In certain cases load power is described by discrete probability distribution rather than normal distribution in the general literature. Which kind of actual load does it corresponds to in the real power system?
Rajnarayan,
I would say this has to do more with the information available when defining the distribution.
If the probability is simply not known in functional form, but simply in terms of probability values corresponding to different ranges of load, what choice does the modeler have ?
-Sanjay
Further, Gaussian distribution assumption is basically to model forecasting uncertainty (small variance). What if the variance of uncertainty of aggregate load is large. Moreover, can you please give one example of such load in power system. Can you provide me a research article describing discrete modeling of load in a study case. Does any book discusses about this issue in detail. Please reply.
Rajnarayanan,
You are right about the Gaussian model being more to do with forecasting uncertainty.
As I said, the discrete probability modeling is more to do with incomplete information. That would generally apply to composite loads that is, a mix of loads at the bus. Therefore "one example" load of precise type will be difficult to cite.
Unless you wish to consider fixed load types that turn ON or OFF based on some probability (say residential composites or irrigation pumps, for instance). Most of the works on loads that I have come across fall in either of two categories:
In either of the two cases, the question of discrete probability does not arise.
Do please let me know as and when you come across examples or references. I will be curious too !!
-Sanjay
You have mentioned Forecasting problem and voltage sensitivity problems. What you say about probabilistic modeling of load for load flow studies. Around 10 number of research works have adopted discrete distribution for load power at certain buses. But neither the reason for such an assumption is mentioned nor citations are provided. Please reply.
Rajanarayan,
Thanks for asking me to give inputs on probabilistic LF.
I have seen a few works (in fact, one of my erstwhile colleagues at IITD used to do something on this as well), but I feel the basic concept itself is flawed, and unrealistic. So I never ventured into it !
Discrete probability distribution for loads itself is OK (as I said earlier, depending on the coarseness of data available). Since most loads in a power flow are indeed composite loads, I personally don't have a problem with the load modeling part.
But because of entirely different reasons, I have never appreciated probabilistic power flows as anything useful for research.
-Sanjay!
Do u have any idea regarding convergence in monte carlo simulation. How to obtain the appropriate number of samples in case of monte carlo simulation.
I do, but as I said I have never worked on probabilistic load flow - so no idea for such problems.
MC convergence can differ from problem to problem.
-Sanjay
Thank you. Suppose someone uses 50000 samples for the MCS. He proposes a new method for the study and compares the computational efficiency of the proposed method with that of MCS as reference. My concern is that, the number of samples assumed for MCS (i.e. 50000) may be either high or insufficient for the accuracy of the obtained result. In this context, is it possible/ appropriate to evaluate a coefficient of uncertainty to determine the convergence of MCS. Is there any other concepts to obtain the convergence of MCS. I hope now you can understand the problem.
Should be possible to derive a measure of convergence error by assuming some realistic distribution for the MC samples.
But I am sure it will be problem specific. Want to attempt it for your research ?
-Sanjay
Yes. Can you please suggest me some papers dealing this issue (in probabilistic load flow). It will be help full to me.
Well, I have not been on the lookout for literature in this area. If I come across any then I can let you know.
All the best.
-Sanjay
How to handle the following problem with Monte Carlo simulation?
Monte Carlo simulation (MCS) may not incorporate "fat tailed" nature of distributions, as well as autocorrelation (which is when returns of a variable are correlated over time).