Analysis of the Thermal Performance of Hydronic Radiators and Building Envelop: Developing Experimental (Step Response) and Theoretical Models and Using Simulink to Investigate Different Control Strategies- Juniper Publishers
Juniper Publishers- Journal of Civil Engineering
Abstract
A common component of many building heating systems
is a thermostat that controls the power on the radiators by changing the
mass flow and/or temperature of the feed water. In some cases, these
old thermostats malfunction or do not work quite as they should. This
can contribute to large indoor-temperature fluctuations, which in turn
can lead to unnecessary energy use and poor thermal indoor climate.
The goal of this paper is to develop a thermal
dynamic model of hydronic radiators as well as a thermal dynamic
building model to build Simulink models and investigate different
control strategies to control the indoor temperature. By adapting better
control strategies, one can reduce indoor-temperature fluctuations and
reduce energy use.
The results of simulations in this paper suggest new
ways of thinking concerning building a model of hydronic radiators and
controlling them and that the temperature control of the studied
building will be improved by using a well-functioning thermostatic
radiator valve (TRV) instead of a poor-functioning TRV. The smaller
fluctuation of the indoor temperature when using a well-functioning TRV
compared to a poor-functioning TRV results in better indoor climate.
Different types of TRV failures might give rise to large
indoor-temperature oscillations, very high/very low indoor temperature
and/or high energy use. In some cases, a poor-functioning TRV results in
unreasonably high indoor temperatures and high energy use, and in other
cases it might result in very low indoor temperatures, whereas the
difference in performance when using well- functioning controllers (P
and PI) is marginal.
Keywords: Hydronic Radiators; Thermostatic Radiator Valves; Control; Simulink; Energy; Building
Abbreviations:
P: Proportional controller; PB: Proportional Band; PI:
Proportional-Integral Controller; PID: Proportional-Integral-Derivative
Controller; TRV: Thermostatic Radiator Valve
Introduction
Buildings account for approximately 40 % of the total energy use in the EU [1].
This means that there is great potential of energy savings in
buildings. A common component of many building heating systems is a
thermostat that controls the power on the radiators by changing the mass
flow and/or temperature of the feed water. In some cases, these old
thermostats malfunction or do not work quite as they should, which can
contribute to large indoor-temperature fluctuations, unnecessary energy
use and a poor thermal indoor climate [2-4].
The energy use of a building can be reduced by approximately 30% by
improving the functionality of thermostatic radiator valves (TRV) [5].
To evaluate the control performance of hydronic radiators, thermal and
hydronic models for both hydronic radiator and building needs to be
considered [6].
To create a good thermal indoor environment, many
factors should be taken into account. One of the most important
parameters is the heating power from the radiators. Heating power is
affected by the feed water temperature, mass flow of the feed water, the
radiator surface area and material and the inertia (time constant) of
the radiators. Radiators output power control is usually achieved using
thermostats connected to the radiators that control the mass flow of hot
feed water by opening or closing a valve. The temperature of the feed
water temperature supplied to the radiators is often a function of the
outdoor temperature, the colder the outside is, the hotter feed water
temperature.
To investigate different control strategies, a model
of radiators must be developed. Once the model is built, different
control strategies can be simulated. A good control strategy can result
in reduced indoor-temperature fluctuations and reduced energy use. The
goal of this paper is to develop a thermal dynamic model of hydronic
radiators and a thermal dynamic building model to build Simulink models
to investigate strategies for controlling the indoor temperature.
Adopting better control strategies can reduce indoor-temperature
fluctuations and reduce energy use.
Theory
In the first part of this section, 4.1, the theory of
heat emission from radiators and the control of radiators will be
presented. In the second part, 4.2, the energy balance for buildings
will be described.
Radiators - control and heat emission
Thermostatic radiator valves (TRVs) usually consist
of a piece of wax that contracts and expands depending on the indoor
temperature. Through this expansion/contraction a pin is pushed into or
out of a packing box to control the mass flow. Changes in the mass flow
of the feed water control the heat flow into the room. TRVs have a
proportionality band or "P range", which is often approximately 2 °C [2],
which means for example that if the indoor temperature is 21 °C (set
point), the valve position will be fully closed and if the temperature
is 19 °C (2 °C deviation from the set point) the valve will be fully
open. The valve position, at temperature deviations between 0 and 2 °C,
is proportional to the temperature deviation. Figure 1a,b shows two different P controllers.
The mechanical thermostat time constant, which is the
time from when the valve starts to react for a given temperature change
until it reaches 63% of the final value, is approximately 15-25 minutes
for new and modern thermostats [5].
Electronic TRVs consist of a motor to control the
valve position of the thermostat. The indoor temperature is measured by
sensors, whose output is interpreted by a microcontroller that controls
how the motor should set the valve. Additional features, such as
schedule management, consideration of external interference and outdoor
temperature, often depend on the manufacturer. Due to the quick sensors
of electronic TRVs, their time constants are generally be much lower
than those of traditional TRVs.
The net energy transferred to the radiator from the water, Qsup p can be described as:
Where is the mass flow, cp is the heat capacity of water, Tinis the inlet temperature of the water Toutand is the outflow temperature of the water.
The power emitted from the radiator, Qem, can be calculated by:
Where U is the heat transfer coefficient, Trad
is the average water temperature (which is equal to the surface
temperature of the radiator if the inside heat resistance is neglected),
is the ambient temperature of the room (air and surrounding surfaces)
and A is the area of the radiator surface.
Another equation used to calculate the emitted power of a radiator can be written as:
Where " n " is a constant that is chosen depending on the type of radiator but can be assumed to be approximately 1.3 [7].
The value of the (U.A) in equation (2) varies depending on the natural convection and the size of the radiator. To calculate (U. A)
at steady state, equations (1) & (2) are used together, with the
assumption that the net power supplied to the radiator by hot water Qsup p,s 2 is equal to the power emitted from the radiator ( Qem,s2) (at steady state, s2 ):
The microcontrollers in electronic TRVs control the
valve position in several ways. The most common are P, PI and PID. An
optimized control method for the radiator system results in better
comfort and less energy use. Rough and poorly designed control of the
flow often result in large variations in the indoor temperature (large
temperature fluctuations) and hence more heat loss from the building,
see Figure 2.
Digital thermostats are an alternative to conventional thermostats that implement numerical methods.
A P controller is a proportional controller with
gain. The control signal u is proportional to the errorsignal u is
proportional to the error signal (deviation between the set point and
real value) [8].
Where K is the controller gain and u0 is the control signal when the error signal is zero (normal value).
A PID controller has both a proportional and an integral part (error-integrating part) [8]:
Where TI is called the integral constant.
A PID controller is a controller with combination of proportional, integral and derivative parts:
Where TD is called the derivative constant. By using different tuning methods, the best values of K , TI, and TD can be calculated [8].
The question that arises regarding PID controllers for indoor temperature control is how these parameters ( K , TI and TD )
should be set in the best way. How to set PID controllers depends on
factors such as the building heat capacityC , building heat loss
(transmission, leakage and ventilation systems), outdoor climate and the
dynamics of the radiator system. There are different tuning methods
(Ziegler-Nichols, Lambda method, etc.) for tuning PID-parameters;
however, Simulink uses algorithms of iterations and numerical methods,
like Euler backward, Euler forward or trapezoidal method to tune the
parameters K , TI and TD [8].
Building model
Assuming that the building is heated uniformly throughout with a single heat capacity, one can write:
Where C [J/K] is the heat capacity, Ti is the indoor
temperature, [W] is the supply power and [W] is the heat loss power from
the building.
The total heat loss coefficient can be written as [9]:
Where, ρair ,Cair , and Vajr
, are the density [kg/m3], capacity [J/(K.kg)] and volume flow [l/(s,
floor area)] of the ventilation air, respectively. η is the efficiency
of the ventilation heat exchanger and Afloor is the floor
area. Since the building has a ventilation system with heat recovery,
the tightness should be very high; therefore, the air leakage assumed to
be almost zero. ∑u-a is the sum of the heat transfer coefficient [W/(m2.K)] multiplied by the heat transfer area [m2] for different parts of the building envelope.
The time constant [h] of a building can be written as [9]:
Since the experimental data for the radiator power
was approximately 660 [W] at maximum capacity, the data for the building
model was adjusted reasonably to this value. The time constant for the
simulated building was estimated at 6 hours. The following data were
used in the simulations:
With these values, the heat capacity, C, of the
building (including envelope and air) is 353 890 [J/K]. This value has
been used in Simulink models. Note that the above values have been
selected in consideration of the maximum capacity of the radiator, which
explains the choice of the very low time constant as it corresponds to a
very light house [9].
Results
Figure 3
shows the experimental setup used to obtain the step response for the
radiator and the input power to the radiator (supply power as shown in
equation 1).
The supply water for the radiator was heated using a
heat exchanger (VVX), and the flow to the radiator was controlled by
valve V1 and bypass BP1. At the start of each experiment, the overall
temperature was 21 °C, and during the heating process, until the desired
supply temperature was reached, BP1 was opened and V1 was closed. When
the water temperature reached the desired level, V1 opened and B P1
closed.
When measuring the step response from the radiator,
it was important to see how the power supplied to the radiator was
affected by various volume flows. To calculate the supplied power using
equation 1, the temperatures of the water to and from the radiator
(supply and return temperatures) and the volume flow through the system
were measured. Figure 4 shows how the power supplied to the radiator (equation 1) changes over time for different volume flows.
When a steady state is attained for each flow, the
difference in supply power between different volume flows is small. The
supply power was calculated using equation 1.
To obtain the step responses at different volume
flows, the power emitted from the radiator must be calculated. This was
done by measuring the surface temperature of the radiator and the room
temperature and using equation 4, where the power supplied at steady
state, , for various volume flows was obtained according to Figure 4.
Figure 5
shows that with higher mass flow, the step response becomes shorter and
the emitted power increases. The steady state emitted power from the
radiator at different volume flows can be seen in Figure 4 & 5. Figure 6
shows the steady state power emitted from the radiator for various
volume flows after data fitting. The relation between and based on
experimental data after data fitting is (equation (11) and Figure 6):
Based on Figure 5,
the time constant for emitted power, i.e., the time to reach 63% of the
final value, can be plotted for different volume flows, as shown in Figure 7.
The obtained relation between the time constant of the radiator, and
based on the experimental data after data fitting is (see equation (12)
and Figure 7):
A simplified overall model for TRVs is shown in Figure 8, and a sub-model of the building model in Simulink is shown in Figure 9. Additional Simulink models are shown in the Appendix.
The output signal of the controller in Figure 8
is a new value for the steady state radiator power, which in turn
determines the mass flow and the time constant of the radiator. When the
time constant and the steady state value of the emitted power from the
radiator are calculated, the emitted power, including the time constant,
will be determined. This is a new way of thinking concerning building a
model of hydronic radiators and controlling them.
The results of simulations for four different cases can be seen in Figures 10-13.
The simulation time is 48 hours. In all cases, the internal power gain
(heat from people, electrical appliances, etc.) alternates from 0 to 200
[W] periodically every 4 hours. The outdoor temperature also varies
sinusoidally between -5 and 5 C with a period of 24 [h]. The total
emitted heat from radiators was integrated during 24 hours to calculate
the energy use. Figure 10, 11 show the results of simulations where a well- functioning TRV is used. Figure 10
shows the results of the simulation when a PI controller is used. The
gain and the integral time are 0.19 and 10x10-5, respectively. Figure 11
shows the result of simulations where a P controller with gain of 0.5
and a P-band of 2 C is used. As many TRVs malfunction, two cases with
poorly functioning TRVs have been simulated. The results of the
malfunctioning TRVs are shown in Figures 12, 13. In some cases, they do not open or close fully, resulting in a low indoor temperature or energy waste.
As shown in Figure 10, a PI controller produces very small indoor-temperature fluctuations (approximately 1 ºC) around the set point (21 "C).
As shown in Figure 11,
a P controller produces very small indoor-temperature fluctuations (1
ºC) around the set point (21 "C). However, there is always residual
error that cannot be eliminated.
As shown in Figure 12,
the mass flow varies between 2x10-3 and 5.2x10-3 [kg/s], which means
that the TRV is never closed. Such errors unfortunately occur in some
TRVs and lead to high temperatures and energy waste.
As shown in Figure 12,
the mass flow varies between 9.20x10-4 and 2.42x10-3 [kg/s], which
means that the TRV does not open fully, resulting in very low indoor
temperature.
In some cases, where the fluctuations are very high
because of a malfunctioning TRV, a higher set point must be chosen to
not undercut the minimum indoor temperature (Figure 13). These results in a waste of energy compared to a well-functioning TRV, as shown in Figure 14.
Discussion and Conclusion
The development of a model of a hydronic radiator to
investigate different control strategies in buildings has not been
extensively researched in previous studies. The key to the investigation
is to build a combined "black box" and physical model, where the hot
water mass flow is used as the input signal and the heat emitted from
radiator is the output signal. The temperature of the hot water is
varied by central heating system as a function of the outdoor
temperature and cannot be affected by individual buildings. This is the
way that the heat from radiators is controlled in most buildings in
Sweden.
The results of simulations in this paper suggest that
the temperature control of the studied building will be improved by
using a well-functioning TRV instead of a malfunctioning TRV. In the
developed Simulink model, different control strategies can be
investigated. The smaller fluctuations of the indoor temperature when
using the well-functioning TRV rather than a malfunctioning TRV result
in a better indoor climate. Different types of TRV failures may produce
large indoor-temperature oscillations, very high/very low indoor
temperature and/or high energy use. In some cases, a poor-functioning
TRV results in unreasonably high indoor temperatures with high energy
use, whereas in other cases, it might cause a very low indoor
temperature. However, the difference between well-functioning
controllers (P and PI) is marginal.
Limitations and Error Sources
a. Different volume flows were tested in duplicate.
The average of the two runs was then used to avoid error.
However, the result could have been different if more runs
for each volume flow were tested.
b. Another limitation was that the simulations were only
run over 48 hours and not throughout a whole year.
c. The results from the experiment are applicable only to
the radiator used in the experiment (Purno C11-compact), different radiators would likely have different responses.
d. The room in which the experiment was conducted had
specific interior and technical equipment that could influence the heat
transfer process; therefore, the results are limited to the specific
room.
e. The experiment was conducted until the surface
temperature of the radiator was constant and had reached a steady state.
However, after some time, it was concluded that the system had reached
steady state even though the temperature was not completely constant.
Had the experiment been run for a longer time, the steady state of the
emitted effect may have been slightly higher.
f. The room temperature varied depending on when the
experiment was conducted. This was particularly noticeable for
subsequent tests as the ambient temperature was slightly higher due to
previous tests. This mainly affects the emitted effect.
g. The experiment was monitored by measuring devices
that were connected to sensors around the radiator. The volume flow
sensor has a stated margin of error of a few percent, making it the
largest source of error from the equipment.
h. One of the focuses of the experiment was to keep
the secondary system as a closed system to maintain the same amount of
water in the system for all the experiments. However, there was a small
leak that allowed water to escape. Moreover, air bubbles entered the
system. Between each test, the secondary system was refilled. The amount
of water could therefore differ from the previous test.
i. Rust inside the radiator could also affect the
heat transfer process, partly by affecting the volume flow, but the
coating could also serve as an extra insulator and thus slow the heat
output in the form of conduction.
j. When the temperature in the system increases, so
does the pressure. To reduce the impact this change would have on the
volume flow, a speed-controlled pump was used. This pump did not fully
compensate for this problem, which led to the volume flow changing
slightly during the heating process.
k. The temperature of the water supplied to the heat
exchanger during the test changed. After a few minutes, there was a dip
in the temperature of the system, which had an impact on the induced,
and thus the emitted, effect.
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