Modelica建模报错：DAE索引缩减失败，无法对自定义函数求导

运行Modelica模型时遇到DAE降阶失败的错误，报错信息如下：

Failed to differentiate the equation
T = Water.ph.T_ph(Ps, Hs*1000, 0);

in order to reduce the DAE index.

Cannot find differentiation function:
Water.ph.T_ph(Ps, Hs*1000, 0)
with respect to time

Failed to reduce the DAE index.

相关代码片段：

V1*der(Ps)=Rs*T*(Ge+Gaux+Geved-Gvo-Gn)/3600;
  rou2=Water.pT.d_pT(Ps,T,0);
  der(rou2*V1*Hs)=(Ge*He+Gaux*Haux+Geved*h1-Gvo*Hs-Gn*Hs)/3600;
function T_ph
  "Return thermodynamic state as function of p, h and phase"
    extends Modelica.Icons.Function;
    input Water.total.Medium.AbsolutePressure p "Pressure";
    input Water.total.Medium.SpecificEnthalpy h "Enthalpy";
    input Water.total.Medium.FixedPhase phase=0
    "2 for two-phase, 1 for one-phase, 0 if not known";
    output Water.total.Medium.Temperature T;
protected 
       Water.total.Medium.ThermodynamicState state;
algorithm 
  state := Water.total.Medium.setState_ph(
        p,
        h,
        phase);
     T:=state.T;
end T_ph;
function total

package Medium
extends ExternalMedia.Media.CoolPropMedium(
    mediumName = "Water")
end Medium;

end total;

问题核心是自定义的T_ph函数使用algorithm段实现，编译器无法自动推导其对时间的符号导数，导致DAE降阶失败。以下是几种解决方法：

• 优先使用ExternalMedia内置可微分函数
  直接替换自定义的T_ph为库中提供的temperature_ph函数，该函数已内置符号可微分支持：

  T = Water.total.Medium.temperature_ph(Ps, Hs*1000, 0);
  

• 将自定义函数改为equation段实现
  如果必须保留自定义函数，把algorithm替换为equation，让编译器能自动解析导数逻辑（仅适用于无顺序依赖的纯数学关系）：

  function T_ph
    "Return thermodynamic state as function of p, h and phase"
    extends Modelica.Icons.Function;
    input Water.total.Medium.AbsolutePressure p "Pressure";
    input Water.total.Medium.SpecificEnthalpy h "Enthalpy";
    input Water.total.Medium.FixedPhase phase=0
      "2 for two-phase, 1 for one-phase, 0 if not known";
    output Water.total.Medium.Temperature T;
  protected 
    Water.total.Medium.ThermodynamicState state;
  equation 
    state = Water.total.Medium.setState_ph(p, h, phase);
    T = state.T;
  end T_ph;
  

• 调整方程结构避免循环导数依赖
  重新整理方程逻辑，比如将der(rou2*V1*Hs)展开，或者直接用状态量关联物性参数，减少对自定义函数输出的导数依赖，降低DAE求解的复杂度。

内容的提问来源于stack exchange，提问作者white