Electricity CO2 content (t/MWh)#
indexed by: data type, node, test case
Description#
This Key Performance Indicator (KPI) computes the electricity CO2 content, with and without taking into account imported emissions across simulation nodes. It accounts for the physical flows of CO2 and therefore does not take into account the cancellation of the carbon footprint of biogas or biomass fueled plants.
Calculation#
The equations below are valid for any realization and are therefore implicitly indexed by test case. Additionally, to simplify the notations, the following equations are given for one timestep and are therefore also implicitly indexed by timestep.
Electricity CO2 content with imported emissions#
To compute electricity CO2 content taking into account imported emissions, we rely on the proportional sharing hypothesis, which states that at every node, the CO2 emissions associated to power generation are distributed according to the value of the flows from this node.
Let us declare the following variables:
\(p_{n}\) the total electricity production at node \(n\) : \(p_{n} = \sum\limits_{a \in A^p_{n, electricity}} p_{a, n, electricity}\)
\(g_{n}\) the total electricity generation at node \(n\) excluding flows
\(e_{n}\) the total nodal CO2 emissions associated to electricity mix at node \(n\). \(e_n = \sum \limits_{a \in A_{n, electricity}^p} p_{a, n, CO2}\)
\(f_{n, m}\) the electricity flow from node \(n\) to node \(m\)
\(q_{n, m}\) the share of electricity consumed at node \(m\) produced by node \(n\)
\(\delta_{n, m} : 1\) if \(n = m\); \(0\) otherwise
\(x_{n, i}\) : the value returned by this KPI accounting for imported emissions
\(x_{n, wi}\) : the value returned by this KPI without taking into account imported emissions
By definition of q, conservation of electricity at node \(n\) gives us:
We can apply this equation for all nodes of the context to have a matrix system such as :
with:
\(I\) : the identity matrix defined by \(I[n, m] = \delta_{n,m}\)
\(D\) : a matrix defined by \(D[n, m] = f_{m, n} / p_n\)
\(P\) : the total electricity production diagonal matrix defined by \(P[n,n] = p_{n}; P[n, m] = 0\)
\(P\) : the total electricity generation diagonal matrix defined by \(G[n,n] = g_{n}; G[n, m] = 0\)
\(F\) : the electricity flows matrix defined by \(F[n,m] = f_{m,n}\)
\(Q\) : the matrix representing the repartition of electricity between nodes defined by \(Q[n,m] = q_{m,n}\)
This gives us the following equation over the electricity sharing matrix :
with:
\(A = (I - D)^{-1} \cdot P^{-1}\)
We can then use the same matrix A to spread the CO2 emissions across nodes and get the electricity CO2 content taking into account imported emissions:
\(X = A \cdot E = (I - D)^{-1} \cdot P^{-1} \cdot E\)
with :
\(X\) : the electricity CO2 content vector taking into account imported emissions defined by \(X[n] = x_{n, i}\)
\(E\) : the total nodal electricity system CO2 emissions vector defined by \(E[n] = e_{n}\)
Calculation hints
Transmission losses are not taken into account in this indicator as long as the electricity flowing through transmission assets is taken from their consumption variables.
CO2 emissions taken into account here are the ones of electricity producing assets.
Electricity CO2 content without imported emissions#
The value returned for the Electricity CO2 content without imported emissions data type is computed for each node regardless on its electricity import and exports. It simply divides the electricity system nodal emissions by the nodal electricity generation.
We can express the displayed value for this data type as:
Global variables and parameters notations definitions can be consulted here.
Indexing#
The data type index of this KPI refers to the accounting type for electricity CO2 content : with and without imported emissions
The node index of this KPI refers to the node at which the electricity CO2 content is displayed
The test case index corresponds the test case of the realization variables and parameters are taken from