with any number in the range having an equal

likelihood of occurrence. Each random value is

to incorporate routine and nonroutine O&M costs

input into the spreadsheet, and the spreadsheet is

for each component over the period of analysis.

recalculated to arrive at an associated outcome.

Each random trial or iteration of the spreadsheet

represents an independent "what-if" game. By

changes in generating unit efficiencies with various

generating hundreds, or in some cases, thousands of

rehabilitation scenarios.

"what-if" games, Monte Carlo sampling will gener-

ate the input distribution and the entire range of

potential outcomes.

consequences of events and repair/rehabilitation

scenarios in terms of changes in hydropower system

benefits and alternative construction costs. Each

alternative produces different hydropower outputs,

system benefits, and O&M costs.

Basic functional requirements are established for

the model. These requirements allow for flexibility

in the analysis, incorporation of basic assumptions,

other economic calculations such as present valua-

and the ability to change parameters as needed.

tion and amortization of costs and incorporation of

Some of these requirements are described below.

interest during construction.

without-project condition. The without-project

condition establishes a base condition from which

all other alternatives are to be evaluated.

spreadsheet is modified to simulate the specific

engineering, operational, and economic conse-

evaluate a full range of alternatives. Alternatives

quences relative to the alternative. Monte Carlo

considered in the analysis often include: enhanced

simulation techniques are incorporated into the

maintenance, use of spare parts, a full array of

spreadsheet. This approach uses random number

rehabilitation scenarios, and, subsequently, appro-

generation to compute an expected result given a

priate timing of any rehabilitation strategy.

combination of probabilities and events. The

program sums the results of multiple iterations of

the simulation and produces expected values and

vidual operating components, and economic conse-

variance. Each simulation should include a mini-

quences of various alternatives, and the timing of

mum of 300 iterations. Up to 5,000 iterations may

events.

need to be computed in some simulations.

incremental analysis of each unit and its separable

without-project and for each alternative considered

components.

in the analysis. Simulations for the Chapman

Powerhouse example (Appendix C) should include:

rehabilitation of one to four turbines; rehabilitation

(35 years is recommended) and for near-term events

of one to four generators; rehabilitation of one or

that could impact future rehabilitation strategies.

two transformers; and all reasonable combinations

of these alternatives. The appropriate timing for

rehabilitation should also be evaluated. Another

engineering reliability and risk and uncertainty

alternative that should be considered is one that

analysis for each time period and each functional

uses an enhanced maintenance strategy. In many

component under evaluation.

cases this may already be implemented in the

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