Recent Advances in Environmental and Earth Sciences and Economics
Modeling Zero Energy Building with a ThreeLevel Fuzzy Cognitive Map
Eleni S. Vergini1, Theodora-Eleni Ch. Kostoula2, P. P. Groumpos3
used in this paper to model the operation of a ZEB, and in the
fifth part the simulation results are discussed. Last but not
least, in the sixth section there are the conclusions along with
thoughts on further research.
Abstract— The concept of Zero Energy Buildings (ZEB) is
briefly reviewed and its characteristics are presented. A number of
categories of ZEBs are defined and briefly are discussed. An
attempt is made to model Zero Energy Buildings (ZEBs) using
theories and algorithms of Fuzzy Cognitive Maps (FCMs). The
basics of FCMs and the Hebbian learning algorithm are briefly
reviewed and outlined. A new three level model for ZEBs using
FCMs is developed. The new model is used to conduct simulation
studies for summer and winter cases. Interesting results are obtained
and briefly discussed.
II. ZERO ENERGY BUILDING DEFINITION
Zero Energy Building (ZEB) is based on the concept of a
building which, within its boundaries, produces as much
energy as it consumes, usually on an annual basis. The
produced energy mainly comes from renewable energy
sources which are located near the building, do not pollute the
environment and their cost is reasonable. Since a specific way
to achieve the desirable energy balance has not yet been
defined and established, the aspect of ZEBs is rather
challenging. The absence of specific characteristics and
equipment requirements is the reason why an accurate
definition has not yet been expressed [1]-[5].
Keywords— Zero Energy Buildings, Fuzzy Cognitive Maps,
Non-linear Hebbian Learning Algorithm.
I. INTRODUCTION
I
N recent years there has been a worldwide effort in
environmental protection and energy saving in any human
activity possible. Buildings, consuming about 30-40% of all
primary energy produced worldwide and being responsible for
36% of CO2 emissions, could not be missing from that effort.
Scientists and engineers, using active and passive techniques,
started to improve buildings’ energy performance, always
taking into consideration the human need to ensure
comfortable living conditions while saving energy and
reducing environmental pollution.
In addition the EU “Energy Performance of Buildings”
Directive (EPBD), released in 2010, and the “Energy
Efficiency Directive”, released in 2012, lead member nations
towards Zero Energy Buildings (ZEBs), with the obligation
that by the end of 2020 all new buildings will have to be
nearly Zero Energy Buildings (nZEBs). The same direction is
given in USA member nations, where the US Department of
Energy (DOE) has set a similar goal.
In the second section there is a brief reference to the
characteristics of a ZEB and its parameters. In the third part
of the paper there is a synoptic presentation of the method of
FCMs and the algorithm of Non Linear Hebbian Learning. In
the fourth section there is a description of the FCM which is
In order to be appropriate for use, buildings should provide
specific comfort conditions for people who are inside. Those
conditions are achieved by consuming energy for heating,
cooling, lighting and other services. Buildings mainly
consume electrical energy, other types of energy which are
consumed, such as thermal, are usually produced either by
converting electrical energy or by passive techniques, such as
solar heating or geothermal energy.
The energy requirements of each building depend on its
utility. There are three categories of buildings according to
their use. These are 1) commercial, 2) public and 3)
residential buildings. Another important factor related to the
required energy is the geographical position of each building.
Usually in regions with lower temperature a larger amount of
energy is consumed in space heating whereas in warmer
regions more energy is consumed in air-conditioning and
cooling.
A ZEB is characterized by its connection to the grid
according to the following reasoning. Usually in regions
where a connection to the grid is not accessible buildings are
not connected to the grid. Those ZEBs are characterized as
autonomous or stand-alone ZEBs.
E.S Vergini, Laboratory of Automation and Robotics, Electrical and
Computer Engineering Department, University of Patras.
Th.E. Kostoula, Laboratory of Automation and Robotics, Electrical and
Computer Engineering Department, University of Patras.
P.P. Groumpos, Laboratory of Automation and Robotics, Electrical and
Computer Engineering Department, University of Patras.
ISBN: 978-1-61804-324-5
On the other hand ZEBs which are connected to the grid
are separated in three categories [6]:
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Recent Advances in Environmental and Earth Sciences and Economics
two concepts Ci and Cj there could be three cases:
wij>0, an increase in Ci causes an increase in concept Cj,
and a decrease in Ci causes a decrease in concept Cj.
wij<0, an increase in Ci causes a decrease in Cj, and a
decrease in Ci causes an increase in Cj.
wij=0, there is no interaction between concepts Ci and Cj.
The amount of influence between the two concepts is
indicated by the absolute value of wij.
Nearly Zero Energy Building (nZEB) is a ZEB
connected to the grid which has nearly zero energy
balance. This means that the consumed energy is slightly
higher than the produced energy.
Net Zero Energy Building (NZEB) is a ZEB
connected to the grid which has zero energy balance. In
that occasion the consumed energy is equal to the
produced energy.
Net plus or Positive Energy Building is a building
with positive energy balance. The positive energy building
consumes less energy than it produces and the excess
energy is supplied to the grid.
In all the above cases the energy balance is calculated on
annual basis.
During simulation, the value of each concept is calculated
using the following rule:
(1)
The design of each building is made taking into
consideration the energy requirements and the applications
which are used to satisfy those requirements. The required
energy is mainly produced by renewable energy sources, but
when those sources are not enough to satisfy the load,
conventional energy sources might be used as well. The
energy sources may be on the building, on its site or at a
distance.
It was mentioned above that in cases of positive energy
buildings excess energy is usually provided to the grid.
Alternatively, that energy might be saved for later use in
energy storage devices. Those devices can also be used in
autonomous buildings in order to save energy for later use.
However those devices have the disadvantages of 1) limited
technology and 2) the need of regular maintenance and
replacement, [7]-[8].
Where t represents time, n is the number of concepts and f
is the sigmoid function given by the following equation:
(2)
In which λ>0 determines the steepness of function f.
Usually in problems there is a number of concepts and A
and w are matrices.
The FCM concepts take initial values and then they are
changed depending on the weights and the way the concepts
affect each other. The calculations stop when a stable state is
achieved and the values of concepts do not change
furthermore.
In some cases, there are systems which can be presented by
a FCM organized in levels. In the lower level there are
concepts which affect only other concepts in the same on in
the above level and not the output, those concepts are Factorconcepts. The concepts which are affected by Factor-concepts
and then they determine the output are called Selectorconcepts and finally, in the higher level, there are the
Output-concepts. [9]
III. FUZZY COGNITIVE MAPS
A. FCM Structure
Fuzzy Cognitive Maps (FCMs) are a combination of fuzzy
logic and neural networks. They are a method of modeling
complex problems, based on human reasoning. A human can
make a decision even if a problem is uncertain or ambiguous,
using his experience and assessment ability. FCMs are based
on that reasoning. They are a graphical presentation of the
problem. Each parameter (variable) is presented with a node
and it is called “concept”. The interaction between concepts
and the way they affect each other are presented with
“weights”. The number of concepts, the kind of interaction
between them and the values of the weights are determined by
experts, who know the dynamics of the system and the way it
reacts to various changes [12]-[13].
B. Non Linear Hebbian Learning
Based on neural networks, FCMs have a non-linear
structure. The algorithm of non-linear Hebbian learning is
used in this paper to train ZEB FCM to predict the energy
balance. The algorithm uses a learning rate parameter ηκ and
a weight decay parameter γ, in order to calculate updated
weight values, changing only non-zero weights that the
expert gave, and then update the concept values. The nonlinear Hebbian learning algorithm is based on the equation:
Concepts take values in the interval [0, 1] and weights
belong in the interval [-1, 1]. The sign of each weight
represents the type of influence between concepts. Between
ISBN: 978-1-61804-324-5
(3)
There are two different termination criteria which
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Recent Advances in Environmental and Earth Sciences and Economics
determine when the algorithm stops. In [10] there is a
detailed description of the algorithm and its parameters.
IV. MODELING A ZEB WITH A THREE LEVEL FCM
In this paper a three level FCM (Fig.1) will be used to
model the operation of a ZEB. In order to make a FCM to
represent the interconnection of the components of ZEB
architecture during real-time operation, an expert should
consider each component as a concept and determine the
weights between them.
In this paper a house was considered to be the ZEB and the
parameters that each concept represents are the following:
Fig.1 Three Level FCM modeling ZEB.
affect the values of the higher level concepts. Those are the
Factor-concepts. In the second level there are concepts C1C6, those are the Selector-concepts. C1 and C2 are the energy
production units, and C3-C6 are the energy consumption
parameters. In the third level C15 and C16 are the output
values, total production and total consumption, since the most
important consideration of a ZEB is the Energy Balance,
which is given by the equation:
C1 : Photovoltaic System
C2 : Wind Turbine
C3 : Lighting
C4 : Electrical/Electronic Devices
C5 : Heating
C6 : Cooling
C7 : Solar Radiation
C8 : Wind Velocity
C9 : Windows
C10 : Natural Light
C11 : Shading
C12 : Internal Temperature
C13 : External Temperature
C14 : Geothermal Energy
C15 : Total Production
C16 : Total Consumption
Energy Balance=Total Production–Total Consumption
The amount of energy that each concept produces or
consumes was considered based in [11], in order to determine
the linguistic values of the concepts and to specify the
weights. More specifically:
C1 (PV): Output Power 0-10KW→Concept value 0–1.
C2 (Wind Turbine): Output power 1KW→Concept
value 0-0.1.
C3 (Lighting): It is estimated that the house has 15
light bulbs, and each bulb has power consumption
In the first level there are concepts C7-C14, which
represent the weather conditions and the parameters which
TABLE 1
SUMMER
C1
C2
C3
C4
C5
C6
C7
C8
C9
C10
C11
C12
C13
C14
C15
C16
C1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0,8
0
C2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0,2
0
C3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0,1
C4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0,3
C5
0
0
0
0
0
0
0
0
-0,5
0
0
0
0
0
0
0,15
0,15
C6
0
0
0
0
0
0
0
0
-0,5
0
0
0
0
0
0
C7
0,95
0
0
0
0
0
0
0
0
0,6
0,1
0
0
0
0
0
C8
0
0,85
0
0
0
0
0
0
0
0
0
0
0
0
0
0
C9
0
0
0
0
0
0
0
0
0
0
0
0,1
0
0
0
0
C10
0
0
-0,3
0
0
0
0
0
0
0
0
0,01
0
0
0
0
C11
0
0
0,3
0
0
0
0
0
0
-0,2
0
-0,01
0
0
0
0
C12
0
0
0
0
0
0,2
0
0
0
0
0
0
0
0
0
0
C13
0
0
0
0
0
0,2
0
0
0
0
0
0
0
0
0
0
C14
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
C15
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
C16
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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20W. An average use of the lighting is estimated,
using 4bulbs × 3h/day, giving a total consumption in
lighting equal to 240W/day→Concept value 0-0.024.
C4 (Electrical/Electronic Devices): The devices that a
typical house has are:
 Fridge: 90W/h→2160W/day
 Electric Oven: 2000W/h
 PC: 300W/h, average use 3 hours per day
 Electric Iron: 1000W/h
 Vacuum Cleaner: 1000W/h
 TV: 41W/h
 Washing Machine: 2800W/h
 Electric Water Heater 80lt: 4000W/h
Considering an average day, using the fridge 24h, the
electric oven 1h, the PC 3h, the vacuum cleaner 1/2h and
the electric iron 1h, the average consumption for the
devices is equal to 6560W/day→Concept value 0-0.656.
C5 (Heating): 2 Air Condition 1000W/h, average use
2h, average consumption 4000W/day→Concept value
0-0.4.
C6 (Cooling): 2 Air Condition 1000W/h, average use
2h, average consumption 4000W/day→Concept value
0-0.4.
Concepts C7-C14 vary between 0 and 1, since their
contribution is considered only linguistically.
both cases, which is reasonable since they refer to the same
system. W7-11 expresses the interaction between solar
radiation and shading. In summer it is positive, since a
thicker shadow is necessary as the solar radiation increases.
On the other hand, in winter it is negative because less
shadow is desired as the radiation increases, in order to take
advantage of it to heat the rooms and have more natural light.
In addition W9-12 expresses the interaction between windows
and inside temperature. During summer, when the outside
temperature is higher than the inside, an open window causes
an increase in the inside temperature. Whereas, in the winter,
when the outside temperature is lower than the inside, an
open window causes a decrease in the inside, that is why W912 is negative in winter and positive in summer. W14-16
expresses the contribution of geothermal energy in the total
consumption, since in order to take advantage of geothermal
energy a heating pump should consume a small amount of
energy.
A. Summer
In order to have a good approach of the buildings’
operation during summer, the appropriate weather conditions
are set to the initial input values, approaching the Greek
climate.
Solar radiation (C7) has been set high and wind velocity
(C8) has been set low, those concepts define the energy
production setting the PV energy production (C1) to high and
wind turbine energy production (C2) to low. Apart from the
production, the weather concepts define the initial values of
natural light (C10), which initially has medium high value
and shading (C11), which has a medium initial value.
V. SIMULATION RESULTS AND DISCUSSION
The simulation procedure was designed for two cases. The
first case is a typical summer day and the second is a typical
winter day. The weight matrix for each case is shown in
Table 1 and Table 2 respectively. Except for the weights W711, W9-12, and W14-16, all the other weights are common in
In addition, the concepts which determine the energy
TABLE 2
WINTER
C1
C2
C3
C4
C5
C6
C7
C8
C9
C10
C11
C12
C13
C14
C15
C16
C1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0,8
0
C2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0,2
0
C3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0,1
C4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0,3
C5
0
0
0
0
0
0
0
0
-0,5
0
0
0
0
0
0
0,15
0,15
C6
0
0
0
0
0
0
0
0
-0,5
0
0
0
0
0
0
C7
0,95
0
0
0
0
0
0
0
0
0,6
-0,2
0
0
0
0
0
C8
0
0,85
0
0
0
0
0
0
0
0
0
0
0
0
0
0
C9
0
0
0
0
0
0
0
0
0
0
0
-0,3
0
0
0
0
C10
0
0
-0,3
0
0
0
0
0
0
0
0
0,01
0
0
0
0
C11
0
0
0,3
0
0
0
0
0
0
-0,2
0
-0,01
0
0
0
0
C12
0
0
0
0
-0,2
0
0
0
0
0
0
0
0
0
0
0
C13
0
0
0
0
-0,05
0
0
0
0
0
0
0
0
0
0
0
C14
0
0
0
0
-0,2
0
0
0
0
0
0
0
0
0
0
0,05
C15
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
C16
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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consumption have been set to the appropriate values. Lights
energy consumption (C3) is low since the natural light is
high. Devices (C4) are set to low, heating (C5) is zero and
cooling (C6) is medium.
for winter building operation and the non-linear Hebbian
learning algorithm, lead to the diagram in Fig.3.
All the above initial values, considering the weight matrix
for summer building operation and the non-linear Hebbian
learning algorithm, lead to the diagram in Fig.2.
In that diagram the total production starts with a higher
value of the total consumption, but in the end it is obvious
that the total consumption exceeds the production. This
means that the Energy Balance is negative during an
average winter day. This result was expected since, most of
winter days the produced energy are not enough to cover the
needs and the energy balance is considered to be negative.
In that diagram the above line represents the total
production and the bottom line is the total consumption. It is
assumed from the diagram that during summer the Energy
Balance is positive. The fact that the balance is positive is
reasonable and expected, since in Greece during summer the
solar energy is intense and some months, such as August, the
wind may be quite strong as well. Those conditions offer
more than the necessary amount of energy, giving the
opportunity not only for a zero energy balance but for a
positive one.
B. Winter
Following the same thoughts as during the summer, the
winter conditions were formed as following. Solar radiation
(C7) has been set low and wind velocity (C8) has been set
high, those concepts lead the PV energy production (C1) to
low and wind turbine energy production (C2) to high. The
weather concepts define the initial values of natural light
(C10), which initially has a low value and shading (C11),
which has zero initial value.
Fig.3 Total Production and Total consumption of a ZEB
during winter.
The above results cover two typical days, with average
weather conditions and average energy consumption, one in
summer and one in winter. It is a fact that not every day will
be like those, but the goal of a Zero Energy building is not the
achievement of balance in only one day, it is within one year.
In summer, when most days have a positive balance, the extra
produced energy will be provided to the grid and in winter,
when the energy balance most of the days is negative, the grid
will provide the necessary energy to the building, balancing
the interchange of energy.
In addition, lights energy consumption (C3) is high since
the natural light is low. Devices (C4) are set to low, it was
assumed that the human activity does not change but it is the
same as in summer, heating (C5) is medium and cooling (C6)
is zero.
Another important factor is that buildings, apart from
production and consumption variables, also have parameters,
such as materials and utility, etc. Those parameters define the
behavior of each building, and play a rather important role in
the energy balance. Buildings with the same size and same
energy production equipment may not cover their needs in the
same way and this is a challenging problem.
VI. CONCLUSIONS AND FUTURE RESEARCH
Fig.2 Total Production and Total consumption of a ZEB
during summer.
ZEBs attract the attention of scientists and engineers in
recent years. However, their modeling has many difficulties,
due to the large number of parameters, the different possible
All the above initial values, considering the weight matrix
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Recent Advances in Environmental and Earth Sciences and Economics
ways of approach and the fact that an accurate definition has
not yet been defined.
This paper is a modeling approach of a ZEB. The
simulation results are promising, since the FCM model
outputs are the same with those which were expected from the
real system. Therefore, FCM could be characterized as a
useful tool and one could assume that a first step towards the
simulation and modeling of a ZEB has been done.
However, there are many unanswered questions on the
aspect of ZEB. The next research steps could be the
application of control methods, in order to make the building
“intelligent”. The implementation of load management and
energy efficiency control systems is necessary for the
achievement of Energy Balance, mainly when the weather
conditions are not cooperative. Definitely, the aspect of ZEB
has still many unlighted sides and scientists should give their
lights towards that direction.
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