F. 1 INTRODUCTION
The following material outlines two approaches used when designing photovoltaic stand-alone systems. Australian Standard AS4509.2, discussed in Chapter 7, is more recent than either and is normally the method to be used by accredited installers in Australia. The first method detailed here was used extensively by Telecom in Australia during its early days of photovoltaics application and represents a very conservative approach in which array size is optimised as a function of battery capacity. The second was developed by Sandia National Laboratories in the USA and is considerably more sophisticated, automatically incorporating many years of accumulated insolation data. Examples of both approaches are provided.
G. 2 STAND-ALONE SYSTEM DESIGN PROCEDURE
The following example deals with the design of a stand-alone PV system for powering a microwave repeater station (based on Mack, 1979).
Step 1—Load determination. A microwave repeater station typically draws 100 W on average and requires voltages in the range 24 ± 5 V. The corresponding average current is therefore 4.17 A.
Step 2—Select battery capacity. For the above load and allowing for 15 days of battery storage, we require a battery capacity of
4.17 A x 24 h x 15 days = 1500 Ah.
Step 3—First approximation of tilt angle. This is based on site information and usually involves selecting a tilt angle 20° greater than the latitude. For example, for Melbourne, which is at latitude 37.8°S, the first approximation for tilt angle is latitude + 20° = 57.8°.
Step 4—Insolation. From available site insolation data, calculate insolation falling on the array at the calculated tilt angle.
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Table G.1. Average monthly readings of direct and diffuse radiation falling on a horizontal plane in Melbourne.
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Example 1—From Table G.1, in January:
S = 629 mWh/cm2 D = 210 mWh/cm2.
Therefore, on a plane tilted at 57.8°, the direct component, from Eqn. 1.21, is
sin (a + 57.8°)
sin a
where
a = 90° – 37.8° – S (from Eqn. 1.6)
S = 23.45° x sin[(15 – 81) x 360 / 365] = -21.3°
given that the day of the year d = 15. Therefore
« = 73.5°
S57.8 = 493 mWh/cm2.
The total insolation (direct + diffuse) falling on the array is therefore
Rp = S57.8 + D
= 703 mWh/cm2.
The assumption is made that D is independent of tilt angle. This is a reasonable approximation provided the tilt angle is not too great.
Example 2—In June
d = 166
d = 23.45° x sin[(166-81) x 3607365]
= 23.3° a = 28.9°
557.8 = 167 x sin(28.9° + 57.8°)/sin(28.9°)
= 345 mWh/cm2 Rp = 424.
Step 5—First approximation of array size
(a) The first approximation for the array size is 5 x 4.17 = 20.9 Ap.
(b) Calculate Ah generated per month, allowing for 10% loss owing to dust coverage. For example, in January: 703 mWh/cm2 x 0.9 x 31 days x 20.9 A / 100 mWcm2 = 4100 Ah.
(c) Calculate the monthly load in Ah, allowing for an additional component of 3% of the battery charge for self-discharge. For example, in January: (4.17 A x 24 h x 31 days) + (0.03 x 1500 Ah) = 3147 Ah, assuming the batteries were initially fully charged.
(d) From the difference between the Ah generated per month (b) and that consumed by the load (c), calculate the state of charge of the batteries at the end of the month.
(e) Repeat (b)-(d) for the other months.
Step 6—Optimising array tilt angle. Retaining the same array size, repeat (4) and (5)(b)-(e) above with small variations in the array tilt angle until the depth-of – discharge of the batteries is minimised. This represents the optimal tilt angle.
Step 7—Optimising array size. Using the optimal tilt angle, by successive approximations, keep repeating (5)(b)-(e) for different array sizes until the maximum depth-of-discharge of the batteries is within the range 50±2%. For example, for 1500 Ah capacity, the maximum depth-of-discharge should be in the range 720-780 Ah.
Step 8—Summarise the design.
