In a three-phase ac system, a power source with three wires delivers ac potentials of equal frequency and amplitudes with respect to a zero-potential wire, each shifted in phase by 120° from one wire to the next. Two possibilities exist for establishing a phase sequence. In the first, voltage on the second wire shifts by 120° relative to the first, and, in the second, a –120° shift occurs with respect to the first wire. Phase order determines the direction of rotation of three-phase ac motors and affects other equipment that requires the correct phase sequence: a positive 120° shift. You can use a few low-cost passive components to build a phase-sequence indicator.

Figure 1. |
This conceptual circuit can detect both phase sequences. |

Figure 1 shows a conceptual circuit that can detect both phase sequences. For certain component values, the following conditions apply: The voltages across R_{1} and C_{2} are equal – that is, their magnitudes and phases are the same – only when V_{S2} occurs exactly 120° ahead of V_{S1}, which indicates the correct phase sequence. In this case, the voltage between points A and B is zero. Conversely, the voltages across C_{2} and R_{3} are equal only when V_{S2} is ahead of V_{S3 }by 120°, which corresponds to a reversed sequence.

Figure 2. |
When the voltages across R_{1} and C_{2} are equal,V _{C1} = –V_{R2}, V_{C1} + V_{R1} = V_{S1}, and V_{C2} + V_{R2} = V_{S2}. |

Referring to the phasor diagram in Figure 2, when the voltages across R_{1} and C_{2} are equal,

and

The following equations satisfy these conditions:

and

You calculate the component values by solving the following equations:

and

where

and f represents the frequency of the V_{S} voltages.

Also, to ensure detection of a reversed phase sequence, C_{1} = C_{3}, and R_{1} = R_{3}; that is, the components in the third branch are identical to those in the first branch. The phase-sequence-detection circuit in Figure 3 eliminates the requirement for an accessible ground wire by adding resistors R_{4} and R_{5} that connect in parallel with the first and third branches. Eliminating the ground-wire requirement also dictates a ratio between |X_{C1} + R_{1} | and |X_{C2} + R_{2 }|. For no current to flow to ground from Node G, the sum of currents in the branches must equal zero, and, if you disconnect Node G from ground, its potential with respect to ground is also zero.

Figure 3. |
This phase-indicator circuit balances branch voltages and currents and requires no ground reference.These component values are for a 60-Hz line frequency. |

As long as the proportions of X_{C1 }to R_{1}, X_{C2} to R_{2}, and X_{C3} to R_{3} remain as noted, the balance of voltage drops remains across R_{1}, C_{2}, and R_{3}. Multiplying the impedance of any branch by a constant influences only the magnitude of the currents through the respective branch. The current through any branch presents the same phase angle as the voltage across a resistor in the branch. The phasor diagram in Figure 4 shows the currents in Figure 3. From this diagram, if

then

Thus, I_{3} has half the magnitude of and an exactly opposite direction from (I_{1} + I_{2}).

Figure 4. |
I_{3} has half the magnitude and an exactly oppositedirection to (I _{1}+ I_{2}) in Figure 3. |

A vector diagram of the currents shows that adding two currents, each with magnitudes equal to I_{3} and the same phases as V_{S1} and V_{S3}, produces a summed current with the same magnitude and phase as I_{3}; therefore, the total current at Node G is zero:

To make the sum of the currents equal zero,

The two LEDs in Figure 3 indicate correct or reversed-phase sequence. When LED_{2} lights and LED_{1} remains dark, the voltage between nodes A and B is 0 V, which corresponds to a correct phase sequence. A reversed-phase sequence lights LED_{1} while LED_{2} remains dark. The diodes connected in parallel with the LEDs protect against exceeding the LEDs' reverse-breakdown voltages, and resistors R_{6} and R_{7} limit forward currents through the LEDs. For greater sensitivity, you can replace the LEDs with high-input-impedance ac-detector circuits.

The circuit's final version includes indicators that show whether all three phases carry voltage. In the circuit in Figure 3, a phase that carries 0 V lights both LEDs. Depending on your application, you can connect voltage-detection circuits comprising LEDs and protection diodes in series with current-limiting resistors between V_{S1}, V_{S2}, and V_{S3} and Node G. You can also use low-wattage neon lamps with appropriate series-current-limiting resistors.

When selecting components, ensure that their values conform to the following proportions. For an arbitrarily chosen value for C_{1},

and

When you select a value for C_{1}, the currents through the detection circuitry should be significantly lower than the currents through the branches, which excludes arbitrarily low values for C_{1}.