Canal

The Canal object models gravity flow through a canal connected to two reservoirs.

General Slots

Elevation 1

Type: Agg Series Slot

Units: Length

Description: Pool Elevation of reservoir 1

Information:

Defined by: Replacement by the linked reservoir Pool Elevation slot (which in turn may be Numerically Approximated).

Elevation 2

Type: Agg Series Slot

Units: Length

Description: Pool Elevation of reservoir 2

Information:

Defined by: Replacement by the linked reservoir Pool Elevation slot (which in turn may be Numerically Approximated).

Flow 1

Type: Agg Series Slot

Units: Flow

Description: flow to or from the canal end connected to reservoir 1

Information: This slot must be linked to the Canal Flow slot on reservoir 1.

Defined by: Explicit Optimization variable as 0.0 = Flow 1 + Flow 2

Flow 2

Type: Agg Series Slot

Units: Flow

Description: flow to or from the canal end connected to reservoir 2

Information: This slot must be linked to the Canal Flow slot on reservoir 2.

Defined by: Numerical 3-D Approximation in terms of Lower Elevation and Delta Elevation. Approximation is based on the Canal Flow Table.

The Flow 2 LP Param table contains a value for Lower Elevation used to index the Lower Elevation column of the Canal Flow Table. This approximated value, therefore, reduces Flow 2 to a function of Delta Elevation. The length values in the Flow 2 LP Param table are then used as approximation points indexing the Delta Elevation column of the Canal Flow Table.

The Canal Flow Table should have increasing values of Lower Elevation and Delta Elevation. The function is expected to be non-convex.

The preferred order of approximation is substitution, piece-wise, two-point line, tangent.

Non-concave, non-convex function. Not drawn to scale.

Canal Flow Table

Type: Table Slot

Units: Length, Length, Flow

Description: 3-D table used to find canal flow by interpolation given a Lower Elevation, Delta Elevation between the lower and higher pool elevations and resulting Flow 2.

Information:

Defined by: User input

Delta Elevation

Type: Agg Series Slot

Units: Length

Description: The average elevation difference between the two reservoirs and across the canal at the current timestep

Information:

Defined by:

Flow 2 LP Param

Type: Table Slot

Units: Length, Length, Length, Length

Description: specifies the Lower Elevation and the Delta Elevation points used to take the tangent, line, and piecewise approximations for numerical approximation of Flow 2 as specified in the Canal Flow Table. The best Lower Elevation to choose should be close to the expected elevation for the whole run. For Delta Elevation the suggested points for tangent approximation is the estimated value for the whole run and for line approximation are 0 flow and some likely value. piecewise linearization is not used.

Information:

Defined by: User input

Lower Elevation

Type: Series Slot

Units: Length

Description: The elevation of the lower of the two reservoirs for the current timestep

Information:

Defined by:

Revised: 08/02/2021