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]>
Date: Tuesday, November 25, 2008 1:14 pm
Subject: Re: MATPOWER QUESTIONS- runopf
To: MATPOWER discussion forum <[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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