EE 448 Laboratory Experiment 1

Single Phase AC Circuits

EE 448

Lab Experiment No. 1

03/24/2008

Single Phase AC Circuits

I.INTRODUCTION

OBJECTIVES:

Study the phasor relationship between Voltage and Current in a single phase AC Circuit.
Study the concept of real power (P), reactive power (Q), apparent power(S) and power factor (cos).
Identify a method to improve the line side power factor with the help of a capacitor bank.

BACKGROUND SUMMARY:

AC circuit elements consist of resistors (R), inductors (L) and capacitors(C) which can be fed from either a 3 phase or 1 phase 60 Hz, 120V source. Resistor and inductor combination connected to a single phase AC source results in a lagging current with respect to voltage. If R & L are connected in series, the phasor sum of the voltages across L and R equals the source voltage. In contrast if they are connected in parallel the phasor sum of the currents drawn by R & L equals the source current. Power factor of any load (source) is defined as the cosine of the angle between the load(source) current and corresponding load(source) voltage. By connecting a capacitor bank in parallel with such a RL circuit can improve the power factor which in turn reduces the current drawn from the source for a given power drawn by the resistor.

Power relations in a single phase system

Real power =Vrms *Irms cos in watts (where  is angle between V and I)

Reactive power = Vrms *Irms * sin(Φ) in VARs

Apparent power = Vrms *Irms in VA

INSTRUMENTS and COMPONENTS:

Power Supply ModuleEMS 8821

AC Voltmeter ModuleEMS 8426

AC Current Meter Module EM.S 8428

Resistance ModuleEMS 8311

Inductance ModuleEMS 8321

Capacitance ModuleEMS 8421

II. PRELAB EXERCISES

The machines we will be working with in this lab have these resistances: R1 = 300, R2 = 600 and R3 = 1200. Identify the parallel combinations of two of the resistors at a time to get equivalent resistances of 200, 240 and 400. This will make using the lab equipment easier.
If R1= 300 is connected in series with an inductive reactance of X1 = j300, what will be the impedance angle of this series combination?
In Fig. 2, If R1 andX1 are connected in parallel across a single phase source. What capacitance C value should be connected in parallel to get unity p.f. Assume the frequency of supply is 60Hz.
Draw the phasor diagrams for the voltages in figure 1. Take voltage across the resistor (Vr) as the reference vector.

Figure 1

For the circuit in Fig.2, draw the phasor diagram for the three currents Is, Irand I1 and prove that Is = 2(Ir).

Figure 2

For the circuit in Fig. 3 find

a)All the currents

b)Real power supplied by the source

c)Reactive power supplied by the source

d)Apparent power supplied by the source

e)Power dissipated in the resistor

f)Real and reactive power in the inductor

g)Real and reactive power in the capacitor

h)Power factor as seen by the source

Assume the source voltage as reference ׃120∟o°

Figure 3

III. LABORATORY EXPERIMENT

NOTE:

Whenever an ammeter is used to measure current in a circuit, one should try to get the most accurate reading. To get a more accurate measurement the DMM(Digital Multi-Meter) should be used. However the DMM is only rated for 3 AMPS MAX! The Lab-Volt ammeters are rated for 8 amps. In most of our circuits the current is below 3 amps, but be sure to check your calculations of the circuit to determine whether to use the DMM or Lab-Volt ammeter for your measurements.

1.Connect the circuit as shown in Figure 4. The transformer is necessary to isolate the scope ground from the line voltage.

2.Observe the voltage waveforms of Vs and Vr on the oscilloscope and identify the phase difference between these two voltages.

3.Disconnect only the inductor and measure the phase difference between Vs and Vr.

4.Now reconnect the inductor, remove the resistor and measure the phase difference between Vs and V1. Does the data from the previous steps match your calculations for step 4 of part II?

5.Connect the circuit as shown in Figure 5.

6.Measure the currents As, Ar and A1.

Does the data from steps e and f match your calculations from step 5 of part II?

7.Calculate the power delivered to the circuit.

8.Calculate the p.f. of the load.

9.Make the circuit connections as shown in Figure 6. Connect R, L & C in parallel according to the table given below. First three readings are for R&L combinations. Last two readings are for R, L & C combinations.
NOTE:
The toggle switches on the inductance, resistance, and capacitive boxes work as follows. A toggle switch in the down position means that item is not in the circuit between the two banana plugs. When switched to the up position, the item is part of the circuit. When two or more toggle switches are up, those two or more items will be in the circuit connected in parallel. Depending on whether it’s a resistor, inductor, or capacitor box will determine the value of the parallel connection.

10.Record your measurements in the table below.
Use V = 120V

I / S / P / R / Xi / Xc / p.f. / Q=S*sin φ
300 / j300 / -
600 / j300 / -
1200 / j300 / -
600 / j300 / -j300
600 / j600 / -j300

11.From looking at the table, which set of values will produce a unity power factor?

12.Study your data and determine the capacitance value that gave you the best power factor (closest to unity). Does this value match what you predicted in step 3 of part II? Why or why not?

13.Again study your data and determine why it might be an important goal to achieve a power factor that is as close to unity as possible.

14.Present the lab results using a spreadsheet computer program and attach it with your lab report.

Figure 4

Resistor Module – 8311

Inductor Module – 8321

Transformer – 8341

AC Source – 8821

Figure 5

Resistor Module – 8311

Inductor Module – 8321

AC Source – 8821 (Power Supply)

Figure 6

Resistor Module – 8311

Inductor Module – 8321

Capacitor Module – 8331

AC Source – 8821