Inverse Optimization and Forecasting Techniques Applied to Decision-making in Electricity Markets

This thesis deals with the development of new mathematical models that support the decision-making processes of market players. It addresses the problems of demand-side bidding, price-responsive load forecasting and reserve determination. From a methodological point of view, we investigate a novel approach to model the response of aggregate price-responsive load as a constrained optimization model, whose parameters are estimated from data by using inverse optimization techniques.

The problems tackled in this dissertation are motivated, on one hand, by the increasing penetration of renewable energy production and smart grid technologies in power systems, that is expected to continue growing in the coming years. Non-dispatchable electricity generation cannot ensure a certain production at all times, since it depends on meteorological factors.

Also, smart grid technologies are affecting the consumption patterns that the load traditionally exhibited. On the other hand, this thesis is motivated by the decision-making processes of market players. In response to these challenges, this thesis provides mathematical models for decision-making under uncertainty in electricity markets.

Demand-side bidding refers to the participation of consumers, often through a retailer, in energy trading. Under the smart-grid paradigm, the demand bids must reflect the elasticity of the consumers to changes in electricity price. Traditional forecasting models are typically not able to reflect this elasticity, hence we propose two novel approaches to estimate market bids.

Both approaches are data-driven and take into account the uncertainty of future factors, as, for example, price. In both cases, demand-side bids that comprise a price-energy term decrease the expected imbalances and also increase the profit of retailers participating in electricity markets. In the field of load forecasting, this thesis provides a novel approach to model time series and forecast loads under the real-time pricing setup.

The relationship between price and aggregate response of the load is characterized by an optimization problem, which is shaped by a set of unknown parameters. Such parameters are estimated from data by using an inverse optimization framework. The usability of the proposed method is studied and we conclude that inverseoptimization-based modeling is a computationally attractive method that outperforms the forecasting capabilities of traditional time series models.

Regarding the reserve determination, the special characteristics of the Danish power system do not allow for co-optimizing the unit commitment and reserve requirements. Hence, we propose a probabilistic framework, where the reserve requirements are computed based on scenarios of wind power and load forecast errors and power plant outages.

The solution of the stochastic optimization models increases the safety of the overall system while decreases the associated reserve costs, with respect to the method currently used by the Danish TSO.