(This Blog is an introductory discussion of the AC power flow at a beginner level. Other Blogs on this site discuss more advanced aspects of the power flow, including convergence and alternative solution methods.)

The Power Flow is a steady-state representation of a meshed three-phase electrical network. It is sometimes characterized as a “snapshot” of electrical operating conditions given a set of assumed electrical customers (loads) and supplies (generators) linked together through a transmission system (grid). A single-phase equivalent of the positive sequence network is used since balanced three-phase conditions are assumed.

A power flow that doesn’t converge is annoying, to say the least. For one, any information you try to use from a non-convergent solution is moot and questionable (recall that a power flow is a solution of a set of equations representing Kirchhoff’s Laws for electric circuits) since the condition it represents may not be physically possible. So what then to do about it?

Divergence Continued

In Part 1, we discussed divergence of the power flow solution. Below is our previous list of reasons for divergence, and additional comments.

Bread and Butter

The power flow is the bread-and-butter tool of power system analysts of large and small-scale transmission systems. It is used in the day-to-day operations of the grid to determine potential congestion, transmission loading relief and need for generation re-scheduling, among others. It is likewise used in short-term and long-term planning to study the potential for thermal overloads, voltage violations and voltage collapse. So it would be disconcerting if a tool of this importance and widespread application should fail, which on occasion it does.

In the accelerated environments of today’s electric energy markets, fast analyses of power flows are a must. Emerging real-time and day-ahead markets require that analysis of infrastructure capacity be performed in a compressed timeframe. Whereas the electric demand of consumers and industry may retain its well-known cyclical nature, varying by time of day, by season and by local weather and social patterns, the supply side of the equation has drastically changed. Competition has engendered even the traditional suppliers of energy to be more flexible and anticipatory to pricing and demand signals, affecting operating and bidding strategy in timeframes that range from the next operating hour to when the next new generation facility can be interconnected. In addition, newer energy sources such as wind and solar power introduce new dependencies which vary hour-to-hour to the supply mix.