The simple 4 arm Wheastone Bridge is a null deflection method. E The detector (or galvanometer) is made more and more sensitive near

Transcription

1 5.0 lectrical Measureents In order to quantify stateents, easureents need to be ade. Without easureents only qualitative stateents ay be ade. Measureents ay be ade either by coparison with a reference quantity of the sae kind or by calculation using known quantities of other types. For exaple, a resistance ay be deterined by coparison with a known resistance, or it ay be deterined by the easureent of voltage, current and the law relating resistance, voltage and current. Applications: lectrical easureents are not restricted to the easureent of electrical quantities such as current, voltage, power and resistance but also non electrical quantities such as speed (tachoeter), teperature (therocouple), pressure (strain gauge), and a host of other quantities. Devices that convert one for of energy to another for for easureent and control, such as above, are known as transducers. 5.1 Accuracy of Measureents The accuracy need for a easureent depends on the application. For exaple if we were easuring tie using a watch, we would like it not to have to be reset ore than once a onth at the ost. Maybe an error of 1 inute per onth ay be considered acceptable. [i.e. 1 inute in inutes or 43,200. i.e. an accuracy of 1 in 43,200 or about %]. On the other hand, a one hour lecture ight actually take about 1 hour ± 5 inute [i.e. 5 inute tolerance in 60 inutes or 1 in 12 or 8.33 %] Accuracy also depends on whether a null deflection ethod is used (bridge ethod) or a direct deflection ethod is used. With a null deflection ethod higher accuracy is obtained, as the error ay be successively reduced, but it is obviously tie consuing. This is siilar to the use of a knife-edge balance (null deflection) or a spring balance (direct deflection) to weigh soething. 5.2 Wheatstone Bridge 1 3 The siple 4 ar Wheastone Bridge is a null deflection ethod. The detector (or galvanoeter) is ade ore and ore sensitive near D the balance point, where the detector current becoes zero and the potential difference across the detector also becoes zero. Under this 2 4 condition, using potential divider action, it can be easily shown that 1 3 = 2 4 It ust be noted that the balance condition of the bridge does not depend on the source voltage, nor on the detector ipedance. At balance, if three of the resistances are accurately known, the reaining resistance will also be calculated to the sae accuracy. For good sensitivity, all 4 ars should have siilar values of resistance. The principle of the Wheatstone Bridge can also be extended to a.c. bridges having inductances and capacitances in addition to resistances. In this case the balance condition is a coplex equation and the source would be an a.c. source. Z1 Z 3 = Z 2 Z 4 Bridges are ostly used when accurate easureents are required such as in calibrating an indicating instruent. Indicating Instruents Unlike null deflection techniques, which require a nuber of steps in the balance process, indicating instruents give the reading directly. 50 They ay be either analogue or digital. Analogue instruents give a continuous range of values, where as in a digital instruent only an exact nuber appears Analogue Meter 0 2 Digital 1. Meter 3 5 Analogue eters ay be direct deflecting (such as an aeter or volteter), integrating (such as an energy eter) or recording (such as a graph plotter). University of Moratuwa JL/Sep

2 101 lectrical ngineering lectrical Measureents 5.3 Principle of operation of analogue deflecting eters Analogue eters show a particular deflection for a given input quantity. For this to happen, there are three ain torques (rotary type of deflection) or forces (linear type). These are (a) the deflecting torque, (b) the controlling torque and (c) the daping torque. The deflecting torque is produced by the easured quantity or a value proportional to it. This causes the pointer or needle to ove away fro the zero position. However, unless there is a balancing torque, the pointer will continue to ove and increase the deflection. This is controlled by a controlling force, which is ost coonly produced by a spring (where the torque is proportional to the deflection fro the initial position). As in any syste, unless daping is provided, the two forces would cause the needle to oscillate about the final position aking reading very difficult. Thus daping is provided, which does not affect the final position, but reduces the over swing aking the final position to be achieved quickly Principle types of analogue eters The principle types of analogue eters in coon use are the (a) peranent agnet oving eters or coonly referred to as oving instruents, (b) oving iron eters, (c) dynaoeter type oving eters, (d) electrostatic eters and (e) induction type eters. (a) Peranent agnet oving eters Pointer In this instruent, a oving is suspended between the poles of a peranent agnet. When a current is passed through the, the N S becoes an electroagnet and tries to align with the peranent agnet. The deflecting torque becoes proportional to the strength iron cylinder of the electroagnet and hence to the current. A spring is used which produces a controlling torque proportional to the deflection. Thus at balance, the deflection becoes proportional to the current. When the current is unidirectional, as with d.c., the deflection would be to one particular side. When the current is varying at a rate which the needle cannot follow, what will be indicated by the eter is the ean value, due to the inertia of the oveent. Thus the oving eter always easures the ean value or d.c. value of a given wavefor. (b) Moving iron eters When a piece of iron is placed in the axis of the agnetic field produced by a, agnetis of opposite polarity would be induced in the iron. Since opposite poles pivot attract, it would be attracted towards the, independent of the direction of agnetis (hence of the current in the ). The force of attraction would be F proportional to the product of the agnetis caused by the and the induced agnetis in the piece of iron. Since the latter is proportional to the forer, and the forer is proportional to the current in the, the force of attraction would be proportional to the square of the current. Thus if a controlling torque is provided by a spring, the deflection at balance would be proportional to the square of the current, or since the oveent would norally not be able to respond at the rate at which the supply is alternating due to its inertia, the deflection would be proportional to the ean value of the square of the current. If the square root of this indication is taken, it would correspond to the root ean square value or rs value. This value can be easured for both a.c. and d.c. Thus the oving iron eter always easures the r..s. value of a given wavefor. (c) Dynaoeter type instruent The dynaoeter type instruent is also a 150 oving instruent. In this case, the peranent agnet is replaced by a pair of fixed s to give the fixed field. Scale 0 Pointer oving 300 fixed eading of pointer tie fixed University of Moratuwa - JL/Oct

3 101 lectrical ngineering lectrical Measureents In this case, the deflection would be proportional to the product of the two agnetic fields, and hence to the product of the currents in the fixed s and the oving. Thus, if used as an aeter will easure the ean square value, or usually calibrated to read the r..s. value. (d) lectrostatic eters lectrostatic eters basically work on the principle that the force (or torque) of attraction is proportional to the product of the charges. Since a single voltage produces the charges, the force is proportional to the square of the voltage. Thus this eter too reads the ean square value and hence is calibrated to read the root ean square value. The electrostatic eter is thus basically a spindle volteter as its operation is based fundaentally on a voltage, where as the oving eter and the oving iron eter are basically disc aeters as their perforance is based on current. Coil A Coil B (e) Induction type eters The induction eter depends on the torque produced by the reaction between a flux (whose value depends on the value of the current in A) and the eddy currents which are induced in a non-agnetic disc (usually aluiniu) by another flux (produced by current in B). Since the action depends on induction, they can be used to easure alternating quantities only. The eter would have a deflection proportional to the product of the two currents. A daping agnet ensures that the speed of rotation is constant for a given set of currents and the eter is not norally used as an aeter or volteter, but as an integrating eter, where the nuber of revolutions would be proportional to the integral of the product of the two currents. 5.4 olteters and Aeters olteters for the easureent of voltage, and aeters for the easureent of current are generally based on the sae principle. However, there is one basic difference in their use. While volteters are connected in parallel to easure the voltage, aeters are connected in series to easure the current. A good eter should not interfere with the quantity that is being easured. That is, the introduction of the eter should not change the quantity that is being easured. Therefore a volteter should rideally have an infinite resistance, and an aeter should ideally have a zero resistance. Obviously this A cannot happen in practice, r so that I a practical volteter should r have I a very high resistance (uch higher than the resistance of the device across which the voltage is being easured) and a practical r I A aeter should have a very low resistance (uch lower than the resistance of the device through which the current is being easured). I =, + r =. + r I = // r + =. + = I, + r.... = +. + r.( + ) I A =, + r+ r =. + r+ r xaple A source with an ef of 12 and internal resistance of 20 Ω, supplies a load of resistance 1000 Ω. Find the current supplied to the load and the voltage across it. The voltage is easured using a volteter with an effective resistance of 5 kω. Find the volteter reading. The current is then easured using a illiaeter with an effective resistance of 120Ω. Find the reading of the aeter. Solution current = 12/( ) = = A, voltage = = When volteter is connected, reading = /( ( )) = When aeter is connected, reading I = 12/( ) = = 10.5 A University of Moratuwa - JL/Oct

4 101 lectrical ngineering lectrical Measureents It can be seen that the eters do not read the exact value, but as can be seen the error is quite sall. olteter usually have a uch higher resistance (order of 100 kω) and aeters a uch lower resistance (order of 10 Ω) so that the errors would generally be even saller Measureent of d.c. quantities Direct quantities are usually easured using the peranent agnet oving (p...c.) instruent. The oving iron (.i.) instruent and the induction instruent can also be used to easure direct quantities Measureent of a.c. quantities Alternating quantities (r..s. value) ay be easured using the oving iron (.i.) instruent and the induction instruent. The peranent agnet oving (p...c.) instruent with a rectifier bridge arrangeent can also be used to easure the r..s. value of sinusoidal wavefors, since we know the relation between the rectified average value and the r..s. value for a sinusoidal wavefor. This factor, known as the for factor has a value of for the sinusoidal wavefor. Since the rectifier type oving eter is eant to easure only the r..s. value of sinusoidal wavefors, the eter is calibrated to read 1.11 ties the average value rather than the ean value of the rectified wavefor. However, when the effective value of other wavefors are easured, there is an error caused. 5.5 Measureent of Power As instantaneous power is obtained fro the product of the instantaneous values of voltage and current, we could use either the dynaoeter instruent or the induction type instruent to easure power. One of the s (called the current ) has the current passing through it, while the other (called the potential ) has a current, proportional to the voltage, passed through it by having a high series resistance. Due to the inertia of the instruent, the pointer does not respond to the instantaneous value but to the ean value of the product of the currents and hence to the ean value of the instantaneous power. The dynaoeter watteter can be used to easure both a.c. as well as d.c., while the induction watteter can only be used to easure a.c. ither the current can be exactly in series with the current or the potential can be exactly in parallel with the voltage. This is shown in the following diagras. Supply v p i p current potential r c i c p i v Supply i c current p r c potential i p v p i v i c = i, v p = v + r c i c, v p = p.i p eading i c.i p i c.v p i.(v + r c. i c ) eading v.i + r c.i c 2 v p = v, i c = i + i p, v p = p.i p eading i c.i p i c.v p (i + i p ).v eading v.i + v p.i p The average value of the instantaneous power v.i is the active power P that has to be easured. It is seen that neither of the watteter connections give the exact reading. In the first connection shown, there is an error of 2 r c.i c corresponding to the power loss in the current. The current of a watteter ust thus have an alost zero resistance in order for the error to becoe negligible [since the current is in series, this is siilar to the case of the aeter]. In the second connection shown, there is an error of v p.i p corresponding to the power loss in the potential. The potential of a watteter ust thus have an alost infinite resistance in order for the error to becoe negligible [since the potential is in parallel, this is siilar to the case of the volteter]. The selection of which connection is to be used, is thus based on which gives the saller loss. 5.6 Measureent of three phase power Y B W 1 W 2 Three Phase Power = eal { N.I * * + YN.I Y + BN.I * B } but I + I Y + I B = 0 Kirchoff s current law P = eal { N.I * + YN.(-I * +-I B * ) + BN.I B * } = eal {( N YN ).I * * + ( BN YN ).I B = eal { Y.I * + BY.I * B } = W 1 + W 2 University of Moratuwa - JL/Oct

5 101 lectrical ngineering lectrical Measureents The power in a three phase syste ay be easured using three watteters between the live and the neutral for each phase. However, in any high power systes, the neutral wire ay not be available. ven when the neutral is available, a convenient way of easuring power in a three phase syste is the two watteter ethod. 5.7 Measureent of nergy potential s disc Supply i current s v lectrical energy is the tie integral of electrical power. Thus to easure energy, we not only need to obtain an expression for power as in the watteter, but also have a tie dependent eleent. This is done by having a continuous rotatation of a disc, rather than a deflection. The nuber of revolutions at a constant speed would be proportional to the tie, and if the speed is ade proportional to the power, then energy would be obtained. The a.c. energy eter (also known as the house service eter or the kwh eter) is usually of the induction type. [Note: Since the basis is the instantaneous values of current and voltage, the effect of power factor angle would autoatically be taken into account] 5.8 Measureent of esistance esistance can usually be easured using a Wheastone Bridge or a volteter-aeter ethod. However neither of these ethods can be used when the value to be easured is a very low resistance (of the order of Ω) or a very high resistance (of the order of MΩ). In these cases special care has to be taken to avoid errors caused by contact resistance (Kelvin Double Bridge is coonly used) for very low resistances, and to avoid leakage currents on the surface of instruents (insulation egger is coonly used). Special ethods are also used to find the effective earth resistance of an installation. These are outside the scope of this lecture and will not be dealt in this course. 5.9 xtension of anges of Instruents Other than for the electrostatic eter, analogue eters are generally basically designed as icro-aeters, typically giving a full scale deflection (f.s.d.) for a current of around 25µA to 25 A. I fsd current at full scale deflection r eter internal resistance They ay be used to easure higher currents and also voltages with suitable resistances in parallel (shunts) or series. xaple I I fsd I fsd sh r r A oving aeter has a basic range of 200 µa with an internal resistance of 800Ω. It is to be used as (a) an aeter with a range of 5A, and (b) as a volteter with a range of 100. Show how resistances ay be connected to obtain the required range. (a) when I fsd = 200 µa, I = 5 A. current through shunt path = , r = 800Ω fro current division rule, sh = /( ) = = 32 Ω in shunt with eter. (b) when I fsd = 200 µa, = 100, r = 800 Ω. 100 = (800 + s ) I fsd r s University of Moratuwa - JL/Oct

6 101 lectrical ngineering lectrical Measureents S = = kω in series with eter Instruent Transforers The range of a eter can also be extended by aking use of the transforer principle. If we wish to easure a larger or saller voltage with a given range volteter, we could use a step down transforer or a step up transforer to achieve the purpose. For exaple, to easure a high voltage of the order of 200 k with a 100 range volteter, we would use a potential transforer of turns ratio 2000:1 (or voltage ratio 200k:100) to reduce the voltage. [You are probably aware that the voltage ratio of a transforer is the sae as the turns ratio] Siilarly larger or saller currents ay be easured using current transforers. For exaple, to easure a current of 200 A using a eter of range 5 A, we would use a current transforer of turns ratio 1:40 (or current ratio 200A:5A) to reduce the current. Such potential transforers and current transforers are known as instruent transforers. They are specifically designed to have high accuracy in easuring voltages and currents respectively, but cannot handle uch power. Like volteters, the priary of the potential transforer is connected in shunt with the quantity to be easured, while the priary of the current transforer is connected in series with the quantity to be easured. The secondary of a current transforer should never be left on open circuit in a live circuit to avoid it Input getting saturated. Attenuation and Analog to Digital Aplification ectification 5.11 Digital ange Meters Selection Conversion Display Analogue instruents display the quantity to be easured in ters of the deflection of a pointer. digital output Digital instruents on the other hand indicate the value of the easured quantity (easurand) in the for of a decial nuber. The digital eter works on the principle of sapling and quantization and their output ay be fed into digital coputers and the like for storage and future coputations. A digital volteter (DM) easuring alternating voltages would typically have the following block diagra. The analogue to digital converter (ADC) is the ost critical coponent of the DM. It deterines the accuracy and peranent the resolution of the DM. agnet oving iron oving induction type electrostatic hot-wire type 5.12 oving Sybols on dials of eters with ectifier The following sybols and abbreviations are used to denote the type of easuring eleent, kind of supply, and noral position of use of a given instruent. for d.c. use only for a.c. use only for a.c. and d.c. use vertical position for noral use horizontal position for noral use Note: The hot-wire type of theral instruent has not been described earlier in the notes. It works on the principle of a wire heating up due to the passage of current and causing an expansion. Details beyond this are beyond the scope of the lecture. University of Moratuwa - JL/Oct