Need some maths help figuring out calculations for Economy 7 electricity tariff

twozeronine

twozeronine

twozeronine

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Hi

I was hoping someone could help me with some calculations I need to do at work, figuring out how much energy someone uses on an Economy 7 electricity tariff. I've been trying to figure it out all day, but haven't got very far, and it's got people at work stumped too.

So a tariff could have 3 rates, the first two are calculated based on how much electricity someone uses during the day, and the third one is calculated based on how much they use at night. The first two rates are tiered, so that the first 720kWh they use is calculated at the first rate, and the remainder is calculated at the second rate.

So let's say someone spends £600 a year, and they use 45% of their electricity during the day, and 55% at night. I need to find out how much electricity they're using in total throughout the year, using these rates:

Tier 1 (day):
25.868 pence per kWh for the first 720kWh

Tier 2 (day):
17.661 pence per kWh for the remainder

Tier 3 (night):
6.123 pence per kWh

I know that they're using the max of 720kWh for the first tier, but I'm stuck trying to figure out how much they're using for the subsequent tiers. It seems like you need to know one before knowing the other. :confused:

Here's a spreadsheet that might explain better, if anyone wants to give this a go. I basically need to fill in the Usage column.

https://www.dropbox.com/s/jpo5898tjn1c375/Untitled 1.xlsx

Thanks for any help. :)
 
You need to clarify the question atm it seems to be confused

If the % day night usage is based on kwh, and the total bill is £600 then a rough split of 720/1440/2640 units works based on the spread sheet, works out as £602.21 with % of 45/55, can refine this to exactly £600 if you tweak the numbers abit more.

If the 45/55 is based on ££ then...its going to be 720/450/5500 roughly...more info needed

Also why?
 
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ok well to start they are using 45% during day and 55% at night if we divide £600 by those figures then we get £270 during day and £330 at night. Multiply £330 x 100 to get an answer in pence 33000 and divide this by 6.123 = 5389.5 ( rounded off to 1 dec point ) kWh for the night time.

So for day they use a guaranteed 720kWh so multiply 720 by 0.25868 which gives you £186.25 ( rounded up again to nearest pence ) leaving a remainder of: 600 - 330 - 186.25 = 83.75 times 100 = 8375 / 17.661 = 474kWh for Tier 2

this is just how I see it. Bearing in mind that in the real wold 1 unit of elec is equal to 1 kilowatt hour

I've not bothered with the spreadsheet by the way
 
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HardwareGeek said:
You need to clarify the question atm it seems to be confused

If the % day night usage is based on kwh, and the total bill is £600 then a rough split of 720/1440/2640 units works based on the spread sheet, works out as £602.21 with % of 45/55
Click to expand...

Could you show me how you worked those out please, because those numbers are a lot closer than I've got, and look correct.
 
djferrick said:
ok well to start they are using 45% during day and 55% at night if we divide £600 by those figures then we get £270 during day and £330 at night. Multiply £330 x 100 to get an answer in pence 33000 and divide this by 6.123 = 5389.5 ( rounded off to 1 dec point ) kWh for the night time.

So for day they use a guaranteed 720kWh so multiply 720 by 0.25868 which gives you £186.25 ( rounded up again to nearest pence ) leaving a remainder of: 600 - 330 - 186.25 = 83.75 times 100 = 8375 / 17.661 = 474kWh for Tier 2

this is just how I see it. Bearing in mind that in the real wold 1 unit of elec is equal to 1 kilowatt hour

I've not bothered with the spreadsheet by the way
Click to expand...

Sorry, just to clarify that the 55/45% is the percentage of what they use, rather than a percentage of what they pay.
 
twozeronine said:
Could you show me how you worked those out please, because those numbers are a lot closer than I've got, and look correct.
Click to expand...

I just played with the spreadsheet, i will leave the maths to those better able...


basically add a few simple excel sums
1 column below usage to give a total kwh overall
2 column to give total kwh for day (add rate 1 and rate 2 usage)
3 column to give total kwh for night
4 2 more columns to give day and night divided by total (%)

then play with the usage figures of day rate 2 and night until they hit 45/55% and total £600 in cost

hopefully someone will pop in with the correct maths soon!!!

ps. abit more refined 720/1432.05/2636.43 = £600.59
 
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If you don't know their total kWhs used then you're going to have a very hard time working this out. Saying they spend £X amount and that's split 45% here and 55% there means nothing when you have changing tariffs like this.
 
HardwareGeek said:
I just played with the spreadsheet, i will leave the maths to those better able...


basically add a few simple excel sums
1 column below usage to give a total kwh overall
2 column to give total kwh for day (add rate 1 and rate 2 usage)
3 column to give total kwh for night
4 2 more columns to give day and night divided by total (%)

then play with the usage figures of day rate 2 and night until they hit 45/55% and total £600 in cost

hopefully someone will pop in with the correct maths soon!!!
Click to expand...

Ah ok, well thanks for giving it a go. I might play around with what you've done and see if I can find something that works. :)

Zefan said:
If you don't know their total kWhs used then you're going to have a very hard time working this out. Saying they spend £X amount and that's split 45% here and 55% there means nothing when you have changing tariffs like this.
Click to expand...

Indeed, however sites like uSwitch are able to do it somehow. Just wish I knew what blackmagic they're using!!
 
Are you sure they're not just doing it by dividing up the daily cost into the percentages?
 
uswitch will work this out for you automatically if you just state your tariff and say you pay £50 a month with 55% night time usage.

what does uswitch give? then whoever wants to do this can know if they have done it correctly.

Putting in the correct formulae and then using solver should give the right answer.
 
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Unfortunately I've been given the task of writing a calculation engine that spits out the same results as uSwitch, so I need to work out what calculations need to be done under the hood.
 
Sorry, I'm a dummy, I'm not sure what a solver algorithm is. :o Could you explain how you got the value in cell E6? Unless it's because I'm using LibreOffice which doesn't understand some Excel function you're using.
 
twozeronine said:
Thank you! This may be the answer I'm looking for. :) I'll just have to see if I can implement this algorithm.... :eek:
Click to expand...

I'm no computer scientist but I'd have thought something using Newton-Raphson would work.

Otherwise I'm sure there are solvable simultaneous equations there which if it wasn't 11pm I could write down.

edit:

720*x + A*y + B*z = 600

(A + 720)/45 = B/55

where prices are x y & z.

Solve by substitution and you get your answer.
 
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