CHAPTER 5
Mathematical Challenges in Energy Sustainability
Chapter 5 examines Energy as an in-depth case study that touches on the
themes in the other four chapters. The energy system needs a radical
transformation, fast, and so does the relation of human activity to energy. This
chapter discusses how mathematical scientists can help us address this huge
challenge.
In the early morning hours of Feb. 2, 2011, temperatures across Texasplummeted into the teens. As people climbed out of bed into their chilly houses,
they simultaneously reached to turn up their electric heaters. Power drained out
of the grid, creating a spike in demand so sudden that the power generators
couldn’t ramp up their production fast enough. Lights dimmed as operators were
forced to drop the voltages for short periods in order to prevent major blackouts.
Worse, the computers that controlled traffic systems, elevator banks and
manufacturing plants couldn’t operate at the lower voltage and failed.
Speculators were reported to have taken advantage of the chaos to charge
$2,000 per megawatt-hour, when the price averages around $50.
The power grid these days is remarkably robust, and such events are rare.But as we push to increase the use of renewable energy with thousands of wind
turbines and millions of solar panels on the roofs of homes and businesses,
avoiding such events is going to become harder and harder. Each time the wind
drops, the power pumping out of wind turbines falls, and if that happens
dramatically and unexpectedly, the grid may not be able to compensate. Utilities
are going to have to manage power grids with a level of uncertainty that has not
been faced since electricity was first harnessed.
The basic problem is that electric power can’t be stored on an industrialscale. It must be made in the exact quantity that users consume it, which varies
unpredictably. Furthermore, turning power plants on or off is often expensive and
can’t be done on a moment’s notice. The power produced by wind turbines varies
as unpredictably as, well, the wind. A given power line can only carry so much
electricity. Utilities and grid operators need to manage energy generators,
anticipate customer needs and balance energy resources under uncertainty from
supplies, prices, customer requirements and equipment failures. Designing