Variable explanations?

[werdnum]

I was trying to hack in support for heating/cooling, but I'm having a bit of trouble understanding the code.

Would be great to have some explanation for what the variables all mean, especially the more obscure ones.

My first question: what is the difference between P_def_bin1 and P_def_bin2?

[davidusb-geek]

Hi sorry for not answering this before.
These are two helper binary variables.
The P_def_bin1 is used in the LP formulation to solve the problem of a semi-continuous variable: https://web.mit.edu/lpsolve/doc/semi-cont.htm
The P_def_bin2 variable is used when implementing the constraint that limits the number of startups for each deferrable load.

[werdnum]

No problem, do they have the same value? I'm not familiar with the library you're using (or LP generally), could they be merged into one variable? — Andrew Garrett

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On Tue, 14 May 2024 at 04:40, David ***@***.***> wrote: Hi sorry for not answering this before. These are two helper binary variables. The P_def_bin1 is used in the LP formulation to solve the problem of a semi-continuous variable: https://web.mit.edu/lpsolve/doc/semi-cont.htm The P_def_bin2 variable is used when implementing the constraint that limits the number of startups for each deferrable load. — Reply to this email directly, view it on GitHub <#273 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AACCFXQKWZQZZBZXFO5WNFTZCECKRAVCNFSM6AAAAABHI5IEA2VHI2DSMVQWIX3LMV43SRDJONRXK43TNFXW4Q3PNVWWK3TUHM4TIMRUHEZTG> . You are receiving this because you authored the thread.Message ID: ***@***.***>

[davidusb-geek]

No they don't have the same value and no we need those two variables to be different.

[werdnum]

Okay, thanks. What do they represent? I figured one of them is "whether the load is on or not at timestep T" - what does the other one represent? — Andrew Garrett

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On Tue, 14 May 2024 at 06:27, David ***@***.***> wrote: No they don't have the same value and no we need those two variables to be different. — Reply to this email directly, view it on GitHub <#273 (reply in thread)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AACCFXU5JFUZJIA75QOOGBDZCEO3HAVCNFSM6AAAAABHI5IEA2VHI2DSMVQWIX3LMV43SRDJONRXK43TNFXW4Q3PNVWWK3TUHM4TIMRVG4ZTC> . You are receiving this because you authored the thread.Message ID: ***@***.***>

[davidusb-geek]

It is an additional binary variable added to be able to solve the problem. These are very typical of the linear programming approach and are basically there to solve for the non-linearities in the equations.
In the specific case of P_def_bin1 it is used to solve the semi-continuous variable problem.
Please see this link, it is well explained with the corresponding equations: https://yetanothermathprogrammingconsultant.blogspot.com/2016/08/semi-continuous-variables.html

[werdnum]

Thanks! Just to check my understanding, it sounds like a semi-continuous variable is a variable x that can either be zero or between two bounds (they use l and u in the explanation). My reading is that you model it by adding a binary variable d, and then you say that x is between dl and du. If d is 0, then x has to also be 0, and if d is 1 then x has to be between l and u.

That all makes sense. But based on that, it sounds like d is 0 when the load is off (planned amount = 0) and 1 when the load is on (planned amount is > 0). That sounds like it's the same? I must be missing something...

I think you've answered my question (that is, that it's there to support modelling the load allocation as a semi-continuous variable) and you don't have to educate me on the ins and outs of linear programming, so I'm happy to take your word for it - just curious...

[davidusb-geek]

Yes they are similar. The difference is in the flexibility allowed within the range [l, u]. Even if the load is on (planned amount > 0), the value of x can vary within that specified range. This will add some flexibility during the optimization solve.