Application of Newton-based load flow methods for determining steady-state condition of well and ill-conditioned power systems: A review

© 2019 Load Flow (or power flow) is the most essential analysis for power system planning, operation and control providing the initial conditions (equilibria) for power system analyses such as stability, and security assessments. The continuous increases in load demand as well as the increased intermittency in generation due to renewable sources without the corresponding augmentation in transmission facilities have forced power systems to operate closer to their limits. Although the load flow solution might be available in such conditions, the classical Newton-based load flow methods may fail due to numerical difficulties such as singularity of Jacobian Matrix. An alternative way is to use methods that are able to find multiple solutions such as Path Following Methods (PFM) and State Space Search Methods (SSSM). However, at close maximum loading point, these methods are unable to determine the appropriate solution that guarantees the system voltage profile. Hence, the main motivation is to give a comprehensive review on power flow methods in well and ill-conditioned power systems. In this context, the first order and second order Newton-based load flow method for well-conditioned power systems are presented. Subsequently, the SSSM and PFM are presented as load flow solution scheme in ill-conditioned transmission systems. This is then followed by reviewing conventional distribution load flow methods. At the end, the Non-Physical Load flow solution zone in an ill-conditioned system is discussed.