why have i this error: "Number of equations exceeds number of variables."

hello all,

i modelize a thermal and hydraulic system and when I count number of variables and equations, I have 18 variables, 16 equations and i get an error:"Number of equations exceeds number of variables." . i can reduce it to 14 variables and 14 equations but i have the same error.

here is the code of my personnal blocks and a picture of my system.

component chaudierepompe
% Chaudiere+pompe
% Ce bloc représente une chaudiere couplée avec une pompe.

    inputs
      R = { 0, 'J/s' }; % R:bottom
      S = { 0, 'm^3/s' }; % S:bottom
    end

    nodes
      A = foundation.thermal.thermal; % A:bottom
      B = foundation.thermal.thermal; % B:top 
      F = foundation.hydraulic.hydraulic; % F:bottom
      G = foundation.hydraulic.hydraulic; % G:top
    end

    variables
      q = { 1, 'm^3/s' }; 
      Q = { 1 , 'J/s' };

    end

    parameters
      Cp = { 4180, 'J/kg/K' }; % Cp eau
      rho = { 1000, 'kg/m^3' }; % Rho de l'eau
    end

    function setup
      through( q, F.q, G.q );
      through( Q, A.Q, B.Q );

    end

    equations
      q == S;
      Q == R;
    end

end

component echangeur
% Echangeur
% Ce composant va modéliser un echangeur de chaleur.

    nodes
      A = foundation.thermal.thermal; % :left
      B = foundation.hydraulic.hydraulic; % :left
      C = foundation.thermal.thermal; % :left
      D = foundation.hydraulic.hydraulic; % :left  
      E = foundation.thermal.thermal; % :right
      F = foundation.hydraulic.hydraulic; % :right
      G = foundation.thermal.thermal; % :right
      H = foundation.hydraulic.hydraulic; % :right
    end

    parameters
      Cp = { 4180, 'J/(kg*K)' };  % Cp eau
      rho = { 1000, 'kg/m^3' };   % Rho eau
      Tini = { 343.15, 'K' };     % Temperature initiale de l'eau
      Rdmnt = { 1, '1' }; % Rendement de l'échangeur
      Pe = { 1000000, 'J/s' }; % Puissance échangeur

    end

    variables

      q1 = { 0, 'm^3/s' };
      q2 = { 0, 'm^3/s' };

    end

    function setup

      through( q1, B.q, D.q );
      through( q2, H.q, F.q );

      C.T = Tini;
      E.T = Tini;

    end

    equations
      Pe * Rdmnt == q1 * rho * Cp * (A.T - C.T);
      Pe * Rdmnt == q2 * rho * Cp * (E.T - G.T);

    end

end

component debitgen
% Generateur de debit

    inputs
      S = { 0, 'm^3/s' }; % S:bottom  
    end

    nodes
      T = foundation.hydraulic.hydraulic; % T:bottom
      P = foundation.hydraulic.hydraulic; % P:top
    end

    variables
      q = { 1 , 'm^3/s' };

    end

    function setup
      through( q, T.q, P.q );

    end

    equations
      q == S;
    end

end

component Consomateur
% Consomateur
% Ce composant symbolise un consomateur de chaleur.

    nodes
      M = foundation.thermal.thermal; % :top
      U = foundation.hydraulic.hydraulic; % :top
      N = foundation.thermal.thermal; % :bottom
      V = foundation.hydraulic.hydraulic; % :bottom
    end

    parameters
      Cp = { 4180, 'J/(kg*K)' };   % Cp eau
      rho = { 1000, 'kg/m^3' };   % rho de l'eau
      Qcons = { 1000, 'J/s' };     % Puissance consommée
      resistance = { 5000 'Pa/(m^3/s)' }; % resistance lineique consomateur
      Tini = { 343.15, 'K' }; %Temperature initiale
    end

    variables
      q = { 0, 'm^3/s' };
      p = { 0, 'Pa' };
    end

    function setup
      through( q, U.q, V.q );
      across ( p, U.p, V.p );
      N.T = Tini;
    end

    equations
      Qcons == q * rho * Cp * (M.T - N.T);
      p == resistance * q;
    end

end

for the picture: http://cjoint.com/?BKAkF19q5S0

P.S: i have more problems when I do my own hydro-thermal domain. So I use the 2 domain thermal and hydraulic.

What can i do to solve this error?

Thanks for your responses.

Answer 1

[Yifeng Tang]

10 years after when the question was asked ... the thermal liquid domain should be able to handle the thermal+hydraulic application you described. It's first introduced in R2013b, I think. The library has been expanding since then, and the Simscape Fluids add-on library now also contains various valves and heat exchanger blocks.

https://www.mathworks.com/help/physmod/simscape/thermal-liquid-models.html?s_tid=CRUX_lftnav

https://www.mathworks.com/help/physmod/hydro/thermal-liquid-modeling.html?s_tid=CRUX_lftnav