Fuzzy curtailment model study for bilateral transaction

Transaction curtailment has become a main measure to relieve congestion so as to maintain system security and reliability. In the NERC´s curtailment model, all parameters are definite. However in practice, the PTDFs are inaccurate and limits for line flows are soft. To represent these fuzzy phenomena, this paper thus proposes the fuzzy curtailment model for bilateral transaction. In this model, the fuzzy curtailment set is defined due to the inaccurate PTDFs, and the fuzzy constraints are presented due to the fuzzy line flow limits. Using the maximum entropy method, this fuzzy optimization problem is solved as the unconstrained optimization problem whose calculation procedure is fast and simple. Test results show that the fuzzy curtailment set can reduce the impact of the computational errors of PTDFs on transaction curtailment, and the fuzzy optimization model leads to less curtailment than the crisp optimization model when small violations of the operational limits are allowed.