U/I Mapping

The problem often arises that the voltages U₁, U₂, and U₃ and the currents I_a, I_b and I_c are connected to a power meter and it must then be determined which voltage corresponds to which current. Formally, the goal is to find a bijective mapping between currents I_a, I_b and I_c to voltages U₁, U₂, and U₃. Since this problem cannot generally be solved (except by tracing the cables), the following assumptions have to be made:

• Right-hand rotation field
• Power flow is either feeding in or consuming

From the assumptions, it follows that the angle between current and voltage is only a maximum of 90 degrees. Therefore, the phases of the resulting currents of the voltages U₁, U₂, and U₃ lie in the following ranges:

  -90° ≤ φ_I1 ≤   90°
-210° ≤ φ_I2 ≤ -30°
   30° ≤ φ_I3 ≤ 210°

This results in areas that are exclusive to some phases and others that are shared by two subsequent phases:

Fig.21: EL3475 - U/I mapping, Phases

The respective relationship between current and voltage can then be derived from these areas using a process of elimination.

Example

Let us assume three currents I_a, I_b and I_c having the following phases:

φ_a =     0°
φ_b =  -90°
φ_c = 150°

The mapping a = L1 is unique.

Since I_L1 is already determined, I_b is mapped to L2.

Finally, c = 3 can be determined.