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Delegates are invited to meet and discuss with the poster presenters in this topic directly after the session 'Electrical aspects and grid integration' taking place on Thursday, 13 March 2014 at 09:00-10:30. The meet-the-authors will take place in the poster area.

Fiona Foucault Mines ParisTech, France
Fiona Foucault (1) F P Robin Girard (1) Georges Kariniotakis (1) Aikaterini Liakopoulou (1)
(1) Mines ParisTech, Sophia Antipolis, France

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Presenter's biography

Biographies are supplied directly by presenters at EWEA 2014 and are published here unedited

Fiona Foucault received the Renewable Energy Science & Technology Masters degree from Ecole Polytechnique in 2013 and a Master degree in Statistical Modeling from Télécom Sudparis. She is currently pursuing a Ph.D degree at the Center PERSEE for Processes, Renewable Energies
and Energy Systems of MINES ParisTech in Sophia Antipolis, France. Her research interests are in the fields of Electricity and nodal prices markets, planning and Optimization.


Wind farm strategic investment considering forecast errors penalties in a nodal prices market


In a fully liberalized context renewable energy is sold on day-ahead market according to production forecasts. However, in the real-time financial penalties are charged for unbalances between expected and delivered injections. This paper addresses this issue by proposing a model to derive optimal bidding strategy taking into account penalties charged for unbalances due to forecast errors. This work is undertaken in a nodal pricing market to take into account grid optimization.


The optimal bidding strategy is obtained by solving a bilevel optimization problem.
The upper level objective function represents the wind producer’s minus profit for a day. A first term corresponds to the earnings on the market, i.e. the product of accepted energy blocks with the corresponding nodal prices. A second term relates to the operational costs. A third term corresponds to the average penalties for imbalances in different scenarios. In this work, we only take into account the imbalances coming from forecast errors for the wind production, but we could easily account for imbalances coming from unexpected breakdowns in the same way. The imbalance pricing system chosen is the same as applied in the American PJM market.
The lower level problems consist of the day-ahead market clearing, and real-time market clearings for different scenarios accounting for the confidence set of the day ahead forecast. The offer prices for wind production are optimization variables while other participants are considered non-strategic i.e they bid their marginal cost of production.
In both cases the market clearing corresponds to the maximization of social welfare. The demand term being fixed in this work, it is equivalent to the minimization of generation cost.
This minimization is carried out under constraints for production levels (which are revised according to the scenarios for real-time market clearing), transmission capacity, and an equilibrium constraint. The latter constraint represents the power balance at each node. The dual variable associated to this equation gives the corresponding nodal price.
In the real time market clearing, an additional reserve term in the objective function accounts for the cost to call an additional production means. This term is the product of energy bought from this new means of production with the marginal cost of such a means of production. The equilibrium constraint is consequently also modified with the reserve volume called in real time.

Main body of abstract

In all electricity markets, penalties for imbalances between actual and expected production are charged to compensate for the system’s extra cost to maintain the system’s balance between production and load at all times. To our knowledge, this aspect is poorly treated in the literature considering wind producers remuneration. “Assessment of wind power predictability as a decision factor
in the investment phase of wind farms” relates to this issue, but sticks to an analysis of historical data. The aim of this paper is to model the penalties in the formation of wind producers’ revenues.
More precisely, the objectives of this paper are threefold :
-To model a wind producer’s revenue formation taking into account the penalties incurred because of forecast errors in a nodal pricing market environment
-Solve the corresponding optimization problem in order to get the optimal grid operations, and the behavior of the wind producer
-Introduce a parameter accounting for the cost of reserve. This parameter enables to model and obtain the wind producer’s remuneration for different scenarios to assess how a potential increase of the cost of reserve might impact the revenue of producers. This enables to transpose this work in a future with high share of renewable energy, where penalties should increase along with reserve cost.

The remuneration of balance responsible parties participating in the market is the product of sales, given by the amount of energy actually sold times the spot price and the imbalance cost, which can be positive or negative and is determined by the amount of error between the forecasted (which serves as an upper bound for the amount bided) and the actual amount of energy delivered times the imbalance price.
Therefore, to carry out this work, a rule to determine imbalance prices has to be chosen.

Considering a nodal prices market environment, we choose to use real-time nodal prices, as is done in the American market PJM.
These real time prices are obtained through market clearings including the actual operations of producers and the participation of reserve. The offer price for reserve is a parameter of the problem.

With this rule, a positive error (i.e. the actual production is superior to expected) is remunerated. However if the market price has decreased enough (because there is too much production compared to demand), this remuneration may not balance the marginal cost of production. If the market price increases (because there is more demand than production) then it is more interesting for the producer as his remuneration will increase. On the contrary, a negative error (i.e. the actual production is inferior to expected) has to be compensated for so that the producer has to buy the missing amount of energy. If the whole system also lacks production then the real-time price increases so that the producer is more penalized than in a case where he is opposing the system’s tendency.

The lower level problems are replaced by their Karush-Kuhn-Tucker conditions so that this stochastic problem is recast as a mathematical program with equilibrium constraints (MPEC ).
It is solved on a three-bus system using CPLEX 12.4.


In a fully liberalized context, the market carries out the electrical system’s operation. Particularly, the grid optimization is carried out through nodal pricing. Nodal prices are obtained by solving a linear DC optimal power flow which serves to carry out the market clearing. In this framework, renewable energy production is no longer remunerated by subsidies, but with its product of sales on the market. In a day-ahead pool-based market, this mode of remuneration implies a risk as penalties are applied for unfulfilled bids, all the more significant as renewable energy such as wind or solar energy knows a greater variability than conventional energy.

To our knowledge, the literature does not consider the impact of penalties for imbalances due to forecast errors when optimizing the operational or investment issues for a wind farm in a market environment. However, these means of production have bigger risks of making such imbalances due to their limited predictability. Moreover, as the share of renewable energy will increase in the energy mix, the imbalances between day-ahead and real-time operations will increase, implying more frequents calls to reserve, especially if production from different sites does not balance out. This should increase the penalties so that this issue will become even more significant.

Our work also introduces the possibility to measure the impact of the cost of reserve on the wind producer’s remuneration. This is a first way to touch on very quickly the problem of the cost for system’s adaptation to a large share of renewable energy.

Learning objectives
This work enables wind producers to choose a strategy to bid in the day-ahead markets taking into account penalties for forecast errors. It helps decision-makers and wind project developers assess the actual revenue of wind farms, as the literature does not take into account penalties in the formation of revenue.

Assessment of wind power predictability as a decision factor in the investment phase of wind farms. R. Girard, K. Laquaine, G. Kariniotakis
Wind power investment within a market environment
L. Baringo, A.J. Conejo
A Benders Decomposition Method for Discretely-Constrained Mathematical Programs with Equilibrium Constraints,S. A. Gabriel, Y. Shim, A. J. Conejo, S. de la Torre, R. García-Bertrand
Pool Strategy of a Producer With Endogenous Formation of Locational Marginal Prices,Carlos Ruiz, Antonio J. Conejo
Transmission and Wind Power Investment, Baringo, Conejo, A.J.