To determine the equivalent circuit parameters of a single-phase transformer using the open and short circuit tests.

Experiment 8. Transformer Equivalent Circuit

OBJECTIVE

• To determine the equivalent circuit parameters of a single-phase transformer using the open and short circuit tests.

DISCUSSION

A real transformer has several inductive and resistive characteristics that can affect performance. A non-ideal transformer is shown in Figure 8-1.A typical equivalent circuit is shown in Figure 8-2.

Figure 8-1. Non-ideal transformer.

Figure 8-2. Typical equivalent circuit of the single-phase transformer.

Several parasitic circuit elements exist in a non-ideal transformer.  The resistances R_pri and R_sec represent the resistance of the copper winding in the primary and secondary coils, respectively. A small amount of flux travels through the air outside the magnetic core.The series inductors with reactances X_pri and X_sec are considered leakage inductances and are a result of leakage flux not linked to the core.  The parallel resistance R_c represents hysteresis and eddies current losses in the core.  The parallel inductance X_m is called the magnetizing reactance and accounts for the finite permeability of the magnetic core.

In this experiment, the equivalent circuit to be constructed is shown in Figure 8-3.

Figure 8-3. Transformer equivalent circuit for laboratory experiment.

Open circuit and short circuit tests can be performed to approximate the parasitic component values of a transformer.  The open circuit test entails applying power to the low voltage (secondary) of the transformer while the high voltage (primary) side is open circuit. The open circuit test is for measuring the transformer core components (R_c and X_m).The series components can be neglected in the open circuit test.

The equivalent resistance of the core can be found by measuring the real power (P­_sec) and voltage (V_sec) applied to the excited (secondary) side of the transformer:

R_c=(1)

The magnetizing reactance X_m can be calculated with the following:

X_m­=(2)

Where I_sec is the current applied to the secondary.

The short circuit test is for determining the parasitic series impedances.  The short circuit test entails shorting the secondary winding while applying power to the primary. Impedances measured in this experiment will include the primary and secondary grouped together, all referenced to the primary side as illustrated in Figure 8-3.

The combined equivalent resistance can be calculated as follows:

(3)

WhereI_pri is the excitation current applied to the primary and P_pri is the real power applied to the primary side.

The total combined primary-referenced leakage reactance is:

(4)

Any individual resistance, reactance or complex impedance can be moved from the secondary side of transformer to the primary with the following equation:

(5)

Also impedance can be moved from the primary to the secondary:

                                                 (6)

When moving an impedance reference location, the element should be moved directly across the isolation symbol without changing its parallel or series orientation.Moving transformer impedances is sometimes called reflecting the impedance from one side to the other.

PROCEDURE:

The grading in this section is 2 points for each correct answer.

1. Open Circuit Test

Circuit:

Open the Virtual Laboratory, and from the Virtual Lab Welcome Window click on the Experiment 8 Procedure 1 button.Your screen should look similar to Figure 8-4.Using your Power Supply, Transformer, AC Voltmeter, AC Ammeter and Wattmeter, connect the circuit shown in Figure 8-5.If you are unsure how to make/remove connections, please refer to the Experiment 1 manual.

Use the adjustable 120 VAC power supply. The AC ammeter should be included in series to measure current (I_sec) applied to the transformer secondary.  The AC voltmeter should be used to measure the applied voltage at secondary side (V_sec).  The low power wattmeter should be used to measure the applied real power.

Figure 8-4. Screen capture for Procedure 1.

Figure 8-5. Connection circuit for Procedure 1.

Measurements / Calculations:

1. Adjust for 120 V AC as indicated by the variable AC power supply.Then, click on the Runbutton.Record the measurements on the ammeter, voltmeter, and wattmeter.  If you receive abnormal/unexpected results, check your wiring and the voltage magnitude.Once you have fixed your circuit, click the Run button again.

P_sec = 6.82W

I_sec = 0.06A

V­_sec = 119.9V

• Based on Equations (1) and (2), calculate the R_c and X_mon the secondary side (show your work):

R_c =V^2sec/Psec = 119.9 V^2/6.82 W= 2107.9                                            Ω

X_m= 1/sqrt((Isec/Vsec)^2-(1/Rc)^2) = 1/sqrt((0.06/119.9)^2-(1/2107.9)^2)

= 6279.96Ω

• Close the Experiment 8 Procedure 1 window.

• Short Circuit Test

Circuit:

Click on the Experiment 8 Procedure 2 button.Your screen should look similar to Figure 8-6. Using your Power Supply, Transformer, AC Voltmeter, AC Ammeter and Wattmeter, connect the circuit shown in Figure 8-7.If you are unsure how to make/remove connections, please refer to the Experiment 1 manual.

Connect an ammeter to the secondary side of the transformer.This will short the secondary winding.

Figure 8-6. Screen capture for Procedure 2.

Measurements / Calculations:

Figure 8-7. Connection circuit for Procedure 2a.

1. At first, keep the AC power supply slider at the 0 V position.  Then, adjust the power supply by slowly increasing the supply voltage from zero until I_sec = 0.5 A.For this, click on the Run button after every time the voltage magnitude is adjusted.Note the voltage is applied to the primary.If you receive abnormal/unexpected results, check your wiring and voltage magnitude.Once you have fixed your circuit, click the Run button again.This is the voltage at which the secondary is at rated current.Note: Increase the supply voltage slowly. The required voltage is less than 20 V.

V_pri = 15.997V

• Turn off the power supply and remove the ammeter which was used to measure I_sec.  This removes the parasitic elements within the meter that could distort the test.
• Connect the circuit shown in Figure 8-8. Adjust the supply voltage until the primary voltage is the same value as in Procedure 2 and click on the Run button.  Record the measurements from the ammeter and wattmeter. If you receive abnormal/unexpected results, check your wiring and the voltage magnitude. Once you have fixed your circuit, click the Run button again.

Figure 8-8. Equivalent circuit for Procedure 2b.

P_pri = 4.735W

I_pri = 0.314A

• Based on Equations (3) and (4), calculate the R_eq and X_eqon the primary side (show your work):

R_eq = Ppri/I^2pri = 4.735 W / 0.314 A^2= 48.024                                       Ω

X_eq = sqrt((Vpri/Ipri)^2-Req^2 = sqrt(15.997 V / 0.314 A)^2 – 48.024 Ohms^2)                        = 17.005Ω

• Close the Experiment 8 Procedure 2 window.

REVIEW QUESTIONS:

1. Draw the equivalent circuit (with all parameters) of the transformer used in this experiment. (5)

• In this experiment, you found the shunt impedance referenced on the secondary and the equivalent series impedance referenced on the primary side of the transformer.

1. Calculate the equivalent series resistance and reactance reflectedto the secondary side of the transformer. (4)

R_eq′=                                                                                                                Ω

X_eq′=                                                                                                                            Ω

• Draw the equivalent circuit with all elements referenced to the secondary side. (4)

• Calculate the shunt resistance and reactance reflectedto the primary side of the transformer. (4)

R_c′ =                                                                                                                            Ω

X_m′=                                                                                                                Ω

• Draw the equivalent circuit with all elements referenced to the primary side. (4)

 

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