# Experiment 3: Phase Sequence Measurements

## Objectives

To understand the phase sequence of a three phase supply and study methods to measure the phase sequence of a given power supply.

## Background:

Given a 3-phase voltage source on the three wires a, b, and, c. If the voltage waveform of wire a, is the one numbered 1 as shown in Fig. 1, which waveform represents the voltage of wire b? If that waveform is the one numbered 2 in Fig. 1, then the voltage sequence is abc. If on the other hand, the waveform representing the voltage of wire b is waveform 3, then the sequence is acb. You will examine several ways that the phase sequence can be determined.

The direction of rotation of polyphase induction and synchronous motors depends on the phase sequence of the applied voltages. Also, the two wattmeters in the two wattmeter method of measuring three-phase power interchange their readings when subjected to a reversal of phase sequence, even though the system is balanced. Magnitudes of the various currents and component voltages in balanced systems are not affected by a reversal of phase sequence.

If the phase sequence of the applied voltages is reversed in an unbalanced system, certain branch currents change in magnitudes as well as in time phase, although the total watts and vars generated remain the same.

In practice it is desirable, and sometimes necessary, to know the phase sequence of a three- phase power system. For example, when paralleling 2 three-phase transformers, if the wrong sequence is assumed the result could be catastrophic.

One method of determining phase sequence is based on the direction of rotation of induction motors. Another method uses the oscilloscope as in the circuit of Fig. 2.

A wattmeter can also be used to determine the phase sequence. A 3-phase inductive load can be connected and a wattmeter is used such that ia is passed through the current coil of the wattmeter, then the reading of the wattmeter will be proportional to either cos( 30 + phi) or cos(30 – phi) depending on whether V12 or V13 is applied to the voltage coil. Other methods, discussed below, depend on unbalanced polyphase circuit phenomena.

### Method 1

Generally, any unbalanced set of load impedances may be employed as a voltage phase sequence checker. The effects produced by change in phase sequence can be determined theoretically, and when an effect peculiar to one sequence is noted, that effect can be used to designate the phase sequence of the system

If lamp a is brighter than lamp b the phase sequence of the line to line voltages is ab, bc, ca. If lamp b is brighter than lamp a, the phase sequence is ab, ca, bc.

The circuit in Fig. 4 (taken from the web, but the source does not exist anymore) uses a capacitor instead of the inductor of Fig. 3.

If lamp S is brighter than lamp T the phase sequence of the phase voltages is RST. If

Lamp T is brighter than lamp S, the phase sequence is RTS.

### Method 2

Another type of circuit for checking phase sequence in 3-phase systems is the unbalanced circuit arrangements shown in Figure 5.

### Method 3

Another voltage sequence checker may be made using the circuits shown in Fig. 5. The current taken by the voltmeter should be negligible compared with the current through X and R.

## Procedure

- Arrange to set up a circuit like the one of Figures 3 or 4. Determine the impedance of each part of the circuit. (Note that the resistance of a lamp measured by an ohm meter is significantly different than the resistance while operating. This is because of the change in resistivity with temperature.)
- Calculate the voltage across lamp a(S) and lamp b (T) for each phase sequence. Apply 208 volts, 3-phase of each phase sequence to circuit, and note which lamp is brightest. Determine the phase sequence from your tests. Measure the voltages across the three load elements (the lamps and the reactive element) and compare your readings to your calculations.
- Verify your determination of the phase sequence at your bench using the circuit of Fig. 2. Ask your instructor to reset your phase sequence to an unknown sequence.
- Arrange to set up one of the circuits in Figure 5. Calculate the voltage read by the voltmeter for each possible phase sequence. Next, use the circuit to determine the phase sequence from test. Compare watts and vars taken by the above circuits for the two possible phase sequences.
- Check this new phase sequence with the circuit of figure 2.

**Historical note:**

Prior to 1887 the scientific world believed that one of the defining features of a metal was its positive temperature coefficient of resistivity (Why?). One of the many inventions of Edward Weston, a founder of NJIT, was a metallic alloy with a negative coefficient of resistivity. This invention was a key to developing stable readings in his development of the portable first direct-reading instruments for the measurement of electricity.

## Analysis

In the circuit of Fig. 4, assume the current entering the terminals RST (towards the C and the lamps) are I_r, I_s, and I_t. Write KVL to give the voltage between R and S in terms of I_r, I_s, and I_t. Similarly write KVL for the V_ST, and V_TR. Since these voltages are known and assumed balanced, you can obtain three equations in the three unknowns I_r, I_s, and I_t. Can you find the currents if the voltages and the circuit elements (Ra, Rb, and C) are known? If not, why not? You may find useful hints in the following Matlab-like statement:

V_rs= (-j/Xc)Ir - Rs*Is

V_tr = (j/Xc)Ir +Rt*It

V_st = -Rt*It + Rs*Is

V_st = 1; V_tr = a^2; V_rs = a; V=[a ;a^2;1];

Z=[-j/Xc -Rs 0; j/Xc 0 Rt; 0 Rs –Rt];

Function[Ir, Is, It]=sequence(a,Xc,Rs,Rt)

## Report

Your report should include a phaser diagram for the circuit of diagram 3 or 4 which you used. You should also calculate the voltages and light bulb powers for the two different possible phase sequences and see if this agrees with the manual text. You should do the same for whichever circuit of figure 5 you built. In addition to this analysis, you should include the usual elements, abstract, procedure, data, analysis and conclusions.

## Bibliography

1- http://www.ibiblio.org/kuphaldt/electricCircuits/AC/AC_10.html under Design Science License.