GiantOutBack
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- Joined
- Feb 18, 2016
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- 1
So I'm trying to describe mathematically something that's used intuitively at my workplace. A HV transformer used in a certain voltage network (say, 22kV) will have a certain KVA (A*V/1000) rating, for a large one, it might be 500 KVA. If that transformer was fully loaded, it would have a load of 22.73 A (22.73*22000/1000). We don't necessarily know how heavily loaded an individual transformer might be unless we look at inferred data, and there are safety implications for guessing, so we don't assume a single transformer's load. The data we DO have is the following;
From the diagram, we have a device that will tell us the total load in Amps. This load (LoadTotal) is somehow distributed among the individual transformers. What is the probability, that for a given 'upstream' measured load, that a subset (say, transformers 1-6) will have a load (LoadSubset) in excess of X, given that this means that the rest of the transformers must have load lower than LoadTotal-LoadSubset.
The intuitive example may be illustrative. Total load is 100A, subset of the transformers 1-6 must not have load higher than 50A, or when we reconfigure the network, an overload will occur. It seems improbable that the subset of transformers, of total capacity 1375 KVA (or ~62.5 A) would be loaded to ~80% or higher and cause an overload, given that the other transformers of total KVA capacity 2275 (103.4 A) must be at 48% or lower. Typically, the intention is that the transformers will be balanced and have an appropriate capacity for their load, but even if we assume a uniform distribution for an individual transformer (any % loading between 0 and 100 is equally likely) a set will still form a normal distribution. It's probably more likely that a transformers likely load is described by a truncated normal distribution, but that's more complex so I'm going with the simpler case for now.
So that's where I'm stuck. I know I need to end up by determining the probability of one set of transformers exceeding X and multiplying that by the probability of the other set of transformers being the LoadTotal-X, but I'm not sure how best to start.
From the diagram, we have a device that will tell us the total load in Amps. This load (LoadTotal) is somehow distributed among the individual transformers. What is the probability, that for a given 'upstream' measured load, that a subset (say, transformers 1-6) will have a load (LoadSubset) in excess of X, given that this means that the rest of the transformers must have load lower than LoadTotal-LoadSubset.
The intuitive example may be illustrative. Total load is 100A, subset of the transformers 1-6 must not have load higher than 50A, or when we reconfigure the network, an overload will occur. It seems improbable that the subset of transformers, of total capacity 1375 KVA (or ~62.5 A) would be loaded to ~80% or higher and cause an overload, given that the other transformers of total KVA capacity 2275 (103.4 A) must be at 48% or lower. Typically, the intention is that the transformers will be balanced and have an appropriate capacity for their load, but even if we assume a uniform distribution for an individual transformer (any % loading between 0 and 100 is equally likely) a set will still form a normal distribution. It's probably more likely that a transformers likely load is described by a truncated normal distribution, but that's more complex so I'm going with the simpler case for now.
So that's where I'm stuck. I know I need to end up by determining the probability of one set of transformers exceeding X and multiplying that by the probability of the other set of transformers being the LoadTotal-X, but I'm not sure how best to start.