Lecture 3-2 Transformers I PDF

Lecture #3 Transformers I Electric Machines ELCT 708 Summer 2020 1  Lecture #3 Transformers I Main Outlines 1. Introduction to transformers 2. Construction of transformers 3. Ideal transformers 4. Practical...

Lecture #3 Transformers I Electric Machines ELCT 708 Summer 2020 1  Lecture #3 Transformers I Main Outlines 1. Introduction to transformers 2. Construction of transformers 3. Ideal transformers 4. Practical transformers  Lecture #3 Transformers I 1. Introduction to transformers What are transformers? A transformer is a device that changes AC electric power at one voltage level to AC electric power at another voltage level through the action of a magnetic field. It consists of two or more coils of wire wrapped around a ferromagnetic core. These coils are (usually) not directly connected. The connection between the coils is the magnetic flux present within the core. 3 Dr. Adel Fouad Electric Machines ELCT 708  Lecture #3 Transformers I 1. Introduction to transformers What are transformers? The ratings of transformers may range from few VA to hundreds MVA 4 Dr. Adel Fouad Electric Machines ELCT 708  Lecture #3 Transformers I 1. Introduction to transformers Why do we need transformers? At the end of the 19th century electric power systems was invented and designed to operate at 120 dc voltage. 5 Dr. Adel Fouad Electric Machines ELCT 708  Lecture #3 Transformers I 1. Introduction to transformers Why do we need transformers? In order to supply enough power for different loads, very large currents at this low voltage need to pass through long transmission lines which will cause huge voltage drops and power losses in the transmission lines. To overcome this problem, power stations should be build beside the loads, a solution that is not efficient. The invention of transformers and the development of AC power sources provides an efficient solution to the above problem. 6 Dr. Adel Fouad Electric Machines ELCT 708  Lecture #3 Transformers I 1. Introduction to transformers Why do we need transformers? A transformer ideally changes one ac voltage level to another voltage level without affecting the actual power supplied. If a transformer steps up the voltage level of a circuit, it must decrease the current to keep the power constant. Therefore, ac electric power can be generated at one central location, its voltage stepped up for transmission over long distances at very low losses, and its voltage stepped down again for final use. 7 Dr. Adel Fouad Electric Machines ELCT 708  Lecture #3 Transformers I 2. Construction of transformers  One type of construction consists of a rectangular laminated piece of steel with the windings wrapped around two sides of the rectangle. This type is known as core form.  One of the windings is called primary winding which is connected to the supply. The other is called secondary which is connected to the load terminals. 8 Dr. Adel Fouad Electric Machines ELCT 708  Lecture #3 Transformers I 2. Construction of transformers  The transformer windings can be classified according to its number of turns and are then called the High voltage side and Low voltage side.  The high voltage side has a number of turns greater than that of the low voltage side.  Any of the two sides can be a primary or a secondary winding based on which is connected to the supply and which is connected to the load.  When the high voltage side acts as the primary coil then the transformer is a step down transformer and if it acts as the secondary coil then the transformer is a step up transformer. 9 Dr. Adel Fouad Electric Machines ELCT 708  Lecture #3 Transformers I 2. Construction of transformers  Another type consists of a three-legged laminated core with the windings wrapped around the central leg. This type is known as shell form.  This type simplifies the problem of insulating the high-voltage winding from the core. And results in much less leakage flux. 10 Dr. Adel Fouad Electric Machines ELCT 708  Lecture #3 Transformers I 3. Ideal Transformer Assumptions The ideal transformer is a theoretical lossless device that has the below assumptions: 1.An infinity permeability core (i.e. reluctance is equal to zero). 2.No Magnetizing current is required. 3.The core has no losses: (no hysteresis losses nor eddy currents losses ). 4.Lossless electrical windings. 5.No leakage fluxes. 11 Dr. Adel Fouad Electric Machines ELCT 708  Lecture #3 Transformers I 3. Ideal Transformer Voltage relation (transformer at no load)  According to faraday’s law the induced emf in primary and secondary are:  From the above equations, it is clear that the voltage per turn is constant on both primary and secondary windings. 12  Lecture #3 Transformers I 3. Ideal Transformer Current relation (transformer at load)  From the magnetic circuit of an ideal transformer we can deduce:  Note that the current of one side is inversely proportional to the turns ratio, while the voltage is directly proportional.  It can be deduced from previous relations that 13 Dr. Adel Fouad Electric Machines ELCT 708  Lecture #3 Transformers I 3. Ideal Transformer Impedance transformation  One of the interesting properties of a transformer is that, impedances can be transferred from on side to the other and hence it is called the apparent impedance of an element. An impedance 𝑍𝐿 in the secondary circuit can be replaced by an equivalent impedance 𝑍𝐿′ in the primary circuit. 14 Dr. Adel Fouad Electric Machines ELCT 708  Lecture #3 Transformers I 3. Ideal Transformer Example 1: A single-phase power system consists of a 450-V 60-Hz generator supplying a load ZL = 4+j3 through transmission line of impedance Zline=0.18+j0.24 Find the value of the load's impedance reflected to the transmission system. 15 Dr. Adel Fouad Electric Machines ELCT 708  Lecture #3 Transformers I 3. Ideal Transformer Example 1: A single-phase power system consists of a 450-V 60-Hz generator supplying a load ZL = 4+j3 through transmission line of impedance Zline=0.18+j0.24 Re-draw the system with the load and transmission line referred to the generator's voltage level. 16 Dr. Adel Fouad Electric Machines ELCT 708  Lecture #3 Transformers I 4. Practical Transformer The assumptions made in ideal transformers are no longer valid in practical(real) transformers; hence in practical transformers we have: 1. Non-infinite permeability (reluctance not equal to zero) 2. Magnetizing current exists 3. Core losses 4. Resistances in windings 5. Leakage fluxes 17 Dr. Adel Fouad Electric Machines ELCT 708  Lecture #3 Transformers I 4. Practical Transformer 1) When ac power source is connected to a transformer, a current flows in its primary circuit, even when the secondary circuit is open circuited. This current is called the no load current (Io) or the excitation current and it consists of two components: 1. Magnetizing current (Im) to overcome the reluctance of the core. 2. Core loss current (Ic ) to overcome the core losses. 𝐼𝑜 = 𝐼𝑚 + 𝐼𝑐 𝑒1 𝑒2 18 Dr. Adel Fouad Electric Machines ELCT 708  Lecture #3 Transformers I 4. Practical Transformer 2) The magnetizing current (Im) is responsible for producing the magnetizing flux that flows in the magnetic core and induces E1 and E2 in the primary and secondary windings respectively. It can be found using the below relation: 𝑁1 𝐼𝑚 = 𝜑ℛ 19 Dr. Adel Fouad Electric Machines ELCT 708  Lecture #3 Transformers I 4. Practical Transformer 3) The induced voltages in primary and secondary can be expressed as: The Max. Value and the RMS value of the induced voltages can be found as: Since the source of the flux is AC, then;  The max value of induced emf is:  The RMS value of induced emf is: 20 Dr. Adel Fouad Electric Machines ELCT 708  Lecture #3 Transformers I 4. Practical Transformer 4) Now if a load is connected across the secondary terminals, a secondary current (I2) will flow in the secondary windings. 5) The secondary current will produce a flux that will decrease the magnetizing flux produced by the primary current. 6) The net flux is decreased compared to the no load case, and consequently the induced emfs E1and E2 will decrease. 21 Dr. Adel Fouad Electric Machines ELCT 708  Lecture #3 Transformers I 4. Practical Transformer 7) A difference between V1 and E1 will appear that is not electrically permitted, hence the flux must be re-increased which can be done by increasing the current in the primary winding. 8) The increase in the primary current due to the effect of the load current I2 is denoted as(𝐼2 ′ ), 9) Now, the total current in the primary is I1and is the sum of 𝐼2 ′ and Io. 𝐼1 = Io+ 𝐼2 ′ 22 Dr. Adel Fouad Electric Machines ELCT 708  Lecture #3 Transformers I 4. Practical Transformer 10) To find 𝐼2 ′ , the equivalent magnetic circuit can be used as follows: 𝑁1 𝐼𝑚 + 𝑁1 𝐼2 ′ = 𝜑ℛ + 𝑁2 𝐼2 ∵ 𝑁1 𝐼𝑚 =𝜑ℛ ∴ 𝑁1 𝐼2 ′ = 𝑁2 𝐼2 𝐼2 ′ 𝑁2 = 𝐼2 𝑁1 23 Dr. Adel Fouad Electric Machines ELCT 708