Anatomy of an equation

The shape

   LHS: things NEMDE can move            RHS: the limit, measured live
 +-----------------------------+       +-------------------------------+
 |   0.8 x Generator A         |       |   line rating                 |
 | + 0.3 x Generator B         |  <=   | - flows measured by SCADA     |
 | - 0.2 x Interconnector      |       | - a safety margin             |
 +-----------------------------+       +-------------------------------+

The left-hand side

The LHS may contain only quantities NEMDE optimises: targets of scheduled and semi-scheduled units (by connection point), interconnector flows, and regional FCAS enablement. It is strictly linear: each term is a factor times a quantity. The factor says how strongly that quantity loads the limit. In the picture, backing Generator A off by 1 MW relieves the line by 0.8 MW; Generator B by 0.3 MW; and the interconnector's negative factor means flow in its positive direction relieves the line, because it carries power away from the congested corridor.

Two conventions make real equations readable. Factors are normalised so the largest is exactly plus or minus 1, and any unit whose factor would be smaller than about 0.07 is dropped from the LHS and folded into the RHS as a measured quantity instead. So a thermal constraint typically shows one dominant unit at 1.0 and a handful of others as fractions, and a long tail of small contributors is invisible on the left.

The right-hand side

The RHS is the limit. It can be a constant (168 MW, full stop), or a live calculation: a line rating from the operator's tables, minus the flow SCADA is measuring on other lines, minus an operating margin, scaled by a sensitivity factor. Because it is computed from measurements, the RHS of the same constraint changes every interval, and AEMO publishes the value it used alongside the solution. Chapter 9 opens the RHS up term by term.

The operator

Most network constraints are <=: a weighted sum of generation must stay below a limit. Most FCAS constraints are >=: a sum of enabled reserve must stay above a requirement. The direction matters for the price consequences in Chapter 5: a binding <= constrains generators off, a binding >= constrains them on. When the operator is unknown, the name is a reliable fallback: F_ constraints are >=, network constraints are <=.

Headroom

The gap between the two sides is the headroom: RHS minus LHS for a <= constraint. A constraint spends most of its life with plenty of headroom, and while it does it has no effect on dispatch at all. It matters only when headroom reaches zero.

 +----------------+      +------------------+      +---------------------------+
 |  Comfortable   | ---> |  Near binding    | ---> |  Binding (LHS = RHS)      |
 |  big headroom  |      |  gap shrinking   |      |  redispatch, prices move  |
 +----------------+      +------------------+      +---------------------------+

A worked example: a real thermal constraint

Here is N>>NIL_70_71, condensed from AEMO's own training material. It protects the Mt Piper to Wallerawang line 70 from overloading if line 71 trips, in New South Wales, with the grid in its normal shape.

Read what the conventions did. Mt Piper carries the factor 1.0 because it is the unit that loads line 70 most; Shoalhaven's 0.0939 sits just above the cut-off. The QNI interconnector enters with a negative sign because exporting to Queensland pulls power away from the corridor. The RHS is in feedback form: it starts from the rating, subtracts what SCADA says is already flowing, keeps a 30 MW operating margin, scales the whole bracket by a sensitivity of 2.462, and then adds back the current LHS so that the equation expresses headroom rather than an absolute limit. That last trick means the constraint self-corrects each interval as the real flows change.

The simplest possible constraint, and what binding looks like

At the other extreme is V_DUNDWF1_2_3_168: . Its LHS is the sum of the three Dundonnell wind farm units with factor 1 each; its RHS is the constant 168. When the wind blows, the farm hits the cap and the equation binds for hours at a time. The chart shows one market day.

Look at the shape: the LHS climbs, touches the RHS, and stays glued to it while the marginal value (next chapter) is non-zero. Headroom is zero for every one of those intervals, and positive whenever the line separates from the cap.