Hello José, I thank you very much for your help, I understood the solution that you proposed. I decreased the cos phi to finally have a max_lambda> 1, after I saw the value of Q which corresponds to the value of max lambda > 1 and I put the Q for each turbine in negative like you did for P.
my questions are: 1/ why did you put the P and Q in negatives because I try to put them in positive and the calculation diverges, 2/ with max_lambda> 1 I got also mean voltage> Vmax = 1.1, is that logical, so I increased Vmax to 1.5 and it did not change the results 3/ in my current case (see image and mfile) I have 2 transmission lines between 1002 and 3001 and between 1001 and 3001, my problem is when I increase the transmission distance (beyond 130 km) so I increase the values of r x and b between these branches, the calculation diverges knowing that it worked for distances <130 km. and I also noticed that the Q losses decrease by increasing the transmission distance which is not logical. what is the problem in your opinion? the solution that i did: I changed the value of system MVA base = 8MW * 100 (which was set to 100) so here my program converges without even injecting reactive power for the turbines and the value of Q increases by increasing the transmission distance. I thought to do that because I saw in other load flow calculation code that the basic value of the system = the production of each wind turbine (8MW) * nb of wind turbines (100) is my logic true and what is the effect of the base MVA value? and my last question: 4/how can I do the compensation of the reactive power at nodes 1002 and 1001 (the 2 substations) and at pdl node 3001 and how can i see the intermediate calculation of the reactive losses for each node because matpower gives us directly the results without seeing the details of the calculations. Thank you again for your help and I hope you will help me since you had an idea about my exemple. Best regards Asma > Hello Asma, > > I gave your case a quick look and I found several problems with the file > format (many extraneous lines in several places). Anyway, I was courious > and I found that I could edit it by hand quickly because it's actually a > rather simple and repetitive topology structure. I'm attaching my fixed > file, have a look at it (I also converted it to MATPOWER version 2). The > second version contains an additional fix that I guessed (bus 1002 > connecting to bus 3001, instead of 1001). By the way, you can quickly > visualize the topology with this handy tool: > http://immersive.erc.monash.edu.au/stac/ > > So it's a *very* radial case, with no loads, only (wind) generators, and > the swing acting as the "sink" for all of the wind-farm power, as it is > the > connection point to the grid. > > From the point of view of powerflow, your case has two kind of problems: > > 1. The main one is that this network just cannot "evacuate" all that > power. The case is infeasible, as you can see by running a CPF. > 2. A smaller problem is that all generators are running in PQ mode, > with > Q=0 (power factor 1.0), which means that you won't have enough > "reactive > support" to maintain voltage levels for such long radial sections. > > Allowing the generators to inject at least some Mvars will let you > transfer > a bit more power from the wind farm. See the attached test script. These > are the results I get (for caseborselle_fixed2): > > - Operating gens at cos_phi=1.0 ==> max_lambda = 0.546875, mean > voltage = 0.802666 > - Operating gens at cos_phi=0.95 ==> max_lambda = 0.807189, mean > voltage = 0.986915 > - Operating gens at cos_phi=0.90 ==> max_lambda = 0.968138, mean > voltage > = 1.104592 > > Hope it helps, > > -- > Jose L. Marin > Grupo AIA > > > > 2018-05-18 18:43 GMT+02:00 Asma DABBABI <[email protected]>: > >> Hello Jose, >> Thank you for rapid response, i'm quite in a rush to finish this study >> case for my thesis research. >> >> - i have a radial topology of wind turbines ( 100 wind turbines with 8 >> MW >> each) like i said i represent all my turbines nodes like a PQ node >> with P=8Mw et Q=0MVAR. and i have 3 AC offshores plateformes (ie 3 >> transformers ) related to my wind farm (each transformer is related to >> one >> cluster in my wind farm) after that i have a long transmission line ( >> distance about 60km) and finally i have a terrestrial network which is >> composed of one final transformer and the output node of the >> transformer >> is my slack bus ( my only generator). >> >> I put you my case file so you can more understand what i mean. >> >> from what I understood from your answer is that I have to add PV nodes >> and >> i have to add also Q for each turbine ? >> >> thank you again and i hope you can help me. >> >> >> Best regards >> >> >> > Hello Asma, >> > >> > Your description is not very clear, so let me ask you a couple of >> things >> > first: >> > >> > - You seem to be saying that your generators should have P=8 MW. >> > That's >> > fine, but then you total load should be balanced according to that >> (is >> > it?). Otherwise the imbalance, which has to be picked up by the >> slack >> > bus, >> > could render the case infeasible. >> > - You also seem to be saying that all your generators are PQ type. >> A >> > case with no PV buses is quite prone to numerical ill-conditioning >> > (unless >> > the total number of buses is low). Worse yet, if all gens have Q=0 >> > then >> > all reactive power will have to be provided by the slack, and then >> > voltages >> > will quickly drop as you move away from the slack bus. And if the >> > network >> > topology is dominantly radial, things are even worse yet. >> > >> > Maybe we can help you faster if you could share your case file here. >> > >> > -- >> > Jose L. Marin >> > Grupo AIA >> > >> > >> > >> > 2018-05-18 17:31 GMT+02:00 Asma DABBABI >> <[email protected] >> >: >> > >> >> the library Matpower works perfectly with small wind farms (30 wind >> >> turbines with >> >> 3 mw each, the turbines are represented as PQnode with P=3MW and >> Q=0MVAR >> >> and i have one slack bus in the terrestrial network) >> >> but when I tried to make an example of a larger farm such as >> Borsselle >> >> Park (100 wind turbines of 8 mw each) I had a divergence of the >> system. >> >> >> >> "Newton's method power flow did not converge in 10 iterations ", >> >> I looked on the internet and I found that in this case we have to do >> a >> >> continuation power flow that gradually increases the >> loading/generation >> >> like this: >> >> >> >> {define_constants; >> >> mpcbase = loadcase ('casefile'); >> >> mpcbase.bus (:, PD) = 0; >> >> mpcbase.bus (:, QD) = 0; >> >> mpcbase.gen (:, PG) = 0; >> >> mpctarget = loadcase ('casefile'); >> >> results = runcpf (mpcbase, mpctarget); >> >> results.cpf.max_lam} >> >> >> >> If the resulting value of results is greater than 1, it indicates >> that >> >> the >> >> load for the box is greater than that of the loading and unloading >> >> system >> >> at least by a factor of results.cpf.max_lam to get a convergent power >> >> flow >> >> solution. >> >> I tried this and actually I found that it shows that >> results.cpf.max_lam >> >> is less than 1 so i must reduce the loads to 1.35 mw for each >> turbine. >> >> in my case i don't need to reduce the loads, i must found the losses >> of >> >> the network with 8mw for each turbine. >> >> I've tried many solutions that i found in matpower page but until now >> I >> >> have not found the right solution to calculate with 8 mw. >> >> >> >> So can you help me please on that, I 'll be so grateful if you answer >> >> me. >> >> >> >> Best regards, >> >> >> >> >> >> >> >> >> > >> >
function [baseMVA, bus, gen, branch] = caseborselle2substations
%case 5 nodes Power flow data for 5 bus, 2 generator case.
% Please see 'help caseformat' for details on the case file format.
%
% case file can be used together with dc case files "case5_stagg_....m"
%
% Network data from ...
% G.W. Stagg, A.H. El-Abiad, "Computer methods in power system analysis",
% McGraw-Hill, 1968.
%
% MATPOWER case file data provided by Jef Beerten.
\%% MATPOWER Case Format : Version 1
\%%----- Power Flow Data -----\%%
\%% system MVA base
baseMVA = 100*8;
\%% bus data
% bus_i type Pd Qd Gs Bs area Vm Va
baseKV zone Vmax Vmin
bus =[3 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
4 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
5 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
6 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
7 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
8 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
9 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
10 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
11 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
12 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
13 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
14 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
15 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
16 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
17 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
18 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
19 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
20 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
21 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
22 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
23 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
24 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
25 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
26 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
27 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
28 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
29 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
30 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
31 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
32 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
33 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
34 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
35 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
36 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
37 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
38 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
39 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
40 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
41 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
42 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
43 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
44 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
45 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
46 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
47 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
48 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
49 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
50 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
51 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
52 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
53 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
54 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
55 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
56 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
57 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
58 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
59 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
60 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
61 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
62 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
63 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
64 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
65 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
66 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
67 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
68 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
69 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
70 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
71 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
72 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
73 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
74 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
75 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
76 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
77 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
78 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
79 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
80 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
81 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
82 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
83 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
84 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
85 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
86 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
87 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
88 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
89 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
90 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
91 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
92 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
93 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
94 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
95 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
96 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
97 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
98 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
99 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
100 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
101 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
102 1 3.89377814200271 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
1 1 0 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
2 1 0 0 0 0 1 1 0 66 1 1.10000000000000 0.900000000000000;
1001 1 0 0 0 0 1 1 0 220 1 1.10000000000000 0.900000000000000;
1002 1 0 0 0 0 1 1 0 220 1 1.10000000000000 0.900000000000000;
3001 1 0 0 0 0 1 1 0 220 1 1.10000000000000 0.900000000000000;
3002 3 0 0 0 0 1 1 0 380 1 1.10000000000000 0.900000000000000];
%bus(1:100,3)=8;% it work even with 8 mW
\%% generator data
% bus Pg Qg Qmax Qmin Vg mBase status
Pmax Pmin
gen = [3002 0 0 200 -200 1 100 1 1000 100];
\%% branch data commençant par 1 en ordre
% fbus tbus r x b rateA rateB rateC
ratio angle status
%branch = [26 1 0.0172855936562986 0.0737162362582345 8.42343855970121e-05 0 0
0 0 0 1;35 1 0.0243547816607643 0.103863533681322 0.000118683228955594 0 0 0 0
0 1;37 1 0.00617786852890702 0.0263461715636985 3.01053565286129e-05 0 0 0 0 0
1;48 1 0.00370216740417866 0.0157882831484080 1.80410232283021e-05 0 0 0 0 0
1;57 1 0.0118059272896418 0.0503476214144171 5.75314363752619e-05 0 0 0 0 0
1;75 1 0.0318041822635946 0.135632287809149 0.000154984885428745 0 0 0 0 0 1;95
1 0.0393009627115836 0.167603098281064 0.000191517428513369 0 0 0 0 0 1;39 2
0.00410718597111310 0.0175155275209628 2.00147182496861e-05 0 0 0 0 0 1;92 2
0.0397570510418288 0.169548135042629 0.000193739991477655 0 0 0 0 0 1;101 2
0.0392660726500572 0.167454305935850 0.000191347405836998 0 0 0 0 0 1;8 3
0.0152644272511473 0.0650967590680456 7.43850443645110e-05 0 0 0 0 0 1;22 4
0.0181135748789532 0.0772472494614949 8.82692189364361e-05 0 0 0 0 0 1;32 4
0.0200580430735703 0.0855396390479402 9.77448023004368e-05 0 0 !
0 0 0 1;3
4 4 0.00976266960402693 0.0416339336300028 4.75744421761401e-05 0 0 0 0 0 1;62
4 0.0308038947833482 0.131366456407221 0.000150110386872646 0 0 0 0 0 1;6 5
0.00912638238744698 0.0389204197225177 4.44737524447050e-05 0 0 0 0 0 1;16 6
0.00538399440034720 0.0229606116585059 2.62367303888197e-05 0 0 0 0 0 1;17 7
0.00556250990428545 0.0237219098427470 2.71066538691915e-05 0 0 0 0 0 1;19 9
0.00490501493335039 0.0209179532312604 2.39026166801269e-05 0 0 0 0 0 1;20 9
0.00921902020705440 0.0393154834693818 4.49251855845113e-05 0 0 0 0 0 1;11 10
0.00976268208386926 0.0416339868516059 4.75745029916303e-05 0 0 0 0 0 1;20 10
0.00499802272865703 0.0213145947784938 2.43558527476387e-05 0 0 0 0 0 1;12 11
0.00961404427872044 0.0410001052633237 4.68501764546220e-05 0 0 0 0 0 1;13 12
0.00960528119464459 0.0409627341675470 4.68074730903210e-05 0 0 0 0 0 1;24 13
0.00975266362101406 0.0415912620606926 4.75256820439664e-05 0 0 0 0 0 1;23 14
0.0123099686965883 0.0524971591264103 5.99876793642972e-0!
5 0 0 0 0
0 1;24 14 0.00477365454099451 0.0203577529910822 2.32624846625697e-05 0 0 0 0
0 1;25 15 0.00486685321703487 0.0207552085693257 2.37166509105339e-05 0 0 0 0 0
1;26 16 0.00534996781921228 0.0228155017164422 2.60709155367031e-05 0 0 0 0 0
1;27 17 0.00548373439278381 0.0233859633700552 2.67227731102560e-05 0 0 0 0 0
1;27 18 0.0121606422830955 0.0518603408952573 5.92599971715949e-05 0 0 0 0 0
1;28 18 0.00482882573552007 0.0205930363658486 2.35313392802311e-05 0 0 0 0 0
1;29 19 0.00542304205266040 0.0231271344878911 2.64270134110294e-05 0 0 0 0 0
1;30 21 0.00899060813334644 0.0383413961036550 4.38121112479109e-05 0 0 0 0 0
1;31 21 0.00495765037258990 0.0211424226103101 2.41591143146963e-05 0 0 0 0 0
1;33 23 0.00479546404119598 0.0204507619036769 2.33687644864611e-05 0 0 0 0 0
1;26 25 0.00969518467342325 0.0413461370297143 4.72455815202965e-05 0 0 0 0 0
1;37 28 0.0118528434397935 0.0505477002822694 5.77600633556933e-05 0 0 0 0 0
1;39 29 0.00485969713995452 0.0207246907242793 2.36!
817786482
250e-05 0 0 0 0 0 1;41 31 0.00495299366745768 0.0211225636004006
2.41364217359213e-05 0 0 0 0 0 1;42 32 0.00525647592980326 0.0224167956988799
2.56153204313651e-05 0 0 0 0 0 1;43 33 0.00546519462231459 0.0233068985645728
2.66324269985958e-05 0 0 0 0 0 1;44 34 0.00508083533829873 0.0216677578817629
2.47594066799800e-05 0 0 0 0 0 1;45 35 0.00473904133109186 0.0202101413088008
2.30938111111914e-05 0 0 0 0 0 1;46 36 0.00533691081518869 0.0227598187464172
2.60072874812522e-05 0 0 0 0 0 1;47 37 0.00560820282914347 0.0239167721373918
2.73293199533351e-05 0 0 0 0 0 1;48 38 0.00535737153202996 0.0228470756301942
2.61069945521384e-05 0 0 0 0 0 1;49 39 0.00557191200112050 0.0237620060757950
2.71524712050593e-05 0 0 0 0 0 1;50 40 0.00548022412965790 0.0233709934829305
2.67056672553126e-05 0 0 0 0 0 1;52 41 0.00919319218281090 0.0392053371374088
4.47993231006074e-05 0 0 0 0 0 1;53 43 0.00503658551663129 0.0214790498527950
2.45437729785841e-05 0 0 0 0 0 1;54 44 0.00547533167466701 0.0233!
501290928
978 2.66818258444584e-05 0 0 0 0 0 1;55 45 0.00488615739105893
0.0208375332543451 2.38107220353507e-05 0 0 0 0 0 1;57 46 0.0121866412009225
0.0519712160209315 5.93866924366168e-05 0 0 0 0 0 1;56 47 0.00970701353612190
0.0413965824615980 4.73032247231591e-05 0 0 0 0 0 1;59 49 0.00476351635453962
0.0203145176262577 2.32130802901151e-05 0 0 0 0 0 1;60 50 0.00559013835758562
0.0238397342942192 2.72412900196767e-05 0 0 0 0 0 1;52 51 0.00910037851010055
0.0388095234464502 4.43470330114608e-05 0 0 0 0 0 1;61 51 0.00547321020917285
0.0233410818796698 2.66714877359723e-05 0 0 0 0 0 1;63 53 0.00528756049852834
0.0225493591188980 2.57667985697599e-05 0 0 0 0 0 1;65 55 0.00558430814001594
0.0238148707168178 2.72128788002159e-05 0 0 0 0 0 1;66 56 0.00525842797697354
0.0224251204098069 2.56248329478174e-05 0 0 0 0 0 1;67 57 0.00527890492596403
0.0225124465172953 2.57246191195517e-05 0 0 0 0 0 1;68 58 0.00477051753406135
0.0203443748943372 2.32471977214971e-05 0 0 0 0 0 1;68 59 0.00904564!
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return;
image-case.pdf
Description: Adobe PDF document
