Experiment No. 3 Transformer Equivalent Circuit, Voltage Regulation, and Efficiency Purpose To determine the equivalent circuit of a transformer by the short-circuit test method and then use the equivalent circuit to determine the voltage regulation and, also using the open-circuit test from last week, the efficiency. Discussion Short-Circuit Test It is possible to represent a transformer as an ordinary series electric circuit (neglecting the small, no-load exciting current) that has three elements: (1) the equivalent resistance, (2) the equivalent leakage reactance, and (3) the load. The short-circuit test is an experimental method of determining the equivalent resistance, impedance, and reactance of a transformer. In this test the windings are made to carry the rated currents without requiring the transformer to deliver a load. This is done by shorting the secondary winding and increasing the primary voltage from zero to that value which causes the rated current to flow. In this way, it is possible to simulate the pattern of flux leakages in the primary and secondary because the latter depend upon the load currents in the two windings. From the data of watts, amperes, and volts obtained from this test, the values of equivalent resistance, impedance, and reactance can then be calculated using the following equations: π π ππ = ππππ = πππ π π π πΌπΌπ π π π 2 πΈπΈπ π π π πΌπΌπ π π π ππππ = οΏ½ππππ 2 − π π ππ 2 Where Re = the equivalent resistance Psc = the measured real power from the short circuit test Isc = the measured current from the short circuit test (this should be the transformer’s rated current) Esc = the measured voltage from the short circuit test (much smaller than the transformer’s rated voltage) Ze = the equivalent impedance (the series combination of the equivalent resistance and reactance) Xe = the equivalent reactance 1 |Page ET-250 Industrial Electrical Machinery Ver. 3.2 Experiment 3 - Equivalent Circuit, Voltage Regulation, and Efficiency Voltage Regulation Voltage regulation is a measure of merit for a transformer. However, it is often impractical, if not impossible, to fully load a large transformer to determine its voltage regulation. This fact presents no problem if the short circuit tests are available, or if they can be performed. From these tests it is possible to determine the equivalent circuit with reference to either the primary or secondary winding. Taken from the secondary, the resistive and reactive voltage drops can be calculated with rated current. Looking at the secondary side, the no-load voltage can be calculated from: πΈπΈπ π = πππ π + πΌπΌπ π × ππππ Where Vs = the rated secondary voltage (this is the full load voltage, VFL) Es = the voltage required to provide rated secondary voltage (this is the no load voltage, VNL) Is = the rated secondary current Ze = the equivalent impedance on the secondary (the series combination of the equivalent resistance and reactance) Then, the voltage regulation (VR) can be calculated from: ππππ = Voltage regulation is usually expressed in percent. ππππππ − πππΉπΉπΉπΉ πππΉπΉπΉπΉ Transformer Efficiency Just like any other device, efficiency of a transformer can be defined as the output power divided by the input power. Transformers are highly efficient devices. Most transformers have full load efficiency from 95% to 98.5%. If the rated open-circuit and short-circuit losses are known, the efficiency (η) can be found from: Where ππ = ππππππππ ππππππππππππ × ππππ = ππππππππ + ππππππ + ππππππ ππππππππππππ × ππππ + ππππππ + ππππππ POut = is the real power output of the transformer in [W] POC = the measured real power from the open-circuit test in [W] PSC = the measured real power from the short-circuit test in [W] Srated = the rated apparent power of the transformer in [VA] pf = the power factor 2 |Page ET-250 Industrial Electrical Machinery Ver. 3.2 Experiment 3 - Equivalent Circuit, Voltage Regulation, and Efficiency Apparatus Required 1. 2. 3. 4. One Hampden ET-100 Transformer One Fluke 435 II Power and Energy Analyzer One fixed 120 volt AC power source One variable 0-140 volt AC power source Procedure Short-Circuit Test 1. Calculate full load current for the primary and secondary of the experimental transformer. (Note: the transformer rating is 140 VA, 240V-120V) I primary = I secondary = mA 583.000 1.160 A 2. Connect the transformer primary (H1 and H5) to a variable voltage source and short the secondary (X1 to X7). Make sure to install a jumper from H3 to H4, and another from X4 to X5, to include all the windings in the measurement. The setup us shown in Figure 1. Slowly adjust voltage from zero up until the point where the ammeter indicates full load current. When you reach full load current, record the voltage, current, real, apparent, and reactive power, and power factor on your engineering note sheet and in Table 1. Using the information from the short circuit test, derive the equivalent circuit parameters. Calculated Measured Table 1. Short-Circuit Values Short-Circuit Values Voltage, Esc Current, Isc Real Power, Psc Apparent Power, Ssc Reactive Power, Qsc Power factor, pf Equivalent Resistance, Re Equivalent Impedance, Ze Equivalent Reactance, Xe 24.990 V 583.000 mA 14.30 W 14.60 VA 2.30 kVAr 0.98 Lead 42.100 kΩ 42.860 Ω Ω 8.200 Question: On which side, primary or secondary, are these values taken? Primary 3 |Page ET-250 Industrial Electrical Machinery Ver. 3.2 Experiment 3 - Equivalent Circuit, Voltage Regulation, and Efficiency Figure 1. Short Circuit Configuration Voltage Regulation 3. Using just the series equivalent circuit referred to the primary, calculate the voltage regulation for the transformer at rated power and 0.8 lagging, unity, and 0.8 leading power factor. Power Factor 0.8 lagging unity 0.8 leading E1 – Voltage on the primary of the Ideal transformer [V] Voltage Drop (π π ππ + ππππππ ) × πΌπΌβ 240.00 25.010 240.00 25.010 240.00 25.010 [V] ∠ ∠ ∠ 11.02 11.02 11.02 ° ° ° V1 – Voltage magnitude on the actual transformer primary [V] 264.588 Voltage Regulation ππ1 − πΈπΈ1 πΈπΈ1 [%] 104.00% 264.588 104.00% 264.588 104.00% Figure 2. Equivalent Circuit Referred to Primary 4 |Page ET-250 Industrial Electrical Machinery Ver. 3.2 Experiment 3 - Equivalent Circuit, Voltage Regulation, and Efficiency 4. Repeat step 6 with the series equivalent circuit referred to the secondary. Power Factor 0.8 lagging unity 0.8 leading V2 – Voltage on the secondary of the actual transformer [V] Voltage Drop E2 – Voltage on the ideal transformer secondary (π π ′ππ + ππππ′ππ ) × πΌπΌβ [V] ∠ ∠ ∠ ° ° ° [V] Voltage Regulation πΈπΈ2 − ππ2 ππ2 [%] 0.000% 0.000% 0.000% Figure 3. Equivalent Circuit Referred to Secondary Efficiency 5. Using the cantilevered equivalent circuit referred to the primary calculate the efficiency of the transformer at rated power and 0.8 lagging, unity, and 0.8 leading power factor. 5 |Page ET-250 Industrial Electrical Machinery Ver. 3.2 Experiment 3 - Equivalent Circuit, Voltage Regulation, and Efficiency Figure 4. Cantilevered Equivalent Circuit Referred to the Primary Questions 1. Include calculations for Re, Ze and Xe on the primary and then referred to the secondary. 6 |Page ET-250 Industrial Electrical Machinery Ver. 3.2