This document is aimed at building mathematical models for calculation of the distance between arrays, to farthest avoid shading and reasonably reduce the land usage of PV farms.<\/p>\n
In general, there will be longest south-north shading on the day of the winter solstice. The boundary condition to calculate the south-north (S-N<\/i>) distance between PV arrays used in this document is based on winter solstice. The longest east-west (E-W<\/i>) shading is on the time when the sun is in the east. The users can change the boundary conditions (date and time) depending on local conditions (latitude, land limitation, facing direction, etc.), the formulas are all the same.<\/p>\n
The shading distance calculation is based on date and time boundaries, not based on shading energy losses that may be very complicated. The no-shading distance calculation in this document is only for the distance between PV arrays, not for other surrounding objects, but the formula can also be used to calculate the no-shading distance between the objects and PV arrays. Where shading occurs on the PV array site other calculations are required that are not within the scope of this document. The no-shading distance calculation is based on the northern hemisphere in this document, but all fomulas can also be used for the southern hemisphere.<\/p>\n
The no-shading calculation model is different for fixed PV arrays and PV systems with solar trackers. This document derives mathematical models for both fixed PV arrays and solar trackers.<\/p>\n
For solar trackers, there are 2 different coordination systems: the Ground Horizontal Coordinates (GHC<\/i>) and Equatorial Coordinates (EC<\/i>).<\/p>\n
This document provides land usage calculations of PV farms for the following array types:<\/p>\n
Fixed PV array on flat-land and face to the south<\/p>\n<\/li>\n
Fixed PV array on flat-land and face to non-south direction<\/p>\n<\/li>\n
Fixed PV array on tilted land and face to the south<\/p>\n<\/li>\n
Horizontal E-W<\/i> tracking in Equatorial Coordinates<\/p>\n<\/li>\n Tilted E-W<\/i> tracking in Equatorial Coordinates<\/p>\n<\/li>\n Pole-Axis tracking in Equatorial Coordinates<\/p>\n<\/li>\n Double tracking in Equatorial Coordinates<\/p>\n<\/li>\n Solar Azimuth tracking in ground horizontal coordinates<\/p>\n<\/li>\n Manual solar altitude tracking in ground horizontal coordinates<\/p>\n<\/li>\n Double tracking in ground horizontal coordinates<\/p>\n<\/li>\n<\/ul>\n In the following clauses, the different coordinates systems are introduced and the land usage calculations for different operational models are provided.<\/p>\n Land usage of photovoltaic (PV) farms. Mathematical models and calculation examples<\/b><\/p>\nPDF Catalog<\/h4>\n
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\n PDF Pages<\/th>\n PDF Title<\/th>\n<\/tr>\n \n 2<\/td>\n undefined <\/td>\n<\/tr>\n \n 4<\/td>\n CONTENTS <\/td>\n<\/tr>\n \n 7<\/td>\n FOREWORD <\/td>\n<\/tr>\n \n 9<\/td>\n INTRODUCTION <\/td>\n<\/tr>\n \n 10<\/td>\n 1 Scope <\/td>\n<\/tr>\n \n 11<\/td>\n 2 Normative references
3 Terms and definitions <\/td>\n<\/tr>\n\n 13<\/td>\n 4 Azimuth and hour angle coordinates <\/td>\n<\/tr>\n \n 14<\/td>\n Figures
Figure 1 \u2013 Current definition of azimuth and hour angle coordinates
Figure 2 \u2013 Definition of azimuth and hour angle coordinates for this document <\/td>\n<\/tr>\n\n 15<\/td>\n 5 Coordinate systems (Figures 3 to 6)
5.1 Ground Horizontal Coordinates (GHC)
Figure 3 \u2013 PV array in ground horizontal coordinates <\/td>\n<\/tr>\n\n 16<\/td>\n 5.2 Equatorial Coordinates (EC)
Figure 4 \u2013 PV array in equatorial coordinates
Figure 5 \u2013 Equatorial tracking systems <\/td>\n<\/tr>\n\n 17<\/td>\n 6 Boundary conditions
Figure 6 \u2013 Relationship between A, \u03a9 and \u03c9 <\/td>\n<\/tr>\n\n 18<\/td>\n Tables
Table 1 \u2013 No-shading set time on winter solstice for various latitudes
Table 2 \u2013 Date and time when solar altitude is 20\u00b0 and the sun is in the east <\/td>\n<\/tr>\n\n 19<\/td>\n Table 3 \u2013 Proposed boundary conditions <\/td>\n<\/tr>\n \n 20<\/td>\n 7 Land use calculations for fixed PV arrays on flat land (Figure 7)
7.1 Boundary conditions
7.2 Calculation models for the fixed PV arrays on flat land
Figure 7 \u2013 Fixed PV array on flat land
Figure 8 \u2013 Relationship of solar beam and PV array <\/td>\n<\/tr>\n\n 21<\/td>\n 7.3 Example of land usage for fixed PV arrays on flat land <\/td>\n<\/tr>\n \n 22<\/td>\n 8 Special consideration of non-south direction and sloped land
8.1 General
8.2 Boundary conditions <\/td>\n<\/tr>\n\n 23<\/td>\n 8.3 Calculation models
Figure 9 \u2013 Relationship of solar beam and PV array and the distance between arrays <\/td>\n<\/tr>\n\n 24<\/td>\n 8.4 Example for fixed PV arrays with non-south direction <\/td>\n<\/tr>\n \n 25<\/td>\n 8.5 Example for fixed PV arrays on sloped land <\/td>\n<\/tr>\n \n 26<\/td>\n 9 Land usage for solar altitude tracking in ground horizontal coordinates (Figures 10 and 11)
Figure 10 \u2013 Manual adjusted supporting structure <\/td>\n<\/tr>\n\n 27<\/td>\n 9.1 Boundary conditions
Figure 11 \u2013 Manual adjusted PV array <\/td>\n<\/tr>\n\n 28<\/td>\n Figure 12 \u2013 2 times adjustment rules
Table 4 \u2013 Adjustment rules for solar altitude tracking <\/td>\n<\/tr>\n\n 29<\/td>\n 9.2 Calculation models for solar altitude tracking
9.3 Example of land usage for 4-times adjustment
Figure 13 \u2013 4 times adjustment rules <\/td>\n<\/tr>\n\n 31<\/td>\n 10 Land usage calculation for horizontal E-W tracking in equatorial coordinates (Figure 14)
10.1 Boundary conditions
10.2 Calculation models
Figure 14 \u2013 Horizontal E-W tracking <\/td>\n<\/tr>\n\n 32<\/td>\n 10.3 Example \u2013 Land usage for horizontal E-W tracking
Figure 15 \u2013 Horizontal E-W tracking <\/td>\n<\/tr>\n\n 33<\/td>\n 11 Land usage for pole-axis tracking (Figure 16)
Figure 16 \u2013 Pole-axis tracking <\/td>\n<\/tr>\n\n 34<\/td>\n 11.1 Boundary conditions
11.2 The calculation for E-W distance <\/td>\n<\/tr>\n\n 35<\/td>\n 11.3 The calculation for S-N distance
11.4 Example 1: no-shading distance is set within 75 % day length on winter solstice <\/td>\n<\/tr>\n\n 36<\/td>\n 11.5 Example 2: no-shading period is from 9:00am to 3:00pm on winter solstice <\/td>\n<\/tr>\n \n 37<\/td>\n 11.6 Example 3: Calculation for high-efficiency PV modules <\/td>\n<\/tr>\n \n 38<\/td>\n 11.7 Land usage for pole-axis tracking <\/td>\n<\/tr>\n \n 40<\/td>\n 12 Land usage calculation for double-axis tracking in equatorial coordinates (Figure 17)
12.1 Boundary conditions
12.2 Calculation model for E-W distance
Figure 17 \u2013 Double tracking systems (hour-angle and solar declination) <\/td>\n<\/tr>\n\n 41<\/td>\n 12.3 Caculation for S-N distance <\/td>\n<\/tr>\n \n 42<\/td>\n Figure 18 \u2013 PV array and solar beam for double-axis tracking <\/td>\n<\/tr>\n \n 43<\/td>\n 12.4 Example 1: no-shading distance is set within 75 % day length on winter solstice
12.5 Example 2: no-shading period is from 9:00am to 3:00pm on winter solstice <\/td>\n<\/tr>\n\n 44<\/td>\n 12.6 Land usage for equatorial double-axis tracking <\/td>\n<\/tr>\n \n 45<\/td>\n 13 Land usage calculation for tilted E-W tracking
13.1 Boundary conditions
13.2 Why optimized S-N tilt is equal to 1\/2 latitude
Figure 19 \u2013 Tilted E-W tracking (horizontal main axis) <\/td>\n<\/tr>\n\n 46<\/td>\n 13.3 The calculation model for E-W distance
13.4 Example of E-W distance calculation
Figure 20 \u2013 E-W distance for tilted E-W tracking
Table 5 \u2013 Annual average incidence angle for different latitudes and different tilts <\/td>\n<\/tr>\n\n 47<\/td>\n 13.5 The calculation model for S-N distance <\/td>\n<\/tr>\n \n 48<\/td>\n Figure 21 \u2013 The relationship between PV array and solar beam
Figure 22 \u2013 S-N distance between PV modules <\/td>\n<\/tr>\n\n 49<\/td>\n 13.6 Example of S-N distance calculation
13.7 Land usage of tilted E-W tracking <\/td>\n<\/tr>\n\n 50<\/td>\n 14 Land usage calculation of double-axis tracking in ground horizontal coordinates (Figure 23)
14.1 Boundary conditions
14.2 Calculation model for S-N distance
Figure 23 \u2013 Double axis-tracking in ground gorizontal coordinates <\/td>\n<\/tr>\n\n 51<\/td>\n Figure 24 \u2013 Distance items relevent with no-shading distance calculation <\/td>\n<\/tr>\n \n 52<\/td>\n 14.3 Example 1: calculation for S-N distance at 75 % day-length on winter solstice (Table 6) <\/td>\n<\/tr>\n \n 53<\/td>\n 14.4 Example 2: calculation for S-N distance at 9:00am on winter solstice (Table 7)
Table 6 \u2013 S-N distances calculation at 75 % day length on winter solstice <\/td>\n<\/tr>\n\n 54<\/td>\n 14.5 Example of E-W distance calculation
Table 7 \u2013 S-N distances calculation at 9:00am on winter solstice <\/td>\n<\/tr>\n\n 55<\/td>\n 14.6 Land usage for horizontal double-axis tracking <\/td>\n<\/tr>\n \n 56<\/td>\n 15 Land usage calculation for azimuth tracking in ground horizontal coordinates (Figure 25)
15.1 Boundary conditions
15.2 Calculation model for S-N distance
Figure 25 \u2013 Solar azimuth tracking (fixed PV tilt) <\/td>\n<\/tr>\n\n 57<\/td>\n 15.3 Example 1: calculation for S-N distance at 75 % day-length on winter solstice (Table 8) <\/td>\n<\/tr>\n \n 58<\/td>\n 15.4 Example 2: calculation for S-N distance at 9:00am on winter solstice (Table 9)
Table 8 \u2013 S-N distances calculation for azimuth tracking at 75 % day length <\/td>\n<\/tr>\n\n 59<\/td>\n 15.5 Example of E-W distance calculation
Table 9 \u2013 Distances calculation from the set time to noon time <\/td>\n<\/tr>\n\n 60<\/td>\n 15.6 Land usage for horizontal azimuth tracking <\/td>\n<\/tr>\n \n 61<\/td>\n 16 Array length and width ratio
Figure 26 \u2013 Array configuration for horizontal double tracking <\/td>\n<\/tr>\n\n 62<\/td>\n Table 10 \u2013 Length and width ratio effect for 3 scenarios <\/td>\n<\/tr>\n \n 63<\/td>\n Table 11 \u2013 Summary of 3 scenarios <\/td>\n<\/tr>\n \n 64<\/td>\n 17 Summary of calculation results (Table 12)
Table 12 \u2013 Summary of the calculated results <\/td>\n<\/tr>\n\n 65<\/td>\n 18 Back tracking technology
18.1 General <\/td>\n<\/tr>\n\n 66<\/td>\n 18.2 E-W tracking in equatorial coordinates
Figure 27 \u2013 Back tracking for E-W tracking <\/td>\n<\/tr>\n\n 67<\/td>\n Figure 28 \u2013 No-shading between PV arrays by back tracking technology <\/td>\n<\/tr>\n \n 69<\/td>\n Table 13 \u2013 Back tracking tilt calculation for E-W tracking on winter solstice <\/td>\n<\/tr>\n \n 70<\/td>\n 18.3 Double axis tracking in ground horizontal coordinates
Table 14 \u2013 Back tracking tilt calculation for E-W tracking on spring equinox <\/td>\n<\/tr>\n\n 71<\/td>\n Figure 29 \u2013 Back tracking for horizontal double-axis tracking <\/td>\n<\/tr>\n \n 73<\/td>\n Table 15 \u2013 Back tracking tilt calculation for D-tracking on winter solstice <\/td>\n<\/tr>\n \n 74<\/td>\n Table 16 \u2013 Back tracking tilt calculation for D-tracking on spring equinox <\/td>\n<\/tr>\n \n 75<\/td>\n Annex A (informative)Acronyms and abbreviated terms <\/td>\n<\/tr>\n<\/table>\n","protected":false},"excerpt":{"rendered":" \n\n
\n Published By<\/td>\n Publication Date<\/td>\n Number of Pages<\/td>\n<\/tr>\n \n BSI<\/b><\/a><\/td>\n 2018<\/td>\n 76<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"featured_media":245126,"template":"","meta":{"rank_math_lock_modified_date":false,"ep_exclude_from_search":false},"product_cat":[2641],"product_tag":[],"class_list":{"0":"post-245122","1":"product","2":"type-product","3":"status-publish","4":"has-post-thumbnail","6":"product_cat-bsi","8":"first","9":"instock","10":"sold-individually","11":"shipping-taxable","12":"purchasable","13":"product-type-simple"},"_links":{"self":[{"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/product\/245122","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/product"}],"about":[{"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/types\/product"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/media\/245126"}],"wp:attachment":[{"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/media?parent=245122"}],"wp:term":[{"taxonomy":"product_cat","embeddable":true,"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/product_cat?post=245122"},{"taxonomy":"product_tag","embeddable":true,"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/product_tag?post=245122"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}