Circular Cell Reference

Question

I have a question regarding a circular cell reference. I have come up with an example that illustrates my dilemma and I attached an illustration.

Here's the deal. My house needs heat and it needs electricity :

My house needs 7 units of heat and 1 unit of electricity.

My generator is 50% efficient. So for every unit of electricity used to power the generator, I only get .5 units of electricity for my house. You can neither create nor destroy energy, so the other 50% that isn't turned into electricity, turns into heat.

My heat pump consumes 1 unit of electricity in order to produce 2 units of heat. This means that the heat pump is 200% efficient. Additionally we get to use the waste heat from the generator.

Please look at the attached example. I drew out the scenario so you can visualize it. Subscript E is used to denote electricity. Subscript H is used to denote heat.

I need to be able to change the generator efficiency, heat pump efficiency, and how much electricity the house needs.​ I would like to be able to manipulate each variable.

Can anyone help me input this into excel???

Thanks!!!

-Jon

Example of Scenario

Answer 1

Although I doubt the physical correctness of your approach, the math problem is solvable in Excel with goal seek.

Let's have the following sheet:

Formulas:

C4 : =-(C2*B4)

D4 : =-(C2+C4)

C6 : =-(C4+C8)

D6 : =-(C6*B6)

D8 : =-(D4+D6)

D10 : =D8/C8

Consumption are negative values, production are positive values.

Now change the variables, for example B4 , B6 or C8 and call What-If Analysis, Goal Seek. D10 must be 7 and C2 is the changing cell.

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A real math solution would be:

Generator Input = gi

Generator Efficiency = geff

Heat Pump Efficiency = hpeff

House Electricity Needed = hen

House Heat Needed = hhn

(gi*geff - hen) * hpeff + gi*(100%-geff) = hhn

gi*geff*hpeff - hen*hpeff + gi*(100%-geff) = hhn
gi*geff*hpeff + gi*(100%-geff) = hhn + hen*hpeff 
gi * (geff*hpeff + (100%-geff)) = hhn + hen*hpeff 

gi = (hhn + hen*hpeff ) / (geff*hpeff + (100%-geff))

6kW = (7kW + 1kW*200%) / (50%*200% + (100% - 50%))

6kW = 9kW / 1,5

Answer 2

You can rearrange this a little to make it more simple.

You're trying to solve for a + b:

a = Heat Pump Input

b = Generator Input

With the following input values:

c = Generator Efficiency

d = Heat Pump Efficiency

H = Heat Needed

W = Electricity Needed

Now, we know:

W = bc

H = ad + b(1-c)

Hence we can derive:

b = W/e

a = (HW(1-c)/c)/d

Input your values for c,d,H and W and you get your result.