Dear professor Zimmerman
Thank you for your explanation, now I understand this point!
I would like to ask you something more, if I can; this is not a question
strictly about runopf but I think it is attributable to fmincon.
When I run my case study i found some constraints are active but their
mulplier is 0, and i don't understend why and if it is correct.
For example the output i get is like this:
Optimization terminated: magnitude of search direction less than
2*options.TolX
and maximum constraint violation is less than options.TolCon.
Active inequalities (to within options.TolCon = 5e-006):
lower upper ineqlin ineqnonlin
1 1 2
33 33
67 50
69 66
73 71
83 72
75
77
79
80
81
82
83
My grid has 32 buses, so 1 and 33 are the constraints on angle and magnitude
of reference bus (Vang=0 Vm=1 p.u., set by me), then i have the upper 50
(which means the voltage magnitude at bus 18 is at its upper limit) and the
inequality non linear 2 (which means S in line 2, starting point, is at its
upper limit too); now the multiplier related to voltage magnitude at bus 18
is not zero, but the one related to line 2 is zero. Any suggestion?
Thanks a lot, have a good day!
Alessandro
Università di Padova, Italia
On Mon, Dec 1, 2008 at 2:39 PM, Ray Zimmerman <[email protected]> wrote:
> Alessandro,
> The system lambda refers to the sensitivity of the system cost to
> perturbations in the total system load. In an AC formulation, however, the
> location of the load perturbation matters (since losses & congestion depend
> on it), so the only way to have a single system lambda is if you define
> precisely the "direction" of the load perturbation vector. For example, a
> load-weighted average of the nodal prices at load buses would (I believe)
> correspond to the sensitivity with respect to a proportional perturbation in
> all loads.
>
> The bottom line is that you normally only talk about a single system lambda
> when using simpler models which do not include a locational component for
> losses. In such cases you only have a single power balance equation and
> therefore a single system lambda. With a full AC model, the power balance
> equations are nodal and so are the lambdas.
>
> --
> Ray Zimmerman
> Senior Research Associate
> 428-B Phillips Hall, Cornell University, Ithaca, NY 14853
> phone: (607) 255-9645
>
>
> On Dec 1, 2008, at 4:00 AM, Alessandro Sacco wrote:
>
> Good day to all of you!
>
> Always talking about AC OPF formulation, I would ask you something more.
>
> When you introduce as constraints (non linear equality constraints) the
> active and reactive power balance at each bus, the result is 2*bus Lagrange
> multipliers on bus power mismatch; now I'm dealing with economic formulation
> of the OPF (such as spot prices) and I need to find out the values of
> Lagrange multiplier on total active and reactive power balance, the so
> called system-lambda.
>
> So I'm trying to obtain this 2 multipliers introducing two more non-linear
> equality constraint in the formulation of the AC OPF, these are the total
> active and reactive power balance:
> sum(Pg_i) - sum(Pd_i) = LP , where LP are active losses
> sum(Qg_i) - sum(Qd_i) = LQ , where LQ are reactive losses
> but in this way I find out new enormous Lagrange multipliers, so I suppose
> something is wrong.
>
> I also tryed to compute the amount of this 2 constraints after solving the
> OPF with your formulation and the result is the 2 new constraints are
> already satisfied, so the formulation of problem takes properly into account
> the losses, too.
>
> So, finally, my question is how we can calculate the system lamba for P and
> for Q.
>
> Thank you,
> have a nice day!
>
> Alessandro
>
> Mutmainna Tania wrote:
>
> thanks so much!!!!
>
> ----- Original Message -----
> From: Ray Zimmerman <[email protected]> <[email protected]>
> Date: Tuesday, November 25, 2008 1:14 pm
> Subject: Re: MATPOWER QUESTIONS- runopf
> To: MATPOWER discussion forum <[email protected]>
> <[email protected]>
>
> By default this section displays a row for each bus at which an
> upper
> (Vmax) or lower (Vmin) voltage limit is binding. These limits are
> defined in the corresponding column of the bus matrix in the input.
>
> The 'mu' values are the shadow prices (Lagrange multipliers) on the
>
> corresponding constraint, so they represent the sensitivity of the
> system cost to a unit change in the limit.
>
> --
> Ray Zimmerman
> Senior Research Associate
> 428-B Phillips Hall, Cornell University, Ithaca, NY 14853
> phone: (607) 255-9645
>
>
> On Nov 25, 2008, at 12:53 PM, Mutmainna Tania wrote:
>
>
>
> dear Professor Zimmerman,
>
> Good Day!!
> I would like your help to understand the "runopf" output values.
> What exactly is defined in "voltage constraints" table and what
>
>
> do
>
>
> "Vmin
> mu" and "Vmax mu" represent?
>
>
> thanks in advance.
>
> Regards.
> Tania
>
>
>
>
> --
> *Alessandro Sacco*
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