Cascading Power Failures

Jonah Brown-Cohen
October 23, 2010

Submitted as coursework for Physics 240, Stanford University, Fall 2010

The 2003 Blackout

On August 14, 2003 a chain of events beginning with the loss of a few powerstations due to high energy load escalated, with help from a combination of human error and tall trees, into the worst blackout in history. All told, 50 million people in the Midwest, Northeast and Ontario, Canada, with a combined load of 61.8 gigawatts lost power for up to 4 days. [1] One of the most interesting, and worrying, points about this blackout is that a relatively small number of failures in generating plants and a few transmission lines shorting out by touching trees were able to set off a massive chain of transmission line and generating failures across a huge portion of the electrical grid. This effect is known as a cascading power transmission failure, and once it begins it is nearly impossible to stop before it has eliminated almost all power transmission in a large area.

The 2003 Blackout originated in Ohio with the FirstEnergy power plants and transmission lines. [1] Under high load, more current flows through a transmission line and some of the power transmitted is dissipated as heat. At high temperatures, the conductors in a high-voltage transmission line expand, causing the line to sag more toward the ground. This effect is amplified on a hot day as less heat can be dissipated to the air. FirstEnergy had failed to trim the trees along several of its power lines, and so when they sagged under load, four lines, three of which were carrying 345 kV, contacted trees and tripped their ciruit breakers. [1] These line failures, combined with an ironic failure in the alarm system meant to notify FirstEnergy of line failures, resulted in a large drop in voltage across the entire FirstEnergy power network. At this point, the low voltage and high current on lines that had not failed, tripped the circuit breaker on the 345 kV Sammis-Star line, setting off the cascade. [2]

Ohm's Law and Cascades

To understand a cascading power failure, one must first understand the relationship between current, voltage and impedance on an AC line. In general, Ohm's law for AC circuits states that V = IZ where V is voltage, I is current and Z is impedance. As load increases on a line in the power system, either because more power is being used at the end, or because generators or other transmission lines fail, the magnitude of impedance drops. Thus, if voltage is held constant by the generators, the amount of current will increase. This is generally what happens under normal operation, and the lines are rated to function with amounts of current much higher than what would be caused by lots of people using air conditioning or a few isolated line failures.

The second key point to understanding a cascade is the protection system used for transmission lines. Long transmission lines are very expensive, so if there is a short-ciruit, it is important to almost instantly isolate the line before high currents can do serious damage. By far the most the most prevalent protection system in place is the impedance relay. [2] These devices measure impedance along the line, and at the junction with lines to which it connects further up in the power grid network. The idea is that if a line, or any of its neighboring lines shorts out (perhaps by touching a tree) the extremely high current from a short circuit to ground will result in very low impedance. Again this is because, by Ohm's law, Z = V/I. The impedance relay then trips circuit breakers to isolate the line from the grid and protect it.

The Dynamics of a Cascade

However, when there is a significant spike in load, as there was on the afternoon of August 14, 2003, the generators are unable to adjust quickly to the change in load, so voltage across the remaining lines also temporarily drops. At this point, current has also increased because load has increased, so impedance is very low. The key point here is that the impedance relays cannot tell the difference between the low impedance caused by a short circuit, and that caused by the sudden drop in voltage and rise in current from the failure of several lines and generators. [2] Thus, when FirstEnergy's lines and generators failed, the impedance relay on the Sammis-Star line interpreted the drop in impedance as a short ciruit and promptly tripped its circuit breakers to protect the line. At this point, it was impossible for any sort of intervention to stop the cascade. [2]

Once one impedance relay trips simply because of a rise in load rather than by an actual short cicuit, the cascading power failure begins. This is essentially because the spike in current and drop in voltage that can cause a relay trip has reached a critical mass. Once the relay trips, the line is isolated from the rest of the grid, so some other line must very rapidly take on the extra load from the tripped relay. Since this rapid change in load was already enough to trip the first line, having it suddenly shifted to some other line again produces low enough impedance to cause a relay trip. This isolates the second line from the grid and the whole process repeats itself, rippling through the grid extremely quickly. In fact, once the Sammis-Star 345 kV line tripped in 2003, it took only a little over 5 minutes for 50 million people to lose power. [2]

Ramifications and Conclusion

All told, a most estimates of the full economic repercussions of the 2003 blackout put the collective damage between $4 and $10 billion. [1] However, the more startling number is the total cost per year to U.S. electricity consumers due to power outages: $79 billion. [3] Though not nearly all of these outages can be attributed to cascades, the effect is related. When load gets too high on some sub grid in the power system, it is necessary to cease power supply to some subset of customers in order to prevent the build up to critical load levels that can cause a cascade. [1] Though much has been done in terms of new regulations and standards to prevent blackouts like that in 2003 from reoccuring, it is important to note that the system is necessarily vulnerable to a cascade. This is because it is still absolutely necessary to protect transmission lines from short-circuits by using impedance relays, so all that can be done to avoid cascades is to attempt to prevent the initial conditions necessary to set one off.

The question then is: how difficult is it to cause a cascade in the current system? A partial answer to this question was quantified in an interesting simulation by Albert et al. [4] They found that the vulnerability to cascade was mostly determined by the structure of the electrical grid. The important numbers to take away from their paper are: 2% and 60%. That is, with the current structure of the grid in the United States, a failure in 2% of the transmission substations can cause a cascade resulting in a loss of 60% in all power connectivity. [4] Though there has not been another cascade since 2003, this indicates that the scale could have be much greater than it was, presumably resulting in even larger economic losses. Thus, when thinking about the grid and cascading power failures, these are the numbers to remember: 2%, 60% and $79 billion dollars.

© 2010 Jonah Brown-Cohen. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.


[1] U.-S. Canada Power System Outage Task Force, Final Report on the August 14, 2003 Blackout in the United States and Canada: Causes and Recommendations," Ottawa: Natural Resources Canada, 2004, Chs. 1-3.

[2] ibid., Ch. 6.

[3] K. H. LaCommare and J. H. Eto, "Understanding the Cost of Power Interruptions to U.S. Electricity Consumers," Lawrence Berkeley National Laboratory, LBNL-55718, September 2004.

[4] R. Albert, I. Albert, and G. L. Nakarado, "Structural Vulnerability of the North American Power Grid," Phys. Rev. E 69, 025103 (2004).