Three Phase Transformer PDF

Electrical Machines Dr. Shikha Marwaha Shiv Nadar University Chennai Real Transformer The ideal transformer model neglects the following basic linear aspects of real transformers: losses due to joule heating in the core that are proportional to the square of the transform...

Electrical Machines Dr. Shikha Marwaha Shiv Nadar University Chennai Real Transformer The ideal transformer model neglects the following basic linear aspects of real transformers: losses due to joule heating in the core that are proportional to the square of the transformer's applied voltage Joule losses due to resistance in the primary and secondary windings Leakage flux that escapes from the core and passes through one winding only resulting in primary and secondary reactive impedance Hysteresis Hysteresis is the dependence of the state of a system on its history Systems with hysteresis are nonlinear Hysteresis occurs in magnetic materials, as well as in the deformation of rubber bands, electronic circuits, biological systems, economic models, shape-memory alloys and many other places Example: If the top of a rubber band is hung on a hook and small weights are attached to the bottom of the band one at a time, it will stretch and get longer When each weight is taken off, or unloaded, the band will contract as the force is reduced Hysteresis Hysteresis Rate Rate Dependent Independent One type of hysteresis is a lag between input and Systems with rate-independent hysteresis have output. a persistent memory of the past that remains An example is a sinusoidal input X(t) that results in a after the transients have died out. The future sinusoidal output Y(t), but with a phase lag φ development of such a system depends on the history of states visited, but does not fade as the events recede into the past If an input variable X(t) cycles from X0 to X1 and back again, the output Y(t) may be Y0 initially but a different value Y2 upon return. The values of Y(t) depend on the path of values that X(t) passes through but not on the speed at which it traverses the path Rate Independent hysterisis Figures (a) and (b) show two different inputs u1(t) and u2(t) that successively assume the same extremum values but vary differently between these values. Then for the rate-independent HT, these two inputs will result in the same f-u diagram (see (c)), provided that the initial state of the transducer is the same for both inputs. Similarities between Electrical and Magnetic Circuits Magnetic Circuits Electrical Circuits The closed path for the magnetic flux is called The closed path for the electric current is called magnetic circuit. electric circuit. The number of magnetic lines of force decide the The flow of electrons decides the current passing magnetic flux. through the conductor. Reluctance (S) is the opposition by the magnetic Resistance (R) is the opposition by the electric path in the material to the flux. path in the material to the flow of current. Magnetomotive force (MMF) 'drives' magnetic flux Electromotive force (EMF) ‘drives’ a current of through magnetic circuits electrical charge in electrical circuits Hopkinson’s law (or Ohm’s law for magnetic Ohm's law is an empirical relation between the circuits) states that, 𝓕 = 𝚽𝓡 where ℱ is the EMF 𝜀 applied across an element and the current magnetomotive force (MMF) across a magnetic 𝐼 it generates through that element. It is written element, 𝛷 is the magnetic flux through the magnetic as:𝜺 = 𝑰𝑹 where R is the electrical resistance of element, and ℛ is the magnetic reluctance of that that material. element. Materials For Electrical Machines The main material characteristics of relevance to electrical machines are those associated with ✓conductors for the electric circuit (Au, Ag, Cu, Al) ✓the insulation system necessary to isolate the circuits ✓the specialized steels and permanent magnets used for the magnetic circuit. Materials for Electrical Machines (brainkart.com) Materials For Electrical Machines Desirable properties of a good conductor: Low value of resistivity or high conductivity High tensile strength, high melting point High resistance to corrosion Allow brazing, soldering, or welding so that the joints are reliable Durable and cheap by the cost of fabrication Materials for Electrical Machines (brainkart.com) Magnetic Materials for Machines Desirable properties of good magnetic material: Low reluctance or should be highly permeable A high curie point. (Above Curie point or temperature the material loses the magnetic property or becomes paramagnetic, that is effectively non-magnetic) Hysteresis loss is less and efficiency of operation is high Materials for Electrical Machines (brainkart.com) Magnetic Materials for Machines Magnetic materials can be classified as Hard or Permanent Magnetic materials and Soft Magnetic materials. Hard or permanent magnetic materials have large size hysteresis loop (obviously hysteresis loss is more). Ex: carbon steel, tungsten steal, cobalt steel, alnico, hard ferrite, etc Soft magnetic materials have a small-size hysteresis loop. Ex: i) cast iron, cast steel, rolled steel, forged steel, etc Materials for Electrical Machines (brainkart.com) Insulating Materials for Machines To avoid any electrical activity between machine parts at different potentials, insulation is used. Required properties to be insulator: o Should have high dielectric strength. o Should withstand high temperatures. o Should have a high value of resistivity o Should withstand vibration, abrasion, and bending, also should not absorb moisture o Should not deteriorate due to higher temperature and repeated heat cycle o Materials for Electrical Machines (brainkart.com) Three Phase Ideal Transformer Three-phase transformers are more economical for supplying large loads and large power distribution. 3 phase power is used in almost all fields of electrical power systems such as power generation, transmission, and distribution sectors, also all the industrial sectors are supplied or connected with the three- phase system Smaller and lighter to construct for the same power handling capacity, better-operating characteristics, etc. Three Phase Transformer (electronicshub.org) Three Phase Ideal Transformer A three-phase transformer can be built in two ways; (A) a bank of three single-phase transformers or (B) A single unit of a three-phase transformer. single unit of a three-phase transformer bank of three single-phase transformers ▪ If we take three single-phase transformers and connect their primary windings to each other and their secondary windings to each other in a fixed configuration, we can use the transformers on a three-phase supply. Differing in phase-time by 120 degrees Three-phase, also written as 3-phase or 3φ supplies are used for electrical power generation, transmission, and distribution, as well as for all industrial uses. Three Phase Transformer Configuration. A three phase transformer or 3φ transformer can be constructed either by a) connecting together three single-phase transformers, thereby forming a so- called three phase transformer bank b) by using one pre-assembled and balanced three phase transformer which consists of three pairs of single phase windings mounted onto one single laminated core. Three Phase Transformer connections The primary and secondary windings of a three phase transformer can be connected in different configurations. In the case of three phase transformer windings, three forms of connection are possible: a) “star” (wye), b) “delta” (mesh) c) and “interconnected-star” (zig-zag). Transformer Star and Delta Configurations Symbols are generally used on a three-phase transformer to indicate the type or types of connections used with a) upper case Y for star connected, D for delta connected and Z for interconnected star primary windings, b) with lower case y, d and z for their respective secondaries Transformer Winding Identification These four standard configurations are given as: Delta-Delta (Dd) Star-Star (Yy) Star-Delta (Yd) Delta-Star (Dy) Three-phase Voltage and Current  Three Phase Ideal Transformer Advantages : ❖Instead of using three single-phase transformers, a three-phase bank can be constructed with a single three-phase transformer consisting of six windings on a common multi-legged core ❖Weight and cost are reduced as compared to three units of the same rating and windings, and the amount of iron in the core and insulation materials are saved ❖Space required to install a single unit is less compared with three unit bank Disadvantages: ❖ If the fault occurs in any one of the phases, then the entire unit must be removed from the service Three Phase Transformer (electronicshub.org)