With the incipient and symbiotic approach using method of compounding.

I don't have any specific experience with that, but I suspect that the techniques to use would be problem-dependent. Can you provide some detail about what sort of effects you're talking about and the nature of the optimization?

The main idea is to represent operational variations of wind power output (those which ocurr between 10min to 2 hours) in capacity expansion problems (which are run for several years (and have the aformentioned time step of several hours).

Thanks so far!

Sanket, where could I find more info about your answer?

Sanket Saxena, I did not undertand your answer. Could you please help me a bit more?

It sounds to me like you need to create some sort of model to approximate the impact of these short-term wind variations on the accumulated energy output over the longer time scales that you are optimizing over. It's hard to be very specific without knowing what sort of data you're working with, but I imagine there are two main options:

(1) If you have wind speed and energy output data from existing wind farms, you could make an empirical model of a turbine or farm's daily/monthly energy output as a function of average wind speed (or the average of the cube of the wind speed, which might work better). You could then predict the output of other hypothetical wind farms using predictions for future average wind speeds - you could make up some scaling factors to account for different wind speeds and turbine quantities/sizes.

(2) If you have wind speed data with higher temporal resolution (on an hourly or 10-minute time scale) you could just apply those wind speeds to an appropriate wind turbine power curve (eg. http://silverford.com/blog/?p=701 for smaller scales) to estimate the power output time series, which you could then aggregate to your longer time scales.

It all depends on what input data you have for your wind speeds. In any case, a key point is that you can do this modelling (of calculating a wind turbine's overall energy output from a time series of wind speed data) as a separate step before the optimization. In the optimization, all you then need to do is scale the appropriate per-turbine energy output values based on the number of turbines. I hope this makes sense and that I'm understanding your problem correctly!

Hi Matt, thanks for your time. Alltough your answer makes a lot of sense, I am still missing the key point of my question.

Let´s say I have an hourly resolution of the wind, and I did the propper scaling for different future wind farms. The time resolution of capacity expansion models usually is not able to see short-term effects, such as the variabiltity of the wind. This variability calls for a need of ramping (reserves) or quick turn on and off of thermal power units, which imply costs and somehow need to be taken into consideration in the capacity expansion.

So what I am trying to do is to tell the capacity expansion model the cost of those ramps and turn on/off of power plants produced by a variable wind generation.

Txs!

If you deals with data analysis method (as I find out from your explanation), you can't see these effects which shorter than your data resolution.

My data resolution is hourly, while to capacity expansion model considers only daily time steps

Ah. I've actually done some generation optimization with integrated wind energy, but only at the hourly timescale. I don't really have any experience in the capacity expansion modelling you're talking about.

If you can't find a time step that works for both models, what about a sort of coupled/hybrid optimization approach? Where for each capacity expansion time step you do a separate optimization for the optimal generation within that day. That sub-optimization would provide the necessary info on ramping reserve capacities, etc. Do you think there's any potential in this idea?

I started to work with the GoldSim simulation software. Although I have never done it myself, I know that there it is possible to include sub-models with shorter time steps into a superior model, which has longer time steps. The sub-model can then run several times if necessary and provide results for the longer time steps.

You could try a FFT (fast Fourier transform) analysis for the whole time series or for a comparable time scale. In case it is possible to find some reasonable correlation in the frequency domain, it may appear justifiable to extrapolate the trend to higher frequencies than the actual sampling frequency. One could then apply the inverse transform to rebuild the signal in the time domain, for the extended frequency range. A more sophisticated approach could alternatively be tried, relying on the wavelet transform theory. Samples of data acquired at a shorter time scale, thus with a significantly higher sampling frequency, could possibly help to validate the approach.

If you are working on a capacity expansion optimization model, I assume you are dealing with a centralised planning model in a regulated market. Capacity expansion models usually have to represent short-term effects in a simplified, aggregated way. The cost of variability in wind power relates to the loss of load probability (LOLP, see [1]), and for wind power there has been a discussion to how much it contributes to "firm capacity". In a liberalised market, the variable cost of wind is usually reflected in the power balancing market, and the wind power producer must purchase the balancing power required. Such costs depends on the prognosis and the price of balancing power, and such costs are usually included in the investment model as a cost per MWh of generation. In liberalised markets, the capacity expansion problem is reduced to individual investment decisions.

When electricity prices and wind production exhibit diurnal and seasonal variations, revenues from production must be adjusted accordingly, and is usually pre-calculated as an adjustment factor.

Hope this helps

[1] L. L Garver, 1966: Effective Load Carrying Capability of Generating Units, IEEE Transactions on power apparatus and systems. ( Many text books and subsequent papers deal with LOLP and the capacity expansion problem )

Thanks you guys for all the answers. I didn't realize this subject was still open, as I stopped receiving emails.