algorithms to balance all these needs makes for a massive mathematical
challenge.
The mathematical problem of planning the operation of power generatingunits has long been recognized, but for decades, utilities resorted to ad hoc
solution methods, and as a result they’ve typically been forced to schedule
excess capacity to compensate for the lack of precise solutions. This approach is
worse than just costly: the fossil fuels wasted are in limited supply, and their
combustion could be threatening the climate of our planet.
In the late 1990’s, mathematicians brought advances in “mixed integerprogramming” to this problem, which new hardware and software had just made
practical for large-scale problems. The result of a simple improvement in an
algorithm was a savings of $250 million per year, along with millions of barrels of
oil.
Utilities have long lived with considerable uncertainty as to demand forpower, requiring what are known as stochastic optimization tools and methods of
reliability analysis in planning for capacity and operation. But now the utilities’
problem is getting even more challenging as wind and solar power become more
prominent. They make the energy supply unpredictable as well as the energy
demand. That is not so hard to deal with in small quantities, but as the
percentage of renewables climbs – as new laws are increasingly mandating – the
difficulty grows dramatically. As long as we know the future, advances in the field
of integer programming have made it possible to solve power generation
problems with thousands of variables in a reasonable time. By contrast, once we
introduce uncertainty, seemingly toy problems with just a few variables can
explode, producing algorithms that exceed the capabilities of the largest
supercomputers. If we are going to find efficient, robust solutions to manage our
power grid in the presence of uncertainty from wind, solar, weather and human
behavior, existing mathematics isn’t enough; new techniques are essential.
This is just one of the challenges we face from the enormous task oftransforming our energy systems. Energy demand is continuing to grow, while
the costs, both monetary and environmental, are becoming harder to bear. We
need new energy solutions that make us less dependent on foreign oil, release
less greenhouse gas into the atmosphere, and are robust and affordable both for