3-Phase Relationships

Introduction

If you are performing electrical work in commercial or industrial settings, it is extremely important that you fully understanding 3-phase relationships. At some point, Electricians or Electrical Engineers in this field will need to work with systems and equipment that are connected to 3-phase power. Such as: services, feeders, circuit breakers, branch circuits, wiring, transformers, load centers, panelboards, switchboards, motors, drives, contactors, HVAC systems, control systems, and a long list of machines. If you work in any of these areas, you need to read this post several times over and commit the basic principles to memory.

At some point, all 3-phase power originates from a 3-phase transformer secondary winding. And that transformer also has a primary winding to receive that power from the utility or some other separately derived system like a generator, or renewable energy source. The winding configurations shown below, called delta and wye (or star), are the most common winding configurations you will see in 3-phase systems. Notice, the delta winding is shaped like the Greek letter “D” and the wye winding is shaped like the English letter “Y” (also sometimes called star).

Although the most common transformer winding configuration you will see is Delta-Wye, there are actually 4 main types of transformer configurations possible:

1. Delta-Wye

2. Wye-Delta

3. Delta-Delta

4. Wye-Wye

Since the topic of this post focuses only on 3-phase relationships, and not on transformers, we will only discuss where the 3-phase electrical power comes from…the transformer secondary winding. We will also discuss the voltages in each electrical system type and how they are derived.

NOTE: All systems are 60HZ unless otherwise noted.

Delta Secondary Connection

The delta connection shown above has each end of the 3 phases connected together to form 3 corners. These corners are then connected to the conductors feeding an electrical system.

Although delta connections are very useful for balanced loads, motor applications, and eliminating 3rd harmonics, if a load requires a truly balanced neutral, it cannot be connected. However, delta systems are often misunderstood. Below are the three common uses of a delta winding on a transformer secondary:

1. Floating: The three corners of the delta arrangement are connected to the line conductors. These line conductors then feed the system accompanied by a system grounding conductor which originates from the transformer chassis ground and the grounding electrode connected to the transformer chassis ground via a bonding jumper (see below). The final bundle of conductors fed to the electrical system are 3 phase conductors and 1 system grounding conductor. This is a 3P4W (3-pole, 4-wire) electrical system.

2. High-Leg (also called wild-leg): The three corners of the delta arrangement are connected to the line conductors. Then a neutral conductor is connected to a grounded center-tap in the phase winding directly across from the customary B-phase (high-leg) line connection. This grounded center tap is also bonded to the grounding electrode. Finally, a system grounding conductor is also added as previously discussed. NOTE: The high-leg phase conductor is required to be permanently labeled and marked at all connection points using either several wraps of orange electrical tape, orange conductor insulation, or orange heat-shrink. The final bundle of conductors fed to the electrical system are 3 phase conductors (one of which is a high-leg), 1 neutral conductor, and 1 system grounding conductor. This is a 4P5W (4-pole, 5-wire) electrical system.

3. Corner-Ground: The three corners of the delta arrangement are connected to the line conductors. Then any corner of the delta arrangement is grounded (the B-corner-ground is customary) to create a neutral in the winding (labeled and colored usually gray and white as a neutral). Finally, an equipment grounding conductor is added as previously discussed (see below). The final bundle of conductors fed to the electrical system are 2 phases, 1 corner-grounded neutral (which is also bonded to the grounding electrode), and 1 system grounding conductor. This is a 3P4W (3-pole, 4-wire) electrical system.

Wye Secondary Connection

The wye connection (shown above) has one end of each winding left open and the other end of each winding connected together to form a neutral. That neutral is grounded and bonded to the system grounding electrode. A wye system should NEVER be floating! The neutral should ALWAYS be grounded AND bonded. Without grounding and bonding in a wye system, load shifting and drift will always be a problem. Even if only a small imbalance is coming from the utility company, it would be impossible to stabilize the system and protect it from transient surges on individual phases. There is only ONE way to wire a wye system, but it is still highly versatile because its neutral is independent from the phases. It is able to supply two independent voltages on 3 different phases, and does not require additional transformers to supply a neutral. This makes a wye system the easiest, most cost-effective, and most versatile option, which explains why it is the most common.

Voltage Derivations & Calculations

For 480VAC, 3-Phase, 60HZ Floating Delta:

3-Phase Voltage = 480VAC

All Line to Line Voltages = 480VAC, Single-Phase

For 240VAC, 3-Phase, 60HZ Delta High-Leg:

3-Phase Voltage = 240VAC

All Line to Line Voltages = 240VAC, Single-Phase

A-Phase to Neutral Voltage = 120VAC, Single-Phase

240VAC / 2 = 120VAC

B-Phase (High-Leg) to Neutral Voltage = 208VAC, Single-Phase

(240VAC * 1.732) / 2 = 208VAC

C-Phase to Neutral Voltage = 120VAC, Single-Phase

240VAC / 2 = 120VAC

A or C-Phase to Ground Voltage = 120VAC (If neutral is properly bonded to ground.)

B-Phase (High-Leg) to Ground Voltage = 208VAC (If neutral is properly bonded to ground.)

For 480VAC, 3-Phase, 60HZ Delta, B-Phase Corner Ground:

3-Phase Voltage = 480VAC (A to B, B to C, A to C)

A or C-Phase to Ground Voltage = 480VAC (if properly grounded.)

B-Phase to Ground Voltage = 0VAC (corner grounded)

For 480Y/277VAC, 3-Phase, 60HZ Wye:

3-Phase Voltage = 480VAC (A to B, B to C, A to C)

Any Phase to Neutral Voltage = 277VAC

480VAC / 1.732 = 277VAC

Any Phase to Ground Voltage = 277VAC (if neutral is properly bonded to earth ground or single point.) NOTE: Neutral should always be bonded and grounded to earth ground or single point to prevent load shifting and drift, and to protect the system from transient surges.

For 208Y/120VAC, 3-Phase, 60HZ Wye:

3-Phase Voltage = 208VAC (A to B, B to C, A to C)

Any Phase to Neutral Voltage = 120VAC

208VAC / 1.732 = 120VAC

Any Phase to Ground Voltage = 120VAC (if neutral is properly bonded to earth ground or single point.) NOTE: Neutral should always be bonded and grounded to earth ground or single point to prevent load shifting and drift, and to protect the system from transient surges.

Schematic/Wiring Diagrams and Voltage Meaurement Points Below:

Delta High-Leg, 240/120/208VAC, 60HZ

Delta High-Leg, 480/240/415VAC, 60HZ

Delta Corner-Ground with Disconnect

Delta Corner-Ground with Service Panel

Wye System: 208Y/120VAC, 60HZ

3-Phase Voltage & Current Relationships

Wye Connection:

• The current in each winding is equal to the line current I.

• The voltage across each winding is equal to the line voltage E divided by 1.73.

• The voltage across the windings are 120 degrees out of phase.

• The currents in the windings are 120 degrees out of phase.

Delta Connection:

• The current in each winding is equal to the line current I divided by 1.73.

• The voltage across each winding is equal to the line voltage E.

• The voltage across the windings are 120 degrees out of phase.

• The current in the windings are 120 degrees out of phase.

Conclusion

It is important to note that 3-phase relationships apply to any load connected in 3-phase. This includes windings (inductive), heater elements (resistive), and capacitive loads (capacitor banks, large filter capacitors, motor starting capacitors, etc.). Exception: If a circuit is purely resistive (non-reactive), power factor = 1. Therefore, PF is not shown in the 3-phase formulas for resistive loads. This is why resistive loads are always rated in KW instead of KVA…because there is no reactive component in resistive loads. Furthermore, with resistive loads, the current and voltage will be in phase but the three ungrounded lines will still be 120 degrees out of phase. For more information on 3-phase systems, see our other posts on 3-Phase Transformers, 3-phase Induction Motors, Power Factor, Panelboards, and Switchboards here at Electrician’s Journal. Enjoy!