Thanks to Paul Dumais for the question and to Wes for the answer. I also couldn't quite follow the contoller logic but wasn't able to figure what I didn't understand about it, I could figure out the fixed overhead cost part but not the "bi-stability" part. I think this is a very useful illustration that reminds me in some respects of M. King Hubbert's analysis of petroleum extraction. At 09:48 AM 7/3/99 EDT, [EMAIL PROTECTED] wrote: >2, To: WesBurt, From: Paul Dumais Q: You wrote in your post of 99-06-29: > >> I corrected my mistake the way our bankers create money, with the stroke of >a >> pen, by drawing a straight line on the chart from the unit cost ($/KWH) at >> design output, back to a slightly lower unit cost ($/KWH) at the no load or >> minimum output on the chart. >>>>>>>>>>>>>> QUESTION # 2 <<<<<<<<<<<<<<<<<<<<<< >You said above that the cost ($/KWH) declined as the output of the >boiler reached designed output. How then can you draw a line from the >unit cost at design output to a slightly -lower- unit cost at the no >load end of the chart? How does the straight line help you to compute >the optimum dispatch? Does this line (the straight one) somehow account >for variable costs that were not included in your cost data? > >A: Every capital asset will have certain fixed cost associated with it such >as mortgage payments and no-load (no output) operating costs. Those capital >assets which produce a product will have, in addition to its fixed costs, >variable costs roughly proportional to output. The decision to build the >asset in the first place, or get it up to temperature and on-line in the >second place, are decisions that cannot be decided by the current markrt >price for the product. On the other hand, once the asset is on line, only >the variable costs can be logically involved in deciding how much output the >asset can produce at unit costs ($/KWh) less than the current unit cost of >power from all other assets presently on-line. Most productive assets will >have a lower variable unit cost at their design output, than at lower >outputs, and higher variable unit costs above the design output. But, a >logical controller (the chart I was discussing) automated to move the asset >from its minimum output, to its design output, and then into its overload >range up to some set limit, as the market price rises, and back again as the >market price declines, must have a control characteristic with an upward >slope over the whole range of output. > >If the control characteristic sloped downward with increasing output, as I >had first drawn the chart, the asset would be bi-stable under automatic >control. At a certain rising price (A), it would move rapidly to near full >output, without regard for the actual output needed to hold frequency and the >scheduled net-exchange of power over the tie-lines constant. When the demand >for power was falling and bringing the price down to near the design cost >(below A) the asset's output under automatic control would move rapidly to >the minimum, again without regard for the actual output needed to hold >frequency and the scheduled net-exchange of power. This type of malfunction >on power systems gives rise to trade disputes between interconnected power >companies, just as failure to stabilize national economies gives rise to >trade disputes among nations in a global economy. Power companies hold such >malfunctions to a minimum, nations refuse to do so. > >Like the stroke of a banker's pen, that straight line on the chart would >ignore no-load losses, which cannot be eliminated and do indeed make the >asset less efficient at low outputs, in order to have a stable control >characteristic over the whole range of output for each productive asset in >the system. Most of the time, the optimum dispatch involves loading the >plants in order of their unit cost at design output. When two or more plants >have their straight lines at the same cost level they will share increments >of additional demand between them until they reach the upper limits. If >additional plants at higher cost were not put on-line in time to carry the >next higher increment of demand, the local automatic dispatching system will >experience run away inflation of the price index, low system frequency, and >excessive incomming power over the tie-lines. Only rising variable unit >costs can be used to compute an optimum dispatch of multiple productive >assets. That is to say, that all productive assets serving a particular >market must exhibit constant or decreasing returns to scale before the market >mechanism can converge to an optimum allocation of resources, just as Henry >Carter Adams said in his 1887 monograph, RELATION OF THE STATE TO INDUSTRIAL >ACTION, Vol. I, American Evonomic Review. >~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ regards, Tom Walker http://www.vcn.bc.ca/timework/worksite.htm
