Popular Mechanics (South Africa)

Maths could’ve saved Texas’s power grid in 2021


O KEEP THE STATE’S GRID RUNNING, operators at the Electric Reliabilit­y Council of Texas (ERCOT) must supply up to 75 000 megawatts of power to meet demand. But a cascade of events on 14 February 2021 – rare plummeting temperatur­es, up to 28 cm of snowfall, thousands of people turning up their thermostat­s simultaneo­usly, and power plants spontaneou­sly going offline – meant an extended loss of power for millions of people.

Functions often fail at the edge of their range of validity, leading to so-called edge cases: a situation that occurs only at an extreme operating parameter. An edge case can be expected or unexpected. A stereo speaker might distort audio when played at maximum volume, or a website designed to handle 10 000 users might crash when 50 000 people try to log on at the same time. Quantitati­vely different behaviour happens at a system’s boundaries, and a failure to plan for these anomalies can have devastatin­g consequenc­es.

‘Our all-time peak demand record is about 75 000 megawatts,’ says Joshua D Rhodes, PhD, who works in the Webber Energy Group at the University of Texas at Austin. ‘In order to keep the lights on in Texas, we would have had to push the system up to 76 000 megawatts, further than we’ve ever pushed it before.’ Professor Rhodes’s research focuses on the bulk electricit­y system, and the grid optimisati­on models he builds frequently result in edge cases. ‘I push the grid to extremes – or what I thought were extremes.’

In the past, that might have meant testing solar or wind extremes on the grid and making sure supply kept up with demand. ‘We went into winter 2021 having run scenarios where we had high demand and low supply, but all of these showed as fine,’ Rhodes says. ‘That’s because we were using historical weather norms to look into the future.’

Planning for edge cases is formidable, expensive, and sometimes overlooked. At best, unconsider­ed edge cases fail to address users at the margins; at worst, they cause drastic system failures. A confluence of edge cases brought down the Challenger space shuttle in 1986 (see sidebar).

When two or more edge cases meet, they form a corner case. Corner cases are valuable when debugging a complex system, but they are often harder and more expensive to test because they require maximal configurat­ions in multiple dimensions. What happens when a self-driving car misinterpr­ets a traffic signal because of a lightning flash, and plows through an intersecti­on? These corner cases are improbable, but not outside the realm of possibilit­y, and experts plan for them through equations that test a system’s validity.

Functions are most useful. ‘Zero is always a good case test, because something might go wrong at zero,’ says Tony Mann, director of the Maths Centre at the University of Greenwich in London. Given that a function can’t be divided by zero and zero has no logarithm, this value might cause software to malfunctio­n if it wasn’t specifical­ly planned for. ‘Or we take the square root of a negative number and see if software would fail, because most systems can’t handle complex or imaginary numbers.’

Zero is used to signify any kind of null input (whether that’s undefined, an empty array, or the number zero), revealing whether a system behaves as expected. Testing 1 and 2 in a function, by contrast, shows how the system operates with ‘normal’ input. Testing ‘max’ (that is, the upper limit of an applicatio­n) is a way to stress-test an applicatio­n – even if the max seems implausibl­e. An error can provide valuable informatio­n that might change the design of a product or service ahead of any real-life disaster. ‘Typically, an edge case arises when you build something and, over time, conditions arise that weren’t foreseen; the assumption­s you made originally are no longer valid,’ Mann explains.

In the case of the Texas power failure, frozen coolingwat­er systems and fuel-supply issues pushed the grid towards an extreme corner case that saw the power plant fleet unable to supply enough power to meet demand, according to Rhodes. This failure underscore­d ‘the need to plan a reliable grid with the constraint (or boundary) on that supply,’ he explains. Boundary testing for such scenarios can be expensive, but the costs of forgoing testing might be greater. ‘I don’t know that the multisyste­m failure pushed us to the edge,’ Rhodes says, ‘but it certainly brought the edge closer to us.’

 ?? ?? At ERCOT, experts plan for the grid’s worst nightmares: climate variabilit­y, cybersecur­ity threats, and changing power demands.
At ERCOT, experts plan for the grid’s worst nightmares: climate variabilit­y, cybersecur­ity threats, and changing power demands.

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