Objectives To determine the polarity of single phase transformer windings. To determine the internal resistance of single phase transformer windings. To determine the efficiency and voltage regulation of a single phase transformer. Windings Polarity Test (Dot Convention) Introduction The dots appearing at the primary winding in Figure 3. indicate the polarity of the voltage and current on the secondary winding of the transformer. The relationship is as follows:. If the primary voltage is positive at the dotted end of the winding with respect to the undotted end, then the secondary voltage will be positive at the dotted end also. Voltage polarities are the same with respect to the dots on each side of the core. If the primary current of the transformer flows into the dotted end of the primary winding, the secondary current will flow out of the dotted end of the secondary winding. Figure 3.: Schematic diagram for a single phase transformer. Procedures Using the lab equipments shown in Figure 3., do the following:. Connect the circuit shown in Figure 3.3.. Read the voltages of Voltmeter () and (). Record that below. If then, the polarity is additive, otherwise if then, the polarity is subtractive. V [V] V [V] The polarity of tested transformer 45344: Electrical Machines for Mechatronics Laboratory
Figure 3.: Real photo of lab equipments needed for the experiment 3. 45344: Electrical Machines for Mechatronics Laboratory 3
a b a b 43V 5A 43V 5A V 8A 4V 8A V A 4V A 5V A % KY DL 3M L L L3 N L L L3 L L L3 L+ L L+ L Figure 3.3.a: Polarity test wiring diagram. Figure 3.3.b: Polarity test schematic circuit. 45344: Electrical Machines for Mechatronics Laboratory 3 3
DC Test Introduction The internal resistance of each winding in a transformer is measured using a small dc current to avoid thermal and inductive effects. If a voltage causes a current to flow throw the transformer windings, then Vdc Internal Resistor = RX = Idc Procedures Using the lab equipments shown in Figure 3., do the following:. Connect the high voltage side of the transformer to a dc power source as shown in Figure 3.4.. Adjust the voltage source such that you measure.a and.4a in the windings. Record the voltage adjusted in Table 3.. 3. Repeat the previous steps to measure the resistance of the low voltage winding. (3.) Winding Ammeter Reading [A] Voltmeter Reading [V] R X [Ω] High voltage side. V.4 Low voltage side.5 x 5V (series).7 Table 3.: DC test readings 45344: Electrical Machines for Mechatronics Laboratory 3 4
Figure 3.4.a: DC test wiring diagram Figure 3.4.b: DC test schematic circuit 45344: Electrical Machines for Mechatronics Laboratory 3 5
Load Test Introduction In the transformer load test the primary winding is connected to the supply voltage and various load levels are applied on the secondary winding. The with-load actual transformer efficiency ( η actual ) can be determined mathematically from experimental readings as P out η actual =.% Pin (3.) where Pout = { V.I* }. If the load is purely resistive, then Pout = V.I (3.3) Note that in practice the output power would be measured. The theoretical on-load transformer efficiency can be predicted from the transformer equivalent circuit using the following equation P + + (3.4) out η actual =.% Pout Pcu Piron Transformer iron core losses P iron and copper losses P Cu are defined as V P iron = Rm ' cu = P I.R (3.5) (3.6) ' where I = I /a. The maximum transformer efficiency occurs when the variable losses (dependent upon the current drawn) equal the fixed losses (independent of the current drawn) P iron = P (3.7) cu For detail about the proof, refer to Appendix 3.. Because a real transformer has series impedance within it, the output voltage of a transformer varies with load even of the input voltage remains constant. With-load voltage regulation (VR) is a quantity that compares the output voltage at no load with the output voltage at certain load. It is defined by the equation V (no-load) - V (with-load) VR actual =.% (3.8) V (with-load) 45344: Electrical Machines for Mechatronics Laboratory 3 6
Procedures Using the lab equipments shown in Figure 3., do the following:. Connect a resistive load to the series combination of the 5V terminals of the tested transformer as shown in Figure 3.5.. Calculate the value of the protection resistance that is inserted in the circuit shown in Figure 3.5. 3. Adjust the primary voltage to V, and keep it constant during the test. 4. Slowly increase the load current by decreasing the ohmic value of the resistive load, and then complete Table 3.. I - primary current[a].7.4..9.5 P -input power[w] V load voltage[v] I load current[a] P output power[w] η Voltage Regulation Table 3.: Load test results 45344: Electrical Machines for Mechatronics Laboratory 3 7
a b a b 43V 5A 43V 5A V 8A 4V 8A V A 4V A 5V A % KY DL 3M L L L3 N L L L3 L L L3 L+ L L+ L 5 5 6 Transformer Resistive Load Protector Figure 3.5.a: Load test wiring diagram Figure 3.5.b: Load test schematic circuit 45344: Electrical Machines for Mechatronics Laboratory 3 8
Appendix 3. The transformer efficiency can be written as V I cosθ η = V I P P cosθ + iron + cu (3.9) to find out the maximum efficiency when the load power factor and secondary voltage are constants, the first time derivative of efficiency is taken to the secondary current as η = I (3.) thus, η V I cosθ I I V I + I R + P = cosθ iron (3.) where R = Req referred to the secondary. Equation (3.) can be re-written as V θ VI θ + Piron + IR VI VI θ + IR = ( cos θ iron ) η cos ( cos ) ( cos ) I V I + P + I R (3.) thus, when equation (3.) is applied, the following expression is obtained θ θ iron θ V cos ( V I cos + P + I R ) V I ( V I cos + I R ) = (3.4) and then iron P = I R = P (3.5) cu 45344: Electrical Machines for Mechatronics Laboratory 3 9