2.1. Welfare maximisation by exchange between two markets
Let us define total welfare here as the total consumer and producer surplus plus congestion rents in all parts of the electricity market. It also includes the consumer and producer surplus caused by the provision of the grid losses including the losses over the interconnections and it includes the consumer and producer surplus in the ancillary services markets.
An exchange is defined here as the hourly energy exchange over an interconnection between two market areas.
The market coupling algorithm makes sure that all exchanges in the capacity allocation are to the level where either:
a) the modelled marginal welfare loss of the exchange is equal to the modelled marginal welfare gain of the exchange and the exchange is not using all exchange capacity (Figure 1, left side) or b) the modelled marginal welfare loss of the exchange is smaller than the modelled marginal welfare
gain of the exchange and the exchange is using all exchange capacity (Figure 1, right side)
Figure 1: optimal exchange level in capacity allocation
Assuming that the modelled marginal welfare loss and gain in the market coupling are an accurate representation of the marginal total welfare loss and gain, it is known from standard economic theory that this leads to a maximum increase of total welfare by the allocated exchanges.
2.2. Modelling of welfare gains and welfare losses in market coupling
In the market coupling model the price difference between the areas on each side of the interconnection represents the marginal total welfare gain of the exchange.
The loss factor for the exchange times the lowest price on either side of the exchange represents the marginal total welfare loss of the exchange. Where no loss factor is taken into account, no marginal welfare loss of the exchange is taken into account. The next section reviews in how far this is an accurate representation of total marginal welfare loss.
7
Welfare distribution effects like from TSO-TSO compensation schemes or congestion income sharing are not taken into account throughout this analysis as they are assumed to have no impact on total welfare.
2.3. Welfare losses induced by exchanges on AC and DC interconnections
The marginal welfare loss that is induced by exchanges over interconnections between market areas can conceptually be divided into marginal costs by DC cable exchanges and marginal costs by exchanges over AC interconnections. The marginal costs that are induced by the exchanges can be further divided into marginal costs on the interconnections itself and marginal costs not on the interconnections (e.g. on the grid inside the interconnected areas).
For DC interconnectors the losses over the interconnector induce a marginal cost that can be approximated by a linear loss factor1 applied to the exchange and multiplied by the lowest market price on either side of the interconnector..
For DC interconnectors, it is assumed that the marginal costs for exchange over the interconnection can be approximated based on a fixed linear loss factor on the exchange. On the other hand, DC interconnector exchanges can also induce marginal costs inside the AC networks of the connected areas.
For AC interconnectors, the relationship between the exchange and the marginal costs over the interconnector is not so clearly to be defined. This is partly due to the non-linear relationship between the AC losses over the interconnector and the exchanges. Another important reason is that the physical flow over an AC interconnector might differ from the commercial exchange over the interconnector as scheduled from market coupling, especially in case of parallel AC network paths. If the marginal costs for exchange over specific AC interconnectors can in principle be expressed by a linear loss factor, then this interconnector should be assigned the respective loss factor accordingly.
The marginal costs incurred by any interconnector exchange (AC or DC) inside the AC network of the connected bidding zones could include for example increase or decrease of internal grid losses and redispatch costs due to internal congestions. This will depend highly on the grid topology and the distribution of load and generation over the grid as well as on the number of flow paths that enable the exchange. As grid topologies are different in different market areas, interconnections generally are meshed and the grid loading pattern changes from hour to hour, the relationship between interconnector exchanges and the marginal costs incurred inside the AC network of the interconnected bidding zones is not obvious. It is assumed that the correlation between an exchange and the marginal cost of the internal grid depends on the grid topology, may include other exchanges and has a more or less random character with a bias depending on the grid topology and market scenarios. For certain topologies a multi-variate correlation may exist between the marginal cost of the internal grid and the exchanges on a set of interconnector. If this multi-variate correlation can be approximated by a linear factor on each of the interconnectors in the set, then all interconnectors in that set should have a marginal cost factor assigned (e.g. a loss factor) in order to ensure overall welfare maximization.
1 In reality the loss factor deviates from this linear approximation depending on DC technology, power flow, voltage level etc
8
Marginal welfare loss element
DC interconnector exchange AC interconnector exchange
Marginal costs on the interconnector
Approximate linear correlation
- Different methods to determine correlation (loss factor)
Linear correlation?
- Losses not linear to physical flow - Physical flow may deviate from exchanges on all interconnectors, AC as well as DC. Correlation may differ, may also depend on exchanges on other interconnectors and will have a certain randomness and correlation bias (positive or negative, negligible or not) depending on the grid topology. For certain topologies a multi-variate correlation may exist with the exchanges on a set of interconnectors. If this multi-variate correlation can be approximated by a linear factor on each of the interconnectors in the set, then all interconnectors in that set should have a marginal cost factor assigned (e.g. loss factor).
Table 1: Marginal welfare losses caused by DC and AC exchanges
Where marginal costs of the grid inside a bidding zone incurred by exchanges with other bidding zones can be higher than the marginal costs incurred on the interconnector itself, there seems no obvious economic argument for activation of only losses on the interconnector as a welfare loss in the allocation or for not including losses on only the interconnector. Vice versa, if it can be made plausible that the marginal costs of flows inside bidding zones incurred by interconnector exchanges are relatively small compared to the marginal costs on the interconnector, this seems a potential economically viable reason to activate only the losses on the interconnector as a welfare loss in the allocation. This does not depend on the kind of interconnector: it is equally applicable for a DC interconnector as well as for an AC interconnector.
2.4. Inclusion of losses in market coupling
.From ENTSO-E investigation on losses it has been concluded that the optimal way to include losses incurred by an exchange in the market coupling algorithm is to include these losses in the overall supply and demand equilibrium constraint. Appendix II describes how this should be represented in the mathematical model of the market coupling. The PCR algorithm is specified according to this model. The ENTSO-E investigation did not make any conclusions on the actual decision to apply a loss factor in the allocation.
9
Main conclusion from the mathematical modelling is that the price characteristics will slightly change between areas that share an interconnection with a loss factor included2:
price on export side <= (1-loss factor)*(price on import side) This can be rewritten as:
loss factor <= (price on import side – price on export side)/(price on import side)
Where the right side of this inequality will be referred to in the rest of this document as remaining relative price difference.
2 Note that this property does not hold in case of adverse flows, e.g. due to intertemporal constraints (e.g. ramping constraints, block orders selections)
10