Re: How do I implement conditional statement for the wind power coefficient mu in the wind power modeling expression into matlab code using YALMIP solver

[Johan Löfberg]

This is a nonconvex constraint I hope you know, i.e, very hard. One way is to model it using binary variables

mu = sdpvar(1)
WC = sdpvar(1)
region = binvar(3,1);

Model = [sum(region)==1,0 <= mu <= 1, WCmin <= WC <= WCmax];
Model = [model, implies(region(1), [mu == 1, WCmin >= WC];
Model = [model, implies(region(2), [mu == blabla, WCmin <= WC<=WCmax];
Model = [model, implies(region(3), [mu == 0, WC>=WCmax];

Make sure you understand what is done here, and note that it leads to a mixed-integer SDP, for which there are no efficient public solvers (YALMIPs internal b&b solver bnb will be used, but it is really slow compared to a real MILP or MIQP solver). Adding integrality to an SDP is much worse than adding integrality to an LP or QP
http://users.isy.liu.se/johanl/yalmip/pmwiki.php?n=Commands.Implies
http://users.isy.liu.se/johanl/yalmip/pmwiki.php?n=Tutorials.Big-MAndConvexHulls

For all your other questions, those question have nothing to do about YALMIP or related modelling, just stuff you have to figure out on your own

[Kolapo Alli]

Thanks for your support sir. I will read more on those aspects sir.And is there a way you can explain better on how YALMIP works and it's functions in optimization process sir?

[Johan Löfberg]

YALMIP is a modelling language. It transform your high-level representation to a low-level solver specific format.

[Kolapo Alli]

I appreciate your suggestion sir but concerning the mu logical constraint definition, there is problem with the third expression after i amended the parenthesis in the definition for mu which you suggested when trying to implement in my m code sir. The code seems to have complain of invalid parenthesis in the third expression i.e Model = [model, implies(region(2)), [mu == WCmax-WC/WCmax-WCmin, WCmin <= WC<=WCmax]; and I have tried all my very best on this to make it works. Is there a way out I can figure out this problem to make the code run?

Thank you sir , I have the amended logical constraint for mu as follows;

mu = sdpvar(1)

WC = sdpvar(1)

region = binvar(3,1);

Model = [sum(region)==1,0 <= mu <= 1, WCmin <= WC <= WCmax];

Model = [model, implies(region(1)), [mu == 1, WCmin >= WC];

Model = [model, implies(region(2)), [mu == WCmax-WC/WCmax-WCmin, WCmin <= WC<=WCmax];

Model = [model, implies(region(3)), [mu == 0, WC>=WCmax];

[Johan Löfberg]

There are missing parenthesis and brackets in all implications

Model = [model, implies(region(1)), [mu == 1, WCmin >= WC])];

etc

[Johan Löfberg]

Sorry, that should of course be

Model = [model, implies(region(1), [mu == 1, WCmin >= WC])];