Help Fitting Exponential Recovery Load Model

Hi I'm relatively new to MatLab and am trying to fit the Exponential Recovery Load Model as shown below to some data:

der(xp) = P0*(V^(as) - V^at) - xp/Tp;

Pl = (xp/Tp + P0*V^at);

whereby xp, tp and at refer to the transient behaviour of the model, while as refers to the steady state modle. I understand I should use curve fitting but am unsure how to do so with 2 equations which I must fit. Any help would be greatly appreciated

Answer 1

[Star Strider]

Parameter estimation is relatively straightforward in MATLAB, although it may not seem to be at first. We need a bit more information on your functions and data.

Specifically:

1. What are your data? What are the independent and dependent variables? Are they vectors or matrices?
2. What are the parameters you want to estimate?
3. What is der(xp)?

Please attach a file of a representative sample of your data long enough to estimate your parameters (usually 10 or more data pairs, triplets, or however your data are organised). I prefer .mat files, since they don’t involve the occasionally daunting complexities of text files.

[Ciaran]

Thanks for getting back to me and apologies for the lack of information.

The data is a time series input PI, the instantansous Power Demand, and V, the instantaneous voltage. They are both vecotrs.

For a specific time period the independent variables are PO, V, as, at, xp and Tp, while the dependent variable is PI.

I have to estimate xp, the power recovery of the load, Tp, the recovery time, as, the steady-state dependency on V, and at, the transient dependency on V.

I have good estimates of what these estimated variables should be, however I need the parameter estimation to fine tune these

der(xp) is the derivative of xp w.r.t to time.

I haven't got a data file at the moment as I'm preparing this script for incoming data but it'll just be a time series of Pi and V.

Hope this is somehwat clear. If not I'll try talk to some collegues and provide a more clear description

[Star Strider]

I may be missing something, but I don’t understand this:

• The data is a time series input PI, the instantansous Power Demand, and V, the instantaneous voltage. They are both vecotrs.
• For a specific time period the independent variables are PO, V, as, at, xp and Tp, while the dependent variable is PI.

The data should be both your independent and dependent variables.

So again, what are your independent and dependent variables, and what parameters are you estimating?

Answer 2

[Rohan Panchal]

https://lup.lub.lu.se/search/ws/files/5605875/587902.pdf

This thesis linearises the exponential recovery model differential equations into state space form. Which can be directly implemented in estimate parameters state space task in the live editor.