The "premium" designation has nothing to do with grading of diesel fuel as #2 or #1 diesel, which basically describes the viscosity of the petroleum. There is no specific standard for what constitutes "premium" in diesel. Instead, as of 2003, any fuel that meets minimum characteristics in at least these 4 categories can be labeled "premium". Categories include lubricity, cetane rating, low temperature operability and thermal stability. As of the 2003 draft standard, it does NOT include energy content, i.e. premium diesel does not imply more power, nor anything about Injector Cleaning (these had been factors prior to 2003).
The National Conference on Weights and Measures is the primary US standards authority because they essentioally control the labeling used at fuel pumps, but the DOE, the Petroleum Council, and others have their oar in the [muddy] water too. CARB has also regulated the use of the word "premium" in CA. Furthermore, forthcoming regulations for low sulphur diesel and other EPA regulations transcend any definition of "premium".
As of this time, it appears to me that there is little benefit to using a "premium" diesel if most of your operation is in "normal" operating conditions, primarily RPM and temperature ranges. Of course, the price difference has to be factored into the purchase decision, but even an extra 2-3 cents/gallon seems questionable to me. The engines are designed to run well on standard diesel fuel and in the absence of extreme operating conditions whatever additional qualities a premium diesel may have are probably unnecessary and a waste of $.
Here is what I found on the "premium" factors:
...any fuel marketer claiming to sell "premium diesel" in the U.S. must have a fuel with:
# at least 47 cetane number by American Society for Testing & Materials (ASTM) D613 method;
# 80% reflectance on ASTM D6468 test for thermal stability, and;
# low-temperature operability (within the 10th percentile of minimum recorded temperature for maps & charts area per ASTM D975 diesel fuel standard, using either low-temperature flow test (LTFT -- ASTM D4539) or cloud point (ASTM D2500).
# improved lubricity (I couldn't find the approved draft version of the lubricity spec)