Loss of load cost (€)

indexed by: node, energy, test case

Description

This indicator is used to estimate the costs associated with system undersizing with regard to an energy.

For each node and each energy in a given system, it indicates the total costs associated to Loss Of Load (LOL) over the considered period. This corresponds to the cost of not satisfying demand over the considered period : that associated costs to all the energy that is not served. From a modelling point of view, this amounts to give a cost to a the volume delivered by Loss Of Load assets.

The number of Loss Of Load hours for each node and energy is indicated in the KPI Loss of Load hours and the volume of energy curtailed during these hours in Loss of Load Volume.

Modelling hint

In classic models, this cost is directly indexed on the value of Loss of Load (VoLL), which is the amount customers would be willing to pay in order to avoid a disruption in their electricity service.

Calculation

All the equations below are valid for any realization and are therefore implicitly indexed by test case.

Let be \(x_{n, e}\) the value returned by this KPI for a given node \(n\) and energy \(e\) and \(A_{n,e}^{lol}\) the set of loss of load assets producing energy \(e\) at node \(n\).

We can then express \(x_{n, e}\) as :

\[x_{n, e} = \frac{\sum\limits_{t, a \in A_{n,e}^{lol}} p_{a, n, e}(t) . c_a}{N_h}\]

with:

• \(c_a\) the Loss Of Load price for the asset \(a\)

Indexing

• The energy index of this KPI refers to the produced energy of Loss of load assets

• The node index of this KPI refers to the node consuming the energy produced by Loss of load assets

• The test case index corresponds the test case of the realization variables and parameters are taken from