Solar Panel Installation: A Cost-Benefit Analysis

Author: Kris Pasia, Priita Peterson & Victor Donnay

Bryn Mawr College features a course in which students do projects analyzing real-world issues of sustainability. In Fall 2023, one project involved a cost-benefit analysis of installing solar panels on two elementary schools in a nearby school district. We tell the story of that project and detail the estimates and mathematics involved in the analysis.

Note: The information below was created with the assistance of AI.

Level of Mathematics

This project aligns with undergraduate-level applied mathematics, particularly in the domains of:

Mathematical modeling
Financial mathematics
Energy systems analysis
Introductory calculus and algebra

It requires understanding and application of:

Exponential functions (e.g., for calculating Net Present Value and bond amortization)
Basic algebraic manipulations
Spreadsheet modeling
Sensitivity analysis
Use of commercial design and analysis tools (SolarEdge, PVWatts®)

It could also be adapted for advanced high school students (AP level or honors courses), particularly in precalculus or AP Calculus, due to its real-world engagement and data-driven modeling.

Application Areas

The document clearly applies mathematics in several real-world, interdisciplinary domains:

Environmental Sustainability & Energy Policy
- Cost-benefit analysis of solar energy systems
- Impact of federal and state grant programs (e.g., IRA, Solar for Schools)
Economics and Finance
- Bond repayment modeling
- Return on investment, NPV, IRR, LCOE
Public Policy and Education
- Decision-making by school boards
- Educational use of renewable energy installations
Engineering/Architecture
- Design constraints and energy generation forecasts for building rooftops
- Analysis of system capacity, tilt, and azimuth of solar panels

Prerequisites

Students engaging with this project would benefit from prior exposure to:

Algebra (equation solving, functions, units conversion)
Geometry and Trigonometry (angles, area, azimuth, tilt)
Basic Statistics and Data Analysis
Introductory Financial Math (interest rates, time value of money)
Spreadsheet Software (e.g., Excel, Google Sheets for proforma modeling)

Students would also benefit from:

An understanding of energy units (kWh, MWh)
Some exposure to climate science or sustainability concepts

Subject Matter

The article covers the following mathematical content areas:

a. Financial Mathematics

Net Present Value (NPV)
Internal Rate of Return (IRR)
Levelized Cost of Electricity (LCOE)
Capital Recovery (Payback) Period
Sensitivity analysis of key financial variables

b. Mathematical Modeling

Real-life data integration (e.g., utility bills, solar output)
Use of estimation and scenario planning (Optimistic, Middle, Conservative, Mixed)
Application of geometric series to bond repayment models (Appendix)

c. Energy and Environmental Calculations

Carbon offset calculations using CO₂ emission factors
Social cost of carbon using policy-defined metrics ($/ton CO₂)
Use of PVWatts® for simulation and solar production estimation

Correlation to Mathematics Standards

This project aligns strongly with national and state-level mathematics standards including:

a. Common Core State Standards – High School

Functions (F.IF): Interpret functions that arise in applications in terms of the context
Algebra (A.SSE, A.CED): Creating and interpreting equations in real-world contexts
Modeling (★): Use of mathematics and statistics to analyze empirical situations

b. NCTM Process Standards

Problem Solving: Real-world application with community implications
Reasoning and Proof: Justification of financial decisions
Communication: Presentation to school boards and community stakeholders
Connections: Linking math to environmental science, public policy, and education
Representation: Use of graphs, spreadsheets, and modeling tools