{"id":393,"date":"2018-11-29T12:13:35","date_gmt":"2018-11-29T12:13:35","guid":{"rendered":"http:\/\/msp04.epgpbooks.inflibnet.ac.in\/?post_type=chapter&p=393"},"modified":"2019-05-01T05:48:07","modified_gmt":"2019-05-01T05:48:07","slug":"low-power-factor-wattmeters","status":"publish","type":"chapter","link":"https:\/\/ebooks.inflibnet.ac.in\/msp04\/chapter\/low-power-factor-wattmeters\/","title":{"rendered":"Low Power Factor Wattmeters"},"content":{"raw":"
\"epgp<\/a>\r\n<\/span><\/div>\r\n
\r\n\r\n\u00a0 \u00a0 Low Power Factor Wattmeters (Electrodynamometer type)<\/strong>\r\n\r\n \r\n\r\n \r\n

Measurement of power in circuits having low power factor by ordinary electrodynamometer wattmeters is difficult and inaccurate due to the following reasons:<\/p>\r\n \r\n

(i)\u00a0 the deflecting torque on the moving system is small (owing to low power factor) even when the current and pressure coils are fully excited;<\/p>\r\n \r\n

(ii) <\/em>errors introduced because of inductance of pressure coil tend to be large at low power factors.<\/p>\r\n \r\n

Special features are incorporated in an electrodynamometer wattmeter to make it a low power factor type of wattmeter. These features are discussed below in detail:<\/p>\r\n \r\n\r\n1. Pressure Coil Current:<\/strong>\r\n\r\n \r\n

The pressure coil circuit is designed to have a low value of resistance, so that the current, f1owing through it, is increased to give an increased operating torque. The pressure coil current in a low power factor wattmeter may be as much as 10 times that employed for high power factor wattmeters.<\/p>\r\n \r\n\r\n2. Compensation for Pressure coil Current:<\/strong>\r\n\r\n \r\n

The power being measured in a low power factor circuit is small and current is high on account of low power factor. Therefore, it is absolutely necessary to compensate for the pressure coil current in a low power factor wattmeter.<\/p>\r\n \r\n\r\n3. Compensation for Inductance of Pressure Coil:<\/strong>\r\n\r\n \r\n

The error caused by pressure coil inductance is: VI sin\u0278 tan\u03b2. Now, with low power factor, the value of \u0278 is large and, therefore, the error is correspondingly large. Hence in a low power factor wattmeter we must compensate for the error caused by inductance of the pressure coil. This is done by connecting a capacitor across a part of series resistance in the pressure coil circuit.<\/p>\r\n \r\n\r\n4. Small Control Torque:<\/strong>\r\n\r\n \r\n

Low power factor wattmeters are designed to have a small control torque so that they may provide full scale deflection for power factors as low as 0.1.<\/p>\r\n \r\n\r\nPower in Poly-Phase Systems:<\/strong>\r\n\r\n \r\n\r\nBlondel\u2019s Theorem:<\/strong>\r\n\r\n \r\n

Consider a network which is supplied with <\/span>n<\/em> conductors, the total power is measured by summing the reading of <\/span>n<\/em> wattmeters so arranged that a current element of a wattmeter is in each line and the corresponding voltage element is connected between that line and a common point. If the common point is located on one of the lines, then the power may be measured by n-1 wattmeters.<\/span><\/p>\r\n\r\n<\/div>\r\n

\r\n\r\n \r\n\r\nMeasurement of Power in Three Phase Circuits:<\/strong>\r\n\r\n \r\n

1.\u00a0Three Wattmeter Method: <\/strong>The connections as employed for a 3 phase 4 wire system are shown in Figure below:<\/p>\r\n\"\"\r\n\r\n \r\n\r\nThe common point C of pressure coils and neutral O of the circuit coincide and therefore, v = 0\r\n\r\n \r\n\r\nAnd v1 = v1\u2019 , v2 = v2\u2019 , v3=v3\u2019\r\n\r\n \r\n\r\nSum of instantaneous reading of the wattmeters = p1 + p2 + p3\r\n\r\n \r\n\r\n= v1i1 + v2i2 + v3i3\r\n\r\n \r\n\r\nHence, these three wattmeters measure the power of the load.\r\n\r\n \r\n\r\n2.\u00a0 Two Wattmeter Method:<\/strong>\r\n\r\n \r\n

In a three phase three wire system we require 3 elements. But if we make the common points of the pressure coils coincide with one of the lines, then we will require only n-1 =2 elements.<\/span><\/p>\r\n \r\n

Instantaneous power consumed by load=v1i1 + v2i2 + v3i3<\/span><\/p>\r\n \r\n

Let us consider two wattmeters connected to measure power in three phase circuits as shown in Star connection and Delta connection.<\/span><\/p>\r\n \r\n

Star (Wye) Connection: <\/strong>Instantaneous reading of P1 wattmeter p1 = i1(v1-v3)<\/span><\/p>\r\n \r\n

Instantaneous reading of P2 wattmeter p2 = i2(v2-v3)<\/span><\/p>\r\n \r\n

Sum of instantaneous reading of two wattmeters = p1 + p2<\/span><\/p>\r\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0= v1i1 + v2i2 \u2013 v3(i1+i2)<\/span><\/p>\r\n\r\n<\/div>\r\n

\r\n\r\n\"\"\r\n\r\n \r\n\r\nFrom kirchhoffs law: i1 + i2 +i3 = 0\r\n\r\n \r\n\r\nTherefore, sum of instantaneous readings of two wattmeters = v1i1 + v2i2 + v3i3\r\n\r\n \r\n\r\nThus, the sum of the two wattmeter reading is equal to the power consumed by the load.\r\n\r\n \r\n\r\nThis is irrespective of whether the load is balanced or unbalanced.\r\n\r\n \r\n\r\nDelta Connection:<\/strong>\r\n\r\n<\/div>\r\n
\r\n\r\n\"\"\r\n\r\n \r\n\r\nInstantaneous reading of P1 wattmeter p1 = v31(i1-i3)\r\n\r\n \r\n\r\nInstantaneous reading of P2 wattmeter p2 = v2(i2+i1)\r\n\r\n \r\n\r\nSum of instantaneous reading of two wattmeters = p1 + p2\r\n\r\n= v3i3 + v2i2 \u2013 i1(v3+v2)\r\n\r\n \r\n\r\nFrom kirchhoffs law: v1 + v2 +v3 = 0\r\n\r\n \r\n\r\nTherefore, sum of instantaneous readings of two wattmeters = v1i1 + v2i2 + v3i3\r\n\r\n \r\n\r\nThus, the sum of the two wattmeter reading is equal to the power consumed by the load.\r\n\r\n \r\n\r\nThis is irrespective of whether the load is balanced or unbalanced.\r\n\r\n \r\n\r\n3.\u00a0One Wattmeter Method:<\/strong>\r\n\r\n \r\n

The method can be used only when the load is balanced. The connections are shown in Figure. The current coil is connected in one of the lines and one end of the pressure coil to the same line, other end being connected alternately to the other two lines.<\/span><\/p>\r\n\r\n<\/div>\r\n

\r\n\r\n\"\"\r\n\r\n \r\n\r\nWe have, V1 = V2 = V3 = V\r\n\r\n \r\n\r\nI1 = I2 = I3 = I\r\n\r\n \r\n\r\nAnd V13 = V12 = V\r\n\r\n \r\n\r\nReading of wattmeter when switch is at 3:\r\n\r\n \r\n\r\nP1 = V13I1cos(30 - \u0278) = VI cos(30 - \u0278)\r\n\r\n \r\n\r\nReading of wattmeter when switch is at 2:\r\n\r\n \r\n\r\nP2 = V12I1cos(30 + \u0278) = VI cos(30 + \u0278)\r\n\r\n \r\n\r\nP1 + P2 = VI [cos(30 - \u0278) + cos(30 + \u0278)] = 3 VI cos \u0278.\r\n\r\n\"\"\r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\nThree Phase Wattmeters:<\/strong>\r\n\r\n \r\n

A dynamometer type three phase wattmeter consists of two separate wattmeter movements mounted together in one case with the two moving coils mounted on the same spindle. There are two current coils and two pressure coils. A current coil together with its pressure coil is known as an element. Therefore, a three phase wattmeter has 2 elements. The connections of 2 elements of a 3 phase wattmeter are the same as that for two wattmeter method using two single phase wattmeters. The torque on each element is proportional to the power being measured by it. The total torque deflecting the moving system is the sum of the deflecting torque of the two elements.<\/p>\r\n \r\n

Deflecting torque of element 1 <\/span>\u03b1<\/em> P1<\/span><\/p>\r\n \r\n

Deflecting torque of element 2 \u03b1 <\/span>P2<\/em>.<\/span><\/p>\r\n \r\n

. \u00b7. Total deflecting torque \u03b1 <\/span>(P1 +<\/em> P2) \u03b1 <\/span>P<\/em><\/p>\r\n \r\n\r\nHence the total deflecting torque on the moving system is proportional to the total power.<\/span>\r\n\r\n \r\n

In order that a 3 phase wattmeter read correctly, there should not be any mutual interference between the two elements. A laminated iron shield may be placed between the two elements to eliminate the mutual effects.<\/span><\/p>\r\n\r\n<\/div>\r\n

\r\n\r\n \r\n\r\nMeasurement of Reactive Power<\/strong>:\r\n\r\n \r\n\r\nThe reactive power in a circuit is Q = VI<\/em> sin\u0278\r\n\r\n \r\n

It is often convenient and even essential that the reactive power be measured. For example, in load monitoring, such a measurement gives the operator or Joad despatcher information concerning the nature of the load. Also the reactive power serves as a check on power factor measurements, since ratio of reactive and active power is tan \u0278 = Q\/P<\/em>.<\/p>\r\n \r\n

Also the apparent power VI,<\/em> which determines the line and generator capacity, may be determined from measurements of active and reactive power.<\/p>\r\n\"\"\r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n1. Single Phase Varmeters:<\/strong>\r\n\r\n \r\n

In a single phase circuit reactive power can be measured by a varmeter (volt-ampere reactive meter). This is an electrodynamic wattmeter in whose pressure coil circuit a large inductive reactance is substituted for the series resistance so that the pressure coil circuit a large inductive reactance is substituted for the series resistance so that a pressure coil current is in quadrature with the voltage. Under these conditions the wattmeter reads :<\/p>\r\n \r\n\r\nVI <\/em>cos (90\u00b0 - \u0278)= VI sin\u0278 = reactive power.\r\n\r\n \r\n

It should be noted that varmeters do not read correctly it harmonics are present or if the frequency is different from that used when calibrating the instrument.<\/p>\r\n \r\n

2. Polyphase Varmeters:<\/strong><\/p>\r\n \r\n

In three phase circuits phase shifting which is necessary for the measurement of reactive power is usually obtained from phase shifting transformers. This phase shifting may be done with two auto-transformers connected in an \u201cOpen Delta\u201d configuration. The current coils of the wattmeters are connected in series with the lines as usual. Phase-line 2 is connected to the common terminals of the two auto-transformers, and phase 1 and 3 lines are connected to 100% taps on the transformer.<\/span><\/p>\r\n \r\n

3. Reactive power measurement in three phase circuits<\/strong><\/p>\r\n \r\n

In the case of balanced three phase circuits, it is simple to use a single wattmeter to read the reactive power. The current coil of the wattmeter is connected in one line and the pressure coil is connected across the other two lines as shown in Figure.<\/span><\/p>\r\n\r\n<\/div>\r\n

\r\n\r\n\"\"\r\n\r\n \r\n\r\nReferring to the Figure\r\n\r\n \r\n\r\nCurrent through the current coil== I2.<\/em>\r\n\r\n \r\n\r\nVoltage across the resistive coil= V13.\r\n\r\n \r\n\r\nTherefore, reading of wattmeter = V13I2 cos (90 + \u0278)\r\n\r\n\"\"\r\n\r\n \r\n\r\n \r\n\r\n \r\n

Total reactive volt amperes of the circuit, Q = 3 VI sin\u0278<\/p>\r\n \r\n\r\nWhere phase angle \u0278 = tan-1 (Q\/P)\r\n\r\n \r\n\r\nQuestionnaire<\/strong>\r\n\r\n<\/div>\r\n

    \r\n \t
  1. Why the measurement of power in circuits having low power factor by ordinary electrodynamometer wattmeters is difficult and inaccurate?<\/li>\r\n \t
  2. What are the special features incorporated in an electrodynamometer wattmeter to make it a low power factor type of wattmeter?<\/li>\r\n \t
  3. Define Blondel\u2019s theorem.<\/li>\r\n \t
  4. Explain the different Measurement of Power in Three Phase Circuits.<\/li>\r\n \t
  5. Explain single and multi-phase varmeters.<\/li>\r\n<\/ol>\r\n\r\n\r\n\r\n
    you can view video on Low Power Factor Wattmeters<\/strong><\/td>\r\n\"\"<\/a><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\u00a0 \u00a0 References:<\/strong>\r\n
      \r\n \t
    1. Electronic Measurements and Instrumentation by Bernard M. Oliver and John M. Cage.<\/li>\r\n \t
    2. Measurement and Instrumentation Principles by Alan S. Morris.<\/li>\r\n \t
    3. Instrumentation and Measurement in Electrical Engineering by Roman Malaric.<\/li>\r\n \t
    4. Measurement and Instrumentation Systems by William Bolton.<\/li>\r\n \t
    5. Engineering Measurements and Instrumentation by Leslie Frank Adams.<\/li>\r\n \t
    6. Electrical Measurements and Instrumentation by U. A. Bakshi.<\/li>\r\n \t
    7. Introduction to Measurements and Instrumentation by Arun K Ghosh.<\/li>\r\n<\/ol>","rendered":"
      \"epgp<\/a>
      \n<\/span><\/div>\n
      \n

      \u00a0 \u00a0 Low Power Factor Wattmeters (Electrodynamometer type)<\/strong><\/p>\n

       <\/p>\n

       <\/p>\n

      Measurement of power in circuits having low power factor by ordinary electrodynamometer wattmeters is difficult and inaccurate due to the following reasons:<\/p>\n

       <\/p>\n

      (i)\u00a0 the deflecting torque on the moving system is small (owing to low power factor) even when the current and pressure coils are fully excited;<\/p>\n

       <\/p>\n

      (ii) <\/em>errors introduced because of inductance of pressure coil tend to be large at low power factors.<\/p>\n

       <\/p>\n

      Special features are incorporated in an electrodynamometer wattmeter to make it a low power factor type of wattmeter. These features are discussed below in detail:<\/p>\n

       <\/p>\n

      1. Pressure Coil Current:<\/strong><\/p>\n

       <\/p>\n

      The pressure coil circuit is designed to have a low value of resistance, so that the current, f1owing through it, is increased to give an increased operating torque. The pressure coil current in a low power factor wattmeter may be as much as 10 times that employed for high power factor wattmeters.<\/p>\n

       <\/p>\n

      2. Compensation for Pressure coil Current:<\/strong><\/p>\n

       <\/p>\n

      The power being measured in a low power factor circuit is small and current is high on account of low power factor. Therefore, it is absolutely necessary to compensate for the pressure coil current in a low power factor wattmeter.<\/p>\n

       <\/p>\n

      3. Compensation for Inductance of Pressure Coil:<\/strong><\/p>\n

       <\/p>\n

      The error caused by pressure coil inductance is: VI sin\u0278 tan\u03b2. Now, with low power factor, the value of \u0278 is large and, therefore, the error is correspondingly large. Hence in a low power factor wattmeter we must compensate for the error caused by inductance of the pressure coil. This is done by connecting a capacitor across a part of series resistance in the pressure coil circuit.<\/p>\n

       <\/p>\n

      4. Small Control Torque:<\/strong><\/p>\n

       <\/p>\n

      Low power factor wattmeters are designed to have a small control torque so that they may provide full scale deflection for power factors as low as 0.1.<\/p>\n

       <\/p>\n

      Power in Poly-Phase Systems:<\/strong><\/p>\n

       <\/p>\n

      Blondel\u2019s Theorem:<\/strong><\/p>\n

       <\/p>\n

      Consider a network which is supplied with <\/span>n<\/em> conductors, the total power is measured by summing the reading of <\/span>n<\/em> wattmeters so arranged that a current element of a wattmeter is in each line and the corresponding voltage element is connected between that line and a common point. If the common point is located on one of the lines, then the power may be measured by n-1 wattmeters.<\/span><\/p>\n<\/div>\n

      \n

       <\/p>\n

      Measurement of Power in Three Phase Circuits:<\/strong><\/p>\n

       <\/p>\n

      1.\u00a0Three Wattmeter Method: <\/strong>The connections as employed for a 3 phase 4 wire system are shown in Figure below:<\/p>\n

      \"\"<\/p>\n

       <\/p>\n

      The common point C of pressure coils and neutral O of the circuit coincide and therefore, v = 0<\/p>\n

       <\/p>\n

      And v1 = v1\u2019 , v2 = v2\u2019 , v3=v3\u2019<\/p>\n

       <\/p>\n

      Sum of instantaneous reading of the wattmeters = p1 + p2 + p3<\/p>\n

       <\/p>\n

      = v1i1 + v2i2 + v3i3<\/p>\n

       <\/p>\n

      Hence, these three wattmeters measure the power of the load.<\/p>\n

       <\/p>\n

      2.\u00a0 Two Wattmeter Method:<\/strong><\/p>\n

       <\/p>\n

      In a three phase three wire system we require 3 elements. But if we make the common points of the pressure coils coincide with one of the lines, then we will require only n-1 =2 elements.<\/span><\/p>\n

       <\/p>\n

      Instantaneous power consumed by load=v1i1 + v2i2 + v3i3<\/span><\/p>\n

       <\/p>\n

      Let us consider two wattmeters connected to measure power in three phase circuits as shown in Star connection and Delta connection.<\/span><\/p>\n

       <\/p>\n

      Star (Wye) Connection: <\/strong>Instantaneous reading of P1 wattmeter p1 = i1(v1-v3)<\/span><\/p>\n

       <\/p>\n

      Instantaneous reading of P2 wattmeter p2 = i2(v2-v3)<\/span><\/p>\n

       <\/p>\n

      Sum of instantaneous reading of two wattmeters = p1 + p2<\/span><\/p>\n

      \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0= v1i1 + v2i2 \u2013 v3(i1+i2)<\/span><\/p>\n<\/div>\n

      \n

      \"\"<\/p>\n

       <\/p>\n

      From kirchhoffs law: i1 + i2 +i3 = 0<\/p>\n

       <\/p>\n

      Therefore, sum of instantaneous readings of two wattmeters = v1i1 + v2i2 + v3i3<\/p>\n

       <\/p>\n

      Thus, the sum of the two wattmeter reading is equal to the power consumed by the load.<\/p>\n

       <\/p>\n

      This is irrespective of whether the load is balanced or unbalanced.<\/p>\n

       <\/p>\n

      Delta Connection:<\/strong><\/p>\n<\/div>\n

      \n

      \"\"<\/p>\n

       <\/p>\n

      Instantaneous reading of P1 wattmeter p1 = v31(i1-i3)<\/p>\n

       <\/p>\n

      Instantaneous reading of P2 wattmeter p2 = v2(i2+i1)<\/p>\n

       <\/p>\n

      Sum of instantaneous reading of two wattmeters = p1 + p2<\/p>\n

      = v3i3 + v2i2 \u2013 i1(v3+v2)<\/p>\n

       <\/p>\n

      From kirchhoffs law: v1 + v2 +v3 = 0<\/p>\n

       <\/p>\n

      Therefore, sum of instantaneous readings of two wattmeters = v1i1 + v2i2 + v3i3<\/p>\n

       <\/p>\n

      Thus, the sum of the two wattmeter reading is equal to the power consumed by the load.<\/p>\n

       <\/p>\n

      This is irrespective of whether the load is balanced or unbalanced.<\/p>\n

       <\/p>\n

      3.\u00a0One Wattmeter Method:<\/strong><\/p>\n

       <\/p>\n

      The method can be used only when the load is balanced. The connections are shown in Figure. The current coil is connected in one of the lines and one end of the pressure coil to the same line, other end being connected alternately to the other two lines.<\/span><\/p>\n<\/div>\n

      \n

      \"\"<\/p>\n

       <\/p>\n

      We have, V1 = V2 = V3 = V<\/p>\n

       <\/p>\n

      I1 = I2 = I3 = I<\/p>\n

       <\/p>\n

      And V13 = V12 = V<\/p>\n

       <\/p>\n

      Reading of wattmeter when switch is at 3:<\/p>\n

       <\/p>\n

      P1 = V13I1cos(30 – \u0278) = VI cos(30 – \u0278)<\/p>\n

       <\/p>\n

      Reading of wattmeter when switch is at 2:<\/p>\n

       <\/p>\n

      P2 = V12I1cos(30 + \u0278) = VI cos(30 + \u0278)<\/p>\n

       <\/p>\n

      P1 + P2 = VI [cos(30 – \u0278) + cos(30 + \u0278)] = 3 VI cos \u0278.<\/p>\n

      \"\"<\/p>\n

       <\/p>\n

       <\/p>\n

       <\/p>\n

      Three Phase Wattmeters:<\/strong><\/p>\n

       <\/p>\n

      A dynamometer type three phase wattmeter consists of two separate wattmeter movements mounted together in one case with the two moving coils mounted on the same spindle. There are two current coils and two pressure coils. A current coil together with its pressure coil is known as an element. Therefore, a three phase wattmeter has 2 elements. The connections of 2 elements of a 3 phase wattmeter are the same as that for two wattmeter method using two single phase wattmeters. The torque on each element is proportional to the power being measured by it. The total torque deflecting the moving system is the sum of the deflecting torque of the two elements.<\/p>\n

       <\/p>\n

      Deflecting torque of element 1 <\/span>\u03b1<\/em> P1<\/span><\/p>\n

       <\/p>\n

      Deflecting torque of element 2 \u03b1 <\/span>P2<\/em>.<\/span><\/p>\n

       <\/p>\n

      . \u00b7. Total deflecting torque \u03b1 <\/span>(P1 +<\/em> P2) \u03b1 <\/span>P<\/em><\/p>\n

       <\/p>\n

      Hence the total deflecting torque on the moving system is proportional to the total power.<\/span><\/p>\n

       <\/p>\n

      In order that a 3 phase wattmeter read correctly, there should not be any mutual interference between the two elements. A laminated iron shield may be placed between the two elements to eliminate the mutual effects.<\/span><\/p>\n<\/div>\n

      \n

       <\/p>\n

      Measurement of Reactive Power<\/strong>:<\/p>\n

       <\/p>\n

      The reactive power in a circuit is Q = VI<\/em> sin\u0278<\/p>\n

       <\/p>\n

      It is often convenient and even essential that the reactive power be measured. For example, in load monitoring, such a measurement gives the operator or Joad despatcher information concerning the nature of the load. Also the reactive power serves as a check on power factor measurements, since ratio of reactive and active power is tan \u0278 = Q\/P<\/em>.<\/p>\n

       <\/p>\n

      Also the apparent power VI,<\/em> which determines the line and generator capacity, may be determined from measurements of active and reactive power.<\/p>\n

      \"\"<\/p>\n

       <\/p>\n

       <\/p>\n

       <\/p>\n

      1. Single Phase Varmeters:<\/strong><\/p>\n

       <\/p>\n

      In a single phase circuit reactive power can be measured by a varmeter (volt-ampere reactive meter). This is an electrodynamic wattmeter in whose pressure coil circuit a large inductive reactance is substituted for the series resistance so that the pressure coil circuit a large inductive reactance is substituted for the series resistance so that a pressure coil current is in quadrature with the voltage. Under these conditions the wattmeter reads :<\/p>\n

       <\/p>\n

      VI <\/em>cos (90\u00b0 – \u0278)= VI sin\u0278 = reactive power.<\/p>\n

       <\/p>\n

      It should be noted that varmeters do not read correctly it harmonics are present or if the frequency is different from that used when calibrating the instrument.<\/p>\n

       <\/p>\n

      2. Polyphase Varmeters:<\/strong><\/p>\n

       <\/p>\n

      In three phase circuits phase shifting which is necessary for the measurement of reactive power is usually obtained from phase shifting transformers. This phase shifting may be done with two auto-transformers connected in an \u201cOpen Delta\u201d configuration. The current coils of the wattmeters are connected in series with the lines as usual. Phase-line 2 is connected to the common terminals of the two auto-transformers, and phase 1 and 3 lines are connected to 100% taps on the transformer.<\/span><\/p>\n

       <\/p>\n

      3. Reactive power measurement in three phase circuits<\/strong><\/p>\n

       <\/p>\n

      In the case of balanced three phase circuits, it is simple to use a single wattmeter to read the reactive power. The current coil of the wattmeter is connected in one line and the pressure coil is connected across the other two lines as shown in Figure.<\/span><\/p>\n<\/div>\n

      \n

      \"\"<\/p>\n

       <\/p>\n

      Referring to the Figure<\/p>\n

       <\/p>\n

      Current through the current coil== I2.<\/em><\/p>\n

       <\/p>\n

      Voltage across the resistive coil= V13.<\/p>\n

       <\/p>\n

      Therefore, reading of wattmeter = V13I2 cos (90 + \u0278)<\/p>\n

      \"\"<\/p>\n

       <\/p>\n

       <\/p>\n

       <\/p>\n

      Total reactive volt amperes of the circuit, Q = 3 VI sin\u0278<\/p>\n

       <\/p>\n

      Where phase angle \u0278 = tan-1 (Q\/P)<\/p>\n

       <\/p>\n

      Questionnaire<\/strong><\/p>\n<\/div>\n

        \n
      1. Why the measurement of power in circuits having low power factor by ordinary electrodynamometer wattmeters is difficult and inaccurate?<\/li>\n
      2. What are the special features incorporated in an electrodynamometer wattmeter to make it a low power factor type of wattmeter?<\/li>\n
      3. Define Blondel\u2019s theorem.<\/li>\n
      4. Explain the different Measurement of Power in Three Phase Circuits.<\/li>\n
      5. Explain single and multi-phase varmeters.<\/li>\n<\/ol>\n\n\n\n
        you can view video on Low Power Factor Wattmeters<\/strong><\/td>\n\"\"<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

        \u00a0 \u00a0 References:<\/strong><\/p>\n

          \n
        1. Electronic Measurements and Instrumentation by Bernard M. Oliver and John M. Cage.<\/li>\n
        2. Measurement and Instrumentation Principles by Alan S. Morris.<\/li>\n
        3. Instrumentation and Measurement in Electrical Engineering by Roman Malaric.<\/li>\n
        4. Measurement and Instrumentation Systems by William Bolton.<\/li>\n
        5. Engineering Measurements and Instrumentation by Leslie Frank Adams.<\/li>\n
        6. Electrical Measurements and Instrumentation by U. A. Bakshi.<\/li>\n
        7. Introduction to Measurements and Instrumentation by Arun K Ghosh.<\/li>\n<\/ol>\n","protected":false},"author":3,"menu_order":22,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":["prof-vinay-gupta"],"pb_section_license":""},"chapter-type":[],"contributor":[58],"license":[],"class_list":["post-393","chapter","type-chapter","status-publish","hentry","contributor-prof-vinay-gupta"],"part":3,"_links":{"self":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-json\/pressbooks\/v2\/chapters\/393","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-json\/wp\/v2\/users\/3"}],"version-history":[{"count":7,"href":"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-json\/pressbooks\/v2\/chapters\/393\/revisions"}],"predecessor-version":[{"id":539,"href":"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-json\/pressbooks\/v2\/chapters\/393\/revisions\/539"}],"part":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-json\/pressbooks\/v2\/chapters\/393\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-json\/wp\/v2\/media?parent=393"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-json\/pressbooks\/v2\/chapter-type?post=393"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-json\/wp\/v2\/contributor?post=393"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-json\/wp\/v2\/license?post=393"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}