Dear Sandford Stebbings,

In fact, the methodology used by the authors you have cited and others not cited is the least complex, knowing that there are hypotheses formulated in order to be able to establish the models which globally constitute this complex system. In other words, this approach is analytically feasible and identifiable and therefore we can easily build around control architectures, which will not be the case if we proceed in a complete way to bring out a model representing the whole.

Best regards

Dear Sandford,

maybe you can be more precise in what you are referring to by 'full state-space model' and where your specific problem is? In the cited papers the authors basically write down the standard component and network ODEs of their considered system, before they just rewrite them into the state-space notation. That is a typical procedure for any technical system independently from the inverter application and a basic task within every system theory course.

Cheers,

Oliver

Oliver Wallscheid ,

Equation (45) in paper number 1 and the second paper doesn't have it numbered but the similar equation on page 4, upper right.

Precise:

I want to create the complete system model of the inverter, so I can simulate it in state space, then I want to be able to do some analysis on it. I have the system working with all individual controllers modelled. I have Droop Controller, Voltage Regulator, Current Regulator and LCL filter. It all works, I now want to lump them together in one state space model similar to paper 2.

Thanks for your response.

First step: ensure that all your subsystem parts are properly represented already as state-space models.

Second step: define your state vector by putting together all states from your submodels. The order of the states is arbitrary.

Third: define your {A,B,C,D} matrices based on the state order in the state vector by inserting your submodels (assuming you are modelling a linear system). States, inputs and outputs which are not connected due to your overall model structure will cause additional zero (scalars/vectors/matrices) within {A,B,C,D} which you need to insert.

In other words: the procedure is basically stichting together your submodels by generating one large state set.

Oliver Wallscheid

I believe what you have described is simply lumping the systems on top of each other. That's not what I am trying to achieve. I want to create a single model that has the 13 states as the state vector, the inputs being the P Q W and Vn. The outputs being the il, vo and io.

The Droop Control should feed the Voltage Regulator, Voltage Regulator feed the Current Regulator and then the LCL feed them all the current and voltage readings.

I can see that they have used the concatenation method for state space models listed below for the Droop, Voltage and Current controllers, that accounts for the first 3 rows and 3 column of the 4x4 complete state space model I pointed out earlier, but the final row and column where they have included the LCL filter, I just cant see how they have done it :

https://www.nasa.gov/centers/dryden/pdf/88038main_H-1264.pdf

Dear Sandford:

You may benefit from these articles about your topic:

1- "System Modeling and Reliability Assessment of Microgrids: A Review"

@https://www.mdpi.com/2071-1050/14/1/126/htm.(section 5).

2- "Control Strategy of Microgrid Inverter Based on H∞ State Feedback Repeated Deadbeat Control"

@https://www.hindawi.com/journals/mpe/2021/8324926/.

3- "State Space Modelling and Control of the Modular Multilevel Converter".

.. The pdf file.

I hope it will be helpful...

Best wishes...