Power Grids

 

It's that time of year again.  Between the hot temperatures and the out of control fires, the power grids are under a lot of stress.  Consequently, there is a lot of math involved in the production and distribution of power.  Power companies have to predict when there are decreased demands on the system to keep them running.  

The math involved includes differential equations, linear algebra, and graph theory which are used in grid simulations designed for operators to both monitor the systems and calculate the requirements of the system.

Power grids are actually complex systems that cover huge geographical areas and are composed of multiple devices.  In addition, the power system is made up of multiple generating sources connected by a network for transmission.  If any part of this stutters, the results are a rolling blackout or a blackout. The system has a weakness when power input changes from one minute to another when electricity is generated by wind power while it's pretty stable when generated from a coal-fired power plant.  So the mathematical models must include these because many systems combine wind, coal-fired, nuclear, and solar systems.

Unfortunately, writing mathematical models must incorporate a lot of different equations that govern every aspect of power, it's transportation, type of current, and so many other factors. The system is constantly solving all these different equations in real time so operators know exactly to correct any instabilities of the power flow. 

Another aspect of this situation is that communication and battery backups have to be factored into the situation because if the power goes out, how long will your cell phone work if the towers go down, or if they manage to stay up, how long can you be without power before your batteries die?  In addition, most power companies rely on cell phones now to communicate with their workers.

So some of the equations deal with the idea of setting repairs so that they are prioritized based on how long certain backup batteries at places such as hospitals or cell phone towers. In addition, they have to factor in where certain breakers lie in the subsystems and which ones have backup batteries.  

Thus the modeling programs used must take into account of so many factors and elements to provide everyone with the best information possible to keep the system working through all of the extra demands.  Math is responsible for the modeling used by power companies to be as efficient as possible. Let me know what you think, I'd love to hear.  Have a great day.