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Dynamometer Wattmeter

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Dynamometer Wattmeter DYNAMOMETER WATTMETER A pair of fixed coils connected in series When energized gives the same effect as that of the permanent magnets In this field there will be a moving coil which when energized acted upon by a torque by which it deflects F1, F2: Fixed coils (Current Coil) ; M: Moving coil (Pressure Coil); R: High resistance in series with Moving coil I1 : load current; I2: current through moving coil DYNAMOMETER WATTMETER 2 fixed coils in series act as the CC and the moving coil in series with R act as the PC MC is pivoted between the 2 fixed coils carries a current I2 proportional to V I2 is fed to M through two springs which also provides the necessary controlling torque Can be used on both ac and dc circuits as both the coils are energized simultaneously by a common source due to which a unidirectional torque is produced Electrodynamometer Wattmeter DYNAMOMETER WATTMETER Principle of operation is the same as that for dynamo-electric machines Working Td is produced by the interaction of two magnetic fluxes One of the fluxes is produced by a fc which carries a current proportional to the load current & therefore called CC CC is thick in cross section and has less number of turns The other flux is created by a mc which carries a current proportional to the load voltage and thus called PC PC is thin in cross - section and has hundreds of turns A high non-inductive R is connected to the PC so that its current is almost in phase with the load voltage Working There are two alternative methods of connection, depending on which coil is connected near the load In dynamometer type instrument deflecting torque is produced by magnetic effect of electric current Control torque (Tc) is provided by control springs Damping torque is provided by Air Friction PC carries a needle that moves over a scale to indicate the measurement On an ac ckt the Td is proportional to the avg. instantaneous product of V and I, thus measuring true power, and possibly (depending on load characteristics) showing a different reading to that obtained by simply multiplying the readings showing on a stand-alone voltmeter & a stand-alone ammeter in the same ckt Working 2 circuits of a wattmeter are likely to be damaged by excessive current The ammeter and voltmeter are both vulnerable to overheating - in case of an overload, their pointers will be driven off scale But in the wattmeter, either or even both the CC and PC circuits can overheat without the pointer approaching the end of the scale! This is because the position of the pointer depends on the power factor, voltage and current Thus, a circuit with a LPF will give a low reading on the wattmeter, even when both of its circuits are loaded to the maximum safety limit Therefore, a wattmeter is rated not only in watts, but also in volts and ampere Deflecting torque Torque expression based on energy concept Assume the self-inductances of fixed and moving coils are Lf & Lm respectively Further it is assumed that the mutual inductance between the fixed and movable coils is M Total energy stored in the magnetic field of the coils is given by where if & im are the currents through the fixed and moving coils From above equation the expression for Td is written as Note Lf & Lm are not functions of θ but „M‟ is a function of the deflection θ (i.e. relative position of moving coil) Deflecting torque Equ. L between fc & mc can be (cumulative manner) and from this the mutual inductance, However, M varies with the relative positions of the mc & fc Mmax occurs when the axes of the mc and fc are aligned with θ = 180º, as this position gives the maximum flux linkage between coils When θ = 0º, M = - Mmax If the plane of the moving coil is at an angle θ with the direction of B that produced by the fixed coil, then M = - Mmax Cos θ D.C operation: Taking, if = IL (dc) and im = V (dc)/ R Deflecting torque At steady deflection Td = Tc A.C operation: In dynamometer instrument Td is proportional to the mean value of the I2 or V2 (note both coils are connected in series for ammeters or voltmeters), and the scale can therefore be calibrated to read r.m.s values of alternating current or voltage Let im (t) = (Vmax/ R) Sin ωt (assuming L of mc is negligible) & if (t) = iL (t) = Im Sin (ωt φ ) where „φ‟ is the pf angle of load where + sign for leading & – sign for lagging where V & I are the r.m.s values of load voltage & current respectively At steady deflection Td = Tc , therefore, θ ∝ power (average) Two Ways of Connections Two Ways of Connections Fig. (a): PC on supply side, CC on load side VPC = VLoad + VCC So the wattmeter reading includes power loss in CC i.e., Fig. (b): PC on load side, CC on supply side ICC = ILoad + IPC So the wattmeter reading includes power loss in PC i.e., If ILoad is small, VCC small so that PC introduced is less i.e., connection in fig. (a) is preferred for small load current and high load voltages If ILoad is high, IPC small so that PP introduced is less i.e., connection in fig. (b) is preferred for high load current and small load voltages Advantages of Dynamometer wattmeters Made to give a very high degree of accuracy – used as a standard for calibration purposes Equally accurate on dc as well as ac measurements Can be used on ac for any waveform – not restricted to sine waveform Disadvantages of Dynamometer wattmeters At LPF, the inductance of PC causes serious error unless special precautions are taken to reduce this effect Three phase power measurement Three - Phase Power Measurement P is measured in 3 phase systems using 3 phase wattmeter (also called as 2 element wattmeter) or 2 or 3 single phase wattmeters Element means a pair of coils ( one CC & one PC) Andre E. Blondel’s Theorem 1893: “In a system of N conductors, N-1 meter elements, properly connected, will measure the power or energy taken” The connection must be such that all potential coils have a common tie to the conductor in which there is no current coil Cost saver in metering installation with fixed transducers Three-Wattmeter Method Power can be measured in a balanced or unbalanced 3-phase load of either Y or type. Current is measured between terminals 1 and 2, Voltage across the load is measured between terminals 3 and 4 Two-Wattmeter Method The voltage coil of each wattmeter is connected across a line voltage and the current has a line current through it. Ptot = P1 P2 Two-Wattmeter Power Measurement cc = current coil vc = voltage coil W1 read PVI11AB A cos W2 read PVI22CB C cos For balanced load with abc phase sequence 12aa30 and 30 a is the angle between phase current and phase voltage of phase a Two-Wattmeter Power Measurement(cont.) PPP12 2VILL cos cos30 3VILL cos To determine the power factor angle PPVI12 LL2cos cos30 PPVI12 LL( 2sin sin30 ) PPVI12 LL2cos cos30 3 PPVI12 LL( 2sin sin30 ) tan PPPP tan 31 2 or tan1 3 1 2 PPPP1 2 1 2 Example 1 P = ? Z 10 45 line-to-line voltage = 220Vrms The phase voltage 220 V 30 A 3 The line current V 220 30 I A 12.7 75 and I 12.7 195 A Z 10 3 45 B PVI11AC A cos 2698 W PPP123421 W PVI22BC B cos 723 W Three Phase Circuit In a four-wire system (3 phases and a neutral) the real power is measured using three single phase wattmeters IA PA Phase A A W VAN V IB PB Phase B A W VBN V IC PC Phase C A W VCN V Neutral (N) Example a) Four wire system WR IR VR Z = 5 30o Ω ER EL = 415 volt R IN EB o VB ZY = 10 90 EY VN Ω WY o ZB = 20 45 Ω IY IB WB Three-phase Load Find the three-phase total power, PT. Example b) Three wire system WR IR VR Z = 5 30o Ω ER EL = 415 volt R EB o ZY = 10 90 EY VN Ω WY o ZB = 20 45 Ω IY IB WB Three-phase Load Find the three-phase total power, PT. Example b) Three wire system WR IR VR Z = 5 30o Ω ER EL = 415 volt R EB VB o ZY = 10 90 EY VN Ω WY o ZB = 20 45 Ω IY IB WB Three-phase Load Find the three-phase total power, PT. Three Phase Circuit Three wire system, The three phase power is the sum of the two watt- meters reading PAB IA Phase A A W VAB = VA - VB V Phase B V = V - V CB C B V Phase C A W IC PCB PT PAB PCB Proving: The three phase power (3-wire system) is the sum of the two watt-meters reading I P Instantaneous power:A A Phase A A W pA = vA iA V V AN I P pB = vB iB B B Phase B A W pC = vC iC VBN V IC PC Phase C A W V pT = pA + pB + pC = vA iA + vB iB +vC iC CN V Neutral (N) PT PAB PCB = vA iA + vB iB +vC iC = vA iA + vB (-iA -iC) +vCiC Proving: The three phase power (3-wire system) is the sum of the two watt-meters reading Instantaneous power: PAB IA Phase A A W pT = vA iA + vB (-iA –iC) +vCiC VAB = VA - VB V = (vA – vB )iA + (vC – vB )iC Phase B V = V - V = vAB iA + vCBiC CB C B V Phase C A W IC PCB pT = pAB + pCB PT PAB PCB Multi - range Wattmeter Current ranges (0.5A and 1A) can be changed by switching two field coils from series to parallel connection Voltage ranges (60V, 120V and 240 V) can be made by switching different values of multiplier resistors 1.
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