Prepared Direct Testimony of Robert McCullough on Behalf of the ...

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Page 18 <strong>of</strong> 76SEATAC-400available generating capacity for each <strong>of</strong> the plants in a particular time period for which theplants' availability factors are relevant. For a particular day that a plant is not on maintenanceoutage, a plant can reasonably assumed to be either available or not available, with a likelihood<strong>of</strong> availability equal to the plant's availability factor. The relevant fimction is then the totalavailable capacity in the pertinent time period, just the sum <strong>of</strong> the available capacities <strong>of</strong> eachplant, divided by the total capacities <strong>of</strong> all the plants, available or not. That is, in a particular timeperiod the value <strong>of</strong> the hndamental variables - each plant's available capacity -- is either thenormal capacity <strong>of</strong> the plant, or, if the plant suffers an outage, zero; and the function <strong>of</strong> interest isjust the proportion that sum is <strong>of</strong> the total possible capacity <strong>of</strong> all the plants if they were allavailable.Second, repeated samples <strong>of</strong> all the fundamental variables must be generated. In owapplication, each repetition or trial consists <strong>of</strong> one complete set <strong>of</strong> available capacities for theplants. For each plant, this can be accomplished by repeatedly simulating a simple yes-noprocess that generates yeses with a probability equal to a particular plant's availability factor; ifthe answer is "yes" then the plant's capacity is available, if "no" then the plants available capacityis zero. For example, a 100 MW plant with a 75% availability factor will <strong>of</strong>fa 100 MW <strong>of</strong>capacity for, on average, 75 out <strong>of</strong> 100 occasions that it is called on for service. This kind <strong>of</strong>behavior is easy to simulate with a computer and can be easily imagined as the throwing <strong>of</strong> diceor coins, or the operation <strong>of</strong> simple machines as seen on "Wheel-Of-Fortune."Third, the function <strong>of</strong> interest is the total capacity available in each time period.. Our applicationis implemented by simply adding up the simulated available capacities <strong>of</strong> all the plants, once for
Page 19 <strong>of</strong> 76SEATAC-400each time period. Some plants are "available" and contribute their total capacity to this sum,while others are "unavailable" and add zero.Fourth, the statistical distribution <strong>of</strong> the variable <strong>of</strong> interest is evaluated. In our application, wehave a particular interest in the probability that the total available capacity is less than someparticular proportion <strong>of</strong> the total possible capacity. As a statistical statement, we are looking forthe value <strong>of</strong> a probability distribution function at a particular availability percentage.Q. Are there other problems that clearly illustrate how this approach works in evaluatingthe likelihood <strong>of</strong> complex events?A. An analogous problem is the question <strong>of</strong> how likely it is to roll ten dice simultaneously, assign avalue <strong>of</strong> zero to a die if it comes up six and a value <strong>of</strong> one otherwise, add up the values and get atotal less than or equal to five. This problem can be solved analytically, but is easily explored byjust throwing ten dice many times and tabulating the results. The problem is more difficult tosolve analytically if the dice have different numbers <strong>of</strong> faces - e.g. a mix <strong>of</strong> normal cubical dice,octrahedral dice, tetrahedral dice - and the values assigned to each die are different functions <strong>of</strong>how the die falls, and if there are many more dice. In that case, a convincing demonstration canstill be made by actually conducting the experiment, throwing the dice many tirnes and keepingtabs on the results.Q. How would this roll-<strong>of</strong>-the-dice example relate to the study you performed?A. The capacity availability Monte Carlo study we performed involved ten thousand ''throws <strong>of</strong> thedice."Q. How likely would the real world capacity availability for these plants be if the simple
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