Hi Onuigbo,
First of all, an answer to your query on pressure compensation because an understanding of this is important to what I will propose (below) as a possible reason for your problem.
The pressure of the steam affects the density, and all meters need to "know" the density of the fluid they are measuring in order to convert the measured variable (usually pressure drop) to a mass flowrate. A pressure compensated meter will have an algorithm that will correct the density as the pressure changes. If the pressure increased, the density would increase as well, but if your meter is not compensated more mass will be flowing through the meter than what it "thinks" is flowing.
I think that TBP has hit the nail on the head when he asks "Are the PRV's ahead of the meters?" I could not pick up an answer from you to that question, and you also do not state what the downstream pressure is (after the PRV's).
If the client meters are on the downstream (i.e. low pressure) side of the PRV's then I think I can explain your problem. The problem will be the quality of the steam deteriorating in summer with the lower loads.
For the purposes of argument let us assume that the losses between your production meter and the client meters are constant in absolute terms (i.e. BTU per hour) for summer and winter. In summer you are putting less steam through the lines, so the losses per pound of steam flowing in the line are greater, and a higher proportion of the steam will condense. Therefore, depending on how good your separators and traps are, it is likely that in summer the steam will be wetter than in winter. If your losses in summer are actually higher than in winter then the summer steam will be of an even worse quality.
Let us assume that in winter the steam reaching the PRV's is dry saturated at 100 psig. It may not be perfectly dry, but I have to assume something to do some calcs. 100 psig dry saturated steam has a heat content of 1189.6 BTU/lb. If this is expanded to 20 psig, and no heat is lost, it will become superheated. The temperature will be 302 F compared with the 20 psig saturated temperature of 259 F, and the density will therefore be less than expected - 0.078 lb/ft3 instead of 0.083 lb/ft3.
If in summer the steam quality deteriorates from 100% to 98% the heat content will reduce to 1172.0 BTU/lb on average. If this is expanded to 20 psig some heat is consumed by evaporating the condensate and the temperature will be only 267 F and the density 0.082 lb/ft3.
What do all these numbers mean? It means that in winter you are selling your customers superheated steam at a lower density than expected, and this will cause uncompensated meters to over-read i.e. in winter you are over-charging your customers. So yes, you have a perceived loss in summer, but it is not a physical loss of steam. You would need to compensate your meters for pressure and temperature to overcome the problem, and to re-negotiate the price to the customers to avoid monetary losses in winter. I would just keep quiet and count the extra pennies in winter as a bonus.
Note that the numbers I have chosen are for illustration only, and do not affect the conclusion. As long as the summer steam is wetter (or less superheated) than the winter steam you will be charging your customers less in summer per useful pound of steam and it will appear that you are losing more steam in summer.
Anyone else have any comments on this theory?