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New approaches on the optimization of directly coupled PV pumping systems
Solar Energy 77 (2004) 81–93 www.elsevier.com/locate/solener
New approaches on the optimization of directly coupled PV pumping systems Z. Abidin Firatoglu, Bulent Yesilata
*
Department of Mechanical Engineering, Harran University, Sanliurfa 63100, Turkey Received 7 July 2003; received in revised form 4 November 2003; accepted 19 February 2004 Available online 17 March 2004 Communicated by: Associate Editor A. Morales-Acevedo
Abstract We here use a multi-step optimization procedure to improve utilization of a direct-coupled photovoltaic water pumping systems. The algorithm developed here is simple, fast, and has no numerical problems. The solution can be obtained by using available long-term meteorological data for the design-site and manufacturer data for the system components. The main steps in the algorithm are outlined below: (i) The long-term (16 years, between 1985 and 2001) meteorological database on hourly basis for the design site (Sanliurfa, Turkey), provided in electronic format by the National Meteorology Center, is constructed. (ii) The optimal PV array slope is determined by the linear search method. (iii) The optimal solar radiation interval is determined by the utilizability method. (iv) The optimum number of PV panels and their optimal electrical configuration in the array are determined by a nonlinear search method based on a statistical parameter. The results show that better system performance with less PV array area can be obtained by accurate selection of the array configuration. 2004 Elsevier Ltd. All rights reserved. Keywords: PV pump; Directly coupled; Multi-step optimization
1. Introduction Photovoltaic (PV) powered water pumping systems have been one of the most popular solar energy applications in the last two decades. The use of such a system is first appropriate since there is a natural relation-ship between the availability of solar energy and the water requirement. That is; the water requirement increases with increasing solar radiation level. PV systems have
* Corresponding author. Tel.: +90-414-344-00201094; fax: +90-414-344-0031. E-mail addresses: fi[email protected] (Z.A. Firatoglu), [email protected], [email protected] (B. Yesilata).
some distinct advantages in electrical power production such as, being environmentally friendly, requiring no fuel cost, operating with no noise and wear due to absence of moving parts, and also requiring little maintenance. Using PV array to drive water pumping units for irrigation and drinking water in remote areas, where other sources of power not available, are found to be the most feasible and economically viable design configuration (Posorski, 1996). The major barriers of using PV systems, in general, are the high installation costs and low energy conversion efficiency of PV cells available in the market. Significant cost penalties therefore result from oversizing a PV system since the cost is mostly dependent on the PV array area (Landridge et al., 1996). The main object in designing a PV pumping system
0038-092X/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.solener.2004.02.006
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Nomenclature A b1 b2 E H h Hb Hd Ho hs Hsc Ht I I0 Ia IEOP IL IMPP
KM Kp KT Kv L m Mm Mp n
thermal voltage (V) height of the blade at the entrance to the impeller (m) height of the blade at the exit of the impeller (m) motor voltage constant (V) total incident radiation on a horizontal surface (W/m2 ) hour angle (deg) beam radiation on a horizontal surface (W/ m2 ) diffuse sky radiation on a horizontal surface (W/m2 ) extra-terrestrial radiation (W/m2 ) sunset hour angle on a horizontal surface (deg) solar constant (W/m2 ) total incident radiation on a tilted surface (W/m2 ) current (A) dark current (A) motor armature current (A) output current at equilibrium operating point of the PV panel configuration (A) light current (A) output current at the maximum power operating point of the PV panel configuration (A) motor torque constant (V s) pump constant (J s) clearness index motor e.m.f. constant (V/rpm) latitude interval number motor electromagnetic torque (N m) pump torque (N m) day number
(PVPS) is that the required pumping power should be generated by a minimum number of PV panels in order to improve the cost effectiveness (Landridge et al., 1996; Firatoglu and Yesilata, 2001). The PVPS consists of at least three basic components: a PV array, a DC motor, and a pump, as shown schematically in Fig. 1. The PV array generates sufficient electrical power from the sun-light to operate the DC motor, which converts the electrical energy into the mechanical energy and drives the pump. The mechanical energy is then converted into the hydraulic energy by the pump to draw water from the well. This type of arrangement is known as directly coupled photovoltaic
Pm PPV Q R1 R2 Ra Rb Rd Rs Rsh Ta V Va Vm VMPP
VEOP d a x q / b1 b2 g gm gp r
motor shaft power (W) output power of the PV panel configuration (W) volumetric flow rate (m3 /s) radius of the water entrance at the impeller blade (m) radius of the water exit at the impeller blade (m) motor armature resistance beam radiation tilt factor diffuse radiation tilt factor series resistance of the PV panel (X) shunt resistance of the PV panel (X) ambient temperature (C) voltage (V) motor armature voltage (V) operating voltage of motor (V) output voltage at the maximum power operating point of the PV panel configuration (V) output voltage at equilibrium operating point of the PV panel configuration (V) solar declination (deg) panel tilt angle (deg) motor shaft speed (rpm) density (kg/m3 ) utilizability factor blade inclination angle at the impeller entrance (deg) blade inclination angle at the impeller exit (deg) PV-panel efficiency motor efficiency pump efficiency defined statistical parameter for selecting of the optimum PV panel configuration
pumping system (DC-PVPS) since PV array is directly connected to the DC motor-pump. There are two other arrangements of the system currently in common use: (i) battery-buffered photovoltaic pumping system (BBPVPS) where a battery is connected across the PV array and the DC motor, to provide a constant voltage output, even with the absence of the sun, (ii) photovoltaic pumping system with a maximum power point tracker (MPPT) where a DC-DC converter is used to continually match the peak-power point characteristics of a PV array to the input characteristics of a DC motor.
Z.A. Firatoglu, B. Yesilata / Solar Energy 77 (2004) 81–93
83
y rg ne re la So
Hydraulic energy Electrical energy
Mechanical energy DC Motor
Pump
PV array Fig. 1. The schematic of a DC-PVPS.
Each of these three configurations has its own advantages (see Short and Oldach (2003) for excellent discussion of the subject). However, the main disadvantage of two latter configurations is that they require at least one additional electronic component; hence, they are more expensive, more complicated, and less reliable. We here consider a DC-PVPS and present a multistep optimization method for its efficient utilization. The analysis of a DC-PVPS is extremely complex since volumetric rate of pumped water is dependent on many factors, which can be described by highly nonlinear equations. These factors can be classified as meteorological parameters (radiation intensity and ambient temperature) of the site, PV array specifications (I–V output, area, conversion efficiency, and slope), and DC motor-pump-hydraulic system characteristics (I–V output of the motor-pump assembly, static and dynamic head of pipeline). The operating point of a DC-PVPS depends on the current-voltage (I–V ) characteristics of both the motor-pump assembly and the PV array. I–V characteristics of the PV array vary nonlinearly with solar radiation, ambient temperature, and the current drawn by the DC motor. For a given solar radiation and ambient temperature, there is a unique point on I–V curve of PV array at which the electrical power output is maximum. This point is known as maximum power point (MPP), and its curve at various solar radiations and ambient temperatures is aimed to match with operating curve of DC-PVPS (Appelbaum, 1981; Hsiao, 1984; Suehrcke et al., 1997; Firatoglu and Yesilata, 2003a). For most DC motors and pumps, however, operating point of the system at most radiation levels is far from the MPP of the PV array, and only few options are available to the system designer to achieve this optimum matching. One of the options is to use a MPPT, as mentioned above. Using an array tracking system or a specially designed DC motor are the other options to maintain optimum matching at most radiation levels. One of the most feasible method of achieving this however is to determine the best series-parallel configuration of PV panels for the array. Application of the method requires the knowledge of long-term meteorological data for the design site and the technical
specifications of the PV-panel, the DC-motor, and the pump (Firatoglu and Yesilata, 2003b,c). Due to nonlinear nature of the equations, the system can not be described with a single model, and a complex numerical simulation is usually necessary. The simulation sometimes is accompanied with graphical solutions and risky approximations. There is also significant computational cost (Firatoglu and Yesilata, 2003c). We here use a multi-step optimization procedure to improve utilization of the DC-PVPS at selected design parameters. The algorithm developed here is simple, fast, and has no numerical problems. The solution can be obtained by using available meteorological data for the site and manufacturer data for the system components. The main steps in the algorithm are outlined below and described in detail in the next section: (i) The long-term (16 years, between 1985 and 2001) meteorological database on hourly basis for the design site (Sanliurfa, Turkey), provided in electronic format by National Meteorology Center, is constructed. (ii) The optimal PV array slope is determined by the linear search method. (iii) The optimal solar radiation interval is determined by the utilizability method. (iv) The optimum number of PV panels and their optimal electrical configuration in the array are determined by a nonlinear search method based on a statistical parameter.
2. The optimal PV array slope 2.1. Long-term weather data for the design site The long-term weather data is extremely important for accurate design and optimization of PVPS since power output from the PV array strongly depends on solar radiation (H ) and cell/ambient temperature (Ta ). We here averaged 16 years’ weather data measured hour-by-hour between years of 1985–2001 for the design site. The hourly mean values of the measured weather
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data (total solar radiation on horizontal plane and ambient temperature) are shown in Fig. 2(a) and (b). It is apparent that the solar radiation data given in Fig.
2(a) contains both direct and diffuse components, H ¼ Hb þ Hd . We need first to decompose H to its direct (Hb ) and diffuse (Hd ) components in order to determine total radiation on a tilted-surface. This can be done by following a multi-step procedure that is well described in the literature (Duffie and Beckman, 1991; Hay, 1979; Klein, 1977). We start by calculating hourly average clearness index (KT ) with the following formula, KT ¼
H ( W/m2 )
1000
H =H0 ; cosðdÞ cosðLÞ cosðhÞ þ sinðLÞ sinðdÞ
800
where
600
360n : H0 ¼ Hsc 1 þ 0:033 cos 365
400 200 100
In equations above; d, L, and h are respectively declination, latitude and sun-hour angles. Hsc is the solarconstant, n is the number of the days from Jan. 1st. The calculated values of KT for the design-site during the average-year are shown in Fig. 2(c). We next decompose the diffuse component of the monthly average daily solar radiation according to the following empirical equation (Klein, 1977),
150 8
200
hou 12 r
250
d ay
300
16
(a)
20
350
Hd ¼ 1 1:112K T ; H
50 40 30 0
T( C)
ð2Þ
50
4
20 10 0
ð1Þ
50 100 4 8 12
ho ur
200 16
(b)
250 20
150 y da
ð3Þ
where bar over the symbols indicates monthly average daily radiation/clearness index. Since H and K T are known, we are able to determine H d by Eq. (3). The hourly average diffuse radiation can then be calculated as, Hd p cosðhÞ cosðhs Þ ¼ ; ð4Þ 24 sinðhs Þ ð2p=360Þ cosðhs Þ Hd
300 24
350
where hs is sunset hour angle. The other component, hourly average direct radiation, is simply the difference between hourly values of total and diffuse radiations, Hb ¼ H Hd . After decomposition process of total radiation on horizontal surface, calculations for tiltedsurfaces as described below can easily be performed.
1
2.2. Optimal monthly slope
0.8
KT
0.6 0.4 0.2
50 100
4
150 200
8
ho u12 r
(c)
250
d ay
300
16 20
350
Fig. 2. The long-term (16 years) averaged weather data for the design site (Sanliurfa, Turkey): (a) the measured solar radiation on the horizontal plane, (b) the measured ambient temperature, and (c) the calculated clearness index.
In order to achieve full utilization of a DC-PVPS an automatic array-tracking unit should be used. The addition of such a unit results in significantly higher costs, more complex and less reliable system structure. We therefore here propose to use a simple manual tracking system in a way that the slope of the array (a) can be adjusted mechanically only once a month. This type of system can be constructed easily with insignificant cost. This approach has not been considered in previous studies; instead, PV array has been installed as south-faced with a yearly constant optimal slope that is equivalent to the site’s latitude angle. We examined
Z.A. Firatoglu, B. Yesilata / Solar Energy 77 (2004) 81–93
In order to determine monthly optimum slope of the PV array, we used the linear search method: Ht values were calculated by scanning various values of a, between amin ¼ 0 and amax ¼ 90 with increments of 1. The slope at which the largest value of Ht is obtained in the scanned range of a is defined as monthly optimum slope (am ) for the corresponding month. The calculations were made for every month of the year and results are given in Table 1. In Fig. 3, for the case 1 (a ¼ ah ), the hourly slope of PV array is continuously changed by an automatic tracking system whereas in the case 2 (a ¼ am ), the slope is manually adjusted only once for each month to the optimal monthly inclination angle. The slight difference between these two cases remarkably suggests that monthly optimal slope approach is quiet feasible. There are several factors that give maximum positive impact on monthly tracking system. First, the methodology is based on a precise linear searching by using site-specific long-term measured data, rather than taking derivative of Eq. (5) and finding its extremum point. The latter approach could be more useful when measured longterm data is not available. Second, the target is welldetermined: maximizing monthly average daily incident total radiation, whereas a tracking system is designed to maximize only direct component of radiation. Finally, in calculations, we use one-axis tracking mode (rather than two-axis) and hourly mean radiation data (rather than the instantaneous ones) for comparison since these choices are good enough for PV systems. Less similar results between the automatic and the monthly manualtracking modes would be obtained, if we had used the two-axis tracking mode and instantaneous solar radiation data that give maximum positive impact on automatic tracking system. We also note that significant energy loss, especially in summer season, occur in yearly use of the system when PV array is installed with the latitude angle of the site ðay ¼ L ¼ 37 here), which is considered as yearly optimal slope in most solar energy applications (Duffie and Beckman, 1991; Dincßer, 1995).
hourly, monthly, and yearly optimum-slope cases in terms of the daily incident total solar radiation per panel surface and the results are shown in Fig. 3. The PV array is oriented as south-faced in all three cases. Calculations were performed over the full-sunny-period of the month. That is; we considered all days of the month, and determined daily total radiation by summing up hourly values between sun-rise and sun-set. The monthly average daily total radiation was then simply obtained by taking arithmetic mean of daily values, dividing monthly radiation (sum of daily values) by the number of days. The calculation of hourly total radiation on a tilted surface (shown with Ht here) is quiet straightforward with the knowledge of Hb , Hd , and a (Hay, 1979). The corresponding equation, with the negligible reflective component, is Ht ¼ Rb Hb þ Rd Hd ;
ð5Þ
where Rb and Rd are direct and diffuse radiation tilt factors. These factors can be determined by Rb ¼
cosðL aÞ cosðdÞ cosðhÞ þ sinðL aÞ sinðdÞ cosðLÞ cosðdÞ cosðhÞ þ sinðLÞ sinðdÞ
ð6Þ
1 þ cosðaÞ : 2
ð7Þ
and Rd ¼
28 26 24
Ht (MJ/m2 day)
22 20 18 16 14
αh
12
αm
10
αy
85
3. Steady-state model for the DC-PVPS
8 6
2
4
6
8
10
The DC-PVPS consists of a PV array, a DC motor, and a centrifugal pump as shown in Fig. 1. The mathematical models of the each component and the whole system under steady-state conditions are presented below.
12
month
Fig. 3. The daily incident total solar flux for hourly (ah ), monthly (am ), and yearly (ay ) optimal panel slopes.
Table 1 The optimal values of the monthly PV array slope (in degree) for the design-site Months ðam Þopt
1 55
2 48
3 34
4 19
5 5
6 0
7 0
8 14
9 31
10 46
11 55
12 57
86
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3.1. The PV array The PV array is a strongly nonlinear power source, and its I–V characteristics depend on the radiation level and ambient/cell temperature. The operating point of the system (PV array coupled with the pump-motor assembly) changes whenever any of these weather parameters changes. The relationship between current (I)-voltage (V ) output is: V þ IRs V þ IRs I ¼ IL ðHt Þ I0 exp 1 ; ð8Þ A Rsh where IL ðHt Þ is the light current (A) at the operation radiation level of Ht ; I0 is the dark current (A); I is the operation current (A); V is the operation voltage (V ); Rs is the series resistance (X); Rsh is the shunt resistance (X); A is the thermal voltage (V ). The effect of Rsh can be neglected for a single-well constructed area cells. This is proven to be particularly true for single crystalline silicon cells, Rsh Rs , (Kou et al., 1998; Akbaba et al., 1998). The Eq. (8) can then be explicitly written as: V þ IRs 1 : ð9Þ I ¼ IL ðHt Þ I0 exp A The importance of this equation is that the values of the four unknown parameters (IL , I0 , Rs , and A) at the standard test conditions (Ht;ref ¼ 1000 W/m2 and Ta;ref ¼ 25 C) can easily be determined from the manufacturer’s technical data sheet. These four parameters are then corrected accordingly for the solar radiation and ambient temperature valid at operating weather condition (see Kou et al. (1998) for the procedure). The I–V characteristics along with conversion efficiency (g) of the selected PV panel at various solar radiances are determined and shown in Fig. 4. In calculations, the technical data given in Appendix A for the PV panel is
I (A)
3.5
MPP
0.12
1000 W/m2
3
0.1 800 W/m2
2
0.08
600 W/m2
0.06
η
2.5
I(A)
η
1.5 400 W/m2
0.04
200 W/m2
0.02
used. In order to determine operating points of the system, I–V relation described below for motor-pump assembly is also necessary. 3.2. The DC motor (brushless permanent magnet motor) Several types of DC (i.e. brushed and brushsless permanent magnet, variable switch reluctance) and AC motors (synchronous and asynchronous) are available for PVPS (Short and Oldach, 2003). The choice of the motor is dependent on numerous factors including size requirements, efficiency, price, reliability and availability. DC motors are attractive since they can directly be connected to the PV array and provide a simple and an inexpensive system. DC motors are however not suitable for high-power (above 7 kW) applications, where an induction (AC) motor with a DC-AC inverter is a better choice even though inverter requirement introduce additional costs and some energy losses. We here consider a DC motor since our system falls into a moderate power (about 3 kW) rated application. The conventional DC motor is itself complicate, expensive, and has all the common disadvantages associated with the sliding brush contacts and the commutator (Mummadi, 2000; Anis and Metwally, 1994). The use of a brushless-DC motor (BDCM) is found to be more suitable for PVPS to avoid from these disadvantages (Kou et al., 1998). The BDCM has a rotating permanent magnet and stationary armature winding instead of a conventional brush-commutator assembly. Commutation of electric current in the stationary armature is done by an electronic circuit in accordance with the rotor position. Because of the electronic commutation, the brushless permanent magnet DC motor has a high efficiency (see for example Whitfield et al., 1995), high reliability and minimum maintenance requirements. Short and Oldach (2003) however have debated that using the BDCM add no less complexity to the system than using an MPPT. This caution should also be considered in use of a BDCM since it hardly satisfies with the village level operation and maintenance (VLOM) criteria described in Short and Thompson (2003). The basic equations of the BDCM at steady-state operating conditions can be expressed as, Vm ¼ E þ Va ¼ Kv x þ Ia Ra ;
ð10Þ
Mm ¼ Pm =x ¼ KM Ia ;
ð11Þ
gm ¼ Pm =PPV ¼ ðMm x=VIÞ;
ð12Þ
1 0.5 0
0
5
10
15
0
V (V)
Fig. 4. The I–V and g–V characteristics of the selected (AP-50) PV panel at various solar radiances.
where Vm is the applied motor voltage (V ); E is the motor electromotor force (V ); Va is the armature voltage (V ); Kv is the motor voltage constant; x is the motor shaft-
Z.A. Firatoglu, B. Yesilata / Solar Energy 77 (2004) 81–93
speed (rpm); Ia is the motor armature current (A); Ra is the motor armature resistance (X); Pm is the motor shaft power (W ); Mm is the motor electromagnetic torque (N m); KM is the torque constant; and gm is the motor efficiency. 3.3. The pump (the centrifugal type) Pumping schemes driven by DC motors have been the object of many studies and it was concluded that BDCM coupled to a centrifugal pump was the most suitable combination for PVPS (Anis and Metwally, 1994). Centrifugal pumps are also simple and inexpensive, require low maintenance and are available in wide range of flow rates and heads. Hence, a centrifugal pump is considered in this study. Pumps can be characterized by their total head (DH ) and hydraulic power (Pp ) versus flow rate profile (Q). The total head loss consists of a static component and a dynamic component. The dynamic head depends on the flow rate whereas the static head is defined as the vertical distance from the water surface to the point of free discharge. In a PVPS, dynamic head is usually minimized by using larger diameter pipes and main contribution to total head, particularly for small-sized systems, comes from the static head. In this case, the total head is assumed to be constant. We here use this approach and perform calculations for a constant total head of DHref ¼ 10 m (1 bar). The selection of 10 m total/static head might seem not appropriate for nearly 3 kW rated DC motor described in the previous section. Although any selected value of head does not affect accuracy and procedure of the optimisation, it affects the flow-rates of pumped-water. In practical applications, one can use a multiplication factor of DHref =H to convert the flow-rates obtained for DHref to the real value of head, DH . The main difficulty in modeling of a pump is that the pump characteristics, such as the head versus flow, are usually specified by the manufacturer for fixed speeds only. However, in the PVPS pump-speed is not constant, varying with the solar irradiance level. Pump affinity or similarity laws are usually used to obtain the required parameters at various speeds. The method is complicated and subject to errors when it is not applied accordingly. The flow curves supplied by the manufacturer has to be carefully digitized and the extension of the data must be made to the points of equal efficiency. Besides, polynomial approximation is necessary to represent both the pump and pipeline characteristics. Because of these limitations, we here express a relation between the pump torque (Mp ) and pump speed (x) in terms of pump dimensions as suggested by (Braunstein and Kornfeld, 1981), Mp ¼ x2 Kp ;
ð13Þ
87
where the pump torque constant Kp depends on pump geometric parameters as R2 b1 tgb1 : ð14Þ Kp ¼ qR21 2pb1 tgb1 R22 þ 1 b2 tgb2 In the last equation; q is water density, R, b, and b are respectively the radius, height, and inclination angle of the impeller-blade. The subscripts ‘1’ and ‘2’ represent impeller-entrance and impeller-exit. The volumetric rate of pumped water is determined by the following relationship: Q ¼ gp Pm =ðqgDHref Þ;
ð15Þ
where gp is the pump efficiency. 3.4. The operating points of the DC-PVPS The Eq. (9) through (15) can be used to determine operating and MPP points of the system after deciding which PV panel, DC motor and pump are used. The selected components for this study and their technical data obtained from the manufacturer’s technical sheets are given in the Appendix A. By neglecting motor-pump coupling losses, the following equations are valid for the system: Ia ¼ I;
Vm ¼ V
and
Mp ¼ Mm :
ð16Þ
The pump-speed can be related to the current provided by PV array, by combining Eqs. (11) and (13), x ¼ ðKM Ia =Kp Þ1=2 :
ð17Þ
As a result, we have three nonlinear equations of (9), (10) and (17) with three unknowns of V , I, and x. For given solar irradiance (Ht ) and the ambient temperature (Ta ), these three equations can simultaneously be solved. We have used Newton-Raphson method to obtain operating points of the system.
4. Optimal PV array configuration The most critical part of the design in DC-PVPS is the PV array configuration, the number of PV modules connected in series and parallel. The main objective in searching the best configuration is, for given solar radiation, to operate the system at points as close to peak/maximum power points. For an unsuccessful design, even by using the same number of PV modules, the equilibrium operating point (EOP) may be far away from MPP of PV array at all radiation levels, resulting in low or no utilization of the system. The MPP nonlinearly varies with radiation and temperature; it is thus difficult to maintain optimum matching at all radiation levels, except for a specially designed DC motor-pump assembly. For most commercially available DC motors
88
Z.A. Firatoglu, B. Yesilata / Solar Energy 77 (2004) 81–93
Fig. 5. The deviation between MPP and EOP curves of the system (reproduced geometric part on the right is only for discussion purpose).
and pumps, the equilibrium operating points of the system are far from the peak power points at most radiation levels, and full utilization can not be achieved. As an example, we show MPP and EOP curves of our system in Fig. 5. The EOPC approaches to MPPC for only certain range of solar radiation. Since the MPPC has the nonlinear nature and the EOPC is restricted with the selected motor-pump assembly, the full match between these two curves can not be expected. Instead, close match at a selected solar radiation interval can be obtained by changing the PV module numbers and the configuration, provided that matching I–V output to drive the DC motor is satisfied. It is obvious that selection of the solar radiation interval is the site and season dependent. We propose a new approach explained below to optimize PV array configuration. 4.1. Optimal solar radiation interval The utilizability is in general the fraction of collected solar radiation, above a critical radiation level (Ht;crit ); that is, useful energy is produced only for solar radiation levels larger than Ht;crit . This radiation level is called the radiation threshold in PVPS, and pumping operation can not start below this value (Fraidenraich and Vilela, 2000). The threshold of PV pumping system depends on the characteristics of the system components including PV array configuration. After the system starts up, it will pump water at a rate that depends on the intensity of the radiation. Ht;crit is thus an important parameter to adjust system operation time during a certain period. The lower value of Ht;crit results in longer operation-time with the expense of more PV array area, and thus it is not an objective function for an efficient optimization. Ht;crit is also not an appropriate choice to predict the useful power for PVPS since the system behavior is nonlinear. Loxsom and Durongkaverdi (1994) have used a super-
position methodology to determine utilizability for PVPS. They have first divided the non-linear curve to two straight/linear lines to apply utilizability concept and then added contributions of these two regions to recover initial solar radiation interval. We here bring out a new approach to perform utilizability calculations by defining an utilizability-factor (/) that appear to be more appropriate in designing DCPVPS. The main objective here is to find the most-utilizable solar radiation interval for the system. This interval will then be used to optimize PV array configuration in the next section. Since PV panel output varies nonlinearly with solar radiation, the utilizability-factor must then be defined in terms of panel-power-output (or pumped-water-rate). We here consider panel-poweroutput since it eventually linearly affects water-output. The / is defined here as the ratio of monthly peakpower-outputs of the single-panel obtained at selected radiation interval (between Ht;1 and Ht;2 ) to that at all radiation levels (between 0 and Ht;max ), /¼
P MPP jHt;1 6 Ht 6 Ht;2 P MPP j0
:
ð18Þ
Needless to say that the necessary condition here is Ht;1 > Ht;crit since we will use this interval to optimize PV array configuration and we would like our optimization to be effective when the system is in operation. For simplicity in determining the radiation interval, we constructed the radiation bins for each month as seen in Fig. 6(a) and calculated each bin’s utilizability-factor / with Eq. (18). The panel is inclined with the optimal monthly slope presented in the previous section. A bottom limit for the value of / has to be specified to further the calculations, but we, at the moment, do not have any mathematical expression or well-defined criteria to accomplish this. The targeted value of /min is
Z.A. Firatoglu, B. Yesilata / Solar Energy 77 (2004) 81–93
its neighbor bin(s) until /min is exceeded. As an example in Fig. 6(a), for the month of May, the most utilizable radiation bin with / ¼ 0:5 is 700–800 (W/m2 ). When we add its neighbor radiation bin (600–700 W/m2 ), total utilization of these two bins reach to the value of / ¼ 0:716 which is now larger than /min . Hence the solar radiation interval to be used in optimization for the corresponding month is Ht;1 ¼ 600 W/m2 and Ht;2 ¼ 800 W/m2 . The utilizability factors of each radiation bin considered here for the all months of the year are shown in Fig. 6(b) whereas the selected radiation intervals for those months are given in Table 2.
60 AP-50
50
φ (%)
40 30 20 10 0
100 200 300 400 500 600 700 800 900 2
(a)
Ht (W/m )
4.2. Optimal PV array configuration
70 60
40
1
30
3
20 7
0 900
9 700 2
500
Ht (W/m )
nth
5
10
mo
φ (%)
50
(b)
89
11 300
100
Fig. 6. The utilizability of each radiation bin: (a) in May, (b) during the year.
chosen here as 0.7, implying that the system will be optimized to operate near MPP during at least 70% of monthly sunny period. We reached this value by numerical observation: significantly higher (lower) values of /min corresponds to wider (narrower) non-linear optimization region, and both cause in cost-penalty to reach the same power-output obtained in the next section. The choice of /min is strongly site-dependent; and hence calculations of system-outputs for various values of /min may help to reach final decision. Once the value of /min is decided, the next step is to start from the most utilizable radiation bin and then add
The objective in optimizing the configuration of the PV array is to maximize the volumetric rate of the pumped water for each month. We seek here a solution that provides the system to operate at or near to MPP in the selected radiation interval. In mathematical sense, we minimize the area between MPPC and EOPC in this region. For a given solar radiation, a perpendicular triangle area can be formed between MPP and EOP, as seen in Fig. 5 (reproduced geometric part on the right is only for discussion purpose). Each perpendicular edge of the triangle represents the differences in voltage (DV ¼ VMPP VEOP ) and the current (DI ¼ IMPP IEOP ) between these two points. We aim to find a relationship between the area of the triangle and area-difference of two rectangulars that corresponds to the power difference between MPP and EOP. From the Fig. 5, it is obvious that the area of triangle (ab=2) decreases as the difference between two rectangular areas (xb ya) decreases although there may be quiet difference between their magnitudes. Let us write the following relations: IMPP VMPP IEOP VEOP ¼ xb ya;
ð19Þ
ðIMPP IEOP ÞðVMPP IEOP Þ ¼ ab=2:
ð20Þ
For a given (solar radiation and panel configuration) case, we can always use the fact that the short edge of the rectangular is a fraction of the long one. That is x ¼ Na and y ¼ Mb, and thus IMPP VMPP IEOP VEOP ¼ Nab Mab ¼ abðN MÞ:
ð21Þ
The power difference is then obtained multiplying the area of triangle by 2ðN MÞ. Although the
Table 2 The optimal values of the monthly solar radiation interval (W/m2 ) Months Ht;1 Ht;2
1 300–400
2 400–700
3 500–700
4 500–800
5 600–800
6 500–900
Months Ht;1 Ht;2
7 500–800
8 600–800
9 500–800
10 400–700
11 400–600
12 300–500
90
Z.A. Firatoglu, B. Yesilata / Solar Energy 77 (2004) 81–93
proportionality is nonlinear since N ¼ N ðVMPP ; VEOP Þ and M ¼ MðIMPP ; IEOP Þ are not constant over various operating conditions, there exist a monotonic relation. That is; among various operating conditions under comparison, the smallest power difference corresponds to smallest area of the triangle created. As elegantly presented by one of the reviewers, one can also reach the same conclusion by considering MPP on one of the I–V curves plotted in Fig. 4 for various solar radiation levels. Any move away from this point must, by definition, reduce the power output from the panel. Similarly the further away the operating point from the MPP, the greater the area of the triangle created provided that the movement away from the MPP must always be in the same direction. The triangle created by an operating point at a lower voltage than VMPP cannot be compared with a triangle created by increasing the voltage, as the g V (or P V ) curve is not symmetrical about the VMPP line. It may also be worth pointing out that the value ðIMPP IEOP ÞðVMPP VEOP Þ has no physical meaning in itself but is an indicator of how close to the MPP the EOP is, and only has relevance when various EOP curves are compared as explained below. For various possible PV-array configurations, we search minimum value of the triangle-area by defining a statistical array-decision parameter defined as "P r¼
n i¼0 ððIMPP
IEOP Þi ðVMPP VEOP Þi =ðHt;1 þ i DHt Þi Þ2 m
#1=2 ; ð22Þ
where m is the number of scanned values of solar radiation between Ht;1 and Ht;2 (also equal to number of triangles formed in the selected interval). The value of m is equal to ðHt;2 Ht;1 Þ=DHt , where DHt is the solar radiation increment at each step. DHt ¼ 10 W/m2 is found to be good enough to reach an accurate solution. The Eq. (22) resembles root-mean-square (RMS) formula but is not the same. It is indeed a relative measure of power difference, total area of n-triangles formed, between the two curves in a given solar radiation interval. The value of r varies with the PV array configuration (panel numbers and their electrical connection), and the lowest r indicates the best configuration among those under examination. One can also directly use ðIMPP VMPP IEOP VEOP Þ instead of ðIMMP IEOP ÞðVMPP IEOP Þ in r equation and lead to selecting the same configuration with the expense of considerably more
computer time because of an additional multiplication of the nonlinear parameter of 2ðN MÞ. We here examined 43 different possible configurations for the PV array with 48, 50, 54, 60, and 64 individual panels. These panel numbers are decided by considering the nominal power of the DC motor used here. The optimal PV array configuration for each month is determined and the results are given in Table 3. It is remarkable that the configuration of 10 in parallel and 5 in series (10P 5S) is the best for most part of the year and there are only three different configurations to be considered in whole-year-use. The analysis also proves that better system performance with less PV array area (PV modules) can be obtained by accurate selection of the configuration. The system operation characteristics for the three configurations are given in Fig. 7 to illustrate that the best math between MPPC and EOPC is obtained in the selected solar radiation interval (circled region).
5. The pumped water-rate and the performance The final step of the method outlined here is to calculate volumetric rate of the water and the system performance throughout the year. The yearly distribution of the pumped water (calculated with Eq. (15) using by DHref ¼ 10 m) is shown in Fig. 8(a). It is important to note that the flow rate profiles are kept quiet similar for most part of the year, which correspond to (10P 5S) array configuration. The jumps in the flow rate for the months of March and November are due to using more PV modules (60 versus 50), and conversely the low flow rates in January and December are because of using less modules (48 versus 50) at much lower radiation level. It should be noted that our objective in optimizing the configuration here is to maximize the delivered water per PV panel over each month during 1-year period. This can be done if the system operates as near as peak-power points for corresponding solar radiation. Therefore, due to significant variation in solar radiation level in various seasons, pumped-water-rate will vary. We expect however from the methodology presented here to provide insignificant variations in the yearly distribution of the dimensionless system performance as shown in Fig. 8(b). The performance is normalized with the performance that would be obtained if system had operated at MPP for all radiation levels. Hence the dimensionless system
Table 3 The optimal configuration for the PV array Months ðP SÞopt
1 12 4
2 10 5
3 12 5
4 10 5
5 10 5
6 10 5
Months ðP SÞopt
7 10 5
8 10 5
9 10 5
10 10 5
11 12 5
12 12 4
Z.A. Firatoglu, B. Yesilata / Solar Energy 77 (2004) 81–93
40
MPP EOP
2
1000 W/m
35
900 W/m
30
800 W/m
2
900 W/m
25
2
2
800 W/m
2
700 W/m
2
I (A)
I (A)
700 W/m
2
600 W/m
20
20
2
600 W/m
2
15
2
500 W/m
15
500 W/m
2
400 W/m
2
400 W/m
10
2
300 W/m
2
300 W/m
10
2
200 W/m
5
2
200 W/m
5
2
100 W/m
2
100 W/m
0
(a)
0
10
20
MPP EOP
2
1000 W/m
30
2
25
91
30
40 V (V)
50
60
70
0
80
0
10
20
30
40
(b)
40 900 W/m
30
800 W/m
70
80
90 100
MPP EOP
2
1000 W/m
35
50 60 V (V)
2
2
2
700 W/m
I (A)
25
2
600 W/m
20
2
500 W/m
15
400 W/m
10
300 W/m
2
2
2
200 W/m
5
2
100 W/m
0
0
10
20
30
40
(c)
50 60 V (V)
70
80
90 100
Fig. 7. The system operation characteristics for the configurations of: (a) 12P 4S, (b) 10P 5S, and (c) 12P 5S.
performance is gs =gMPP . The 3-D plot impressively show that the system operate close to MPP for most part of the day and year as well. This final illustration can be considered as an indication for success of the optimization procedure outlined and applied here. There are some cautions in interpretations of these results to real-life situations. First of all the methodology is based on long-term monthly averaged data during 1-year period, and thus differences in PV system parameters (numbers of modules and their electrical configurations) and system-outputs (i.e. water-flow-rate) for various months are expected due to differences in incident solar radiation and ambient-temperature for different seasons. Neither connecting/disconnecting various panels nor changing panel configuration may seem practical for users. There is however possibility of using a constant number of panels with a fixed array configuration for a specified time-period. For example, in seasonal use of the system, one can choose to use 10P 5S array configuration for spring, summer, and
even for fall and 12P 4S for winter. In whole-year-use of the system, one can again decide using 10P 5S array configuration. The trade-off is to operate the system further from the peak-power-points for some months than the calculated optimum array configuration. For instance, in yearly use case for this site, the user needs to re-examine the water outputs for the months of January, March, November, and December since in those months the selected 10P 5S array configuration is not the optimum one. There are some cases in real application where theflow rate is far more important than optimum matching of the array to the pump. Even in these cases, pumpedwater-rate will vary during the selected time-period for a fixed array configuration. The array configuration must then be decided to meet minimum daily, monthly, or annual water requirements. The system is designed by considering the worst conditions (i.e. the lowest solar radiation), and excess water obtained at better weather condition is stored for the other needs. Although the
Z.A. Firatoglu, B. Yesilata / Solar Energy 77 (2004) 81–93
Q (lt/s)
92
voltaic water pumping systems. The algorithm developed here includes three new and important approaches that result in a simple, fast, and reasonably accurate solution with no numerical problems. The available long-term meteorological data on hourly basis for the design-site (Sanliurfa, Turkey) and manufacturer data for the system components (given in the Appendix A) are necessary to perform calculations. The proposed three approaches are:
16 12 8 4 0 5
11
7
9
9
(i) calculating the optimal monthly slope by a linear search method from the measured meteorological data; (ii) determining optimal solar radiation interval with the aid of utilizability concept; (iii) selecting the optimal PV array configuration by searching minimum value of a statistical array-decision parameter.
7 13 15
3 17
(a)
19
on
5
th
11
m
hour
1
90
ηeop η mmp(%)
80 70 60 50 11 40
(b)
7
5 9
11
hour
13
3 15
17
19
nth
7 5
mo
30
9
1
Fig. 8. The yearly variation of: (a) the pumped water and (b) the dimensionless system performance.
methodology described here is not based on for a specified minimum water requirement and total head loss, the monthly configurations determined here are still the best ones for the site as long as the amount of monthly pumped water fulfills the need and are consumed in the corresponding month. Alternatively; if there is no specific monthly water-use-profile whilst only the deliveredannually water amount is important, the sum of those found here for each month is also the maximum water to be delivered in a year with the determined optimum array configurations for the site. As mentioned before, in real application, if the total head loss (DH ) is different than the selected value of DHref here, one must then multiply the flow-rates given in Fig. 8(a) by DHref =DH to find the corresponding one.
These approaches appear to be quiet feasible. In application of the first approach, a simple manual tracking system to adjust the PV array-slope, only once in a month, to the optimal monthly slope is necessary. The collected monthly average daily solar radiation remarkably increases with this treatment. We move from the utilizability concept in implementing the second approach that enables us to concentrate on the most effective solar radiation region for the optimization. Hence, we have considered a certain part of the nonlinear curve rather than dealing with the full curve, resulting in less computer load/time and better chance for approaching peak-power points in this interval. In the last approach, defining a statistical parameter that is monotonic function of power difference between peak-power and operation points enables us easy, fast and accurate selection of the optimal array configuration. We have been able to examine 43 different array configurations to reach final decision for each month. The methodology presented here is applicable to any other site in the world as long as long-term weather data is available. Such data are already present for most part of the world. The use of such a substantial weather data may seem a disadvantage for the methodology although the proposed approaches significantly reduce the amount of computation. However, the subject deserves every effort to provide full and efficient utilization since at the present time PV systems still suffer from high installation costs and low efficiencies.
6. Summary and conclusions
Acknowledgements
We here present a multi-step optimization methodology to improve utilization of a direct-coupled photo-
We acknowledge The Scientific Research Committee of Harran University for the financial support (under
Z.A. Firatoglu, B. Yesilata / Solar Energy 77 (2004) 81–93
HUBAK Project# 440) and one of the anonymous reviewers for contributing to clarify many serious points.
Appendix A PV module (AP-50) Standard test conditions (STC) Voc ¼ 21:5 V, Vmmp ¼ 16:7 V, Isc ¼ 3:3; Immp ¼ 3:0 A Cell temperature coefficients Short circuit temperature coefficient ðlIsc Þ ¼ 0:9 mA/C Open circuit temperature coefficient ðlVoc Þ ¼ 0:10 V/C Module features Number of cells in series in one module ðNs Þ ¼ 40 Dimensions (in mm) ¼ 858.0 · 660.0 · 35.0 Transmissivity (s) ¼ 1 (no glass cover) Absorbsivity (a) ¼ 0.8 (single-crystal silicon) DC motor (permanent magnet) Nominal test conditions (NTC) P ¼ 2983 W, V ¼ 115 V, I ¼ 35 A, Ra ¼ 0:17 X
Pompa (centrifugal) z ¼ 5, b1 ¼ 50, b2 ¼ 40, R1 ¼ 0:032 m, R2 ¼ 0:088 m, b1 ¼ 0:012 m, b2 ¼ 0:02 m.
References Akbaba, M., Qamber, I., Kamal, A., 1998. Matching of separately excited DC motors to photovoltaic generators for maximum power output. Solar Energy 63, 375–385. Anis, W.R., Metwally, H.M.B., 1994. Dynamic performance of a directly coupled PV pumping system. Solar Energy 53, 369–377. Appelbaum, J., 1981. Performance analysis of DC motorphotovoltaic converter system-II. Solar Energy 27, 421–431. Braunstein, A., Kornfeld, A., 1981. Analysis of solar powered electric water pumps. Solar Energy 27, 235–240. Dincßer, I., 1995. Optimum tilt angle for solar collectors used in cyprus. Renew. Energy 6, 813–819. Duffie, J.A., Beckman, W.A., 1991. Solar Engineering of Thermal Processes, second ed. Wiley Interscience, New York.
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Firatoglu, Z.A., Yesilata, B., 2001. Investigation of optimum design conditions in PV-powered submersible pumps. J. HVAC Eng., 59–66 (in Turkish). Firatoglu, Z.A., Yesilata, B., 2003a. Investigation of Optimum Design and Operation Conditions for Photovoltaic Systems with MPPT. Dokuz Eyl€ ul University. Science and Engineering J. 1, 13/1–13/10 (in Turkish). Firatoglu, Z.A., Yesilata, B., 2003b. Investigation of operation characteristics for battery-buffered and directly-coupled pv pumping systems. Journal of Yıldız Technical University 2, 1–11 (in Turkish). Firatoglu, Z.A., Yesilata, B., 2003c. Optimization of PV panels coupled with a linear electrical load and investigation of its regional utililization. J. Aeronaut. Space Technol. 1, 65–72 (in Turkish). Fraidenraich, N., Vilela, O.C., 2000. Performance of solar systems with non-linear behavior calculated by the utilizability method: application to PV solar pumps. Solar Energy 69, 131–137. Hay, J.E., 1979. Calculation of monthly mean solar radiation for horizontal and inclined surfaces. Solar Energy 23, 301– 307. Hsiao, Y.R., 1984. Direct coupling of photovoltaic power source to water pumping system. Solar Energy 32, 489–498. Klein, S.A., 1977. Calculation of monthly average insolation on tilted surfaces. Solar Energy 19, 325–329. Kou, S.A., Klein, A., Beckman, W.A., 1998. A method for estimating the long-term performance of direct coupled PV pumping systems. Solar Energy 64, 33–40. Landridge, D.W., Lawrance, W., Wichert, B., 1996. Development of a photo-voltaic pumping system using a brushless D.C. motor and helical rotor pump. Solar Energy 56, 151– 160. Loxsom, F., Durongkaverdi, P., 1994. Estimating the performance of a photovoltaic pumping system. Solar Energy 52, 215–219. Mummadi, V.C., 2000. Steady-state and dynamic performance analysis of PV supplied DC motors fed from intermediate power converter. Solar Energy Mater. Solar Cells 61, 365– 381. Posorski, R., 1996. Photovoltaic water pumps, an attractive tool for rural drinking water supply. Solar Energy 58, 155– 163. Short, T.D., Thompson, P., 2003. Breaking the mould: Solar water pumping-the challenges and the reality. Solar Energy 75, 1–9. Short, T.D., Oldach, R., 2003. Solar powered water pumps: The past, the present-and the future. Solar Energy Eng. 125, 76– 82. Suehrcke, H., Appelbaum, J., Reshef, B., 1997. Modeling a permanent magnet DC motor/centrifugal pump assembly in a photovoltaic energy system. Solar Energy 59, 37– 42. Whitfield, G.R., Bentley, R.W., Burton, J.D., 1995. Increasing the cost effectiveness of small solar photovoltaic pumping systems. Renew. Energy 6, 483–486.
New approaches on the optimization of directly coupled PV pumping systems Z. Abidin Firatoglu, Bulent Yesilata
*
Department of Mechanical Engineering, Harran University, Sanliurfa 63100, Turkey Received 7 July 2003; received in revised form 4 November 2003; accepted 19 February 2004 Available online 17 March 2004 Communicated by: Associate Editor A. Morales-Acevedo
Abstract We here use a multi-step optimization procedure to improve utilization of a direct-coupled photovoltaic water pumping systems. The algorithm developed here is simple, fast, and has no numerical problems. The solution can be obtained by using available long-term meteorological data for the design-site and manufacturer data for the system components. The main steps in the algorithm are outlined below: (i) The long-term (16 years, between 1985 and 2001) meteorological database on hourly basis for the design site (Sanliurfa, Turkey), provided in electronic format by the National Meteorology Center, is constructed. (ii) The optimal PV array slope is determined by the linear search method. (iii) The optimal solar radiation interval is determined by the utilizability method. (iv) The optimum number of PV panels and their optimal electrical configuration in the array are determined by a nonlinear search method based on a statistical parameter. The results show that better system performance with less PV array area can be obtained by accurate selection of the array configuration. 2004 Elsevier Ltd. All rights reserved. Keywords: PV pump; Directly coupled; Multi-step optimization
1. Introduction Photovoltaic (PV) powered water pumping systems have been one of the most popular solar energy applications in the last two decades. The use of such a system is first appropriate since there is a natural relation-ship between the availability of solar energy and the water requirement. That is; the water requirement increases with increasing solar radiation level. PV systems have
* Corresponding author. Tel.: +90-414-344-00201094; fax: +90-414-344-0031. E-mail addresses: fi[email protected] (Z.A. Firatoglu), [email protected], [email protected] (B. Yesilata).
some distinct advantages in electrical power production such as, being environmentally friendly, requiring no fuel cost, operating with no noise and wear due to absence of moving parts, and also requiring little maintenance. Using PV array to drive water pumping units for irrigation and drinking water in remote areas, where other sources of power not available, are found to be the most feasible and economically viable design configuration (Posorski, 1996). The major barriers of using PV systems, in general, are the high installation costs and low energy conversion efficiency of PV cells available in the market. Significant cost penalties therefore result from oversizing a PV system since the cost is mostly dependent on the PV array area (Landridge et al., 1996). The main object in designing a PV pumping system
0038-092X/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.solener.2004.02.006
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Z.A. Firatoglu, B. Yesilata / Solar Energy 77 (2004) 81–93
Nomenclature A b1 b2 E H h Hb Hd Ho hs Hsc Ht I I0 Ia IEOP IL IMPP
KM Kp KT Kv L m Mm Mp n
thermal voltage (V) height of the blade at the entrance to the impeller (m) height of the blade at the exit of the impeller (m) motor voltage constant (V) total incident radiation on a horizontal surface (W/m2 ) hour angle (deg) beam radiation on a horizontal surface (W/ m2 ) diffuse sky radiation on a horizontal surface (W/m2 ) extra-terrestrial radiation (W/m2 ) sunset hour angle on a horizontal surface (deg) solar constant (W/m2 ) total incident radiation on a tilted surface (W/m2 ) current (A) dark current (A) motor armature current (A) output current at equilibrium operating point of the PV panel configuration (A) light current (A) output current at the maximum power operating point of the PV panel configuration (A) motor torque constant (V s) pump constant (J s) clearness index motor e.m.f. constant (V/rpm) latitude interval number motor electromagnetic torque (N m) pump torque (N m) day number
(PVPS) is that the required pumping power should be generated by a minimum number of PV panels in order to improve the cost effectiveness (Landridge et al., 1996; Firatoglu and Yesilata, 2001). The PVPS consists of at least three basic components: a PV array, a DC motor, and a pump, as shown schematically in Fig. 1. The PV array generates sufficient electrical power from the sun-light to operate the DC motor, which converts the electrical energy into the mechanical energy and drives the pump. The mechanical energy is then converted into the hydraulic energy by the pump to draw water from the well. This type of arrangement is known as directly coupled photovoltaic
Pm PPV Q R1 R2 Ra Rb Rd Rs Rsh Ta V Va Vm VMPP
VEOP d a x q / b1 b2 g gm gp r
motor shaft power (W) output power of the PV panel configuration (W) volumetric flow rate (m3 /s) radius of the water entrance at the impeller blade (m) radius of the water exit at the impeller blade (m) motor armature resistance beam radiation tilt factor diffuse radiation tilt factor series resistance of the PV panel (X) shunt resistance of the PV panel (X) ambient temperature (C) voltage (V) motor armature voltage (V) operating voltage of motor (V) output voltage at the maximum power operating point of the PV panel configuration (V) output voltage at equilibrium operating point of the PV panel configuration (V) solar declination (deg) panel tilt angle (deg) motor shaft speed (rpm) density (kg/m3 ) utilizability factor blade inclination angle at the impeller entrance (deg) blade inclination angle at the impeller exit (deg) PV-panel efficiency motor efficiency pump efficiency defined statistical parameter for selecting of the optimum PV panel configuration
pumping system (DC-PVPS) since PV array is directly connected to the DC motor-pump. There are two other arrangements of the system currently in common use: (i) battery-buffered photovoltaic pumping system (BBPVPS) where a battery is connected across the PV array and the DC motor, to provide a constant voltage output, even with the absence of the sun, (ii) photovoltaic pumping system with a maximum power point tracker (MPPT) where a DC-DC converter is used to continually match the peak-power point characteristics of a PV array to the input characteristics of a DC motor.
Z.A. Firatoglu, B. Yesilata / Solar Energy 77 (2004) 81–93
83
y rg ne re la So
Hydraulic energy Electrical energy
Mechanical energy DC Motor
Pump
PV array Fig. 1. The schematic of a DC-PVPS.
Each of these three configurations has its own advantages (see Short and Oldach (2003) for excellent discussion of the subject). However, the main disadvantage of two latter configurations is that they require at least one additional electronic component; hence, they are more expensive, more complicated, and less reliable. We here consider a DC-PVPS and present a multistep optimization method for its efficient utilization. The analysis of a DC-PVPS is extremely complex since volumetric rate of pumped water is dependent on many factors, which can be described by highly nonlinear equations. These factors can be classified as meteorological parameters (radiation intensity and ambient temperature) of the site, PV array specifications (I–V output, area, conversion efficiency, and slope), and DC motor-pump-hydraulic system characteristics (I–V output of the motor-pump assembly, static and dynamic head of pipeline). The operating point of a DC-PVPS depends on the current-voltage (I–V ) characteristics of both the motor-pump assembly and the PV array. I–V characteristics of the PV array vary nonlinearly with solar radiation, ambient temperature, and the current drawn by the DC motor. For a given solar radiation and ambient temperature, there is a unique point on I–V curve of PV array at which the electrical power output is maximum. This point is known as maximum power point (MPP), and its curve at various solar radiations and ambient temperatures is aimed to match with operating curve of DC-PVPS (Appelbaum, 1981; Hsiao, 1984; Suehrcke et al., 1997; Firatoglu and Yesilata, 2003a). For most DC motors and pumps, however, operating point of the system at most radiation levels is far from the MPP of the PV array, and only few options are available to the system designer to achieve this optimum matching. One of the options is to use a MPPT, as mentioned above. Using an array tracking system or a specially designed DC motor are the other options to maintain optimum matching at most radiation levels. One of the most feasible method of achieving this however is to determine the best series-parallel configuration of PV panels for the array. Application of the method requires the knowledge of long-term meteorological data for the design site and the technical
specifications of the PV-panel, the DC-motor, and the pump (Firatoglu and Yesilata, 2003b,c). Due to nonlinear nature of the equations, the system can not be described with a single model, and a complex numerical simulation is usually necessary. The simulation sometimes is accompanied with graphical solutions and risky approximations. There is also significant computational cost (Firatoglu and Yesilata, 2003c). We here use a multi-step optimization procedure to improve utilization of the DC-PVPS at selected design parameters. The algorithm developed here is simple, fast, and has no numerical problems. The solution can be obtained by using available meteorological data for the site and manufacturer data for the system components. The main steps in the algorithm are outlined below and described in detail in the next section: (i) The long-term (16 years, between 1985 and 2001) meteorological database on hourly basis for the design site (Sanliurfa, Turkey), provided in electronic format by National Meteorology Center, is constructed. (ii) The optimal PV array slope is determined by the linear search method. (iii) The optimal solar radiation interval is determined by the utilizability method. (iv) The optimum number of PV panels and their optimal electrical configuration in the array are determined by a nonlinear search method based on a statistical parameter.
2. The optimal PV array slope 2.1. Long-term weather data for the design site The long-term weather data is extremely important for accurate design and optimization of PVPS since power output from the PV array strongly depends on solar radiation (H ) and cell/ambient temperature (Ta ). We here averaged 16 years’ weather data measured hour-by-hour between years of 1985–2001 for the design site. The hourly mean values of the measured weather
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data (total solar radiation on horizontal plane and ambient temperature) are shown in Fig. 2(a) and (b). It is apparent that the solar radiation data given in Fig.
2(a) contains both direct and diffuse components, H ¼ Hb þ Hd . We need first to decompose H to its direct (Hb ) and diffuse (Hd ) components in order to determine total radiation on a tilted-surface. This can be done by following a multi-step procedure that is well described in the literature (Duffie and Beckman, 1991; Hay, 1979; Klein, 1977). We start by calculating hourly average clearness index (KT ) with the following formula, KT ¼
H ( W/m2 )
1000
H =H0 ; cosðdÞ cosðLÞ cosðhÞ þ sinðLÞ sinðdÞ
800
where
600
360n : H0 ¼ Hsc 1 þ 0:033 cos 365
400 200 100
In equations above; d, L, and h are respectively declination, latitude and sun-hour angles. Hsc is the solarconstant, n is the number of the days from Jan. 1st. The calculated values of KT for the design-site during the average-year are shown in Fig. 2(c). We next decompose the diffuse component of the monthly average daily solar radiation according to the following empirical equation (Klein, 1977),
150 8
200
hou 12 r
250
d ay
300
16
(a)
20
350
Hd ¼ 1 1:112K T ; H
50 40 30 0
T( C)
ð2Þ
50
4
20 10 0
ð1Þ
50 100 4 8 12
ho ur
200 16
(b)
250 20
150 y da
ð3Þ
where bar over the symbols indicates monthly average daily radiation/clearness index. Since H and K T are known, we are able to determine H d by Eq. (3). The hourly average diffuse radiation can then be calculated as, Hd p cosðhÞ cosðhs Þ ¼ ; ð4Þ 24 sinðhs Þ ð2p=360Þ cosðhs Þ Hd
300 24
350
where hs is sunset hour angle. The other component, hourly average direct radiation, is simply the difference between hourly values of total and diffuse radiations, Hb ¼ H Hd . After decomposition process of total radiation on horizontal surface, calculations for tiltedsurfaces as described below can easily be performed.
1
2.2. Optimal monthly slope
0.8
KT
0.6 0.4 0.2
50 100
4
150 200
8
ho u12 r
(c)
250
d ay
300
16 20
350
Fig. 2. The long-term (16 years) averaged weather data for the design site (Sanliurfa, Turkey): (a) the measured solar radiation on the horizontal plane, (b) the measured ambient temperature, and (c) the calculated clearness index.
In order to achieve full utilization of a DC-PVPS an automatic array-tracking unit should be used. The addition of such a unit results in significantly higher costs, more complex and less reliable system structure. We therefore here propose to use a simple manual tracking system in a way that the slope of the array (a) can be adjusted mechanically only once a month. This type of system can be constructed easily with insignificant cost. This approach has not been considered in previous studies; instead, PV array has been installed as south-faced with a yearly constant optimal slope that is equivalent to the site’s latitude angle. We examined
Z.A. Firatoglu, B. Yesilata / Solar Energy 77 (2004) 81–93
In order to determine monthly optimum slope of the PV array, we used the linear search method: Ht values were calculated by scanning various values of a, between amin ¼ 0 and amax ¼ 90 with increments of 1. The slope at which the largest value of Ht is obtained in the scanned range of a is defined as monthly optimum slope (am ) for the corresponding month. The calculations were made for every month of the year and results are given in Table 1. In Fig. 3, for the case 1 (a ¼ ah ), the hourly slope of PV array is continuously changed by an automatic tracking system whereas in the case 2 (a ¼ am ), the slope is manually adjusted only once for each month to the optimal monthly inclination angle. The slight difference between these two cases remarkably suggests that monthly optimal slope approach is quiet feasible. There are several factors that give maximum positive impact on monthly tracking system. First, the methodology is based on a precise linear searching by using site-specific long-term measured data, rather than taking derivative of Eq. (5) and finding its extremum point. The latter approach could be more useful when measured longterm data is not available. Second, the target is welldetermined: maximizing monthly average daily incident total radiation, whereas a tracking system is designed to maximize only direct component of radiation. Finally, in calculations, we use one-axis tracking mode (rather than two-axis) and hourly mean radiation data (rather than the instantaneous ones) for comparison since these choices are good enough for PV systems. Less similar results between the automatic and the monthly manualtracking modes would be obtained, if we had used the two-axis tracking mode and instantaneous solar radiation data that give maximum positive impact on automatic tracking system. We also note that significant energy loss, especially in summer season, occur in yearly use of the system when PV array is installed with the latitude angle of the site ðay ¼ L ¼ 37 here), which is considered as yearly optimal slope in most solar energy applications (Duffie and Beckman, 1991; Dincßer, 1995).
hourly, monthly, and yearly optimum-slope cases in terms of the daily incident total solar radiation per panel surface and the results are shown in Fig. 3. The PV array is oriented as south-faced in all three cases. Calculations were performed over the full-sunny-period of the month. That is; we considered all days of the month, and determined daily total radiation by summing up hourly values between sun-rise and sun-set. The monthly average daily total radiation was then simply obtained by taking arithmetic mean of daily values, dividing monthly radiation (sum of daily values) by the number of days. The calculation of hourly total radiation on a tilted surface (shown with Ht here) is quiet straightforward with the knowledge of Hb , Hd , and a (Hay, 1979). The corresponding equation, with the negligible reflective component, is Ht ¼ Rb Hb þ Rd Hd ;
ð5Þ
where Rb and Rd are direct and diffuse radiation tilt factors. These factors can be determined by Rb ¼
cosðL aÞ cosðdÞ cosðhÞ þ sinðL aÞ sinðdÞ cosðLÞ cosðdÞ cosðhÞ þ sinðLÞ sinðdÞ
ð6Þ
1 þ cosðaÞ : 2
ð7Þ
and Rd ¼
28 26 24
Ht (MJ/m2 day)
22 20 18 16 14
αh
12
αm
10
αy
85
3. Steady-state model for the DC-PVPS
8 6
2
4
6
8
10
The DC-PVPS consists of a PV array, a DC motor, and a centrifugal pump as shown in Fig. 1. The mathematical models of the each component and the whole system under steady-state conditions are presented below.
12
month
Fig. 3. The daily incident total solar flux for hourly (ah ), monthly (am ), and yearly (ay ) optimal panel slopes.
Table 1 The optimal values of the monthly PV array slope (in degree) for the design-site Months ðam Þopt
1 55
2 48
3 34
4 19
5 5
6 0
7 0
8 14
9 31
10 46
11 55
12 57
86
Z.A. Firatoglu, B. Yesilata / Solar Energy 77 (2004) 81–93
3.1. The PV array The PV array is a strongly nonlinear power source, and its I–V characteristics depend on the radiation level and ambient/cell temperature. The operating point of the system (PV array coupled with the pump-motor assembly) changes whenever any of these weather parameters changes. The relationship between current (I)-voltage (V ) output is: V þ IRs V þ IRs I ¼ IL ðHt Þ I0 exp 1 ; ð8Þ A Rsh where IL ðHt Þ is the light current (A) at the operation radiation level of Ht ; I0 is the dark current (A); I is the operation current (A); V is the operation voltage (V ); Rs is the series resistance (X); Rsh is the shunt resistance (X); A is the thermal voltage (V ). The effect of Rsh can be neglected for a single-well constructed area cells. This is proven to be particularly true for single crystalline silicon cells, Rsh Rs , (Kou et al., 1998; Akbaba et al., 1998). The Eq. (8) can then be explicitly written as: V þ IRs 1 : ð9Þ I ¼ IL ðHt Þ I0 exp A The importance of this equation is that the values of the four unknown parameters (IL , I0 , Rs , and A) at the standard test conditions (Ht;ref ¼ 1000 W/m2 and Ta;ref ¼ 25 C) can easily be determined from the manufacturer’s technical data sheet. These four parameters are then corrected accordingly for the solar radiation and ambient temperature valid at operating weather condition (see Kou et al. (1998) for the procedure). The I–V characteristics along with conversion efficiency (g) of the selected PV panel at various solar radiances are determined and shown in Fig. 4. In calculations, the technical data given in Appendix A for the PV panel is
I (A)
3.5
MPP
0.12
1000 W/m2
3
0.1 800 W/m2
2
0.08
600 W/m2
0.06
η
2.5
I(A)
η
1.5 400 W/m2
0.04
200 W/m2
0.02
used. In order to determine operating points of the system, I–V relation described below for motor-pump assembly is also necessary. 3.2. The DC motor (brushless permanent magnet motor) Several types of DC (i.e. brushed and brushsless permanent magnet, variable switch reluctance) and AC motors (synchronous and asynchronous) are available for PVPS (Short and Oldach, 2003). The choice of the motor is dependent on numerous factors including size requirements, efficiency, price, reliability and availability. DC motors are attractive since they can directly be connected to the PV array and provide a simple and an inexpensive system. DC motors are however not suitable for high-power (above 7 kW) applications, where an induction (AC) motor with a DC-AC inverter is a better choice even though inverter requirement introduce additional costs and some energy losses. We here consider a DC motor since our system falls into a moderate power (about 3 kW) rated application. The conventional DC motor is itself complicate, expensive, and has all the common disadvantages associated with the sliding brush contacts and the commutator (Mummadi, 2000; Anis and Metwally, 1994). The use of a brushless-DC motor (BDCM) is found to be more suitable for PVPS to avoid from these disadvantages (Kou et al., 1998). The BDCM has a rotating permanent magnet and stationary armature winding instead of a conventional brush-commutator assembly. Commutation of electric current in the stationary armature is done by an electronic circuit in accordance with the rotor position. Because of the electronic commutation, the brushless permanent magnet DC motor has a high efficiency (see for example Whitfield et al., 1995), high reliability and minimum maintenance requirements. Short and Oldach (2003) however have debated that using the BDCM add no less complexity to the system than using an MPPT. This caution should also be considered in use of a BDCM since it hardly satisfies with the village level operation and maintenance (VLOM) criteria described in Short and Thompson (2003). The basic equations of the BDCM at steady-state operating conditions can be expressed as, Vm ¼ E þ Va ¼ Kv x þ Ia Ra ;
ð10Þ
Mm ¼ Pm =x ¼ KM Ia ;
ð11Þ
gm ¼ Pm =PPV ¼ ðMm x=VIÞ;
ð12Þ
1 0.5 0
0
5
10
15
0
V (V)
Fig. 4. The I–V and g–V characteristics of the selected (AP-50) PV panel at various solar radiances.
where Vm is the applied motor voltage (V ); E is the motor electromotor force (V ); Va is the armature voltage (V ); Kv is the motor voltage constant; x is the motor shaft-
Z.A. Firatoglu, B. Yesilata / Solar Energy 77 (2004) 81–93
speed (rpm); Ia is the motor armature current (A); Ra is the motor armature resistance (X); Pm is the motor shaft power (W ); Mm is the motor electromagnetic torque (N m); KM is the torque constant; and gm is the motor efficiency. 3.3. The pump (the centrifugal type) Pumping schemes driven by DC motors have been the object of many studies and it was concluded that BDCM coupled to a centrifugal pump was the most suitable combination for PVPS (Anis and Metwally, 1994). Centrifugal pumps are also simple and inexpensive, require low maintenance and are available in wide range of flow rates and heads. Hence, a centrifugal pump is considered in this study. Pumps can be characterized by their total head (DH ) and hydraulic power (Pp ) versus flow rate profile (Q). The total head loss consists of a static component and a dynamic component. The dynamic head depends on the flow rate whereas the static head is defined as the vertical distance from the water surface to the point of free discharge. In a PVPS, dynamic head is usually minimized by using larger diameter pipes and main contribution to total head, particularly for small-sized systems, comes from the static head. In this case, the total head is assumed to be constant. We here use this approach and perform calculations for a constant total head of DHref ¼ 10 m (1 bar). The selection of 10 m total/static head might seem not appropriate for nearly 3 kW rated DC motor described in the previous section. Although any selected value of head does not affect accuracy and procedure of the optimisation, it affects the flow-rates of pumped-water. In practical applications, one can use a multiplication factor of DHref =H to convert the flow-rates obtained for DHref to the real value of head, DH . The main difficulty in modeling of a pump is that the pump characteristics, such as the head versus flow, are usually specified by the manufacturer for fixed speeds only. However, in the PVPS pump-speed is not constant, varying with the solar irradiance level. Pump affinity or similarity laws are usually used to obtain the required parameters at various speeds. The method is complicated and subject to errors when it is not applied accordingly. The flow curves supplied by the manufacturer has to be carefully digitized and the extension of the data must be made to the points of equal efficiency. Besides, polynomial approximation is necessary to represent both the pump and pipeline characteristics. Because of these limitations, we here express a relation between the pump torque (Mp ) and pump speed (x) in terms of pump dimensions as suggested by (Braunstein and Kornfeld, 1981), Mp ¼ x2 Kp ;
ð13Þ
87
where the pump torque constant Kp depends on pump geometric parameters as R2 b1 tgb1 : ð14Þ Kp ¼ qR21 2pb1 tgb1 R22 þ 1 b2 tgb2 In the last equation; q is water density, R, b, and b are respectively the radius, height, and inclination angle of the impeller-blade. The subscripts ‘1’ and ‘2’ represent impeller-entrance and impeller-exit. The volumetric rate of pumped water is determined by the following relationship: Q ¼ gp Pm =ðqgDHref Þ;
ð15Þ
where gp is the pump efficiency. 3.4. The operating points of the DC-PVPS The Eq. (9) through (15) can be used to determine operating and MPP points of the system after deciding which PV panel, DC motor and pump are used. The selected components for this study and their technical data obtained from the manufacturer’s technical sheets are given in the Appendix A. By neglecting motor-pump coupling losses, the following equations are valid for the system: Ia ¼ I;
Vm ¼ V
and
Mp ¼ Mm :
ð16Þ
The pump-speed can be related to the current provided by PV array, by combining Eqs. (11) and (13), x ¼ ðKM Ia =Kp Þ1=2 :
ð17Þ
As a result, we have three nonlinear equations of (9), (10) and (17) with three unknowns of V , I, and x. For given solar irradiance (Ht ) and the ambient temperature (Ta ), these three equations can simultaneously be solved. We have used Newton-Raphson method to obtain operating points of the system.
4. Optimal PV array configuration The most critical part of the design in DC-PVPS is the PV array configuration, the number of PV modules connected in series and parallel. The main objective in searching the best configuration is, for given solar radiation, to operate the system at points as close to peak/maximum power points. For an unsuccessful design, even by using the same number of PV modules, the equilibrium operating point (EOP) may be far away from MPP of PV array at all radiation levels, resulting in low or no utilization of the system. The MPP nonlinearly varies with radiation and temperature; it is thus difficult to maintain optimum matching at all radiation levels, except for a specially designed DC motor-pump assembly. For most commercially available DC motors
88
Z.A. Firatoglu, B. Yesilata / Solar Energy 77 (2004) 81–93
Fig. 5. The deviation between MPP and EOP curves of the system (reproduced geometric part on the right is only for discussion purpose).
and pumps, the equilibrium operating points of the system are far from the peak power points at most radiation levels, and full utilization can not be achieved. As an example, we show MPP and EOP curves of our system in Fig. 5. The EOPC approaches to MPPC for only certain range of solar radiation. Since the MPPC has the nonlinear nature and the EOPC is restricted with the selected motor-pump assembly, the full match between these two curves can not be expected. Instead, close match at a selected solar radiation interval can be obtained by changing the PV module numbers and the configuration, provided that matching I–V output to drive the DC motor is satisfied. It is obvious that selection of the solar radiation interval is the site and season dependent. We propose a new approach explained below to optimize PV array configuration. 4.1. Optimal solar radiation interval The utilizability is in general the fraction of collected solar radiation, above a critical radiation level (Ht;crit ); that is, useful energy is produced only for solar radiation levels larger than Ht;crit . This radiation level is called the radiation threshold in PVPS, and pumping operation can not start below this value (Fraidenraich and Vilela, 2000). The threshold of PV pumping system depends on the characteristics of the system components including PV array configuration. After the system starts up, it will pump water at a rate that depends on the intensity of the radiation. Ht;crit is thus an important parameter to adjust system operation time during a certain period. The lower value of Ht;crit results in longer operation-time with the expense of more PV array area, and thus it is not an objective function for an efficient optimization. Ht;crit is also not an appropriate choice to predict the useful power for PVPS since the system behavior is nonlinear. Loxsom and Durongkaverdi (1994) have used a super-
position methodology to determine utilizability for PVPS. They have first divided the non-linear curve to two straight/linear lines to apply utilizability concept and then added contributions of these two regions to recover initial solar radiation interval. We here bring out a new approach to perform utilizability calculations by defining an utilizability-factor (/) that appear to be more appropriate in designing DCPVPS. The main objective here is to find the most-utilizable solar radiation interval for the system. This interval will then be used to optimize PV array configuration in the next section. Since PV panel output varies nonlinearly with solar radiation, the utilizability-factor must then be defined in terms of panel-power-output (or pumped-water-rate). We here consider panel-poweroutput since it eventually linearly affects water-output. The / is defined here as the ratio of monthly peakpower-outputs of the single-panel obtained at selected radiation interval (between Ht;1 and Ht;2 ) to that at all radiation levels (between 0 and Ht;max ), /¼
P MPP jHt;1 6 Ht 6 Ht;2 P MPP j0
:
ð18Þ
Needless to say that the necessary condition here is Ht;1 > Ht;crit since we will use this interval to optimize PV array configuration and we would like our optimization to be effective when the system is in operation. For simplicity in determining the radiation interval, we constructed the radiation bins for each month as seen in Fig. 6(a) and calculated each bin’s utilizability-factor / with Eq. (18). The panel is inclined with the optimal monthly slope presented in the previous section. A bottom limit for the value of / has to be specified to further the calculations, but we, at the moment, do not have any mathematical expression or well-defined criteria to accomplish this. The targeted value of /min is
Z.A. Firatoglu, B. Yesilata / Solar Energy 77 (2004) 81–93
its neighbor bin(s) until /min is exceeded. As an example in Fig. 6(a), for the month of May, the most utilizable radiation bin with / ¼ 0:5 is 700–800 (W/m2 ). When we add its neighbor radiation bin (600–700 W/m2 ), total utilization of these two bins reach to the value of / ¼ 0:716 which is now larger than /min . Hence the solar radiation interval to be used in optimization for the corresponding month is Ht;1 ¼ 600 W/m2 and Ht;2 ¼ 800 W/m2 . The utilizability factors of each radiation bin considered here for the all months of the year are shown in Fig. 6(b) whereas the selected radiation intervals for those months are given in Table 2.
60 AP-50
50
φ (%)
40 30 20 10 0
100 200 300 400 500 600 700 800 900 2
(a)
Ht (W/m )
4.2. Optimal PV array configuration
70 60
40
1
30
3
20 7
0 900
9 700 2
500
Ht (W/m )
nth
5
10
mo
φ (%)
50
(b)
89
11 300
100
Fig. 6. The utilizability of each radiation bin: (a) in May, (b) during the year.
chosen here as 0.7, implying that the system will be optimized to operate near MPP during at least 70% of monthly sunny period. We reached this value by numerical observation: significantly higher (lower) values of /min corresponds to wider (narrower) non-linear optimization region, and both cause in cost-penalty to reach the same power-output obtained in the next section. The choice of /min is strongly site-dependent; and hence calculations of system-outputs for various values of /min may help to reach final decision. Once the value of /min is decided, the next step is to start from the most utilizable radiation bin and then add
The objective in optimizing the configuration of the PV array is to maximize the volumetric rate of the pumped water for each month. We seek here a solution that provides the system to operate at or near to MPP in the selected radiation interval. In mathematical sense, we minimize the area between MPPC and EOPC in this region. For a given solar radiation, a perpendicular triangle area can be formed between MPP and EOP, as seen in Fig. 5 (reproduced geometric part on the right is only for discussion purpose). Each perpendicular edge of the triangle represents the differences in voltage (DV ¼ VMPP VEOP ) and the current (DI ¼ IMPP IEOP ) between these two points. We aim to find a relationship between the area of the triangle and area-difference of two rectangulars that corresponds to the power difference between MPP and EOP. From the Fig. 5, it is obvious that the area of triangle (ab=2) decreases as the difference between two rectangular areas (xb ya) decreases although there may be quiet difference between their magnitudes. Let us write the following relations: IMPP VMPP IEOP VEOP ¼ xb ya;
ð19Þ
ðIMPP IEOP ÞðVMPP IEOP Þ ¼ ab=2:
ð20Þ
For a given (solar radiation and panel configuration) case, we can always use the fact that the short edge of the rectangular is a fraction of the long one. That is x ¼ Na and y ¼ Mb, and thus IMPP VMPP IEOP VEOP ¼ Nab Mab ¼ abðN MÞ:
ð21Þ
The power difference is then obtained multiplying the area of triangle by 2ðN MÞ. Although the
Table 2 The optimal values of the monthly solar radiation interval (W/m2 ) Months Ht;1 Ht;2
1 300–400
2 400–700
3 500–700
4 500–800
5 600–800
6 500–900
Months Ht;1 Ht;2
7 500–800
8 600–800
9 500–800
10 400–700
11 400–600
12 300–500
90
Z.A. Firatoglu, B. Yesilata / Solar Energy 77 (2004) 81–93
proportionality is nonlinear since N ¼ N ðVMPP ; VEOP Þ and M ¼ MðIMPP ; IEOP Þ are not constant over various operating conditions, there exist a monotonic relation. That is; among various operating conditions under comparison, the smallest power difference corresponds to smallest area of the triangle created. As elegantly presented by one of the reviewers, one can also reach the same conclusion by considering MPP on one of the I–V curves plotted in Fig. 4 for various solar radiation levels. Any move away from this point must, by definition, reduce the power output from the panel. Similarly the further away the operating point from the MPP, the greater the area of the triangle created provided that the movement away from the MPP must always be in the same direction. The triangle created by an operating point at a lower voltage than VMPP cannot be compared with a triangle created by increasing the voltage, as the g V (or P V ) curve is not symmetrical about the VMPP line. It may also be worth pointing out that the value ðIMPP IEOP ÞðVMPP VEOP Þ has no physical meaning in itself but is an indicator of how close to the MPP the EOP is, and only has relevance when various EOP curves are compared as explained below. For various possible PV-array configurations, we search minimum value of the triangle-area by defining a statistical array-decision parameter defined as "P r¼
n i¼0 ððIMPP
IEOP Þi ðVMPP VEOP Þi =ðHt;1 þ i DHt Þi Þ2 m
#1=2 ; ð22Þ
where m is the number of scanned values of solar radiation between Ht;1 and Ht;2 (also equal to number of triangles formed in the selected interval). The value of m is equal to ðHt;2 Ht;1 Þ=DHt , where DHt is the solar radiation increment at each step. DHt ¼ 10 W/m2 is found to be good enough to reach an accurate solution. The Eq. (22) resembles root-mean-square (RMS) formula but is not the same. It is indeed a relative measure of power difference, total area of n-triangles formed, between the two curves in a given solar radiation interval. The value of r varies with the PV array configuration (panel numbers and their electrical connection), and the lowest r indicates the best configuration among those under examination. One can also directly use ðIMPP VMPP IEOP VEOP Þ instead of ðIMMP IEOP ÞðVMPP IEOP Þ in r equation and lead to selecting the same configuration with the expense of considerably more
computer time because of an additional multiplication of the nonlinear parameter of 2ðN MÞ. We here examined 43 different possible configurations for the PV array with 48, 50, 54, 60, and 64 individual panels. These panel numbers are decided by considering the nominal power of the DC motor used here. The optimal PV array configuration for each month is determined and the results are given in Table 3. It is remarkable that the configuration of 10 in parallel and 5 in series (10P 5S) is the best for most part of the year and there are only three different configurations to be considered in whole-year-use. The analysis also proves that better system performance with less PV array area (PV modules) can be obtained by accurate selection of the configuration. The system operation characteristics for the three configurations are given in Fig. 7 to illustrate that the best math between MPPC and EOPC is obtained in the selected solar radiation interval (circled region).
5. The pumped water-rate and the performance The final step of the method outlined here is to calculate volumetric rate of the water and the system performance throughout the year. The yearly distribution of the pumped water (calculated with Eq. (15) using by DHref ¼ 10 m) is shown in Fig. 8(a). It is important to note that the flow rate profiles are kept quiet similar for most part of the year, which correspond to (10P 5S) array configuration. The jumps in the flow rate for the months of March and November are due to using more PV modules (60 versus 50), and conversely the low flow rates in January and December are because of using less modules (48 versus 50) at much lower radiation level. It should be noted that our objective in optimizing the configuration here is to maximize the delivered water per PV panel over each month during 1-year period. This can be done if the system operates as near as peak-power points for corresponding solar radiation. Therefore, due to significant variation in solar radiation level in various seasons, pumped-water-rate will vary. We expect however from the methodology presented here to provide insignificant variations in the yearly distribution of the dimensionless system performance as shown in Fig. 8(b). The performance is normalized with the performance that would be obtained if system had operated at MPP for all radiation levels. Hence the dimensionless system
Table 3 The optimal configuration for the PV array Months ðP SÞopt
1 12 4
2 10 5
3 12 5
4 10 5
5 10 5
6 10 5
Months ðP SÞopt
7 10 5
8 10 5
9 10 5
10 10 5
11 12 5
12 12 4
Z.A. Firatoglu, B. Yesilata / Solar Energy 77 (2004) 81–93
40
MPP EOP
2
1000 W/m
35
900 W/m
30
800 W/m
2
900 W/m
25
2
2
800 W/m
2
700 W/m
2
I (A)
I (A)
700 W/m
2
600 W/m
20
20
2
600 W/m
2
15
2
500 W/m
15
500 W/m
2
400 W/m
2
400 W/m
10
2
300 W/m
2
300 W/m
10
2
200 W/m
5
2
200 W/m
5
2
100 W/m
2
100 W/m
0
(a)
0
10
20
MPP EOP
2
1000 W/m
30
2
25
91
30
40 V (V)
50
60
70
0
80
0
10
20
30
40
(b)
40 900 W/m
30
800 W/m
70
80
90 100
MPP EOP
2
1000 W/m
35
50 60 V (V)
2
2
2
700 W/m
I (A)
25
2
600 W/m
20
2
500 W/m
15
400 W/m
10
300 W/m
2
2
2
200 W/m
5
2
100 W/m
0
0
10
20
30
40
(c)
50 60 V (V)
70
80
90 100
Fig. 7. The system operation characteristics for the configurations of: (a) 12P 4S, (b) 10P 5S, and (c) 12P 5S.
performance is gs =gMPP . The 3-D plot impressively show that the system operate close to MPP for most part of the day and year as well. This final illustration can be considered as an indication for success of the optimization procedure outlined and applied here. There are some cautions in interpretations of these results to real-life situations. First of all the methodology is based on long-term monthly averaged data during 1-year period, and thus differences in PV system parameters (numbers of modules and their electrical configurations) and system-outputs (i.e. water-flow-rate) for various months are expected due to differences in incident solar radiation and ambient-temperature for different seasons. Neither connecting/disconnecting various panels nor changing panel configuration may seem practical for users. There is however possibility of using a constant number of panels with a fixed array configuration for a specified time-period. For example, in seasonal use of the system, one can choose to use 10P 5S array configuration for spring, summer, and
even for fall and 12P 4S for winter. In whole-year-use of the system, one can again decide using 10P 5S array configuration. The trade-off is to operate the system further from the peak-power-points for some months than the calculated optimum array configuration. For instance, in yearly use case for this site, the user needs to re-examine the water outputs for the months of January, March, November, and December since in those months the selected 10P 5S array configuration is not the optimum one. There are some cases in real application where theflow rate is far more important than optimum matching of the array to the pump. Even in these cases, pumpedwater-rate will vary during the selected time-period for a fixed array configuration. The array configuration must then be decided to meet minimum daily, monthly, or annual water requirements. The system is designed by considering the worst conditions (i.e. the lowest solar radiation), and excess water obtained at better weather condition is stored for the other needs. Although the
Z.A. Firatoglu, B. Yesilata / Solar Energy 77 (2004) 81–93
Q (lt/s)
92
voltaic water pumping systems. The algorithm developed here includes three new and important approaches that result in a simple, fast, and reasonably accurate solution with no numerical problems. The available long-term meteorological data on hourly basis for the design-site (Sanliurfa, Turkey) and manufacturer data for the system components (given in the Appendix A) are necessary to perform calculations. The proposed three approaches are:
16 12 8 4 0 5
11
7
9
9
(i) calculating the optimal monthly slope by a linear search method from the measured meteorological data; (ii) determining optimal solar radiation interval with the aid of utilizability concept; (iii) selecting the optimal PV array configuration by searching minimum value of a statistical array-decision parameter.
7 13 15
3 17
(a)
19
on
5
th
11
m
hour
1
90
ηeop η mmp(%)
80 70 60 50 11 40
(b)
7
5 9
11
hour
13
3 15
17
19
nth
7 5
mo
30
9
1
Fig. 8. The yearly variation of: (a) the pumped water and (b) the dimensionless system performance.
methodology described here is not based on for a specified minimum water requirement and total head loss, the monthly configurations determined here are still the best ones for the site as long as the amount of monthly pumped water fulfills the need and are consumed in the corresponding month. Alternatively; if there is no specific monthly water-use-profile whilst only the deliveredannually water amount is important, the sum of those found here for each month is also the maximum water to be delivered in a year with the determined optimum array configurations for the site. As mentioned before, in real application, if the total head loss (DH ) is different than the selected value of DHref here, one must then multiply the flow-rates given in Fig. 8(a) by DHref =DH to find the corresponding one.
These approaches appear to be quiet feasible. In application of the first approach, a simple manual tracking system to adjust the PV array-slope, only once in a month, to the optimal monthly slope is necessary. The collected monthly average daily solar radiation remarkably increases with this treatment. We move from the utilizability concept in implementing the second approach that enables us to concentrate on the most effective solar radiation region for the optimization. Hence, we have considered a certain part of the nonlinear curve rather than dealing with the full curve, resulting in less computer load/time and better chance for approaching peak-power points in this interval. In the last approach, defining a statistical parameter that is monotonic function of power difference between peak-power and operation points enables us easy, fast and accurate selection of the optimal array configuration. We have been able to examine 43 different array configurations to reach final decision for each month. The methodology presented here is applicable to any other site in the world as long as long-term weather data is available. Such data are already present for most part of the world. The use of such a substantial weather data may seem a disadvantage for the methodology although the proposed approaches significantly reduce the amount of computation. However, the subject deserves every effort to provide full and efficient utilization since at the present time PV systems still suffer from high installation costs and low efficiencies.
6. Summary and conclusions
Acknowledgements
We here present a multi-step optimization methodology to improve utilization of a direct-coupled photo-
We acknowledge The Scientific Research Committee of Harran University for the financial support (under
Z.A. Firatoglu, B. Yesilata / Solar Energy 77 (2004) 81–93
HUBAK Project# 440) and one of the anonymous reviewers for contributing to clarify many serious points.
Appendix A PV module (AP-50) Standard test conditions (STC) Voc ¼ 21:5 V, Vmmp ¼ 16:7 V, Isc ¼ 3:3; Immp ¼ 3:0 A Cell temperature coefficients Short circuit temperature coefficient ðlIsc Þ ¼ 0:9 mA/C Open circuit temperature coefficient ðlVoc Þ ¼ 0:10 V/C Module features Number of cells in series in one module ðNs Þ ¼ 40 Dimensions (in mm) ¼ 858.0 · 660.0 · 35.0 Transmissivity (s) ¼ 1 (no glass cover) Absorbsivity (a) ¼ 0.8 (single-crystal silicon) DC motor (permanent magnet) Nominal test conditions (NTC) P ¼ 2983 W, V ¼ 115 V, I ¼ 35 A, Ra ¼ 0:17 X
Pompa (centrifugal) z ¼ 5, b1 ¼ 50, b2 ¼ 40, R1 ¼ 0:032 m, R2 ¼ 0:088 m, b1 ¼ 0:012 m, b2 ¼ 0:02 m.
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