Probability distribution analysis of Energy Consortium

Acme Energy Consortium

Acme Energy Consortium consists of 15 power stations that operate in and serve a county that consists of 20 cities. Each station has a number of generators, with each station generator being capable of producing a uniform number of megawatts (MW) per day. Also, each generator has a uniform probability p of not operating on a given day. The table below provides this information for each station.

Note that all generator non-operations are assumed to occur independently. Each city has a daily demand (in megawatts) for energy, as shown in the following table.

For this reason it has contracts with some of the power stations, where a contract requires a station to commit a fixed percentage of its output to that city. As a result, for each station, the distribution of its generated power to each city is fixed, and shown in the matrix A below, where aij is the percent of energy that station i has committed to city j. Note that stations 14 and 15’s distributions do not sum to 100, since they have contracts with cities in a neighboring county.

Exercises

1.       Implement the zero-input R function daily power that has the effect of generating a power supply for a random day, and printing a table that shows for each city i) its daily demand, ii) the amount power supplied to the city on this random day, and iii) the difference between supply and demand. Note: a negative difference means the city experienced a blackout, meaning that part of the city went without power for part of the day.

2.      Acme Power Consortium defines a day as being a failure if one or more cities have a black out on that day. Implement the zero-input function failure which returns 1 for a failure day and zero otherwise. Use IMC with 106 samples in order to estimate pf, the probability of a failure day. Provide your estimate, along with the sample variance, standard error, and 0.90-confidence interval as a comment in the R file.

3.    Implement failure2 which is the same as failure, except that now it accepts the inputs i) station number s, and ii) a probability p that is the new probability that a generator at station s will fail.

4.      The energy consortium is interested in upgrading one of its stations. This upgrade would have the effect of cutting in half the probability that a generator does not operate on a given day. It will perform the upgrade if it can be shown that the mean time between failure days is extended by at least four days. Implement the zero-input void R function consortium report that has the effect of printing the following information for each station: i) station number, ii) estimate of pf using IMC with 106 samples assuming this is the station that is upgraded, iii) 0.90-confidence interval for pf, and iv) mean time between failure days if this station is upgraded.

5.      Do you recommend the consortium perform the upgrade based on their criteria? If so, which station should be upgraded? If not why?

Solution :  Acme_Energy-_Consortium_Prediction/Exercise.txt