Overview
A new option called 'Use Airspace' has been added to the 'Ownership' in storages in Source. As a result, some modifications are done to the 'Ownership in Storages - SRG' page. Only the additions/modifications made to the original storage ownership SRG are explained here and hence for the unchanged sections, one should refer to the original page of previous releases. For example, only the changed and new equations are mentioned here. The modifications are done to explain the calculation method behind the 'Use Airspace' option.
Description and rationale
In some circumstances certain storage owners may be able to exceed their share of storage temporarily. These owners should only spill when external spill occurs, and they should be the first to spill in that case. The owner who can exceed their share using the available airspace is called an airspace owner. There are certain conditions of ownership while enabling this functionality. They are:
Non-airspace owners spill among themselves and they have the priority to use airspace until they reach their maximum volumes. Then they spill externally
While the non-airspace owners are under their maximum combined volume, the airspace owner volume can exceed its share of volume
At a given time, only one owner can use the option to exceed their share or ‘use airspace'
An addition to Table 1 (Requirements) is as given below.
Table 1. Addition to partner user requirements
No | Requirement |
|---|---|
8.3 | An owner can exceed it's share of storage capacity temporarily by enabling the 'Use Airspace' option. The owner which uses the airspace option does not internally spill and if there is external spill, the airspace owner spills first. |
Assumptions
Table 2. Assumptions and Constraints
No | Assumption/Constraint |
|---|---|
5 | The owner which uses 'Use Airspace' option can have 0% capacity share. |
6 | Only one owner can enable the 'Use Airspace' option at a time. |
Definitions
Use Airspace | Functionality used by an owner to exceed its share of storage capacity without internally spilling to other owners |
Airspace sharing and working volume proportional loss calculation method
The new method makes the proportional loss calculation fixed at the start of the timestep and thus allows for the calculation of spills required for the airspace owner logic. And it also happens to simplify the other calculations meaning that there's no iterations and the logic for positive and negative losses are exactly the same. The fundamental difference is that the losses are calculated based on the owners' maximum release for the timestep rather than based on the owners' storage at the end of the timestep. In this method, instead of sharing the losses based on the proportion of capacity share of each owner, the losses are shared based on each owner's share of working volume. Therefore, for an owner i, the working volume is calculated as:
Equation 1 |
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where:
Wi - Working volume of owner i.
Vi1 - Owner ’s volume of water in the reservoir last time step.
Ii - Volume of inflow this time step belonging to owner i.
Ci - Net volume of water ceded by owner i this time step to all other owners, negative if this owner has ceded less water to other owners than received.
Fi - Fixed loss attributed to owner i, negative if a gain.
The total working volume for all owners is:
Equation 2 |
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where:
Ti - Total working volume.
The proportional loss attributed to owner i is Pi and is given by:
Equation 3 |
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where:
P is the total proportional loss, negative if a gain (rainfall).
If the storage working volume is less than or equal to ownership tolerance level (0.0001 m3), then proportional loss Pi becomes:
| Equation 4 |
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where:
ri - Owner i’s ratio share of the reservoir’s storage capacity.
Based on the working volume, release, borrow, internal spill, external spill and proportional loss, an owner's final storage volume is calculated as:
Equation 5 |
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where:
Vi2 - Owner ’s volume of water in the reservoir at the end of time step.
Bi - Total borrowed from other owners by owner i, negative if the owner is lending to other owners.
Ri - Volume of regulated water released this time step for owner i.
The final storage volume is updated after calculating the internal and external spills. The changes in the spill calculations are illustrated in the later sections.
Borrow calculations
If the storage working volume is less than or equal to ownership tolerance level, the maximum release for an owner is:
Equation 6 |
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where:
Pi is as in Equation 4 as the proportional loss volume is already known.
Previously, losses would not affect borrowing as the losses were based on end of timestep storages.
Identifying spilling owners
Total External Spill
The total external spill by all owners is known and is given by total outflow minus the total release of all owners as in:
Equation 7 |
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Spill by individual owner
Before each owner’s share of spills can be determined, it is necessary to determine which owners will spill. Where the spill calculation returns a negative value, owners can receive internal spill, while a positive value indicates that the owner is spilling (has filled their storage share).Based on the working volume calculation method, Equation (5) is rearranged to give an expression for the volume of water that can spill (internally and externally) from an owner’s capacity share:
Equation 8 |
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where:
Vimax - Owner i’s maximum allowed volume of water in the reservoir this time step.
The equations 26 to 29 in the previous version of SRG are made redundant due to the inclusion of proportional loss based on storage working volumes.
Spill by the 'Use Airspace' owner
If there is an owner which uses the 'Use Airspace' option, the spill is given by:
Equation 9 |
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It is to be noted that the spill by the 'Use Airspace' owner Spilla is included in Spilli.
The internal spill by 'Use Airspace' owner can be negative when there are internal spills to it. The airspace owner does not internally spill to other owners but can receive internal spills from other owners if it is under its capacity share. Therefore, the spill amount is the minimum of it's calculated spill and the total external spill of the storage.
The external spill of the 'Use Airspace' owner when its spill is greater than zero is given by:
| Equation 10 |
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The internal spill of the 'Use Airspace' owner when its spill is greater than zero is given by:
| Equation 11 |
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Calculating internal and external spill shares for the owners
The calculations in the previous sections established which owners are spillers when working volume based proportional losses are taken into account. The next step is to determine the internal (between owners) and external (leaving the reservoir) components of the spill by the owners. The steps included are explained below.
| Equation 12 |
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Equation 11 |
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Then the external spills by the owners who do not use 'Use Airspace' option is calculated and it is given by:
Equation 10 |
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Case where internal spills are disabled
If internal spill is disabled the internal spill volume is zero (ISi = 0). The ownership of the external spills is set based on how much each owner would spill in total if internal spill was operating:
Equation 11 |
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Case where internal spills are enabled
When internal spills are enabled, the equations 33 to 43 are followed as in the previous version of SRG with no changes. These equations are based on the equations 9 and 10, which are in turn based on owners who do not use 'Use Airspace' option.
Furthermore, the equations 44 to 50 in the previous version of SRG are made redundant due to the adoption of the new method of proportional loss calculation as in Equation 3 above.
The remaining is the same as in the previous SRG version.