System costs view (€/h)

indexed by: asset, cost type, node, technology, test case

Description

This indicator is used to analyse the system costs of each asset, i.e., the costs directly associated to the operations of each asset present in the system, from a system point of view. The following costs are taken into account, under the cost type index:

• Production costs

• Consumption costs

• Storage costs

• Loss of load costs

• Curtailment costs

• Start-up costs

• Running bound costs

• Stopping costs

• Entry fees

• Exit fees

• Reserve costs

• Not running reserve costs

• Interruptible load costs

Modelling hint

All these costs are those added in the objective function that the solver minimizes when running the optimization. For the Simulation context, this KPI summed up then equals to the value obtained for the objective function of the optimization problem, called reward.

Specific investment costs are not displayed in this indicator, please refer to the Investment costs KPI for more details on investment costs. For Optim capa context, this KPI summed up does not equal to the reward of the optimization problem.

In pathway model, please refer to the Total costs KPI.

Calculation

Comment on the absence of energy indexing

Please note that all costs of a given asset must always be considered together, and not depending on their energies, since some costs are shared. For instance, in the system cost part of the asset cost, the runningCapacityCost is linked to the electricity production as much as to the reserve production. Therefore, indexing these costs by energy would be misleading.

Costs shared between nodes

Additionally, as an asset could produce or consume energy at several nodes. For practicality purposes and to share costs between those nodes, the whole system cost of an asset is equally divided between the nodes for which the asset is linked. Then, for instance, a transmission between the nodes A and B will see its asset costs equally shared between A and B.

All the equations below are valid for any realization and are therefore implicitly indexed by test case. Index Technology is directly deduced from the asset. For a given asset \(a\) and node \(n\) the above costs are calculated as follows:

Production costs

Production costs \(pc_{a, n}\) timeseries of on asset \(a\) at a node \(n\) depends on the active behaviour of the asset considered and are given by:

• For asset with behaviour FUEL active:

\[pc_{a, n} = \sum_{e \in E_{a, n}^p} p_{a, n, e}(t) * variable\_cost_a\]

• For asset with no behaviour FUEL:

\[pc_{a, n} = \sum_{e \in E_{a, n}^p} p_{a, n, e}(t) * (production\_cost_a - incentive_a)\]

With:

• \(variable\_cost_a\) : The variable cost parameter of asset \(a\)

• \(production\_cost_a\) : The production cost parameter of asset \(a\)

• \(incentive_a\) : The incentive to produce parameter of asset \(a\)

All the above parameters can be either a float or a timeseries.

For asset with a PRODUCTION_COST_CURVE parameter we take its production cost directly from the cost variable associated to its energy production.

Consumption costs

Consumption costs \(cc_{a, n}\) timeseries of an asset \(a\) at node \(n\) are given (depending on the asset parametrization) by:

• For asset with the parameter Consumption cost:

  \[cc_a = \sum\limits_{e \in E}c_{a, e, n} * consumption\_cost_a\]

• For asset with the parameter Price:

  \[cc_a = \sum\limits_{e \in E}c_{a, e, n} * price_a\]

\(consumption\_cost\) and \(price\) parameters can be either a float or a timeseries.

Consumption costs of WELL type assets are not included here but in curtailment cost instead.

Storage costs

Storage costs timeseries of a storage asset \(a\) is given by:

\[sc_a = sl_a * storage\_cost_a\]

With:

• \(sl_a\) : The storage level timeseries of storage asset \(a\) across the realization

Loss of load costs

Loss of load costs timeseries is the multiplication of energy production of LOSS_OF_LOAD type assets multiplied by their price parameter. For a LOSS_OF_LOAD asset \(a\) producing energy \(e\) at node \(n\), we then have :

\[lc_a = p_{a, n, e} * price_a\]

Curtailment costs

Curtailment costs timeseries is the multiplication of energy consumption of WELL type assets multiplied by their price parameter. For a WELL asset \(a\) consuming energy \(e\) at node \(n\), we then have:

\[cuc_a = c_{a, e, n} * price_a\]

This cost type also include CO2 captured sequestration by dedicated assets. For an asset \(a\) of type COE_SEQUESTRATION consuming CO2 captured at node \(n\) we have:

\[cuc_a = c_{a, n, CO2 captured} * consumption\_cost_a\]

Start-up costs

Starting costs are computed separately between assets with UNIT and CLUSTER behaviours. Let’s consider an asset \(a\).

with behaviour UNIT active

\[stac_a = sup_a * startup\_cost_a + ramping\_up\_cost_a\]

With :

• \(sup_a\) : the starting up timeseries of asset \(a\), i.e. the binary timeseries of switching from state OFF to state ON

• \(startup\_cost_a\) : the cost of starting a unit in euro per start-up

• \(ramping\_up\_cost_a\) : the additional ramping up cost which is equals to \(\frac{1}{2} * production\_cost * p\_max_a * av_a * startup\_up\_time_a\)

with behaviour CLUSTER active

\[stac_a = sup_a * cluster\_startup\_cost_a\]

With :

• \(sup_a\) : the cluster started capacity timeseries

• \(cluster\_startup\_cost_a\) : the cost of starting 1 additional MW of capacity for the asset \(a\) given in euro/MW

Running bound costs

The running bound costs only apply to assets with behaviour CLUSTER active. This cost is directly taken from the cost variable such as declare in the optimization problem. It corresponds to the cost of keeping started capacity on, regardless of the plant’s level of production.

Stopping costs

The stopping costs timeseries only apply to assets with UNIT behaviour active. For such an asset \(a\) we have:

\[stopc_a = stop_a * stopping\_cost_a\]

With :

• \(stopc_a\) : the stopping timeseries of asset \(a\), i.e. the binary timeseries of switching from state ON to state OFF

• \(stopping\_cost_a\) : the stopping cost parameter of asset \(a\), given in euros

Entry fees

Entry fees costs apply to all assets producing energy and having an ENTRY_FEE parameter. For such an asset \(a\) producing energy \(e\) at node \(n\):

\[enfc_a = p_{a, n, e} * entry\_fee_a\]

Exit fees

Exit fees costs apply to all assets consuming energy and having an EXIT_FREE parameter. For such an asset \(a\) consuming energy \(e\) at node \(n\):

\[exfc_a = c_{a, e, n} * exit\_fee_a\]

Reserve costs

Reserve costs are given by the multiplication of each reserve production timeseries with its associated production cost:

\[resc_a = \sum_\limits{e \in E^{reserve}} p_{a, n, e} * production\_cost_{a, e}\]

With :

• \(E^{reserve}\) : The set of possible reserve energies : MFRR_UP, MFRR_DOW, SYNC_RES_DOWN and SYNC_RES_UP

Not running reserve costs

The MFRR (Manual Frequency Restoration Reserve) up not running reserve cost refers to the cost associated with maintaining reserves that are available for immediate deployment in case of a frequency deviation in the power grid. MFRR up not running reserve costs are given by the multiplication of reserved not running capacity and the associated cost parameter:

\[mnrc_a = mnr_a * mfrr\_up\_not\_running\_cost_a\]

Interruptible load costs

Interruptible load costs are given by the shed energy timeseries with its associated production cost:

\[ilc_a = shed_{a, n} * production\_cost_a\]

With :

• \(shed_{a, n}\) : the shed energy by the asset \(a\) for the node \(n\)