LITERATURE REVIEW. 2.1 General. 2.2 Water and Energy: Global crisis and emerging trends. Chapter 2

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1 Chapter 2 LITERATURE REVIEW 2.1 General A comprehensive literature survey was carried out in order to determine the following: 1. Water and Energy: Global crisis and emerging trends 2. RWH systems and optimization of system components for WSE and overflow 3. Solar pumping systems 4. System sizing of SAPV systems for non-load shedding 5. Development of correlations to calculate solar radiation from weather data 6. Impact of tilt angle on incident solar radiation It is found that the emerging global trend with regard to water and energy is to optimize the utilization of these natural resources by adhering to sustainable principles so as to minimize the waste in order to avert a global crisis. In that, particular attention is focused on rain water harvesting and the use of solar power, two areas when effectively combined can be used to provide water and energy security to millions of people around the world. The need in this regard is pressing in the developing countries and urgent addressing of the issue is relevant, appropriate and timely, especially for the nations in the tropical belt. 2.2 Water and Energy: Global crisis and emerging trends The proportion of world s population that lives in urban areas is constantly increasing. During the last 150 years, the global urban population has increased from a mere 3% in the 1850s to more than 45% in While global population has increased only six 8

2 times during the last 200 years, urban population has grown 128 times. Even though the global population growth rates seem to abate somewhat, global urbanization shows no signs of retreat (Emmanuel, 1999). The fastest urbanization is now occurring in Africa and Asia, and it is believed that by about the year 2015, most of the population in developing countries will live in towns (Grundstrom et al., 2004). This rapid urbanization has created a major strain on the resources, providing the basic amenities such as water and power supply, so that the living standards of the growing population can be maintained at an acceptable level. The rural population on the other hand faces different set of problems with regard to access to clean water and energy due to the requirement of vast resources in providing such supplies to remote areas, apart from the wide spread pollution of water sources and global warming due to fossil fuel burning in generating power. Even though earth s hydrosphere contains a total volume of 1386 million m 3 of water, only 2.5% of that amounting to 35 million m 3 consists of fresh water fit for human consumption. Of the rest 1% amounting to 13 million m 3 is saline ground water while 96.5% amounting to 1338 million m 3 is in the oceans and salt lakes. As such, the accessibility to clean water has become a major problem for the ever growing population, particularly those living in the tropical belt, as shown in Figure

3 Figure 2.1: Access to improved water source in % of total population Though the annual average rainfall is more than 2000 mm in most of the tropical countries, rapid degradation of water sources and lack of funds to invest in water supply schemes has made accessibility to clean water beyond many, increasing the spreading of water related health hazards and resultant higher mortality rates. Figure 2.2 shows the per capita world fresh water resources (UNICEF, 2004). The map clearly indicates that the tropical belt, where most of the developing countries with high population densities are located, is comparatively poor in per capita fresh water resources. 10

4 Figure 2.2: World fresh water resources per capita The energy issue, on the other hand, is more globalized. In the last few decades, energy related problems have become more and more important involving the rational use of resources, the environmental impact due to the emission of pollutants and the consumption of non-renewable resources. With regard to energy systems, the focus is to mitigate such problems while fulfilling more and more restrictive environmental laws. This include the increase of traditional plant and device efficiency (Mirandola, 2003), the diffusion of cogenerative systems, the study of innovative plant configurations and the use of non-traditional fuels and renewable resources. In this last context, solar energy is commonly considered as an ideal solution, particularly for small distributed (household) thermal and/or electric energy production. Many countries have introduced policy to promote the installation of new renewable source plants in order to reach the Kyoto protocal targets, and often a specific mention to photo voltaic plants is reported (Waldau, 2005). As a result, the capacity of photo voltaic power plants, converting solar energy directly to electricity, has incresed 16 11

5 times during and set to show even a higher growth rate in the next decade (British Petroleum Energy Statistical Review, 2006). At present, large scale fossil energy production is cheaper than the available solar alternatives (Chakravorty et al., 1997). However, conventional energy generation technologies, based on fossil fuel, has reached maturity leaving little room for significant cost reduction. Infact, current research on these technologies is mainly concerned with pollution abatement rather than with improving fossil fuel conversion efficiencies which are nearing their theoritical limits. Similarly, the important progress in energy conservation serves mainly to mitigate the rapid increase in energy demand, but does not contribute directly to reduce the production costs of fossil energy. In contrast, solar technologies still have large potential for improvement, pending appropriate research and development. Moreover, the true price of fossil energy must include scarcity and polllution components to allow a valid evaluation of social costs and benefits of alternative energy options (Tsur and Zemel, 1992). In regard to socioeconomic view point, the benefits of the exploitation of solar energy technologies comprise: Increase of the regional/national energy independency; Provision of significant work opportunities; Diversification and security of energy supply; Support of the deregulation of energy markets; and Acceleration of the rural electrification in developing countries. (Tsoutsos, 2003) 2.3 Optimization of rain water harvesting systems Performance optimization of the components in rain water harvesting systems is a well researched area. While advances in improving the collection efficiency and filtering devices have been continuing, highest attention has been paid to optimize the storage capacity, identifying the rain water storage tank as the highest cost component of a rain water harvesting system. 12

6 2.3.1 Rain water harvesting Rain water harvesting has been in practice all over the world for centuries. However, much attention has been focused on it in recent decades as a result of worldwide shortage of potable water and the trend to adhere to principles of sustainability in infrastructure development. The need of rain water harvesting and benefits accrued from it are manifold. It is pertinent to discuss them to better understand the importance of RWH Optimization of system components Optimizing of the storage capacity of RWH systems is looked at intuitively usually taking the longest duration of dry spell as the yard stick to calculate the desirable size of the storage tank. However, recent research has undertaken a more scientific approach to the issue, taking all the contributing parameters such as annual rainfall, demand pattern and the collection area in to consideration Optimization techniques Behavioral models simulate the operation of the reservoir with respect to time by routing simulated mass flows through an algorithm which describes the operation of the reservoir. The operation of the rainwater collection will usually be simulated over a period of years. The input data, which is in time series form, are used to simulate the mass flow through the model and will be based upon a time interval of either a minute, hour, day or month. Fewkes (1999a) used behavioral model to simulate the performance of rainwater collectors and incorporated the spatial variations of rainfall into the model by using rainfall time series from five different locations and temporal fluctuations in rainfall by using two behavioral models each with different time intervals Performance of RWH Systems using Behavioral model 13

7 Behavioral models have been used by other researchers (Jenkins, Pearson, Moore, Sun & Valentine, 1978, Latham, 1983) to investigate the performance of rain water stores. The generic configuration of a rainwater collection system is illustrated in Figure 2.3 Where, R t is Rainfall in time t D t is the Demand (time t) Y t is the Yield (time t) A is the roof area S is the storage volume Q t is the roof runoff (t) O t is the overflow Figure 2.3: Generic configuration of a rainwater collection system Jenkins (1978) developed a behavioral model and identified two fundamental algorithms to describe the operation of the rainwater store. They are: a) The Yield After Spillage (YAS) operating rule b) The Yield Before Spillage (YBS) operating rule a) Yield after spillage (YAS) operating model YAS operating rule is; Y t = min {D t t; V t-1 } (2.1) V t = min {V t-1 + Q t Y t ; S Y t } (2.2) Where, R t is the rainfall (m) during time interval, t, 14

8 Q t is the rainwater run-off (m 3 ) during time interval, t, V t is the volume in store (m 3 ) during time interval, t, Y t is the yield from store (m 3 ) during time interval, t, D t is the Demand (m 3 ) during time interval, t, S is the Store capacity (m 3 ) A is the roof area (m 2 ) The YAS operating rule assigns the yield as either the volume of rainwater in storage from the preceding time interval or the demand in the current time interval whichever is the smaller. The rainwater run-off in the current time interval is then added to the volume of rainwater in storage from the preceding time interval with any excess spilling via the overflow and then subtracts the yield Predicting the performance of RTRWH System using behavioral model Jenkins (1978) used the YAS algorithm and a monthly time interval. The reliability or performance of the rainwater store can be expressed using either a time or volume basis. In either case, a reliability or performance of 100% indicates complete security in provision of service water. However, research undertaken by Jenkins and Latham (1983) related to a limited range of volume sores aimed at conserving an excess of 95% of household water and does not readily cater to centralized Roof Top Rain Water Harvesting (RTRWH) systems where lower conservation percentages are viable. Butler (2000) report the results of a preliminary mapping exercise which evaluated the accuracy of behavioral models for the sizing of rainwater collection systems using both different time intervals and reservoir operating algorithms applied to a comprehensive range of operational conditions. The preliminary analysis of their study indicated the hourly YAS model could be used as a standard of comparison against which other models could be compared and calibrated. The YAS reservoir operating algorithm was found to give a conservative estimate of system performance irrespective of the model time interval and therefore preferred for design purposes compared to the YBS operating algorithm. Fewkes (1999b) developed 15

9 a generic set of curves using a YAS daily time interval model, for a range of storage and demand fractions. Different combinations of roof area, store capacity and demand were expressed in terms of two dimensionless ratios, namely the demand fraction and storage fraction. Figure 2.4: Components of a rainwater collector sizing model The Demand fraction is given by D/AR, where D is the annual demand (in m 3 ), A is the roof area (in m 2 ), and R is the annual rainfall (in m). The Storage fraction is given by S/AR, where S is the store capacity (in m 3 ). The above fractions can be used to predict the performance of rainwater collectors within a particular geographical area. Components of a rainwater collector sizing model is given in Figure 2.4 In developing the system performance curves, two models were used to incorporate the temporal fluctuations of rainfall. The first model uses a daily time interval, which ignores fluctuations with a time scale less than a day, to predict system performance for different combinations of roof area, demand, storage volume and rainfall level. A set of 16

10 curves is produced which enable the performance of rainwater collection systems to be predicted in different locations. The main limitation of this approach is the requirement of daily rainfall time series, which can be both costly and difficult to manipulate. The second method of modeling uses a larger time interval of one month resulting in a more compact model and economic data set. However, the coarser monthly time interval does not take into account rainfall fluctuations with a time scale less than one month, which may result in an inaccurate prediction of system performance. The poor resolution of the monthly interval model compared to the daily model is countered by the introduction of a parameter, referred to as the storage operating parameter. The short time scale fluctuations of the daily model are in effect replicated in the monthly model by the storage operating parameter. Values of the parameter are selected so that the monthly model mimics the system performance predicted by the corresponding model using a daily time interval. This approach provides a simple and versatile method of modeling the performance of rainwater collectors which takes into account temporal fluctuations in rainfall. The performance of the rainwater collection system is described by its Water Saving Efficiency (WSE) (Dixon et al., 2000) Water Saving efficiency is a measure of how much mains water has been conserved in comparison to the overall demand and is given by, t = T t= 1 Yt WSE = x 100% (2.3) t = T t= 1 Dt 17

11 Where, Y t is the yield from storage facility (m 3 ) during time interval, t, D t is the demand (m 3 ) during the time interval, t. T is the total time under consideration. In the study conducted by Fewkes (1999b), the demand component of the models was limited to WC usage which accounts for approximately 30% of potable household water usage in the UK (Department of the Environment and Welsh office 1992) and was assumed to occur at a constant daily or monthly rate. This assumption was reasonable because the demand time series generated by WC usage did not exhibit excessive daily or monthly variance (Fewkes 1999a). However, if the demand from other domestic appliances such as washing machine was considered the demand pattern would not be constant and the demand time series required. The detailed analysis undertaken by Fewkes and Butler (2000) enabled constraints to be proposed for the application of hourly, daily and monthly models expressed in terms of storage fraction. It was recommended that hourly models should be used for sizing small stores with a storage fraction below or equal to Daily models can be applied to systems with storage fraction within the range 0.01 to Monthly models were only recommended for use with storage fractions in excess of Generally, daily models can be used to predict the performance of all stores except small stores with a storage fraction less than or equal to Optimization of storage size using water saving efficiency curves Generic curves for system performance of a RTRWH System were developed based on the generic configuration of the rainwater collection system illustrated in Figure 4.2 and the YAS form of the reservoir operating algorithm used in the system simulation models. For each of the sites investigated, computer coded system simulation models were developed based upon both monthly and daily time intervals. Twenty years of either 18

12 daily or monthly historical rainfall time series were used as input to the respective system simulation models. It was observed that the Water Saving Efficiency (WSE) curves at each demand fraction ratio for different sites are of close proximity to each other suggesting system performance could be adequately represented by a set of average or generic curves. The average water saving efficiency of a rainwater collector at demand fractions of 0.25, 0.50, 0.75, 1.00, 1.25, 1.50, 1.75 and 2.00 each with a storage fraction range of is illustrated in Chart 2.1 Chart 2.1: Generic curves for Water Saving Efficiency (WSE) (Fewkes, 1999b) Important observations with regard to generic curves on WSE Three important factors are considered in developing the generic curves for their effects on performance of the curves. They are; the effect of demand pattern, the roof run-off coefficient (C f ) and rainfall data. (a) Effect of demand pattern (b) Effect of roof run-off coefficient (C f ) (c) Variation in rainfall data 19

13 (a) Effect of demand pattern The generic curves of WSE were plotted against different storage fractions (S/AR) for a given demand fraction (D/AR). In doing so, demand is assumed to be a constant for a particular situation and in the case of WC flushing appears to hold true. It was observed that for a period of 12 months, that WC flushing water demand remained at a fairly consistent level from day to day (Fewkes, 1999b). Butler (2000) in his survey of domestic water usage in United Kingdom also observed that the variation of WC flushing usage on different weekdays was low. Therefore, it can be deduced that system by Fewkes (1999) investigated above is adequately modeled using average demand data. However, this observation may not be universally applicable to all rainwater collection systems. Demand patterns which exhibit significant daily variance will require more precise modeling. Therefore, the generic curves for WSE can be fairly accurately used where demand can assumed to be a constant. (b) The effect of roof run-off coefficient (C f ) Rainfall loss during collection occurs due to absorption by the roofing material and wind effects around the roof. The rainfall loss can be modeled using an initial depression storage loss (L) with a run-off coefficient (C f ). The model is of the general form; Qt = T t= 1 T Qt = ( RtACf ) L t= 1 (2.4) Where, Qt is the rainwater run-off during rainfall event, t, T is duration of rainfall event, t (min) L is the depression storage loss (L) C f is the run-off coefficient R t is rainfall during rainfall event, t (mm). 20

14 It is noted that L can also be expressed in mm by dividing the depression loss by collection area. L can also be used to accommodate the first flush volume in a rain event which contributes to storage loss. The sensitivity of WSE to rainfall loss is illustrated in Chart 2.2 Chart 2.2: The sensitivity of WSE to rainfall loss (Fewkes 1999a) In the analysis the depression storage loss was set to zero and the sensitivity of the rainwater collection sizing (RCS) model investigated using constant proportional losses or run-off coefficients ranging from 0.8 to 1.00 (Fewkes, 1999a). The amount of rainwater collected was not found to be significantly affected by wind speed and direction. The accuracy of the (RCS) model maintained within the range is indicating that a simplified approach to the modeling of rainfall losses appears valid. Therefore, the overall run-off coefficient for the trial period can be estimated using the relationship: C f = Q T /R T.A (2.5) 21

15 Where, Q T is the quantity of rain water collected in time T R T A is the rainfall in time T is the capture area Calculation of Roof run-off Coefficient (C f ) The roof run-off coefficient was measured using the simplified equation C f = Q t /R t A (2.6) Where, Q t is rainwater collected at storage for a rain event in time t, A is the roof area and R t is the rainfall in time t. In finding the roof run off coefficient, it is assumed that the depression storage volume is zero and the first flush device was sealed off with its discharge orifice closed. Then, for a given capture area, a series of rain water quantities could be collected for a known time series. By determining the corresponding rainfall within the same time series, C f can be calculated. A series of values were calculated for C f for different roof types available in Sri Lanka the summary of which is shown in Table 2.1 Table 2.1: C f for different roof types Roof type C f Clay Tiles 0.82 Concrete Tiles 0.85 Asbestos 0.87 Metal 0.89 (c) Variation in rainfall data 22

16 The generic curves developed by Fewkes (1999b) for Water Saving Efficiency (WSE) were developed for a particular set of rainfall data. The model was simulated with rainfall data collected in 5 sites where average annual rainfall varies from mm/year (Forster, 1991). The performance curves predicted for each site were found to be close together, almost coalescing into a single curve. The modeled performance of rainwater collectors at various demand fractions appears to be relatively insensitive to fluctuations in daily rainfall patterns experienced at each location, except when D/AR is closer to 1.00, when slight sensitivity is shown. Therefore, for the given rainfall range, the generic curves developed can be adequately used to suggest system performance for given demand and storage fractions Validation of water saving curves for Sri Lanka It is necessary to find the usage patterns and to monitor the performance of a prototype RWH system to validate the generic curves for Sri Lanka. The intermediate climate zone of Sri Lanka receives annual rainfall of 1000 to 2000 mm (National Meteorological Department of Sri Lanka) with average annual rainfall being 1500 mm which is well within the range covered in the generic curves on system performance (WSE) developed by Fewkes (1999b). It is also observed that, the demand for WC flushing water remains a close constant at 25% of the service water requirement in both the average household and per capita basis (Sendanayake, 2007). Therefore, in the absence of system performance curves for rainwater collection developed for Sri Lanka, the generic curves can be employed as a standard design tool, once validated, for roofs with a run-off coefficient in the range of 0.80 to Jayasinghe (2002) calculated water saving efficiencies (WSE) for RWH systems in 4 major cities of Sri Lanka based on generic curves for water saving efficiency for a range of demand and storage fractions. It was observed that high water saving efficiencies was possible for storage capacities in the range of 2 3 m 3 in the wet zone of Sri Lanka. 23

17 In a study carried out by Sendanayake (2007), service water saving efficiency of a prototype RTRWH system located in the North Western Province (NWP) in the intermediate climate zone of Sri Lanka was monitored to ascertain whether the system performance validates the generic curves for water saving efficiency in Sri Lankan situations which is tropical in nature. To obtain the required data, the following activities were carried out in the research: a) The annual demand figures used (WC flushing) are based on a four month survey (from July to October covering both wet and dry seasons) and can assumed to be a stable demand thereby confirming to the simulation model. Further, the demand patterns in five sites in the same area were surveyed to verify the stability of demand figures. b) The variation of water Saving Efficiency (WSE) was monitored for different sets of demand and storage fractions. In order to collect data a prototype was set up with the following characteristics: A rainwater collector with a storage tank of 1500 litres was installed at Marawila in the North Western Province of Sri Lanka and its performance was monitored over a four month period. The system was installed in a house of single storey construction with a pitched roof covered with profiled, granular face concrete tiles. Rainwater was collected from a roof area of 25m 2 and water was drawn-off the tank via the outlet, in measured quantities corresponding to demand figures. An over flow was fitted to the storage tank which discharges into the households surface water drain. The prototype RWH system is shown in Figure

18 Figure 2.5: The prototype RWH System The details of the prototype installed at the test site are as follows: Effective roof area = 25 m 2 (C f = 0.85) The conveying system consists of a 100 mm diameter PVC down pipe connected to the roof guttering is used to convey the collected rain water into the tank. The First Flush (FF) device is an extended PVC pipe 1700 mm in length end capped at base with a volume of 13 litres. This volume is equivalent to 0.5 mm of rain on 25m 2 of roof area. It should be noted that 0.5 mm of rain is considered sufficient to clean the collector surface of impurities in the absence of vegetation and dust. This is particularly valid since the system is located in an isolated site. However in built-up areas, generally 1 mm of rainfall is considered the First Flush (FF) volume equivalent. 25

19 The selected rain water storage facility is a galvanized steel tank of net capacity 1500 Litres with an outlet at the bottom and an overflow at the top. Therefore the corresponding value for S according to the generic curve is 1500 L. The validation of the generic curves of WSE for climatic conditions in Sri Lanka was carried out by Sendanayake (2007) with the collection of following data on a daily basis:. a) For a given demand D, the Yield from store S and the rainfall was recorded on daily time series. b) For a given demand D, Water Saving Efficiency (WSE) was calculated taking 30 consecutive days as a month. c) WSE figures obtained for a given Demand and Storage fraction were plotted against generic curves for WSE to ascertain whether the above figures confirm to the curves. The points obtained matched the generic curves reasonably well. The following observations are made with regard to the development of the generic curves by Fewkes (1999b) and the subsequent validation of the curves for Sri Lanka in this research. The generic curves developed by Fewkes (1999b) for WSE were plotted against a dimensionless storage fraction (S/AR) for a given demand fraction (D/AR). This step makes the results derived from the curve independent of the location parameters (i.e. roof area, annual rainfall and run-off coefficient) which are common to a given set of demand and storage values. It also makes the curves to be used as a design tool that can be applied for collection area of any size subject to constraints proposed by Fewkes (1999a). Since the performance curves for different locations with different annual rainfall figures almost coalescing into a single curve in Fewkes (1999b) study, these curves can be used for a wide range of annual rainfall figures corresponding to different locations. In the research carried out by Fewkes (1999b), the annual rainfall varies from 26

20 650 mm 1700 mm. Thus, variation in rainfall figures is almost 30% and hence the generic curves validated to the Intermediate Climate Zone (ICZ) can successfully be employed in any location in Sri Lanka. The usage surveys have indicated that the water usage for WC flushing can be about 25% of the total service water demand. Thus, for validation, water demand value of 180 L/day was used. This can correspond to a household with four people under normal circumstances or five people where some water conservation measures have also been promoted. A usage higher than this will need a larger roof area and larger tank capacities. Creation of additional data (The moving average method) The rainfall recorded over 12 months could yield only 12 points for validation. In order to create extra points, a fifteen day period from each day is considered a time interval. This means, for a set of readings taken over a period of 123 days with a given demand, it is possible to create 96 reading points with different rainfalls values. This way, it was possible to create sufficient number of points for validation. Validation of WSE curves for Sri Lanka This validation is very important for Sri Lanka due to widely varying annual rainfall figures and also due to different rainfall patterns prevailing in wet, intermediate and dry climatic zones of Sri Lanka. The ability to predict the water saving efficiencies can also be used to strike a good balance between reticulated supply and supplementary rainwater harvesting systems. The capital outlay required for rainwater harvesting can be considered as one of the main reasons for low penetration of it when reticulated supply is available. Therefore the generic curves for WSE can also assist in optimizing the capital out lay required by performing calculations for different water usages and tank capacities Overflow quantities in rain water harvesting systems 27

21 Limited research has been carried out on overflow quantities when RWH systems are employed as supplementary to reticulated service water supply. If the overflow quantities can be related to system parameters such as the daily demand, storage volume, annual rainfall and the effective collection area, the optimum storage volume required to minimize the overflow while maintaining the desired water saving efficiency (WSE) for a given demand can be determined. This will not only enhance the system efficiency but will also reduce the stress on the local drainage system in storm events Relating overflow to specific volume and specific demand In a series of research work carried out by Herrmann & Schmida (2000), overflow volume in percentage of roof runoff is plotted against specific rain water consumption for a range of specific storage volumes as shown in Chart 2.3. To condense different daily consumption rates and roof areas into one parameter, the specific rain water consumption is taken as the daily consumption rate (m 3 /day) divided by the effective roof area (m 2 ) and will be given in mm/day while the specific storage volume is taken as storage capacity in litres divided by the effective roof area in m 2. Development of such graphs for a given climatic region could provide a useful design tool to determine additional storage capacity required to minimize overflow for a given specific demand. 28

22 Chart 2.3: Relationship between overflow and specific rainwater consumption for various specific storage volumes. 2.4 Solar pumping Pump coupled to a motor driven by electric power generated through solar energy is generally termed as solar pumping. As one of the most widely used application of solar energy, solar pumping has attracted much attention in contemporary research Pump types Of the commonly used pump types, centrifugal and positive displacement pumps are discussed in detail as the availability and cost dictate that these two types dominate Centrifugal pumps Centrifugal pumps by far are the most widely used pump type in water pumping applications. Depending on the centrifugal force exerted by the rotating vane to transfer energy to water, centrifugal pumps are generally considered to operate productively in high flow, low head situations. 29

23 A schematic drawing of a typical centrifugal pump system is given in Figure 2.5. V S and V D denotes the suction and discharge velocities respectively. Figure 2.6: Schematic drawing of a centrifugal pump Characteristic curves of a centrifugal pump Ordinarily a centrifugal pump is expected to work under its maximum efficiency conditions. However, when a pump is run at conditions different from the design conditions, it performs differently. Therefore, to predict the behavior of the pump under varying conditions of speeds, heads, discharges or powers characteristic curves are used. These curves delineate useful information about the performance of a pump in its installation. (a) The main characteristic curves The main characteristic curves for a centrifugal pump is shown in Charts 2.4 to

24 Chart 2.4: Head vs. Discharge for different pump speeds Chart 2.5: Output power vs. Discharge for different pump speeds Chart 2.6: Efficiency vs. Discharge for different pump speeds 31

25 The operating characteristic curves The operating characteristic curves for a centrifugal pump is shown in Chart 2.7. When a centrifugal pump operates at the design speed (same as the speed of driving motor), the maximum efficiency occurs. Evidently, for optimum performance, the pump needs to be operated at the design speed. The operating characteristic curve is obtained by varying the discharge when the pump is running at the design speed. The design discharge and head are obtained from the corresponding curves where the efficiency is a maximum. Chart 2.7: Operating characteristic curves The constant efficiency or Muschel curves: The constant efficiency or Muschel curves (also called the iso-efficiency curves), depict the performance of a pump over its entire range of operations. These curves are obtained from the main characteristic curves. The constant efficiency curves help to locate the regions where the pump would operate with maximum efficiency. An example is given in Chart

26 Chart 2.8: Constant efficiency curves for centrifugal pumps Constant head and constant discharge curves: The performance of a variable speed pump for which the speed constantly varies can be determined by these curves. When the pump has a variable speed, the plots between Q and N, and H mano and N can be obtained. The curves are shown in Chart 2.9 Chart 2.9: Constant Head and Constant Discharge curves. 33

27 Affinity laws for centrifugal pumps The Head and Capacity produced by a centrifugal pump is dependent on the velocity with which the liquid leaves the impeller, and is referred to as the peripheral velocity Therefore the output of the pump can be adjusted by changing the peripheral velocity. This can be achieved by changing the speed of rotation (N) or by changing the diameter of the impeller (D). The relationship that exist between the pump output and the peripheral speed of the impeller are identified collectively as the Affinity Laws and is depicted in Equations 2.7 to 2.9 Q 2 = D 2 = N 2 (2.7) Q 1 D 1 N 1 H 2 = (D 2 ) 2 = (N 2 ) 2 (2.8) H 1 (D 1 ) 2 (N 1 ) 2 P 2 = (D 2 ) 3 = (N 2 ) 3 (2.9) P 1 (D 1 ) 3 (N 1 ) System load curve-batch transferring As the pumping head to overcome in the CTTRWH model is of a variable nature, the behavior of a system load curve in batch transferring situation is explored. In a batch transfer system, emptying or filling of the supply tank results in change of the liquid level in that tank and the equivalent change in the static head that the pump should overcome. The behavior of the load curve in a typical batch transfer is depicted in Chart

28 Chart 2.10: Typical load curve in batch transfer process It is observed that as the head increases, the load curve moves up for a given pump speed N. To operate the pump closer to the Best Efficient Point (BEP) and to avoid unstable pumping conditions, ideally the system should be designed to operate at point B Positive displacement pumps Figure 2.7: Schematic diagram of a positive displacement pump 35

29 Characteristic curves of PD pumps The characteristic curve of a reciprocating pump is usually described as an indicator diagram. It shows the pressure head of the liquid in the cylinder corresponding to any position during the suction and delivery strokes. It is a graph between pressure head and stroke length of the piston for one complete revolution. The indicator diagram obtained by neglecting the loss of head due to friction in the suction and delivery pipes and the effect of acceleration of piston is known as an ideal indicator diagram. Such diagram for a single-cylinder, single-acting pump is shown in Chart 2.11 Chart 2.11: Indicator diagram for a single-cylinder, single-acting PD pump Where, h s and h d are suction and delivery heads respectively The line EF represents the atmospheric pressure head, H atm equal to 10.3 m of water 36

30 The pressure head in the cylinder (represented by line AB) during suction stroke is constant and equal to suction head (h s ), which is below the atmospheric pressure head (H atm ) by a height h s. The absolute pressure head in cylinder during the suction stroke will be (H atm - h s.); It is shown by ordinate AS in Chart 2.11 at the beginning of the stroke and by ordinate BT at the end of stroke and is uniform throughout the stroke. During the delivery stroke, the pressure head in the cylinder (represented by line CD) is constant and equal to delivery head (h d ). The uniform absolute pressure head throughout the delivery stroke is (H atm + h d ) and is denoted by the ordinate TC or SD The work done by the pump per second (from Equation 2.10) is, P p = ρgq(h s +h d ) (2.10) 1000 As the area of the indicator diagram is AB*BC, It can be shown that, Work done by the pump area of the indicator diagram Thus, Work done by the pump per second = ρgan x Area of the indicator diagram (2.11) 60 If the pump is double-acting, neglecting the area of the piston rod, work done per second is proportional to twice the area of the indicator diagram. However in practice the effect of acceleration of the piston in suction and delivery pipes should be analyzed and the resultant impact on the shape of the indicator diagram should be determined. As the piston (considering it as the beginning of the stroke) moves outward, it should create not only a negative pressure equal to the suction head (h s ) but it should also accelerate the liquid. If h as is the acceleration head, then total negative pressure head at 37

31 the beginning of the suction stroke is (h s + h as ), the ordinate EA. The absolute pressure head at this point is denoted by ordinate A S. It should be noted that the absolute pressure at the beginning of the stroke should not fall below the vapor pressure so as to prevent separation taking place. The modified indicator diagram showing the effect of acceleration is given in Chart 2.12 Chart 2.12: The modified indicator diagram showing the effect of acceleration Though the shape of the indicator diagram changes from ABCD to A B C D, the area of the indicator diagram remains unaltered. Thus, the total work done remains the same. The main effect of the acceleration head is that it increases the negative head at the beginning of the suction stroke. If the simple harmonic motion does not take place, the straight lines A B and C D will become slightly curved. When the effect of friction in the suction and delivery pipes on the indicator diagram is considered, it can be seen that the shape of the diagram changes increasing the area as shown in the Chart It is observed that the highest friction losses occur at the middle of the strokes with zero losses at the beginning and end of the strokes. As the head losses in suction and delivery pipes are proportional to the angular velocity of the motor shaft, it can be deduced that the friction head losses increase with the increase in pump speed. 38

32 Chart 2.13: The friction effect in the suction & delivery pipes on the indicator diagram As the area of the indicator diagram is proportional to work done by the pump, it can be shown that the work done by the pump per second (P p ); P p {h s + h d + 2 h fs + 2 h fd }L (2.12) 3 3 Where, h fs and h fd are suction and delivery friction head losses respectively Sizing of battery assisted SAPV systems Battery assisted Stand Alone Photo Voltaic (SAPV) systems consists of a PV module, a storage battery and a charge regulator to control the overcharging and discharging of the battery when not coupled to a load. If an optimum cost solution is to be found for the system, proper sizing of the PV module and the battery with regard to their capacities is important Stand Alone Photo Voltaic (SAPV) systems In many distributed PV systems, PV module or array connected to a given load, with or without the back up battery, is considered as a stand alone photo voltaic system. Of the components, the PV module, consisting of parallel and series connected solar cells, can be considered the heart of the system. 39

33 Solar cell Solar cells are made of semi conductor material of either elemental type like Si, Ge or Oxides (BeTiO 3, Ge 2 O 3,TiO 2 ), Sulphides (CdS, CuS), Selenides (CdSe, MoSe 2 ) Tellurides (CdTe) or a mixture of type(inp, GaAs) which in combination facilitates a net electron flow in the presence of an electric field created by the incident photon from the sun. A typical commercial silicon solar cell is shown in Figure.2.8 Figure 2.8: A typical commercial silicon solar cell When photons of light energy, from the sun, fall on the cell, a part of that will be reflected back. The non reflected photons incident on the surface of the cell enter the thin outer layer of the semiconductor and are either converted into heat or produce ionpair by stripping the valence electrons from the semiconductor atoms. Ion-pairs are produced when the incoming energy is in excess of excitation energy (Magal, 1984). Some carriers escape the electric field of the junction and contribute to decreased electric field at the junction and this in turn increases the flow of the majority carriers producing the current flow. Chart 2.14 depicts the typical current-voltage characteristics of the solar cell. 40

34 Chart 2.14: The typical current-voltage characteristics of the solar cell It should be noted that the maximum conversion efficiency of a solar silicon cell is about 25% (but in actual practice it is between 8% to 20%) primarily due to excess or shortage of excitation energy in incident photons. The typical losses in a solar cell can be categorized as a percentage of incident solar radiation as given in Table 2.2 (Magal, 1993). Table 2.2: Loss percentage in Silicon solar cell systems Energy loss % Sunlight not converted in to electricity Excess energy photons 32 Deficient energy photons 24 Other internal cell losses 21 Reflection 3 Shading 3 Cell packing density 2 Total 85 The maximum conversion efficiency of some of the other promising semi conductor materials are Germanium 13%, Cadmium Sulphide 13%, Cadmium Selluride 25%, 41

35 Indium Phosphide 26%, Gallium Arsenide 27%and Aluminium Antimonide 27% of which the actual efficiency is about 80% of the above (Evelin et.al Photovoltaic materials Science 1980). Though the conversion of solar energy in to electrical energy is still limited to relatively low conversion efficiency, the advantages of photovoltaic generators over other solar converters are many. These are simple to fabricate, compact to operate and have high power output per weight ratio and practically with unlimited life. These have no moving parts and probably yield the highest overall conversion efficiency of solar energy into electricity (Magal, 1993). Further, they could generally be used for a period of about 25 years Electric load circuit of a simple cell Figure 2.9: Electric load circuit of a simple cell A simplified equivalent circuit of a PV cell is given in Figure 2.8. It consists of a constant current generator, non linear junction impedance and a load resistance R. Light causes a current to flow in the load equivalent to I, which is the difference between I S the generated short-circuit current and current flowing in the nonlinear junction I J, Ij = Io(e λv 1) (2.13) 42

36 When I O is the reverse saturation current, V is the voltage applied to the junction and λ = e/kt where K is the Boltzmann constant and T is the absolute temperature. Since I S = I + I J (2.14) I = I S I O ( e λv 1) (2.15) The maximum voltage Vmax occurs when I=0, then the above equation can be reduced to, Vmax=I/λ[lnIs/Io + 1] (2.16) The above equations show that the output voltage and current varies with respect to the operating temperature of the solar cell. Therefore, it can be deduced that when the operating temperature increases, the output current and voltage decreases and vice-versa impacting the conversion efficiency of the cell Performance characteristics of a solar cell Chart 2.15 shows how the voltage and current vary as functions of the flux density in silicon cells. The current is directly proportional to the flux, while the voltage is proportional to the log of the flux according to Equation Chart 2.16 shows how the voltage and current vary as a function of cell temperature. 43

37 Chart 2.15: V-I curve with the variation of solar radiation Chart 2.16: V-I curve with the variation of cell temperature 44

38 It is also shown that the maximum conversion efficiency, η max, is proportional to log of generated current Is. i.e., η max ln I S (2.17) Therefore it can be shown that when the incident solar flux increases, so does the maximum efficiency, η max Sizing methods Various approaches to sizing of SAPV systems are available in literature which can be broadly categorized in to 3 main methods: Intuitive methods Numerical methods Analytical methods Intuitive methods In this method, the size of the generator is chosen to ensure that the average energy produced during this period in which the least amount of solar irradiation occurs exceeds the energy demand of the load by a safety margin which is based on the designers own experience. A similar procedure is used when sizing the accumulator. These intuitive methods can be useful in situations where only an initial, rough approximation of the size of the PV system is required. However, it does not quantify the system reliability nor attempt to optimize the system outputs Numerical methods These methods are based on detailed simulation of PV system behavior, which are performed over a specific period of time. The energy balance of the PV system and the 45

39 state of charge (SOC) of the battery are calculated for each time interval assuming that generator efficiency is constant. The degree of reliability with which the system supplies electrical energy to the load is quantified by means of the Loss of Load Probability (LLP) LLP = E t EnergyDefi cit EnergyDema nd The maximum energy that can be extracted from the accumulator or in statistical terms, the LLP value refers to the probability that the system is unable to meet the demand. For most domestic applications, LLP for SAPV systems is acceptable in the range of 10-2 LLP 10-1 Numerical methods, besides producing precise outcomes, can be used to analyze the sizing of different models for the PV system components. According to Klein et.al (1994) and Lorenzo et.al (2000), length of the available data sequences pose limitations on the validity or reliability of these models. It is proposed, that only LLP values greater than 10-2 can be studied using data series of years due to the natural variations in climate. Klein et.al (1994) Analytical methods Having functional relationships between the variables of interest, these methods are based on the graphical information of iso-reliability curves. However, as pointed out by Hontoria et.al (1998), they are of local nature if not otherwise considered in the model Development of Cs charts Development of accumulator capacity (C S ) charts is an important step in sizing of SAPV systems. This numerical-analytical method can be considered much superior in 46

40 matching the capacities of the PV generator and the storage battery and many battery manufacturers provide C S charts generalized for different battery types. However, such charts generally do not provide the accuracy needed in location specific SAPV design as the incident solar radiation is variable depending on temporal as well as spatial parameters Numerical-Analytical approach to SAPV sizing The methodology developed by Fragarki et al. (2007) is based on the concept in which supply reliability is defined in terms of the length of time that the system supplies load without interruptions. Considering the system load or demand to be constant in time, the study attempts to characterize the daily energy balances. When dimensionless variables are used to analyze these balances, more universal results are obtained. To obtain the most general description, a sizing curve can be plotted in terms of the dimensionless variables C A and C S. The generator C A, is defined as the ratio of the daily energy produced by the generator divided by the daily energy consumed by the load (L). The storage capacity C S is defined as the total maximum energy that can be extracted from the battery (C U ), divided by the daily energy consumed by the load. Therefore, C S expresses the normalized useful battery capacity (C U ) in terms of the daily storage: C S = C U (2.18) L C A = η G A G G m= β (2.19) L where A G and η G are the exposed area and the conversion efficiency of the PV generator, G m- β is the monthly mean value of daily irradiation on the south facing generator surface at a tilt angle of β. L is the mean value of the daily energy consumption of the load and C U is expressed as; C U = C B. PD max (2.20) 47

41 Where C B is the nominal capacity of the accumulator and PD max is the maximum depth of discharge. Considering the basic engineering design concept of Q t < C t for any t, Where Q t is the demand in time t, and C t is the capacity in time t, for the functional reliability of the system. Applying same for a SAPV battery charging system; Q max < C min for any given t, assuming that both the system capacity and the demand vary with time. Using measured and synthetically generated radiation data at site, a sizing curve is derived using the dimensionless parameters C A and C S, calculated using daily energy balance. C S is calculated as a function of the generator over the period of time and thus determining the maximum storage required for the system to operate without shedding load for the minimum generator size. Chart 2.17 shows C A against C S Chart developed for a few selected European Cities (Hermann & Schmida, 2000) 48