A Robust Optimization Approach to Bidding Strategy for Generation Companies in Electricity Competitive Market Using Fuzzy Possibility and Necessity Theory

Abstract
The main aim of this research is to obtain the optimal bidding and offering curves of electricity generation company (GenCo) to determine the price and the amount of power for offering in day-ahead electricity market based on a step-wise offering approach to maximize the profit. The proposed model has two sections; in the first section, a method is suggested to obtain step-wise price bids, and in the second part, different amounts of offering power for each bidding price to electricity market is determined by modeling a self-scheduling problem. The robust optimization method investigates the effect of market price uncertainty on the optimal profit, in order to reduce the sensitivity of the optimal result to the deviation of uncertain parameter. This paper proposes a robust optimization approach by applying fuzzy methods to achieve the optimal self-scheduling solution. The robust mixed-integer linear programing model is formulated in a robust manner against different levels of the electricity price uncertainty. Finally, sensitivity analysis is used to validate and evaluate the performance of the proposed model under different uncertainty situation and the resistance of the model in variations of uncertain parameter is illustrates the robustness of model.
Introduction
In a competitive market environment, a GenCo, attempt to acquire an optimal bidding strategy in a secure way, which hedged against any realization of the electricity prices deviation. The uncertainty associated with the electricity market prices is modeled via the fuzzy forecasted value to be used for solving self-scheduling problem and offering to electricity market. The self-scheduling of a GenCo is a complex optimization problem. The first aspect of this complexity is the necessity to encounter all equality and inequality constraints of the generating units such as minimum on/off duration, generation capacity limits, ramping up/down limits of generating units. The second aspect is electricity market price uncertainty and its volatility which affects the optimal result. This paper proposes a robust optimization framework to optimize self-scheduling and bidding strategy to electricity market considering pay-as-bid pricing mechanism, which enables the GenCo to make robust decisions and to schedule the power generation of units against the uncertain energy price.
Case study
To evaluate effectiveness of the proposed robust optimization model, it is employed on the gas-fired thermal generation units with Siemens V94.2 turbines.
Materials and methods
To propose a robust self-scheduling technique, a mathematical modeling approach is applied by using a mixed-integer linear programming problem considering fuzzy price uncertainty, which is implemented in Lingo software for a case study of thermal generation unit to investigate the efficiency of the proposed model. Fuzzy possibility and necessity techniques are used for robust optimization modeling to solve self-scheduling problem and offering strategy to electricity market. Robust optimization approach is a form of risk management methods that has a low computing volume comparing to other methods such as stochastic programming and nonlinear methods to address data uncertainty in mathematical programming model.
Discussion and results
In this paper the construction of hourly offer curves is designed based on a robust approach and the price forecast are obtained by fuzzy concepts. The robust methods can deal with uncertainty of market price is more desirable rather than deterministic and stochastic methods. In deterministic methods price uncertainty can’t be considered and in stochastic methods the probability of the uncertain parameters needs to be determined which is a difficult job.
In the proposed method, step-wised price bids are generated by a fuzzy measure based on possibility and necessity technique. The proposed method enables decision makers to adjust their desired level of robustness by fuzzy measure confidence adjustment parameter (π) and to arrange bidding price from lower risk and upper acceptance level to higher risk and lower acceptance level. Also in the self-scheduling model, a fuzzy credibility technique is introduced to deal with fuzzy constraint. This technique empowers decision makers to adjust the level of conservatism and fuzzy constraint satisfaction based on their risk aversion or risk seeking manner. Since robustness level is antithetical to profit values, a higher degree of conservatism or robustness, leads to the lower values of profit. The proposed model lets decision makers to choose optimal bidding strategy by adjusting the robustness level according to their risk aversion level. If decision makers want the greater profit values, they should adjust lower robustness level, but if they want to be resistant to the risk of bidding rejection in electricity market, they must intend the higher degrees of conservatism and robustness.
Conclusion
In this paper the sensitivity of a GenCo’s profit to the level of market price uncertainty is investigated. In this regard, a robust approach is proposed by applying fuzzy possibility and necessity measure to deal with uncertainty which enables decision makers to adjust their desired risk level. In addition, sensitivity analysis is used to validate and evaluate the performance of the proposed model and a simulation method is applied to indicates the robustness of model. By comparing the results of the robust model and the deterministic model, it can be concluded the solution of the proposed model is more robust dealing with variations of price uncertainty. As results indicate, the risk aversion decision makers should adjust higher robust level to hedge themselves from the risk of rejection in electricity market and risk seeker decision makers should adjust lower robustness to gain higher profit. Accordingly, the proposed approach is suitable for both risk averse and risk seeker decision makers participating in pay-as-bid electricity market.