Designing a hybrid wind and solar energy supply system for a rural residential building

Transcription

1 Designing a hybrid wind and solar energy supply system for a rural residential building Dr. Mir-Akbar Hessami Monash University, Department of Mechanical Engineering, Clayton, Victoria, Australia Akbar.hessami@eng.monash.edu.au Abstract The aim of this project was to design a hybrid wind and solar energy supply system for a rural residential building in order to satisfy its energy requirements. The system under consideration included the hot water service, the space heating system, and all the power requirements involving both electricity supply and a storage system. The optimum design was obtained by performing a costbenefit analysis for each of the individual systems. The monthly average daily energy consumption for the dwelling was found to vary between 19 and 36 kwh. The hot water system was designed to be based on flat plate collectors with a back up LPG (liquefied petroleum gas) tank. The optimum hot water hardware included 3 flat plate collectors, a 315 L storage tank and a 135 L auxiliary LPG tank. The large dimensions of the house were the limiting factor when investigating the feasibility of a solar powered space heating system. Use of very large windows made space heating a very difficult and expensive task. The high capital cost of a totally solar power system far outweighed the benefits of such a supply. Hence, it was decided to use LPG or wood for space heating. The electricity supply design was based on the building s demand schedule which during summer was 13 kwh per day and in winter it was 9 kwh per day. The power supply system was designed to be comprised of five 80-W photovoltaic (PV) modules and a 2.5 kw output wind turbine. However, the total cost of the final design was found to be much higher than connecting to the grid if the intangible benefits to the environment (eg, reduced green house gas emissions) are not quantified and are not taken into consideration. Keywords solar energy; wind energy; hybrid system; heat and power generation Nomenclature Symbol Description a Solar altitude angle (rad) b Tilt angle (rad) h Efficiency q Angle of incidence = (b + a) p/2 (rad) A Surface area (m 2 ) A L Area subject to heat loss (m 2 ) c Wind speed (m/s) C p Specific heat (J/kg-K) G H Global radiation normal to a horizontal surface (W/m 2 ) G T Global radiation normal to a tilted surface (W/m 2 ) m Mass flow rate (kg/s) P Wind power (W) Q L Heat losses (W) Q u Useful heat (W) R Turbine blade radius (m) Ambient temperature ( C) T amb

2 Designing a hybrid wind and solar energy supply system for a rural residential building 113 T in T out T t U Inlet temperature ( C) Outlet temperature ( C) Tank temperature ( C) Overall heat transfer coefficient (W/m 2 -K) Introduction The energy requirements of any residential building can be studied by considering the total demand for hot water, space heating and electricity for lighting and operation of various appliances. For urban dwellings, in general, natural gas is used for the first two and mains grid power for the latter, both of which are readily available. However, this is not the case with rural properties and the cost of connecting to the grid may render this option prohibitive since the power supplier has the responsibility of bringing the service to the property boundary nearest to the grid, and the owner has to bear the cost thereafter. Therefore, the use of renewable energy such as solar, wind, biomass and/or hydro might be an attractive alternative for rural properties. This is the topic that is investigated and reported in this paper for a rural property in the southern coast of Australia. The paper starts with a discussion of the required solar and wind data, followed by a general description of the hot water and space heating systems, and the provision of power using photovoltaic (PV) panels and wind turbines. Connection to the power grid is discussed in the last section of the paper. The proposed dwelling Based on the architectural drawings, the proposed dwelling has a floor plan of about 360m 2, and a floor to ceiling height of 2.5 m. The heat transferring wall and window areas for the different elevations of the building are estimated from the building plans and are provided in Table 1. The dwelling is planned for a location at S. This is about 150 km south east of Melbourne, in the state of Victoria. Due to the ideal location of the property being on the southern coast of Australia near Bass Strait, approximately 40% of the external walls (see Table 1) are covered by windows and glazed sliding doors in order to take advantage of the natural views surrounding the building. The dwelling is proposed to be of brick-veneer type Table 1. Wall and window areas for each elevation of the proposed dwelling Elevation Walls (m 2 ) Windows (m 2 ) Total (m 2 ) East West North South Total

3 114 M.-A. Hessami Rolling hills North Proposed dwelling Figure 1. Beach Beach Location of the proposed dwelling with respect to the beach and the rolling hills on the property. (timber frame, external brick wall and internal plaster board) with mineral fibre insulation. The building has a pitched roof (34 pitch angle) with terracotta tile cover, built on a 125-mm thick concrete slab. The insulation for the walls and roof was specified to be 100 mm for the walls and 150 mm for the ceilings. Taking advantage of the topography of the land, as shown in the sketch of Figure 1, the house was planned to be built with the south and east sides overlooking the beach and backing into the rolling hills justifying the use of large window areas on the south and east elevations of the building. The proposed location of the house was some 500 m away from the main property boundary on the north. The wind turbines were planned to be installed along the ridge of the hill (about 250m away from the house to eliminate any probable problem with the wind turbine s noise and interference effects) taking advantage of the prevailing winds coming from the sea as well as inland. Solar and wind data The solar and wind data for the exact location of the building were not available from the Australian Bureau of Meteorology (BOM). The cost of gathering such data was not justified and the time required to properly complete this task was not available. Consequently, available solar and wind data for the neighbouring locations from the BOM were used. For the wind data which included wind velocity and direction on hourly basis, an average value for three sites surrounding the property was obtained. The average wind speed distribution for these locations is provided in Figure 2. For solar heating, radiation data for a site at S were the best that could be found. Although solar data were available on hourly basis, for simplicity, mean daily global radiation data were used; calculations with hourly radiation data are reported to differ from global radiation data by less than 5% as discussed in Rheem (1988) [1]. The global radiation data for a tilt angle of b = 34 are provided in Figure 3; these data are also included in Table 2 for b = 34 and 38.5 to show

4 Designing a hybrid wind and solar energy supply system for a rural residential building 115 Wind Speed Distribution Chart for 3 Locations Cerberus Stony point Schanck Average Daily average radiation (MJ/m^2) Days per year < Wind Speed (km/hr) Figure 2. Average wind speed distribution curve Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Figure 3. Incident daily average solar radiation on a tilted surface with β =34.

5 116 M.-A. Hessami Table 2. Daily global radiation data on horizontal and tilted surfaces Global Global radiation on a radiation on a Global tilted surface tilted surface radiation on (34 deg) at (38.5 deg) at a horizontal Midday solar midday solar midday solar Percentage surface altitude angle altitude angle altitude angle difference Month (MJ/m 2 /day) (degrees) (MJ/m 2 /day) (MJ/m 2 /day) (%) Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec that the tilt angle does not have a significant effect on the incident radiation. The analysis presented here is based on these solar and wind data. Hot water system The study of the proposed hot water system was carried out using commercially available hardware comprised of flat plate collectors, a main tank and an auxiliary tank burning LPG (liquefied petroleum gas). The main tank was selected to have a capacity of 315 L to satisfy the needs of a family of four. The total size of the collector was determined using the solar radiation data obtained from the BOM and the system was optimised by performing a cost-benefit analysis. Although the optimum tilt angle of the collector should have been equal to the latitude at the point of installation as described by Duffie and Beckmann (1991, pp 13 21) [2], for reasons of practicality, a tilt angle of 34 (equal to the pitch angle of the roof of the building so that the collectors can be simply placed on the roof without the need for additional frame) was used in the simulation. As the data of Table 2 show, the maximum difference in radiation on the tilted surface is less than 4% for a tilt angle of 34 compared to The solar radiation data from the BOM are provided in terms of the mean daily global radiation on a horizontal surface (G H ) (MJ/m 2 ). Following the method developed by Duffie and Beckman (1991) [2], these data were converted to G T (global radiation normal to the tilted surface). The formulation for this conversion of the data for a simplified situation of midday solar radiation is given below using the

6 Designing a hybrid wind and solar energy supply system for a rural residential building 117 Sun geometric relations which can be deduced from Figure 4; the more detailed formulation is available in [2]. cos() q GT = GH (1) sin( a) In the above equation q = (b + a) π/2 where q is the beam radiation s angle of incidence and a is the solar altitude angle. Values of solar altitude angle at midday provided in column 3 of Table 2 are obtained using Equations (1.6.2) and (1.6.3) of Duffie and Beckman (1991, p 15) [2]. It should be noted that the values in columns 4 and 5 of Table 2 are based on the daily global radiation data for a horizontal surface given in column 2 evaluated at the solar altitude angle at midday given in column 3. The alternative would be to evaluate these values using hourly global radiation data on a horizontal surface with the corresponding hourly solar altitude angle together with the detailed formulation of Duffie and Beckman [2]. The maximum difference in the values would not exceed 5% as explained in [1]. In order to find the total size of the collector, operating conditions and the performance data for commercially available flat plate collectors given in Table 3 and the definition of collector efficiency (h) given by Equation (2) were used: h = Q u (2) AGT where Q u which is given by the following equation represents the useful heat delivered by a solar collector system when a water mass flow rate of m is flowing through it: ( ) Q = mc T -T u p out in G T G H Figure 4. α θ Collector plate β Solar radiation on a tilted surface. (3)

7 118 M.-A. Hessami Table 3. Performance data and operating conditions for solar collectors The heat losses (Q L ) from all external surfaces (A L ) such as that of the storage tank was found by using the following equation: ( ) Q = U A T -T L L t amb Inlet water temperature ( C) (T in ) Maximum (summer) 15 Minimum (winter) 12 Average daily ambient temperature ( C) (T amb ) Maximum 19.9 Minimum 9.5 Outlet water temperature ( C) (T out ) 55 Flat plate collector efficiency 0.6 Flat plate collector area (m 2 ) 1.81 Area subject to heat loss (m 2 ) 2.1 In the above equation U is the overall heat transfer coefficient calculated to be 2.25 W/m 2 -K using the method described in [3]. Using the above formulae and the data it was calculated that five flat plate panels would provide the necessary energy to the solar hot water system. However, to allow for unforeseen circumstances and to improve the reliability of the supply system, the aforementioned back-up LPG hot water tank (135 L) was included in the analysis. The system was optimised by performing a cost-benefit analysis in which the required rate of return was specified to be 10% and the system s life was given to be 20 years. For this purpose, the number of collectors was varied, and the required energy was compared with the available solar energy, with the shortfall being supplied by the LPG tank. These results are plotted for 2, 3 and 4 collector panels in Figure 5. The system with the minimum cost was found to have 3 collector panels at a total cost of A$2740 as shown in Figure 6. This cost is the sum of the costs due to (i) the consumption of LPG, (b) the cost of solar collectors, and (c) the depreciation cost of the solar collectors (calculation of depreciation cost is explained later by Equation (6) and the accompanying notes); the cost of the tanks was not included since this is common whether the energy supply is totally solar based, or it also uses the back-up system. Taking into account the A$1000 government subsidy towards the installation of solar hot water systems, the discounted cost was found to be A$1740. It is worthwhile to note that during January-March and October-December the 3 collector panel system is capable of supplying more heat than required; this excess heat can be directed to the LPG tank to reduce the cost of its operation. The overall effect would be to lower the total system cost; this has not been investigated in this analysis. (4)

8 Designing a hybrid wind and solar energy supply system for a rural residential building Required Heat (MJ/month) Solar Heating by 2 Collectors (MJ/month) Solar Heating by 3 Collectors (MJ/month) Solar Heating by 4 Collectors (MJ/month) MJ/month Months Figure 5. Energy requirements of the hot water system and what can be provided by 2, 3 and 4 solar collector panels. Present Value (A$) Figure 6. Number of Collectors The cost of the optimum solar hot water system. Space heating and cooling In determining the heating and cooling loads for the proposed building, a number of assumptions were made regarding the building materials used, the orientation of the house, the type of appliances present, the number of occupants and their living patterns, and the ventilation and infiltration/ex-filtration rates so that these loads

9 120 M.-A. Hessami Table 4. U values used in load calculations Items Materials U (W/m 2 -K) Windows Double glazed, 6mm air gap 3.4 Sliding glass doors Single glazed 6.1 Walls Brick veneer (90mm brick, 100mm mineral fibre, 20mm air gap, mm plaster board) Doors 40mm wood 2.6 Floor 100mm concrete slab, 25mm cement and sand, underlay, carpet 1.5 Roof Terracotta tiles, 150mm mineral fibre, 12mm plaster board 1.8 could be estimated. The calculation procedure was based on the method described in [4]. While the method of air change per hour was used for ventilation and infiltration/ex-filtration, the concept of degree day was used to estimate the monthly space heating and cooling demands. The heat transmission through various surfaces can be calculated from Equation (4) after replacing T t by the temperature of the surface being studied, using the U values provided in Table 4; these values are obtained by first calculating the total thermal resistance of each building component listed in the said Table and then taking its inverse. As mentioned before, the floor plan of the house was about 360m 2 in size, built on a concrete slab. The 2.5 m high walls created an external glazed area of about 100 m 2 and a wall area of about 150 m 2. Due to the pitch of the roof and the larger than average eaves, the exposed area of the roof was just over 430m 2. With these large surface areas exposed to the ambient conditions, the heat transmission contribution to the heating and cooling loads was found to be significant. The load calculations performed for this study showed a maximum daily heating load of 533 MJ for the month of July. To satisfy this heating demand by solar collectors, over 55 collectors at an exorbitant capital cost of over A$30,000 would be required. Hence, it was decided that under the prevailing assumptions with regards to the building orientation, construction material, large glazed areas and so on solar space heating was not economically feasible when compared with the alternatives of using LPG or biomass. Therefore the space heating requirements were considered to be met by LPG or wood which is abundantly available in rural communities. The maximum cooling load was calculated so that its contribution on the power demand can be estimated. In determining the cooling load, not only the effect of external solar radiation but also the effect of internal loads (see details in Table 5) as well as infiltration were included. The maximum cooling load was found to be 993 MJ/day for January, and a 2.5 hp (6.1 kw cooling with 1.8 kw input power) split air conditioning system was found to be adequate for this purpose. The total capital cost of this system was estimated to be A$3500.

10 Designing a hybrid wind and solar energy supply system for a rural residential building 121 Table 5. Types of appliances used to calculate the power demand for the proposed dwelling. Daily Rated No. Weekly Energy Types of appliances considered Power (W) Hours/Week Energy (Wh) (Wh) Toaster Fridge (410L 580kWh/yr) 11,154 1,593 Microwave 1, , Dishwasher (256kWh/yr) 2, Hairdryer 1, Shaver Three Exhaust Fans Standby Function Television , VCR/DVD Player Stereo Computer , Answering Machine Air Conditioning 1, ,000 3,857 Clothes Dryer (720 kwh/yr) 6, Washing Machine Front loader (224kWh/yr) 4, Iron 1, , Vacuum (in built) 1, Power Tools 1, Two Water Pumps (500W each) 1, ,000 1,000 Internal Lighting (50 50W and 50 25W) 3, ,500 1,500 Five External Lighting (200W each) 1, , Six Bed-side Lamps (40W each) Total Demand (Summer) 92,259 13,180 Total Demand (Winter) 65,259 9,323 Electricity supply Due to the rural setting of the building and its ideal location, the power requirement of the property was envisaged to be met from renewable sources. The available alternatives are solar, wind, biomass, or a combination thereof. This section provides the details of the procedure followed and the calculations performed in order to find the optimum system to suit the needs of the proposed building. Power demand calculations Power is needed not only for lighting but also for the operation of the airconditioner as well as various appliances that are normally used in the house. For this purpose, first a list of all the necessary appliances was prepared, then the power ratings were obtained from manufacturers, and finally a usage pattern was assumed. Using this information, the power demand was calculated as shown in Table 5. Based on these data, the power demand was estimated to be 13 kwh/day for summer and

11 122 M.-A. Hessami 9 kwh/day for winter; this is a revised power demand compared to the original 20 kwh/day for summer and 14 kwh/day for winter, and was obtained by removing some of the non-essential appliances such as chest freezer and by adjusting the usage factor. These estimates are in general agreement with those published in [5]. Photovoltaic modules For the purpose of determining the number of PV modules needed for the power supply system for the proposed building, the global radiation data on the tilted surface provided in Table 2 for the same tilt angle as the flat plate collectors were used. The solar radiation data were first changed to sun peak hours by dividing the daily radiation of Table 2 by 3.6 [6] in order to find the equivalent hours for a standard incident solar radiation of 1000W/m 2. The total number of arrays was then found by dividing the daily loads (kwh) given in Table 5 by the said sun peak hours (h). After taking the efficiency of the inverter (82%), the battery (80%) and the battery charger (85%) [5] into account, it was found that fifty 80-W module would generate the required power. The total cost of this system was estimated to be about A$75,000. In order to determine the storage system required to meet the needs of the proposed dwelling, the method described by Roberts (1991) [7] and illustrated by the following steps was used: 1. Multiply the daily load by the number of autonomous power supply days (assumed to be 4). 2. Divide the above number by the inverter efficiency, the depth of discharge (0.6), the battery efficiency, and the system voltage (24 V) to find the storage capacity in A-h (ampere-hours) at 24 V. The above calculations showed that a storage system with a capacity of 1350 A-h available at 6 V would be sufficient. The cost of such a storage bank was estimated to be A$11,500 which was considered to be significant especially when the useful life of the batteries (which is about a third of the other hardware) is factored in. Wind turbines The wind frequency data obtained from the BOM included both wind velocity and direction measured at a height of 10 m above the ground, approximately where the hub of a wind turbine is normally mounted. Although the wind direction is not important since horizontal axis wind turbines easily align themselves with the wind direction, the wind speed data given in Figure 2 were used to find the wind power. It should be noted that the wind frequency data provided by BOM were given for specific ranges of wind speed (ie, 0 to <1, 1 10, 11 20, and >30 km/h). In the following calculations, the average speed for every range was used except for the last one which was taken to be 35 km/h. The average power generated by a turbine is a function of its radius and the average wind speed as given by the following equation [8]:

12 Designing a hybrid wind and solar energy supply system for a rural residential building P= 24. p R c (5) where R is the turbine blade radius and c is the wind speed. However, this equation can introduce significant errors if the wind speed is not correctly estimated due to the cubic relation of power with speed. Hence, a better method of determining wind turbine output is to use the available wind speed frequency data with the turbine wind speed-power curve which can be obtained from the turbine manufacturer. By multiplying the wind speed and the rated output of the turbine at that speed, the expected energy at that speed can be found. Repeating this calculation for all wind speeds would give the total energy output of the turbine. The results of such calculations are generally presented in the form of the wind energy distribution curve for that turbine erected at that particular location [8]. For the purpose of the analysis in this paper, four different wind turbines listed in Table 6 with a power output ranging from 400 W to 3.2 kw were considered. The wind energy distribution curve for these turbines is provided in Figure 7, and the average values are summarised in Table 6. The power demand of the proposed building was found to be adequately satisfied with the West Wind 2.5 kw output wind turbine listed in the table. The present value of this system was estimated to be just over A$12,000 as indicated in the table. The present value was found by adding the purchase price with the depreciation cost of the turbine given by Purchase Price () $ n È 1 Depreciation cost ()= $ - (6) Î Í1 i ( 1 + i) n where n = 25 years is assumed for the life of the turbine, and i = 10% is assumed for the rate of return on investment. For example, the purchase price of Monthly average turbine output (kwh/day) Soma1000 Soma 400 Whisper 175 Westwind Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Figure 7. Energy output for 4 different turbines for different months of the year.

13 124 M.-A. Hessami Table 6. Energy output for 4 different wind turbines Turbine type Rating (W) Energy output (kwh/day) Present value of turbine (A$) SOMA ,500 SOMA 1,000 1, ,540 West Wind 2.5kW 2, ,270 Whisper 175 3, ,630 SOMA 400 is A$5500 and using Equation (6) its present value is calculated to be A$7500. As the data of Table 6 indicate, the cost of Whisper 175 is marginally higher than that of West Wind 2.5 kw but the output of the former is much higher than that of the latter. Hence, it may be beneficial to seriously consider the former instead of the latter in the optimum system design. A hybrid power supply system Although either of the two systems described above would meet the power requirements of the building, wind energy seems preferable based on the calculated cost estimates. However, wind energy is not a very reliable source as Brammer and Hessami (2005) [9] using statistical analysis found that only 3% of the installed capacity can be considered as firm capacity defined as the power that can be statistically available for at least 95% of the time [10]. Therefore, in order to improve the reliability of the power supply, it was considered preferable if a hybrid system could be designed. A cost-benefit analysis was performed with the power being supplied by the PV system as well as the wind turbine. In this analysis, a small number of PV modules was first chosen, and then the output from the various wind turbines was considered, and finally a cost-benefit analysis was undertaken. The number of the PV modules was then gradually increased until a system with the minimum cost was identified. The final outcome of this calculation procedure for this study was a hybrid system comprised of a 2.5-kW output wind turbine and five 80-WPV modules. The total cost of this system was estimated to be A$41,000. Although this cost is significantly higher than that for a totally wind based power supply, for reasons of having a more reliable system based on two different sources of solar and wind, the hybrid power supply was considered to be preferable. The energy supply by this hybrid system in kwh/day for different months of the year is provided in Table 7 where the energy demand is also shown. As the data indicate, the proposed system is capable of satisfying the energy demand of the proposed dwelling throughout the year. It should be noted that the demand data of column 5 represent average values for summer and winter months and are therefore not highly accurate for comparison with daily energy supply. Therefore, it is possible that there would be a need for additional power during the summer months of December, January and February.

14 Designing a hybrid wind and solar energy supply system for a rural residential building 125 Table 7. Daily energy supply and demand for the proposed system West Wind Output of 5 Total energy Energy Hot Water Total energy 2.5kW PV modules supply Demand System consumption (kwh/day) (kwh/day) (kwh/day) (kwh/day) (kwh/day) (kwh/day) Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Also included in Table 7 is the energy supply by the hot water system so that the total daily energy consumption given in the last column can be found. The minimum and maximum monthly average daily energy consumptions for this application are 19.2 kwh in June and 35.7 kwh in January-February. As a final note, it should be mentioned that the required power could be obtained from the mains grid at a lower cost than what was found for the hybrid system. However, the calculations performed in this analysis have not taken into account any of the intangible benefits of the proposed hybrid power supply. These benefits include lower greenhouse gas emissions, self-satisfaction that by using renewable energy one is helping with the protection of the environment, lower operating cost, more reliable power supply, and so on. If these and other environmental advantages are quantified and included in the analysis, it is likely that the two systems would have a comparable cost-benefit curve. Also, the solar and wind energy system designed for this dwelling will be independent of the mains grid and would therefore not suffer from the consequence of general blackouts. Conclusions The purpose of this investigation was to design a renewable energy supply system for a rural property with a high level of reliability and total independence from the mains grid. This was achieved by using solar and wind energy with a backup source powered by LPG. The final design was comprised of the following components: A 315 L solar hot water system heated by 3 flat plate collectors (1.81 m 2 each) and a backup LPG tank (135 L) at a total cost of A$1740; this figure does not include the cost of the storage and back up tanks.

15 126 M.-A. Hessami The space heating load was found to be large and the capital cost of a solar system was calculated to be prohibitively high compared to alternative methods using LPG or biomass. Consequently, space heating was left to LPG heaters or wood stoves; wood is an abundant commodity in the rural communities and would therefore be appealing. The space cooling was found to be adequately satisfied by a 2.5 hp (6.1 kw) cooling capacity split air conditioning unit at an estimated cost of A$3500. The power requirements of the dwelling was designed to be met by five 80-W PV modules and a 2.5-kW output wind turbine at a total cost of A$41,000. The estimated total cost of the power generation system (A$41,000) was found to be higher than connecting to mains grid. However, for reasons of environment benefits and independence from the grid, this system was considered to be appropriate for this application. Acknowledgement The author acknowledges with gratitude the assistance of Richard Feenaughty (a former student) with the collection of relevant data for this project. References [1] Rheem Australia Limited. Hot Water Manual (Surrey Beatty & Sons, 1988), Sydney (ISBN ). [2] J. A. Duffie and W. A. Beckman, Solar Engineering of Thermal Processes (Wiley, 1991), New York (ISBN ). [3] J. P. Holman, Heat Transfer (McGraw Hill, 1997), New York (ISBN ). [4] E. Baker, C. J. Floro, J. P. Gostelow and J. J. McCaffrey, Solar Heating and Cooling Systems: Design for Australian Conditions (Pergamon Press, 1984), Rushcutters Bay (ISBN ). [5] S. R. Wenham, M. A. Green and M. E. Watt, Applied Photovoltaics (Centre for Photovoltaic Devices and Systems, 1994), Sydney (ISBN ). [6] A. Zahedi, Solar Photovoltaic Energy Systems: Design and Use (New World Publishing, 1998), Melbourne (ISBN ). [7] S. Roberts, Solar Electricity: A practical guide to designing and installing small photovoltaic systems (Prentice Hall, 1991), Cambridge (ISBN ). [8] M-A. Hessami, Applied Thermodynamics: Power production from conventional and renewable sources (Erudition Publishing, 2001), Emerald (ISBN ). [9] N. Brammer and M-A. Hessami, Contribution of Distributed Generation: an Australian case study, Proc. of 14 th International Conference on Thermal Engineering and Thermogrammetry, June, 2005, Budapest, Hungary. [10] H. L. Willis and W. G. Scott, Distributed Power Generation: Planning and Evaluation (Marcel Dekker, 2000) New York (ISBN ).