Increasing energy efficiency of a building with [600264]

Increasing energy efficiency of a building with
minimal computational demands using Model
Predictive Control

Giorgian Neculoiu, Valentin Sgarciu
Faculty of Automatic Control and Computers
Politehnica University of Bucharest
Bucharest , Romania
neculoiu. giorgian@ gmail .com ,
[anonimizat]

Alexandru Viorel Marinescu, Mariana Marinescu
Laboratory of Automation and Applied Informatics
Technical University of Civil Engineering of Bucharest
Bucharest, Romania
[anonimizat] ,
mmarines [anonimizat]

Abstrac t—This work is a aggregated perspective of previous
papers studying advanced control strategy applicable in
intermittently heated buildings. This strategy mainly aims to
optimize the energy efficiency of heating systems taking in to
consideration the minimization of the needful time and the
computational resources necessary to this process. Model
Predictive Control is the control strategy used in this work and
the main purpose (ensuring maximum comfort with minimum
energy consumpti on) is satisfied by using weather forecasts and
building occupancy program. Several architectures presented
can be used to implement the proposed solution. The main goal is
to minimize the computational requirements achieving the best
performance. To solve the problems from previous studies, this
paper studied the solutions implemented on a single thermal zone
and multiple thermal zones .
Keywords —control strategy, thermal control, predictive control,
computational resources, process, energy efficiency, ener gy
consumption, thermal comfort, model predictive control .
I. INTRODUCTION
Some of the biggest problems of the XXI century are the
global warming and the depletion of natural resources. In this
is way, most of the scientific community is concerned in
finding solutions to these problems so the effect can be
minimized. In order to achieve this goal and to minimize the
deployment time, the European Union supports the
community and establishes a number of objectives among we
found: a 20% reduction in emissions of greenhouse gases and
increasing energy efficiency, which reaches the threshold of
20 % by 2020. So the objectives mentioned above can be
achieved, the solutions found are: less developed member countries were concerned to renovate the existing buildings,
but, on the other hand, developed countries have found
another solution for this issue, building new homes, efficient
and energy independent and with near -zero emissions. These
answers to the existing issue are not the best, but they bring
some improvement, this is what the researchers said. The
problem key is optimizing the energy consumption of the
buildings, especially for the existing ones [1,2].
The studies from the field have shown that in the member
states, the residential sector handles over 40% of total energy
consumption and about 35% of emissions of greenhouse
gasses. Moreover, in this sector, heating systems fitted to
buildings consume about 50% of energy, which represents
over 20% of total energy consumption. Studying these data,
the conclusions are: the member states need to optimize the
energy consumption and to develop advanced thermal control
strategies that can be applied in buildings [2,3].
Given the interest in this field, several studies have been
made , so the energy consumption of buildi ngs is optimized
[4,5,6,7]. One of the major issues of the building thermal
control field is the big inertia of the system. T he thermal
control problem is not as simple as it looks like , and the
pursuit benchmark cannot solve all. For the implementation of
appropriate strategies, series of several factors are taking into
consideration. Studies have shown that significant
improvements can be made in terms of comfort and energy
consumption using future program of building occupancy and
the weather forecast. I n this respect, the best solution is
increasing the use of predictive thermal control strategies
based on building mathematical model [7,8,9,10,11, 12].

Among the control method drawbacks mentioned in the
above are: the necessity of a building mathematical model to
characterize better its thermal behavior, the computational
resources and the time needed to do the large amount of
mathematical operations in order to minimize the cost
function .
As this was mentioned in the above, a thermal control
strategy bas ed on predictive control (MPC – Model Predictive
Control) is studied in this paper, the main aim being to
minimization of the need time and computational resources
required.
By applying this control strategy on buildings, a dynamic
model of the respective building is required. We obtained this
model of the building using the data from a house of 100 m2 in
a previous study [2]. It has been developed for a house with a
single thermal zone. For the cases presented in this paper,
where the building is considere d to have two thermal zones,
the model is obtained for each thermal zone in part using the
same principle. This solution was discussed based the previous
study discoveries [2]. The scaling of the actual system was
made by taking into consider ation the syst em inputs and it
does not allow more than two thermal zones for the presented
system.
Thus, considering the model, weather forecast and
employment program, we demonstrated previously in [12] as a
control strategy that we propose meets main goal in building
thermal control (ensuring comfort with minimal energy
consumption). The experiment was conducted on a house
viewed as a single thermal zone , but the test resultats we made
lead to the idea that this can be seen as a global optimal
solution . By implementin g this control strategy, the bonus
efficiency has been presented as a result of our previous work
in [12].
Further implementation architectures of Model Predictive
Control – MPC will be studied in this paper. The
implementation architectures are also mea nt to take into
account the limitations in terms of time spent and the
computational resources that are necessary to minimize the
cost function. The purpose of their implementation is to obtain
a minimization of application processing computational
calcula tions needed to achieve the process, besides the
primary endpoint of thermal control in buildings .
II. EXPERIMENT ’S DESCRIPTION AND EX PERIMENTAL DATA
This section des cribes the experiment used in this paper
represented by an experimental house with 100 m2, located in
the south of Germany – Holzkirchen – Fig. 1. The house is
equipped with a range of sensors to capture certain indicators
related to indoor and outdoor environment (indoor
temperature, the flow of solar radiation, etc.), and with a
weather station t o measure outdoor temperature [13].
This experiment was used before, but unlike the current
study, previous studies house was approximated as a single
thermal zone Fig. 1 – a). Accordin gly to previous study conclusions, in this paper, the house will be app roximated as
two separate thermal zones Fig 1 – b). This decision was taken
because there is a difference between the two thermal zones
(different inputs of the system ), this is way fo r the single
thermal zone house we have perturbations quite large and we
need to create a better model with some improve ments in
order to eliminate the difference [13].
Experiment data come from the sensors of the house tested
under the action of external weather conditions and external
weather station between 09.04.2014 – 28.04.2014, with a
sampling period of 60 minutes [13]. In Fig. 2 is plotted the
evolution of indicators for each thermal area monitored and
taken into consideration in this paper.
The house can also be represented as a system with
multiple inputs and single output – MISO. Unlike previous
experiments, in this study, the entry number of the system
varies from one zone to another . Thus, the system may be
represented by a block diagram with four inputs and an output
for "Zone 1" – Fig. 3 – a). The system inputs a re the external
air temperature, the ventilation air temperature, incident solar
radiation on the building envelope and heat flux density, and
the output of the system is represented by indoor temperature .
The system is represented by a block diagram with three
inputs and one output for "Zone 2" – Fig. 3 – b). In this case,
the entry of ventilated air temperature was eliminated because
air insertion through ventilation does not exist in these thermal

Fig. 1. The plan of the reference building with: a) a thermal zone;
b) multiple thermal zones

Fig. 2. Measured data (outdoor temperature, supply air temperature, solar
irradiance, heat flux densities) for thermal zone 1 and thermal zone 2

zones [2,13].
Starting from the equation of thermal bal ance for each of
the two thermal areas of the building, a mathematical model is
obtained for each one that can be represented in state space as
following form [2]:

uD CuB A
S CS zS CS C

  
By applying Laplace transform for the set of (1) equations
for each thermal zone, a transfer matrix with four and three
transfer functions is obtained for each zone [2]:

S S S S S D B AsIC H  1) ( 
Finally, using identification method of least squar es are
identified parameters of the system discrete transfer function
for each model of the two thermal zones [2]:












      


2
21
12
421
412
21
12
322
21
12
222
21
12
121
11
11111111
1
1111
)()()()()()()()(
)(
zm zmzn znzm zmznzm zmznzm zmzn zn
z QzzQzzTzzTz
zH
elpzszepzevz
 
for the fi rst thermal zone :












    


2
21
12
321
312
21
12
222
21
12
12
111111
1
111
)()()()()()(
)(
zm zmzn znzm zmznzm zmzn
z QzzQzzTz
zH
elpzszepz
 
and for the second thermal zone .
For each thermal zone, the system response is represented
graphically in Fig. 4 .
By using the mathematical representations of the two
thermal zones to describe the thermal behavior of entire
building, the next section will present an implementing issue
of thermal control strate gy using Model Predictive Control.
The problem studied in this section refers to the choice of a
suitable architecture to implement an optimal control strategy to minimize the computational demand and the time used to
calculate the cost function.
III. MINIMAL C OMPUTATIONAL DEMANDS USING MODEL
PREDICTIVE CONTROL (MPC)
The current requirements that are imposed on building
thermal control involve not only to the mere rejection of
disturbances and temperature stabilization, but also thermal
comfort and minimize ener gy consumption. In order to achieve
them, this section will be considered as thermal control strategy
– Model Predictive Control. This optimal control strategy based
on building mathematical model takes into account its
employment program and the weather f orecast. Thus, we have
shown in [12] that the results obtained through the
implementation of such a strategy are better compared with
conventional thermal control strategies.
By using this thermal control strategy, the command
sequence is obtained by minim izing a cost function. In the case
of predictive control, the most common form of the cost
function is :

 
  1
02 2) ( )] ( ) (ˆ)[( )(
1u y N
iN
Niiku ikyikyi kJ   
The main section purpose is to find the optimal
implementing architecture for these thermal control strategies

Fig. 3. The block diagram of the MISO system for: a) thermal zone 1;
b) thermal zone 2

Fig. 4. Comparison between the measured data and the response of the model
for: a) thermal zone 1; b) the rmal zone 2.

in multi -zone buildings , so they benefit from reduced
computational requirements and as small as possible a cost
function calculatio n time. These requirements are imposed by
the large amount of calculation that has to be done so the
mathematical cost function could be solved , and a minimal
value of the function could be found.
In most multi -zone buildings equipped with controllers for
thermal control, these controllers work independently.
However, in order to achieve the best results, the parameters
controllers of surrounding areas and the energy contribution
transferred through neighboring inner walls have to be taken
into account. To simplify the study experiment, as you can
observe in Fig. 1 – b), the building was approximated as two
thermal zones. Each area is composed of several rooms with
inside equal temperature, the same structural characteristics of
walls and equipped with indep endent convector heaters.
Using daily occupancy program of the building presented
in Table 1, the results shown in the following sections were
obtained.
A. Decentralized MPC architecture
As we mentioned earlier, in the case of most multi -zone
buildings, the t hermal control is independent. Starting from this
idea from the above, we will present a thermal control
architecture MPC in which the air temperature of each zone is
independently automatically adjusted by a controller that has
implemented this optimal co ntrol strategy – Fig. 5 ( top).
Among the shortcomings of this approximation , we have
thermal influences from neighboring areas and through interior
walls . The thermal influences may not be taken into
consideration by the MPC control strategy , and they are still considered unknown external disturbances. These perturbations
cannot be rejected on short term by using a model for each
zone , this is way reference value exceeding of the output
system exists – Fig. 5 ( bottom ). The graphed values were
obtained on d aily occupancy program of the building, for one
of the days of the monitoring period house set in section 2.
This architecture is a generalization of the solution we
proposed in [12], but this time for a two thermal zone building,
where the control strateg y is applied independently . In terms of
demand computational , this architecture is a good solution, the
time required to calculate the cost function being quite small.
The problem is that the comfort requirements and energy
consumption are not respected, t he reason being the lack of
communication between the systems.
B. Centralized MPC architecture
Another possible architecture to implement MPC control
strategy in multi -zone buildings is represented by the use of the
single controller. This solution consists in a single controller
that implements the optimal control strategy for the whole
building (both thermal zones) – Fig. 6 (top). On the other hand,
by using this architecture, the input/ output parameters for each
neighboring zone are constantly known .
The advantage of this architecture is the knowledge of
thermal system influences from neighboring areas through
interior walls. This leads to the disturbances rejection in good
time using each zone model. In this case, by using the same
daily occupancy program of the building, exceeding reference
values of the output system no longer appear – Fig. 6 ( bottom ).
The main architecture disadvantage , in this case, is that
computational demand and calculation time increases in direct
proportion with the system size. Basically, the longer the
system composed of several heating zones, the needed time to
implement the control strategy increases. It is important to
mention that this due to limited computing power controller.
Another disadvantage relates to the fact that the failure
controller used to implement the control strategy will lead to

Fig. 6. Centralized MPC architecture TABLE I. ZONE OCCUPATION PROGR AM
Zone Daily occupation program Setpoint
Zone 1 8:00 – 20:00 22.5 °C
Zone 2 9:00 – 18:00 23 °C

Fig. 5. Decentralized MPC architecture

the discontinuity of the optimal control strategy for the entire
heating system.
C. Distributed MPC architecture
The system described in this paper is seen as a multiple
inputs and sin gle output system (MISO) and it has two thermal
zones. Regarding the model system, in order to implement an
optimal thermal control strategy, we need to take into
consideration the architecture that uses as little as possible the
controller from the point of computational demand. As we can
observe in the above study architecture, the centralized
architecture is limited by the size of the ordered system and the
decentralized architecture does not meet the requirements
relating to thermal comfort and energy c onsumption. Thus, one
can easily observe that the solution for all the issues we
mentioned is using a distributed architecture – Fig. 7 (top). This
architecture combines the way of functioning of the two
solutions presented and thereby the results of the e ntire system
are improved from all points of view.
This type of architecture is recommended for multiple
thermal zone systems whose parameters are influenced by the
neighborhood. The architecture has a structure similar to the
decentralized architecture. E ach thermal zone is controlled
automatically by an independent controller, but in order to
obtain an optimal solution for the entire system, these
independent controllers need to communicate and change
information on neighborhood parameters and their futur e
behavior [14]. This information exchange is made through a
communication network that links the independent controllers
of the system between them, as it can be seen in Fig. 7 (top).
Compared to the other two architecture presented, from the
point of vi ew of computation, the distributed approximation
has the same complexity level as the decentralized architecture
level, but the optimal solution for the entire system is found in
a much smaller time. The distributed MPC proposal benefits in
terms of commun ication efficiency. When one of MPC
controllers is down, the rest of the system continues to function by contrast to centralized MPC solution. This is another
important advantage of this solution.
This architecture type is considered to be the best soluti on
to implement an optimal thermal control strategy for several
thermal zone building. Its improvements lead to disturbance
rejection in good tim e using the model of each zone. By using
this architecture, the requirements of thermal comfort and
energy cons umption are satisfied with a computing power
necessary as low as it is possible and in less time than
normally. In this way, by taking advantages of the daily
occupancy program of the building also employed previously,
exceeding of system exit reference va lue no longer appears –
Fig. 7 ( bottom ).
All the above tests were carried out using Matlab program,
using a computer with an i5 processor at 2.9 GHz. After we
had tested the programs written in Matlab, the following
running time average was obtained: 0,574 seconds for
centralized MPC solution, respectively 0,234 seconds for each
controller of the distributed MPC solution. Even if the time
difference is not very large for two thermal zone building
presented in this paper, the results are visible for multiple
thermal zone systems, where the required time for centralized
solution increases directly with system size.
CONCLUSIO NS
In this paper, three different types of architecture were
presented. Using this architecture types , an optimal thermal
control strategy can be implemented for a building. Advantages
and disadvantages were mentioned for each type of architecture
both in terms of fulfilling the requirements on thermal control
and computational demand.
The building presented in this work was approximated as
two thermal zones. State space mathematical models were
obtained for each zone based on our previous work, work that
our paper refers to. The study aim was to find solutions so that
a control strategy can be implemented , and so we can obtain
the best resul ts for our paper purpose.
After all our studies, we can observe that the best
performance on thermal comfort and energy consumption are
obtained by using centralized and distributed MPC
architectures. In addition, the solution implemented by MPC
distribute d architecture is consuming fewer resources and time
in terms of computational demand. This represents the optimal
architecture to integrate such a control strategy.
In order to improve the results, as future prospects, we wish
to obtain an algorithm that can be used to describe how the
control strategy is applied by using distributed MPC
architecture. Data transfer will be also studied in order to see
how the data is delivered via the communication network used
in architecture.
ACKNOWLEDGMENT
The work has been funded by the Sectoral Operational
Programme Human Resources Development 2007 -2013 of the

Fig. 7. Distributed MPC architecture

Ministry of European Funds through the Financial Agreement
POSDRU/159/1.5/S/132397.
The experimental data used in this paper were obtained by
INSA Lyon, France, from Fraunhover -Institut fur Bauphysik
IBP, Germany. The authors would like to express their
gratitude for these data.
We also would like to express our gratitude and
appreciation to Ingo Heusler (Fraunhover -Institut fur
Bauphysik IBP, Germany) and Christi an Ghiaus (INSA Lyon,
France) for their support and advice.
REFERENCES
[1] ―Energy yearly statistics 2007 ‖, Office for Official Publications of the
European Communities , ISBN 978 -92-79-12787 -8, EUROSTAT, 2009.
[2] G. Neculoiu, V . Dache, G . Stamatescu, V . Sgarciu , ―Buildings modeling
in order to implement optimal temperature control ‖, Electronics,
Computers and Artificial Intelligence 2015 – International Conference,
7th Edition , vol. 1, pp. S43 -S48, 2015;
[3] Rod Janssen, ―Towards energy efficient buildings in Europe – Final
Report ‖, EuroACE, 2004.
[4] I. Hazyuk, C. Ghiaus, D. Penhouet, ―Optimal temperature control of
intermittently heated buildings using Model Predictive Control: part II –
control algorithm ‖, Build ing and Environ ment, vol. 51, pp. 388–394,
2012.
[5] M. Kummert , P. Andr e, J. Nicolas, ―Optimised Thermal Zone Controller
for Integration Within a Building Energy Management System ‖,
Proceedings of CLIMA 2000 confe rence, 1997 . [6] CEN, ―Controls for Heating Systems — Part 2: Optimum Start –Stop
Control Equipment for Hot Wa ter Heating Systems ‖, European
Committee for Standardization, Brussels, Belgium, 2001.
[7] D. Gyalistras, M. Gwerder , ―Use of weather and occupancy forecasts for
optimal building climate control (OptiCont rol): two years progress
report ‖, Terrestrial Systems Ec ology ETH Zurich and Building
Technologies Division, Siemens Switzerland Ltd., Zug, 2010.
[8] S. Privara, J . Sirok y, L. Ferkl, J . Cigler , ―Model predictive control of a
building heating system: the first experience ‖, Energ y and Buildings ,
vol. 43, pp. 564 -572, 2011 .
[9] D. Kolokotsa, A. Pouliezos, G. Stavrakakis, C. Lazos, ―Predictive
control techniques for energy and indoor environmental quality
management in buildings ‖, Build ing and Environ ment, vol. 44, pp.
1850 -1863, 2009 .
[10] T.Y. Chen , ―Application of adaptive p redictive control to a floor heating
system with a large thermal lag ‖, Energ y and Buildings , vol. 34, pp. 45 –
51, 2002 .
[11] B. Paris, J. Eynard, S. Grieu, T. Talbert, M. Polit , ―Heating control
schemes for energy management in buildings ‖, Energ y and Buildings,
vol. 42, pp. 1908 -1917, 2010.
[12] G. Neculoiu, V . Dache, G . Stamatescu, V . Sgarciu , ―Model Predictive
Control applied for building thermal control ‖, IEEE ACEMP -OPTIM –
ELECTROMOTION 2015 – International Conference, 2015 (i n press,
corrected ).
[13] Paul Strachan, Ingo Heusler, Matthias Kersken , Maria Jose Jimenez,
―Test Case Twin_House_Experiment_2. Validation of Building Energy
Simulation Tools (Subtask 4). Version 4‖, IEA ECB Annex 58, 2014.
[14] M.D. Doan, T. Keviczky, I. Necoara, M. Diehl, B.D. Schutter, ―A
distributed version of Han’s method for dMPC using local
communications only ‖, Journal of Process Control, vol. 17, pp. 37 -50,
2007.