Convergent Outage Method

Aurora’s convergent outage capability provides a flexible way to model random resource outages. In contrast with the Frequency Duration outage method available in the model, this capability ensures convergence to an input forced outage rate in every risk iteration. The logic considers each unit’s forced outage rate, mean repair time, and planned maintenance schedule, while at the same time seeking to adhere to expected overlapping outages for groups of resources. The setup also affords a straightforward way to change some input data while still keeping the outage pattern for resources the same. This document discusses the user setup, core logic, output reporting, and other important considerations when using the convergent outage logic.

Setup Requirements

Logic Selection

The use of the convergent method for random resource outages is selected in the Resource folder of Simulation Options:

There are two fields related to the convergent outage method:

Outage method – Select Convergent in the drop down to enable the convergent outage method for selected resources.
Convergent cycle length (months) – This informs the program of the time period over which the forced outages should converge to the input rate. For example, if a value of 4 is input and a simulation is run for one full year, the model will force convergence to the forced outage rate over the hours in the first four months of the year, over the middle four months of the year, and over the last four months of the year. If the number of months specified is greater than the number of months in the study, the program will force convergence over the entire study period. If the number of months in the study is not evenly divisible by the cycle length input, the last convergence period will be shorter than the input cycle length.

An input Risk table is not required and the setting Perform general risk study need not be selected. When it is not selected, the model will perform a standard run and assume internally a risk iteration number of 1. When multiple iterations are to be run, the setting Perform general risk study in the Risk folder must be selected. The model will then use the value in the Number of iterations to determine how many iterations should be performed. Aurora will ensure convergence to the input forced outage rate in each iteration. The actual timing of the outages, however, will change from iteration to iteration.

NOTE: The risk seed, also located in the Risk folder, is used whenever the convergent outage method is selected. The model will default to a value of 0.5 whenever this is not input by the user.

Resource Inputs

These are the columns in the input Resource and Resource Modifier tables which are used when employing random resource outages:

Risk Outage – A value of 1 in this column informs the program that the resource should be modeled with random outages instead of the standard hourly derate.
Forced Outage – This is the expected forced outage rate, entered as a percentage. Time series and CDS entries are allowed, but when using the convergent outage method the value will only be resolved at the beginning of each convergence period.
Mean Repair Time – The mean time to repair is the expected number of hours that the unit will be down when a random outage occurs. The convergent outage logic will produce down times which deviate from this entry, but the algorithm will seek to converge to this value if possible over each convergence period.
Outage Group – The outage group entry should be an integer between 1 and 30,000, inclusive. It is used to divide the resources using convergent random outages into groups, and each group will have the random outages “scheduled” independent of the other groups. Resources with the same number will be assigned to the same group.

The logic will schedule the resources in a given group together, taking into account the expected distribution of overlapping outages among members of the group. The actual value of the group number is used in the random number generator and allows for repeatability of results when it remains unchanged (see discussion on this below). Resources on random outage for which this field has not been specified will be grouped by zone.

Risk Resource Link – If this field is populated for a given resource, using a valid ID, the model will ignore its input forced outage rate and force it to exactly follow the outage pattern of the referenced resource.

Core Logic

At the beginning of each convergence period, the simulation schedules the random outages for the resources in each group for the length of the current cycle. Each group is scheduled independently of the others. The logic does the following to determine the outages for the resources in each group:

Calculates the number of hours each resource should be down within the period. For example, if a given resource’s forced outage rate was 10%, the cycle length was one month, and the current month had 744 hours, the model would seek to schedule 74 hours with the unit on outage. The calculation will always round to the nearest integer.
Calculates the expected number of outages events. This is equal to the expected hours in the period on outage divided by the mean time to repair. Again, this will be rounded to the nearest integer.
Determines the expected distribution of overlapping outages, assuming that outage events for the resources within the group are independent. If the number of resources in the group is small, this will be calculated using the expected mathematical probabilities. For example, if Resource A and Resource B each had a forced outage rate of 10% and were the only two members of an outage group, we would expect:

- Both resources to be on outage 1% of the time
- Resource A on outage alone 9% of the time
- Resource B on outage alone 9% of the time
- Neither resource on outage 81% of the time

When the number of resources in a group is large and such a calculation would be undesirable to perform, the expected distribution of outages is estimated using a mini simulation. Both methods produce a tiered expected distribution of MW on outage for the group which will guide the scheduling of outages.
Schedules the outages for the resources, one outage event at a time. The logic will pick a random hour in the period, check to ensure that an additional outage in this period does not violate the expected distribution (e.g., not too many MWs in the group on outage that hour), and select a random down time for the outage, limited generally by the mean repair time and the expected outage distribution. After scheduling the first outage event for each resource in the group, it will move on to the subsequent events until each resource is fully scheduled for the period. Each time an outage event is scheduled the expected outage distribution is considered.

Reporting

The forced outages for all resources are reported in each of the Resource output tables in the Forced_Outage column. A MW amount is reported, so for hourly output when random outages are being employed this value will equal either the available resource capacity or 0. The daily, monthly, yearly, and study reporting will report the average MW on outage for the respective time periods. The total MW on forced outage in each zone and pool is also reported in the Resource_Forced_Outage column of the Zone and Pool output tables.

Some general information about the outage scheduling will be sent to the status screen during the run if Informational Level 3 messages are turned on (Simulation Options > Miscellaneous), including the time it took to schedule the forced outages:

More detailed data about the scheduling of outage resources will also be sent to the Study Log table. The set of resources using the convergent outage method will be listed as well as the cycle length. When running a simulation with all hours, the model will also report the percent adherence to the expected outage distribution for each group with two or more resources:

Other Considerations

Repeatability of Results

Often it is desirable to be able to change some input parameters without changing the outage pattern of certain resources. The Outage Group structure allows users to easily control when the outage pattern will change for any given resource. If the following inputs remain unchanged, then the outage pattern will stay the same for a given resource:

The outage group number for the resource
The resources in the outage group
The relevant characteristics of the members of the outage group: Capacity, Forced Outage, Maintenance Schedule, Mean Repair Time
The study period and sampling configuration
The risk seed
The risk iteration number (when running in risk mode)

If those parameters are the same between two runs, then the resource (and all other resources in the same outage group) will have the same outage pattern even if other data parameters change. So for example, if a user wants to keep all outage patterns from a previous run the same but realizes that there is one more resource that should be modeled with random outages, then that new resource can simply be placed in a group of its own (i.e., with a unique Outage Group number). It will then be scheduled independently of all the other resources and the outage patterns will remain the same as the previous run for the rest of the system.

Using Sampled Hours

When using the convergent outage method with sampled hours (i.e. not simulating every hour in the study time period), then the logic will still converge as close as possible to the input forced outage rate for each resource over the sampled hours. The model will do this for any sampling configuration, but the user should take care to ensure the sampled hours are not too sparse. For best results in terms of adhering to the expected outage distribution for each group, all hours should be simulated.

Planned Maintenance Outages

When the unit has planned maintenance outages which take the entire unit offline, the model will ignore those hours in the random outage scheduling. This will affect both the number of hours on outage as well as when the outages will take place. For example, if a unit were on maintenance outage the last 7 days of April, had a forced outage rate of 10%, and the convergent period was 1 month, the model would find 0.1*(30-7)*24 = 55 hours that it would be on outage during the first 23 days.

Random Number Generator

The random number generator used for the convergent outage draws is based upon the random function in Microsoft Excel 2003. See this article for more information: http://support.microsoft.com/kb/828795

NOTE: The random draws for the standard risk logic in Aurora are independent of the random draws for the convergent outage logic. Both do utilize the user input risk seed, however.

Run Time Impacts

The run time increase from using the convergent outages will depend on several factors. In general, the shorter the convergent cycle the longer the extra processing time to schedule the outages. Likewise, the more resources that are in each outage group, the more time it will take to set the forced outages. Usually the run time impacts will be minimal. As an example, for a standard one year WECC study with the convergent cycle set to twelve months and 1000 resources on random outage in one unique group, the scheduling time for the random outages will be approximately 2% of the overall study time.

Knowledge Base

Convergent Outage Method