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<br />002030 <br /> <br />Advanced Concert~ <br /> <br />Parameter/Function Tables <br /> <br />5.6 Parameter/Function Tables <br />Parameter/function tables occur in pairs, and define a relation between a function value and a <br />(variable) parameter value. For example, reservoir elevation as a function of the reservoir content is <br />given in a parameter/function table. These tables require at least two, and no more than 99 entries. <br />HYDROSS performs linear interpolation to derive a function value for a given parameter value. <br />Parameter/function tables may also be staged. <br />The function must be a single-valued function of the parameter; each value of the parameter <br />must be associated with only one value of the function. <br />Parameter tables must be monotone increasing or monotone decreasing. Either each entry <br />(except the first) is larger than its predecessor, or each entry is smaller than its predecessor. This <br />restriction does not apply to function tables. <br />Function tables involving time (Le. flow tables) should not be expressed in 'per-month' units. <br />Since HYDROSS must work with months of 28, 29, 30 or 31 days, it uses acre-feet/day units <br />internally and multiplies by the number of days in the month to arrive at a monthly value; this is a <br />necessary consequence of having to use the same table for an entire year. If you do express a flow <br />table in 'per-month' units, HYDROSS will quietly divide by 30 to obtain a daily flow, and you may <br />notice monthly results which vary 3-6% from what you thought you gave the model. <br />HYDROSS uses linear interpolation between the parameter table and the function table to <br />establish a function value for a given parameter value. If the given parameter value is outside the <br />range of table values, HYDROSS will return a function value equal to the nearest extreme value of <br />the function table (Le. the first or last value). <br /> <br />5.7 Power Tabl~ <br />The preceding paragraph on interpolation has special significance at power plants which use <br />parameter/function tables for efficiency. <br />The basic equation for power plants is: <br />Energy = Constant x Discharge x Head x Efficiency <br />All of the components are either constant or functions of the flow, directly or indirectly. <br />Where there is a power requirement HYDROSS sets up and solves a partial differential equation to <br />determine the flow that would produce the required energy; this is returned to the calling routine as <br />either a requirement for more water (if positive) or water available for storage or other purpOSes (if <br />negative). The derivatives used in the equation are local: they are calculated for the segment in which <br />the parameter value happens to fall, and an iteration process refines them further. <br />If your efficiency table goes to zero and stays there over any range of parameter values, then <br />you may cause problems for the model. If the parameter (either head or flow) gets into the range of <br />zero efficiency, then the value and the derivative of the efficiency are both zero: there is no energy <br />generated and there is no apparent way to produce any by changing the flow. HYDROSS is then <br />stuck, and there will be no power generated for that month. <br />The solution is to not allow the efficiency table to go to zero, but to use a very small number <br />(such as .0001) instead. <br /> <br />HYDROSS 4.1 <br /> <br />March 25, 1991 <br /> <br />Page 34 <br />