lab 6 - balanced 3-phase power measurements

Lab 6 - Balanced 3-Phase Power Measurements.docx page-1

EE221L — Circuits II Lab Exercise #6

Balanced 3φ Power Measurements

I. Objectives

The objectives of this exercise are to:

1. To become familiar with: a) Three-phase (3φ) 4-wire and 3-wire systems, for both wye (Y) and

∆−SOURCES, connected to a combination of a Y / ∆−LOAD. Gain insight to the inherent 30o phase shifts between line and phase quantities.

b) The two-wattmeter method for 3φ power measurements of balanced loads. c) The significance of pf = 0.5 (lead or lag) when using the two watt-meter

method. d) High-Voltage differential probes and current probes.

2. Conduct 3φ measurements on two distinctly different balanced systems a) 4-Wire 208 Vac Y-SOURCE (grounded neutral system), connected to a

Y−reactive (inductive) load (inductors are in the line between source and resistive load) in parallel with a ∆−resistive load.

(1) Predict and measure Line and Line-to-Neutral Voltages, both magnitude and phase (2) Predict and measure Line currents, both magnitude and phase (3) Measure total power, using the Two-Watt Meter Approach

b) 3-Wire 240 Vac ∆-SOURCE (floating supply system), connected to a Y−reactive (capacitive) load in parallel with a ∆−resistive load.

(1) Determine an appropriate location for placing a ground into the system (2) Predict and measure Line Voltages and Line-to-Neutral Voltages, both magnitude and phase (3) Predict and measure Line currents, both magnitude and phase (4) Measure total power, using the Two-Watt Meter Approach


II. Introduction

A. Discussion on each of the 3-phase sources

The three-phase circuit studied in this lab is represented in Fig. 1. While the load can be either Y- or ∆-connected, through Y-∆ transformation, the load has an equivalent Y representation. The source will either by Y (208 Vac) or ∆ (240 Vac). For this figure, the source is Y connected.

3-phaseLoad

0AN LNV V=

+

-

A LI I θ=

A

BC

30AB LV V

+

=

−

3 3 3

3 3 3

3 3 3

Z

LN L L L

S P jQ

S S S

S V I V I

φ φ φ

φ φ φ

φ

θ θ

= +

= = −

= =

YEQ YEQZ Z θ= −

YEQ YEQ ZZ Z θ=

Zwhere θ θ= −

3L LN

where

V V=

Figure 1: 3-phase circuit.

1. 4-Wire 208 Vac Y-SOURCE

The 208 source does not come directly from the utility room (where the ALBs reside), but rather from the service entrance to the building. The 208 outlet at the station wall is always “hot”, assuming no breakers have been tripped. When this 208 source is connected to the back panel, and through the metered 3φ breaker on the bench front panel, the neutral is connected to the ground of the bench.

2. 3-Wire 240 Vac ∆-SOURCE

The 240 source comes directly from the utility room at the output of a 75 kVA 3φ Y-∆ , 480-to-240 Vrms transformer. Sometimes, the secondary winding of one of the phases has the center of the winding tapped, giving the user a fourth wire, which can be connected to ground. This is not the case for our transformer. Hence, there are only three wires, each being one phase of the output of the transformer. The 240 outlet at the station wall only becomes “hot”, when a contactor is closed within the


power processing system (PPS) – the big grey cabinet where the ALBs are connected to a bench via the touch screen interface. The mechanical switches to activate these contactors are located on the side of the PPS cabinet.

When this 240 source is connected to the back panel of the bench, and through the metered 3φ breaker on the bench front panel, the user could safely connect any one of the three phases to the bench ground (only one at a time!), if so desired, but not necessary. This is because the output of the 3φ Y-∆ transformer is considered to be “floating” with respect to ground.

B. 3-Phase Power Theory:

Based on Fig. 1 and lecture notes, it is shown that

a) 3 3 L LS V Iφ = ,

b) ( ) ( ) ( )

( )

3

3

3Re 3 cos 3 cos3

cos

LLN L L L L

VP V I I V I

P S

φ

φ

θ θ θ

θ

= − = − =

=, (1)

c) ( ) ( )3 3

3 3

3Im 3 sin sin( )3

sin( )

LLN L L

VQ V I I S

Q S

φ φ

φ φ

θ θ θ

θ

= − = − = −

= −.

C. Two-Watt Meter Method The following equations hold when measuring power delivered to a balanced or unbalanced 3-wire 3φ load, or a balanced1. Consider the diagram of Fig. 1, where the equivalent Y-load is attached to the

equivalent Y-source. If the load is purely real,

4-wire 3φ load.

0θ = , and line current will be in phase with the line-to-neutral voltage.

2. It is possible to use two Watt meters to measure the total power delivered to the load.

Let Watt Meter 1, (W1) have its positive voltage lead connected to Line A and the minus lead be connected to Line C (when using the Fluke 41, any of the lines can be used as a common terminal, here we let C be the common

Let Watt Meter 2, (W2) have its positive voltage lead connected to Line B and the minus lead be connected to Line C. The current probe should be connected to Line B with its arrow pointing towards the load.

). Following passive sign convention, the current probe should be connected to Line A with its arrow pointing towards the load.


3-phaseLoad

Resistive, Inductive, Capacitive

0AN LNV V=

+

-

A LI I θ=

A

BC

1W

2W

Figure 2: Two-Watt Meter method for measuring power in a 3-phase circuit.

With the meters connected as such, assuming that AC BC LV V V= = ,

1 cos(30 )L LW V I θ= + (2)

2 cos(30 )L LW V I θ= − (3)

and that the total power to the 3φ load is

3 1 2 = + P W Wφ (4)

The proof for this follows below.


PROOF: The Fluke 41 meter essentially computes power according to: ( )*

1

*

Re ,

120 30AC A

AC CA L A L

W V I

where V V V and I I θ

=

= − = − + = −

( ) ( )1 cos 120 30 cos 30L L L LW V I V Iθ θ= − + − = +

( )*2

*

Re ,

120 30 120BC B

BC L B L

W V I

where V V and I I θ

=

= − + = −

( ) ( )2 cos 120 30 120 cos 30L L L LW V I V Iθ θ= − + + − = −

Q.E.D.

Here, we see that if the load is purely real, the inherent 30 degree phase shift is easily seen between the line current and the respective line voltage.

3. It is not difficult to see that if θ lags by as much as 60 degrees (inductive load), 2W

approaches 0 and 1W approaches 32 L LV I . If θ leads by as much as 60 degrees

(capacitive load), 1W approaches 0 and 2W approaches 32 L LV I . If the pf angle

increases beyond 60 degrees (lag or lead), one wattmeter will become negative and the other will remain positive – and this is perfectly ok

The important observation to realize is that when real power is held constant and the reactive load is uniformly increased or decreased,

, i.e., don’t be in a hurry to switch the current probe around just to obtain a positive power reading – in the end, the power readings from each meter are added together to obtain the total power delivered to the load.

1 2 + W W will always remain constant and the true value for the total power delivered to the load is obtained.

4. The only time the Watt meters are equal in magnitude3 1 2 1 W 2P W Wφ = + =

is when θ is 0 degrees, i.e., pf=1 (pure resistive). Hence, when pf = 1, .

5. When θ is + or - 90 degrees, i.e., pf = 0 (pure reactive), 1 2 = - W W , and

3 1 2 W 0P Wφ = + = . This is expected, since the load is purely reactive. This begs the question then … “Is there a simple equation that gives you Q when given 1 2 and W Wmeasurements?” The answer is yes (in the ideal situation – perfect measurements) and the equation is given by:

( )1 23 - Q W W= (5)


D. Phase Shift Measurement Methods: When using the oscilloscope, there are two methods for obtaining phase shift information.

a) METHOD 1ANt

: Use cursors to measure the time shift between these two voltages, and convert this to an equivalent phase shift. For example, let be the time at which the first ANV

zero crossing of occurs. Let ABt be the time

at which the first ABV

zero crossing of occurs. The phase shift is calculated as

( )( )

*360

* *360

60* *360

AN AB

AN AB

AN AB

t tT

f t t

t t

φ −=

= −

= −

(6)

b) METHOD 2

E. Extra Credit

: Now use the oscilloscope MEASUREMENT features to measure phase shift and rms values.

1. Show (Prove) that ( )1 23 - Q W W= by first showing that

( )3 cos cos(30 ) cos(30 )θ θ θ = + + −

You may use the following standard formulas for balanced 3φ power calculations as well as the identities given below:

a) 3S V IL L=

b) sin( ) sin( ) sin( )zQ S S Sθ θ θ= = − = −

c) trigonometric identities, (1) cos(α+β) = cos(α)cos(β) - sin(α)sin(β) (2) cos(α−β) = cos(α)cos(β) + sin(α)sin(β).

2. Show that when PF equals 0.5, Q results in: 3Q P= .

(hint: recall that PF = cos( ) cos( )PS θ θ= − = , and that sin( ) sin( )Q S Sθ θ= − = − ).


III. Laboratory Exercise When making voltage and current measurements, with the purpose to obtain an understanding of inherent phase shift between line and phase quantities, you will use the oscilloscope, high-voltage differential probes, and current probes. When making power measurements, you will use two Fluke 41 Power Analyzers.

A. Station 1 and 2:

1. Use a sequence meter to determine if the supply is positive sequence (ABC) or negative sequence (ACB). Before doing this, the user will define which line is A, which is B, and which is C. Then the corresponding leads from the sequence meter will be attached to these respective lines.

3-Wire, 3φ, Y-connected 208 Vac source

Turn the power on. The meter will indicate if indeed you have the correctly identified A, B, and C lines. Try switching the leads from the meter between two phases – what did you notice? Turn the power off.

2. Connect the ∆-resistance (ALB) at

per phaseR = 60 Ω (line to line).

DRAW A CIRCUIT DIAGRAM IN YOUR NOTEBOOK showing the Y-connected source and ∆-connected load.

NOTE: since the load is ∆-connected, the system is actually a 3-wire system. If a load with a ground is introduced to the system, then the circuit becomes a 4-wire system

( )2

3 3 L

per phase

VP

Rφ

=

. To determine the 3-phase power level the ALB must be set to, apply this formula:

.

Once the total power level is determined, you should turn the power on and place the ALB in closed-loop mode, and confirm your setting at the LabVIEW meters. Place the ALB in open-loop mode, and turn the power off

3. Use High-Voltage Differential Probes to show the theoretical phase shift between a line voltage (i.e., line-to-line) and the line-to-neutral voltage.

.

Predict the phase and RMS value of BCV

with respect to (WRT) ABV

(i.e., trigger off channel connected to ABV

)?

a) Connect the differential probes to the power supply side for measuring BCV

and ABV

. Set probe values correspondingly.

Turn the power on

and place the ALB in closed-loop mode. Implement both phase shift measurement methods.


For METHOD 1, use cursors to measure the amplitudes of each voltage, and convert these values to their RMS values. Save data and produce plots to be placed in your notebook. Compare each of these methods to your predicted values. Place the ALB in open-loop mode, and turn the power off

b) Connect the current probe to phase A line between Y-source and ∆-load, with arrow pointing towards the load (i.e., ALB). Set probe to values corresponding to expected current magnitudes. Predict the RMS value of Line A current and its phase WRT

.

ABV

? (consider (2) … hmmm.) Display on the oscilloscope only ABV

and AI

. Using both phase shift measurement METHODS 1 and 2 to make the appropriate measurements for AI

, with respect to ABV

. Save data and produce plots to be placed in your notebook. Place the ALB in open-loop mode, and turn the power off

.

Predict the RMS value of Line A current and its phase WRT ANV

?

Display on the oscilloscope only ANV

and AI

. Using one of the METHODS 1 or 2, as described above, make the appropriate measurements for AI

, with respect to ANV


4. 3-Wire, 3φ ∆-connected resistive (ALB) and series-connected (line) inductive-reactive load –

.

DRAW A CIRCUIT DIAGRAM IN YOUR NOTEBOOK showing the Y-connected source, in-line inductors, and ∆-connected load.

a) With power off, place an inductor in each line between the input and the ALB.

Set the reactances to 10 Ω. By the method of converting the ∆-connected resistance (ALB) of 60 Ω to an equivalent Y-load, use the single phase equivalent circuit to compute the expected line current (phase and magnitude WRT ANV

for this configuration.


Turn the power on and place the ALB in closed-loop mode, such that the desired power is being drawn. Using METHOD 2, confirm these values. Place the ALB in open-loop mode, and turn the power off

.

b) For this load configuration, predict the total LOAD (which includes the inductors and ALB) VA, Watts and VARs the relationships in (1a, 1b, 1c). Referring to Fig. 2, use the Fluke 41 for conducting the two-watt meter approach to confirm this prediction. Estimate the value for W1 and W2, using (2) and (3). Turn the power on

and place the ALB in closed-loop mode and record W1 and W2.

Compare results of a) W1 to estimated result (2) b) W2 to estimated result (3) c) (4) to predicted result (1.b) d) (5) to predicted result (1.c)

The VAR computation (5) may have the most error compared to the error in (4). Provide a reasonable explanation as to why there might be more error with this calculation for VARs then for Watts?

c) Adjust the decade reactance to successively larger or smaller values. At each increment/decrement, record W1 and W2 and note the direction each measurement is taking, i.e., is the value increasing or is it decreasing towards a negative value. Explain to your lab instructor what pattern develops and why. Do you expect that W1 or W2 to change sign? How should each measurement change as the reactance is adjusted? Explain to your instructor.

5. 3-Wire, 3φ ∆-source (240 Vac), ∆-connected resistive (ALB) and Y-connected capacitive-reactive load.

DRAW A CIRCUIT DIAGRAM IN YOUR NOTEBOOK showing the ∆-connected source, Y-connected capacitive-reactive load, and ∆-connected load.

a) With power off, place three capacitors in a Y-configuration in parallel with the

ALB. Set the capacitive reactances to 83 Ω. By the method of converting the ∆-connected load to an equivalent Y-load, use the single phase equivalent circuit to compute the expected line current (phase and magnitude WRT ANV


for this configuration). Turn the power on

and place the ALB in closed-loop mode.

Use METHOD 2 for phase measurements and confirm these values. Place the ALB in open-loop mode, and turn the power off

.

Referring to Fig. 2, use the Fluke 41 for conducting the two-watt meter approach to confirm this prediction. Estimate the value for W1 and W2, using (2) and (3). Turn the power on



b) The VAR computation (5) may have the most error compared to the error in

(4). Explain. c) Adjust the decade reactance box to successively larger or smaller values. At

each increment/decrement, record W1 and W2 and note the direction each measurement is taking, i.e., is the value increasing or is it decreasing towards a negative value. Explain to your lab instructor what pattern develops and why. Do you expect that W1 or W2 to change sign? How should each measurement change as the reactance is adjusted? Explain to your instructor.

B. Station 3 and 4:

1. Use a sequence meter to determine if the supply is positive sequence (ABC) or negative sequence (ACB). Before doing this, the user will define which line is A, which is B, and which is C. Then the corresponding leads from the sequence meter will be attached to these respective lines.

3-Wire, 3φ, ∆-connected 240 Vac source

Turn the power on. The meter will indicate if indeed you have the correctly identified A, B, and C lines. Try switching the leads from the meter between two phases – what did you notice? Turn the power off.

2. Connect the ∆-resistance (ALB) at

per phaseR = 80 Ω (line to line).

DRAW A CIRCUIT DIAGRAM IN YOUR NOTEBOOK showing the ∆-connected source and ∆-connected load.


To determine the 3-phase power level the ALB must be set to, apply this formula: ( )2

3 3 L

per phase

VP

Rφ

=

.

Once the total power level is determined, you should turn the power on and place the ALB in closed-loop mode, and confirm your setting at the LabVIEW meters. Place the ALB in open-loop mode, and turn the power off

3. Use High-Voltage Differential Probes to show the theoretical phase shift between a line voltage (i.e., line-to-line) and the line-to-neutral voltage.

.

Predict the phase and RMS value of BCV

with respect to (WRT) ABV

(i.e., trigger off channel connected to ABV

)?

a) Connect the differential probes to the power supply side for measuring ABV

and BCV

. Set probe values correspondingly.

Turn the power on

and place the ALB in closed-loop mode. Implement both phase shift measurement methods.

For METHOD 1, use cursors to measure the amplitudes of each voltage, and convert these values to their RMS values. Save data and produce plots to be placed in your notebook. Compare each of these methods to your predicted values. Place the ALB in open-loop mode, and turn the power off

b) Connect the current probe to phase A line between Y-source and ∆-load, with arrow pointing towards the load (i.e., ALB). Set probe to values corresponding to expected current magnitudes. Predict the RMS value of Line A current and its phase WRT

.

ABV

? (consider (2) … hmmm.) Display on the oscilloscope only ABV

and AI

. Using both phase shift measurement METHODS 1 and 2 to make the appropriate measurements for AI

, with respect to ABV


.

Place the ALB in open-loop mode, and turn the power off.


4. 3-Wire, 3φ ∆-source (240 Vac), ∆-connected resistive (ALB) and series-connected (line) inductive-reactive load.

DRAW A CIRCUIT DIAGRAM IN YOUR NOTEBOOK showing the ∆-connected source, in-line inductors, and ∆-connected load.

a) With power off, place an inductor in each line between the input and the ALB.

Set the reactances to 10 Ω. By the method of converting the ∆-connected resistance (ALB) of 80 Ω to an equivalent Y-load, use the single phase equivalent circuit to compute the expected line current (phase and magnitude WRT ABV

for this configuration.

Turn the power on and place the ALB in closed-loop mode, such that the desired power is being drawn. Using METHOD 2, confirm these values. Place the ALB in open-loop mode, and turn the power off

.

b) For this load configuration, predict the total LOAD (which includes the inductors and ALB) VA, Watts and VARs the relationships in (1a, 1b, 1c). Referring to Fig. 2, use the Fluke 41 for conducting the two-watt meter approach to confirm this prediction. Estimate the value for W1 and W2, using (2) and (3). Turn the power on



The VAR computation (5) may have the most error compared to the error in (4). Provide a reasonable explanation as to why there might be more error with this calculation for VARs then for Watts?


c) Adjust the decade reactance to successively larger or smaller values. At each increment/decrement, record W1 and W2 and note the direction each measurement is taking, i.e., is the value increasing or is it decreasing towards a negative value. Explain to your lab instructor what pattern develops and why. Do you expect that W1 or W2 to change sign? How should each measurement change as the reactance is adjusted? Explain to your instructor.

5. 4-Wire, 3φ, Y-source (208 Vac), ∆-connected resistive (ALB) and Y-connected capacitive-reactive load.

DRAW A CIRCUIT DIAGRAM IN YOUR NOTEBOOK showing the Y -connected source, in-line inductors, and ∆-connected load.

a) With power off, place three capacitors in a Y-configuration in parallel with the

ALB. Connect the neutral of the capacitive Y-load to ground. Set the capacitive reactances to 110 Ω. By the method of converting the ∆-connected resistance (ALB) of 80 Ω to an equivalent Y-load, use the single phase equivalent circuit to compute the expected line current (phase and magnitude WRT ANV

for this configuration. Turn the power on

and place the ALB in closed-loop mode.

Using a current probe to see if the neutral current is relatively small compared to each capacitor current? If it is (which is to be expected since the ∆-source is does not have a tap to ground), then proceed with all measurements WRT

ANV

If it is not, then turn power off, remove the neutral from ground, and make all measurement WRT ABV

. Use METHOD 2 for phase measurements and confirm these values. Place the ALB in open-loop mode, and turn the power off

.

Referring to Fig. 2, use the Fluke 41 for conducting the two-watt meter approach to confirm this prediction. Estimate the value for W1 and W2, using (2) and (3). Turn the power on


Compare results of a) W1 to estimated result (2)


b) W2 to estimated result (3) c) (4) to predicted result (1.b) d) (5) to predicted result (1.c)

b) The VAR computation (5) may have the most error compared to the error in

(4). Explain. c) Adjust the decade reactance box to successively larger or smaller values. At

each increment/decrement, record W1 and W2 and note the direction each measurement is taking, i.e., is the value increasing or is it decreasing towards a negative value. Explain to your lab instructor what pattern develops and why. Do you expect that W1 or W2 to change sign? How should each measurement change as the reactance is adjusted? Explain to your instructor.

IV. Post Analysis and Report

Present your data with tables including percent error calculations and phasor diagrams showing the 30o and 120o phase shifts throughout the system.

Also, be sure to answer questions that were asked throughout the procedure.

You may also want to work the extra credit.

lab 6 - balanced 3-phase power measurements

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