Reservoir Convergence Algorithms

1
Reservoir Convergence Algorithms
Convergence Algorithm Previously Used Current
Convergence Algorithm
2
General

• Convergence algorithm used in functions that
  require the simultaneous solving of a set of 2
  equations
• Bisection algorithm used in all reservoir types
  in
• getMaxOutflowGivenInflow
• getMaxReleaseGivenInflow
• getMinSpillGivenInflowRelease
• solveMB_givenInflowRelease

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Example - getMaxOutflowGivenInflow
outflow
fMAX(stor,Q)
QMAX,MB
fMB(stor,Q)
storMAX,MB
storage
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1. Simple Convergence Algorithm

• Iterates by updating the dependent variable
  (outflow) based on the changing of the
• independent variable (storage)

outflow
outflow
fMAX(stor,Q)
fMAX(stor,Q)
fMB(stor,Q)
fMB(stor,Q)
storage
storage
Ideal
Problematic
5
Bisection Algorithm

• Incremental search method where the interval is
  divided in half at each iteration

outflow
outflow
QMBave
fMAX(Q,stor)
fMAX(Q,stor)
QMAXave
QMBave
fMB(Q,stor)
fMB(Q,stor)
QMAXave
storage
stor_high
stor_ave
stor_low
stor_high
stor_ave
stor_low
storage
stor_low
stor_ave
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2. Bisection Replaces Simple Algorithm

• The simple algorithm was replaced with the
  bisection algorithm. This approach also
• proved to be problematic.

fMAX(Q,stor)
outflow
outflow
fMAX(Q,stor)
QMBave
QMAXave
fMB(Q,stor)
fMB(Q,stor)
stor_high
stor_ave
stor_low
storage
stor_high
stor_low
storage
stor_low
stor_ave
Ideal
Problematic
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3. Current Algorithm - Combination of Simple
Bisection

• If the simple convergence routine fails, the
  bisection routine is employed.
• The last 4 points of the simple routine become
  the bisection routines starting points.

outflow
outflow
fMAX(Q,stor)
fMAX(Q,stor)
QMBave
QMAXave
fMB(Q,stor)
fMB(Q,stor)
storage
stor_high
stor_ave
stor_low
storage
Simple
Bisection