I have written a program I call PLF (Probabilistic Load Flow) to
perform a variety of engineering studies concerning generation and
transmission network reliability.

Program PLF has five generation and transmission reliability models:

1. 50k bus AC load flow and probabilistic fast AC load flow for N-1,
   N-2, and N-3 outages.  Use of double precision voltages allows
   ring buses to be explicitly modeled as transmission circuits.
   A fast AC load flow (zipflow) can simulate millions of line
   outage cases within minutes.  The IEEE paper on zipflow describes
   how the multiple line outages are set up and solved.  The PLF
   program outage statistics for line overloads are organized for
   easy readability of results.  A PLF type 1 solution automatically
   writes out a script file for rerunning the cases with line
   overloads using full AC load flow in type 2 (below).

2. 50k AC load flow and probabilistic AC load flow for determining
   transmission reliability.  Full AC load flow is used to provide
   accurate reactive and voltage control representation.  Line over-
   loads and voltage problems are presented in an easy to read format
   allowing the quick pinpointing of problematic areas affecting
   reliability in the network.  Generators are not outaged.  Line
   outage probabilities are estimated for the purpose of ranking
   the severities of contingencies for islanding, voltage problems,
   and line overloadings.  The full AC load flow solution provides
   a means for checking the accuracy of the zipflow in type 1 cases.

3. 50k bus FCITC and ATC for power transfers, automatic selection of
   monitored/outaged lines, has excellent representation of real and
   reactive flows, which result in much better accuracy than DC load
   flow models.  Line outages that cause system separation are
   automatically skipped since the results would be meaningless.
   Output results are sorted and presented in an easy to read format
   with the most limiting constraints listed at the top of the report.
   The maximum ATC limits are displayed as well as the number of miles
   of lines being overloaded.  PLF also finds and lists line overloads
   that are reduced in loading (helped) by the transfer.  PLF ATC
   accuracy is excellent because full AC load flow is solved for both
   the base case and a high transfer level case.  Then interpolation
   of both real and reactive powers on all lines is performed using
   the zipflow mathematics described in type 1 for the two AC load
   flow cases.  The zipflow ATC results are nearly identical with
   full AC load flow, but execute at speeds hundreds of times faster
   than AC load flow.

4. Composite multi-area generation and transmission (50k bus)
   reliability model uses full transmission and generation network
   representation.  Probabilistic line flows are calculated from
   random outages of generators and lines.  An efficient convolution
   process models all possible generator outage states, which results
   in more accurate results than Monte Carlo models can provide,
   especially for problems with small modifications to the network.
   The transmission model is general and can include any number of
   loop flows that would be encountered in a large network.  No
   transmission equivalents are taken or are necessary.  At the
   present time, generators and lines are limited to two states
   (available and forced out of service).

5. Single area generation reliability model (no transmission
   constraints) uses an efficient convolution procedure to model all
   generator outage states as a direct calculation, which avoids
   problems associated with use of Monte Carlo in other models.  The
   mathematical procedure is described in the IEEE paper and
   dissertation posted on this web site.  Generators can have up to
   three states (up, down, and derated), seasonal capacities, and
   weekly maintenance.  The loss of load statistics are calculated for
   both hourly loads and for daily peak loads for all days and hours
   in a year.  Load uncertainty is modeled as a percent deviation for
   a Normal Distribution.  Results are tabulated in an easy to read
   format.