Pumped Storage Reservoir

The Pumped Storage Reservoir object models a level reservoir where there are facilities that can release water to generate power but can also be pump water into the reservoir to increase storage.

General Slots

Canal Flow

Type: Agg Series

Units: Flow

Description: Flow into (out of) the reservoir from (to) a canal

Information:

Defined by: Explicit Optimization variable in the mass balance constraint

Diversion

Type: Series Slot

Units: Flow

Description: Flow from the reservoir to a diverting object

Information:

Defined by: Explicit Optimization variable in the mass balance constraint

Elevation Volume Table

Type: Table

Units: Length vs Volume

Description: Table relating elevation of the reservoir to volume stored in the reservoir

Information:

I/O: Input only

Defined by: Input only

Energy

Type: Agg Series Slot

Units: Energy

Description: Product of the power generated by flow through the turbines and the length of the timestep.

Information:

Defined by: Replaced by Power * Timestep Length

Description:

Flow FROM Pumped Storage

Type: Agg Series Slot

Units: Flow

Description: Flow into the reservoir from a pumped storage reservoir

Information:

Defined by: Explicit Optimization variable in the mass balance constraint. This slot should be linked to Outflow on a Pumped Storage object. The Pumped Storage object constrains its Outflow.

Flow TO Pumped Storage

Type: Agg Series Slot

Units: Flow

Description: Flow out of the reservoir into a pumped storage reservoir

Information:

Defined by: Explicit Optimization variable in the mass balance constraint. This slot should be linked to Pumped Flow on a Pumped Storage object.

Inflow

Type: MultiSlot

Units: Flow

Description: Inflow into the reservoir from upstream

Information:

Defined by: Explicit Optimization variable in the mass balance constraint

Information:

Operating Head

Type: Agg Series Slot

Units: Length

Description: Elevation difference between the average Pool Elevation and the average Tailwater Elevation during a timestep

Information:

Defined by: Replacement by (Pool Elevation(t) + Pool Elevation(t-1)) / 2 - Tailwater Elevation

Outflow

Type: Agg Series Slot

Units: Flow

Description: Outflow from the reservoir

Information:

Defined by: Explicit Optimization variable as Outflow = Turbine Release + Spill

Information:

Pool Elevation

Type: Agg Series Slot

Units: Length

Description: Elevation of the water surface of the Reservoir

Information: When Pool Elevation is a part of the optimization problem, as it is in all conceivable RiverWare Optimization applications, this slot is numerically approximated as a function of Storage (Numerical 2-D Approximation). The relationship between Pool Elevation and Storage will come from the user-input Elevation Volume Table. The table will be queried either using user-input points defined in the Pool Elevation LP Param table.

Defined by: Numerical 2-D Approximation in terms of Storage, based upon the Elevation Volume Table. The Pool Elevation LP Param table values are used as approximation points indexing the Elevation Volume Table. The Elevation Volume Table should have increasing values of Pool Elevation and Storage. Storage is required to be a concave function of Pool Elevation. The preferred order of approximation is substitution, piece-wise, tangent, two-point line.

Pool Elevation LP Param

Type: Table Slot

Units: Volume

Description: Specifies the Storage points used to take the tangent, line and piecewise approximations for Pool Elevation linearization

Information: This table is used for linearization unless Pool Elevation Linearization Automation category has selected Plant Automation. The best Storage point to choose for tangent approximation would be the expected storage expected during the run; for the line approximation, the expected maximum and minimum Storage; for piecewise approximation, use points that cover the full range of expected Storage during the run with intermediate points such that a piecewise linear curve reasonably approximates the actual curve.

Defined by: User input

Pool elevation storage relationship. Not drawn to scale.

Power

Type: Agg Series Slot

Units: Power

Description: Power generated by flow through the turbines

Information:

Defined by: Numerical 3-D Approximation in terms of Operating Head and Turbine Release. Approximation is based on the Plant Power Table. The Power LP Param table contains a value for Operating Head used to index the Operating Head column of the Plant Power Table. This approximated value, therefore, reduces the Power to a function of Turbine Release at the given Operating Head.

The flow values in the Power LP Param table are then used as approximation points indexing the Turbine Release column of the Plant Power Table. The Plant Power Table should have increasing values of Operating Head and Turbine Release. Power should be a concave function of Operating Head, but concavity is not strictly enforced; mild non-concave regions are permissible to allow for round-off error, and so on. The preferred order of approximation is substitution, piece-wise, two-point line, tangent.

Return Flow

Type: MultiSlot

Units: Flow

Description: Flow returning from a diversion object

Information:

Defined by: Explicit Optimization variable in the mass balance constraint (see Storage)

Spill

Type: Agg Series Slot

Units: Flow

Description: Sum of the Bypass, Regulated Spill and Unregulated Spill

Information:

Defined by: Explicit Optimization variable as Spill = Bypass + Regulated Spill + Unregulated Spill

Storage

Type: Series Slot

Units: Volume

Description: Volume of water stored in the reservoir

Information:

Defined by: Explicit Optimization variable as Storage = Storage(t-1) + Precipitation Volume - Evaporation - Change in Bank Storage + timestep * ( Inflow + Canal Flow + Flow TO Pumped Storage + Hydrologic Inflow Net + Return Flow - (Outflow + Diversion + Flow FROM Pumped Storage))

Tailwater Base Value

Type: Series Slot

Units: Length

Description: Elevation of tailwater or base elevation used to compute elevation of tailwater

Information:

Defined by: Explicit Optimization variable should be input or linked. See Pump Power Numerical Approximation in Optimization for descriptions of related constraints and other objects to which the slot is linked.

Tailwater Elevation

Type: Agg Series Slot

Units: Length

Description: Water surface elevation on the downstream side of the dam

Information:

Defined by: Various approaches dependent on the method selected in the Optimization Tailwater category.

Turbine Capacity LP Param

Type: Table

Units: Length, Length, Length

Description: LP Param table for turbine capacity

Information: See power methods for details

Turbine Capacity

Type: Agg Series Slot

Units: Flow

Description: Flow capacity of the entire power plant’s turbines

Information:

Defined by: Numerical 2-D Approximation in terms of Operating Head, based upon a maximum turbine capacity table. This capacity table is determined in various ways according to the Power method.

Turbine Release

Type: Agg Series Slot

Units: Flow

Description: Flow through the turbines of a power reservoir

Information:

Defined by: Explicit Optimization variable as Turbine Release <= Power Plant Cap Fraction * Turbine Capacity

Revised: 08/02/2021