Identification of the Worst-case Static Voltage Stability Margin Interval of AC/DC Power System Considering Uncertainty of Renewables

Calculation of static voltage stability margin(SVSM)of AC/DC power systems with lots of renewable energy sources(RESs)integration requires consideration of uncertain load growth and renewable energy generation output.This paper presents a bi-level optimal power flow(BLOPF)model to identify the worst-case SVSM of an AC/DC power system with line commutation converter-based HVDC and multi-terminal voltage sourced converter-based HVDC transmission lines.Constraints of uncertain load growth’s hypercone model and control mode switching of DC converter stations are considered in the BLOPF model.Moreover,uncertain RES output fluctuations are described as intervals,and two three-level optimal power flow(TLOPF)models are established to identify interval bounds of the system worst-case SVSM.The two TLOPF models are both transformed into max–min bi-level optimization models according to independent characteristics of different uncertain variables.Then,transforming the inner level model into its dual form,max–min BLOPF models are simplified to single-level optimization models for direct solution.Calculation results on the modified IEEE-39 bus AC/DC case and an actual large-scale AC/DC case in China indicate correctness and efficiency of the proposed identification method.

Distributionally Robust Optimal Dispatch of Offshore Wind Farm Cluster Connected by VSC-MTDC Considering Wind Speed Correlation

Multi-terminal voltage source converter-based highvoltage direct current(VSC-MTDC)transmission technology has become an important mode for connecting adjacent offshore wind farms(OWFs)to power systems.Optimal dispatch of an OWF cluster connected by the VSC-MTDC can improve economic operation under the uncertainty of wind speeds.A two-stage distributionally robust optimal dispatch(DROD)model for the OWF cluster connected by VSC-MTDC is established.The first stage in this model optimizes the unit commitment of wind turbines to minimize mechanical loss cost of units under the worst joint probability distribution(JPD)of wind speeds,while the second stage searches for the worst JPD of wind speeds in the ambiguity set(AS)and optimizes active power output of wind turbines to minimize the penalty cost of the generation deviation and active power loss cost of the system.Based on the Kullback–Leibler(KL)divergence distance,a data-driven AS is constructed to describe the uncertainty of wind speed,considering the correlation between wind speeds of adjacent OWFs in the cluster by their joint PD.The original solution of the two-stage DROD model is transformed into the alternating iterative solution of the master problem and the sub-problem by the column-and-constraint generation(C&CG)algorithm,and the master problem is decomposed into a mixedinteger linear programming and a continuous second-order cone programming by the generalized Benders decomposition method to improve calculation efficiency.Finally,case studies on an actual OWF cluster with three OWFs demonstrate the correctness and efficiency of the proposed model and algorithm.