Hello,
I am working on an energy system optimization with a storage device. I need the power stored or delivered by the battery to be = 0 when the state of charge is max (>= 100%) or min (<= 0%) respectively. The problem is both the power and the SOC are variables defined at each timestep. The parts of my code related to this are:
Set t hours /t1*t24/;
Scalar PdisN /241.5/; *Discharge power of 1 cell
Scalar PchN /395/; *Charge power of 1 cell
Scalar DSOCdis /-0.01/; *SOC decrease while discharging at max power
Scalar DSOCch /0.01/; *SOC increase while charging at max power
[...]
Variables SOC(t);
Integer variables N_cells;
Positive variables pSTOR_Dis(t), pSTOR_Ch(t), [...];
Binary variable U;
N_cells.lo = 1;
SOC.lo(t) = 0; SOC.up(t) = 1; SOC.l(t) = 0.5;
Equations STORdis, STORch, SOCchange [...];
STORdis(t).. pSTOR_Dis(t) =l= N_cells * PdisN * U(t);
STORch(t).. pSTOR_Ch(t) =l= N_cells * (-PchN) * (U(t) - 1);
SOCchange(t).. SOC(t) =e= SOC(t-1) + (pSTOR_Dis(t) / (PdisN * N_cells)) * DSOCdis - (pSTOR_Ch(t) / (PchN * N_cells)) * DSOCch;
[...]
I tried inserting two other equations:
STORfull(t) $ (SOC(t) ge 0.95).. pSTOR_Ch(t) =e= 0;
STORempty(t) $ (SOC(t) le 0.05).. pSTOR_Dis(t) =e= 0;
but it didn’t work. What can I do instead?
(I am using MINLP solver for now, but I still have to choose the best solver for the problem)
Thank you in advance!
You can’t use conditions on variables. Until you solve, variables don’t have a value and using $ condition on variable while defining your constraint does not make much sense. Please refer to the following FAQ.
https://newforum.gams.com/t/how-do-i-formulate-logical-expressions-in-equations/3738/1
Hope this helps.
Thank you Atharv!
I understood why I can’t use conditional statements on variables.
I also looked into the bigM method, which would work perfectly if my “control” variable was binary, for example:
Set t 'time' /1:24/
Binary variable U(t) 'State of the battery ON-OFF'
Variable Pbatt
Parameters V, I
Equations
if U(t) = 1 then Pbatt(t) = V*I
if U(t) = 0 then Pbatt(t) = 0
But in my case the control variable is a real positive number (the state of charge, varying from 0 to 1), therefore the bigM method cannot be applied.
I also tried to reformulate the parameters so that one of the Pbatt factors would be 0 in case of SOC = 0 (or 1 for charging), but there is no function of SOC that can replicate this behaviour.
Do you know any other way to model this?
Thank you!
You can use big-M to declare another variable that is 1 if say SOC is greater than 0.95 or less than 0.05 based on your need.
Let’s say you want a binary variable to be 1 if SOC(t) is greater than 0.95. You can do the following:
binary variable b(t);
SOC(t) - 0.95 =l= M * b(t);
The idea is that if soc(t) -0.95 is greater than 0 then b(t) has to be 1.
You can then use b(t) to model your constraint.
Thank you very much, this worked!
Sorry if I insist with questions, but this is really helping me a lot 
Is it normal that the binary variable ( b(t) in your example ) is not really binary in the solutions? It often (i.e. in many of the timesteps) assumes values very close to 1 or 0, but not exactly 1 or 0. This causes problems in my model.
Of course, I introduce it as binary variable in the code. I tried increasing the magnitude of M but after a certain value I get errors while compiling. Is there anything else I can do, or is this how it should be?
Thank you again for your kind help!
Francesca,
Regarding the value of big-M, please read the following FAQ.
https://newforum.gams.com/t/how-large-should-big-m-be/3129/2
Regarding non-binary values of binary variables, please read the last three paragraphs of binary variables section in GAMS documentation
https://www.gams.com/36/docs/UG_LanguageFeatures.html?search=binary%20variable#UG_LanguageFeatures_BinaryVariables
Hope this helps.