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PAGE 1 1 DESIGN OF AN ENERGY EFFICIENT BUILDING VIA MULTIVARIATE STOCHASTIC OPTIMIZATION By DIWAKAR SINHA A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2012 PAGE 2 2 2012 Diwakar Sinha PAGE 3 3 To t he Almighty Lord Hare Krishna PAGE 4 4 ACKNOWLEDGMENTS I want to give my appreciation to my advisor, Dr. Mrinal Kumar, for his encouragement and invaluable help in helping me start this project. I would like to express my sincere gratitude for his continuous support of my thesis and research, for his patience, motivation and the experience. I would like to thank Dr. Thomas Smith and his students for their help in the architectural aspect of my design. I wou ld like to thank Dr. Parbir Baro oah for his useful advice during the early stage of my research and for hi s role on my Supervisory Committee as well. I wish to thank Dr. Ravi Srinivasan for his tips in terms of building design parameters and for his advice on the overall shape of this work. PAGE 5 5 TABLE OF CONTENTS page ACKNOWLEDGMEN TS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 7 LIST OF FIGURES ................................ ................................ ................................ .......... 8 LIST OF ABBREVIATIONS ................................ ................................ ............................. 9 ABSTRACT ................................ ................................ ................................ ................... 10 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .... 11 Building Optimization Methods in Literature ................................ ............................ 13 Delimitation of this Study ................................ ................................ ........................ 18 2 PROBLEM FORMULATION ................................ ................................ ................... 19 Decision V ariables ................................ ................................ ................................ .. 21 Constant Parameters ................................ ................................ .............................. 26 Optimization Constraints ................................ ................................ ......................... 27 Discrete and Continuous Variables ................................ ................................ ......... 28 3 SOLUTION METHOD ................................ ................................ ............................. 41 Simulated Annealing ................................ ................................ ............................... 41 Combinatorial Optimization: ................................ ................................ ............. 41 Physical Annealing ................................ ................................ ........................... 42 A Simple Versi on of SA Algorithm: ................................ ................................ ... 43 Asymptotic Convergence Characteristics ................................ ......................... 44 Finite time approximations: ................................ ................................ ........ 44 Implementation ................................ ................................ .......................... 44 Issue with Simulat ed Annealing ................................ ................................ .............. 45 Information Guided SA ................................ ................................ ............................ 45 Guided Annealing Temperature: ................................ ................................ ...... 45 Modified Algorithm ................................ ................................ ............................ 47 Enforcement of optimization constraints ................................ ................................ 48 4 OBSERVATIONS AND RESULTS ................................ ................................ ......... 53 On Validity of Modeling Approach ................................ ................................ ........... 53 Space Heating ................................ ................................ ................................ .. 53 Ventilation and Ai r Conditioning ................................ ................................ ....... 53 PAGE 6 6 Windows ................................ ................................ ................................ ........... 54 Daylighting ................................ ................................ ................................ ........ 54 User Behavior ................................ ................................ ................................ ... 55 Results: ................................ ................................ ................................ ................... 56 Building Shape: ................................ ................................ ................................ 57 Thermal Insulati on: ................................ ................................ ........................... 58 Windows and Daylighting: ................................ ................................ ................ 58 Solar Thermal and Photovoltaic Systems: ................................ ........................ 59 Heating and Cooling: ................................ ................................ ........................ 59 Lighting Control: ................................ ................................ ............................... 59 Optimum Trade off Strategy: ................................ ................................ ............ 59 Battery Storage: ................................ ................................ ............................... 60 5 CONCLUSION ................................ ................................ ................................ ........ 74 APPENDIX: NOMENCLATURE ................................ ................................ .................... 75 LIST OF REFERENCES ................................ ................................ ............................... 78 BIOGRAPHICAL S KETCH ................................ ................................ ............................ 83 PAGE 7 7 LIST OF TABLES Table page 2 1 PV array, Solar noon tilt data. ................................ ................................ ............. 36 2 2 Window type and area ................................ ................................ ........................ 36 2 3 Description of design variables ................................ ................................ ........... 37 2 4 Solar thermal collector type ................................ ................................ ................ 37 2 5 PV system capacity ................................ ................................ ............................ 37 2 6 Lighti ng type ................................ ................................ ................................ ....... 38 2 7 Input parameters ................................ ................................ ................................ 38 2 8 Heating, cooling and economic data ................................ ................................ ... 39 2 9 ASHRAE Building envelope requirements for climate zone 3A. ......................... 4 0 3 1 Comparison between simulated annealing and physical annealing .................... 52 4 1 Hourly load and usage patterns ................................ ................................ .......... 68 4 2 Describing the output values when the simulation is run for one year ................ 69 4 3 D escribing the output values when the simulation is run for two years ............... 70 4 4 D escribing the output values when the simulation is run for five years ............... 71 4 5 D escribing the outpu t values when the simulation is run for ten years ............... 72 4 6 Design variables and annual energy consumption data for minimum cost and l ow energy designs ................................ ................................ ............................. 73 PAGE 8 8 LIST OF FIGURES Figure page 2 1 Plan of the ground floor ................................ ................................ ...................... 29 2 2 Plan of all floors above the ground floor ................................ ............................. 30 2 3 Thermal model ................................ ................................ ................................ .... 31 2 4 The building daylight zones for all floors ................................ ............................. 32 2 5 Solar water heating ................................ ................................ ............................. 33 2 6 Heating system. ................................ ................................ ................................ .. 33 2 7 The elevation of the building and the solar panels ................................ .............. 34 2 8 Temperature chart of Asheville, NC, USA for the year 2011. ............................. 35 2 9 Daylight zone chart of Asheville, NC, US A for the year 2011. ............................ 35 3 1 Simulated Annealing ................................ ................................ ........................... 50 3 2 A flowchart for the Modified SA algorithm ................................ ........................... 51 4 1 U values of Wall Insulation and Windows ................................ ........................... 63 4 2 Percentage of total window area to floor area ................................ .................... 63 4 3 Auxiliary lighting load ................................ ................................ .......................... 64 4 4 Daylight contribution of lighting load ................................ ................................ ... 64 4 5 Solar fraction of thermal load ................................ ................................ .............. 65 4 6 Contribution of PVs to the electricity load ................................ ........................... 65 4 7 Net primary e nergy ................................ ................................ ............................. 66 4 8 Energy consumption (kW hr/ m 2 /year) with different simulation periods. ............ 66 4 9 Cost of operating the building. Break even point is at 9.4 years ......................... 67 PAGE 9 9 LIST OF ABBREVIATION S ASHRAE American Society of Heating, Refrigerating and Air conditioning Engineers HVAC (Heating Ventilating and Air Conditioning) refers to the equipment, distribution network, an d terminals that provide either c ollective ly or individually the heating, v entilating, or air conditioning processes for a building. LCC (Life Cycle C ost ) refers to the concept of including acquisition, operating, and disposal costs when evaluating various alternatives. LCEI (Life Cycle Environmental Impact) refers to the impact on the environment during the total life of an operating device. SA (Simulated Annealin g) this abbreviation has been properly explained in Chapter 3. PAGE 10 10 Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science DESIGN OF AN ENERG Y EFFICIENT BUILDING VIA MULTIVARIATE STOCHASTIC OPTIMIZATION By Diwakar Sinha May 2012 Chair: Mrinal Kumar Major: Mechanical Engineering In this thesis, the model of a four storey office building has been designed with two objectives in mind: (a) minimu m usage of energy and (b) minimum installation and utility cost for operating the building. A modified version of simulated a nnealing has been used to address the underlying multivariate coupled problem and an optimum trade off amongst the desig n parameters has been found as a result. The approach is based on the fact that there is presence of multiple local minima, and the modified simulated annealing is expected to perform better than standard annealing in finding the global minimum. PAGE 11 11 CHAPTER 1 INTRODUCTION T he problem of designing a building with the objective of minimization of running energy or the cost associated with the running energy presents the designer with numerous optio ns to choose from [1] This is true i n spite of the pres ence of various construction code s and building guidelines [25 55 56 ] By the use of renewable sources the amount of electricity required to be drawn from the existing grid can be driven to zero. However this entails a significant increase in the associa ted cost of installation. Hence the optimal design of the building if performed only in the sense of minimum cost or minimum energy design has conflicting requirements. In a real life scenario both need to be considered and a trade off must be performed. In addition optimal design models could be linear [33 ] in nature or have a nonlinear and possibly non convex and highly multivariate form [ 3, 6, 27] In the existing literature various optimization techniques [ 1, 3, 6, 12, 13, 26] have been proposed to determine optimal building designs. When real life problems are considered the optimization model is invariably nonlinear, non convex and multivariate. This creates the problem of determining a global minimum among numerous local minima. For such problems there is no universally applicable optimization algorithm to determine the global minimum [29] This is due to the very well known theorems [42] according to which an al gorithm that is effective on a particular class of problems is guarant eed to be ineffective on other class es of problems. To the best knowledge of the author there is no consensus on the existence of a well established algorithm suited for solving optimal building design problems. Moreover, wide variety of algorithms is used and one must often settle for a local minimum. In addition, the PAGE 12 12 multivariate nature of the optimization problem demands excessive computational effort which often grows geometrically as the number of f ree variables increase s [29]. Given these observations there is a need for an optimization method that seeks to find the globally optimal design while also reducing computational effort. I n pra ctice, the first step towards development of such an optimization method is the determination of the feasible design variables Unfortunately the design variables are normally pre fixed due to architectural, aesthetic or technical requirements and hence the window for modification or of any kind of alteration is not very large. Energy conservation usually com es as a less of a priority. Moreover the design choices are normally discrete i.e. the products available in the markets do not come in all possible shapes and sizes. Such discrete nature of the parameters adds to the difficulty of solving the problem of energy efficient building design. Furthermore a t the early stage of design, the designer needs to choose the different properties of design variables (e.g. dimension, U value, cost etc.) based on their availability in the markets [30] and then f ormulate the problem accordingly to find an optimum design. The process will likely be repeated a number of times, with different set s of design variables in each run to determine the final set of variables to be used for optimization to keep the initial c ost predicted by the design to remain within feasible limits. In view of all the above restrictions the designer needs to be presented with some guidelines that would help him play with the input parameters (design variables) to obtain the final design of an energy efficient building that would be possible to build today. Therefore the presence of a set of idealized models, which are sophisticated enough to deal with the coupled PAGE 13 13 problems with respect to the ener gy utilization of the building, would be very useful during early stage of design. Once a model has been created, the optimum value of all involved design variables with respect to a generic building is calculated. In this thesis the objective function is assumed known and has been derived from existi ng literature. The objective of the current stud y is to make use of a simple model of a solar low energy building and to optimize its design so that the optimum design variables minimize the energy use as well as the running utility cost. These design vari ables include building geometry, thermal insulation, windows, solar thermal collectors, PVs, battery capacity to name a few. The optimization scheme used over here is a modified version of simulated annealing which attempts to find the design trade off pat hs between conflicting and coupled design decisions in order to find the global optimum. In summary, t here has been marked increase in the energy performance [31 32 ] of new solar low energy buildings which has been constructed in recent years. The causes for this phenomenon are multifold T here is an increased awareness about the impact of the use of non renewable resources on the environment. Additionally the soaring cost of everyday living brought on by the current economic crisis has drawn the issue of energy efficiency to the forefront. Hence the motivation s of this study are environment al economic and social benefits. In future too, it is verily expected that demand for energy performance of new buildings will play a big role in shaping the buildings. B uilding Optimization Methods in L iterature Numerous schemes for optimization of the performance of buildings have been proposed by researchers The more recent among these are described in this section PAGE 14 14 The optimization techniques used by d ifferent researchers were based on the problem they were trying to solve and there was hardly any attempt to improve upon the previously published algorithms. In Ref. [1], Peippo et al. attempted to solve the problem of finding the optimum technology mix f or building projects using multiple parameter s such as shape of the building its orientation the amount of insulation, area of windows, volume of stored water etc. In their analysis, they considered the total amount of energy required to run the building o n an annual basis. A c yclic coordinate search me thod was used in conjunction with the method of Hooke and Jeeves (pattern search) [2] to reach a solution Although their method was easy to visualize and impl ement, the convergence was slow. Bouchlaghem [3] studied t he thermal performance of a building using simulation models and obtained an optimum set of design variables by numerical techniques so as to achieve best thermal comfort conditions B uilding parameters such as building envelope, f abric, aspect ratio, the orientation of the building, the glazing ratio of the windows etc were used to study the building design and the best thermal comf ort level was determined S ix different o bjective functions were optimized so as to get six differen t ways of quantifying thermal com fort. In addition t he decision variables were linearly constrained Two method s wer e used to perform the optimization : (a) the highly popular simplex method of Nelder and Mead [4 ] and (b) the so called c omplex method proposed by Mitchell and Kaplan [5]. Although the convergence rate is high for both these methods neither guarantees a globally optimal result. G enetic algorithm s [7] constitute another class of frequently used optimization techniques for building optimiza tion Fonseca and Fleming [15] use d multi criterion PAGE 15 15 genetic algorithm to solve the ir optimization problem. They applied the Pareto optimal points for solving a two objective prob lem. Their objective function was the cost of the building and the environment al impac t of the building. Wright et.al. [13] also used the multi criterion genetic algorithm [7] to optimize the design and the operation of th e Heating Ventilation and Air Conditioning(HVAC) system for a building. Caldas and Norford [6 ] used a method th at took into account the dimensions of the windows in order to determine th e least amount of energy for heating and artificial lighting. They too solved the optimization problem using genetic algorithm s [7]. Wang et.al. [14] also applied genetic algorithm although their study was focused towards the design of green buildings. The optimization algorithm attempted to determine the numerical values of the orientation, the aspect ratio of the rooms, and the ratio of window to wall area in ord er to optimize the Life Cycle C ost (LCC) and Life Cycle E nvironment al I mpact (LCEI). Although genetic algorithm s ha ve several advantages such as their universal applicability and ease of implementation there is no assurance that it will find the global min imum Moreover, the large optimization response time for genetic algorithm limits it applicability in practical problems. Jadrzejuk and Ma rk s [8, 9, 10] descr ibe a method in which t he y divide the problem into three sub problems: (i) optimization of internal portions, (ii) the shape of the building and (iii) coordination of the solutio ns. The shape of the building was studied through parameters such as wall length indow to wall areas etc. This was also a constrained multivariate problem which considered the construction cost the seasonal demand for heating, pollut ants emitted by heat sources to name a few. T he solution method attempted to determine the optimum value using either an PAGE 16 16 analytical technique e xplained by Hwang CL [ 50], or numeric al technique explained by S. Jendo and W. Marks [51] Although these techniques are capable in finding the solution, there is no guarantee of reaching a global optimum. Additionally they take a long time to converge on a solution. Nielsen and Svendsen [11] use d their method to find the optimum value of the parameters such as amount of insulation, type of glazing, window fraction of external walls etc using a constrained optimization problem formu l ation for determining th e optimum life cycle cost of the building. They also studied the energy consumed by the building and the position and duration of the overheating if any inside the building. These parameter s define the upper limit of their cons traints and the lower limits were defined by the daylight factor. Their problem formulation was quite realistic and it took into account both discrete and continuous variables. Simulated annealing has been used by Gonzalez Monroy and Cordoba [12] for optimizing the discrete parameters, and th e method by Hooke and Jeeves [2 ] for optimizing the conti nuous variables. In a nutshell, this algorithm executes a randomized exploration of the optimization domain in order to determine the optimum solution. Although simulated annealing has numerous advantages e.g. it applies to arbitrary cost functions and is eas y to implement, it is difficult to ascertain wh ether an optimal solution has been reached or not. Yet it is not only a very simple but also a very po werful technique for solving problems that are composed of many variables. Furthermore it seeks to find a global optimum and statistically guarantees that the global optimum would be found [49]. PAGE 17 17 From the above survey, it is apparent that there have been a number of studies [20] in optimizing various parameters defining the design of a building We can see that all the above mentioned papers consider the following desi gn variables to be significant: 1. The shape of the rooms of the building or the overall shape of the building expressed in terms of aspect ratio, the number of floors or the three dimensions. 2. The orientation of the building 3. The volume/thickness of the insulation 4. The dimension/area of the windows with respect to the dimension/area o f the wall 5. The type of window utilized 6. The shape of the windows 7. The amount of energy utilized in a. HVAC systems b. Hot water provisions c. Artificial lighting measures 8. The cost of building operation Hence these variables must be consider ed for optimization of a building design A modified version of simulated a nnealing algorithm (called the information guided simulated annealing) h as been used in this study for optimization of the above mentioned parameters. The optimization procedure makes use of the information gathered in the process of randomized exploration of the optimization domain to direct the search direction. The information is used as a feedback with progressively increasing gain to drive the optimization procedure [54 ] This method is easy to implement and has been shown to provide significant improvement over standard simulated annealing algorithms for certain optimization problems In particular the information guided s imulated a nnealing succeeds in finding the global optimum in PAGE 18 18 nu merous situation s where standard s imulated a nnealing fails [54] However no theoretical results exist to back this claim for more general situations. By virtue of its randomized exploration approach the information guided version works well with high dimen sional problems and typically converges in a reasonable period of time. In this thesis the i nformation g uided s imulated a nnealing has been used due to its above mentioned advantages and has been shown to provide improvement over the standard simulated annealing algor ithm. Delimitation of this Study In this work, a uni objective optimization study of a building model has been performed and consequent design decisions valid for formulations have bee n presented. The design parameters are constrained within reasonable limits which are decided upon by using various practical examples and available design codes This study focuses on methods intended for the early stage of design. Consequently the detailed plan of the building has not been taken into account i n the solution steps. The principle design parameters are the aspect ratio of the rooms, the ar ea of the windows, the U value of the thermal insulation the amount of building envelope etc. The parameters that decide the design and operation of HVAC syste ms are not considered T he performance of the building has been studied through a period of ten year s with respect to energy, economy, and indoor environment. The study is mainly focused on office building s and is not suitable for r esidential buildings. T he reliability and sensitivity analysis has not been considered in this study. Volatility in cost of various system elements has not been included. Development of the database management systems which may be required for managing t he information fo r doing the calculations has not been carried out in this study PAGE 19 19 CHAPTER 2 PROBLEM FORMULATION A simplified model of the building has been created for this study The layout of the building is rectan gular. All the rooms in the building are identical in shape and there are 9 rooms in each floor (F igure 2 1 2 2 ). The building is composed of four identical floors. The walls of each of the room s have a window if they are exposed to direct sunlight. The staircase tower or the elevator tower is not consid ered in this study The foundatio n of the building is assumed to be annular but it has not been included in calculation s of energy performance. The orientation of the building has been defined as the counterclockwise angle from due south to the main axis o f the building. I nsulation has been provided to all the walls that are in direct contact with outside atmosphere. Since this is an office building, each storey is provided with bathrooms, a storage room, a mechanical/electrical room, a conferen ce room and other offices (see F igure 2 1). The elevators and the staircases create a two way exit from the building, which is compliant with the international building code [52]. The economic analysis is done by summing up all the costs for running the systems in the building for a given number of years T his total cost forms the objective function of this study and is expressed as : C a = C i i + E th c th + E el c el E sp c sp (2 1) where C i is the cost of installing and employing a given design option i and it has been defined as follows: C i = A f c A i + c i x i (2 2) PAGE 20 20 where A f is the total room floor area c A i is the cost of installing the design option per floor area, and x i is the degree of design option employed and c i is the associated cost with the design o ption. Here is a fuzzy variable of sorts and allows us flexibility in designing the objective function. More detail is provided in the sequel. The coefficient is the energy price escalation over a period of time t and is formulated as = ( 1 + s 1 + r ) k t k = 1 (2 4) where s is the annual real inc rease in energy price and r is the real interest rate Therefore, the cost function of Eq. 2 2 represents the financial burden accrued over the time t E th is the annual thermal energy (energy derived from fossil fuels which is different from the energy drawn from the grid) and E el is the annual e lectricity taken from the grid. E sp is the energy given back to the grid ; or in other words it is the surplus PV electricity. The coefficient s c th c el and c sp a re the unit costs of the thermal, electrical and surplus energy respectively. The building is connected to the utility grid. It has also been assumed that the fossil f uel s are an additiona l source of electricity A factor of 0.35 has be en implemented whenever electricity has been expressed in terms of the raw sources of energy such as fuel etc. This factor of 0.35 may be thought of as the efficie ncy of the power plant. Note here that from the point of view o f environmental conservation using electricity from fossil fuels is considered less favorable than using it from solar panels or from gird. Therefore, t he annual net primary energy requirement E of the building is [1] : PAGE 21 21 E = E th + E el E sp (2 5) T he cost of installing various design options C i (in equation 1) in terms of its constituent parts c A i and c i has been tabulated in table 2 1 and table 2 2. In the following passages, different de cision variables (design options) have been explained in reference to their position and use in th e building Decision Variables The f ollowing design options have been considered in this study : 1. The shape of the rooms, and the shape of the building (in terms in of aspect ratio) 2. The area and type of windows with respect to the floor area 3. The U value and thickness of the insulation over the walls 4. The capacity the PV array required for electricity generation 5. The area solar thermal systems for room heating and hot water 6. Battery capacity Shap e of r ooms The shape of the rooms is defined by the following aspect ratios: S h = w B d B and S v = h B d B (2 6) w here w B is the width, d B is the depth and h B is the height of each room respectively. S h and S v are the optimization parameters. The factors that directly related to the aspect ratios are the cost of the building envelope, the cost of insulating the walls, the cost of heat loss and the passive solar light gains. The need for optimization arises because there is a trade off between the cost of building envelope, the building insulation and PAGE 22 22 heat losses on one side, and passive solar heat gain and daylight gains on the other side. Each one of these is described below. Building e nvelope : The building envelope is the physical separator between the interior and the exterior environments of a building [53] Insulation has been provided on all the exterior walls It has been assumed that t he roof and the ground floor is also insulated with the envelope. An attempt is made to opti mize the volume of insulation which is defined using the three parameters namely, the two aspect ratios and the thickness of insulation The cost of installing the envelope may be expressed using E quation 2 2 as follows: C en = A f c A en + c en x en (2 7) Where the cost of e nvelope per unit area of the fl oor c A en = th x [ 10 x s h + 14 x s v } x 4 + 2 A windows A F (2 8) where th is the thickness of insulation and A windows A F is the total area of the windows per unit area of floor. The value of coefficient c A en and c en may be found from T able 2 2 to T able 2 8 The overall shape of the building is a function of the number of floors and the dimension of the envelope In this study, t he building is assumed to have four floors The cost of building envelope is an essential becau se the geometry of the building is a variable parameter and optimizing it will save money and energy. Heating and cooling: T he temperature is maintained between two fixed limits which define the maximum and minimum limits using a thermostat. The cost of in stalling and operating the air conditioning (i.e. heating and cooling) system may be expressed using equation 2 as follows: PAGE 23 23 C ac = A f c A ac + c ac x ac (2 9) Where A f c A ac represents the investment cost, c ac is the unit cost of heat energy supplied/absorbed from the building and x ac is the amount of heat supplied/absorbed from the building. Note that t he HVAC system (which is significantly more sophisticated has not been stud ied here in detail The heating or cooling mechanism kicks in only when the temperature goes beyond the maximum set limit or minimum set limit point respectively. When this is not the case, the natural ventilation is assumed to be sufficient to provide for enough fresh air and comfortable temperature. The heat loss/gain is assumed to take place through conduction according model has been illustrated in F igure 2 3 and may be formulated very simply as = (2 10) where, Q i s the heat lost across a boundary, K is the conduction heat transfer coefficient, A is the s urface, is the temperature difference across the boundary ( = in F igure 2 3) and is the thickness of the boundary. Heat is lost through the external walls, the roof and the ground floor. Lighting control. L ighting control is either through on/off switches (which must be manually operated), or regulators, which are much more sophisticated. Regulators can be used to determine the exact level of lighting required by the room and to adjust the output accordingly The cost of installing lighting control, C lcon may be expressed as C lcon = A f c A lcon (2 10) w here A f is the area of floor and c A lcon is the cost of installing lighting control per unit are of floor. Clearly, the cost per unit will be different for toggle switches and regulators. PAGE 24 24 Building windows and daylighting. The windows in the buildings are normally the weakest link with respect to energy conservation [28]. The building under study is assumed to have same kind of window on all the sides of outer facing walls. The daylighting model used over here is a modified version of the one which was used by J.A. Lynes, P.J. Littlefair [16]. The horizontal daylight level in the room is calculated using the following formula: I d = 2 25 A w ( 1 2 ) A R d I rr (2 11) Where, is the window light transmittance, A w is the window area of the room, is the average indoor surface reflectance, A R is the total room interior surface area I rr is the hourly solar irradiance on a vertical surface and d is the efficacy of daylight. It was assumed that d = 110 lm / W since studies have shown that 110 is a good approximation [17]. The factor 2.25 is used to convert radiation from vertical to horizon tal level. The building has been divided horizontally into zones in each storey, so that availability for daylighting in each of the zones may be studied separately (F igure 2 4 ) If the sum total of I d available from all the windows in a given room is less than 500lx, then, then electricity will be drawn to light up the bulbs. Hence the cost of artificial lighting is: C al = A f c A al + c al x al (2 12) W here c A al wi ll constitute the cost of bulbs and lighting control cost c A lcon c al is the cost of electricity for operating the bulbs for x al amount of time. Solar thermal collectors. Solar thermal collectors have been used to store the warm water for domestic use. This is a practical approach because of many reasons [40]. Solar water h eaters do not depend on electricity which means hot water is PAGE 25 25 available even during power cuts. They reduce chances of running out of hot water as long as there is sufficient sunlight. The heat from the sun would heat up the requisite volume of water and on ce that is accomplished, the heat will then be used for heating of the rooms. In case of shortage of solar energy, i.e. during cloudy or rainy days, the electricity from the grid would fulfill the needs of warm water and room heating. The variables here ar e the collector type and the volume of water stored. Amount of hot water required per hour has been assumed to be 0.05 liters per sq. meter of floor area [1]. Figure 2 5 depicts a solar water heating equipment installed on the roof of a residential buildi ng. The working p rinciple has been explained in F igure 2 6. The solar collectors warm up the water and the air for the circulation in rooms by a heat exchanger, which also acts as a storage device Photo voltaic cells In case of shortage of solar energy, i.e. during cloudy or rainy days, the electricity from the grid would fulfill the needs. Excess electricity, whatever produced, is saved in the battery or is sold to the grid Cost of installing and money saved in running them may be expressed as C sol = A f c A sol c sol x sol (2 14) w here A f c A sol is the installation cost x sol is the PV capacity in Watt peak ( ) and c sol is the amount of money saved or earned per Watt ( ) in selling the electricity to the grid. I t can be expected that t he PV will not be sufficient in meeting all the requirements of running the utilities of an office building [39] This is because of two factors: a. T he cost of installing the PV to cover a large enough surface to provide sufficient electricity is quite large. PAGE 26 2 6 b. The space crunc h is a predomin ant problem, especially in case of high rise buildings because while the open roof space remains constant as the building grows taller, the number of rooms and hence the need for electricity increases. In spite of the above issues, PV system s can be very effective and practical if they are installed with proper planning. The tilt angle of the solar panels was found by determining the average of solar noon tilt data for the 12 months of the year [57] and has been depicted in table 2 1 B attery s torage When energy requirements are not realized wi th the available resources, the battery is used to fulfill the demand. Currently lead acid batteries are primarily used( e.g in manufacturing plants where power lapses cannot be tolerated ) to compensate for energy requirements in a variety of applications [48]. The battery is charged using the solar power. In this study, it i s considered full when the optimization schedule is initiated T he battery efficiency is a ssumed to be 90% and it is a lso assumed to have a discharge rate of 10hrs. Battery capacity has been considered as an optimization variable in this study. Cost of installing and running the battery may be expressed as C bat = A f c A bat c bat x bat (2 15) w here A f c A bat is the investment c ost, is the efficiency of the battery, x bat is the battery capacity per hr in KW and c bat is the total number of hours of its use Constant Parameters A number of constant parameters have been introduced in this study because the building model has been kept as simple as possible without compromising on important details The thickness of the un insulated parts of the ground slab, the exter nal and PAGE 27 27 internal walls and the roof are fixed The internal and external walls have a thickness of 8 inches and the ground slab is 10 inches thick. The floor ceiling assembly is made of concrete, wood and plaster and it is assumed to be 2 feet in thickness. The window panes are assumed to be 2 inches in thickness and their propertie s are tabulated in table 2 2. The buil ding planned to be constructed in the city of Asheville, NC, USA ( Lat/Lon: 35.57N 82.54W Elevation: 1981 ft ) because rebates and incentives are given by the government of this state upon use of solar energy for satisfying electricity needs [58]. Howeve r these tax rebates and incentives are not a part of this research work. The building is assumed to be facing south The HVAC systems used inside the building are pre The physical properties of the materials used in constructi on of walls, roofs, windows etc are assumed unchangeable. The weather conditions, such as temperature and sunlight are taken from the archives containing the temperature and solar irradiation values recorded on an hourly basis for the past years [18]. The input data for optimization has also been enlisted in table 2 1 to table 2 7 Much of the data has been obtained from a paper by Pieppo et al [1]. Optimization Constraints All the variable parameters have been constrained to be positive values. The area of the windows cannot be larger than the area of the walls The solar thermal collectors are constrained by the upper limit of 25 m 2 The PV cells and battery capacity have not been constraine d by any upper limit because their cost and battery life respectively limit their use. The building envelope has been restricted by the requirements of the building standards laid down by ASHRAE (American Society of Heating, Refrigerating a nd Air conditioning Engineers) [55]. The R values from the table 2 9 have been used for PAGE 28 28 calculation of insulation for the roofs with metal building, steel framed walls and slab on grade floors. Discrete and Continuous Variables Both these kinds of variabl es are used in the building design. For example, the thickness of the building material might be as such that it is easily varied between its maximum and minimum values. Window dimensions, the ventilation system etc are not as flexible as the insulation. H ence although the actual dimension of these aspects of the building may not match perfectly with the optimum solution found out by the program, i.e. it may lie between two v alues. At this point of time, optimum design is dependent upon the discretion of th e designer as to wh ich of the values should be cho se n for the design. PAGE 29 29 Figure 2 1. Plan of the ground floor PAGE 30 30 Figure 2 2. Plan of all floors above the ground floor PAGE 31 31 Figure 2 3. Thermal model PAGE 32 32 Figure 2 4. The building daylight zones for all floors PAGE 33 33 Figure 2 5. Solar water heating (Photo credit: The Australian Greenhouse Office) Figure 2 6. Heating system. PAGE 34 34 Figure 2 7 The elevation of the building and the solar panels PAGE 35 35 Figure 2 8 Temperature chart of Asheville, NC, USA for the year 2011. (Adapted from: http://www.climate charts.com/, 9th Feb. 2012) Figure 2 9 Daylight zone chart of Asheville, NC, USA for the year 2011. (Adapted from: http://www.climate charts.com/, 9th Feb. 2012) 0 5 10 15 20 25 30 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Time of the day (hours) Axis Title No daylight zone 1 Daylight zone No daylight zone 2 PAGE 36 36 Table 2 1. PV array, Solar noon tilt data. Month Sun latitude Array tilt Array points to January 34 56 South February 43 47 South March 54 36 South April 66 24 South May 74 16 South June 77 13 South July 74 16 South August 66 24 South September 54 36 South October 42 48 South November 34 56 South December 31 59 South Table 2 2 Window type and area Window type Direct normal transmittance U value (W/ m 3 K ) SGHC (Solar Heat Gain Coefficient) Total cost (USD/ m 2 ) Single glazed 0.90 6.0 0.4 100 Double glazed 0.80 3.0 0.4 150 Triple glazed 0.75 1.8 0.4 200 advanced 0.65 1.0 0.4 300 PAGE 37 37 T able 2 3 Description of design variables Design Variable Modeling Approach Building geometry Horizontal and vertical aspect ratios of the parallelepiped building, cost of the building envelope: 100USD/ m 2 Building orientation Building azimuth angle from south (fixed to 0 degrees) Collector insulation One tilt angle for both thermal collectors and PV arrays Thermal insulation Opaque insulation of uniform thickness on the building e nvelope: heat conductivit y: 0.07 to 0.01 w/mK, specific heat capacity 70kJ/ m 3 K, cost 70USD/ m 3 Thermal mass Volume of uniformly distributed thermal mass: specific heat capacity 1600kJ/ m 3 K cost 200USD/ m 3 Energy storage volume Fully mixed hot water storage, cost 500 USD/ m 3 Solar Irradiation V ertical solar irradiation on the north and south walls of the building =0.75x amount of irradiation on the east and west side walls. T able 2 4 Solar thermal collector type Collector type 0 U c (W/ m 2 K) Total cost (USD/ m 2 ) Simple flat plate 0.8 5.0 500 Advance flat plate 0.7 3.0 700 Evacuated tube 0.5 1.5 1100 T able 2 5 PV system capacity Module type Efficiency Total system cost Crystalline silicon 0.12 10 USD/ W p + 100USD/ m 2 PAGE 38 38 T able 2 6 Lighting type Luminaire type Efficacy (lm/w) Lifetime (h) Cost (USD/W) incandescent 10 1000 0.01 fluorescent 80 8000 0.3 Table 2 7 Input p arameters (source: Pieppo et. a l see ref. [1]) Parameters Description Building geometry Building volume: Office building 50,000 m 3 Virtual room dimension: width 5m, depth 5m (for lighting calculations) Room heat height: office building 3.5m Average indoor surface reflectivity: 0.5 Surroundings Work plane height: 0.75m (for lighting calculations) Ground reflectance: 0.2 Shading of the horizon: 0 degrees Land area restrictions: none Battery Cost 700 USD. Estimated life 17years. Lighting Control On/Off control cost 0 USD / m f 2 Top up control, cost 5 USD/ m f 2 Exhaust air heat recovery No heat recovery 0 USD / m f 2 Heat recovery, cost 10 USD/ m f 2 Control of passive gain s 1. Global radiation admitted at all times 2. Only diffuse radiation admitted if room temperature exceeds comfort limit Building cost 1000USD/ m f 2 Energy price escalation rate Annual energy price increase s= 1% Real interest rate r=3% PAGE 39 39 Table 2 8 Heating, cooling and economic data (source: Pieppo et. a l see ref. [1]) Parameters Properties and cost Heating and cooling characteristics Heating system efficiency (from fuel to thermal energy) 0.9 Refrigeration system COP: 3.0 Heating system cost 0.3 USD/ W th Cooling system cost (mechanical cycle): 5USD/ W el Air infiltration rate: 0.11/h Hot water temperature: 55 o C Minimum usable space heating temperature: 40 o C Maximum water storage temperature: 90 o C Water storage insulation U val ue: 0.5W/ m 2 K Fraction of water storage heat loss for space heating: 50% Average cold water inlet temperature: 10 o C Economic data Real interest rate: 3 % Price of fuel for heating c th : 0.05 USD/kW h el Price of surplus PV electricity sold to utility c sp : 0.03 USD/kW h el Primary energy to electricity conversion factor: 0.35 PAGE 40 40 Table 2 9 ASHRAE Building envelope requirements for climate zone 3A. Opaque Elements Assembly Maximum Insulation Min. R Value Roofs with Metal Building U 0.055 R 13.0 Roofs with attic and other U 0.027 R 38.0 Steel Framed Walls, Above Grade U 0.064 R 13.0 Wood Framed Walls, Above Grade U 0.089 R 13.0 Below Grade Walls C 1.140 Not Required Steel Joist Floors U 0.052 R 19.0 Slab On Grade floors, Unheated F 0.730 Not Required PAGE 41 41 CHAPTER 3 SOLUTION METHOD Simulated Annealing Simulated annealing was introduced as an in teresting technique for optimizing multivariate non convex functions in ea rly 1980s by Kirkpatrick et al [21] and independently by Cerny [22] It is a robust, general purpose combinatorial optimization technique (explained in the next section) which uses probabilistic methods to find an optimum solutio n. Its uses today are as varied, e.g. in neural networks image processing, code design VLSI design and many more. S imulated annealing and other similar heuristic approaches are usually applied to NP hard problems that otherwise require exponen tial amount of computation time [43] Since the problem in this study is non convex and multivariate, it is an e ligible candidate for application of this algorithm The basic idea behind simulated annealing is to allow positive increments in the cost function during the search. This helps igure 3 1), while avoiding getting trapped in l ocal troughs. This acceptance of cost function increase is implemented via the so called metropolis acceptance criteria described in the next sections The name simulated annealing comes from its basis in combinatorial optimization and its similarity to the physical process of annealing In the succeeding section s combinatorial optimization and physical annealing will be explained in order to provide a better appreciation of the simulated annealing algorithm. Combinatorial Optimization: Combinatorial optimization problem s are su ch problem s where maximization or minimization of an objective function is executed by determination of the optimum or PAGE 42 42 lution out of a given/possible set of choices/alternatives. These kind s of problems are fully defined by the search space and the cost function. The search space S is the set containing the possible choices that can be accepted by the algorithm as a valid solution The objective function is defined as f: S such that it maps every possible solution in the search space to the real line. This is a measure of how good the solution is with respect to the other possible solutions For an ob jective function f, such that there is a point in search space x opt which makes f( x opt )< f x ; for all x S then the problem is described as x opt = argmin x S f x (3 1) x opt and f( x opt ) are known as the global optimum and the optimal cost respectively Physical Annealing In anneali ng, a solid body is cooled from a very high temperature to ambient temperature at a very slow rate. The aim of this process is to achieve a state of minimum internal energy. The cooling rate is slow because lowering the temperature slowly maintains a thermal equilibrium at each stage of the cooling. The thermal equilibrium can be described by the following Boltzmann distribution P T X = x = e E x k B T e E i k B T all states i (3 2) w here X is a random variable which describes the current state, E x is the energy of state x and k B In order to emulate this process in simulated annealing Monte Carlo techniques proposed by Metropolis et al [23] in 1953 are used to simulate the phenomenon of evolution of the state of solid body in a heated bath undergoing a process of slow PAGE 43 43 cooling. The algorithm basically makes use of the current state x and gen erates a new state y by application of a small perturbation. Then the transition from x to y is done with follow ing probability: P accept x y = { 1 if E x E y 0 e ( E x E y ) / k B T if E x E y > 0 (3 3) If the value of y is accepted, then it becomes the current state and the whole step is repeated. This act of accepting the new value over the current value based on the probability is known as Metropolis criterion. The optimization function f( x ) a bove represents the rrent the combina torial optimization procedur e and is equivalent to the current energy le vel of the solid in the physical process. An analogy between simulated annealing and the physical process of annealing has been show n in table 3 1. A Simple Version of SA A lgorithm: Following algorithm is used : 1. Initialization: Initial temperature is put at T = T max and a starting value is chosen for the search, x 0 = x curr The value of L ( x curr ) is calculated. 2. Random Jump Proposal : A new value x new is found from proposal density N ~ ( x curr P ) where N is a N dimensional Gaussian distribution with mean x curr and covarianc e matrix P. The value of L ( x new ) is calculated. 3. Acceptance : Two cases are possible depending on the value of L x new L( x curr ). 1. Cost reduction: If < 0 x new is accepted and x curr is updated with x new Also, L( x curr ) is updated with L( x new ) 2. Cost increase : If 0 then the new value, x new is accepted if u exp ( kT ) where u is a random number from a uniform distribution between 0 and 1. This is known as the Metropolis acceptance step. Next, x curr is updated with x new Also, L( x curr ) is updated with L( x new ) Else, x new is rejected. 4. End Chain for Current : M ore values are sampled t ill the stopping criteria is reached, i.e. computational resources are exhausted or ending temperature is reached o r there have been too many rejections at step 3(2), etc. PAGE 44 44 5. Cooli ng : T he temperature T is reduced according to a predefined cooling schedule e.g. S teps from 2 are repeated after updating T new = T curr 6. End : If T new a predefined threshold temperature or other stopping criteria h ave been satisfied, then the program is ended Optimum value or solution is the most current value of x. Asymptotic Convergence Characteristics Finite time a pproximations : SA is an exploratory algorithm and the extent of exploration is governed by the temperature T. The c ooling schedule is a very important parameter in this regard mainly because it defines the progressive change of the standard annealing temperature i.e. the rate of cooling. Much research has been done on use of different types of cooling schedules [24] an d a range of such cooling schedules [45, 46, 47] has been created In case of discrete domain of optimization s simulated annealing converges in probability if the cooling schedule is proportional to 1/log k (k = iteration number) [47]. Resu lts for more ge neral conditions especially for continuous optimiza tion domains are not available. The same jump in cost function is accepted with lower probability when temperature is lower. Thus exploration decreases over time with fall in numerical value of temperature When high temperature is given, jump is accepted with higher probability; hence there is more exploration of S. Implementation This algorithm is quite easy to implement in any standard computer software The program code need s the following four things t o be specified: 1. The search space 2. The objective function 3. The perturbation mechanism 4. The cooling schedule PAGE 45 45 Issue with Simulated Annealing It has already been stated that simulated annealing (SA) accepts an increase in the cost function via the metropolis criterion This is actually helpful in reducing the probability of getting trapped in local minimum points and in searching the entire domain to determine the global minima (F igure 3 1) But the same can become a shortcoming because the algorithm may jump out of the trough containing the global min. The design problem of this study consists of 18 differe nt variables The implementation of simulated annealing algorithm gave different results at each run Sometimes it was quite evident that the solution given by the SA algorithm was definitely not an optimum one. This could either mean that there are multiple minimum points where the SA algorithm gets trapped or that its cooling schedule was not slow enough to converge to the opti mum value. Information Guided SA To address the above problem, a modified form of SA has been used which is termed as inform ation guided SA [49], which involved the addition of an information feedback term d ( explained in the next section). The n ew algorithm tries to guide the search process on the basis of exploration performed during its run I n other words it adds an exploitation feature to the purely exploratory nature of the basic simulated annealing algorithm. The modified form of standard a nnealing temperature in information guided simulated annealing is termed as guided annealing temperature ( T g ). Guided Annealing Temperature: In this algorithm, the Metropolis acceptance step is calculated using guided annealing temperature T g instead of us ing the standard annealing temperature T We PAGE 46 46 shall define the guided annealing temperature as T g = T + ( 1 ) d where T is the standard annealing temperature which is identical to the annealing temperature used in SA algorithms; d is the information feedback t erm that is used to track the progress of the algorithm. d has been defined as follows: d =   x e x curr   (3 4) where, x curr is the current estimate of the global minimum, x e is the ending position of the algorithm for the pervious value of T g Thus it can be inferred that x e is the end point of the Markov chain made for the latest value of T g Hence d is the estimate of how far away is the end point of the algorithm from the currently discovered of global minimum. In order to control this par ameter, the variable has been used. It is called the information effectiveness parameter. [ 0 1 ] which is a function of standard annealing Temperature, T. I nformation effective parameter may be defined as follows: T = [ 1 exp { c ( T T max ) 2 } ] (3 5) It mi ght be remarked that T g = T + k d where k is the feedback gain term. This ga in term is controllable with use of the variab le c. Let us see how this works: At the time when the algorithm begins, the value of is too close to 1 to have any appreciable effect in T g and hence T g T .As standard annealing temperature T is progressively reduced according to the cooling schedule, the numerical value of starts to decrease. Altho ugh it decreases very slowly yet soon aft er its value becomes small enough such that the k term in T g = T + k d can no more be neglected. But before reaching this stage, the program has explored much of the domain and it might be hoped that it has crossed through the global minima. When the value o f T T max reaches a PAGE 47 47 predefined value, then the information feedback starts dominating the exploration procedure and it starts influencing the algorithm. Modified Algorithm Due to the introduction of the information effectiveness parameter, the algorithm h a s been divided into two phases. During the first phase is the same as the SA discussed before. The program mainly tries to explore the entire domain of search and tries to find out the optimum value of the objective function. But at the same time, due to metropolis acceptance step, it also runs a probability of rejecting the optimum value and move on to different values inside the domain. x curr keeps track of the present estimate of global optimum that the algorithm has been able to find out. T he second phase ensues once the above mentioned random exploration is completed, At this time, T has sufficiently cooled down and the feedback from the information function d decides what to do The first phase continues as long as T T max the feedback gain star ts to become greater and greater in value and plays an important part in trying to direct the program towards the present estimate of global optimum. It is essential to understand that this step should continue only after T has sufficiently cooled down bec ause otherwise, the program will have higher chance of converging to a local optimum point. Following steps are used in the algorithm (s ee F igure 3 2) : 1. Initialization : Initial temperature was put at T = T max and a starting value was chosen for the search, x 0 = x curr x curr and x e were initialized with x 0 The value of L ( x curr ) and d =   x e x curr   were calculated. 2. Determination of information effectiveness : the value of was calculated and the guided annealing temperature was calculated. PAGE 48 48 3. Random Jump proposal : the value of was compared and based on that, one of the following two steps were executed: Information not effective : if the n draw a new sample x new from proposal density q(x)=N( x curr P ) Objective function was calculated i.e. the value of L( x new ) Information effective: if < then draw a sample from the proposal density q(x)= N( x curr d ) This step means that new value of x is calculated from a normal density whose standard deviation is dependent on how far the end point of the algorithm is fro m its estimate of global minimum. Objective function was calculated i.e. the value of L( x new ) 4. Acceptance: There are two cases here depending on the value of L x new L( x curr ). 1. Cost reduction: If < 0 x new is accepted and x curr is updated with x new Also, L( x curr ) is updated with L( x new ) A check is done to see if the global minimum was found a. New Global minimum found: If L( x new ) < L( x curr ) x curr is updated with x new L( x curr ) is updated with L( x new ) and information function is updated to d =   x e x new   b. Global minimum not found: no new steps taken 2. Cost increase: If 0 then the new value, x new is accepted if u exp ( kT ) where u is a random number from a uniform distribution between 0 and 1. This is known as the Metropolis acceptance step. Next, x curr is u pdated with x new Also, L( x curr ) is updated with L( x new ) Else, x new is rejected. 5. End Chain for Current : the process from step 3 is continue d until the ending criteria is satisfied i.e. computational resource for the current value of T g is exhausted etc. 6. Co oling : T he temperature T is r educe d according to a predefined cooling schedule e.g. update T new = T curr and repeat steps from 2 5. 7. End: The algorithm is stopped if the guided annealing temperature has reached a value below a predefined threshold value. The global minimum found by the algorithm is the optimal solution for the given objective function. Enforcement of optimization constraints The perturbation mechanism is designed in such a fashion that it would not generate states that fall outside the boundar ies specified by the constraints. This is done by putting a check each time a new value has been proposed. If the value does PAGE 49 49 not lie within the defined constraints, then it is discarded and the process is repeated till constraints are satisfied. PAGE 50 50 Figure 3 1. Simulated Annealing (source: http://ashakhov.wordpress.com/2011/01/27/ simulated annealing/ 9 th Feb. 2012) PAGE 51 51 Figure 3 2. A flowchart for the Modified SA algorithm PAGE 52 52 Table 3 1 Comparison between simulated annealing and physical annealing Optimization using SA Physical Annealing process Solution x Current (hidden) state s of the solid Objective function f(x) Current Energy level of solid, E x Optimal solution Ground (~ minimum energy) state Control parameter Temperature PAGE 53 53 CHAPTER 4 O BSERVATIONS AND RESU LTS On Validity of Modeling Approach The modeling features have been made appropriately detailed and numerous so as to reflect the design requirements of an actual building but at the same time, the focus is on the simplicity of the design so that this problem will be solved without excessive computing power or time. The results obtained were cross checked with the available information about the existing and running buildings in order t o assure that the results mad e sense. Following key points were considered in order to verify the validity of the results obtained: Space H eating The results obtained for space heating were compared with more detailed simulations [34] and were found to be in good agreement, to within 10 %, with the pred icted annual space heating load for office building that has been modeled in this study However, there is a need to go deeper into more detailed n umerical simulations to make this study more accurate, e.g. the thermal comfort in different zones etc. Venti lation and Air C onditioning N atural ventilation has been utilized for this study. This choice amply simplifies the model. The model of the building in the problem statement is assumed to be situated in Asheville, North Car olina, USA. In a state such as Nor need to provide measures to cool the buildings because the ambient air temperature is quite low and opening the building windows etc, would be sufficient to cool the room interiors for most months of the year Passive cooling might also be a good way to go about cooling the buildings, but this is not yet a viable technology to use with respect to cost PAGE 54 54 considerations. This kind of treatment of the problem might underestimate the need of auxiliary cooling load, but this consideration has been left for future studies. Windows It was assumed that the light transmission properties and the heat transmission properties of the windows were eq ual. This is not a perfectly practical approach since it is known that there are numerous kinds of wi ndows available in the market [28] and hence the present properties of the available windows will not be properly utilized unless a detailed study is conducted e.g. making use of wavelength dependent model s etc. which wou ld consider the above two properties separately. But in case of windows, the aesthetic value and the visual comfort are as important as the usefulness of windows in terms of lighting and heating. Hence the assumption made over here is not too far a stretch from reality. Daylighting It has been found that 20 30% of the electricity needs is used up by the artificial lighting in office buildings equipped with air conditioners [42] Hence use of daylighting opens up a wide window for energy saving opportunity. T he model under study has been found to be in good agreement with the previous numerical calculations [ 1 ] for similar kind of rooms situated in similar areas, to w ithin 10% accuracy. Henc e this model works well for the present design under consideration. One might want to use autom ated light ing control. But that is a rather complicated issue, since user behavior is random and therefore it is still one of the open areas of research, as to how to make a simple enough model to capture the user behavior in terms of use of lighting for l ow energy buildings. Off site Electricity G eneration PAGE 55 55 Photo Voltaic panels are the sources of electricity generation. It might be possible that the owner of building has a renewable alternative that is lower than the cost of PV. But the pre assumption of availability of PV system is very applicable since it is one of the best ways t o harness solar power [31 41 ]. User B ehavior User behavior is very non deterministic and it needs to be modeled so that the results may reflect an ac tual situation. In practice it has been observed that heating requirements of the same establishment might be 1.5 times of expected load [36] due to the user behavior. So this uncertainty would definitely affect the optimum value of the building parameters One way to model this would be to study the distribution of the variables and then sample the values from a p.d.f. during the running of the p rogram. That process would require enough data in the first place to form a p.d.f before sample s may be drawn Another way would be to use previously recorded data. It appears that for this study both me thods are equally practical since the use of either of the methods do not give different results. The main objective of this study is to optimize and find out a set of parameters that will give an economic/minimum value of the objective fu nction, i.e. optimum design. The objective here is not to model the building very intricately. Some studies even insinuate that user behavior does not appreciativel y affect the b uilding design [3 5 ]. Hence if making use of deterministic parameters gives agreeable results, then it might be understood that such a process is viable since not only does it gives good solution, but it bring s down the computation cost also In this study the user behavior has been assumed to be deterministic and the data have been taken from a publica tion by PAGE 56 56 Pieppoet.al. [1]. N umber of people in the office at a given hour is however assumed to follow a normal distribution as shown in the table 4 1 In th e design of the building, normally the consideration of energy conservation is not a major concern. There are other criteria which take priority, such as archit ecture, functional requirements, end use efficiency [19] and user preference. It is also worth m entioning that designer tend s to neglect some parameters such as interest rate, and rise in price of energy and the value of electricity itself may not be properly portrayed while it affects the optimum design to a good extent. Also, construction of a buil ding is very area specific. The same building may be built at much lower cost somewhere else and that might as well be a better idea to be implemented such a case Results: The program code for modified SA was written in Matlab 7 .0 and was run on a 1.74MHz core2duo lapt op and it takes 3 9 hours (depending on whether the calculation is done for 1 yr. or 10 yrs.) to run one simulation. At first, the code is run to obtain th e optimal system configuration in the sense of annual total of the building i.e. to determine the cost of installing and operating the building for one year In order to achieve confidence, the optim ization procedure is repeated 5 times, following which a mean is computed. The consumed energy which corresponds to this minimum cost was recorded and was termed as 100% relative primary energy Clearly this consumed energy was received from non renewable sources since minimum cost was a priority. Next the target was to see how the design configurations were influenced by use of 75%, 50% an d 0% of this energy. Due to such a constraint, the algorithm will have to explore the renewable energy options to complete the energy demand. Hence the whole optimization process was rep e ated with the above stated constraint Thus four PAGE 57 57 separate cases for cost minimization were considered (i.e. 100%, 75%, 50% and 0% of relative primary energy) The entire above stated process was repeated ten times; with progressively increasing simulation run time(starting from 1 year to 10 years) in order to record the cha nge in the parameters over a 10 year period. Although slashing the energy received from non renewable sources save d money in running utility cost, th ere was be a noticeable increase the installation cost. However t he calculation of optimum design by this m ethod has one i mportant advantage. It reveal ed amount by which the energy consumption through non renewable sources should be reduced so that the increased cost of the whole project may still remain within affordable limits. Additionally, if the simulation is run for a longer time then breakeven point could be estimated. Following are the results obtained that reflect how the configurations must change with inclusion of renewable energy sources. Building Shape: In order to sav e energy ideally the optimum shape is when the rooms are the most compact i.e. when their shape is a cube. This leads to minimum heat loss without affecting the amount of sunlight entering the room through the windo ws. From the table 4 2 it is evide nt tha t the simulation too determined the aspect ratios to be 1:1 for optimum design for the minimum cost case with 100% relative primary energy target As the relative primary energy target is reduced from 100%, the need for utilizing the heat coming through th e walls from the east and west directions increases. As a result the rooms tend to have greater area of walls on the east and west and lesser area of walls on the other two sides. This is evident as the aspect ratios change from 1:1 in case of relative aux iliary primary energy target at 100% to 1.2:1 in case of 0% relative auxiliary primary energy target (table 4 3, 4 4, 4 5) As the size of rooms is increased, the amount PAGE 58 58 of daylight required is of greater importance than that of the heat loss or the cost of the envelope. Hence the shape of the room becomes such that the ratio of floor area to that of walls starts to approach 1. Thermal I nsulation: The U value for the objective of minimum cost at 100 % relative primary energy is 0.19 W/ m 2 K ( F igure 4 1 ) for the insulation thickness of 50cm of fiber glass For the minimum cost with 0% primary energy targe t the U values of the wall are 0 06 W/ m 2 K, which might be noticed to be a little lesser than the U values u (0.07W/ m 2 K ) If insulation is increased the chances of saving energy also increase and so insulation plays a major role in saving energy. But after a certain level, adding more insulation stops having any appreciative effect on the heat loss. Windows and D aylighting: Presence of l arge windows causes heat loss which results in rise of utility bills. That is why the minimum cost design ( at 100% relative primary energy target ) shows the percent age of window area to floor area to be a little more than 5% (Figure 4 2 ). However, larger w indows allow daylighting. When PV system s are available for electricity the optimal window area increases to 15%. The daylight contribution to room illumination in office buildings can be anywhere in the range of 20% to 90% of the lighting load [1]. It is actually good that the illumin ation requirements are high at time s when the daylight is strong In the F igure 4 3 the plot for 100% relative primary energy target depicts how the lighting load progressively decreases for minimum energy design over a 10 year period. However the minimum cost design, i.e. 0% relative primary energy target can be seen to have remained unaffected with time. PAGE 59 59 Without daylight contribution the annual lighting load requirement is 146 M J el / m F 2 The daylight contribution in this stu dy increases as the simulation is run for longer and longer periods of time for all the four cases It eventually saturates at 77 % of the lighting load ( Figure 4 4 ) There are rooms in the interior of the building which are not open to the external sunligh t. In such rooms the only available option is the use of stored energy or electricity from grid for artificial lighting. Solar Thermal and P hotovoltaic S ystems: Contribution of PVs to thermal load of the building i.e. the s olar fraction of thermal load inc reases constantly with time (Figure 4 5 ) but it saturates at 51% at the end of 10 year equivalent of simulation run time for all four cases PVs contribute to the electricity load and eventually they end up producing more than t he electricity needs ( Figure 4 6 ). This excess energy is either stored in the batteries or sold to the grid. Heating and Cooling: The exhaust heat recovery systems have been applied in this model and as a result, the heating load was considerably reduced. N atural ventilation has been assumed although practical experience from the of fice buildings does not match with this assumption. Th is area will be in focus for future studies. Lighting C ontrol: It is very clear from the table that an automated lighting control is the best way to go. It not only saves energy but also helps in maintaining a uniform illumination level inside all the rooms separately. Optimum Trade o ff S trategy: Since the installati on of PV is the costliest investment in the whole project, therefore the best way will be to utilize all the other sources of en ergy which are PAGE 60 60 available at hands of the designer that are lower in cost than the PVs. Once such resourc es are exhausted, then i nvest ment should be made into PVs. In this manner, it has been observed that 20% energy savings could be realized at only 6 .7% increase in the total building cost. Hence really need to go for minimum cost design, rather a middle path, where the re is energy saving and at the same time there is a presence of affordable cost can be realized. Battery Storage: Optimum battery capacity has been found to be 35kW hr. This capacity is influenced by the discharge time of 10hrs for the battery. Hence with the present technologies and cost, it is a good idea to sell some of the excess energy instead of storing all of it because the battery loses its capacity over a short period of time. The net primary energy of the building at 100% relative primary energy target progressively reduces to zero over a period of about 10 years ( Figure 4 7 ). Even when both the renewable and non renewable sources of energy are available, it can be seen that use of renewable resources is economically rewarding after about a decade Space heating con sumes maximum energy ( Figure 4 8 ) per year. However, if the electrical appliances in the office are also considered, then they are great est energy consumers. Figure 4 9 shows that after a period of 9.4 years, the building owner will not have to pay for the monthly utility bills if the building is designed with 0% relative primary energy target Additional ly the investment in installation of renewable devices of energy will be returned in form of the savings made from the lowered utility b ills. A similar study was optimization variable, the number of the rooms on each floor and the input data for all the calculations used by them is identical to the study done in this thesis. Although their PAGE 61 61 work was based on a building in a different city, the weather conditions (in terms of maximum/minimum temperature per month and average number of hours of available daylight) too are very similar to the city that has been chosen for this work. Additionally this study also considers the electricity requirements of the hallways, bathrooms, a mechanical/electrical room and a storage room on each floor. Pieppo et. al. had employed the method of Hooke a nd Jeeves to solve their optimization problem. As a result of the optimization, they suggested that total annual cost of 82 USD/ m 2 of floor area wou ld be generated. From Figure 4 9 it is clear that information guided simulated annealing has provided bette r results. The suggested total annual cost for 10 0% relative primary energy target is 78 USD/ m 2 Hence there is an improvement of 4.8% over the previously available results. It has already been mentioned that the standard SA did not converge at all whereas information guided SA gave better results. Hence the above improvement is due to the information guided feedback part of the SA algorithm. In depth analysis of all the results obtained has been tabulated in table 4 2, 4 3, 4 4 and 4 5. The floor area of e ach room was assumed to be 25 2 Thereafter the numerical values of the results shown in table 4 2 to table 4 5 were calculated again. Table 4 6 enlists the important parameters and the difference in the ir numerical value for the minimum cost design (at 1 00% primary energy target) and minimum non renewable energy design (i.e. 0% primary energy target). Climate plays an important role in the whole plan [37] In this study the location of the building is quite sunny but at the same time, the average temper ature is about 1 4.5 degrees. Henc e the room heating takes up a major part of the energy resources. At the PAGE 62 62 same time, artificial lighting too consumes a significant part of t he total electricity ( Figure 4 8 ). However, this kind of a house represents most of the places in USA; hence a design under these climatic conditions is useful. The pr ogram was run for a period of 10 years and it was observed that the cost of installing the building starting from construction to paying for the utility cost without the us e of renewable sources or energy efficient methods was equal to the cos t of running the building for 9.4 years with the use of renewable resources and e ne rgy efficient methods (table 4 7 ). Hence if the office building is constructed along with installation of the PVs and other energy efficient devices, then the cost will be high initially. However after a period of about 10 years, the invested money will reap its benefits. The breakeven point for this design has been calculated to be 9.4 years. PAGE 63 63 Figure 4 1. U values of Wall Insulation and Windows Figure 4 2 Percentage of total window area to floor area 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 With 100% Relative Primary Energy Target With 75% Relative Primary Energy Target With 50% Relative Primary Energy Target With 0% Relative Primary Energy Target U values Axis Title Insulation Windows 0 2 4 6 8 10 12 14 16 1 2 3 4 5 6 7 8 9 10 %age of window area to floor area Years With 100% Relative Primary Energy Target With 75% Relative Primary Energy Target With 50% Relative Primary Energy Target With 0% Relative Primary Energy Target PAGE 64 64 Figure 4 3 Auxiliary lighting load Figure 4 4 Daylight contribution of lighting load 0 10 20 30 40 50 60 70 80 90 1 2 3 4 5 6 7 8 9 10 Auxiliary Lighting load (MJ/sq.m of floor area) Years 100% Relative primary energy target 75% Relative primary energy target 50% Relative primary energy target 0% Relative primary energy target 0 10 20 30 40 50 60 70 80 90 1 2 3 4 5 6 7 8 9 10 Daylight contribution in %age Years 100% Relative primary energy target 75% Relative primary energy target 50% Relative primary energy target 0% Relative primary energy target PAGE 65 65 Figure 4 5 Solar fraction of thermal load Figure 4 6 Contribution of PVs to the electricity load 0 10 20 30 40 50 60 1 2 3 4 5 6 7 8 9 10 Solar fraction in %age 100% Relative primary energy target 75% Relative primary energy target 50% Relative primary energy target 0% Relative primary energy target 0 20 40 60 80 100 120 1 2 3 4 5 6 7 8 9 10 Contribution of PVs in %age Years 100% Relative primary energy target 75% Relative primary energy target 50% Relative primary energy target 0% Relative primary energy target PAGE 66 66 Figure 4 7 Net primary e nergy Figure 4 8. Energy consumption (kW h r/ m 2 /year) with different simulation periods. 0 200 400 600 800 1000 1200 1 2 3 4 5 6 7 8 9 10 Primary Energy (MJ/sq.m of floor) Years 100% Relative primary energy target 75% Relative primary energy target 50% Relative primary energy target 0% Relative primary energy target 0 20 40 60 80 100 120 Space heating Ventilation Hot water Lights Fans/Pumps year 1 year 2 year 5 year 10 PAGE 67 67 Figure 4 9 Cost of operating the building. Break even point is at 9.4 years 0 20 40 60 80 100 120 140 160 1 2 3 4 5 6 7 8 9 10 11 Annual Cost (USD/sq.m of floor) Years 100% Relative primary energy target 75% Relative primary energy target 50% Relative primary energy target2 0% Relative primary energy target PAGE 68 68 Table 4 1. Hourly load and usage patterns Load/Usage Hour 8am to 6pm 7pm to 7am Occupancy 0 Lighting (lx) 500 0 Minimum temperature ( ) 20 17 Maximum temperature ( ) 25 25 Air change (l/h) 1 0.2 Hot water (l/ ) 0.05 0 PAGE 69 69 Table 4 2. D escribing the output values when the simulatio n is run for one year Output Values at four different relative auxiliary primary energy targets Relative auxiliary primary energy targ et 100% 75% 50% 0% Relative annual total cost 100% 112 % 1 3 1 % 187 % Building aspect ratios s h : s v 1.8 :1. 8 9.1:11 12: 8.8 14 .1:11 Wall to floor area ratio 0. 4 5 1.0 1.0 1.0 Insulation U value (W/ m 2 K) 0.19 0.19 0.06 0.06 Window type 3 4 4 4 South window to floor area ( m w 2 : m F 2 ) 1.0 % 6.6 % 6.6 % 6.6 % East window to floor area ( m w 2 : m F 2 ) 1.5 % 0.09 % 0.09 % 0.09 % West window to floor area ( m w 2 : m F 2 ) 1.2 % 0.09 % 0.09 % 0.09 % North window to floor area ( m w 2 : m F 2 ) 1.5 % 7 % 7 % 7 % Total window area of floor area ( m w 2 : m F 2 ) 5.2 % 13.78 % 13.78 % 13.78 % Collector and PV array tilt ( 0 ) 54 54 54 54 Collector area of floor area ( m c 2 : m F 2 ) 0.4% 1.5 % 4 .0% 4 .0% PV capacity per floor area ( w p : m F 2 ) 0 6 35 86 Thermal storage (l/ m f 2 ) 3.9 10.8 10 .9 11.1 Lighting control Top up Top up Top up Top up Battery Capacity(kW hr) 0 12 24 35 Auxiliary Lighting load ( M J el / m F 2 ) 80 45 42 32 Hot water heating load ( M J th / m F 2 ) 38 39 36 38 Space heating load ( M J th / m F 2 ) 112 46 46 46 Appliances load ( M J el / m F 2 ) 246 246 246 246 Solar fraction of thermal load 9.5 % 15 % 20 % 50 % PV generation/electricity load 0 8.3 % 39 % 10 6 % Daylight contribution of lighting load 3 0 % 66 % 76 % 78 % Purchased thermal energy (M J fuel / m F 2 ) 107 71 66 65.5 Purchased gross electricity (M J el / m F 2 ) 352 258 171.5 131 Surplus of gross PV generation 0 0 20 .5 % 5 1 % Net auxiliary primary energy (M J prim / m F 2 ) 1120 840 560 0 Annual total cost (USD/ m F 2 ) 80 90 105 150 PAGE 70 70 Table 4 3. D escribing the output values when the simulation is run for two years Parameters Values at four different relative auxiliary primary energy targets Relative auxiliary primary energy targ et 100 % 75% 50% 0% Relative annual total cost 99.5 % 111 % 125 % 185% Building aspect ratios s h : s v 11.3:13.1 9.1:11 10:8.3 1 9 2 .1:1 8 1 Wall to floor area ratio 0. 41 5 1.0 1.0 1.0 Insulation U value (W/ m 2 K) 0.19 0.18 0.06 0.06 Window type 3 4 4 4 South window to floor area ( m w 2 : m F 2 ) 1.2 % 6.6 % 6.6 % 6.8% East window to floor area ( m w 2 : m F 2 ) 1.7 % 0.09 % 0.09 % 0.1% West window to floor area ( m w 2 : m F 2 ) 1.3 % 0.09 % 0.09 % 0.1% North window to floor area ( m w 2 : m F 2 ) 1.7 % 7 % 7 % 6.9% Total window area of floor area ( m w 2 : m F 2 ) 5.9 % 13.78 % 13.78 % 14.0% Collector and PV array tilt ( 0 ) 54 54 54 54 Collector area of floor area ( m c 2 : m F 2 ) 0.4% 1.5 % 4 .0% 4.1 % PV capacity per floor area ( w p : m F 2 ) 1 8 39 84 Thermal storage (l/ m f 2 ) 4 10 .6 10 .9 11.0 Lighting control Top up Top up Top up Top up Battery Capacity (kW hr) 10 26 30 35 Auxiliary Lighting load ( M J el / m F 2 ) 78 44 41 32 Hot water heating load ( M J th / m F 2 ) 38 39 36 38 Space heating load ( M J th / m F 2 ) 112 46 46 46 Appliances load ( M J el / m F 2 ) 246 246 246 246 Solar fraction of thermal load 1 4 % 20% 25 % 50 % PV generation/electricity load 2% 9 % 47 % 109% Daylight contribution of lighting load 32% 62 % 75 % 77% Purchased thermal energy (M J fuel / m F 2 ) 96 70 69 66 Purchased gross electricity (M J el / m F 2 ) 23 5 160 192 132 Surplus of gross PV generation 0% 0% 22 % 60 % Net auxiliary primary energy (M J prim / m F 2 ) 1096 824 549 0 Annual total cost (USD/ m F 2 ) 79.6 89 10 0 148 PAGE 71 71 Table 4 4. D escribing the output values when the simulation is run for five years Parameters Values at four different relative auxiliary primary energy targets Relative auxiliary primary energy target 100% 75% 50% 0% Relative annual total cost 97 % 100 % 120 % 130 % Building aspect ratios s h : s v 1.0:1.8 8.1:12.3 60:52.1 16:13.3 Wall to floor area ratio 0.5 1.0 1.0 1.0 Insulation U value (W/ m 2 K) 0.19 0.10 0.06 0.06 Window type 4 4 4 4 South window to floor area ( m w 2 : m F 2 ) 1.1% 6.6 % 6.9 % 7.3 % East window to floor area ( m w 2 : m F 2 ) 3.3 % 0.09 % 0.1% 0.2 % West window to floor area ( m w 2 : m F 2 ) 4.4 % 0.09 % 0.1% 0.5 % North window to floor area ( m w 2 : m F 2 ) 1.6% 7 % 7 % 7.0 % Total window area of floor area ( m w 2 : m F 2 ) 10 .4% 13.78 % 14.1 % 15 .0% Collector and PV array tilt ( 0 ) 54 54 54 54 Collector area of floor area ( m c 2 : m F 2 ) 0.4% 1.6 % 4 .0% 4.1 % PV capacity per floor area ( w p : m F 2 ) 25 3 5 60 90 Thermal storage (l/ m f 2 ) 6 10.5 10 .9 10.9 Lighting control Top up Top up Top up Top up Battery Capacity (kW hr) 36 35 36 35 Auxiliary Lighting load ( M J el / m F 2 ) 66 43 40 32 Hot water heating load ( M J th / m F 2 ) 38 39 36 38 Space heating load ( M J th / m F 2 ) 88 46 46 46 Appliances load ( M J el / m F 2 ) 246 246 246 246 Solar fraction of thermal load 20 % 24 % 37 % 50 % PV generation/electricity load 56% 6 7% 8 1% 109% Daylight contribution of lighting load 5 2% 64 % 71% 78 % Purchased thermal energy (M J fuel / m F 2 ) 89 67.7 66 65 Purchased gross electricity (M J el / m F 2 ) 203 147 137 132 Surplus of gross PV generation 10% 15% 24 % 5 8% Net auxiliary primary energy (M J prim / m F 2 ) 700 5 2 5 3 4 9 0 Annual total cost (USD/ m F 2 ) 78 80 96 104 PAGE 72 72 Table 4 5. D escribing the output values when the simulation is run for ten years Parameters Values at four different relative auxiliary primary energy targets Relative auxiliary primary energy target 100% 75% 50% 0% Relative annual total cost 96 % 95 % 95 % 96 % Building aspect ratios s h : s v 45.0:40 .8 1.2:2.2 18 :1 5 17:14.1 Wall to floor area ratio 1 1.0 1.0 1.0 Insulation U value (W/ m 2 K) 0.07 0.06 0.06 0.06 Window type 4 4 4 4 South window to floor area ( m w 2 : m F 2 ) 7.2 % 7.3 % 7.3 % 7.3 % East window to floor area ( m w 2 : m F 2 ) 0.2 % 0.2 % 0.2 % 0.2 % West window to floor area ( m w 2 : m F 2 ) 0.4 % 0.5 % 0.4 % 0.5 % North window to floor area ( m w 2 : m F 2 ) 7.1 % 7.0 % 7.0 % 7.0 % Total window area of floor area ( m w 2 : m F 2 ) 14.9 % 15 .0% 14.9 % 15 .0% Collector and PV array tilt ( 0 ) 54 54 54 54 Collector area of floor area ( m c 2 : m F 2 ) 4% 4 % 4.1 % 4.1 % PV capacity per floor area ( w p : m F 2 ) 90 91 92 91 Thermal storage (l/ m f 2 ) 11.4 11.5 11.1 11.1 Lighting control Top up Top up Top up Top up Battery Capacity (kW hr) 36 36 35 35 Auxiliary Lighting load ( M J el / m F 2 ) 30 32 31 32 Hot water heating load ( M J th / m F 2 ) 38 39 36 38 Space heating load ( M J th / m F 2 ) 46 46 46 46 Appliances load ( M J el / m F 2 ) 246 246 246 246 Solar fraction of thermal load 50 % 50 % 51 % 52 % PV generation/electricity load 107% 107 % 106 % 109% Daylight contribution of lighting load 78 % 77 % 76 % 77% Purchased thermal energy (M J fuel / m F 2 ) 65 66 66 66 Purchased gross electricity (M J el / m F 2 ) 131 132 13 1 132 Surplus of gross PV generation 60% 59% 58 % 58% Net auxiliary primary energy (M J prim / m F 2 ) 0 0 0 0 Annual total cost (USD/ m F 2 ) 77 76.4 76.8 76.9 PAGE 73 73 Table 4 6. Design variables and annual energy consumption data for minimum cost and low energy designs Parameters Minimum cost design (For 1 year simulation run) Low(zero) energy design (For 10 year simulation run) Wall U value (W/ m 2 K ) 0.19 0.06 Window U value (W/ m 2 K ) 1.8 1.0 Total window area ( m 2 ) 53.1 135 Heat lost through windows (G J th ) 98.9 49.2 Exhaust air heat recovery Yes Yes Lighting control No Yes Solar thermal collectors ( m 2 ) 3.6 37 Battery capacity ( kw hr ) 0 36 PVs (k W p ) 0 24 Space heating load (G J th ) 100.9 4 1.2 Water heating load (G J th ) 29 .3 0 Lighting load (G J el ) 70 .5 26.9 Appliance load (G J el ) 45 45 Annual total cost (USD) 69300 69210 PAGE 74 74 CHAPTER 5 CONCLUSION In this study an economic analysis was done by summing up all the costs for running the systems in the building for a given number of years. Energy efficient resources such as solar panels, PVs systems, daylighting measures were employed in order to reduce energy drawn from the ele ctricity grid. A set of 18 variable parameters were used to formulate the total cost. The problem formulated in this manner was first solution, information guided simula ted algorithm was used. The results obtained were compared with the existing literature and were found to be in good agreement. Furthermore the results showed a 4.8% improvement over the previous research work done in this field. While much promise is sho wn by the present work a lot remains unexplored. For example, more work will be required to develop the model for incorporating detailed study of HVAC systems, ventilation and daylighting measures. The maintenance and repair aspects of various systems need to be incorporated. A more refined cost structure would be helpful simulating a more realistic design of the building. A different research direction would explore how the model of the building ma y be further modified. This model did not include the staircases and the elevators. Further research is required for an improved performance of the optimization procedure and faster convergence. PAGE 75 75 APPENDIX NOMENCLATURE 1 a Uniform capital recovery factor 2 A Area ( ) 3 c Specific cost (USD/unit) 4 COP Coefficient of performance 5 d Depth (m) 6 Estimated distance 7 E Energy (J) 8 G Solar Irradiance (W/ ) 9 h Height (m) 10 I Illuminance (lx) 11 k Feedback gain term 12 n Number of samples 13 PV Photovoltaics (s) 14 Q Heat gains and losses (W) 15 r Real interest rate 16 s Aspect ratio; annual energy price increase 17 t Time (s) 18 T Temperature ( ) 19 Guided Temperature ( ) 20 U Collector heat loss factor ((W/ K) 21 w Width (m) 22 x The degree that a design option is deployed ; variable 23 Vector variable ( 24 Y Variable Subscripts 1 0 Zero loss 2 a Annual 3 amb Ambient PAGE 76 76 4 A Area based 5 B Building 6 C Collector 7 curr Current 8 d Indoor horizontal daylight 9 el Electricity 10 F Floor 11 fuel Heating fuel 12 g Guided 13 h Horizontal 14 i Design option ; index variable 15 max Maximum 16 min Minimum 17 new New Value 18 opt Optimum 19 OV Outdoor vertical 20 p Peak capacity 21 prim Primary energy 22 R Room 23 sp Surplus 24 th Thermal 25 v Vertical 26 W Window Greek characters: 1 Luminous efficacy (lm/W) 2 Efficiency 3 Energy price escalation factor 4 Primary energy to electricity conversion factor 5 Reflectance 6 Transmittance PAGE 77 77 7 Difference 8 Cooling Schedule 9 Information effectiveness parameter PAGE 78 78 LIST OF REFERENCES [1] K. 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Archives of Civil Engineering 1984;30(1):3 21 [in Polish]. [52] Febr uary, 25 2012. http://www.iccsafe.org/Store/Pages/Product.aspx?id=3000X12 [53] February, 25 2012. http://en.wikipedia.org/ wiki/Building_envelope PAGE 82 82 [54] Mrinal American Control Conference, Jun 27 29, 2012, Montreal, Canada. [55] February, 29 2012. http://openpub.realread.com/rrserver/browser?title=/ASHR AE_1/ashrae_90_1_2010_IP_1024 [56] February, 29 2012. http://resourcecenter.pnl.gov/cocoon/morf/Resourc eCenter/article//103 [57] February, 29 2012. http://www.wattsun.com/misc/photovoltaic_tilt.html [58] March 7 2012. http://solarpowerrocks.com/north carolina/ PAGE 83 83 BIOGRAPHICAL SKETCH Diwakar Sinha was born in the city of Patna, India. He lived in the city till he completed his high school in 2005. In 2006 he was enrolled as a full time student in Mechanical Engineering at the Jadavpur University, Kolkata. He studied over there for 4 years in pursuit of an undergraduate degre e in mechanical e ngineering. During his undergraduate years, he came in close contact with his professors and the r esearch work they were involved in at that time. Within the course of the next 3 years, he co authored a number of publications. After his graduation in July 2010, he was admitted to University of Florida, Gainesville, Florida in order to pursue a degree in mechanical e ngineering. 