# 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.

## Prelab

Read the Experiment through. Analyze the circuit in Figure 6 for a capacitance of 50 µF and a few values of R (R = |X_{c}|, R = |X_{c}|/2 and R = 2|X_{c}|) to determine which gives you the largest difference in the magnitude of **Vbn** in the figure for the two different phase sequences, abc and acb. You will use the values ofR (R = |X_{c}|, R = |X_{c}|/2 and R = 2|X_{c}|) and C = 50 µF in Fig. 6 of method 3.

## Equipment

- Phase sequence detection box (in lab)
- 3-phase Variac (in lab)
- Capacitor Box
- Resistive Load Cart or Variable Resistor/Rheostat
- Coax cable (BNC to BNC – Check out of stockroom (SR))
- Power lab box with cables and Fluke meter (SR)

## 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**. This is a clockwise rotation or positive sequence with waveform 1 our “reference” voltage source for phase angle (0o), then waveform 2 will have a phase angle of -120o (120o lagging, or 240o leading) and waveform 3 an angle of -240o (or 120o leading). If on the other hand, we have the representation of Fig. 2, then the sequence is

**with a counter-clockwise rotation or negative sequence. Now, waveform 2 will be**

__acb__*leading*120o ahead of 1 instead of lagging, and 3 will be another 120o ahead of 2. 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. The phase sequence also determines the direction induction motors will turn.

There are many possible ways to determine the sequence. A wattmeter can be used to determine the phase sequence. A 3-phase inductive load can be connected and a wattmeter is used such that I_{a} 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

One method of determining phase sequence is based on the direction of rotation of induction motors. This is called **Rotating** type. A three phase supply is connected to the same number of coils producing a rotating magnetic field, and this rotating magnetic field produces eddy EMF in the rotatable aluminum disc.

This eddy EMF produces eddy current on the aluminum disc, due to the interaction of the eddy currents with the rotating magnetic field a torque is produced which causes the aluminum disc to rotate. The clockwise direction rotation of the disc indicates the sequence as __a____b__**c**, and the anti-clockwise rotation of the disc indicates the change in phase sequence (

__a__

__c__**).**

__b__Another method uses the oscilloscope as in the circuit of Fig. 3.

### Method 2

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.

A common type of circuit for checking phase sequence in three-phase systems is the unbalanced circuit arrangements shown below

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

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 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

You are to make measurements on each of the three methods described above to determine the phase sequence and to allow checking of the result by calculations. Generally you will want to know all of the voltages and currents in each of the branches of the circuitry for methods 2 and 3.

### Method 1

Verify the phase sequence at your bench using the circuit of Fig. 3.

- Connect your three phases and neutral from the Variac to the phase-sequence detector.
- Connect the output of the phase sequence detector (BNC) to the oscilloscope.
- Set the scope to trigger on the AC line.
- Adjust the Variac to 20 V
_{LN}. - You should be able to see a waveform similar to Fig. 3 on the scope by adjusting the potentiometers to different levels.
- Save the waveform for this phase sequence and for other possibilities by swapping any two of the wires at a time. Make sure you turn off power every time you swap the wires.

### Method 2

- Arrange to set up a circuit like the one of Figures 5 to 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.)
__Remember, you will have to measure and record the voltages and currents across the three load elements (the lamps and the reactive element) in the following steps for use in your calculations.__ - Apply 208 V
_{LL}from the 3-phase Variac to your circuit without capacitor. Which lamp is brightest? - Apply 5 different values of capacitance to the circuit. Record and measure the voltages and currents across the elements in each step. Turn off the power to circuit.
- Swap any two of the power wires of your circuit. Apply power and repeat step (3).

### Method 3

- Arrange to set up the circuits in Figure 6 with capacitor.
- Connect circuit using R = |Xc|.
- Apply 208 VLL from the 3-phase Variac to your circuit.
- Record and measure V
_{an}, V_{bn}, V_{cn}, I_{ac }, and the powers (S, Q, and P) flowing into your circuit between terminals**A-n**and**C-n**. - Turn off the power and reverse phases
**A**and**C**. Measure V_{an}, V_{bn}, V_{cn}, I_{ac }, and the powers (S, Q, and P) for this phase sequence into terminals**A-n**and**C-n**. - Repeat steps 3 to 5 with new values of R = |Xc| /2 and R = 2|Xc| in circuit of Figure 6.

## Analysis

- Assume both bulbs have resistances equal to the average of their in-circuit operating resistance. Do the following for either the circuit of Fig. 4 or of figure 5. Call the current entering the terminals ABC (towards the C (or L) and the lamps) IA, IB, IC. Write KVL to give three equations for the voltages, VAB, VBC, and VCA in terms of the three currents. Since these voltages are known and assumed balanced, you have three equations in three unknowns. Using KCL at the node labelled n one can easily reduce the number of unknowns to two and use only two of the KVL equations. Some may find this approach easier to follow. A third approach is to use the superposition principle to find the voltage at the central node and from it the voltages across each element and the individual currents. Obviously, a third approach is to simulate the circuit in multi-sim. You may choose any method to solve for the expected currents, voltages and powers into each light bulb for the phase sequence you assume to confirm how this circuit works (see report section). Ask your instructor if you need more help. You may find useful hints in the following Matlab-like statement:
- The circuits of figure 6 are significantly easier to solve. Once you define a phase sequence you can write down VA, VB, and VC. Then calculate VAC, and IAC. From this you can calculate the voltage at the node labelled n and hence Vbn for each of the two possible phase sequences.

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:

- An explanation of how method 1 works.
- Show and indicate the phase sequence of the waveforms saved
- Explain how the circuit of figure 3 works and how it allows you to determine the phase sequence.
- Phasor diagrams for the two circuits that you used (method 2 and 3) for at least one sequence.
- Why you cannot determine the phase sequence in method 2 without capacitor?
- Your calculated values for the powers dissipated in each light bulb in the circuit used for method 2 for one of the phase sequences.
- The expected
**V**for your circuit of figure 6 for each of the phase sequences as well as the Power and VARS consumed._{bn } - How did the power flow and VARS for the two phase sequences for the circuit of figure 6 compare? Explain your observation on Power flow and VARS.
- 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.