This BBC article says that nuclear power notes came about when the French energy company EDF purchased British Energy in 2008:
The note changes in value with wholesale energy prices and power output levels from British Energy's existing nuclear stations.
EDF Energy's website describes these notes under the section titled "Nuclear Power Notes":
When EDF acquired British Energy in January 2009, Nuclear Power Notes were issued to British Energy shareholders who chose to take them in lieu of 74 pence of cash per British Energy share held.
The Nuclear Power Notes are ten year financial instruments (2009 – 2019) which give ex British Energy shareholders a continuing interest in the “EDF Energy Nuclear Generation Fleet”. They are traded on the ICAP Securities & Derivatives Exchange (formerly known as the PLUS Quoted exchange).
Each year a pre-defined calculation is performed to determine whether any cash will be paid to Nuclear Power Note holders. The calculation is dependent on the nuclear output of the EDF Energy Nuclear Generation Fleet (“Eligible Nuclear Output”) and market power prices (“Power Prices”). This calculation may or may not result in a cash payment each year to Nuclear Power Note holders.
The MWh/TWh are figures you see are measures of watt-hours, i.e. energy output. The value of nuclear power notes is tied to this output.
Looking at the most recent statement (June 2013), you can see a line that looks like this:
Month Ahead Price in respect of July 2013: 47.46 GBP/MWh
which is an energy spot price for the output of the nuclear plants. I'm not entirely sure of the relationship between this and the payment to shareholders, but if you look at the 2012 Yearly Payment Calculation Notice on the same page, you'll see this in the first section:
(a) the Yearly Payment for the period 1 January 2012 to 31 December 2012, (the
Relevant Year ) payable in respect of each CVR on 31 January 2013 shall be zero;
The payments were also zero for 2010 and 2011. The 2009 calculation notice, however, states that
(a) the Yearly Payment for the period 1 January 2009 to 31 December 2009, (the Relevant Year) payable in respect of each CVR on 31 January 2010 shall be 11.497164 pence stated to 6 decimal places
I presume that payment would have appeared in whatever account holds these notes, e.g. your brokerage account.
Technically, the financial statements above refer to a Contingent Value Rights (CVR) instrument, which is a derivative linked to the Nuclear Power Notes. This site sums it up better than I can:
The British Energy CVRs were created by the issue of nuclear power notes (NPNs) to the target’s shareholders who opted to take up this alternative. The NPNs were issued by Barclays Bank plc and were linked to guaranteed contingent value rights instruments that were issued to Barclays by EDF’s acquisition vehicle (Lake Acquisitions) and which were ultimately guaranteed by EDF Energy plc (Lake CVRs). Barclays is required to make yearly payments to noteholders for 10 years, the amount of which is limited to the corresponding amount paid by Lake Acquisitions to Barclays for the Lake CVRs.
Basically, there is a chain of payments through these derivatives that eventually links back to nuclear energy output.