In this problem you will use a combination of Monte Carlo analysis and multiple
ID: 3144832 • Letter: I
Question
In this problem you will use a combination of Monte Carlo analysis and multiple linear regression to investigate trends in simulated data. This type of analysis is known as “response surface analysis.” There are no new methods here, just the combination of two methods with which you are already familiar from class. You will need to use BOTH Monte Carlo and regression in your response. There is no way around using Monte Carlo in this problem! The Entergia Corporation is considering the purchase of the Vermont Yankee nuclear power plant. They are concerned about their exposure to the New England electricity market, because low natural gas prices are depressing the market price of electricity. They are also concerned about their exposure to increased fuel costs, because of government policy that may place tariffs on imported nuclear fuel in the future (nearly all nuclear fuel in the US is refined from raw materials that are imported from outside of the US). We will use the following assumptions about the Vermont Yankee plant: Annual electricity production follows a triangular distribution with a minimum of 1 million MWh, a mode of 2 million MWh and a maximum of 5 million MWh. O&M costs are expected to be between $5 per MWh and $15 per MWh. You may assume that the O&M costs follow a U($5, $15) distribution Fuel costs are expected to follow a triangular distribution with a minimum of $3 per MWh, a maximum of $15 per MWh and a mode of $10 per MWh. Based on electricity prices in New England over the last several years, Entergia believes that the sales price for the plant’s electricity output would follow a normal distribution with a mean of $35 per MWh and a standard deviation of $20 per MWh.
Explanation / Answer
Annual Electricity Production follows a trinagular distribution on [1, 5] with mode 2
E = ((x - a)2)/ [(b - a)(c - a)] for a <=x <= c
= 1 - ( b-x)2/ [(b - a)(b - c)] for c <x <= b
where , a = 1, b = 5, c = 2
O&M costs follow a U($5, $15) distribution
OM(t) = (t - a)/(b - a) = (t - 5)/10
Fuel Costs follow a triangular distribution on [3, 15] and a mode of 10
F(x) = ((x - a)2)/ [(b - a)(c - a)] for a <=x <= c
= 1 - ( b-x)2/ [(b - a)(b - c)] for c <x <= b
where , a = 3, b = 15, c = 10
Sales price for the plant’s electricity output would follow a normal distribution with a mean of $35 per MWh and a standard deviation of $20 per MWh.
Z = (x - 35) / 20
Response Surface Analysis
The structure of the relationship between the response and the independent variables is unknown. The first step in RSM is to find a suitable approximation to the true relationship. The most common forms are low-order polynomials (first or second-order). The structure of the approximation is not assumed in advance, but is given as part of the solution, thus leading to a function structure of the best possible quality. In addition, the complexity of the function is not limited to a polynomial but can be generalised with the inclusion of any mathematical operator (e.g. Response surface methodology 18 trigonometric functions), depending on the engineering understanding of the problem. The regression coefficients included in the approximation model are called the tuning parameters and are estimated by minimizing the sum of squares of the errors (Box and Draper, 1987).
G(a) = Summation (1,p) of { wp(Fp - Fp(a))2 }
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