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Question: Solve a System of Equations With an Unknowns of f(x)

Question:Solve a System of Equations With an Unknowns of f(x)

dareimert 35 Maple 2020
solve syntax parameter plotting
November 29 2020
0

I am trying to plot generator reactive output (Q) over a range of generator power output (P) with field current (Ifldc) and terminal voltage (Et) constant using “solve”. The system of equations includes an interpolating fiction Ifld(el).

I’m looking for some help as to how to configure a solution. Attached are a few of my failed attempts.

The upload of my file deleats the "solve" fo my first try it is:

     


 

``

``

MvaGen := 1354; PfGen := .935; KvGen := 24

                   

           Xd__u := 1.89 - Synchronous reactance of d-axis, Unsatuarted

              Xq__u := 1.80 - Synchronous reactance of q-axis, Unsatuarted

              X__l := .26   - leakage reactance d or q-axis``

``

            Ifld__base := 3114

``

Open Ckt Sat Curve DS807-1a

     First col=Ifld amps   

     Second col= el voltage behind leakage reactance

 

OC_SatDat := Matrix(16, 2, {(1, 1) = 0, (1, 2) = 0., (2, 1) = 655.6456, (2, 2) = .3422578, (3, 1) = 1009.961, (3, 2) = .5331404, (4, 1) = 1253.12, (4, 2) = .6492209, (5, 1) = 1562.724, (5, 2) = .8014143, (6, 1) = 1893.545, (6, 2) = .9329786, (7, 1) = 2201.68, (7, 2) = 1.033593, (8, 1) = 2487.276, (8, 2) = 1.108416, (9, 1) = 2793.943, (9, 2) = 1.157452, (10, 1) = 3122.338, (10, 2) = 1.203911, (11, 1) = 3690.959, (11, 2) = 1.263294, (12, 1) = 4259.141, (12, 2) = 1.307202, (13, 1) = 4827.028, (13, 2) = 1.340795, (14, 1) = 5351.085, (14, 2) = 1.366646, (15, 1) = 5787.775, (15, 2) = 1.387329, (16, 1) = 6224.391, (16, 2) = 1.405433})

  ido := It*sin(theta+delta)

Plot OC saturation with field current in pu

 

with(LinearAlgebra)

with(ArrayTools)

with(plots)

      OC_Sat_Ifld_pu := Column(OC_SatDat, [1])/Ifld__base

         OC_Sat := Concatenate(2, Column(OC_SatDat, [2]), OC_Sat_Ifld_pu) 

````

iterpolate values of field current vs el from OC sat curve

 

                                    pts_el := Column(OC_Sat, [1]); pts_Ifldpu := Column(OC_Sat, [2])

 

 

                         Ifield as a function of el  ->  Ifld := LinearInterpolation(pts_el, pts_Ifldpu)

``

 

Solve for Q with

    

P = .935; Iflc := 1.88; Et := 1.0

 

NULL

TRY1

``

 Eq1 := Ir = P/Et; Eq2 := Ix = Q/Et    Eq3 := It*sqrt(Ir^2+Ix^2)     Eq4:=theta = arctan(Q, P)

``

    Eq5 := el = abs(Et+X__l*(Ix+I*Ir))      Eq6 := `ΨAG__d` = Xad__u*Ifld(el)   Eq7:=K__ds = el/`ΨAG__d`

     NULL 

NULL Eq8 := Xd__s = K__ds*Xad__u+X__l   Eq9 := `ΨAG__q` = Xaq__u*Ifld(el)    Eq10 := K__qs = el/`ΨAG__q`

 

   Eq11 := Xq__s = X__l+K__qs(el)*Xaq__u      Eq12 := Eq = Et+Xq__s(el)*(Q/Et+I*P/Et)

NULLNULL

    

Eq13 := delta = argument(Eq)        Eq14 := eqo = Et*cos(delta)    Eq15 := ido = It*sin(theta+delta)

``

Eq16 := EI = Xd__s*Iflec; Eq17 := EI = Ido*Xd__s+eqo

``

 
syst := {E15, Eq1, Eq10, Eq11, Eq12, Eq13, Eq14, Eq16, Eq17, Eq2, Eq3, Eq4, Eq5, Eq6, Eq7, Eq8, Eq9}

 

   

NULL

solve(sys, {Eq, Ir, It, Ix, K__ds, K__qs, Q, Xd__s, Xq__s, el, eqo, ido, theta, `ΨAG__d`, `ΨAG__q`})

Warning, solving for expressions other than names or functions is not recommended.

  

 

NULL         

TRY 2

              NULL

`` Ix := proc (Q) options operator, arrow; Q/Et end proc   It := proc (Q) options operator, arrow; sqrt(Ir^2+Ix^2) end proc     theta := proc (Q) options operator, arrow; arctan(Q, P) end proc

``

 el := proc (Q) options operator, arrow; abs(Et+X__l*(Ix(Q)+I*Ir)) end proc      `ΨAG__d` := proc (Q) options operator, arrow; Xad__u*Ifld(el(Q)) end proc   K__ds := proc (Q) options operator, arrow; el(Q)/`ΨAG__d`(el(Q)) end proc``

NULL Xd__s := proc (Q) options operator, arrow; X__l+K__ds(el(Q))*Xad__u end proc   `ΨAG__q` := proc (Q) options operator, arrow; Xaq__u*Ifld(el(Q)) end proc    K__qs := proc (Q) options operator, arrow; el(Q)/`ΨAG__q`(el(Q)) end proc

Xq__s := proc (Q) options operator, arrow; X__l+K__qs(Q)*Xaq__u end proc      Eq := proc (Q) options operator, arrow; Et+Xq__s(Q)*(Q/Et+I*P/Et) end proc

``

delta := proc (Q) options operator, arrow; argument(Eq(Q)) end proc        eqo := proc (Q) options operator, arrow; Et*cos(delta(Q)) end proc    ido := proc (Q) options operator, arrow; It*sin(theta(Q)+delta(Q)) end proc``

``

EI := proc (Q) options operator, arrow; Xd__s(Q)*Iflec end proc    EI := proc (Q) options operator, arrow; eqo(Q)+Xd__s(Q)*Ido(Q) end proc

``

NULL

solve(EI(Q) = eqo(Q)+Xd__s(Q)*Ido(Q), {Eq, Ir, It, Ix, K__ds, K__qs, Q, Xd__s, Xq__s, el, eqo, ido, theta, `ΨAG__d`, `ΨAG__q`})

{Eq = Eq, Ir = Ir, It = It, Ix = Ix, K__ds = K__ds, K__qs = K__qs, Q = Q, Xd__s = Xd__s, Xq__s = Xq__s, el = el, eqo = eqo, ido = ido, theta = theta, `ΨAG__d` = `ΨAG__d`, `ΨAG__q` = `ΨAG__q`}

 (1)

NULL

TRY3

 

     "Eq20:=Ir=P/(Et): Eq21:=Ix=Q->Q/(Et):"

Error, invalid operator parameter name

"Eq20:=Ir=P/Et: Eq21:=Ix=Q->Q/Et:"

  

``

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