### Load Flow of 33 buses distribution system, current in between buses equal zero

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**Sat May 25, 2019 3:14 pm**I Have a problem using GAMS in load flow modelling on 33 buses distribution system,

The problem is that when I display the values of the current in between buses C(I,j,t) after running it gives me all zeros and all voltages equal 1, why the voltage values are fixed at all buses and why the current are zeros ???

The resistance, reactance and current limit of each line is already defined in amp.at the beginning of the model as per the below table

Table LN(i,j,*) 'network technical characteristics'

r x Limit

1 .2 0.057625 0.029375 200

2 .3 0.308125 0.156937 200

3 .4 0.228750 0.116500 200

4 .5 0.238187 0.121312 200

5 .6 0.511875 0.441875 200

6 .7 0.117000 0.386750 200

7 .8 0.444625 0.146937 200

8 .9 0.643750 0.462500 200

9 .10 0.652500 0.462500 100

10.11 0.122875 0.040625 100

11.12 0.234000 0.077375 100

12.13 0.917500 0.721875 100

13.14 0.338500 0.445562 100

14.15 0.369375 0.328750 100

15.16 0.466437 0.340625 100

16.17 0.805625 1.075625 100

17.18 0.457500 0.358750 100

2 .19 0.102500 0.097812 100

19.20 0.940125 0.847125 100

20.21 0.255937 0.299000 100

21.22 0.443062 0.585812 100

3 .23 0.282000 0.192687 100

23.24 0.561250 0.443187 100

24.25 0.560000 0.438187 100

6 .26 0.126875 0.064625 100

26.27 0.177625 0.090437 100

27.28 0.661875 0.583562 100

28.29 0.502625 0.437875 100

29.30 0.317187 0.161562 100

30.31 0.609000 0.601875 100

31.32 0.194062 0.226187 100

32.33 0.213125 0.331375 100

8 .21 1.250000 1.250000 100

9 .15 1.250000 1.250000 100

12.22 1.250000 1.250000 100

18.33 0.312500 0.312500 100

25.29 0.312500 0.312500 100;

the demand load is set at each bus as per the below table

Table BD(i,*) 'demands of each bus in KW'

Pd Qd

2 100 60

3 90 40

4 120 80

5 60 30

6 60 20

7 200 100

8 200 100

9 60 20

10 60 20

11 45 30

12 60 35

13 60 35

14 120 80

15 60 10

16 60 20

17 60 20

18 90 40

19 90 40

20 90 40

21 90 40

22 90 40

23 90 50

24 420 200

25 420 200

26 60 25

27 60 25

28 60 20

29 120 70

30 200 600

31 150 70

32 210 100

33 60 40 ;

Set

i 'network buses' / 1*33 /

slack(i) / 1 /

Alias (i,j);

LN(i,j,'x')$(LN(i,j,'x')=0) = LN(j,i,'x');

LN(i,j,'r')$(LN(i,j,'r')=0) = LN(j,i,'r');

LN(i,j,'Limit')$(LN(i,j,'Limit')=0) = LN(j,i,'Limit');

LN(i,j,'bij')$LN(i,j,'Limit') = 1/LN(i,j,'x');

LN(i,j,'z')$LN(i,j,'Limit') = sqrt(sqr(LN(i,j,'x')) + sqr(LN(i,j,'r')));

LN(j,i,'z')$(LN(i,j,'z')=0) = LN(i,j,'z');

LN(i,j,'Yij')$LN(i,j,'Limit') = 1/LN(i,j,'Z');

LN(i,j,'th')$(LN(i,j,'Limit') and LN(i,j,'x') and LN(i,j,'r')) = arctan(LN(i,j,'x')/(LN(i,j,'r')));

LN(i,j,'th')$(LN(i,j,'Limit') and LN(i,j,'x') and LN(i,j,'r')=0) = pi/2;

LN(i,j,'th')$(LN(i,j,'Limit') and LN(i,j,'r') and LN(i,j,'x')=0) = 0;

LN(j,i,'th')$LN(i,j,'Limit') = LN(i,j,'th');

Parameter cx(i,j);

cx(i,j)$(LN(i,j,'limit') and LN(j,i,'limit')) = 1;

cx(i,j)$(cx(j,i)) = 1;

Variable OF,Pij(i,j,t), Qij(i,j,t),C(i,j,t);

Free Variable V(i,t), Va(i,t);

The power flow equations are modelled as per the below equations

eq1 (i,j,t)$cx(i,j)..

Pij(i,j,t) =e= (V(i,t)*V(j,t)*cos(Va(i,t) - Va(j,t) + LN(i,j,'th')))*LN(i,j,'Yij'); power in between buse I,j

eq2 (i,j,t)$cx(i,j)..

Qij(i,j,t) =e= (V(i,t)*V(j,t)*sin(Va(i,t) - Va(j,t) + LN(i,j,'th')))*LN(i,j,'Yij'); reactive power in between bus I,j

eq3 (i,t)..

BD(i,'pd')/Sbase =e=Sum (j, Pij(i,j,t));

eq4 (i,t)..

BD(i,'qd')/Sbase =e=Sum (j, Qij(i,j,t));

The absolute value of current of the lines in between buses modelled by the below equation

eq11 (i,j,t)..

C(i,j,t)=e=abs((V(i,t)*cos(Va(i,t))-(V(j,t)*cos(Va(j,t))))*LN( j , i ,' Yij '));

constraint of the of lower and upper limit of the absolute value of current in between buses is given by the below equation

C.lo(i,j,t)=0;

C.up(i,j,t)=1*LN(i,j,'Limit')/Ibase;

I set the upper and lower limits of the voltage and voltage angle as follow:

V.lo(i,t) = 0.9;

V.up(i,t) = 1.1;

V.l(i,t)=1;

Va.l(i,t) = 0;

Va.up(i,t) = pi/2;

Va.lo(i,t) =-pi/2;

mean while the slack bus voltage and angle are set to be fixed

V.fx(slack,t)=1;

Va.fx(slack,t) = 0;

The problem is that when I display the values of the current C(I,j,t) after running it gives me all zeros and all voltages equal 1, why the voltage values are fixed at all buses and why the current are zeros ???

Thanks in advance for your cooperation

The problem is that when I display the values of the current in between buses C(I,j,t) after running it gives me all zeros and all voltages equal 1, why the voltage values are fixed at all buses and why the current are zeros ???

The resistance, reactance and current limit of each line is already defined in amp.at the beginning of the model as per the below table

Table LN(i,j,*) 'network technical characteristics'

r x Limit

1 .2 0.057625 0.029375 200

2 .3 0.308125 0.156937 200

3 .4 0.228750 0.116500 200

4 .5 0.238187 0.121312 200

5 .6 0.511875 0.441875 200

6 .7 0.117000 0.386750 200

7 .8 0.444625 0.146937 200

8 .9 0.643750 0.462500 200

9 .10 0.652500 0.462500 100

10.11 0.122875 0.040625 100

11.12 0.234000 0.077375 100

12.13 0.917500 0.721875 100

13.14 0.338500 0.445562 100

14.15 0.369375 0.328750 100

15.16 0.466437 0.340625 100

16.17 0.805625 1.075625 100

17.18 0.457500 0.358750 100

2 .19 0.102500 0.097812 100

19.20 0.940125 0.847125 100

20.21 0.255937 0.299000 100

21.22 0.443062 0.585812 100

3 .23 0.282000 0.192687 100

23.24 0.561250 0.443187 100

24.25 0.560000 0.438187 100

6 .26 0.126875 0.064625 100

26.27 0.177625 0.090437 100

27.28 0.661875 0.583562 100

28.29 0.502625 0.437875 100

29.30 0.317187 0.161562 100

30.31 0.609000 0.601875 100

31.32 0.194062 0.226187 100

32.33 0.213125 0.331375 100

8 .21 1.250000 1.250000 100

9 .15 1.250000 1.250000 100

12.22 1.250000 1.250000 100

18.33 0.312500 0.312500 100

25.29 0.312500 0.312500 100;

the demand load is set at each bus as per the below table

Table BD(i,*) 'demands of each bus in KW'

Pd Qd

2 100 60

3 90 40

4 120 80

5 60 30

6 60 20

7 200 100

8 200 100

9 60 20

10 60 20

11 45 30

12 60 35

13 60 35

14 120 80

15 60 10

16 60 20

17 60 20

18 90 40

19 90 40

20 90 40

21 90 40

22 90 40

23 90 50

24 420 200

25 420 200

26 60 25

27 60 25

28 60 20

29 120 70

30 200 600

31 150 70

32 210 100

33 60 40 ;

Set

i 'network buses' / 1*33 /

slack(i) / 1 /

Alias (i,j);

LN(i,j,'x')$(LN(i,j,'x')=0) = LN(j,i,'x');

LN(i,j,'r')$(LN(i,j,'r')=0) = LN(j,i,'r');

LN(i,j,'Limit')$(LN(i,j,'Limit')=0) = LN(j,i,'Limit');

LN(i,j,'bij')$LN(i,j,'Limit') = 1/LN(i,j,'x');

LN(i,j,'z')$LN(i,j,'Limit') = sqrt(sqr(LN(i,j,'x')) + sqr(LN(i,j,'r')));

LN(j,i,'z')$(LN(i,j,'z')=0) = LN(i,j,'z');

LN(i,j,'Yij')$LN(i,j,'Limit') = 1/LN(i,j,'Z');

LN(i,j,'th')$(LN(i,j,'Limit') and LN(i,j,'x') and LN(i,j,'r')) = arctan(LN(i,j,'x')/(LN(i,j,'r')));

LN(i,j,'th')$(LN(i,j,'Limit') and LN(i,j,'x') and LN(i,j,'r')=0) = pi/2;

LN(i,j,'th')$(LN(i,j,'Limit') and LN(i,j,'r') and LN(i,j,'x')=0) = 0;

LN(j,i,'th')$LN(i,j,'Limit') = LN(i,j,'th');

Parameter cx(i,j);

cx(i,j)$(LN(i,j,'limit') and LN(j,i,'limit')) = 1;

cx(i,j)$(cx(j,i)) = 1;

Variable OF,Pij(i,j,t), Qij(i,j,t),C(i,j,t);

Free Variable V(i,t), Va(i,t);

The power flow equations are modelled as per the below equations

eq1 (i,j,t)$cx(i,j)..

Pij(i,j,t) =e= (V(i,t)*V(j,t)*cos(Va(i,t) - Va(j,t) + LN(i,j,'th')))*LN(i,j,'Yij'); power in between buse I,j

eq2 (i,j,t)$cx(i,j)..

Qij(i,j,t) =e= (V(i,t)*V(j,t)*sin(Va(i,t) - Va(j,t) + LN(i,j,'th')))*LN(i,j,'Yij'); reactive power in between bus I,j

eq3 (i,t)..

BD(i,'pd')/Sbase =e=Sum (j, Pij(i,j,t));

eq4 (i,t)..

BD(i,'qd')/Sbase =e=Sum (j, Qij(i,j,t));

The absolute value of current of the lines in between buses modelled by the below equation

eq11 (i,j,t)..

C(i,j,t)=e=abs((V(i,t)*cos(Va(i,t))-(V(j,t)*cos(Va(j,t))))*LN( j , i ,' Yij '));

constraint of the of lower and upper limit of the absolute value of current in between buses is given by the below equation

C.lo(i,j,t)=0;

C.up(i,j,t)=1*LN(i,j,'Limit')/Ibase;

I set the upper and lower limits of the voltage and voltage angle as follow:

V.lo(i,t) = 0.9;

V.up(i,t) = 1.1;

V.l(i,t)=1;

Va.l(i,t) = 0;

Va.up(i,t) = pi/2;

Va.lo(i,t) =-pi/2;

mean while the slack bus voltage and angle are set to be fixed

V.fx(slack,t)=1;

Va.fx(slack,t) = 0;

The problem is that when I display the values of the current C(I,j,t) after running it gives me all zeros and all voltages equal 1, why the voltage values are fixed at all buses and why the current are zeros ???

Thanks in advance for your cooperation