# Calculating 3-Phase Line Currents

## Inside this Article

**In PV systems where the 3-phase source is made up of three or more interconnected single-phase inverters, line currents are affected by the arrangement and power rating of the inverters.**

To correctly size line conductors and overcurrent protection devices in a 3-phase system, it is necessary to compute the line currents. This calculation is relatively easy for a wye (Y) connected configuration or for a delta (Δ) connected configuration if the three phases are in balance. If the currents are not balanced across the three phases in a Δ system, however, difficulties arise. In that case calculating the line currents requires an understanding of trigonometry and vector math. With the application of some basic trig and an understanding of the relationships between the phase currents, it is not too difficult to find the line currents. A few shortcuts make the process easier.

**THREE-PHASE SYSTEMS**

There are two types of 3-phase systems in use: Y and Δ. Diagram 1 shows how three single-phase inverters would connect to form each type of system. The a-, b- and c-node labels and arrows indicating the direction of current flow are used for the example calculations that follow.

**Wye.** In the Y connected system, the ac neutral conductors of each inverter are connected at a node, forming the neutral; the ac line conductor of each inverter becomes the line side connection. It is simple to find the line currents, since they are equal to the phase currents in both balanced and unbalanced conditions.

**Delta.** In the Δ connected system, the ac line conductors of the inverters are connected at each corner of the Δ. These three nodes form the line side connection points. There is no neutral node in a Δ system. Even where the building distribution system is connected in a Y configuration, the Δ configuration is commonly used for inverter interconnections. Because there is no neutral current in the Δ configuration, there is no need to reevaluate the existing service neutral conductor ampacity.

**Balanced.** In a balanced 3-phase system, the inverters on each of the three phases have the same voltage and power rating. A balanced system can be made up of any number of inverters connected in parallel in each phase, as long as the total power on each of the three phases is equal. The following are examples of balanced systems.

Phase A | Phase B | Phase C | |

Example 1 | one 6 kW inverter | one 6 kW inverter | one 6 kW inverter |

Example 2 | two 6 kW inverters | two 6 kW inverters | two 6 kW inverters |

Example 3 | two 6 kW inverters | one 12 kW inverter | one 12 kW inverter |

**Unbalanced.** In an unbalanced 3-phase system, the inverter voltage ratings are the same on all the phases, but the power ratings per phase are different. An unbalanced system can be made up of any number of inverters connected in parallel in each phase. The following are examples of unbalanced systems.

Phase A | Phase B | Phase C | |

Example 1 | two 6 kW inverters | one 6 kW inverter | one 6 kW inverter |

Example 2 | no inverter | one 6 kW inverter | one 6 kW inverter |

Example 3 | two 6 kW inverters | one 6 kW inverter | one 8 kW inverter |

While it is possible in theory to have any combination of inverters in an unbalanced system, the local utility interconnection standards typically set a maximum value for the phase imbalance.