.Spot.UsersGuide.Introduction.Simulation

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Transient and Steady-State Simulation of three-phase models

The terms 'transient' and 'steady-state' simulation of three-phase systems always refer to the electrical equations within a model. Other equations are not affected. The steady-state simulation is a meaningful approximation, if dynamic time-constants of electrical components are short compared to other time-constants as for example mechanical or thermal ones.

The standard transient form of an inductive and a capacitive device (for simplicity with constant coefficient matrices L and C) is given by the dual equations

  L*der(i) + omega[2]*L*J*i + R*i = v
  C*der(v) + omega[2]*C*J*v + G*v = i

where

  omega[2] = der(theta[2])

      [ 0, -1,  1]
  J = [ 1,  0, -1] /sqrt(3)  (abc-representation)
      [-1,  1,  0]

      [ 0, -1,  0]
  J = [ 1,  0,  0]           (dqo-representation)
      [ 0,  0,  0]

The simulation of a model in steady-state must assume a synchronous reference frame, i.e.

  theta[1]=0

The steady-state approximation is then obtained from the above by setting the time-derivative der = 0.

  omega[2]*L*J*i + R*i = v
  omega[2]*C*J*v + G*v = i

It is obvious that going from transient to steady-state mode, differential equations are replaced by algebraic ones.

As each model-component contains both types of equations, transient and steady, the desired case can be selected by an appropriate choice of the parameter 'sim' in 'system'.

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