Steady state HVDC modelling


For the last year or so I have been intermittently reading about HVDC modelling. My goal with this is to implement some sort of AC/DC steady state modelling in GridCal.

Unlike the AC equations, which are quite clear by now, the HVDC modelling is scattered and unclear in the literature (at least for me) despite being investigated since the 1960’s.

So far I have made the following conclusions:

  • The simplest model is to replace an HVDC line with a positive power generator on the sending side and a negative power generator on the receiving side. I’d rather implement something better than this…

  • There are plenty of articles modifying the Jacobians of Newton-Raphson for specific converters and what not. I would rather not do that, since I am not interested on automatically tuning the parameters.

  • Then, there is the MatACDC approach: decouple the AD and DC parts and simulate iteratively.

  • On the other side there are is legendary work by Jos Arrillaga and Bruce Smith that leads me to believe that a unified way is totally viable. This is also the way that Enrique Acha (from the same school) maintains in his latest book with a proposition for an AC/DC unified formulation.

So, I’d love to have a healthy discussion on the pros and cons of all the above.

Best regards,

Hi Santiago,

What range of dynamics are you interested to model? i.e. what time scales? I imagine this would influence pros and cons.


Hi Braulio,

I am looking at steady state, meaning intervals of 1 hour, maybe 10 or 15 minutes.

Best regards,

Hi, Then I would guess then that load flow equations models are really sufficient, correct?

That is my point precisely.

Some sources say so, others do not (they model the DC part aside)

Maybe in some network configurations a given distortion could induce oscillations for several minutes … or if the variability of power generation plays an important role? For the steady state model did you look at this type of approach: ?


That is one approach I am considering. Early tests on GridCal show that it is feasible to have this model solved in a regular Newton-Raphson.

My question is; Looking at the figure 2, I observe 2 generators that are probably used to force the flow by setting one to +P and the other to -P. Is this really necessary? Is there not any other way?

What about this approach in meshed DC grids?