Thanks Tobias! I was just about to respond to your first message when I saw
this. I’ve linked to this from https://github.com/MATPOWER/matpower/issues/38
so I have it right there when I get some time to try to integrate this into
makePTDF().
Ray
On Feb 18, 2020, at 2:07 AM,
[email protected]<mailto:[email protected]> wrote:
Finally with some more thoughts I figured it out and want to apologize, that I
asked in the first place. Now I get for a sample of buses the same PTDF values
as with the makePTDF function.
Here is my solution, if anyone might be interested:
"
OutmailID: 124387247, List: 'matpower-l', MemberID: 82861091
SCRIPT: "% alternative as in
https://github.com/MATPOWER/matpower/issues/37#issuecomment-391459159
nb = size(mpc.bus, 1);
slack_bus = find(mpc.bus(:, BUS_TYPE) == REF); % Ref. slack
slack = slack_bus;
noslack = find((1:nb)' ~= slack_bus);
[Bbus, Bf, Pbusinj, Pfinj] = makeBdc(mpc);
Bbus(slack, :) = []; % remove slack row
Bbus(:, slack) = []; % remove slack col
for it = 1:numel(exemplary_subSet_slack)
dP = zeros(nb, 1); % init
dP(slack) = []; % remove slack
i = exemplary_subSet_slack(it);
if i > slack
i = i-1;
end
dP(i) = 1;
dx = Bbus \ dP;
dTheta = zeros(nb, 1); % init
dTheta(noslack) = dx;
H_altern(:,it) = Bf * dTheta;
end"
TCL MERGE ERROR ( 02/18/2020 17:30:52 ): "syntax error in expression "i":
variable references require preceding $% slack distribution
slack_weights(1:numel(exemplary_subSet_slack)) =
1/numel(exemplary_subSet_slack);
v = H_altern * slack_weights';
for k = 1:numel(exemplary_subSet_slack)
H_newAndDistributed(:, k) = H_altern(:, k) - v;
end
With best regards,
Tobias Hoffmann
Von:
[email protected]<mailto:[email protected]>
<[email protected]<mailto:[email protected]>>
Im Auftrag von Marwan Ahmed Alasali
Gesendet: Montag, 17. Februar 2020 10:22
An: MATPOWER discussion forum
<[email protected]<mailto:[email protected]>>
Cc: [email protected]<mailto:[email protected]>
Betreff: Re: alternative to makePTDF for a subset of busses (with distributed
slack)
Dear all,
I want data for IEEE30 bus system
On Mon, 17 Feb 2020 at 14:49,
<[email protected]<mailto:[email protected]>> wrote:
Dear all,
I would like to calculate the PTDFs of a subset of ~500 nodes for a large
network of > 10,000 nodes. Since the whole calculation of the PTDF matrix is
very CPU-intensive (as I have already read in
https://github.com/MATPOWER/matpower/issues/37 and
[email protected]/msg05580.html<http://[email protected]/msg05580.html>), I
tried to orientate myself on this:
https://github.com/MATPOWER/matpower/issues/37#issuecomment-391459159.
Here is my consideration using the example of the test scenario "case30":
mpc = loadcase(case30);
mpc = ext2int(mpc);
"
OutmailID: 124387247, List: 'matpower-l', MemberID: 82861091
SCRIPT: "% Referenz PTDF
% distributed_slack_setNodes = [1, 7, 15, 24];
define_constants()
mpc = loadcase(case30);
exemplary_subSet_slack = randi(30,1,5);
weightSlack = zeros(size(mpc.bus,1),1);
weightSlack(exemplary_subSet_slack) = 1;
slackForPTDF = weightSlack/numel(exemplary_subSet_slack);
H_makePTDF = makePTDF(mpc,slackForPTDF);%,slackForPTDF)%,slack);
H_makePTDF_rel = H_makePTDF(:,exemplary_subSet_slack);"
TCL MERGE ERROR ( 02/18/2020 17:30:52 ): "invalid command name "1,"%
alternative as in
https://github.com/MATPOWER/matpower/issues/37#issuecomment-391459159
nb = size(mpc.bus, 1);
slack_bus = find(mpc.bus(:, BUS_TYPE) == REF); % Ref. slack
slack = slack_bus;
noslack = find((1:nb)' ~= slack_bus);
[Bbus, Bf, Pbusinj, Pfinj] = makeBdc(mpc);
Bbus(slack, :) = []; % remove slack row
Bbus(:, slack) = []; % remove slack col
for it = 1:numel(exemplary_subSet_slack)
dP = zeros(nb, 1); % init
dP(slack) = []; % remove slack
i = exemplary_subSet_slack(it);
tmpDistributed_slack_set = exemplary_subSet_slack;
tmpDistributed_slack_set(it) = [];
dP(i) = 1;
j = tmpDistributed_slack_set;
dP(j) = -1 / numel(j);
dx = Bbus \ dP;
dTheta = zeros(nb, 1); % init
dTheta(noslack) = dx;
H_altern(:,it) = Bf * dTheta;
end
"
OutmailID: 124387247, List: 'matpower-l', MemberID: 82861091
SCRIPT: "% slack distribution
slack_weights(1:numel(exemplary_subSet_slack)) =
1/numel(tmpDistributed_slack_set) - 1/numel(exemplary_subSet_slack);
v = H_altern * slack_weights';
for k = 1:numel(exemplary_subSet_slack)
H_altern_2(:, k) = H_altern(:, k) - v;
end
Unfortunately, the calculation does not lead to the desired result. I suspect
my error in the distribution of the slack, but I am not sure.
I would be very happy about a help. Thanks a lot!
With best regards,
Tobias Hoffman
--
Thanks & Regards
Marwan Ahmed Alasali
Research Scholar
Department of Electrical Engineering,
Aligarh Muslim University, Aligarh
Contact:+91-9634376962
[email protected]<mailto:[email protected]>
[email protected]<mailto:[email protected]>
skype : marwan.alaslay
--_000_5E99F7502F324D4380330801FFA0A276cornelledu_ Content-Type: text/html;
charset="utf-8" Content-ID:
<[email protected]>
Content-Transfer-Encoding: base64 <html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
</head>
<body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break:
after-white-space;" class="">
Thanks Tobias! I was just about to respond to your first message when I saw
this. I’ve linked to this from
<a href="https://github.com/MATPOWER/matpower/issues/38";
class="">https://github.com/MATPOWER/matpower/issues/38</a> so I have it right
there when I get some time to try to integrate this into
<font face="Courier" class="">makePTDF()</font>.
<div class=""><br class="">
</div>
<div class=""> Ray</div>
<div class=""><br class="">
</div>
<div class="">
<div class="">
<div><br class="">
<blockquote type="cite" class="">
<div class="">On Feb 18, 2020, at 2:07 AM, <a
href="mailto:[email protected]"; class="">
[email protected]</a> wrote:</div>
<br class="Apple-interchange-newline">
<div class="">
<div class="WordSection1" style="page: WordSection1; caret-color: rgb(0, 0,
0); font-family: Helvetica; font-size: 12px; font-style: normal;
font-variant-caps: normal; font-weight: normal; letter-spacing: normal;
text-align: start; text-indent: 0px; text-transform: none; white-space: normal;
word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;">
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" class="">Finally with some more thoughts I figured it out
and want to apologize, that I asked in the first place. Now I get for a
sample of buses the same PTDF values as with the makePTDF function.<o:p
class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" class="">Here is my solution, if anyone might be
interested:</span><span lang="EN-GB" class=""><o:p class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 12pt; font-family: "Courier
New";" class=""><o:p class=""> </o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New"; color: forestgreen;" class="">"
TCL MERGE ERROR ( 02/18/2020 17:30:52 ): "wrong # args: should be "for start
test next command"% alternative as in<span
class="Apple-converted-space"> </span><a
href="https://github.com/MATPOWER/matpower/issues/37#issuecomment-391459159";
style="color: purple; text-decoration: underline;"
class="">https://github.com/MATPOWER/matpower/issues/37#issuecomment-391459159</a></span><span
lang="EN-GB" style="font-size: 8pt; font-family: "Courier New";"
class=""><o:p class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class="">nb = size(mpc.bus, 1);<span
class="Apple-converted-space"> </span></span><span lang="EN-GB"
style="font-size: 8pt; font-family: "Courier New";" class=""><o:p
class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class="">slack_bus = find(mpc.bus(:, BUS_TYPE) == REF);<span
class="Apple-converted-space"> </span></span><span lang="EN-GB"
style="font-size: 9pt; font-family: "Courier New"; color:
forestgreen;" class="">%
Ref. slack</span><span lang="EN-GB" style="font-size: 8pt; font-family:
"Courier New";" class=""><o:p class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class="">slack = slack_bus;</span><span lang="EN-GB"
style="font-size: 8pt; font-family: "Courier New";" class=""><o:p
class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class="">noslack = find((1:nb)' ~= slack_bus);</span><span
lang="EN-GB" style="font-size: 8pt; font-family: "Courier New";"
class=""><o:p class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class="">[Bbus, Bf, Pbusinj, Pfinj] = makeBdc(mpc);</span><span
lang="EN-GB" style="font-size: 8pt; font-family: "Courier New";"
class=""><o:p class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class="">Bbus(slack, :) = []; <span
class="Apple-converted-space"> </span></span><span lang="EN-GB"
style="font-size: 9pt; font-family: "Courier New"; color:
forestgreen;" class="">% remove
slack row</span><span lang="EN-GB" style="font-size: 8pt; font-family:
"Courier New";" class=""><o:p class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class="">Bbus(:, slack) = []; <span
class="Apple-converted-space"> </span></span><span lang="EN-GB"
style="font-size: 9pt; font-family: "Courier New"; color:
forestgreen;" class="">% remove
slack col</span><span lang="EN-GB" style="font-size: 8pt; font-family:
"Courier New";" class=""><o:p class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 8pt; font-family: "Courier
New";" class=""><o:p class=""> </o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier New";
color: blue;" class="">for</span><span lang="EN-GB" style="font-size: 9pt;
font-family: "Courier New";" class=""><span
class="Apple-converted-space"> </span>it =
1:numel(exemplary_subSet_slack)</span><span lang="EN-GB" style="font-size: 8pt;
font-family: "Courier New";" class=""><o:p
class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class=""> <span
class="Apple-converted-space"> </span></span><span lang="EN-GB"
style="font-size: 8pt; font-family: "Courier New";" class=""><o:p
class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class=""> dP = zeros(nb, 1);<span
class="Apple-converted-space"> </span></span><span lang="EN-GB"
style="font-size: 9pt; font-family: "Courier New"; color:
forestgreen;" class="">% init</span><span lang="EN-GB" style="font-size: 8pt;
font-family: "Courier New";" class=""><o:p
class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class=""> dP(slack) = []; <span
class="Apple-converted-space"> </span></span><span lang="EN-GB"
style="font-size: 9pt; font-family: "Courier New"; color:
forestgreen;" class="">% remove
slack</span><span lang="EN-GB" style="font-size: 8pt; font-family:
"Courier New";" class=""><o:p class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class=""> <span
class="Apple-converted-space"> </span></span><span lang="EN-GB"
style="font-size: 8pt; font-family: "Courier New";" class=""><o:p
class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class=""> </span><span lang="EN-GB"
style="font-size: 8pt; font-family: "Courier New";" class=""><o:p
class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class=""> i =
exemplary_subSet_slack(it);</span><span lang="EN-GB" style="font-size: 8pt;
font-family: "Courier New";" class=""><o:p
class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class=""> <span
class="Apple-converted-space"> </span></span><span lang="EN-GB"
style="font-size: 8pt; font-family: "Courier New";" class=""><o:p
class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class=""> </span><span lang="EN-GB"
style="font-size: 9pt; font-family: "Courier New"; color: blue;"
class="">if</span><span lang="EN-GB" style="font-size: 9pt; font-family:
"Courier New";" class=""><span
class="Apple-converted-space"> </span>i
> slack</span><span lang="EN-GB" style="font-size: 8pt; font-family:
"Courier New";" class=""><o:p class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class=""> i =
i-1;</span><span lang="EN-GB" style="font-size: 8pt; font-family: "Courier
New";" class=""><o:p class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class=""> <span
class="Apple-converted-space"> </span></span><span lang="EN-GB"
style="font-size: 9pt; font-family: "Courier New"; color: blue;"
class="">end</span><span lang="EN-GB" style="font-size: 8pt; font-family:
"Courier New";" class=""><o:p class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class=""> <span
class="Apple-converted-space"> </span></span><span lang="EN-GB"
style="font-size: 8pt; font-family: "Courier New";" class=""><o:p
class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class=""> dP(i) = 1;</span><span
lang="EN-GB" style="font-size: 8pt; font-family: "Courier New";"
class=""><o:p class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class=""> <span
class="Apple-converted-space"> </span></span><span lang="EN-GB"
style="font-size: 8pt; font-family: "Courier New";" class=""><o:p
class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class=""> dx = Bbus \ dP;</span><span
lang="EN-GB" style="font-size: 8pt; font-family: "Courier New";"
class=""><o:p class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class=""> <span
class="Apple-converted-space"> </span></span><span lang="EN-GB"
style="font-size: 8pt; font-family: "Courier New";" class=""><o:p
class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class=""> dTheta = zeros(nb, 1);<span
class="Apple-converted-space"> </span></span><span lang="EN-GB"
style="font-size: 9pt; font-family: "Courier New"; color:
forestgreen;" class="">%
init<span class="Apple-converted-space"> </span></span><span lang="EN-GB"
style="font-size: 8pt; font-family: "Courier New";" class=""><o:p
class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class=""> </span><span lang="EN-GB"
style="font-size: 8pt; font-family: "Courier New";" class=""><o:p
class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class=""> dTheta(noslack) = dx;</span><span
lang="EN-GB" style="font-size: 8pt; font-family: "Courier New";"
class=""><o:p class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class=""> H_altern(:,it) = Bf *
dTheta;</span><span lang="EN-GB" style="font-size: 8pt; font-family:
"Courier New";" class=""><o:p class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier New";
color: blue;" class="">end</span><span lang="EN-GB" style="font-size: 8pt;
font-family: "Courier New";" class=""><o:p
class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 8pt; font-family: "Courier
New";" class=""><o:p class=""> </o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier New";
color: forestgreen;" class="">%%% slack distribution</span><span lang="EN-GB"
style="font-size: 8pt; font-family: "Courier New";" class=""><o:p
class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class="">slack_weights(1:numel(exemplary_subSet_slack)) =
1/numel(exemplary_subSet_slack);</span><span lang="EN-GB" style="font-size:
8pt; font-family: "Courier New";" class=""><o:p
class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class="">v = H_altern * slack_weights';</span><span lang="EN-GB"
style="font-size: 8pt; font-family: "Courier New";" class=""><o:p
class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier New";
color: blue;" class="">for</span><span lang="EN-GB" style="font-size: 9pt;
font-family: "Courier New";" class=""><span
class="Apple-converted-space"> </span>k =
1:numel(exemplary_subSet_slack)</span><span lang="EN-GB" style="font-size: 8pt;
font-family: "Courier New";" class=""><o:p
class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class=""> H_newAndDistributed(:, k) = H_altern(:,
k) - v;</span><span lang="EN-GB" style="font-size: 8pt; font-family:
"Courier New";" class=""><o:p class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier New";
color: blue;" class="">end</span><span lang="EN-GB" style="font-size: 8pt;
font-family: "Courier New";" class=""><o:p
class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 8pt; font-family: "Courier
New";" class=""><o:p class=""> </o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
With best regards,<o:p class=""></o:p></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
Tobias Hoffmann<o:p class=""></o:p></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span class=""><o:p class=""> </o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span class=""><o:p class=""> </o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<b class="">Von:</b><span class="Apple-converted-space"> </span><a
href="mailto:[email protected]"; style="color: purple;
text-decoration: underline;"
class="">[email protected]</a><span
class="Apple-converted-space"> </span><<a
href="mailto:[email protected]"; style="color: purple;
text-decoration: underline;"
class="">[email protected]</a>><span
class="Apple-converted-space"> </span><b class="">Im
Auftrag von<span class="Apple-converted-space"> </span></b>Marwan Ahmed
Alasali<br class="">
<b class="">Gesendet:</b><span
class="Apple-converted-space"> </span>Montag, 17.<span
class="Apple-converted-space"> </span><span lang="EN-GB" class="">Februar
2020 10:22<br class="">
<b class="">An:</b><span class="Apple-converted-space"> </span>MATPOWER
discussion forum <<a href="mailto:[email protected]"; style="color:
purple; text-decoration: underline;"
class="">[email protected]</a>><br class="">
<b class="">Cc:</b><span class="Apple-converted-space"> </span><a
href="mailto:[email protected]"; style="color: purple; text-decoration:
underline;" class="">[email protected]</a><br class="">
<b class="">Betreff:</b><span class="Apple-converted-space"> </span>Re:
alternative to makePTDF for a subset of busses (with distributed slack)<o:p
class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" class=""><o:p class=""> </o:p></span></div>
<div class="">
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" class="">Dear all,<o:p class=""></o:p></span></div>
<div class="">
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" class=""><o:p class=""> </o:p></span></div>
</div>
<div class="">
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" class="">I want data for IEEE30 bus system<o:p
class=""></o:p></span></div>
</div>
</div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" class=""><o:p class=""> </o:p></span></div>
<div class="">
<div class="">
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" class="">On Mon, 17 Feb 2020 at 14:49, <</span><a
href="mailto:[email protected]"; style="color: purple;
text-decoration: underline;" class=""><span lang="EN-GB"
class="">[email protected]</span></a><span lang="EN-GB"
class="">>
wrote:<o:p class=""></o:p></span></div>
</div>
<blockquote style="border-style: none none none solid; border-left-width: 1pt;
border-left-color: rgb(204, 204, 204); padding: 0cm 0cm 0cm 6pt; margin: 5pt
0cm 5pt 4.8pt;" class="" type="cite">
<div class="">
<div class="">
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" class="">Dear all,<o:p class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" class="">I would like to calculate the PTDFs of a subset of
~500 nodes for a large network of > 10,000 nodes. Since the whole
calculation of the PTDF matrix is very CPU-intensive (as I have already read
in<span class="Apple-converted-space"> </span></span><a
href="https://github.com/MATPOWER/matpower/issues/37"; target="_blank"
style="color: purple; text-decoration: underline;" class=""><span lang="EN-GB"
class="">https://github.com/MATPOWER/matpower/issues/37</span></a><span
lang="EN-GB" class=""><span class="Apple-converted-space"> </span>and
_</span><a href="http://[email protected]/msg05580.html"; target="_blank"
style="color: purple; text-decoration: underline;" class=""><span lang="EN-GB"
class="">[email protected]/msg05580.html</span></a><span lang="EN-GB"
class="">), I tried to orientate
myself on this:<span class="Apple-converted-space"> </span></span><a
href="https://github.com/MATPOWER/matpower/issues/37#issuecomment-391459159";
target="_blank" style="color: purple; text-decoration: underline;"
class=""><span lang="EN-GB"
class="">https://github.com/MATPOWER/matpower/issues/37#issuecomment-391459159</span></a><span
lang="EN-GB" class="">.<span class="Apple-converted-space"> </span><o:p
class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" class="">Here is my consideration using the example of the
test scenario "case30":<span
class="Apple-converted-space"> </span><o:p class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 7pt;" class=""> </span><span
lang="EN-GB" class=""><o:p class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class="">mpc = loadcase(case30);</span><span lang="EN-GB"
class=""><o:p class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class="">mpc = ext2int(mpc);</span><span lang="EN-GB" class=""><o:p
class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier New";
color: forestgreen;" class="">%%% Referenz PTDF</span><span lang="EN-GB"
class=""><o:p class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier New";
color: forestgreen;" class="">% distributed_slack_setNodes = [1, 7, 15,
24];</span><span lang="EN-GB" class=""><o:p class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class="">define_constants()</span><span lang="EN-GB" class=""><o:p
class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class="">mpc = loadcase(case30);</span><span lang="EN-GB"
class=""><o:p class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class="">exemplary_subSet_slack = randi(30,1,5);</span><span
lang="EN-GB" class=""><o:p class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class="">weightSlack = zeros(size(mpc.bus,1),1);</span><span
lang="EN-GB" class=""><o:p class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class="">weightSlack(exemplary_subSet_slack) = 1;</span><span
lang="EN-GB" class=""><o:p class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class="">slackForPTDF =
weightSlack/numel(exemplary_subSet_slack);</span><span lang="EN-GB"
class=""><o:p class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class="">H_makePTDF = makePTDF(mpc,slackForPTDF);</span><span
lang="EN-GB" style="font-size: 9pt; font-family: "Courier New";
color: forestgreen;" class="">%,slackForPTDF)%,slack);</span><span lang="EN-GB"
class=""><o:p class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class="">H_makePTDF_rel =
H_makePTDF(:,exemplary_subSet_slack);</span><span lang="EN-GB" class=""><o:p
class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier New";
color: forestgreen;" class="">%%% alternative as in<span
class="Apple-converted-space"> </span></span><a
href="https://github.com/MATPOWER/matpower/issues/37#issuecomment-391459159";
target="_blank" style="color: purple; text-decoration: underline;"
class=""><span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";"
class="">https://github.com/MATPOWER/matpower/issues/37#issuecomment-391459159</span></a><span
lang="EN-GB" class=""><o:p class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class="">nb = size(mpc.bus, 1);<span
class="Apple-converted-space"> </span></span><span lang="EN-GB"
class=""><o:p class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class="">slack_bus = find(mpc.bus(:, BUS_TYPE) == REF);<span
class="Apple-converted-space"> </span></span><span lang="EN-GB"
style="font-size: 9pt; font-family: "Courier New"; color:
forestgreen;" class="">%
Ref. slack</span><span lang="EN-GB" class=""><o:p class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class="">slack = slack_bus;</span><span lang="EN-GB" class=""><o:p
class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class="">noslack = find((1:nb)' ~= slack_bus);</span><span
lang="EN-GB" class=""><o:p class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class="">[Bbus, Bf, Pbusinj, Pfinj] = makeBdc(mpc);</span><span
lang="EN-GB" class=""><o:p class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class="">Bbus(slack, :) = []; <span
class="Apple-converted-space"> </span></span><span lang="EN-GB"
style="font-size: 9pt; font-family: "Courier New"; color:
forestgreen;" class="">% remove
slack row</span><span lang="EN-GB" class=""><o:p class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class="">Bbus(:, slack) = []; <span
class="Apple-converted-space"> </span></span><span lang="EN-GB"
style="font-size: 9pt; font-family: "Courier New"; color:
forestgreen;" class="">% remove
slack col</span><span lang="EN-GB" class=""><o:p class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier New";
color: blue;" class="">for</span><span lang="EN-GB" style="font-size: 9pt;
font-family: "Courier New";" class=""><span
class="Apple-converted-space"> </span>it =
1:numel(exemplary_subSet_slack)</span><span lang="EN-GB" class=""><o:p
class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class=""> <span
class="Apple-converted-space"> </span></span><span lang="EN-GB"
class=""><o:p class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class=""> dP = zeros(nb, 1);<span
class="Apple-converted-space"> </span></span><span lang="EN-GB"
style="font-size: 9pt; font-family: "Courier New"; color:
forestgreen;" class="">% init</span><span lang="EN-GB" class=""><o:p
class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class=""> dP(slack) = []; <span
class="Apple-converted-space"> </span></span><span lang="EN-GB"
style="font-size: 9pt; font-family: "Courier New"; color:
forestgreen;" class="">% remove
slack</span><span lang="EN-GB" class=""><o:p class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class=""> <span
class="Apple-converted-space"> </span></span><span lang="EN-GB"
class=""><o:p class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class=""> </span><span lang="EN-GB"
class=""><o:p class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class=""> i =
exemplary_subSet_slack(it);</span><span lang="EN-GB" class=""><o:p
class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class=""> tmpDistributed_slack_set =
exemplary_subSet_slack;</span><span lang="EN-GB" class=""><o:p
class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class=""> tmpDistributed_slack_set(it) =
[];</span><span lang="EN-GB" class=""><o:p class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class=""> <span
class="Apple-converted-space"> </span></span><span lang="EN-GB"
class=""><o:p class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class=""> dP(i) = 1;</span><span
lang="EN-GB" class=""><o:p class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class=""> j =
tmpDistributed_slack_set;</span><span lang="EN-GB" class=""><o:p
class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class=""> dP(j) = -1 / numel(j);<span
class="Apple-converted-space"> </span></span><span lang="EN-GB"
class=""><o:p class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class=""> </span><span lang="EN-GB"
class=""><o:p class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class=""> </span><span style="font-size:
9pt; font-family: "Courier New";" class="">dx = Bbus \ dP;</span><o:p
class=""></o:p></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span style="font-size: 9pt; font-family: "Courier New";"
class=""> <span
class="Apple-converted-space"> </span></span><o:p class=""></o:p></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span style="font-size: 9pt; font-family: "Courier New";"
class=""> dTheta = zeros(nb, 1);<span
class="Apple-converted-space"> </span></span><span style="font-size: 9pt;
font-family: "Courier New"; color: forestgreen;" class="">% init<span
class="Apple-converted-space"> </span></span><o:p class=""></o:p></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span style="font-size: 9pt; font-family: "Courier New";"
class=""> </span><o:p class=""></o:p></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span style="font-size: 9pt; font-family: "Courier New";"
class=""> </span><span lang="EN-GB" style="font-size:
9pt; font-family: "Courier New";" class="">dTheta(noslack) =
dx;</span><span lang="EN-GB" class=""><o:p class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class=""> H_altern(:,it) = Bf *
dTheta;</span><span lang="EN-GB" class=""><o:p class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier New";
color: blue;" class="">end</span><span lang="EN-GB" class=""><o:p
class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier New";
color: forestgreen;" class="">%%% slack distribution</span><span lang="EN-GB"
class=""><o:p class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class="">slack_weights(1:numel(exemplary_subSet_slack)) =
1/numel(tmpDistributed_slack_set) -
1/numel(exemplary_subSet_slack);</span><span lang="EN-GB" class=""><o:p
class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class="">v = H_altern * slack_weights';</span><span lang="EN-GB"
class=""><o:p class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier New";
color: blue;" class="">for</span><span lang="EN-GB" style="font-size: 9pt;
font-family: "Courier New";" class=""><span
class="Apple-converted-space"> </span>k =
1:numel(exemplary_subSet_slack)</span><span lang="EN-GB" class=""><o:p
class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier
New";" class=""> <span
class="Apple-converted-space"> </span></span><span style="font-size: 9pt;
font-family: "Courier New";" class="">H_altern_2(:, k) = H_altern(:,
k) - v;</span><o:p class=""></o:p></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9pt; font-family: "Courier New";
color: blue;" class="">end</span><span lang="EN-GB" class=""><o:p
class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" class=""> <o:p class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" class="">Unfortunately, the calculation does not lead to the
desired result. I suspect my error in the distribution of the slack, but I am
not sure.<o:p class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" class="">I would be very happy about a help. Thanks a
lot!<o:p class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" class=""> <o:p class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" class="">With best regards,<o:p class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" class="">Tobias Hoffman<o:p class=""></o:p></span></div>
</div>
</div>
</blockquote>
</div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" class=""><br clear="all" class="">
<o:p class=""></o:p></span></div>
<div class="">
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" class=""><o:p class=""> </o:p></span></div>
</div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" class="">--<span
class="Apple-converted-space"> </span><o:p class=""></o:p></span></div>
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<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 12pt;" class=""><o:p
class=""> </o:p></span></div>
</div>
<div class="">
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 12pt;" class="">Thanks & Regards<o:p
class=""></o:p></span></div>
</div>
<div class="">
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 12pt;" class=""><o:p
class=""> </o:p></span></div>
</div>
<div class="">
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<b class=""><span lang="EN-GB" style="font-size: 13.5pt; color: blue;
background-color: white; background-position: initial initial;
background-repeat: initial initial;" class="">Marwan Ahmed
Alasali</span></b><span lang="EN-GB" style="font-size: 12pt;" class=""><o:p
class=""></o:p></span></div>
</div>
<div class="">
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9.5pt; color: rgb(136, 136, 136);"
class="">Research Scholar</span><span lang="EN-GB" style="font-size: 9.5pt;"
class=""><o:p class=""></o:p></span></div>
<div class="">
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9.5pt; color: rgb(136, 136, 136);"
class="">Department of Electrical Engineering,</span><span lang="EN-GB"
style="font-size: 9.5pt;" class=""><o:p class=""></o:p></span></div>
</div>
<div class="">
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span lang="EN-GB" style="font-size: 9.5pt; color: rgb(136, 136, 136);"
class="">Aligarh Muslim University, Aligarh<br class="">
Contact:+91-9634376962</span><span lang="EN-GB" style="font-size: 9.5pt;"
class=""><o:p class=""></o:p></span></div>
</div>
<div class="">
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<a href="mailto:[email protected]"; target="_blank" style="color: purple;
text-decoration: underline;" class=""><span lang="EN-GB" style="font-size:
9.5pt;" class="">[email protected]</span></a><span lang="EN-GB"
style="font-size: 9.5pt;" class=""><o:p class=""></o:p></span></div>
</div>
<div class="">
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<a href="mailto:[email protected]"; target="_blank" style="color: purple;
text-decoration: underline;" class=""><span lang="EN-GB" style="font-size:
9.5pt;" class="">[email protected]</span></a><span lang="EN-GB"
style="font-size: 9.5pt;" class=""><o:p class=""></o:p></span></div>
</div>
<div class="">
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri,
sans-serif;" class="">
<span style="font-size: 9.5pt;" class="">skype : </span><span
style="font-size: 10.5pt; font-family: Arial, sans-serif; color: rgb(84, 102,
109);" class=""> marwan.alaslay</span></div>
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</blockquote>
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