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Offering strategy of a price-maker PV power plant: multi-stage stochastic programming with probabilistic constraints

Due to the implementation of Feed-in-tariffs and government subsidies, the solar and wind power industries have experienced a period of rapid growth with an ever increasing installation rate. However, as solar and wind power industries mature, more and more governments have announced cuts to subsidies. As a consequence, PV and wind power producers urgently need to develop optimal offering strategies to make a profit when depending entirely on markets instead of government supports and incentives.
A lot of work has been done on the topic, but so far most of it orients at developing strategies for PV power plants or virtual power plants in a price-taker setting, or modeling it as a price-maker considering only two conventional electricity markets: day-ahead and balancing market. However, because of the uncertainty nature of PV output and the fact that the forecast error is highly related to the lead time, the intraday market is more interesting to PV plant operators. The intraday trading takes place closer to real-time and it provides opportunities to adjust schedules and to trade with lower uncertainty levels. Therefore, considering a complete market structure (including day-ahead, intraday and balancing market) is highly important when designing the optimal offering strategies for PV power plants. Furthermore, as the trading volume in intraday market is generally lower than that in the day-ahead market, the intraday market price is more vulnerable to PV energy offers and the market power of PV should be taken into account in intraday markets.
To our knowledge, no prior work considers the market power of PV power plants in both day-ahead and intraday markets. However, with the further expansion of PV capacity and the deepening interests of PV power operators in market participation, this is becoming increasingly interesting. The goal of the paper is threefold, to optimize the offering strategies for a PV power plant in a multi-market environment, to investigate the impacts of PV power offers on electricity markets and the effects of different uncertainties on the results.
We design optimal offering strategies for a PV power plant considering three trading floors: 1) The day-ahead markets that clears the day before energy delivery; 2) The intraday market that allows for modifications after the closure of day-ahead markets; and 3) Balancing markets that are used to correct all remaining imbalances.
The PV power plant is modeled as a price-maker in both day-ahead and intraday markets, and as a deviator in the balancing market. Optimal offerings in day-ahead and intraday markets are formulated using complementarity models and the hierarchical structure is presented as a three-level optimization problem. The two lower-levels represent the market clearing of the day-ahead and the intraday market, respectively. The upper-level represents the profit maximization of the PV power plant. The three-level optimization problem is transformed into a mixed integer linear programming model using the Karush-Kuhn-Tucker (KKT) optimality conditions and the strong duality theory.
The PV plant operator faces different levels of uncertainties such as rival producers’ offers and PV outputs. Uncertainties concerning rival’s offers are modeled using scenarios, and the optimization problem is solved using multistage stochastic programming. To ensure the robustness of the model, instead of using scenarios, the PV output uncertainty is taken into consideration by formulating probabilistic constraints. The PV forecast error is modeled as Gaussian random variables and the chance constraints are analytically reformulated into deterministic ones without adding computational complexity to the original problem.
Within the context, the contributions of this paper are threefold:
1) To propose a stochastic three-level model that allows strategic offerings for a PV power plant that acts as a price-maker in both day-ahead and intraday markets, and as a deviator in the balancing market.
2) To model the uncertainty regarding PV production using probabilistic constraints and combine it with stochastic programming
3) To validate the model using a modified Swiss system.
A real-world case study based on a modified Swiss system is used to demonstrate the effectiveness of the proposed model. In conclusion, in this paper, we have presented a stochastic three-level model to derive optimal price-maker trading strategies for a PV power plant in a multi-market environment incorporating probabilistic constraints.

Author(s):

Xuejiao Han    
ETH
Switzerland

Evaggelos Kardakos    
ETH
Switzerland

Gabriela Hug    
ETH
Switzerland

 

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