Average production at peak demand (MW)

indexed by: asset, energy, node, number of hours, technology and test case

Description

The aim of this KPI is to study the production means used to respond to demand peaks. This makes it possible to identify the peak capacity of an electricity system or to better understand investments in peakers.

Then, for each energy and node, the KPI calculates the average production of each production asset during the hours of highest demand.

This KPI directly returns optimized production variables. This means, for instance, that for a storage asset, it displays its average raw production over the hours of highest demand without deducting any consumption.

As far as demand is concerned, it is not electricity demand directly that is considered, but residual demand (unoptimized electricity demand minus renewable generation).

Modelling hint

The KPI displays this indicator for the 10, 100, 250 or 400 timesteps with the highest demand. This number of timesteps is an index of the KPI. As the hourly basis is the standard timescale, the index is called number of hours.

Calculation

Residual load

All the equations below are valid for any realization and are therefore implicitly indexed by test case. For each realization, the KPI relies first on the calculation of the residual load. Let be \(y_{e,n}(t)\) the residual load of energy \(e\) of node \(n\). This can be express as:

\[y_{n,e}(t) = d_{n,e}(t) - \sum\limits_{a \in A_{n,e}^{p,RES}} p_a(t)\]

with \(d_{n,e}(t)\) the unoptimized demand of pure demand assets (storages, transmissions are not included here) of energy \(e\) at node \(n\).

For electricity, hydraulic minimal generation needs to be add to the formula. This leads to the following formula:

\[y_{n,e}(t) = d_{n,e}(t) - \sum\limits_{a \in A_{n,e}^{p,RES}} p_a(t) - \sum\limits_{b \in B_{n,e}^{p,Hydro}} p^{*}_a(t).min\_load_a(t)\]

Average production over the highest demand hours

Let define \(I_{n,e,N}\) the N timesteps of highest residual load \(y_{n,e}(t)\).

\[I_{n,e,N} = argmax_{t}\{y_{n,e}(t)|t \in K, |K|=N\}\]

Then, for all the assets \(a\) producing energy \(e\) at node \(n\) (\(A_{n,e}\)), the average production at peak demand \(x_{a,n,e,N}\) is defined as:

\[x_{a,n,e,N} = \langle p_a(t) \rangle_{t \in I_{n,e,N}}\]

Note

In case of dataset with a temporal horizon less than N the number of timesteps considered, N is taken as the total number of timesteps of the temporal horizon.

Global variables and parameters notations definitions can be consulted here.