe network, constant water leakage rate, considered pipe insulation heat loss, no solar radiation and internal gains), the simulated stable results from OLTs are listed in Table 2 as set

Five cases are selected for dynamic simulations (given in Table 3) to study the system responses, the energy consumption (heat consumed in the cases) and the thermal comfort of the end-user [14–17]. Note that typical PI algorithm is used to all controllers to gather output signals [18].

Many operators run DHSs according to their experience if they cannot realize the set points of supply water temperature from the boiler. In this case with 5 days consciously, the dynamic

To, C 15 10 5 0 5 10 16.9 20 Ts1, C 37.5 49.1 54.2 70.6 81.1 91.4 104.2 111.8 Tw2arg1, C 24.5 28.5 29.2 35.3 38.4 41.3 44.5 46.9 Tw2arg2, C 25.1 29.3 30.2 36.6 39.8 43.0 46.5 49.0 Tw2arg3, C 20.4 22.7 21.8 26.5 28.3 29.9 31.6 33.2

,

101

http://dx.doi.org/10.5772/intechopen.72290

5.1. System disturbance

5.2. Control signals

5.3. Control strategies

5.4.1. Case 1

While outside and indoor air temperature and water mass flow rate in primary and secondary system are identical to their design values, no solar radiation and internal gains exist, the water leakage and heat losses from pipe segments are considered, the control signal of fuel equals to 0.854 and the dynamic responses of the temperatures from actual model are shown in Figure 4. In this figure, the steady-state values of the supply and return water temperatures from the heat source and Substations #1–#3 are 97.5, 33.2, 57.6, 31.6, 58.6, 33.6, 38.4 and 28.1C, while the zone air temperatures equal to 20.8, 19.6 and 18.8C, respectively. From the values, the supply water temperature from the heat source is not necessary to satisfy its design value (120C), while outside air temperature is 16.9C. Meanwhile, the zone air temperatures are not same as the design values. The reason behind is that the affluent factors of the heat transfer area affect the operation very much in the DHS. It is also hinted that the zone air temperature should be controlled separately because they cannot approach its design value simultaneously.

Figure 4. Dynamic responses of actual model (a) Time(h), (b) Time(h), (c) Time(h), (d) Time(h).
