Three-Wattmeter Method of Three Phase Power Measurement



VELAMMAL INSTITUTE OF TECHNOLOGY, CHENNAI- 601204DEPARTMENT ELECTRICAL AND ELECTRONICS ENGINEERINGBE8254 - BASIC ELECTRICAL AND INSTRUMENTATION ENGINEERINGPART B WITH HINTUNIT I ACCIRCUIT AND POWER SYSTEMWith a neat circuit and phasor diagram explain the three phase power measurement by two wattmeter methodlefttopNow, the sum of two Wattmeter readings will be given asThe above equation (1) gives the total power absorbed by a 3 phase balanced load.Thus, the sum of the readings of the two Wattmeters is equal to the power absorbed in a 3 phase balanced load.Determination of Reactive Power by Two Wattmeter MethodTo get the reactive power, multiply equation (3) by √3.Therefore, the Reactive Power is given by the equation shown below.Draw the interconnection between three phase, delta connected source and star connected source When we measure?voltage and current?in three-phase systems, we need to be specific as to?where?we’re measuring.?Line voltage?refers to the amount of voltage measured between any two line conductors in a balanced three-phase system. With the above circuit, the line voltage is roughly 208 volts.?Phase voltagerefers to the voltage measured across any one component (source winding or load?impedance) in a balanced three-phase source or load. For the circuit shown above, the phase voltage is 120 volts. The terms?line current?and?phase current?follow the same logic: the former referring to current through any one line conductor, and the latter to current through any one component.What are the different methods of three phase power measurement? Explain them in detailsPower measurement?in an AC circuit is measured with the help of a Wattmeter. A Wattmeter is an instrument which consists of two coils called?Current coil?and?Potential coil.?The current coil having low resistance is connected in series with the load so that it carries the load current. The potential coil having the resistance is connected across the load and carries the current proportional to the potential difference.Three-Wattmeter Method of Three Phase Power MeasurementThree Wattmeter method is employed to measure power in a 3 phase, 4 wire system.However, this method can also be employed in a 3 phase, 3 wire delta connected load, where power consumed by each load is required to be determined separately.-85725382270 W1?= V1I1 W2?= V2I2 W3?= V3I3Two Wattmeter Method of Power Measurement What is meant by tariff? Explain in details?Background: Tariffs Tariffs are the most common kind of barrier to trade; indeed, one of the purposes of the WTO is to enable Member countries to negotiate mutual tariff reductions. Before we consider the legal framework that provides the discipline regarding tariffs, we must understand the definition of tariffs, their functions, and their component elements (rates, classifications, and valuations). (a) Definition of “Tariff” A tariff is a tax imposed on the import or export of goods.1 In general parlance, however, a tariff refers to “import duties” charged at the time goods are imported.2 (b) Functions of Tariffs Tariffs have three primary functions: to serve as a source of revenue, to protect domestic industries, and to remedy trade distortions (punitive function). The revenue function comes from the fact that the income from tariffs provides governments with a source of funding. In the past, the revenue function was indeed one of the major reasons for applying tariffs, but economic development and the creation of systematic domestic tax codes have reduced its importance in the developed countries. For example, Japan generates about 90 billion yen in tariff revenue, but this is only 1.7 percent of total tax revenues (fiscal 1996). In some developing countries, however, revenue may still be an important tariff function.(c) Tariff Rates Obviously, one of the most important components in tariff measures is the rate at which the tariff is imposed. As noted in the discussion of the three functions of tariffs, any imposition of a tariff has the potential to reduce the welfare of the world economy as a whole. Since 1947, the GATT has been the standard bearer in an on-going process of reducing tariff levels.Explain in details about power factor improvement.Static CapacitorSynchronous CondenserPhase AdvanceStatic CapacitorThese static capacitors provides leading current which neutralize (totally or approximately) the lagging inductive component of load current (i.e. leading component neutralize or eliminate the lagging component of load current) thus power factor of the load circuit is improved.Synchronous CondenserWhen a Synchronous motor operates at No-Load and over-exited then it’s called a synchronous Condenser. Whenever a Synchronous motor is over-exited then it provides leading current and works like a capacitor.Advantages:Long life (almost 25 years)High ReliabilityStep-less adjustment of power factor.No generation of harmonics of maintenance?The faults can be removed easilyIt’s not affected by harmonics.Require Low maintenance (only periodic bearing greasing is necessary)Disadvantages:It is expensive (maintenance cost is also high) and therefore mostly used by large power users.An auxiliary device has to be used for this operation because synchronous motor has no self starting torqueIt produces noisePhase AdvancerPhase advancer is a simple AC exciter which is connected on the main shaft of the motor and operates with the motor’s rotor circuit for power factor improvement. Phase advancer is used to improve the power factor of induction motor in industries.Advantages:Lagging kVAR (Reactive component of Power or reactive power) drawn by the motor is sufficiently reduced because the exciting ampere turns are supplied at slip frequency (fs).The phase advancer can be easily used where the use of synchronous motors is UnacceptableDisadvantage:Using Phase advancer is not economical for motors below 200 H.P. (about 150kW)Power Factor Improvement in single phase and three phase star & delta connectionsPower factor improvement in three phase system by connecting a capacitor bank in(1). Delta connection(2). Star Connection) UNIT IITRANSFORMERSExplain in detail constructional and operational features of transformer.These can be broadly divided intoCore construction 2. Winding arrangements 3. Cooling aspectsCore construction Transformer core for the power frequency application is made of highly permeable material. The high value of permeability helps to give a low reluctance for the path of the flux and the flux lines mostly confine themselves to the iron. Relative permeability ?r well over 1000 are achieved by the present day materials. Generally, the name associated with the construction of a transformer is dependant upon how the primary and secondary windings are wound around the central laminated steel core. The two most common and basic designs of transformer construction are the?Closed-core Transformer?and the?Shell-core Transformer.Transformer Core TypesTransformer Core LossesThe ability of iron or steel to carry magnetic flux is much greater than it is in air, and this ability to allow magnetic flux to flow is called?permeability.Hysteresis LossesTransformer Hysteresis Losses are caused because of the friction of the molecules against the flow of the magnetic lines of force required to magnetise the core, which are constantly changing in value and direction first in one direction and then the other due to the influence of the sinusoidal supply voltage.Deduce the emf equation of a transformer. Prove that induced emf will lag the alternating flux producing that emf. EMF Equation of TransformerLet, N1=Primary number of turnsN2?=Secondary number of turnsf = Frequency of supply in HzThe flux in the core increases from zero to Φm?in one quarter cycle (1/4 second) Therefore, average rate of change of flux = Φm/(1/4f) = 4f ΦmAverage emf induced per turn = Average rate change of flux x 1 =4f Φm?Volts?RMS value of induced emf per turn = 1.11 x 4f Φm?= 4.44f Φm?VoltsRMS value of induced emf in primary, E1?= 4.44f Φm?N1?Volts?RMS value of induced emf in secondary, E2?= 4.44f Φm?N2?VoltsIn an ideal transformer on no load, V1?= E1, V2?= E2Define voltage regulation of a transformer. Deduce the expression for voltage regulation. The voltage regulation is the percentage of?voltage?difference between no load and full load voltages of a transformer with respect to its full load voltage.Voltage Regulation of Transformer for Lagging Power FactorNow we will derive the expression of voltage regulation in detail. Say lagging?power factor?of the load is cosθ2, that means angle between secondary current and voltage is θ2.Explain OC and SC test on a transformer, Develop the equivalent circuit from the above test.Explain in details about three phase transformer connectionshree-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.UNIT III DC MACHINESDescribe with neat sketches the constructional features of a dc machine, stating the material and uses of each component. Stator????????? The stator of the dc machine has poles, which are excited by either dc current or ?permanent magnets to produce magnetic fields.?In the neutral zone, in t he middle between the poles, commutating poles are placed to reduce sparking of the commutator.?Compensating windings are mounted on the main poles. These reduce flux weakening commutation problems.The poles are mounted o n an iron core that provides a closed magnetic circuit.?Rotor????????? The rotor has a ring-shaped laminated iron core with slots. Coils with several turns are placed in the slots. The distance between the two legs of the coil is about 180 electric degrees.?The rotor coils are connected in series through the commutator segments.The ends of each coil are connected to a commutator segment.What is meant by speed control of a dc motor. Explain the various methods in detail. Flux controlThe flux is dependent on the current through the shunt field winding. Thus flux ?can be controlled by adding a rheostat (variable resistance in series with the shunt field winding as shown in above figure.Armature voltage control or rheostatic control? The speed is directly proportional to the voltage applied across the armature.Applied voltage controlDerive the torque equation of a dc motor .?Torque EquationTurning or twisting force about an axis is called torque.Consider a wheel of radius R meters acted upon by a circumferential force F Newton’s as shown in above figure. The wheel is rotating at a speed of N rpm.?The angular speed of the wheel ω = 2πN/60 rad/secWork done in one revolution W= Force x distanced travelled in one revolutionW = FX2πR joules?Power developed, P = Work done/time = W/Time for 1 rev.???? P = FX2πR/(60/N) = (FXR)(2πN/60)?P = T x ω watts?Power in armature = armature torque x ω?EbIa?= Ta?x (2ΠN/60)?Where, Ta???????????? = Armature torque.Eb?= PΦZN/60ASubstituting Eb?values, we get,?Ta = 0.159ΦIa?(PZ/A) N-mDiscuss the characteristics of all types of dc motorsD.C Shunt MotorD.C Series MotorD.C Compound MotorLong shunt connectionDraw and Explain the operation of universal motorThe?universal motor?is so named because it is a type of electric?motor?that can?operate?on AC or DC power. It is a commutated series-wound?motor?where the stator's field coils are connected in series with the rotor windings through a commutator. It is often referred to as an AC series?motor.UNIT IV AC MACHINESExplain construction and principle of working of a 3-phase Induction motor. A stator consists of steel frame that supports a hollow cylindrical core of stacked laminations.Slots on the internal circumference of stator house the stator winding.?A rotor also composed of punched laminations, with rotor slots for the rotor winding.There are two types of rotor windings:Squirrel cage windings, which produce squirrel cage induction motor.Conventional three phase windings made up of insulated wire, which produce a wound rotor induction motor.Squirrel cage rotor consists of copper bars slightly longer than rotor which is pushed in to the slots.The ends are welded to copper end rings, so that all the bars are short circuited.?A wound rotor has three phase winding similar to the stator winding.?The rotor winding terminals are connected to three slip rings which turn with the rotor.?The slip rings/brushes allow external resistors to be connected in series with the winding.The external resistors are mainly used during start up. Under normal running conditions the windings short circuited externally.WorkingInduction motor works on the principle of Faraday’s laws of electromagnetic induction.When the three supply is given to the stator of an induction motor, rotating magnetic field is produced around the stator.This field cuts the rotor conductors; an emf is produced as per Faraday’s laws of electromagnetic induction.The induced voltage produces currents which circulate in a loop around the conductors.Since the current carrying conductors lie in the magnetic field, they experience mechanical force (Torque).The force is always acts in a direction to drag the conductor along with the magnetic field.Draw and explain the torque- slip characteristic of 3-phase Induction motor.Torque Slip Characteristics of Three Phase Induction Motor. The torque slip curve for an induction motor gives us the information about the variation of torque with the slip. The slip is defined as the ratio of difference of synchronous speed and actual?rotor speed?to the synchronous speed of the machine.Develop the equivalent circuit for a 3-phase Induction motor and explain. Where?ER?is the induced voltage in the rotor and?RR?is the rotor resistance.Now we can calculate the rotor current as,Explain the double revolving field theory for operation of single phase induction motorDefine regulation of alternator and explain the experimental procedure to predetermine the same using synchronous impedence methodThe?Synchronous Impedance?Method or Emf Method?is based on the concept of replacing the effect of armature reaction by an imaginary reactance. For calculating the regulation, the synchronous method requires the following data; they are the armature resistance per phase and the open circuit characteristic.The open circuit characteristic is the graph of the circuit voltage and the field current. This method also requires short circuit characteristic which is the graph of the short circuit and the field current.For a synchronous generator following are the equation given belowWhere,Calculation of Synchronous ImpedanceThe following steps are given below for the calculation of the synchronous impedance.The open circuit characteristics and the short circuit characteristic are drawn on the same curve.Determine the value of short circuit current Isc?and gives the rated alternator voltage per phase.The synchronous impedance ZS?will then be equal to the open circuit voltage divided by the short circuit current at that field current which gives the rated EMF per phase.The synchronous reactance is determined asExplain the construction and operation of brushless DC motorConstructionBLDC motors have many similarities to AC induction motors and brushed DC motors in terms of construction and working principles respectively. Like all other motors, BLDC motors also have a rotor and a stator.StatorSimilar to an Induction AC motor, the BLDC motor stator is made out of laminated steel stacked up to carry the windings. Windings in a stator can be arranged in two patterns; i.e. a star pattern (Y) or delta pattern (?).RotorThe rotor of a typical BLDC motor is made out of permanent magnets. Depending upon the application requirements, the number of poles in the rotor may vary. Increasing the number of poles does give better torque but at the cost of reducing the maximum possible speed.UNIT V MEASUREMENT AND INSTRUMENTATIONDescribe the static and dynamic characteristics of measuring instrumentAccuracy depends on inherent limitations of instrument and shortcomings in measurement process.Precision Precision is defined as the ability of instrument to reproduce a certain set of readings within given accuracyRepeatability Repeatability is defined as ability of instrument to reproduce a group of measurements of same measured quantity, made by same observer, using same instrument, under same conditionsResolution (Discrimination) It is the minimum change or smallest increment in the measured value that can be detected with certainty by the instrument.Dead SpaceDead space/ Threshold is defined as the range of different input values over which there is no change in output value.ToleranceTolerance is a term that is closely related to accuracy and defines the maximum error that is to be expected in some valueRange or spanThe range or span of an instrument defines the minimum and maximum values of a quantity that the instrument is designed to measure.Sensitivity of measurement The sensitivity of measurement is a measure of the change in instrument output that occurs when the quantity being measured changes by a given amount. Instrument DriftIt is defined as the variation of output for a given input caused due to change in sensitivity of the instrument due to certain interfering inputs like temperature changes, component instabilities, etc.Draw the block diagram of functional elements of measuring system & explain the function of each block.Primary Sensing Element.Variable Conversion Element?Variable Manipulation Element?Data Transmission ElementData Presentation ElementExplain the different types of errors in measurements. Gross ErrorsThis category of errors includes all the human mistakes while reading, recording and the readings. Mistakes in calculating the errors also come under this category.Systematic ErrorsIn order to understand these kinds of errors, let us categorize the systematic errors as Instrumental ErrorsThese errors may be due to wrong construction, calibration of the measuring instruments. These types of error may be arises due to friction or may be due to hysteresis. These types of errors also include the loading effect and misuse of the instruments.Environmental ErrorsThis type of error arises due to conditions external to instrument. External condition includes temperature, pressure, humidity or it may include external magnetic field.Describe the construction and working of oscilloscopeThe instrument employs a?cathode ray tube?(CRT), which is the heart of the oscilloscope. It generates the electron beam, accelerates the beam to a high velocity, deflects the beam to create the image, and contains a phosphor screen where the electron beam eventually becomes visible. For accomplishing these tasks various electrical??signals and voltages are required, which are provided by the power supply circuit of the oscilloscope. Low voltage supply is required for the heater of the electron gun for generation of electron beam and high voltage, of the order of few thousand volts, is required for cathode ray tube to accelerate the beam. Normal voltage supply, say a few hundred volts, is required for other control circuits of the oscilloscope.Explain the principle of operation of piezoelectric transducers with the help of neat diagram. A quartz crystal is a piezoelectric material that can generate a voltage proportional to the stress applied upon it. For the application, a natural quartz crystal has to be cut in the shape of a thin plate of rectangular or oval shape of uniform thickness. ?Each crystal has three sets of axes – Optical axes, three electrical axes OX1, OX2, and OX3 with 120 degree with each other, and three mechanical axes OY1,OY2 and OY3 also at 120 degree with each other. The mechanical axes will be at right angles to the electrical axes. Some of the parameters that decide the nature of the crystal for the application areAngle at which the wafer is cut from natural quartz crystalPlate thicknessDimension of the plateMeans of mountingExplain the workingprinciple of LVDT with neat sketch & characteristics. Give advantages, disadvantages and applications of LVDT. As the primary is connected to an AC source so alternating current and voltages are produced in the secondary of the LVDT. The output in secondary S1 is e1 and in the secondary S2 is e2. So the differential output is, eout = e1 - e2 ................
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