Close multiple power flow solutions in power networks

A well-known fact is that power flow problems may have more than one solution, which suggests that power systems may have more than one stable point. While this subject has been explored since the 60´s, the exact conditions for the existence and uniqueness of solutions in power flow problems has never been established. A common assumption is that these solutions are generally either far apart or nonphysical, so power systems operate at one stable operating point. However, this paper shows that any power system may have solutions that are arbitrarily close to each other. Because multiple solutions are not discovered by regular power flow analysis, the existence of two close solutions implies that the real operating point of the system cannot be located. Another outcome is instability. Systems with close solutions are inherently unstable, because they have more than one stable operating point. This paper shows that every network have at least one combination of load powers for which at least two solutions exist. This theoretical result is demonstrated in several power networks.