Static Voltage Stability and DGs Integration Capacity Quantification Method With Extended Power Flow for ADNs With Grid-Forming and Grid-Following DGs

Power flow calculation and static voltage stability (SVS) analysis of active distribution networks (ADNs) are facing convergence and applicability issues caused by extreme conditions and control strategies of grid-forming (GFM) and grid-following (GFL) distributed generations (DGs). To solve these challenges, an SVS and DG integration capacity quantification method based on extended holomorphic embedding power flow (EHEPF) is proposed which includes four aspects: 1) an EHEPF algorithm is developed that accommodates both convergence and converter’s internal primary and secondary control characteristics of DGs; 2) the unsolvable mathematical expression of EHEPF is derived using Padé approximant to clearly distinguish between no solution and lower-branch (inoperable) solution; 3) the voltage sensitivity and SVS indexes of EHEPF combining different control strategies of DGs are formulated to analyze the weak bus and SVS of ADNs; 4) the DGs integration capacity is quantified by balancing SVS and network loss under voltage distribution calculated in EHEPF. Case studies are carried out on 12 bus, IEEE 33 and IEEE 123 bus systems. Numerous test results are analyzed to verify the applicability, convergence and effectiveness of proposed EHEPF for SVS and DGs integration capacity quantification in ADNs.