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Error in NDSolve of transmission line?

Posted 5 months ago
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ClearAll["Global '*"]; NN = 11;

tmax = 6.0;

fN = 1.0;
Rs = 50.0;
Resc_impair = Table[Rc[k] = 0.0, {k, 1, NN, 2}];
Resc_pair = Table[Rc[k] = 0.0, {k, 2, NN, 2}];
Rc[NN] = 1100.0;
Resl_impair = Table[Rl[k] = 0.0, {k, 1, NN, 2}];
Resl_pair = Table[Rl[k] = 0.0, {k, 1, NN, 2}];
Rl[NN] = 200.0;
t0 = 0.0; ts = 1.7 + t0; tflat = 300.0; tfall = 1.7; tc = ts + tflat;
td = tc + tfall; a0 = -10.0*10^3; {ts, tflat, tfall, td - tc}
Vs[t_] := Which[t <= t0, 0, t > t0  && t <= ts, a0 *(t - t0)/ts - t0,
  t > ts && t <= tc, a0, t > t0 && t <= td, a0*((-t + td)/(td - tc)), 
  t > td, 0]
TabVs = Table[{t, Vs[t]/1000}, {t, 0, tmax, 0.01}];
VoltVs = ListPlot[TabVs, PlotRange -> All, 
  PlotStyle -> {AbsoluteThickness[1.4], RGBColor[0, 0, 1], 
    Thickness[0.008]}, FrameLabel -> {"Time(ns)", "Voltage(kV)"}, 
  Joined -> True, GridLines -> {Automatic, Automatic}, 
  FrameTicks -> {Automatic, Automatic}, Frame -> True, 
  LabelStyle -> Directive[Black, 17]]

np = 256; tfourier = 1000;
pulse = Table[Vs[t]/1000, {t, 0, tfourier, 0.05}];
datafin = Table[{f/(1.2), Abs[Fourier[pulse]][[f]]}, {f, 1, 60, 1}];
pVs = ListPlot[datafin, PlotRange -> {{0, 50}, All}, 
  PlotStyle -> {AbsoluteThickness[1.8], RGBColor[0, 1, 0], 
    Thickness[0.008]}, FrameLabel -> {"Frequence(Mhz)", "Voltage(V)"},
   Joined -> True, GridLines -> {Automatic, Automatic}, 
  FrameTicks -> {Automatic, Automatic}, Frame -> True, 
  LabelStyle -> Directive[Black, 17]]
NIntegrate[Vs[t]/1000, {t, 0, 200}]
(*non linear capacitor*)
m = 1.08; V0 = 0.7; Cs0 = 0.000095;
p = (1.0 + 1*V[k][t]/V0)^m
Cv[k_][t_] := which[V[k][t] > -V0, Cs0/p, V[k][t] <= -V0, 10.0]
Cv[k_][t_] := Cs0/p
Ca[Va_] := Cs0/(1.0 + 1*Va/V0)^m 
Cv[NN][t] := 10000000.0;
Plot[{Ca[Va]}, {Va, 0, 15}, AxesLabel -> {"Va", "Ca"}, 
 PlotRange -> {0, Cs0}, PlotStyle -> {Thickness[.01], Red}, 
 TicksStyle -> Directive["Black", 14], 
 AxesStyle -> {{Thick, Black}, {Thick, Black}}, 
 AxesLabel -> {Style["t", Black, Italic, 30], 
   Style["x,Vin", Black, Italic, 30]}, Frame -> False, 
 PlotRange -> All]
(*non linear inductance*)
L0 = 465; La = 4.65; Is = 3.76;
Ls[k_][t_] := (L0 - La)*(Sech[i[k][t]/Is]^2) + La
La1[Ia_] := (L0 - La)*(Sech[(Ia/Is)]^2) + La
Plot[{La1[Ia]}, {Ia, 0, 100}, AxesLabel -> {"Ia", "La1"}, 
 PlotRange -> {0, L0*1.2}, PlotStyle -> {Thickness[.01], Orange}, 
 TicksStyle -> Directive["Black", 14], 
 AxesStyle -> {{Thick, Black}, {Thick, Black}}, 
 AxesLabel -> {Style["t", Black, Italic, 30], 
   Style["x,Vin", Black, Italic, 30]}, Frame -> False, 
 PlotRange -> All]
Ls[NN][t] := 1.0*10^-8
Ls[k_][t_] := 280.0
(*Equation for the First Section*)
eqi = Table[{-i[k]'[t] + 
      Vs[t]/Ls[k][t] - (Rs/Ls[k][t])*
       i[k][t] - (Rc[k]/Ls[k][t] )*(i[k][t] - i[k + 1][t]) - (V[k][
         t])/Ls[k][t] - (Rl[k]/Ls[k][t] )*(i[k][t]) == 
     0, -V[k]'[t] + (i[k][t] - i[k + 1][t])/Cv[k][t] == 0}, {k, 1, 1}];

(*Equation for the intermediate Section*)
eqs = Table[{-i[k]'[
        t] + (Rc[k - 1]/Ls[k][t]) *(i[k - 1][t] - 
         i[k][t]) + (V[k - 1][t])/
       Ls[k][t] - (Rc[k]/Ls[k][t] )*(i[k][t] - i[k + 1][t]) - (V[k][
         t])/Ls[k][t] - (Rl[k]/Ls[k][t] )*(i[k][t]) == 
     0, -V[k]'[t] + (i[k][t] - i[k + 1][t])/Cv[k][t] == 0}, {k, 2, 
    NN - 1}];
eqpartial = Join[eqi, eqs, eqf];
eqfinal = Flatten[eqpartial];
(*Equation for the finale Section*)
eqf = Table[{-i[k]'[
        t] + (Rc[k - 1]/Ls[k][t] )*(i[k - 1][t] - 
         i[k][t]) + (V[k - 1][t])/
       Ls[k][t] - (Rc[k]/Ls[k][t] )*(i[k][t] ) - (V[k][t])/
       Ls[k][t] - (Rl[k]/Ls[k][t] )*(i[k][t]) == 
     0, -V[k]'[t] + (i[k][t])/Cv[k][t] == 0}, {k, NN, NN}];
eqpartial = Join[eqi, eqs, eqf];
eqfinal = Flatten[eqpartial];
initial1 = Flatten[Table[{i[k][0] == 0., V[k][0] == 0.}, {k, 1, NN}]];
Vlist = Flatten[Table[{V[k][t], i[k][t]}, {k, 1, NN}]];
sol = NDSolve[Join[eqfinal, initial1], Vlist, {t, 0., tmax}, 
   MaxSteps -> Infinity];
sol1 = Flatten[sol];
inputiv = 
  Table[{i[k][t] = i[k][t] /. sol1, V[k][t] = V[k][t] /. sol1}, {k, 1,
     NN}];
outiv = Flatten[inputiv];
V[0][t_] := Vs[t] - Rs*i[1][t];
Vfp = Table[
   V[k][t_] = Rc[k]*(i[k][t] - i[k + 1][t]) + V[k][t], {k, 1, NN - 1}];
V[NN][t_] := Rc[NN]*(i[NN][t]) + V[NN][t]
Pload[t_] := V[NN][t] i[NN][t]
Pint[t_] := Vs[t] i[1][t]
VoltFim = 
 ListPlot[outiv, PlotRange -> All, 
  PlotStyle -> {AbsoluteThickness[1.4], RGBColor[0, 0, 1], 
    Thickness[0.008]}, FrameLabel -> {"Time(ns)", "Voltage(kV)"}, 
  Joined -> True, GridLines -> {Automatic, Automatic}, 
  FrameTicks -> {Automatic, Automatic}, Frame -> True, 
  LabelStyle -> Directive[Black, 17]]
Show[VoltVs, VoltFim]
Error:NDSolve::nlnum: The function value {-0.00174035,-1. (1.68378*10^-10-1.66057*10^-17 Rl[2]),0.,0.,0.,0.,0.,0.,0.,0.,<<12>>} is not a list of numbers with dimensions {22} at {t,i[1][t],i[2][t],i[3][t],i[4][t],i[5][t],i[6][t],i[7][t],i[8][t],i[9][t],<<17>>} = {0.0000828415,-1.0813*10^-7,-4.64959*10^-15,0.,0.,0.,0.,0.,0.,0.,<<17>>}.
7 Replies

The NDSolve worked for me, once I first made the following correction in your code:

Resl_pair = Table[Rl[k] = 0.0, {k, 2, NN, 2}];
POSTED BY: Frank Iannarilli

Hi Frank... Please show your graph.

Posted 5 months ago

In the WL underscore is interpreted as Blank, so Resl_pair is not a symbol with that name.

Resl_pair // FullForm
(* Pattern[Resl, Blank[pair]] *)

Don't use _ in symbol names.

POSTED BY: Rohit Namjoshi
ClearAll["Global '*"];
NN = 11;

tmax = 6.0;

fN = 1.0;
Rs = 50.0;
Rescimpair = Table[Rc[k] = 0.0, {k, 1, NN, 2}];
Rescpair = Table[Rc[k] = 0.0, {k, 2, NN, 2}];
Rc[NN] = 1100.0;
Reslimpair = Table[Rl[k] = 0.0, {k, 1, NN, 2}];
Reslpair = Table[Rl[k] = 0.0, {k, 2, NN, 2}];
Rl[NN] = 200.0;
t0 = 0.0; ts = 1.7 + t0; tflat = 300.0; tfall = 1.7; tc = ts + tflat;
td = tc + tfall; a0 = -10.0*10^3; {ts, tflat, tfall, td - tc}
Vs[t_] := Which[t <= t0, 0, t > t0  && t <= ts, a0 *(t - t0)/ts - t0,
  t > ts && t <= tc, a0, t > t0 && t <= td, a0*((-t + td)/(td - tc)), 
  t > td, 0]
TabVs = Table[{t, Vs[t]/1000}, {t, 0, tmax, 0.01}];
VoltVs = ListPlot[TabVs, PlotRange -> All, 
  PlotStyle -> {AbsoluteThickness[1.4], RGBColor[0, 0, 1], 
    Thickness[0.008]}, FrameLabel -> {"Time(ns)", "Voltage(kV)"}, 
  Joined -> True, GridLines -> {Automatic, Automatic}, 
  FrameTicks -> {Automatic, Automatic}, Frame -> True, 
  LabelStyle -> Directive[Black, 17]]

np = 256; tfourier = 1000;
pulse = Table[Vs[t]/1000, {t, 0, tfourier, 0.05}];
datafin = Table[{f/(1.2), Abs[Fourier[pulse]][[f]]}, {f, 1, 60, 1}];
pVs = ListPlot[datafin, PlotRange -> {{0, 50}, All}, 
  PlotStyle -> {AbsoluteThickness[1.8], RGBColor[0, 1, 0], 
    Thickness[0.008]}, FrameLabel -> {"Frequence(Mhz)", "Voltage(V)"},
   Joined -> True, GridLines -> {Automatic, Automatic}, 
  FrameTicks -> {Automatic, Automatic}, Frame -> True, 
  LabelStyle -> Directive[Black, 17]]
NIntegrate[Vs[t]/1000, {t, 0, 200}]
(*non linear capacitor*)
m = 1.08; V0 = 0.7; Cs0 = 0.000095;
p = (1.0 + 1*V[k][t]/V0)^m
Cv[k_][t_] := which[V[k][t] > -V0, Cs0/p, V[k][t] <= -V0, 10.0]
Cv[k_][t_] := Cs0/p
Ca[Va_] := Cs0/(1.0 + 1*Va/V0)^m 
Cv[NN][t] := 10000000.0;
Plot[{Ca[Va]}, {Va, 0, 15}, AxesLabel -> {"Va", "Ca"}, 
 PlotRange -> {0, Cs0}, PlotStyle -> {Thickness[.01], Red}, 
 TicksStyle -> Directive["Black", 14], 
 AxesStyle -> {{Thick, Black}, {Thick, Black}}, 
 AxesLabel -> {Style["t", Black, Italic, 30], 
   Style["x,Vin", Black, Italic, 30]}, Frame -> False, 
 PlotRange -> All]
(*non linear inductance*)
L0 = 465; La = 4.65; Is = 3.76;
Ls[k_][t_] := (L0 - La)*(Sech[i[k][t]/Is]^2) + La
La1[Ia_] := (L0 - La)*(Sech[(Ia/Is)]^2) + La
Plot[{La1[Ia]}, {Ia, 0, 100}, AxesLabel -> {"Ia", "La1"}, 
 PlotRange -> {0, L0*1.2}, PlotStyle -> {Thickness[.01], Orange}, 
 TicksStyle -> Directive["Black", 14], 
 AxesStyle -> {{Thick, Black}, {Thick, Black}}, 
 AxesLabel -> {Style["t", Black, Italic, 30], 
   Style["x,Vin", Black, Italic, 30]}, Frame -> False, 
 PlotRange -> All]
Ls[NN][t] := 1.0*10^-8
Ls[k_][t_] := 280.0
(*Equation for the First Section*)
eqi = Table[{-i[k]'[t] + 
      Vs[t]/Ls[k][t] - (Rs/Ls[k][t])*
       i[k][t] - (Rc[k]/Ls[k][t] )*(i[k][t] - i[k + 1][t]) - (V[k][
         t])/Ls[k][t] - (Rl[k]/Ls[k][t] )*(i[k][t]) == 
     0, -V[k]'[t] + (i[k][t] - i[k + 1][t])/Cv[k][t] == 0}, {k, 1, 1}];

(*Equation for the intermediate Section*)
eqs = Table[{-i[k]'[
        t] + (Rc[k - 1]/Ls[k][t]) *(i[k - 1][t] - 
         i[k][t]) + (V[k - 1][t])/
       Ls[k][t] - (Rc[k]/Ls[k][t] )*(i[k][t] - i[k + 1][t]) - (V[k][
         t])/Ls[k][t] - (Rl[k]/Ls[k][t] )*(i[k][t]) == 
     0, -V[k]'[t] + (i[k][t] - i[k + 1][t])/Cv[k][t] == 0}, {k, 2, 
    NN - 1}];
eqpartial = Join[eqi, eqs, eqf];
eqfinal = Flatten[eqpartial];
(*Equation for the finale Section*)
eqf = Table[{-i[k]'[
        t] + (Rc[k - 1]/Ls[k][t] )*(i[k - 1][t] - 
         i[k][t]) + (V[k - 1][t])/
       Ls[k][t] - (Rc[k]/Ls[k][t] )*(i[k][t] ) - (V[k][t])/
       Ls[k][t] - (Rl[k]/Ls[k][t] )*(i[k][t]) == 
     0, -V[k]'[t] + (i[k][t])/Cv[k][t] == 0}, {k, NN, NN}];
eqpartial = Join[eqi, eqs, eqf];
eqfinal = Flatten[eqpartial];
initial1 = Flatten[Table[{i[k][0] == 0., V[k][0] == 0.}, {k, 1, NN}]];
Vlist = Flatten[Table[{V[k][t], i[k][t]}, {k, 1, NN}]];
sol = NDSolve[Join[eqfinal, initial1], Vlist, {t, 0., tmax}, 
   MaxSteps -> Infinity];
sol1 = Flatten[sol];
inputiv = 
  Table[{i[k][t] = i[k][t] /. sol1, V[k][t] = V[k][t] /. sol1}, {k, 1,
     NN}];
outiv = Flatten[inputiv];
V[0][t_] := Vs[t] - Rs*i[1][t];
Vfp = Table[
   V[k][t_] = Rc[k]*(i[k][t] - i[k + 1][t]) + V[k][t], {k, 1, NN - 1}];
V[NN][t_] := Rc[NN]*(i[NN][t]) + V[NN][t]
Pload[t_] := V[NN][t] i[NN][t]
Pint[t_] := Vs[t] i[1][t]
VoltFim = 
 ListPlot[outiv, PlotRange -> All, 
  PlotStyle -> {AbsoluteThickness[1.4], RGBColor[0, 0, 1], 
    Thickness[0.008]}, FrameLabel -> {"Time(ns)", "Voltage(kV)"}, 
  Joined -> True, GridLines -> {Automatic, Automatic}, 
  FrameTicks -> {Automatic, Automatic}, Frame -> True, 
  LabelStyle -> Directive[Black, 17]]
Show[VoltVs, VoltFim]

the plot is empty, please i need help

Hi,

Ah - try this modification:

VoltFim = Plot[outiv, {t, 0, 6},

and eliminate from that expression the option `Joined -> True, then in your final

Show[...]

add the option PlotRange->All

You are plotting both the voltages and currents, even though your y-axis label indicates volts (!) Resulting Show[] plot

`

POSTED BY: Frank Iannarilli

Thanks, Frank.....

In[1]:= ClearAll["Global '*"];
NN = 11;

tmax = 6.0;

fN = 1.0;
Rs = 50.0;
Rescimpair = Table[Rc[k] = 0.0, {k, 1, NN, 2}];
Rescpair = Table[Rc[k] = 0.0, {k, 2, NN, 2}];
Rc[NN] = 1100.0;
Reslimpair = Table[Rl[k] = 0.0, {k, 1, NN, 2}];
Reslpair = Table[Rl[k] = 0.0, {k, 2, NN, 2}];
Rl[NN] = 200.0;
t0 = 0.0; ts = 1.7 + t0; tflat = 300.0; tfall = 1.7; tc = ts + tflat;
td = tc + tfall; a0 = -10.0*10^3; {ts, tflat, tfall, td - tc}
Vs[t_] := Which[t <= t0, 0, t > t0  && t <= ts, a0 *(t - t0)/ts - t0,
  t > ts && t <= tc, a0, t > t0 && t <= td, a0*((-t + td)/(td - tc)), 
  t > td, 0]
TabVs = Table[{t, Vs[t]/1000}, {t, 0, tmax, 0.01}];
VoltVs = ListPlot[TabVs, PlotRange -> All, 
  PlotStyle -> {AbsoluteThickness[1.4], RGBColor[0, 0, 1], 
    Thickness[0.008]}, FrameLabel -> {"Time(ns)", "Voltage(kV)"}, 
  Joined -> True, GridLines -> {Automatic, Automatic}, 
  FrameTicks -> {Automatic, Automatic}, Frame -> True, 
  LabelStyle -> Directive[Black, 17]]

np = 256; tfourier = 1000;
pulse = Table[Vs[t]/1000, {t, 0, tfourier, 0.05}];
datafin = Table[{f/(1.2), Abs[Fourier[pulse]][[f]]}, {f, 1, 60, 1}];
pVs = ListPlot[datafin, PlotRange -> {{0, 50}, All}, 
  PlotStyle -> {AbsoluteThickness[1.8], RGBColor[0, 1, 0], 
    Thickness[0.008]}, FrameLabel -> {"Frequence(Mhz)", "Voltage(V)"},
   Joined -> True, GridLines -> {Automatic, Automatic}, 
  FrameTicks -> {Automatic, Automatic}, Frame -> True, 
  LabelStyle -> Directive[Black, 17]]
NIntegrate[Vs[t]/1000, {t, 0, 200}]
(*non linear capacitor*)
m = 1.08; V0 = 0.7; Cs0 = 0.000095;
p = (1.0 + 1*V[k][t]/V0)^m
Cv[k_][t_] := which[V[k][t] > -V0, Cs0/p, V[k][t] <= -V0, 10.0]
Cv[k_][t_] := Cs0/p
Ca[Va_] := Cs0/(1.0 + 1*Va/V0)^m 
Cv[NN][t] := 10000000.0;
Plot[{Ca[Va]}, {Va, 0, 15}, AxesLabel -> {"Va", "Ca"}, 
 PlotRange -> {0, Cs0}, PlotStyle -> {Thickness[.01], Red}, 
 TicksStyle -> Directive["Black", 14], 
 AxesStyle -> {{Thick, Black}, {Thick, Black}}, 
 AxesLabel -> {Style["t", Black, Italic, 30], 
   Style["x,Vin", Black, Italic, 30]}, Frame -> False, 
 PlotRange -> All]
(*non linear inductance*)
L0 = 465; La = 4.65; Is = 3.76;
Ls[k_][t_] := (L0 - La)*(Sech[i[k][t]/Is]^2) + La
La1[Ia_] := (L0 - La)*(Sech[(Ia/Is)]^2) + La
Plot[{La1[Ia]}, {Ia, 0, 100}, AxesLabel -> {"Ia", "La1"}, 
 PlotRange -> {0, L0*1.2}, PlotStyle -> {Thickness[.01], Orange}, 
 TicksStyle -> Directive["Black", 14], 
 AxesStyle -> {{Thick, Black}, {Thick, Black}}, 
 AxesLabel -> {Style["t", Black, Italic, 30], 
   Style["x,Vin", Black, Italic, 30]}, Frame -> False, 
 PlotRange -> All]
Ls[NN][t] := 1.0*10^-8
Ls[k_][t_] := 280.0
(*Equation for the First Section*)
eqi = Table[{-i[k]'[t] + 
      Vs[t]/Ls[k][t] - (Rs/Ls[k][t])*
       i[k][t] - (Rc[k]/Ls[k][t] )*(i[k][t] - i[k + 1][t]) - (V[k][
         t])/Ls[k][t] - (Rl[k]/Ls[k][t] )*(i[k][t]) == 
     0, -V[k]'[t] + (i[k][t] - i[k + 1][t])/Cv[k][t] == 0}, {k, 1, 1}];

(*Equation for the intermediate Section*)
eqs = Table[{-i[k]'[
        t] + (Rc[k - 1]/Ls[k][t]) *(i[k - 1][t] - 
         i[k][t]) + (V[k - 1][t])/
       Ls[k][t] - (Rc[k]/Ls[k][t] )*(i[k][t] - i[k + 1][t]) - (V[k][
         t])/Ls[k][t] - (Rl[k]/Ls[k][t] )*(i[k][t]) == 
     0, -V[k]'[t] + (i[k][t] - i[k + 1][t])/Cv[k][t] == 0}, {k, 2, 
    NN - 1}];
eqpartial = Join[eqi, eqs, eqf];
eqfinal = Flatten[eqpartial];
(*Equation for the finale Section*)
eqf = Table[{-i[k]'[
        t] + (Rc[k - 1]/Ls[k][t] )*(i[k - 1][t] - 
         i[k][t]) + (V[k - 1][t])/
       Ls[k][t] - (Rc[k]/Ls[k][t] )*(i[k][t] ) - (V[k][t])/
       Ls[k][t] - (Rl[k]/Ls[k][t] )*(i[k][t]) == 
     0, -V[k]'[t] + (i[k][t])/Cv[k][t] == 0}, {k, NN, NN}];
eqpartial = Join[eqi, eqs, eqf];
eqfinal = Flatten[eqpartial];
initial1 = Flatten[Table[{i[k][0] == 0., V[k][0] == 0.}, {k, 1, NN}]];
Vlist = Flatten[Table[{V[k][t], i[k][t]}, {k, 1, NN}]];
sol = NDSolve[Join[eqfinal, initial1], Vlist, {t, 0., tmax}, 
   MaxSteps -> Infinity];
sol1 = Flatten[sol];
inputiv = 
  Table[{i[k][t] = i[k][t] //. sol1, V[k][t] = V[k][t] //. sol1}, {k, 
    1, NN}, {t, 0., tmax}];
outiv = Flatten[inputiv];
V[0][t_] := Vs[t] - Rs*i[1][t];
Vfp = Table[
   V[k][t_] = Rc[k]*(i[k][t] - i[k + 1][t]) + V[k][t], {k, 1, 
    NN - 1}, {t, 0., tmax}];
V[NN][t_] := Rc[NN]*(i[NN][t]) + V[NN][t]
Pload[t_] := V[NN][t] i[NN][t]
Pint[t_] := Vs[t] i[1][t]
VoltFim = 
 ListPlot[outiv, PlotRange -> All, 
  PlotStyle -> {AbsoluteThickness[1.4], RGBColor[0, 1, 1], 
    Thickness[0.008]}, FrameLabel -> {"Time(ns)", "Voltage(kV)"}, 
  Joined -> True, GridLines -> {Automatic, Automatic}, 
  FrameTicks -> {Automatic, Automatic}, Frame -> True, 
  LabelStyle -> Directive[Black, 17]]
Show[VoltVs, VoltFim]

Out[13]= {1.7, 300., 1.7, 1.7}

Out[16]= \!\(\*
GraphicsBox[{{}, {{}, {}, 
{RGBColor[0, 0, 1], PointSize[0.007333333333333334], Thickness[0.008],
       LineBox[CompressedData["
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