Modeling Zero Energy Building with a Three- Level Fuzzy Cognitive Map

Modeling Zero Energy Building with a Three- Level Fuzzy Cognitive Map Eleni S. Vergini 1, Theodora-Eleni Ch. Kostoula 2, P. P. Groumpos 3 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. Keywords Zero Energy Buildings, Fuzzy Cognitive Maps, Non-linear Hebbian Learning Algorithm. I I. INTRODUCTION 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 CO 2 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 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. 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. 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]. 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. On the other hand ZEBs which are connected to the grid are separated in three categories [6]: ISBN: 978-1-61804-324-5 275

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. 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]. A. FCM Structure III. FUZZY COGNITIVE MAPS 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]. 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 two concepts C i and C j there could be three cases: w ij >0, an increase in C i causes an increase in concept C j, and a decrease in C i causes a decrease in concept C j. w ij <0, an increase in C i causes a decrease in C j, and a decrease in C i causes an increase in C j. w ij =0, there is no interaction between concepts C i and C j. The amount of influence between the two concepts is indicated by the absolute value of w ij. During simulation, the value of each concept is calculated using the following rule: Where t represents time, n is the number of concepts and f is the sigmoid function given by the following equation: 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] 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 η κ 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: There are two different termination criteria which (1) (2) (3) ISBN: 978-1-61804-324-5 276

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: 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 In the first level there are concepts C7-C14, which represent the weather conditions and the parameters which 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 C1- C6, 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: 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 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 C6 0 0 0 0 0 0 0 0-0,5 0 0 0 0 0 0 0,15 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 ISBN: 978-1-61804-324-5 277

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 W9-12 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. 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 W7-11, W9-12, and W14-16, all the other weights are common in 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. 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 C6 0 0 0 0 0 0 0 0-0,5 0 0 0 0 0 0 0,15 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 ISBN: 978-1-61804-324-5 278

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. 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 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. for winter building operation and the non-linear Hebbian learning algorithm, lead to the diagram in Fig.3. 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. 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. 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. 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. 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. All the above initial values, considering the weight matrix 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 ISBN: 978-1-61804-324-5 279

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. REFERENCES [1] Torcellini, Paul, et al. "Zero energy buildings: a critical look at the definition."national Renewable Energy Laboratory and Department of Energy, US (2006). [2] Marszal, Anna Joanna, et al. "Zero Energy Building A review of definitions and calculation methodologies." Energy and Buildings 43.4 (2011): 971-979. [3] Kapsalaki, M., V. Leal, and M. Santamouris. "A methodology for economic efficient design of Net Zero Energy Buildings." Energy and Buildings 55 (2012): 765-778. [4] Sartori, Igor, et al. "Criteria for definition of net zero energy buildings."international Conference on Solar Heating, Cooling and Buildings (EuroSun 2010). 2010. [5] Hernandez, Patxi, and Paul Kenny. "From net energy to zero energy buildings: Defining life cycle zero energy buildings (LC-ZEB)." Energy and Buildings 42.6 (2010): 815-821. [6] Voss, Karsten. "Nearly-zero, Net zero and Plus Energy Buildings." REHVA Journal, Dec (2012). [7] Pérez-Lombard, Luis, José Ortiz, and Christine Pout. "A review on buildings energy consumption information." Energy and buildings 40.3 (2008): 394-398. [8] Vergini E., Kostoula Th.E., Groumpos P. "Areview on Zero Energy Buildings and Intelligent Systems." This paper has been accepted to the Conference IISA 2015 [9] Parsopoulos, Konstantinos E., et al. "A first study of fuzzy cognitive maps learning using particle swarm optimization." Evolutionary Computation, 2003. CEC'03. The 2003 Congress on. Vol. 2. IEEE, 2003. H. Poor, An Introduction to Signal Detection and Estimation. New York: Springer- Verlag, 1985, ch. 4. [10] Kannappan, Arthi, A. Tamilarasi, and Elpiniki I. Papageorgiou. "Analyzing the performance of fuzzy cognitive maps with non-linear hebbian learning algorithm in predicting autistic disorder." Expert Systems with Applications 38.3 (2011): 1282-1292. [11] Public Power Corporation S.A. Hellas https://www.dei.gr/en [12] Kosko, Bart. "Fuzzy cognitive maps." International journal of manmachine studies 24.1 (1986): 65-75. [13] Groumpos, Peter P. "Fuzzy cognitive maps: Basic theories and their application to complex systems." Fuzzy cognitive maps. Springer Berlin Heidelberg, 2010. 1-22. ISBN: 978-1-61804-324-5 280