27 May 2013

Deterministic Predictability and the Power Grid


Yep, the lights are definitely gonna go out.

This year we celebrate the formal 50th anniversary of chaos theory and the end of deterministic predictability. The latter is the wonderfully intuitive idea that if you understand the physics principles and the starting parameters, you could then predict where a system would be at any time in the future. It’s seems intuitive: set up a row of dominos and you know exactly how things will end when you tip the first one, right? 

That everything-is-predictable-from-the-beginning-conditions idea, however, got us into the Viet Nam war.

Around that same time in 1963 a meteorologist named Edward Lorenz showed that this idea was a failure, at least for most systems beyond what you could set up on a table. The reason? Most “systems” (like the weather, or transform faults, or power grids) are not linear, nor are they simple, like a row of dominos. A slight change in an initial parameter in your weather model (the temperature at one of millions of points over the tropical Atlantic, the amount of dust sent westward by a sandstorm in the Sahara a week earlier, the number of sunspots on the approaching limb of the Sun, etc.) and your final calculated outcome for the Atlantic Hurricane season can be totally different from what your computer had calculated just an hour earlier.

DANG, you say. I really need to know when a hurricane/tornado is going to hit! I’m running a BUSINESS here for heaven’s sake.

Well, don’t give up hope – we can’t predict earthquakes, but meteorologists have made huge progress in the past two decades. Nate Silver in his book “The Signal and the Noise” points out that massive new computing power, coupled with the vaster integrative capacity of thousands of human minds, have together contributed to huge progress in predicting weather out for more than a week at a time. They correctly and precisely predicted the landfalls of Hurricanes Katrina and Sandy. For human reasons, however, very few people took the warnings for Katrina seriously and thus many people died as a result.

However, weather forecasters still can’t predict when a hurricane will start (though they know when the hurricane season will “light up” their boards), nor can they predict very well the power of these monsters when they hit. The damage usually comes not from the wind, but from the so-called low-pressure storm surge that lifts the ocean up 5 or 10 meters as the eye of the storm approaches land. Think: a 20-foot wall of ocean pouring in on your neighborhood at 20 miles per hour. As an interesting anecdote, Nate Silver shows that local television weather people have a truly abysmal predictive record, far worse than the NOAA weather forecasters, whose data they can easily access for free. How could this possibly be? The reason for this is very human: no forecaster wants to get flogged for UNDER estimating the likelihood of precipitation.

Let’s go back again to the foundations of predicting things. This is, basically, prophesying. Deterministic predictability actually does hold, at least theoretically. The problem is having ALL the parameter data PRECISELY correct in your weather model. It is also important to have a computing grid fine enough that when you do your calculations the temperature and pressure on any given point is not that different from that of any adjacent point. In other words, so the point-to-point behavior can be treated mathematically as approximately linear. Some of Lorenz’ earlier computer models used to try to predict the weather gave different results when run more than once. What? But everything input was the same! Not quite, it turned out. The starting numbers were returned to the computation with only the third decimal place retained – in other words the numbers were rounded up. 26.2653 became 26.265 - and the final results were startlingly different. It took Lorenz awhile to realize this, but there was a big clue down there in the minute decimals.

Classical physics teaches that given the current state of a system, all future states can be calculated. It seemed to work in the 19th Century: it was used to predict the orbits of planets and comets, and slight perturbations successfully guided the search for Uranus and then Neptune (and in 1930 a small perturbation in the orbit of Neptune led to the discovery of Pluto, though that case is arguable). 

However, back in the 1880’s, Henri Poincar√© was studying the three-body problem, in which three bodies continuously influence each other in celestial mechanics in complex and overlapping ways. Poincar√© noticed “…that small differences in the initial conditions produce very great ones in the final phenomena.” He concluded that prediction is impossible for three bodies orbiting in space. Contemporaries thought they just had a data quality problem, but the root was much deeper than that.

So chaos theory, but without that name, preceded Lorenz by nearly a century. Chaos theory, by the way, has a common metaphor that is fairly widespread: the so-called “The Butterfly Effect”. This stems from the title of Lorenz’s 1972 presentation to the American Association for the Advancement of Science: “Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas?” This is also called ‘sensitive dependence on initial conditions’, and it’s a trademark characteristic of a complex non-linear system. On the other hand, the trademark behavior of a chaotic system is apparent randomness – but this is deceiving. Determinism actually works, but you have to know ALL the initial data and ALL the force actors to high precision.
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Well, what has all this got to do with the electric grid in the title? In the United States there are really three quasi-independent power grids: The Eastern Interconnection for the entire eastern US to about the Kansas-Colorado border, the Western Interconnection from there to the Pacific coast… and the Texas grid. We always knew Texas would insist on being different. It may surprise you to know that these grids are the largest engineering structures ever built, and consist of thousands of energy sources from coal-fired power plants, to the huge Bonneville and Grand Coulee Dam hydro-electrical generators, feeding ultimately to billions of power outlets in our homes. These systems affect virtually every aspect of our day-to-day lives. If you are reading this, it means the grid is working.

However, within each of these domains – and increasingly across their boundaries – a perturbation in one place will cascade across the rest of the network with usually unpredictable consequences.

While there are power generating stations everywhere throughout the three grids, there are powerful sources of irregularity in the entire system. Wind energy sources can drop suddenly, and the growing solar input systems are diurnal (they produce nothing at night), or a power plant may go offline for maintenance. Furthermore, a Coronal Mass Ejection (see  http://jeffwynn.blogspot.com/2012/01/cme-events-how-they-affect-your-life.html) can send a huge bolus of charged particles at our planet. The Earth’s magnetic field is a pretty good defensive barrier, but it can be – and has been – beaten down to the ground. When that happens there are huge telluric currents set up – vast flows of electricity along the ground. When this hits a power substation it can cause huge shorts in the giant accumulators. If you’ve never seen a power transformer “pop”, then you are in for a spectacular surprise as long as you are not next to it. I’ve watched video of a tornado approaching Oklahoma City, and its approach is marked distinctly by bright flashes as these pole-top transformers explode.

When a small transformer like this goes down, it blacks out a part of the network and is repairable within a few days at most. When a larger accumulator explodes in a power substation, it’s a different matter, and there will be huge surges of power coming in on the grid to try to compensate for its loss. Enough of these kinds of events and the instability they bring will cause vast areas to go down. 

The most famous of these events happened in the summer of 1965, when New York City was blacked out. Interestingly, there was a huge surge of births in the area precisely 9 months later. More recently, a CME shut down the Canadian provinces of Quebec and Ontario, when they experienced a huge and long-lasting blackout in the middle of winter. If electricity is your source of heat, this could be a life-threatening event. If you survive, your water pipes will freeze and burst, and you will have heck to pay when it warms up again.

When these surge-and-sag events happen, human operators jump in and try to stop the cascading failure from propagating. But they don’t always succeed, in part because the entire grid is fundamentally a non-linear system, sensitive to the tiniest things. In other words, we can’t predict ahead what is going to happen to our home power supply, because there are too many variables involved and we don’t understand the behavior of the system except in statistical ways.

But the human and growing automation reasons for grid instability are perhaps the most interesting – and the least predictable. Thousands of induction motors in air conditioners can all surge at once and drag down (“brown out”) the entire system when a sudden heat wave hits California, or New York, or any other major collection of humanity. As more and more renewable energy sources come online, the points of failure and surge grow even further. Newer smart appliances just add to this mix because human control steadily diminishes.

It’s perhaps not really surprising, then, that Chinese military hackers have turned their attention to the North American power grid, and have persistently probed the computer control systems monitoring and adjusting against just these sorts of failures.

Yes, chaos theory rules our world. Another way to say this is that our small part of the universe is chock full of nonlinear systems, including especially humans, and nonlinear systems are very hard to forecast.
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One final quote, this time from the famous mathematician Pierre Simon Laplace: “An Intelligence which could comprehend all the forces by which nature is animated and the respective situation of the beings who compose it – an Intelligence sufficiently vast to submit these data to analysis… for It, nothing would be uncertain and the future, as the past, would be present to It’s eyes.”
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