Power Flow Analysis (3.5): Corrections and Comments of the HELM Video
Channel: Tony the Taiwanese Turtle
Date: 09/04/2022

In the previous power flow analysis video of the holomorphic embedding load flow method (HELM), I said that in the power flow equation, because the node admittance matrix [Y_eq] has rank n–1 (where n is the number of nodes), we need a slack bus whose voltage is pre-determined and fixed. However, as I rethink the problem for a while, I realized that this is not entirely true. While setting up a slack bus is the simplest way to reduce the number variables, there are other possibilities. 

What then, is the implication of the fact that the node admittance matrix [Y_eq] has rank n–1 for HELM? Since there is a non-zero vector {\eta} that satisfies [Y_eq]{\eta} = 0, a non-zero trivial high voltage solution is guaranteed; therefore, HELM will always work for any practical cases.

Click into the following link for the video referred (“Power Flow Analysis (3): Holomorphic embedding load flow method (HELM)”): https://www.youtube.com/watch?v=jn4dKlzjHAQ

Parts of the Video: 
00:00 Main Title
00:08 Statement of the Error
00:56 Reformulation of the Power Flow Equation
01:50 Linking Constraint for Variable Reduction
02:12 Demonstration with an Example where {S} is Known for All Nodes
02:40 Implementation of the Example with HELM
04:00 What does “[Y_eq] has rank n–1” actually mean (for HELM)?
04:17 Main Takeaway of This Video

Information of the series “System Science of Energy Transition”: 
This video is part of the learning material series “System Science of Energy Transition”. The series will cover every aspect of energy transition.

Source of Icons: https://www.flaticon.com/

Software used for making this video:
- Audacity was used for eliminating the white noises of the recordings
- Blender was used for video editing
- Microsoft Powerpoint was used for making the slides