Exercise 10 Transformers EXERCISE OBJECTIVE When you have completed this exercise, you will be familiar with the basic operating principles of transformers, as well as with the different ratios of transformers: turns ratio, voltage ratio, and current ratio. You will know the difference between step-up and step-down transformers. You will also be introduced to the voltage regulation of a transformer. You will be familiar with three basic types of transformers: control transformers, power transformers, and isolation transformers. DISCUSSION OUTLINE The Discussion of this exercise covers the following points: Introduction to transformers Transformer operation Transformer turns, voltage, and current ratios Step-up and step-down transformers Step-up transformers. Step-down transformers. Transformer voltage regulation Magnetizing current Types of transformers Control transformers. Power transformers. Isolation transformers. Training system module Control Transformer module. DISCUSSION Introduction to transformers Transformers basically consist of two inductors (i.e., coils of wire) wound around a common core of ferromagnetic material such as iron. One coil is called the primary while the other is called the secondary. Each of these s is electrically isolated one from the other (no current flows between the two s). The primary is the one connected to the ac power source, while the secondary is the one connected to the load. Since transformers are bidirectional devices, any of a transformer can be used as the primary or secondary. Transformers allow power to be transferred from the primary to the secondary through the magnetic field produced by each inductor. They also allow voltage and current to be modified from one to the other. Due to these properties, transformers are commonly found in ac circuits. Table 19 shows the electrical diagram symbol for a transformer. The symbol for the transformer shows two inductors separated by two lines. Those lines indicate that each is wrapped around an iron core. Festo Didactic 89688-00 205
Exercise 10 Transformers Discussion Table 19. Transformer symbol. Component Symbol Transformer operation Consider the circuit shown in Figure 171. This circuit illustrates an ac power source connected to the primary of a transformer. A resistor is connected to the secondary of the transformer. Figure 172 shows the transformer in Figure 171 in more detail. Note that terminals A, B, C, and D in the circuit correspond to the same terminals in the detailed view. A C AC power source 24 V Primary 100 turns Secondary 100 turns Resistor 60 B D Figure 171. Circuit of an ac power source connected to a resistor through a transformer. A Primary 100 turns B C Secondary 100 turns D Magnetic field Figure 172. Detailed view of the transformer in Figure 171. When the ac power source in Figure 171 applies a voltage to the primary of the transformer, current flows in the circuit connected to the primary. 206 Festo Didactic 89688-00
Exercise 10 Transformers Discussion This causes the primary to produce a magnetic field in the iron core of the transformer, as shown in Figure 172. This magnetic field then induces a voltage across the secondary of the transformer. This voltage is applied to the resistor, causing current to flow in the circuit connected to the secondary. Therefore, power has been transferred from the primary of the transformer to the secondary through electromagnetic induction, with no electric contact between the primary and secondary. This explains why transformers have the property to isolate the ac power source from the load. Transformer turns, voltage, and current ratios As mentioned previously, transformers have a primary and a secondary. The ratio between the number of turns of wire in the primary ( ) and the number of turns of wire in the secondary ( ) is called the turns ratio. This ratio determines the voltage and current ratios between the input and output of the transformer. In this manual, the voltage across the primary of a transformer is referred to as the primary voltage, while the voltage across the secondary of a transformer is referred to as the secondary voltage. Consider, for example, the transformer in Figure 171. In the figure, the transformer primary is wound with the same number of turns as the secondary. Therefore, the turns ratio : of the transformer is 1:1. Knowing the turns ratio of a transformer allows for the calculation of its voltage ratio. This ratio is equal to the ratio between the primary voltage of the transformer and the secondary voltage. It is expressed as a ratio : and is calculated using the following equation: (26) where is the primary voltage of the transformer, expressed in volts (V) is the secondary voltage of the transformer, expressed in volts (V) is the number of turns in the primary of the transformer is the number of turns in the secondary of the transformer The secondary voltage of a transformer can thus be calculated using the following equation: (27) Festo Didactic 89688-00 207
Exercise 10 Transformers Discussion In this manual, the current flowing in the primary of a transformer is referred to as the primary current, while the current flowing in the secondary of a transformer is referred to as the secondary current. Knowing the turns ratio of a transformer also allows for the calculation of its current ratio. This ratio determines the ratio between the primary current of the transformer and the secondary current. It is expressed as a ratio : and is calculated using the following equation: (28) where is the primary current of the transformer, expressed in amperes (A) is the secondary current of the transformer, expressed in amperes (A) The secondary current of a transformer can thus be calculated using the following equation: (29) Using these equations, it is possible to calculate both the primary and secondary voltages and currents in the circuit of Figure 171. The secondary voltage is equal to: The secondary current is equal to: Finally, the primary current is equal to: These values indicate that, when the turns ratio of a transformer is 1:1, the primary voltage and current are equal to the secondary voltage and current. Therefore, the voltage and current ratios of the transformer are both also 1:1. Using the above values, it is also possible to calculate the power supplied to the transformer, as well as the power supplied by the transformer to the load. The power at the primary is equal to: The power at the secondary is equal to: As you can see, the power at the primary is equal to the power at the secondary. This is an important property of transformers and is always 208 Festo Didactic 89688-00
Exercise 10 Transformers Discussion true in theory, no matter the turns, voltage, and current ratios of the transformer. In practice, however, the power at the secondary of a transformer is always slightly lower than the power expected in theory. This is because transformers are never 100% efficient and certain power losses occur during the power transfer from the primary to the secondary. Step-up and step-down transformers In the previous section, you saw that a transformer with a turns ratio of 1:1 has the same number of turns in the primary as in the secondary. Therefore, the transformer voltage and current ratios are also equal to 1:1. However, most transformers have a turns ratio different than 1:1. These transformers are referred to as step-up transformers and step-down transformers. Step-up transformers In step-up transformers, the number of turns in the transformer primary is lower than the number of turns in the secondary, as illustrated in Figure 173. In the figure, the transformer has twice as many turns in the secondary as in the primary. Therefore, the transformer turns ratio is 1:2. A Primary 100 turns B C Secondary 200 turns D Figure 173. Step-up transformer with a turns ratio of 1:2. If terminals A, B, C, and D of the transformer in Figure 173 are connected to the corresponding terminals of the circuit in Figure 171, it is possible to calculate both the primary and secondary voltages and currents in the circuit. The secondary voltage is equal to: The secondary current is equal to: Magnetic field Festo Didactic 89688-00 209
Exercise 10 Transformers Discussion Finally, the primary current is equal to: Using the above values, it is also possible to calculate the power supplied to the transformer, as well as the power supplied by the transformer to the load. The power at the primary is equal to: The power at the secondary is equal to: As you can see from these calculations, the secondary voltage of a step-up transformer is higher than the primary voltage by a ratio equal to the turns ratio. Conversely, the secondary current of a step-up transformer is lower than the primary current by a ratio equal to the turns ratio. Finally, the power at the primary is equal to the power at the secondary. The characteristics of step-up transformers are summed up below. Step-down transformers In step-down transformers, the number of turns in the transformer primary is higher than the number of turns in the secondary, as illustrated in Figure 174. In the figure, the transformer has twice as many turns in the primary as in the secondary. Therefore, the transformer turns ratio is 2:1. A Primary 200 turns B C Secondary 100 turns D Magnetic field Figure 174. Step-down transformer with a turns ratio of 2:1. 210 Festo Didactic 89688-00
Exercise 10 Transformers Discussion If terminals A, B, C, and D of the transformer in Figure 174 are connected to the corresponding terminals of the circuit in Figure 171, it is possible to calculate both the primary and secondary voltages and currents in the circuit. The secondary voltage is equal to: The secondary current is equal to: Finally, the primary current is equal to: Using the above values, it is also possible to calculate the power supplied to the transformer, as well as the power supplied by the transformer to the load. The power at the primary is equal to: The power at the secondary is equal to: As you can see from these calculations, the secondary voltage of a step-down transformer is lower than the primary voltage by a ratio equal to the turns ratio. Conversely, the secondary current of a step-down transformer is higher than the primary current by a ratio equal to the turns ratio. Finally, the power at the primary is equal to the power at the secondary. The characteristics of step-down transformers are summed up below. Transformer voltage regulation In actual transformers, the higher the current flowing in the secondary, the more the secondary voltage decreases. The graph in Figure 175 shows the typical curve of the secondary voltage of a transformer as a function of its secondary current. This curve is the voltage regulation curve of the transformer. As you can see, the transformer secondary voltage decreases as the secondary current increases (i.e., as the load connected to the transformer becomes more important). Festo Didactic 89688-00 211
Exercise 10 Transformers Discussion 120 Secondary voltage (% of transformer voltage rating) 110 100 90 80 70 60 50 40 30 20 10 0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 Secondary current (% of transformer current rating) Figure 175. Typical voltage regulation curve of a transformer. The extent of the decrease in the secondary voltage as the secondary current increases depends on the transformer voltage regulation. Therefore, the voltage regulation of a transformer is its ability to maintain the secondary voltage constant as the secondary current increases. The better the voltage regulation of a transformer, the less the secondary voltage decreases as the secondary current increases. The voltage regulation of a transformer is calculated using Equation (30). (30) where is the no-load (when secondary current is null) secondary voltage of the transformer, expressed in volts (V) is the full-load (when secondary current is equal to current rating) secondary voltage of the transformer, expressed in volts (V) In order to obtain the rated voltage at full load, the transformers are winded to produce a voltage higher than the rated voltage when the load is null (to compensate for the voltage drop caused by the current increase). This explains why you measure more than 24 V ac at the output of the transformer of the Control Transformer module. Magnetizing current Even with no load connected to the secondary of a transformer, current flows through the primary as soon as ac voltage is applied to the primary 212 Festo Didactic 89688-00
Exercise 10 Transformers Discussion. This current produces the magnetic field required for the operation of the transformer, and is commonly referred to as the magnetizing current, or exciting current. Consequently, some power is lost as heat in an actual transformer even when no load is connected to the secondary. Types of transformers There are many different types of transformers defined by both the function of the transformer and its characteristics. The most important types of transformers are covered in the following subsections. Control transformers Control transformers are generally used in electronic applications requiring a steady voltage or current. Control transformers usually have a low voltage and current rating, which means that they are used for applications requiring a relatively low power. They are often used to step-down the voltage. Figure 176 shows a typical control transformer; the transformer in the Control Transformer module is another example of this type of transformer. Figure 176. Control transformer ( Siemens AG 2014, all rights reserved). Power transformers Power transformers are generally used to step-up or step-down the voltage of ac transmission lines. Because such transmission lines transfer large amounts of power, power transformers usually have high voltage, current, and power ratings. Also, since transformers have a better efficiency when they do not operate at their maximal ratings, power transformers often have a higher rating than necessary. This ensures that power transformers are highly efficient, an important property considering the amount of power that they transfer. Figure 177 shows a typical power transformer. Festo Didactic 89688-00 213
Exercise 10 Transformers Discussion Figure 177. Power transformer. Isolation transformers Isolation transformers are used primarily for the electrical insulation provided by transformers. Although most transformers provide electrical insulation, the materials composing isolation transformers as well as their construction ensure a maximal electrical insulation. Because of this, isolation transformers prevent electric shocks, suppress electrical noise, and transfer power between two circuits which must not be connected. Isolation transformers are often used in circuits containing sensitive electrical loads, such as in a hospital. Isolation transformers usually have a turns ratio of 1:1 and thus have virtually no effect on the voltage and current in a circuit. Training system module Control Transformer module Control transformer Fuse Primary terminals (high voltage) Secondary terminals (low voltage) IEC symbol for a transformer and a fuse (a) Control Transformer (120 V version). 214 Festo Didactic 89688-00
Exercise 10 Transformers Discussion Control transformer Fuse Primary terminals (high voltage) Secondary terminals (low voltage) IEC symbol for a transformer and a fuse (b) Control Transformer (220-240 V version). Figure 178. Control Transformer module. The Control Transformer module is supplied with intermediate points of connection called "tap" on the primary to adjust the transformer voltage to the correct input voltage. Consider the control transformer of the Control Transformer module. This control transformer is winded to produce 24 V when a voltage of 480 V is applied to its primary. The transformer will also produce 24 V when voltages are applied to the corresponding intermediate terminals at the primary. The maximum voltage that should be applied to the primary of the transformer is 480 V (turns ratio of 20:1) and the maximal power that the transformer should transfer is 75 VA. Not respecting these ratings could damage the transformer. Note that the power rating of transformers is usually given in VA, which stands for volt-amperes, instead of in watts. This value is equal to the product between current and voltage, just like for regular power values. The reasoning behind the use of volt-amperes instead of watts for the power rating of transformers is beyond the scope of this manual. The connections to the primary of the control transformer are made through 4 mm terminals (high voltage connections), and the connections to the secondary are made through 2 mm terminals (low voltage connections). Intermediate points of connection to the primary as well as the connection to the secondary are fuse protected. The Control Transformer module is also equipped with four fault switches and two ground terminals. Festo Didactic 89688-00 215
Exercise 10 Transformers Procedure Outline PROCEDURE OUTLINE The Procedure is divided into the following sections: Setup Calculating the ratios and ratings of a transformer Troubleshooting a transformer Measuring the ratios and ratings of a transformer Transformer voltage regulation PROCEDURE High voltages are present in this laboratory exercise. Do not make or modify any banana jack connections with the power on unless otherwise specified. Setup In this section, you will install the training system modules in the workstation. 1. Refer to the Equipment Utilization Chart in Appendix A to obtain the list of equipment required to perform this exercise. Install the equipment required in the workstation. Make sure that all fault switches are set to the O (off) position. Calculating the ratios and ratings of a transformer In this section, you will consider a circuit containing an ac power source connected to a resistor through a transformer. You will determine the turns, voltage, and current ratios of the transformer. Using these ratios, you will determine the transformer secondary voltage and current, as well as its primary current. Finally, knowing the transformer power rating, you will determine its current rating at the secondary. 2. Consider the circuit in Figure 179 of an ac power source connected to a resistor through a transformer. AC power source 120 V L N Transformer primary 50 turns Transformer secondary 25 turns Resistor 300 Figure 179. AC power source connected to a resistor through a transformer. 216 Festo Didactic 89688-00
Exercise 10 Transformers Procedure 3. Knowing that the transformer in Figure 179 has 50 turns of wire in the primary ( ) and 25 turns of wire in the secondary ( ), calculate the turns ratio of the transformer. a The turns ratio of a transformer is given as follows: : Transformer turns ratio 4. Knowing the transformer turns ratio, determine the voltage ratio and current ratio of the transformer. a The voltage ratio of a transformer is calculated using the following equation: The current ratio of a transformer is calculated using the following equation: Transformer voltage ratio Transformer current ratio 5. Calculate the transformer secondary voltage in the circuit of Figure 179. a The secondary voltage of a transformer is calculated using the following equation: Transformer secondary voltage V 6. Knowing that the resistance of the resistor is equal to 300 and the transformer secondary voltage you calculated in the previous step, calculate the secondary current in the circuit of Figure 179. a Ohm s law states that: Transformer secondary current A Festo Didactic 89688-00 217
Exercise 10 Transformers Procedure 7. Knowing the transformer secondary current, calculate the primary current in the circuit of Figure 179. a The primary current of a transformer is calculated using the following equation: Transformer primary current A 8. Knowing that the power rating of the transformer in Figure 179 is 20 VA, calculate the current rating of the transformer secondary. a The current rating of the transformer can be calculated using the following equation: Current rating of secondary A 218 Festo Didactic 89688-00
Exercise 10 Transformers Procedure Troubleshooting a transformer In this section, you will use an ohmmeter to measure the resistance between all terminals of the control transformer. You will use the measured values to confirm whether continuity is present or not between the different pairs of terminals, and analyze the results. 9. Consider the circuit in Figure 180 showing the control transformer of the Control Transformer module. Primary 480 V 24 V 240 V 208 V 120 V Secondary 0 V 0 V (a) Control Transformer (for 120 V model) Primary Secondary 480 V 24 V 240 V 208 V 0 V 0 V (b) Control transformer (for 220-240 V model) Figure 180. Control transformer of the Control Transformer module. Festo Didactic 89688-00 219
Exercise 10 Transformers Procedure 10. Using an ohmmeter, measure the resistance between the terminals of the control transformer indicated below. Record the resistance values in Table 20 (for 120 V) or Table 21 (for 220-240 V). Table 20. Resistance between the terminals of the control transformer (120 V model). Resistance between the terminals of the control transformer () Secondary Primary 0 V 24 V 0 V 120 V 208 V 240 V 480 V Secondary 0 V 24 V 0 V Primary 120 V 208 V 240 V 480 V Table 21. Resistance between the terminals of the control transformer (for 220-240 V model). Resistance between the terminals of the control transformer () Secondary Primary 0 V 24 V 0 V 208 V 240 V 480 V Secondary Primary 0 V 24 V 0 V 208 V 240 V 480 V 11. From the resistance values you recorded in the previous step, what can you conclude regarding the continuity between the different terminals of the transformer? 220 Festo Didactic 89688-00
Exercise 10 Transformers Procedure 12. Can you conclude that the transformer provides electrical insulation between the primary and secondary s? Briefly explain. Measuring the ratios and ratings of a transformer In this section, you will connect an ac power source to a resistor through the control transformer of the Control Transformer module. You will measure the primary and secondary voltages and currents, and use these values to determine the transformer turns, voltage, and current ratios. You will calculate the power at the primary and at the secondary s of the transformer. You will determine if the transformer is currently a step-up transformer, or a step-down transformer. 13. Make sure that the main power switch on the Power Source module is set to the O (off) position, then connect it to an ac power outlet. Set up the circuit shown in Figure 181. Connect the two 50 resistors of the Resistors module in parallel to implement the 25 resistor. Primary Secondary Connect to the tap that corresponds to your line voltage 480 V 24 V AC power source L N 240 V 208 V 120 V Resistor 25 0 V 0 V (a) For 120 V model. Festo Didactic 89688-00 221
Exercise 10 Transformers Procedure Primary Secondary Connect to the tap that corresponds to your line voltage 480 V 24 V AC power source L N 240 V 208 V Resistor 25 0 V 0 V (b) For 220-240 V model. Figure 181. AC power source connected to a resistor through a transformer. 14. Turn the power source on. Measure the transformer primary voltage and secondary voltage. Record the values below. Transformer primary voltage V Transformer secondary voltage V 15. Measure the transformer primary current and secondary current by successively connecting the ammeter at the two positions shown in Figure 181. Record the values below. b Make sure to turn the power source off before making any change to the circuit connections. Also make sure to turn it back on before taking any measurements. Transformer primary current A Transformer secondary current A 16. Using the voltage and current values you measured in steps 14 and 15, determine the transformer turns, voltage, and current ratios. Transformer turns ratio Transformer voltage ratio Transformer current ratio 222 Festo Didactic 89688-00
Exercise 10 Transformers Procedure a Note that the transformer current ratio does not correspond to the expected ratio. The difference is caused by the magnetizing current and by losses in the transformer. 17. Using the primary and secondary voltages and currents you measured in steps 14 and 15, calculate the power at the primary of the transformer and the power at the secondary. a Power is calculated using the following equation: Primary power VA Secondary power VA a Note that because of the magnetizing current and losses in the transformer, the power is significantly higher than the power for this type of transformer. For larger transformers such as power transformers, the efficiency is higher and the power at the secondary is more similar to that at the primary. 18. When connected as shown in Figure 181, does the control transformer operate as a step-up transformer, or as a step-down transformer? Briefly explain. 19. Turn the power source off. Festo Didactic 89688-00 223
Exercise 10 Transformers Procedure Transformer voltage regulation In this section, you will vary the load connected to the control transformer. For each load change, you will measure the transformer secondary voltage and current. Using the measured values, you will determine the relationship between the transformer secondary voltage and current. 20. Using the transformer secondary voltage and current values you measured in steps 14 and 15, fill in the first row of Table 22. Table 22. Transformer secondary current and voltage for different loads. Resistance () 25 50 100 Secondary voltage (V) Secondary current (A) 21. Modify the circuit in Figure 181 to obtain a resistance of 50 (by removing one of the 50 resistors connected in parallel). 22. Turn the power source on. Measure the control transformer secondary voltage and current. Record the values in the corresponding row of Table 22. 23. Turn the power source off. Modify the circuit in Figure 181 to obtain a resistance of 100 (by connecting the 50 resistors in series). 24. Turn the power source on. Measure the control transformer secondary voltage and current. Record the values in the corresponding row of Table 22. 25. Observe the transformer secondary current and voltage values you recorded in Table 22. What is the relationship between the secondary voltage and the secondary current of the transformer? Briefly explain in regard to the transformer voltage regulation. 224 Festo Didactic 89688-00
Exercise 10 Transformers Conclusion 26. Turn the power source off. Disconnect your circuit. Return the leads and the multimeter(s) to their storage location. CONCLUSION In this exercise, you were introduced to transformers. You became familiar with the basic operating principles of transformers, as well as with the different ratios of transformers: turns ratio, voltage ratio, and current ratio. You learned the difference between step-up and step-down transformers. You were also introduced to the voltage regulation of a transformer. You became familiar with three basic types of transformers: control transformers, power transformers, and isolation transformers. Finally, you were introduced to the Control Transformer module. REVIEW QUESTIONS 1. Briefly define what a transformer is, as well as its basic functions. 2. What is the turns ratio of a transformer and which other ratios does it determine? 3. What are the main differences between a step-down transformer and a stepup transformer? Briefly explain. Festo Didactic 89688-00 225
Exercise 10 Transformers Review Questions 4. Name and briefly define two types of transformers. 5. A step-down transformer has 480 turns of wire in the primary ( ) and 120 turns of wire in the secondary ( ). Determine the secondary voltage of the transformer, knowing that its primary voltage is equal to 100 V. 226 Festo Didactic 89688-00