Does anyone know of or have a closed form solution that calculates the delta of a spark spread option as a function of each asset?

they are several available: you can stay in the BS framework and consider the spread as an asset just as an exchange option, step a little bit away from BS but still assume the spread is one asset but this time following a normal distrbution (arithmetic brownian motion), or start going away from the BS and approximate the distribution as in Zhang for which you also have a closed form solution. In all these cases the delta of the option as a function of the two asset are available.Now because you are dealing with electricity, you probably want a much fater tailed underlying distribution than the normal or the log normal can offer. FFT or Garch are interesting alternatives with quasi closed form solutions.

This would give me the delt of the option ... but I am looking for the change in value of the option related to a change in the underlying gas price (Delta for gas) and then the change in value of the option related to a change in the underlying power price (Delta for power). So the spread option would have two deltas, one for each asset. Similarly, it would have two gammas.

The delta with respect to the spread in the models described by DogonMatrix can probably be extended to provide deltas on the two underlyings. First, solve for the positions in each underlying that you would use to hedge an outright forward position in the spread (rather than an option) and then multiply those positions by the option model spread delta. If you want to stay in the BS paradigm, you can also use a 2-factor tree model with an explicit correlation term. You can finds such models in the books Clewlow/Strickland and probably also by Haug (known as the "Collector" on this website) and other places. Such models naturally give 2 deltas as well as a sensitivity to the correlation paramater.You should be able to find more details on either approach using the search facility on this website.

I found a paper by Rene Carmona and Valdo Durrleman (2003) that has some good information and a solution to approximate the greeks on spread options. Does anyone have any criticizm of thier work?

If you have a model to price a basket option that knows how to deal with negative weights, you are there.On sparks, you cannot make the assumption of lognormality of the spread, therefore you HAVE to work with a two factor model.Send me a private and i'll drop you a paper.

I have a good, simple closed form model for all greeks, d1, d2, g1, g2, v1, v2, rho, xgam. It assumes lognormality, but also has a normal (wilcox)function as well. Normally u can use this model pretty well adjusting an implied correlation parameter to fit the skew in the traded market. send me a pm.