Dear Ray et al
Thank you for your earlier answer.
Returning to my original question, Implementing line loading constraints in
for own method, I have tried to obtain the line loading equations and
compare them with MATPOWER results. To obtain the line loading, I first run
a power flow calculation, using MATPOWER to get the voltage magnitude and
angle at each buses.
Here I post my script. If you have some time, please help me to find the
reason of this difference:
% calculating line loading via Matpower:
define_constants;
mpc = loadcase('case4gs');
RES=runpf(mpc);
flow_from = sqrt(RES.branch(:, PF).^2 + RES.branch(:, QF).^2);
flow_to = sqrt(RES.branch(:, PT).^2 + RES.branch(:, QT).^2);
flow = (flow_from + flow_to)/2;
MATPOWER_loading = flow ./ RES.branch(:, RATE_A);
% Here is my script .
% obtained from Matpower case4gs.m
from=[ 1 1 2 3]';
to= [ 2 3 4 4]';
r=[ 0.01008 0.00744 0.00744 0.01272]';
x=[ 0.0504 0.0372 0.0372 0.0636]';
B=[ 0.1025 0.0775 0.0775 0.1275]';
Rating=[ 250 250 250 250]';
% Load flow results
v_m=[ 1 0.982 0.969 1.02]';
v_deg=[ 0 -0.976 -1.872 1.523]';
v_a = v_deg.*(pi/180); % convert degree to rad
Z_m=sqrt(r.^2+x.^2);
Z_phi=acos(r./Z_m);
pij=(v_m(from)./Z_m).*(v_m(from).*cos(Z_phi)-v_m(to).*cos(Z_phi-v_a(to)+v_a(from)));
qij=(v_m(from).*((-0.5*v_m(from).*B)+(sin(Z_phi).*v_m(from)./Z_m)-v_m(to).*sin(Z_phi-v_a(to)+v_a(from))));
Sij=sqrt(pij.^2+qij.^2);
pji=(v_m(to)./Z_m).*(v_m(to).*cos(Z_phi)-v_m(from).*cos(Z_phi-v_a(from)+v_a(to)));
qji=(v_m(to).*((-0.5*v_m(to).*B)+(sin(Z_phi).*v_m(to)./Z_m)-v_m(from).*sin(Z_phi-v_a(from)+v_a(to))));
Sji=sqrt(pji.^2+qji.^2);
S=(Sji+Sij)./2;
My_loading=S./Rating;
table(from,to,MATPOWER_loading,My_loading)
Output :
from to MATPOWER_loading My_loading
____ __ ________________ __________
1 2 0.18842 0.070916
1 3 0.46338 0.096366
2 4 0.60769 0.099696
3 4 0.47707 0.055883
Bests.
On Fri, Apr 17, 2015 at 6:05 PM, Ray Zimmerman <r...@cornell.edu> wrote:
> Yes, it is possible, as long as your costs can be put in the form of
> (6.27)-(6-31) in the User’s Manual
> <http://www.pserc.cornell.edu/matpower/docs/MATPOWER-manual-5.1.pdf>. And
> you can simply set the appropriate parameters in the gencost matrix to
> zero, rather than forming user-defined cost terms to cancel out their
> contribution to the objective function.
>
> It looks like your costs are simple linear functions of up and down
> generation shift variables. The standard optimization variables contain
> generation, but not separate up and down shifts in generation from a
> reference. You can define those by introducing a set of user-defined linear
> constraints, in the form of (6.25) …
>
> Pg – Pup + Pdn = Pref
>
> … where Pref is a constant reference dispatch, Pg is part of the existing
> optimization variable *x*, and Pup and Pdn are new vectors of variables
> (blocks in *z*) defined by additional columns in the *A* matrix. You also
> need to set z_min to zero to enforce ...
>
> Pup >= 0
> Pdn >= 0
>
>
> Then, I believe, your costs are purely linear functions of these new
> user-defined optimization variables, so you can use the simplest form of
> the user-defined cost, where parameters d_i and m_i are all 1, k_i and
> r_hat are all zero (so *w* = *r*), the *H* matrix is zero and the *C*
> vector is all ones. In that case, (6.27) and following simply reduces to …
>
> f_u(x, z) = C' * N * [x; z]
>
> All you need to do then is create N in two blocks, stacked vertically, one
> for your f1 and one for your f2.
>
>
> --
> Ray Zimmerman
> Senior Research Associate
> B30 Warren Hall, Cornell University, Ithaca, NY 14853 USA
> phone: (607) 255-9645
>
> On Apr 16, 2015, at 1:04 PM, Electric <electricaltranslat...@gmail.com>
> wrote:
>
> Dear Prof Ray
>
> I studied extended OPF function to adopt my problem to be run with
> MATPOWER package as you recommended already, so I could avoid implementing
> standard OPF constraints like line loadings and voltage range. As I am
> running a multi-objective congestion management problem (equivalently,
> maybe called multi-objective OPF), is it possible to include other
> objective functions separately in the OPF cost function?
> for example :
>
> f1= I have my own cost function, so I can minus the existed cost function
> to cancel it and add my own cost functions that are still directly depended
> on the optimization vector. f1=sum(X[i].Bup[i]+Y[i].Bdown[i]), where X and
> Y are up and down generation shift of unit i and Bup[i] and Bdown[i] are
> their corresponding bid.
>
> f2= security function.
> f2 is also directly depended on the optimization vector.
> f2=sum(X[i].S[i]), where x[i] is up generation shift of unit i and S[i] is
> its corresponding sensitivity to the stability margin.
>
> Your help is much appreciated.
>
>
> On Fri, Apr 10, 2015 at 9:11 PM, Electric <electricaltranslat...@gmail.com
> > wrote:
>
>> Dear Prof Ray and Shiri
>> Thank you so much for your help. I am going to study opf_consfcn()
>> <http://www.pserc.cornell.edu//matpower/docs/ref/matpower5.1/opf_consfcn.html>
>> and find out how to implement the constraints I want.
>> Kind regards.
>>
>> On Fri, Apr 10, 2015 at 5:43 PM, Ray Zimmerman <r...@cornell.edu> wrote:
>>
>>> Specifically, you might look at how the power flow and line limit
>>> constraints are implemented in opf_consfcn()
>>> <http://www.pserc.cornell.edu//matpower/docs/ref/matpower5.1/opf_consfcn.html>.
>>> However, for a problem that includes the standard OPF constraints I still
>>> think it would be simpler and cleaner to set up your problem to use the
>>> extended OPF formulation in MATPOWER, unless of course you have some
>>> requirement the precludes that option.
>>>
>>> Ray
>>>
>>>
>>> On Apr 9, 2015, at 10:40 PM, Abhyankar, Shrirang G. <abhy...@mcs.anl.gov>
>>> wrote:
>>>
>>> http://www.pserc.cornell.edu//matpower/docs/ref/
>>>
>>> On Apr 9, 2015, at 4:00 PM, "Electric" <electricaltranslat...@gmail.com>
>>> wrote:
>>>
>>> Dear Shri
>>> Thanks for your answer. But I don't want to use runopf(). I want to
>>> write these constraint manually with Ybus and equations I've written. Is
>>> that possible? How should I start?
>>>
>>> Thank you.
>>>
>>> On Fri, Apr 10, 2015 at 1:24 AM, Abhyankar, Shrirang G. <
>>> abhy...@mcs.anl.gov> wrote:
>>>
>>>> I don't know what your algorithm does but I think you can do the
>>>> same, determine optimal generation and load, using MATPOWER's optimal power
>>>> flow (runopf). runopf supports all the constraints that you've listed.
>>>>
>>>>
>>>> Shri
>>>>
>>>> ------------------------------
>>>>
>>>> *From:* bounce-119032919-33970...@list.cornell.edu [
>>>> bounce-119032919-33970...@list.cornell.edu] on behalf of Electric [
>>>> electricaltranslat...@gmail.com]
>>>> *Sent:* Thursday, April 09, 2015 3:18 PM
>>>> *To:* MATPOWER discussion forum
>>>> *Subject:* How to verify the feasibility of your solution without
>>>> running Power flow?
>>>>
>>>> I am using an algorithm that changes the amount of demand
>>>> and generation at each bus (Pd,Pg) to mitigate over load of lines and
>>>> enhance the security. The output of my algorithm (Pd,Pg) must be checked to
>>>> insure that they are feasible. So, it is obvious that by assigning this new
>>>> calculated values instead of old Pg and Pd (generation and demand ) at each
>>>> bus and running a simple power flow (pf), I can find out if the calculated
>>>> results are feasible.
>>>> However, this is an optimization problem. Therefore, feasibility
>>>> of the suggested values of Pd and Pg by fmincon must be verified at each
>>>> iteration(1000 times). Basically, it can be accomplished by running a power
>>>> flow in constraint function of fmincon and checking lines loading and
>>>> voltage range.
>>>> But, doing so is very time consuming and takes more than an hours
>>>> to calculate the feasible Pg and Pd. So I was wonder if there is another
>>>> faster way to check the feasibility of the calculated Pd,Pg without running
>>>> power flow.
>>>> I think, if the solution (calculated Pd,Pg) satisfies these
>>>> constraints,the answer is then feasible and there is no need to run power
>>>> flow.
>>>> But I have some problems in considering the constraints 5,8,9,10.
>>>>
>>>> 1) Pgmin(j) <Pg(j) <Pgmax(j) % j indicates buses with generator
>>>> 2) Qgmin(j) <Qg(j) <Qgmax(j) % j indicates buses with generator
>>>> 3) Pdmin(k) <Pd(k) <Pdmax(k) % k indicates buses with demand
>>>> 4) Qd(k)=Pd(k)*tan(phi(k)) % ph(k) is load P.F at bus K
>>>> Nodal active balance:
>>>> 5) Pg(n) -Pd(n)=|V(i)| sum( |Y(h,n)| .V(h)*Cos(del(n)-del(h)-teta(n,h)))
>>>> where Pg(n) is nodal generation which is calculated as:
>>>> 6) Pg(n)=sum (Pg(j)) at bus n
>>>> 7) Pd(n)=sum (Pd(k)) at bus n
>>>> teta(n,h) is the angle of Y(n,h), del(n) and del(h) are bust angle of
>>>> n and h.
>>>> Nodal reactive balance:
>>>> 8) Qg(n) -Qd(n)=|V(i)| sum( |Y(h,n)| .V(h)*Sin(del(n)-del(h)-teta(n,h)))
>>>>
>>>> 9) Vmin(n)<V(n)<Vmax(n) % voltage range at all buses.
>>>> 10) S(i,j)<Smax(i,j). transmitted apparent power from i,j must be
>>>> less than capacity of line.
>>>>
>>>> Thanks in advance
>>>>
>>>>
>>>>
>>>
>>>
>>
>
>
