Maximum order constraint - SRG

The Maximum Order Constraint node constrains releases from upstream storages to the defined maximum order at a point in the river network. The process of limiting releases considers the contribution from tributary inflows between the upstream storage(s) and the location of the maximum order constraint.

This functionality is required in eWater Source to enable it to model situations where it is necessary to limit the flow at a location, for example, to prevent it from going overbank.

Scale

This node is implemented at point scale and is used at every model time-step.

Principal developer

eWater 

Scientific provenance

Maximum flow constraints have been implemented in water sharing arrangements in practice in a number of regulated river systems in Australia. The implementation in eWater Source is designed to be able to replicate these practices and be flexible enough to accommodate new variations if required.

Version

eWater Source version 4.3

Dependencies

This node is only relevant to models of regulated systems at locations where there are upstream storage node(s) present.

Structure and processes

When rules based ordering is used, a constraint phase precedes the ordering phase of every model time-step. In this phase, the modelled river network is processed from upstream to downstream to determine at each node the flow range that is possible when upstream management rules are met. This flow range is defined by a minimum and maximum constraint flow volume. The constrained flow range for each node is forecast so that releases can be made at the appropriate time by upstream storages. The forecast time period covers the shortest to the longest estimated time taken for water to travel from upstream storages to the location.

At the head of the river, the constrained flow range is from zero to infinity. At each node, the upstream constrained flow range is known. This flow range is updated for any additional constraints (physical or management) defined at the node. The updated flow range is then passed down to the next node downstream. In this way the constrained flow range at any node downstream of the Maximum Order Constraint will incorporate restrictions imposed by this node.

In the ordering phase, orders are adjusted as required, as described in the SRG entry on Rules Based Ordering, to ensure that total flow at the node will fall within the constrained flow range for the future time-step in which the order is to be delivered. As water is released from upstream storages to meet the ordered volume, the flow volume at a Maximum Order Constraint node will usually not exceed its maximum order constraint for the time-step,

Note that it is possible to configure the model in a way such that flow exceeds the maximum order constraint for a time-step - for example by configuring storage nodes in a way such that they spill more than the maximum order.

These concepts are described in more detail in the Scientific Reference Guide entry on the Rules-Based Ordering - SRG.

The way ordering is handled in NetLP, and the application of a maximum order constraint in this context, is described in the Scientific Reference Guide entry on NetLP - SRG.

Time-step: Constraint phase

At a Maximum Order Constraint node, the constrained flow range passed down from upstream is reduced where necessary to the node’s defined maximum order. It is not, however, reduced below the minimum constraint passed from the upstream node, ie:

Equation 1

A more detailed description of the calculations performed, particularly where ownership is enabled, is given in the Scientific Reference Guide entries on Rules-Based Ordering - SRG and Ownership at nodes and links - SRG.

Input data

When ownership is not enabled, the maximum order constraint is specified by the modeller as a value or function.

Constraint levels are used when ownership is enabled. One or more of these levels are specified, with each level corresponding to a constraint volume (defined via function), and owner proportions. The highest constraint level represents the total maximum order constraint volume. Owner proportions apply to the volume between the previous level’s volume, and the volume for the level at which they are defined.

Equation 2

Output data

The recorded output variables relevant to a maximum order constraint node are described in Table 1.