Modeling Solar Grid Integration with Math

notoptimizedSolar Energy Integration Lesson


The purpose of this high school level lesson is to introduce the students to the challenges of integrating solar energy to the electricity grid with the use of numerical simulations that run on an excel spreadsheet. More specifically, it is meant to shed light on the advantages (mentioned in the introduction of this document) and on the challenges (challenges 1 and 2 from the introduction) of solar energy.

Download solar-integration-lesson

Download power-simulation spreadsheet (you must enable the Solver addin in Excel and enable macros when it opens)


Solar energy production has seen fast gains in the past few years. The falling cost of photovoltaic (PV) cells and increased political support are major drivers of these gains.

Some of the advantages of solar power are the following:

  1. Cleaner production of energy compared to conventional sources such as natural gas and coal.
  2. Near zero operating costs. Light from the sun is free and maintenance costs are low.optimized

However, despite the attractiveness of solar energy in light of the current environmental and climate crisis, solar energy still has challenges to overcome.  Some of these challenges are:

  1. Solar panels do not produce electricity at night; People use electricity at night. Since the electric grid currently does not have the energy storage capabilities needed to store some of the energy produced during the day and use it to supply energy during the night, we need to find ways to do so.
  2. Investment costs are still relatively high.
  3. Its production is, to some extent, hard to predict. Although we are pretty good at predicting sunrise and sunset, predicting when a cloud is going to cover the sky is hard.


The students will be familiar with the following concepts:

  • Electric load, load profile, and net load
  • Fixed and flexible load
  • Solar power
  • Electricity production costs
  • Optimization

The skills that the students will learn/strengthen are:

  • Interpreting and extracting information from plots and graphs
  • Adjust parameters and run numerical simulations
  • Solve word problems using a numerical simulation package
  • Translate policy into numerical simulations
  • Recognize a small optimization problem

Concepts/ vocabulary

Electrical Grid

An electrical grid is an interconnected network for delivering electricity from suppliers to consumers. It consists of generating stations that produce electrical power, high-voltage transmission lines that carry power from distant sources to demand centers, and distribution lines that connect individual customers.

Electrical load

An electrical load, or simply load, is an electrical component or portion of a circuit that consumes electric power. In electric power circuits examples of loads are appliances and lights.

Load profile

A load profile is the variation in the electrical load versus time. A load profile will vary according to customer type (typical examples include residential, commercial and industrial), temperature and holiday seasons.