Probability of Energy Shortage

[lcolli71]

To anyone who can help,

I am trying to ascertain the likelihood that the UK will experience a power shortage this winter, ie, the probable amount of time that the UK energy production capacity will be less than demand. I have one constant and two variables. The constant is fixed energy capacity - derived from sources such as coal plants, nuclear plants, etc. Then there is a variable capacity - wind. Total capacity is therefore fixed capacity plus wind capacity. The other variable is demand.

I have a data set that gives the wind capacity and demand for every 5 minutes of the past 8 years. From this I have been able to establish the probable frequency distribution of wind capacity and demand capacity for this coming winter, attached in a pdf. How do I calculate the probability that for any given 5min time stamp the wind capacity will be sufficiently small and the demand sufficiently high that total capacity is smaller than demand?

what is the probability that F+w<d, where:
F - constant
w - unevenly distributed variable between wmin and wmax
d -

unevenly distributed variable between dmin and dmax
F+wmin<dmax​

Any help would be very much appreciated.​

 

[Miner]

The easiest way that I could come up with was a Monte Carlo simulation using your empirically derived distributions. I came up with a probability that demand would exceed capacity approximately 0.55% of the time.

 

[lcolli71]

That's really helpful thank you very much, it's exactly what I needed.

I will need to do this calculation for a range of different datasets. I'm a bit of an amateur when it comes to statistics and I've never modelled a monte carlo simulation before. I was just wondering what software you used to conduct this analysis, and if you know of anywhere I might be able to find a step by step guide as to how to do it?

 

[Miner]

I used Quantum XL. It is an Excel add-in, and is currently priced at $549 USD.

This link has a step-by-step for Minitab. While there are some Minitab-specific instructions, the actual steps are fairly generic. There are also a lot of YouTube videos that may be helpful.