Synchronous machine model incorrectly initializes when taking into account saturation
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I have been experiencing an issue for a while now when simulating any synchronous machine model with saturation. I will explain this issue through the following simple system:
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1666866/image.png)
Here we have a Synchronous Machine pu Standard model (Simscape -> Electrical -> Specialized Power Systems -> Electrical Machines) connected to a Three-Phase Series RLC Load (Simscape -> Electrical -> Specialized Power Systems -> Passives). The synchronous machine parameters are as follows:
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1666871/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1666876/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1666881/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1666886/image.png)
The three-phase load has been parameterized so that is a purely resistive load with a very high impedance value, so the synchronous machine is practically open circuited:
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1666891/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1666896/image.png)
The initial conditions of the synchronous machine model have been computed using the "machine initialization" tool, so that the machine is initialized open circuited (no active and reactive power) to a terminal voltage of 1.1 pu (440 V):
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1666901/image.png)
It can be seen that the initial value of all the magnitudes are correctly computed. The excitation voltage (Vf), however, is not correctly initialized. Looking at the previously shown open-circuit saturation curve, for a terminal voltage of 1.1 pu the required excitation current (and in steady-state also the required excitation voltage) should be 1.19 pu. Thus, it seems that the excitation voltage is initialized to the terminal voltage value, neglecting saturation. Actually, in a more general sense, what seems to be happening is that the "machine initialization" tool always initializes the excitation voltage to the magnetizing flux value which, in per unit and with no active and reactive power, is equal to the terminal voltage in per unit.
Even if the correct value of the excitation voltage (Vf=1.19 pu) is introduced in the input and in the initial conditions of the synchronous machine model, when simulating a significant initial transient is observed:
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1666906/image.png)
I have also looked under the mask of the synchronous machine model and there seems to be some some unit delays and state variables whose initial value is the unsaturated one, instead of the saturated value.
So to sum up, there are two problems:
- The "machine initialization" tool incorrectly initializes the excitation voltage. It initializes it without taking into account the open-circuit saturation curve.
- Even when stablishing the correct initial values in the inputs and initial conditions of the synchronous machine model, the initial value of some magnitudes are incorrectly calculated, resulting in an initial transient.
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