A risk-based distributionally robust real-time dispatch approach is proposed to strike a balance between the operational costs and risk as well as considering the nodal voltage security even when the distribution of uncertainties cannot be precisely estimated. To model uncertainties, a data-drive ambiguity set is developed based on the imprecise probability theory without any presumption on the probability distribution of uncertainties. The obtained ambiguity set is based on the confidence interval, which can be constructed according to actual needs by choosing the point-wise or family-wise confidence interval. Two strategies for wind farms to provide voltage support are incorporated in the proposed approach so that the nodal voltage security can be ensured. By incorporating the risk tractable estimation method and sequential convex optimization method, an efficient algorithm is developed to release the computational burden. Numerical results show that compared with the regular robust optimization, the proposed approach reduces the total operational cost to achieve statistically optimal dispatch decisions. The proposed approach also outperformances the stochastic programming in term of the operational risk reliability. Meanwhile, the nodal voltage security issues can be mitigated with the voltage support from wind farms. In conclusion, under the uncertainty of probability distributions, the proposed approach can efficiently strike a balance between the operational cost and risk while ensuring the nodal voltage security.
- Confidence interval
- Distributionally robust optimization
- Real-time dispatch
- Voltage security