PMMC 2024 Lecture Notes PDF

Electrical Measurement and Instrumentations 1st Sem 2024 Course Code: EE11102 Branch: EED Lecture 1 : PMMC Dr. Saumendra Sarangi...

Electrical Measurement and Instrumentations 1st Sem 2024 Course Code: EE11102 Branch: EED Lecture 1 : PMMC Dr. Saumendra Sarangi Electrical Engineering Asst. Professor, EED, MNNIT, Allahabad Dr. Haitham El-Hussieny Course structure: 1 2 Dr. Haitham El-Hussieny Course structure: 1 2 Dr. Haitham El-Hussieny Outline: Why we Require Measurements Measurement of DC quantity Working Principle PMMC Construction of PMMC Errors Merits and Demerits PMMC as an Ammeter 1 PMMC as a Voltmeter 2 Range Extension of range Use of SWAMPING Resistance Dr. Haitham El-Hussieny Why to measure: For Monitoring and Testing: Simplified Parallel Electrical Circuit Simplified Electrical Circuit For safety : Fault in Power system Circuit Breaker Operation by Using relay by CTs NB: Fault is cleared by disconnecting the faulty section but Increase in current is Sensed by measuirng instruments : CT current Transformer  Permanent Magnet Moving Coil (PMMC) Instruments To measure DC current or voltage Can be used for measuring AC currents and voltages by introducing additional circuit(using rectifiers) and with proper calibration Source: https://www.google.com/search?q=PMMC+meters&tbm=isch&ved=2ahUKEwj8ruqC26f6AhUejtgFHdITBfAQ2cCegQIABAA&oq=PMMC+meters&gs_ Permanent Magnet Moving Coil (PMMC): Deflection Instrument Fundamentals: To move the pointer and keep steady at a final position in PMMC over the scale, three forces are required: ▪ Deflection force. ▪ 2 Controlling force. ▪ Damping force. Construction of PMMC Dr. Haitham El-Hussieny  Constructional Features of PMMC Magnetic system: Permanent magnet U Shaped Magnet material used is Alnico Moving System Control System Damping system Source: https://www.google.com/search?q=PMMC+meters&tbm=isch&ved=2ahUKEwj8ruqC26f6AhUejtgFHdITBfAQ2cCegQIABAA&oq=PMMC+meters&gs Constructional Features of PMMC Source: https://www.google.com/search?q=PMMC+meters&tbm=isch&ved=2ahUKEwj8ruqC26f6AhUejtgFHdITBfAQ2cCegQIABAA&oq=PMMC+meters& gs_  Constructional Features of PMMC Moving Coil Rectangular coil Ratio L/b= 1.3 to 1.5 to have high Torque efficiency Aluminium is Preferred to reduce weight Ampere turns : 0.4 to 0.7 Radius of jewel: 0.01 mm to 0.02 mm Source: https://www.google.com/search?q=PMMC+meters&tbm=isch&ved=2ahUKEwj8ruqC26f6AhUejtgFHdITBfAQ2cCegQIABAA&oq=PMMC+meters& gs_  Constructional Features of PMMC Controlling System Hair springs are used Made up of Phosphorous , bronze Helical or spiral: Coiled in opposite directions Current flows through the spring, Note : Designed to carry less current Source: https://www.google.com/search?q=PMMC+meters&tbm=isch&ved=2ahUKEwj8ruqC26f6AhUejtgFHdITBfAQ2cCegQIABAA&oq=PMMC+meters&gs Two methods of supporting the moving system Source: https://www.google.com/search?q=PMMC+meters&tbm=isch&ved=2ahUKEwj8ruqC26f6AhUejtgFHdITBfAQ2cCegQIABAA&oq=PMMC+meters& gs_  Deflecting Torque 1) Deflection Torque : Force on current carrying conductor due Magnetic field B IdL Source: https://www.google.com/search?q=PMMC+meters&tbm=isch&ved=2ahUKEwj8ruqC26f6AhUejtgFHdITBfAQ2cCegQIABAA&oq=PMMC+meters& gs_ Permanent Magnet Moving Coil (PMMC): Force Equation and Scale: The deflection force acting on each side of the coil: F =BIL newtons B is the flux density (tesla) I the current (ampere) L coil length (meter) The force acting on two sides with N turns coil: F = B I L N newtons Dr. Haitham El-Hussieny  Deflecting Torque The deflection torque acts at radius r: Td = B I L N 2 r = B L I N D = N B I A (N.m) w h e r e D is the coil diameter. Source: https://www.google.com/search?q=PMMC+meters&tbm=isch&ved=2ahUKEwj8ruqC26f6AhUejtgFHdITBfAQ2cCegQIABAA&oq=PMMC+meters& gs_ Permanent Magnet Moving Coil (PMMC): Force Equation and Scale: The controlling torque is proportional to the deflection of the pointer: Tc = K θ (N.m) K is spring constant θ is the deflection angle(rad.) The pointer stops when T d =Tc: K θ =B I N A All quantities are constants except I and θ, θ = CI Note: The pointer deflection is always proportional C: is constant to the coil current and the scale is linear. Dr. Haitham El-Hussieny Damping Torque Why it is required : To reduce the oscillations of the pointer at the final position EDDY CURRENT DAMPING Source: https://www.google.com/search?q=PMMC+meters&tbm=isch&ved=2ahUKEwj8ruqC26f6AhUejtgFHdITBfAQ2cCegQIABAA&oq=PMMC+meters& gs_  EDDY CURRENT DAMPING EDDY CURRENT is induced on the core when pointer oscillates at the final point Applying Lenz's Law: Effect opposes the cause Effect is : Eddy Current Cause is Oscillation Induced Eddy Current opposes the Oscillation and it damps out Source: https://www.google.com/search?q=PMMC+meters&tbm=isch&ved=2ahUKEwj8ruqC26f6AhUejtgFHdITBfAQ2cCegQIABAA&oq=PMMC+meters& gs_ REASON of Errors in PMMC FRICTION Td = NBIA TEMPERATURE Tc = Kθ WEAKENING OF MAGNETIC FIELD θ = CI STRAY MAGNETIC FIELD THERMO ELECTRIC ERROR REASON of Errors in PMMC FRICTION To avoid the error due to friction very high torque-weight ratio is used Reason Small air gap difficult to prepare a light former winding tension Small air gap Can be avoided winding the coil carefully DC Ammeters: Swamping Resistance: To minimize the effect of temperature change on the PMMC resistance, a swamping resistance is connected in series with PMMC. The swamping resistance is made from magnain or constantan that have zero temperature coefficients. If the swamping resistance is nine times the coil resistance, a 1 % change in coil resistance would result in a total resistance change of 0.1 %. Dr. Haitham El-Hussieny REASON of Errors in PMMC WEAKENING OF MAGNETIC FIELD Weakening of Permanent Magnet Reason vibration Change in Position Stray Magnetic field can be avoided by replacing the control mechanics  Limitations They are suitable for direct current only The instrument cost is higher than Moving Iron instruments Variation of magnetic strength with time causes error in reading Errors can be reduced by Proper pivoting and balancing weight may reduce the frictional error Considering the aging can reduce errors due to magnetic field decay Manganin in series with coil reduces temperature effects Maintaining nominal temperature. The stiffness of spring, permeability of magnetic core decreases with increase in temperature Advantages Linear and Uniform scale Power consumption can be made very low (25 µW to 200 µW) Torque to weight ratio can be made high with a view to achieve high accuracy (typically 2%) Single instrument can be used for multi range ammeters and voltmeters Error due to stray magnetic field is very small No Hysteresis Loss  (PMMC):AS Ammeter and Voltmeter Connection as an ammeter connection as a voltmeter  DC Ammeters: Ammeter Circuit: The PMMC instrument could be used as an ammeter to measure DC current. 20 mA. For large currents, a PMMC could be modified by adding a parallel (shunt) resistance R s. 200 A Most of the measured current will pass through R s and a small portion of it will pass through the moving coil. Shunt Resistance It is a small resistance connected in parallel with PMMC to allow measuring large currents. It is a four-terminal resistance to neglect the resistance of the current terminal. Dr. Haitham El-Hussieny DC Ammeters: Ammeter Circuit with shunt Basic Equations: Voltage across meter. Vm = I m R m I m = Vm / R m (1) Voltage across shunt I s R s = V m , Is= V m / R s (2) 𝐼𝑠 𝑅𝑚 Ammeter circuit D i v i d i n g b o t h e q u a ti o n s ( 2 ) / ( 1 ), = 𝐼𝑚 𝑅𝑠 R m : coil resistance. 𝐼𝑠 𝑅𝑚 R s : shunt resistance. Add 1 on both side, +1= +1 𝐼𝑚 𝑅𝑠 𝐼𝑠 + 𝐼𝑚 𝑅𝑚 = +1 𝐼 𝐼𝑚 𝑅𝑠 Where m= multiplyin g factor = 𝐼𝑚 𝐼 𝑅𝑚 = +1 𝐼𝑚 𝑅𝑠 Total current: I = I s +I m 𝑅𝑚 𝑅𝑠 𝑚= 𝑅𝑚 𝑅𝑠 +1 , 𝑚−1= 𝑅𝑠 𝑅𝑚 = 𝑚−1 Dr. Haitham El-Hussieny  Effect of ammeter on circuit Measuring current in a simple circuit: connect ammeter in series Are we measuring the correct current? (the current in the circuit without ammeter) any ammeter has some resistance r. V current in presence of ammeter is I=. R +r V current without the ammeter would be I=. R To minimize error, ammeter resistance r must be very small. (ideal ammeter would have zero resistance) Example: an ammeter of resistance 10 m is used to measure the current through a 10  resistor in series with a 3 V battery that has an internal resistance of 0.5 . What is the relative (percent) error caused by the ammeter? Actual current without ammeter: V I= V=3 V R= R +r 10  3 r= 0.5  I= A 10 + 0.5 You might see the symbol  used instead of V. I = 0.2857 A = 285.7 mA Current with ammeter: V I= R +r +R A r=0.5  3 I= A 10 + 0.5 + 0.01 V=3 V R= I = 0.2854 A = 285.4 mA 10  0.2857 - 0.2854 % Error = 100 0.2857 % Error = 0.1 % DC Ammeters: Ammeter Circuit: Example An ammeter has a PMMC instrument with a coil resistance of R m = 99 Ω and FSD current of 0.1 mA, a shunt resistance R s = 1 Ω. Determine the total current passing through the Ammeter circuit R m : ammeter at (a) FSD, (b) 0.5 FSD, and (c) 0.25 FSD. coil resistance. R s : Solution: [a] at FSD: shunt resistance. V m = I m R m = 0.1 × 99 = 9.9 mV Vm 9.9 Is = = = 9.9 m A Rs 1 Total current: I = I s + I m = 9.9 +0.1 = 10 m A Dr. Haitham El-Hussieny DC Ammeters: Multirange Ammeter: A rotary switch is employed to select anyone of several shunt resistances with different values. A make-before-break switch must be used so that the instrument is not left without a shunt in parallel with it even for a brief instant. Make-before-break switch DC Voltmeter: Voltmeter Circuit: The scale of the PMMC meter could be calibrated to indicate voltage since the current through the coil is proportional to the voltage. The PMMC could be modified by adding a series resistance to measure higher voltmeter range. Because it increases the range of the voltmeter, the series resistance is termed a multiplier resistance. A multiplier resistance that is nine times the Construction of DC Voltmeter coil resistance will increase the voltmeter range by a factor of 10. Dr. Haitham El-Hussieny DC Voltmeter: Voltmeter Circuit: The scale of the PMMC meter could be calibrated to indicate voltage since the current through the coil is proportional to the voltage. The PMMC could be modified by adding a series resistance to measure higher voltmeter range. Because it increases the range of the voltmeter, the series resistance is termed a multiplier resistance. A multiplier resistance that is nine times the Construction of DC Voltmeter coil resistance will increase the voltmeter range by a factor of 10. Dr. Haitham El-Hussieny DC Voltmeter: Voltmeter Circuit: Example A PMMC instrument with FSD of 100 µA and a coil resistance of 1 kΩ is to be converted into a voltmeter. Determine the required multiplier resistance if the voltmeter is to measure 50 V at full scale. Also, calculate the applied voltage when the instrument indicates 0.8, 0.5, and 0.2 of FSD. Dr. Haitham El-Hussieny Effect of voltmeter on circuit RV Measuring voltage (potential difference) Vab in a simple circuit: IV connect voltmeter in parallel R=10  Are we measuring the correct voltage? a b (the voltage in the circuit without voltmeter) voltmeter has some resistance RV r=0.5  =3 V current IV flows through voltmeter extra current changes voltage drop across r and thus Vab To minimize error, voltmeter resistance must be very large. (ideal voltmeter would have infinite resistance) Example: Effect ofavoltmeter galvanometeron resistance 60  of circuit is used to measure the voltage drop across a 10 k resistor in series with an ideal 6 V RV Measuring battery and voltage (potential a 5 k resistor. difference) What is the V in relative ab a simple circuit: error caused by the nonzero IV resistance ofvoltmeter connect in parallel the galvanometer? R=10  a b Actual voltage drop without instrument: R eq = R1 +R 2 =15 103  r=0.5  =3 V V 6V I= = 3 = 0.4 10-3 A R eq 15 10  Vab = IR = ( 0.4 10-3 )(10 103  ) = 4 V Effect of voltmeter on circuit The measurement is made with the galvanometer. RV 60  and 10 k resistors in parallel are equivalent to 59.6  resistor. IV R=10  Total equivalent resistance: 5059.6  a b Total current: I=1.186x10-3 A r=0.5  =3 V Vab = 6V – IR2 = 0.07 V. The relative error is: 4 -.07 % Error = 100 = 98% 4 DC Voltmeter:Range Extension Dr. Haitham El-Hussieny DC Voltmeter: Voltmeter Sensitivity: The sensitivity of a voltmeter is equal to the resistance per volt: R m +R s Sv = Ω/V FSD The voltmeter sensitivity is always specified by the manufacturer. If the sensitivity is known, the total voltmeter resistance is easily calculated as (sensitivity × range). Ideally, a voltmeter should have an extremely high resistance. If the voltmeter resistance is too low, it can alter the circuit voltage. This is known as voltmeter loading effect. Dr. Haitham El-Hussieny DC Voltmeter: Multirange Voltmeter: A multirange voltmeter consists of a PMMC with several multiplier resistors, and a rotary switch. The range of this voltmeter is: V = I m ( R m +R) where R can be R 1 , R 2 ,or R3. Dr. Haitham El-Hussieny AC Voltmeter: Introduction: PMMC as AC instrument: When an alternating current with a very low frequency (0.1 Hz) is passed through a PMMC, the pointer will follow the instantaneous level of the ac signal. Since the PMMC is polarized, the pointer will move when ac goes positive only and will stop when acgoes negative. With higher frequencies, the PMMC will not be able to follow the changing ac level due to its damping force and the pointer will stop on the average level (zero for pure sinusoidal wave). So, a modification has to be done on PMMC tomeasure Construction of PMMC alternating current and voltage. Dr. Haitham El-Hussieny AC Voltmeter: Full-Wave Rectifier Voltmeter: Four diodes rectifiers are added to the PMMC to convert the AC signal into a series of uni-directional current pulses that pass through the PMMC instrument to cause positive deflection. On positive half cycle: Diodes D1 and D4 conduct and the current flows through the PMMC meter from top to bottom. On negative half cycle: Diodes D2 and D3 to conduct causing the current to flow again through the meter in the same direction. The multiplier resistance R s is connected to allow higher Full-Wave Rectifier Voltmeter voltage to the meter in the same way as in the case of DC voltmeter. Dr. Haitham El-Hussieny AC Voltmeter: Full-Wave Rectifier Voltmeter: The rectifier meter will deflect in proportional to the average value of the current (0.637 × peak current). However, the meter must indicate the RMS value, (that is, 0.707 × peak value) of the voltage. Therefore, the linear scale of the meter can be calibrated accordingly to indicate the RMS value (1.11 × average value). Limitation: The diodes drop will limit the measurement of low levels of AC signals. Dr. Haitham El-Hussieny  AC Voltmeter: Full-Wave Rectifier Voltmeter: Example A PMMC instrument with meter resistance 1 kΩ gives a full-scale deflection of 80 µA. It is to be used as a full-wave rectifier voltmeter to give FSD of 80 V (rms). Determine the required value of multiplier resistance if silicon diodes are used in the circuit. V m peak − 2VD I m peak = , VD = 0.7 V R s +R m V m peak − 2V D Rs = −R m Im p e a k V m peak = 1.414 × V R M S = 1.414 × 80 = 113.12 V I av 80 µA I m peak = = = 125.6 µA 0.637 0.637 So, R s = 888.5 kΩ  ANY QUESTIONS Dr. Haitham El-Hussieny