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Product No. 99796 Supplementary Print Price: FREE with membership
 

Photovoltaic Systems Off-Grid (UMAP)

Paul Isihara, Joshua Whitmore


Mathematics Topic:
Differential Calculus
Application Areas:
Solar energy
Prerequisites:
Vector calculus and basic electronics as covered in first year physics courses.

| ©2007 by COMAP, Inc. | UMAP Journal 28.1 | 34 pages |



This module introduces photovoltaic systems for use off-grid, including analytical and Mathematica construction of sun path charts, I–V characteristic curves that indicate PV cell output, and graphs showing battery capacity as a function of operating current and temperature.

Table of Contents:

INTRODUCTION

OVERVIEW OF PV SYSTEMS
Facts and Forecasts
How Silicon Solar Cells Work
PV Modules
Balance of System Components
Batteries
Controllers
Inverters

MATHEMATICAL MODELS
Sun Path Charts
Equations for the azimuth and altitude
Determining the hours of daylight
The I–V Characteristic Curve
Formulae governing I–V characteristics
Computation of the maximum power point
Temperature effect
Insolation effect
Battery Capacity

FURTHER DIRECTIONS

APPENDIX A: MATHEMATICA CODE FOR SUN PATH CHARTS

APPENDIX B: MATHEMATICA CODE FOR I–V CHARACTERISTIC CURVES