The Single Phase Transformer - Lab Report Example

Introduction Transformer is a device that transfers electrical energy from one circuit to another which are kept electrically isolated. It does it through inductive or more specifically magnetic coupling. As shown in figure 1, change in voltage in primary winding creates changing magnetic flux that cuts the secondary winding and produces a proportionate secondary voltage. Its major application is to change the current or voltage level before transmitting electrical energy over long distance. Figure 1 shows the transformer schematic symbol and the corresponding commonly used Steinmetz model is shown in Figure 2. Therein, the model voltage and current phasors are defined as: Primary side voltage (V) Primary side current (A) Referred secondary side voltage (V) Referred secondary side current (A) Magnetizing current (A) The model parameters are: R1 Primary coil resistance () Xl1 Primary coil leakage reactance (H) Rc Core loss resistance () Xm Core magnetizing reactance () R2 Referred secondary coil resistance () Xl2 Referred secondary coil leakage reactance (H) N1/N2 Transformer turns ratio Note that this Steinmetz model utilizes the referred secondary quantities related to the physical quantities by (1) (2) (3) (4) Furthermore, this Steinmetz model can be augmented with a core loss term Rc in parallel with Xm that approximately accounts for the hysteresis and eddy current losses. The more appropriate form of transformer equivalent circuit is shown inn figure 2.a below. Figure 2.a Determining resistance The resistance parameters R1 and R2 can be found by applying DC voltage to the respective windings. For example, if a DC voltage is applied to the primary winding, the Steinmetz model predicts the equivalent circuit shown in Figure 3. The primary resistance can then be determined by (5) The same procedure can be used to find the secondary resistance R2. Note that the turns ratio is needed to refer this resistance to the primary. This is usually given by the transformer manufacturer. Reactances If the secondary of the transformer is short-circuited, the equivalent circuit can be approximated as shown in Figure 4. In this case, the magnetizing impedance is assumed to be much larger than the secondary resistance and leakage impedance. This is typically a good assumption for practical transformer designs. From the voltage, current, and power measurements, the magnitude and angle of the short-circuit impedance can be determined as (6) (7) (8) From the imaginary part of this impedance, the sum of the primary and secondary leakage reactance can be found. In particular, (9) The individual leakage reactance can be determined if it is assumed that (10) Although it is possible to perform other tests on the transformer to determine a more exact relationship between Xl1 and Xl2, (10) is a good approximation. An alternate method of determining the leakage reactances is to set (7) equal to the short-circuit impedance magnitude which can be written as (11) Using (11) along with the resistances, the sum of Xl1 and Xl2 can be determined. This method is convenient when watt-meters are not accessible. The next test involves open-circuiting the secondary winding and applying rated voltage to the primary winding. Under this condition, the Steinmetz equivalent circuit, including the core loss term, reduces to that shown in Figure 5. As can be seen, the open-circuit impedance is (12) (13) (14) Using the measured open-circuit impedance as well as R1 and Xl1, the core admittance can be determined by (15) Using this admittance, the magnetizing reactance and core loss resistance can be found from (16) (17) An alternate method for determining Xm is to set the magnitude of the measured open-circuit impedance equal to (18) This method does not require measurement of power. However, there is not enough information to calculate the core loss resistance. Equipment 1) Single phase transformer: The Lab’s variable AC source is a complex device, which is designed to provide safety conditions of an experiment. It consists of single phase transformer, variac and lamp bulb is series with the output. 2) AC wattmeter: Electric power is measured by means of a wattmeter. This instrument is of the dynamic type. It consists of a pair of fixed coils, known as current coils, and a movable coil known as the potential coil. A simplified electrodynamics wattmeter circuit is shown in figure below. Figure: AC Wattmeter The current coil of the wattmeter is connected in series with the circuit (load), and the potential coil (movable coil) is connected in parallel. When line current flows through the current coil of a wattmeter, a field is set up around the coil which is proportional to the line current and in phase to it. The actuating force comes from the field of its current coil and and fields of potential coil. 3) Two digital multimeters 4) Variable AC source: Its nothing but one variac which consists of one single winding. Tapping is done in order to get input and output connections. Varying the knob, output to input turn ration is varied and hence, the resulting output voltage. Figure below is the schematic diagram of autotransformer or variac. Laboratory Work Practically, all the transformers are non-ideal and hence, show some non-ideal characteristics like: 1) Electrical Loss 2) Flux coupling between primary and secondary windings is not perfect. 3) Core has some finite permeability and, 4) Magnetic losses Referring to figure 2.a, we can notice twp resistances R1 and R2 which incorporate power loss. As a result, E1 is not equal to V1 rather, less than that. Same way, V2 is less than E2. Also, not all the flux created by the primary winding confines itself to the transformer core. A portion of it takes the path through air and introduces loss. Non-idealistically, Determining Turns Ratio In order to determine the turns ration of a transformer, connect the circuit as shown below: Figure: Circuit arrangement for determining turns ratio. The transformer is supplied with a variable voltage and both primary and secondary voltages are measured and recorded. After that, the mean value is granted as standard. DC Resistance Test Connect the transformer as shown in Figure 6. In this case, a DC power supply with a current limit is used to supply the primary winding. Increase the DC voltage until the primary current is equal to the rated RMS current (2A). Record values of VDC and IDC for calculation of R1. Perform the same DC test on the secondary coil to find R2. Short-Circuit Test Using two phases of the AC source panel and a resistance from the load panel, connect the transformer as shown in Figure 7. Increase the voltage applied to the primary until the primary current reaches its rated value. Record the primary voltage and current. In this case, the power is too low to be measured by the laboratory watt-meters so (7) and (10-11) can be used to calculate Xl1 and Xl2. Through this test winding loss or copper loss is measured. Open-Circuit Test Remove the resistor and short-circuit wire from the transformer so that the setup is that shown in Figure 8. Apply rated voltage to the transformer and determine the magnitude of the open-circuit impedance. Since the power is not measurable, use the impedance magnitude and (18) for determining Xm. Open circuit test is done to get the idea of core loss of a transformer. Transformer Load Test Connect the transformer to the three-phase source and load as shown in Figure 9. Apply rated voltage to the primary winding and record the primary and secondary voltages and currents. Perform this test for various combinations. Lower the voltage to zero before switching from one load configuration to another. Result From the tests, transformer model parameters and its efficiency are calculated and tabulated in table 1. Table 1 1. Open Circuit Test Voltage, V1 Current, Io Wattmeter Readings Voltage, V2 Turns Ratio θ Current, Ic Current, Im Rc Xm Current, Iw Voltage, Vw Factor, Fw Power, Wopen 220 0.16 0.2 200 0.34 13.6 120 1.83 67.27 0.0618 0.1476 3558.82 1490.76 Rc=V1/Ic Ic=IoCosθ Cosθ=P/V1*Io Xm=V1/Im Im=IoSinθ V1/V2=N1/N2 2. Short Circuit Test Voltage, V1 Current, I1 Wattmeter Readings Current, I2 Turns Ratio R1 equivalent Z1 equivalent X1 equivalent   Current, Iw Voltage, Vw Factor, Fw Power, Wsc   6.5 2.30 2.0 10 0.74 14.8 4.3 1.87 2.80 2.83 0.40   Wsc=I2R1eq X1eq=√Z1eq2-R1eq2 Z1eq=V1/I1 I2/I1=N1/N2 3. Load Test Voltage, V1 Current, I1 Wattmeter Readings Voltage, V2 Current, I2 Efficiency, η Current, Iw Voltage, Vw Factor, Fw Power, Wload 220 1.10 2 200 0.60 240 121.4 1.8 91% 220 1.22 2 200 0.67 268 121.2 2.0 90% 220 1.47 2 200 0.81 324 121.0 2.5 93% 220 1.74 2 200 0.96 384 120.6 3.0 94% 220 1.97 5 200 0.44 440 120.5 3.5 96% 220 2.22 5 200 0.50 500 120.1 4.0 96% 220 2.45 5 200 0.56 560 119.0 4.5 96% Figure 10 depicts the variation in transformer efficiency with load current. With the experimental obtained data efficiency is calculated at various load current and plotted below. Figure 10 Conclusion It is said that, in engineering, everything as well as nothing both are true simultaneously unless and until one is experimenting. In reality, transformer, is not ideal and has various non-ideal parameters. By Open and short circuit tests, these lossy behaviors are studied and recorded. Finally, its efficiency is observed with load current varying. From efficiency plot, it can be inferred that, loss is dependent on load current which makes sense too. As load is varied, Xm and Io also vary which has a direct impact on its power transmission. References 1) Charles I. Hubert. “Electric Machines: Theory, Operating Applications, and Controls” 2nd Edition. 2) B. L. Theraja and A.K. Theraja, “A Textbook of electrical Technology” Read More