Research Plan for Estimating Cascading Blackout Risk
Objective : Estimate overall
cascading blackout risk from simulated and real power transmission
system data
Problem description and definitions
Overall cascading blackout risk
is described by the distribution of risk of blackouts of various sizes;
for example the risk of small, medium and large blackouts or the
blackout risk as a function of blackout size. Since Risk = Cost x
Probability, we need to know the cost of blackouts as a function of
blackout size and the probability of blackouts as a function of
blackout size. It is necessary to consider all sizes of blackouts
because managing only the risk of small blackouts could neglect a
substantial risk of larger blackouts. Estimating overall blackout
risk is different than computing the risk of some particular and likely
cascading failure sequences because it aims to also evaluate the risk
of unlikely, unusual and unforeseen failure sequences.
There are an enormous number of these failure sequences and it is
impossible to carry out a detailed analysis of them. Therefore
overall blackout risk is evaluated using a bulk statistical approach
that neglects many details. (In a different line of research, it
is useful to compute particular high risk cascading failure sequences
in detail because mitigating the highest risk sequences is a plausible
strategy to reduce blackout risk.)
Blackout size can be measured
by load shed or energy unserved or customers unserved. These are
measures of blackout size that matter to the public, business, and
government. Number of transmission lines outaged is a
measure of blackout size that can be observed within the transmission
system.
Cascading can be quantified by the size of the initial disturbance and lambda, the
average tendency of failures to propagate. lambda < 1 gives
cascades that die out and lambda > 1 gives cascades that can blow up
exponentially to give large blackouts.
As a power transmission system is loaded or stressed, there is a
transition in the blackout risk at a critical
loading. (At the critical loading, there is a sharp change
in the rate of increase of average blackout size and a power law in the
distribution of blackout sizes.) lambda = 1at the critical loading. It
is useful to be able to determine the margin to the critical loading by
estimating how close lambda is to 1.
Failure refers to component
outage for any reason, including tripping out and being unavailable to
transmit power as a well as being damaged or misoperating.
PSerc cascading project thrust at Wisconsin
We have developed new methods to estimate lambda and the distribution
of blackout size from simulated blackout data. Methods for
number of line outages are in HICSS06
paper and methods for MW shed are in preprint06.
The methods are tested on data produced by the OPA simulation of
cascading line outages and overloads. The methods are efficient
in that only dozens of blackouts need to be simulated. (Running a
simulation exhaustively to obtain the distribution of blackout size by
brute force requires many thousands of blackouts to be simulated.)
We informally explain lambda, the average tendency of failures to
propagate, and how to estimate lambda (saturation effects are ignored
for this explanation). The simulation produces failure data such as
number of transmission lines outaged in stages. Each failure in
each stage produces on average
lambda failures in the next stage. Think of the failures that
produce further failures as "parent failures" and the further failures
as "children failures". Then lambda is simply the average family
size. The intuition is that if each parent produces on average
0.5 children and each of those children produces on average 0.5
children and so on, then the extended family size will vary randomly
but will certainly die out after a few generations. This
corresponds to a small total number of failures and a small
blackout. On the other hand, if each parent produces on average 2
children and each of those children
produces on average 2 children and so on, then the extended family will
vary
randomly but can blow up to the population limit. This
corresponds to a large blackout. To estimate lambda, run the
simulation to produce dozens of cascades. Then lambda is
estimated as the total number of children failures divided by the total
number of parent failures.
Once lambda and the size of the initial disturbance are estimated from
the data, the distribution of the blackout size can be estimated using
mathematical formulas. Comparing this estimated distribution of
blackout size to the empirical distribution of blackout size produced
by exhaustively running the simulation tests how well lambda works.
Sample results predicting the distribution of blackout size via lambda.
Distribution of number of transmission lines failed. Data
produced by OPA cascading failure simulation on the IEEE 118 bus system
at the base case loading. Dots are the empirical distribution produced
by running the simulation exhaustively. The dashed and solid
lines are produced by first estimating lambda and the initial number of
line failures and then computing the distribution of line
failures. The estimate of lambda = 0.4. The probabilities assume
at least one line failure.
Distribution of power shed, expressed as a fraction of total system
power so that total system blackout = 1. Data produced by
OPA cascading failure simulation on the IEEE 118 bus system at 0.85
times base
case loading. Dots are the empirical distribution produced by running
the simulation exhaustively. The solid line is produced by first
estimating lambda and the initial load shed and then
computing the distribution of the total power shed. The estimate
of lambda = 0.1.
Limitations of the work so far:
- Methods only tested on a few sample cases such as IEEE 118 bus
system using only the OPA simulation. Systematic validation is
needed on a range of simulations modeling other cascading interactions.
- Cascading process in the OPA simulation seems to saturate in
highly stressed cases (blackouts tend to stop near a particular
blackout size) and this effect is not well understood. Lambda
estimation method can neglect saturating data, but this requires a
guess of where saturation occurs.
- Better understanding of cascading processes and statistical
methods is needed to improve the methods.
- Blackout cost for large blackouts is poorly understood.
- Work opens up significant possibilities of directly monitoring
overall risk from real power system data such as line outages, but
little has been done on selecting and processing the real power system
data so that the methods can be applied.
Overall research plan for estimating cascading failure risk
(* = part of current PSerc project)
(1) Develop and test methods of determining lambda and
distribution of blackout size on a range of cascading failure blackout
simulations such as:
- CMU cascading model *
- OPA*
- Manchester model
- TRELSS
Outcomes if work succeeds:
- Validation of methods on a range of cascading failure simulations.
- Can efficiently evaluate impact of simulated transmission system
upgrades on overall blackout risk.
- Understanding of cascading failure.
(2) Extend methods developed for determining lambda and
distribution of blackout size from simulated blackouts to monitoring
real blackout data such as transmission line outages. This
includes data processing and algorithm development. Monitoring
precursor events is desirable.
Outcome if work succeeds:
- Monitoring overall blackout risk by accumulating data such as
transmission line outages.
(3) Find correlates to lambda that can be monitored in near real
time and validate on simulations.
Outcome if work succeeds:
- Near real time monitoring of overall blackout risk.
