POLITECHNIKA WROCŁAWSKA
|
Soroko Jacek | Rok studiów V Studia dzienne Semestr IX Rok Akademicki 2010/2011 |
|---|---|---|
LABORATORIUM PRACY SYSTEMÓW ELEKTROENERGETYCZNYCH |
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Data wykonania ćwiczenia 04.11.2010 |
Numer ćwiczenia: 6 |
Temat: Obliczanie rozpływu mocy metodą hybrydową w wielonapięciowych systemach elektroenergetycznych |
Data oddania ćwiczenia: . |
Cel ćwiczenia
Celem ćwiczenia jest zapoznanie studenta:
z przygotowaniem danych gałeziowych i wezłowych w jednostkach wzglednych
z techniką obliczania rozpływów mocy czynnych i biernych w systemach zasilanych z kilku źródeł połaczonych treansformatorami i liniami elektroenergetycznymi
postępowaniem w sytuacji, gdy rozpływ jest zbieżny
obliczeniami wielowariantowymi
analizą otrzymanych wyników pod kątem pracy systemu rzeczywistego
Opis ćwiczenia:
Program komputerowy wyznaczania rozpływów mocy w dużych systemach jest oparty o metodę Newtona-Raphsona, z wykorzystaniem macierzy admitancji węzłowych. Napisany jest w MATLABie, korzysta z techniki macierzy rzadkich. Metoda ta jest zbieżna, gdy tzw. punkt startowy znajduje się „dostatecznie” blisko rozwiązania. Zdarzają się sytuacje systemowe, gdy szybko zbieżna metoda Newtona zawodzi. Należy w takim przypadku zastanowić się i przeanalizować dane wejściowe pod kątem ich poprawności. Przy ocenie pozytywnej należy zastosować inną metodę, np. wolno zbieżną Gaussa lub hybrydową łączącą zalety obu metod. Początkowe iteracje wykonywane są według metody Gaussa, odpornej na punkt startowy. Wektor napięć węzłowych „podprowadzany” jest pod rozwiązanie, aby następnie przy pomocy szybko zbieżnej metody Newtona otrzymać końcowe rozwiązanie.
Rys.1. Schemat systemu elektroenergetycznego.
Dane wejściowe do symulacji:
wezly={
%nazwanr typ Un_kV Um k_st Pd Qd Pg Qg Psh Qsh Pgmin Pgmax Qgmin Qgmax
% 1 2 3 4 5 6 7 8 9 10 11 12 13 14
'wezel 1' [1 110.00 1.000 0.0 0.100 0.060 0.000 0.0000 0.000 0.000 0.0 0.0 0.0 0.0];
'wezel 2' [1 110.00 1.000 0.0 0.400 0.300 0.000 0.0000 0.000 0.000 0.0 0.0 0.0 0.0];
'wezel 3' [1 110.00 1.000 0.0 0.400 0.300 0.000 0.0000 0.000 0.000 0.0 0.0 0.0 0.0];
'wezel 4' [1 110.00 1.000 0.0 0.000 0.300 0.000 0.0000 0.000 0.000 0.0 0.0 0.0 0.0];
'wezel 5' [1 110.00 1.000 0.0 0.000 0.000 0.000 0.0000 0.000 0.000 0.0 0.0 0.0 0.0];
'wezel 6' [1 30.00 1.000 0.0 0.200 0.100 0.000 0.0000 0.000 0.000 0.0 0.0 0.0 0.0];
'wezel 9' [1 10.00 1.000 0.0 0.100 0.060 0.000 0.0000 0.000 0.000 0.0 0.0 0.0 0.0];
'wezel 10' [2 10.00 1.000 0.0 0.000 0.000 0.300 0.0000 0.000 0.000 0.0 0.0 0.0 0.0];
'wezel 11' [2 10.00 1.000 0.0 0.000 0.000 0.300 0.0000 0.000 0.000 0.0 0.0 0.0 0.0];
'wezel 12' [2 10.00 1.000 0.0 0.000 0.000 0.300 0.0000 0.000 0.000 0.0 0.0 0.0 0.0];
'wezel 13' [2 10.00 1.000 0.0 0.000 0.000 0.300 0.0000 0.000 0.000 0.0 0.0 0.0 0.0];
'wezel 14' [3 220.00 1.100 0.0 0.000 0.000 0.000 0.0000 0.000 0.000 0.0 0.0 0.0 0.0];
};
linie={
% nazwawp nazwawk R X G B Imax st
% 1 2 3 4 5 6 7 8
'linia 1' 'wezel 1' 'wezel 2' [0.01802 0.72070 0.00 0.05280 4000 1];
'linia 2' 'wezel 1' 'wezel 2' [0.01802 0.72070 0.00 0.05280 4000 1];
'linia 3' 'wezel 2' 'wezel 3' [0.37690 0.75370 0.00 0.00552 4000 1];
'linia 4' 'wezel 2' 'wezel 3' [0.37690 0.75370 0.00 0.00552 4000 1];
'linia 5' 'wezel 3' 'wezel 5' [0.15540 0.62150 0.00 0.04550 4000 1];
'linia 6' 'wezel 3' 'wezel 5' [0.15540 0.62150 0.00 0.04550 4000 1];
'linia 7' 'wezel 5' 'wezel 4' [0.25290 0.50580 0.00 0.03700 4000 1];
'linia 8' 'wezel 5' 'wezel 4' [0.25290 0.50580 0.00 0.03700 4000 1];
'linia 9' 'wezel 3' 'wezel 4' [0.10990 0.43970 0.00 0.03220 4000 1];
'linia 10' 'wezel 3' 'wezel 4' [0.10990 0.43970 0.00 0.03220 4000 1];
'linia 11' 'wezel 4' 'wezel 1' [0.11820 0.47270 0.00 0.03460 4000 1];
'linia 12' 'wezel 4' 'wezel 1' [0.11820 0.47270 0.00 0.03460 4000 1];
};
transf={
% nazwawp nazwawk R X G B Imax tm k_st tmin tmax dtr st
% 1 2 3 4 5 6 7 8 9 10 11 12 13
'transf 1' 'wezel 2' 'wezel 10' [0.00710 0.24130 0.00020 -0.00230 5000 0.9957 0.0 0.8364 1.1550 0.013 1];
'transf 2' 'wezel 2' 'wezel 11' [0.00710 0.24130 0.00020 -0.00230 5000 0.9957 0.0 0.8364 1.1550 0.013 1];
'transf 3' 'wezel 3' 'wezel 12' [0.00740 0.23490 0.00070 -0.00560 5000 0.9669 0.0 0.8122 1.1216 0.013 1];
'transf 4' 'wezel 3' 'wezel 13' [0.00740 0.23490 0.00070 -0.00560 5000 0.9669 0.0 0.8122 1.1216 0.013 1];
'transf 5' 'wezel 5' 'wezel 6' [0.01810 0.60690 0.00010 -0.00090 5000 1.0455 0.0 0.8778 1.2127 0.014 1];
'transf 6' 'wezel 5' 'wezel 6' [0.01810 0.60690 0.00010 -0.00090 5000 1.0455 0.0 0.8778 1.2127 0.014 1];
'transf 7' 'wezel 14' 'wezel 4' [0.00570 0.25740 0.00020 -0.00080 5000 0.9583 0.0 0.0 0.0 0.0 1];
'transf 8' 'wezel 14' 'wezel 4' [0.00570 0.25740 0.00020 -0.00080 5000 0.9583 0.0 0.0 0.0 0.0 1];
'transf 9' 'wezel 1' 'wezel 9' [0.02520 0.40270 0.00010 -0.00140 3000 0.9504 0.0 0.7984 1.1025 0.013 1];
};
Obliczenia rozpływów mocy systemu dla warunków początkowych – Metoda Newtona:
Iteration process of Netwon-Raphson method
IT= 4, SignDetJ=-1, Unbalance=3.905e-007 - bus with Max. Unbal. 12: Um=1.1000, dpmax= -0.02164
Bus Voltages and Powers obtained from Load Flow Solution
===============================================================================================
BUS VOLTAGE GENERATION LOAD const LOAD shunt
Nr Name type U_pu angle U_kV Pg(MW) Qg(MVAR) Pd(MW) Qd(MVAR Psh(MW) Qsh(MVAR)
===============================================================================================
1 wezel 1 1 1.0103 -0.0 111.1 0.00 0.00 10.00 6.00 0.00 0.00
2 wezel 2 1 0.9755 3.5 107.3 0.00 0.00 40.00 30.00 0.00 0.00
3 wezel 3 1 0.9800 2.4 107.8 0.00 -0.00 40.00 30.00 0.00 0.00
4 wezel 4 1 1.0462 -0.0 115.1 0.00 -0.00 0.00 30.00 0.00 0.00
5 wezel 5 1 1.0010 -0.2 110.1 0.00 0.00 - - - -
6 wezel 6 1 0.9201 -4.1 27.6 0.00 0.00 20.00 10.00 0.00 0.00
7 wezel 9 1 1.0364 -2.0 10.4 0.00 0.00 10.00 6.00 0.00 0.00
8 wezel 10 2 1.0000 7.7 10.0 30.00 8.71 - - - -
9 wezel 11 2 1.0000 7.7 10.0 30.00 8.71 - - - -
10 wezel 12 2 1.0000 6.4 10.0 30.00 -5.39 - - - -
11 wezel 13 2 1.0000 6.4 10.0 30.00 -5.39 - - - -
12 wezel 14 3 1.1000 0.0 242.0 2.16 90.69 - - - -
----- ----- ----- ----- ----- -----
Total: 122.16 97.34 120.00 112.00 0.00 0.00
Effective load coefficients: pSF = Ifrom/Imax*100%, pST = Ito/Imax*100%
========================================================================================================================
FROM TO FLOW at begin FLOW at end straty I^2*Z str.(Up^2+Uk^2)Ysh
Nr BUS BUS P(MW) Q(MVAR) pSF P(MW) Q(MVAR) pST dP(MW) dQ(Mvar) dPsh(MW) dQsh(Mvar)
========================================================================================================================
Razem LINIE 1.367 5.947 0.000 -42.094
Razem TRANSF 0.539 19.400 0.258 2.092
Razem STRATY 1.906 25.346 0.258 -40.002
Obliczenia rozpływów mocy systemu dla warunków początkowych – Metoda Gaussa:
Iteration process of Guass-Seidl method
ITERATION =127 normaNZB= 0.00000001
Bus Voltages and Powers obtained from Load Flow Solution
===============================================================================================
BUS VOLTAGE GENERATION LOAD const LOAD shunt
Nr Name type U_pu angle U_kV Pg(MW) Qg(MVAR) Pd(MW) Qd(MVAR Psh(MW) Qsh(MVAR)
===============================================================================================
1 wezel 1 1 1.0103 -0.0 111.1 0.00 0.00 10.00 6.00 0.00 0.00
2 wezel 2 1 0.9755 3.5 107.3 0.00 0.00 40.00 30.00 0.00 0.00
3 wezel 3 1 0.9800 2.4 107.8 0.00 0.00 40.00 30.00 0.00 0.00
4 wezel 4 1 1.0462 -0.0 115.1 0.00 0.00 0.00 30.00 0.00 0.00
5 wezel 5 1 1.0010 -0.2 110.1 0.00 -0.00 - - - -
6 wezel 6 1 0.9201 -4.1 27.6 0.00 -0.00 20.00 10.00 0.00 0.00
7 wezel 9 1 1.0364 -2.0 10.4 0.00 -0.00 10.00 6.00 0.00 0.00
8 wezel 10 2 1.0000 7.7 10.0 30.00 8.71 - - - -
9 wezel 11 2 1.0000 7.7 10.0 30.00 8.71 - - - -
10 wezel 12 2 1.0000 6.4 10.0 30.00 -5.39 - - - -
11 wezel 13 2 1.0000 6.4 10.0 30.00 -5.39 - - - -
12 wezel 14 3 1.1000 0.0 242.0 2.16 90.69 - - - -
----- ----- ----- ----- ----- -----
Total: 122.16 97.34 120.00 112.00 0.00 0.00
Effective load coefficients: pSF = Ifrom/Imax*100%, pST = Ito/Imax*100%
========================================================================================================================
FROM TO FLOW at begin FLOW at end straty I^2*Z str.(Up^2+Uk^2)Ysh
Nr BUS BUS P(MW) Q(MVAR) pSF P(MW) Q(MVAR) pST dP(MW) dQ(Mvar) dPsh(MW) dQsh(Mvar)
========================================================================================================================
Razem LINIE 1.367 5.947 0.000 -42.094
Razem TRANSF 0.539 19.400 0.258 2.092
Razem STRATY 1.906 25.346 0.258 -40.002
Obliczenia rozpływów mocy systemu dla warunków początkowych – Metoda hybrydowa:
Iteration process of Guass-Seidl method
ITERATION = 18 normaNZB= 0.01032987
Bus Voltages and Powers obtained from Load Flow Solution
===============================================================================================
BUS VOLTAGE GENERATION LOAD const LOAD shunt
Nr Name type U_pu angle U_kV Pg(MW) Qg(MVAR) Pd(MW) Qd(MVAR Psh(MW) Qsh(MVAR)
===============================================================================================
1 wezel 1 1 1.0103 -0.0 111.1 0.00 0.00 10.00 6.00 0.00 0.00
2 wezel 2 1 0.9755 3.5 107.3 0.00 0.00 40.00 30.00 0.00 0.00
3 wezel 3 1 0.9800 2.4 107.8 0.00 0.00 40.00 30.00 0.00 0.00
4 wezel 4 1 1.0462 -0.0 115.1 0.00 0.00 0.00 30.00 0.00 0.00
5 wezel 5 1 1.0010 -0.2 110.1 0.00 -0.00 - - - -
6 wezel 6 1 0.9201 -4.1 27.6 0.00 -0.00 20.00 10.00 0.00 0.00
7 wezel 9 1 1.0364 -2.0 10.4 0.00 -0.00 10.00 6.00 0.00 0.00
8 wezel 10 2 1.0000 7.7 10.0 30.00 8.71 - - - -
9 wezel 11 2 1.0000 7.7 10.0 30.00 8.71 - - - -
10 wezel 12 2 1.0000 6.4 10.0 30.00 -5.39 - - - -
11 wezel 13 2 1.0000 6.4 10.0 30.00 -5.39 - - - -
12 wezel 14 3 1.1000 0.0 242.0 2.16 90.69 - - - -
----- ----- ----- ----- ----- -----
Total: 122.16 97.34 120.00 112.00 0.00 0.00
Effective load coefficients: pSF = Ifrom/Imax*100%, pST = Ito/Imax*100%
========================================================================================================================
FROM TO FLOW at begin FLOW at end straty I^2*Z str.(Up^2+Uk^2)Ysh
Nr BUS BUS P(MW) Q(MVAR) pSF P(MW) Q(MVAR) pST dP(MW) dQ(Mvar) dPsh(MW) dQsh(Mvar)
========================================================================================================================
Razem LINIE 1.367 5.947 0.000 -42.094
Razem TRANSF 0.539 19.400 0.258 2.092
Razem STRATY 1.906 25.346 0.258 -40.002
Obliczenia rozpływów mocy systemu dla grupy połączeń T1, T2, T3, T4 –Yd11; T5, T6, T9 –Yd5; T7, T8 –Yy0 : Metoda Newtona:
Iteration process of Netwon-Raphson method
IT=12, SignDetJ=-1, Unbalance=2.455e-007 - bus with Max. Unbal. 12: Um=1.1000, dpmax= -0.3154
Bus Voltages and Powers obtained from Load Flow Solution
===============================================================================================
BUS VOLTAGE GENERATION LOAD const LOAD shunt
Nr Name type U_pu angle U_kV Pg(MW) Qg(MVAR) Pd(MW) Qd(MVAR Psh(MW) Qsh(MVAR)
===============================================================================================
1 wezel 1 1 0.6302 -1.6 69.3 0.00 -0.00 10.00 6.00 0.00 0.00
2 wezel 2 1 0.8742 2.6 96.2 0.00 0.00 40.00 30.00 0.00 0.00
3 wezel 3 1 0.8605 0.6 94.7 0.00 -0.00 40.00 30.00 0.00 0.00
4 wezel 4 1 0.8708 -1.9 95.8 0.00 -0.00 0.00 30.00 0.00 0.00
5 wezel 5 1 0.6261 1.4 68.9 0.00 0.00 - - - -
6 wezel 6 1 0.1288 160.6 3.9 0.00 0.00 20.00 10.00 0.00 0.00
7 wezel 9 1 0.0763 158.4 0.8 0.00 -0.00 10.00 6.00 0.00 0.00
8 wezel 10 2 1.0000 37.1 10.0 30.00 50.94 - - - -
9 wezel 11 2 1.0000 37.1 10.0 30.00 50.94 - - - -
10 wezel 12 2 1.0000 34.9 10.0 30.00 47.25 - - - -
11 wezel 13 2 1.0000 34.9 10.0 30.00 47.25 - - - -
12 wezel 14 3 1.1000 0.0 242.0 31.54 246.98 - - - -
----- ----- ----- ----- ----- -----
Total: 151.54 443.37 120.00 112.00 0.00 0.00
Effective load coefficients: pSF = Ifrom/Imax*100%, pST = Ito/Imax*100%
========================================================================================================================
FROM TO FLOW at begin FLOW at end straty I^2*Z str.(Up^2+Uk^2)Ysh
Nr BUS BUS P(MW) Q(MVAR) pSF P(MW) Q(MVAR) pST dP(MW) dQ(Mvar) dPsh(MW) dQsh(Mvar)
========================================================================================================================
Razem LINIE 20.417 77.483 0.000 -25.194
Razem TRANSF 31.316 906.946 0.208 1.642
Razem STRATY 51.733 984.429 0.208 -23.552
Obliczenia rozpływów mocy systemu dla grupy połączeń T1, T2, T3, T4 –Yd11; T5, T6, T9 –Yd5; T7, T8 –Yy0 : Metoda Gaussa:
Iteration process of Guass-Seidl method
ITERATION =142 normaNZB= 0.00000001
Bus Voltages and Powers obtained from Load Flow Solution
===============================================================================================
BUS VOLTAGE GENERATION LOAD const LOAD shunt
Nr Name type U_pu angle U_kV Pg(MW) Qg(MVAR) Pd(MW) Qd(MVAR Psh(MW) Qsh(MVAR)
===============================================================================================
1 wezel 1 1 1.0103 -0.0 111.1 0.00 0.00 10.00 6.00 0.00 0.00
2 wezel 2 1 0.9755 3.5 107.3 0.00 0.00 40.00 30.00 0.00 0.00
3 wezel 3 1 0.9800 2.4 107.8 0.00 0.00 40.00 30.00 0.00 0.00
4 wezel 4 1 1.0462 -0.0 115.1 0.00 0.00 0.00 30.00 0.00 0.00
5 wezel 5 1 1.0010 -0.2 110.1 0.00 -0.00 - - - -
6 wezel 6 1 0.9201 -154.1 27.6 0.00 -0.00 20.00 10.00 0.00 0.00
7 wezel 9 1 1.0364 -152.0 10.4 0.00 -0.00 10.00 6.00 0.00 0.00
8 wezel 10 2 1.0000 37.7 10.0 30.00 8.71 - - - -
9 wezel 11 2 1.0000 37.7 10.0 30.00 8.71 - - - -
10 wezel 12 2 1.0000 36.4 10.0 30.00 -5.39 - - - -
11 wezel 13 2 1.0000 36.4 10.0 30.00 -5.39 - - - -
12 wezel 14 3 1.1000 0.0 242.0 2.16 90.69 - - - -
----- ----- ----- ----- ----- -----
Total: 122.16 97.34 120.00 112.00 0.00 0.00
Effective load coefficients: pSF = Ifrom/Imax*100%, pST = Ito/Imax*100%
========================================================================================================================
FROM TO FLOW at begin FLOW at end straty I^2*Z str.(Up^2+Uk^2)Ysh
Nr BUS BUS P(MW) Q(MVAR) pSF P(MW) Q(MVAR) pST dP(MW) dQ(Mvar) dPsh(MW) dQsh(Mvar)
========================================================================================================================
Razem LINIE 1.367 5.947 0.000 -42.094
Razem TRANSF 114.827 2712.003 0.258 2.092
Razem STRATY 116.193 2717.950 0.258 -40.002
Obliczenia rozpływów mocy systemu dla grupy połączeń T1, T2, T3, T4 –Yd11; T5, T6, T9 –Yd5; T7, T8 –Yy0 : Metoda hybrydowa:
Iteration process of Guass-Seidl method
ITERATION = 32 normaNZB= 0.01125349
Bus Voltages and Powers obtained from Load Flow Solution
===============================================================================================
BUS VOLTAGE GENERATION LOAD const LOAD shunt
Nr Name type U_pu angle U_kV Pg(MW) Qg(MVAR) Pd(MW) Qd(MVAR Psh(MW) Qsh(MVAR)
===============================================================================================
1 wezel 1 1 1.0103 -0.0 111.1 0.00 0.00 10.00 6.00 0.00 0.00
2 wezel 2 1 0.9755 3.5 107.3 0.00 0.00 40.00 30.00 0.00 0.00
3 wezel 3 1 0.9800 2.4 107.8 0.00 0.00 40.00 30.00 0.00 0.00
4 wezel 4 1 1.0462 -0.0 115.1 0.00 0.00 0.00 30.00 0.00 0.00
5 wezel 5 1 1.0010 -0.2 110.1 0.00 -0.00 - - - -
6 wezel 6 1 0.9201 -154.1 27.6 0.00 -0.00 20.00 10.00 0.00 0.00
7 wezel 9 1 1.0364 -152.0 10.4 0.00 -0.00 10.00 6.00 0.00 0.00
8 wezel 10 2 1.0000 37.7 10.0 30.00 8.71 - - - -
9 wezel 11 2 1.0000 37.7 10.0 30.00 8.71 - - - -
10 wezel 12 2 1.0000 36.4 10.0 30.00 -5.39 - - - -
11 wezel 13 2 1.0000 36.4 10.0 30.00 -5.39 - - - -
12 wezel 14 3 1.1000 0.0 242.0 2.16 90.69 - - - -
----- ----- ----- ----- ----- -----
Total: 122.16 97.34 120.00 112.00 0.00 0.00
Effective load coefficients: pSF = Ifrom/Imax*100%, pST = Ito/Imax*100%
========================================================================================================================
FROM TO FLOW at begin FLOW at end straty I^2*Z str.(Up^2+Uk^2)Ysh
Nr BUS BUS P(MW) Q(MVAR) pSF P(MW) Q(MVAR) pST dP(MW) dQ(Mvar) dPsh(MW) dQsh(Mvar)
========================================================================================================================
Razem LINIE 1.367 5.947 0.000 -42.094
Razem TRANSF 114.827 2712.003 0.258 2.092
Razem STRATY 116.193 2717.950 0.258 -40.002
Obliczenia rozpływów mocy systemu dla napięcia w węźle 9 równemu 0.1 : Metoda Newtona:
Iteration process of Netwon-Raphson method
IT= 5, SignDetJ= 1, Unbalance=8.041e-008 - bus with Max. Unbal. 12: Um=1.1000, dpmax= -0.1734
Bus Voltages and Powers obtained from Load Flow Solution
===============================================================================================
BUS VOLTAGE GENERATION LOAD const LOAD shunt
Nr Name type U_pu angle U_kV Pg(MW) Qg(MVAR) Pd(MW) Qd(MVAR Psh(MW) Qsh(MVAR)
===============================================================================================
1 wezel 1 1 0.6714 0.2 73.8 0.00 0.00 10.00 6.00 0.00 0.00
2 wezel 2 1 0.8967 4.3 98.6 0.00 0.00 40.00 30.00 0.00 0.00
3 wezel 3 1 0.9330 1.2 102.6 0.00 0.00 40.00 30.00 0.00 0.00
4 wezel 4 1 0.9507 -0.9 104.6 0.00 0.00 0.00 30.00 0.00 0.00
5 wezel 5 1 0.9241 -1.5 101.7 0.00 -0.00 - - - -
6 wezel 6 1 0.8427 -6.2 25.3 0.00 0.00 20.00 10.00 0.00 0.00
7 wezel 9 1 0.0709 -50.5 0.7 0.00 0.00 10.00 6.00 0.00 0.00
8 wezel 10 2 1.0000 8.7 10.0 30.00 41.55 - - - -
9 wezel 11 2 1.0000 8.7 10.0 30.00 41.55 - - - -
10 wezel 12 2 1.0000 5.3 10.0 30.00 15.33 - - - -
11 wezel 13 2 1.0000 5.3 10.0 30.00 15.33 - - - -
12 wezel 14 3 1.1000 0.0 242.0 17.34 175.65 - - - -
----- ----- ----- ----- ----- -----
Total: 137.34 289.42 120.00 112.00 0.00 0.00
Effective load coefficients: pSF = Ifrom/Imax*100%, pST = Ito/Imax*100%
========================================================================================================================
FROM TO FLOW at begin FLOW at end straty I^2*Z str.(Up^2+Uk^2)Ysh
Nr BUS BUS P(MW) Q(MVAR) pSF P(MW) Q(MVAR) pST dP(MW) dQ(Mvar) dPsh(MW) dQsh(Mvar)
========================================================================================================================
Razem LINIE 9.014 48.442 0.000 -32.301
Razem TRANSF 8.095 159.429 0.233 1.845
Razem STRATY 17.109 207.871 0.233 -30.455
Obliczenia rozpływów mocy systemu dla napięcia w węźle 9 równemu 0.1 : Metoda Gaussa:
Iteration process of Guass-Seidl method
ITERATION =131 normaNZB= 0.00000001
Bus Voltages and Powers obtained from Load Flow Solution
===============================================================================================
BUS VOLTAGE GENERATION LOAD const LOAD shunt
Nr Name type U_pu angle U_kV Pg(MW) Qg(MVAR) Pd(MW) Qd(MVAR Psh(MW) Qsh(MVAR)
===============================================================================================
1 wezel 1 1 1.0103 -0.0 111.1 0.00 0.00 10.00 6.00 0.00 0.00
2 wezel 2 1 0.9755 3.5 107.3 0.00 0.00 40.00 30.00 0.00 0.00
3 wezel 3 1 0.9800 2.4 107.8 0.00 0.00 40.00 30.00 0.00 0.00
4 wezel 4 1 1.0462 -0.0 115.1 0.00 0.00 0.00 30.00 0.00 0.00
5 wezel 5 1 1.0010 -0.2 110.1 0.00 -0.00 - - - -
6 wezel 6 1 0.9201 -4.1 27.6 0.00 -0.00 20.00 10.00 0.00 0.00
7 wezel 9 1 1.0364 -2.0 10.4 0.00 -0.00 10.00 6.00 0.00 0.00
8 wezel 10 2 1.0000 7.7 10.0 30.00 8.71 - - - -
9 wezel 11 2 1.0000 7.7 10.0 30.00 8.71 - - - -
10 wezel 12 2 1.0000 6.4 10.0 30.00 -5.39 - - - -
11 wezel 13 2 1.0000 6.4 10.0 30.00 -5.39 - - - -
12 wezel 14 3 1.1000 0.0 242.0 2.16 90.69 - - - -
----- ----- ----- ----- ----- -----
Total: 122.16 97.34 120.00 112.00 0.00 0.00
Effective load coefficients: pSF = Ifrom/Imax*100%, pST = Ito/Imax*100%
========================================================================================================================
FROM TO FLOW at begin FLOW at end straty I^2*Z str.(Up^2+Uk^2)Ysh
Nr BUS BUS P(MW) Q(MVAR) pSF P(MW) Q(MVAR) pST dP(MW) dQ(Mvar) dPsh(MW) dQsh(Mvar)
========================================================================================================================
Razem LINIE 1.367 5.947 0.000 -42.094
Razem TRANSF 0.539 19.400 0.258 2.092
Razem STRATY 1.906 25.346 0.258 -40.002
Obliczenia rozpływów mocy systemu dla napięcia w węźle 9 równemu 0.1 : Metoda Hybrydowa:
Iteration process of Guass-Seidl method
ITERATION = 21 normaNZB= 0.01110284
Bus Voltages and Powers obtained from Load Flow Solution
===============================================================================================
BUS VOLTAGE GENERATION LOAD const LOAD shunt
Nr Name type U_pu angle U_kV Pg(MW) Qg(MVAR) Pd(MW) Qd(MVAR Psh(MW) Qsh(MVAR)
===============================================================================================
1 wezel 1 1 1.0103 -0.0 111.1 0.00 0.00 10.00 6.00 0.00 0.00
2 wezel 2 1 0.9755 3.5 107.3 0.00 0.00 40.00 30.00 0.00 0.00
3 wezel 3 1 0.9800 2.4 107.8 0.00 0.00 40.00 30.00 0.00 0.00
4 wezel 4 1 1.0462 -0.0 115.1 0.00 0.00 0.00 30.00 0.00 0.00
5 wezel 5 1 1.0010 -0.2 110.1 0.00 -0.00 - - - -
6 wezel 6 1 0.9201 -4.1 27.6 0.00 -0.00 20.00 10.00 0.00 0.00
7 wezel 9 1 1.0364 -2.0 10.4 0.00 -0.00 10.00 6.00 0.00 0.00
8 wezel 10 2 1.0000 7.7 10.0 30.00 8.71 - - - -
9 wezel 11 2 1.0000 7.7 10.0 30.00 8.71 - - - -
10 wezel 12 2 1.0000 6.4 10.0 30.00 -5.39 - - - -
11 wezel 13 2 1.0000 6.4 10.0 30.00 -5.39 - - - -
12 wezel 14 3 1.1000 0.0 242.0 2.16 90.69 - - - -
----- ----- ----- ----- ----- -----
Total: 122.16 97.34 120.00 112.00 0.00 0.00
Effective load coefficients: pSF = Ifrom/Imax*100%, pST = Ito/Imax*100%
========================================================================================================================
FROM TO FLOW at begin FLOW at end straty I^2*Z str.(Up^2+Uk^2)Ysh
Nr BUS BUS P(MW) Q(MVAR) pSF P(MW) Q(MVAR) pST dP(MW) dQ(Mvar) dPsh(MW) dQsh(Mvar)
========================================================================================================================
Razem LINIE 1.367 5.947 0.000 -42.094
Razem TRANSF 0.539 19.400 0.258 2.092
Razem STRATY 1.906 25.346 0.258 -40.002
Wnioski:
Dla wariantu podstawowego metoda Newtona-Raphsona zakończyła się już po czterech iteracjach, metoda Gaussa po 127 a metoda hybrydowa po 18. W tym przypadku uzyskaliśmy dokładnie takie same wartości rozpływów mocy. Można stwierdzić, że najkorzystniejsza tutaj była metoda Newtona-Raphsona ze względu na małą liczbę iteracji, lecz w przypadku gdy punkt startowy jest daleko od rozwiązania metoda ta staje się bezużyteczna.
W przypadku symulacji rozpływów mocy dla transformatorów z rzeczywista przekładnią wynikającą z grupy połączeń wyniki były rozbieżne. Można także było zauważyć znaczny wzrost całkowitych strat mocy.
Dla wariantu gdy napięcie w węźle 9 jest równe 0.1 widać, że metoda Newtona-Raphsona się nie sprawdza.