American Meter Practice

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CHAPTER I. Measurement of Power in Direct Current Circuits

Electrical measurements in the laboratory have been carried on for many years with great accuracy. The conditions are carefully studied when a determination of some quantity is sought, and the errors which effect the accuracy of the measurement eliminated. The study of the phenomena of electricity is rightly called an exact science, but the perfecting of an accurate commercial meter has been a slow and tedious process. At first the principles of correct design were not embodied in the meters put on the market, and no matter how perfect they were made mechanically a correct registration of the power consumed could not be obtained. But, as a rule, the mechanical features were more defective than the theoretical ones, and the combination of these defective elements has given the meter of commerce an unenviable reputation.

Such great inventors as Edison, Thomson, Shallenberger and Duncan have spent much time in trying to get together various elements in suitable combination to meet the requirements and accurately measure the current or the power in the many various applications and uses to which electricity is put. Edison gave us the chemical ampere hour meter, which has done yeoman service in the metering of direct currents; and Thomson gave us his recording wattmeter, which has gradually been developed into an excellent meter, and which can be used for both direct and alternating current. Shallenberger and Duncan produced at first ampere hour meters for alternating current, but in later years wattmeters, also, for alternating current. There is a large number of other meters, but these four are the pioneers in the meter field. In each meter different principles are involved, which meet more or less successfully the requisite of a good commercial meter. Heat and cold, moisture, dust, insects and vibration are some of the physical obstacles to be met and overcome by the successful meter; and short circuits, overloads, light loads and no loads are some of the electrical conditions under which it must operate. The wearing qualities of all of the elements of the meter must be taken into consideration. As in the one-horse chaise, each part of the meter should be as strong as any other part. The ability to withstand the test of time; the property of being the same meter at the end of one year's use, is the real test of the value of an instrument. The problem, then, becomes one of combining certain elements in such relation to each other as to form a perfect measuring device, and the maintaining of this same relation in the face of the various conditions which are partially enumerated above. However clearly these principles were recognized twent> years ago, the state of the art was such that only very imperfect devices were produced as meters. It has been only within the last few years that commercial meters have been brought to a reasonable state of efficiency. The vast interests involved have quickened the managements of central stations to the importance of having better meters and meter service, and the field of invention is so attractive along these lines that we see each year a gradual improvement in the design and performance of the meters placed on the market.

The measurement of any form of transmitted energy is always attended by a diminution of the energy transmitted equal to the amount consumed in the measuring device.

Hence all instruments that measure transmitted energy are shunt instruments, the power shunted or diverted from the transmission being usually a very small fraction of the total power. We may class all such devices as shunt dynamometers to distinguish them from absorption dynamometers, which usually translate the energy to be measured into heat or mechanical work and destroy its original properties.

The measurement of electrical energy which is transmitted is accomplished by means of shunt dynamometers. Its translation into useful commercial forms is accomplished by absorption dynamometers of various classes, such as motors and incandescent lamps.

For the sake of analysis the flow of electrical energy is usually considered by treating its two components, quantity and intensity, as individual entities, and instruments are constructed which will measure each separately as well as the product of the two. .

In commercial circuits the voltage or intensity usuallyremains constant, in which case a measurement of the power flowing in a circuit may be obtained by the recording of the variable quantity of current in amperes and multiplying by the known voltage. If the amperes remain constant, and the voltage vary, a record can be obtained of the power flowing by recording the variable voltage and multiplying by the known amperes of the circuit. If both the voltage and the amperage of the circuit be variable their product gives the power flowing, which, for convenience, is usually indicated by one instrument called a wattmeter.

In the first class of instruments, the ammeter class, the loss in energy due to the insertion of the instrument in the circuit is directly proportional to the current flowing.

The voltmeter, if on a constant potential circuit, has a constant energy consumption The wattmeter has a constant energy consumption in its potential circuit plus a variable energy loss in the series circuit proportional to the current flowing.

From the foregoing the deduction follows that on constant potential circuits of known intensity the measurement of the energy passing is the most economically carried out by an ammeter, on circuits of constant and known amperage with variable voltage by a voltmeter, and where both current and voltage are variable by a wattmeter.

These general statements hold true for the measurement of the power in a direct current circuit, or a non-inductive alternating circuit, but must be modified for inductive alternating circuits containing reactance and capacity, the effects of which will be brought out in Chapter II.

It is assumed that the reader is familiar with the well- . known forms of indicating ammeters, voltmeters and wattmeters on the market, the descriptions of which are, therefore, omitted.

Many of these instruments record the passing power of a circuit with extreme accuracy, but being simply indicators of the instantaneous values of the power they do not give a summation of this power during the elapsed time.*

♦See Flather's Dynamometers and Measurement of Power.

MEASUREMENT OF POWER. i 1

In order that an instrument may bring in the element of time in the measurement of power, it must constantly move some object, for one unit of energy passing, through unit distance in unit time; and this movement must be permanently recorded by means of a dial train, or some similar summation device. Then, when n units of energy are passing, the recording object will be moved through n units of distance in unit of time. The application of this principle to commercial recording meters has resulted in

B

/wvLJ/vyl

Fig. 1.

a great number of types, the most prominent of which are described in succeeding chapters.

The various classes of electrical energy to be measured commercially resolve themselves into:

Direct current as distributed by two or three-wire systems.

Alternating current, single and polyphase systems.

Direct current distributed by means of a five-wire system is also used to some extent, but, as the principles involved in its measurement are identical with those of the two and three-wire systems, the five-wire system will not be considered separately.

Two-wire direct current systems are usually confined to 500 volt, and arc circuits. The three- wire system is the well known Edison system, the local distribution of which may be either two or three- wire.

The amperes flowing in the simple two- wire circuit with load at C, Fig. 1, are the same in every part of the circuit.

An ammeter placed at A reads the same as if placed at B, but the energy in the circuit varies as the distance from Z? ? becoming less as C is approached, and is directly proportional in a circuit of uniform resistance to the distance from D. Hence the mean power in the circuit would be found at some point between D and C.

It is customary in an ordinary two-wire service to meter the energy passing at A y and, if the fall of potential, or loss of energy, between A and C be small, the error is not great, the allowable loss usually not exceeding two per cent., hence one per cent, less energy than that recorded at A would represent the mean energy passing in the given circuit.

As the meter in commercial practice is placed at the entrance of the service into a building, the consumer usually pays for about one per cent, more energy than he actually receives at his translating devices.

Should the meter be a recording ammeter, one leg of the circuit only passes through the instrument ; if a wattmeter be used the other leg of the circuit must be brought into the meter to enable the potential coils of the instrument to be energized.

In a recording wattmeter, the product of the magnetization set up by the series and shunt field coils must exert a resultant torque on some movable member of the meter which will cause it to move in a manner to record n units of energy in n units of time.

The movable members of a recording instrument have, unfortunately, an appreciable amount of friction which introduces an inertia factor operating as a counter torque to the product of the energy torque by a function of time. This friction of the moving parts is small, and, at full load of the meter, the ratio between the counter torque, due to friction, and the energy torque is negligible. As the load decreases, the ratio between the counter frictional torque and the energy torque approaches unity ; in other words, there is a certain point in every recording instrument where the energy torque and frictional torque are equal. When this point is reached the instrument remains at rest.

The counter frictional torque varies in different instruments of the same and different makes from a fraction of one per cent, to three or four per cent, of full load energy torque, the large losses often being due to causes arising in service.

For this reason, it is customary in commercial recording instruments to compensate for this friction by introducing

B

Fig. 2.

an additional torque which is a definite fraction of full load value, and which compensates through all ranges of load for the initial friction of the meter.

Theoretically this is a very pretty way of accomplishing the result, but exactions of service introduce frictions which this compensation does not entirely eliminate.

The power passing in a three-wire circuit is usually measured by metering the two outside legs, although equally good results can be obtained by metering one outside leg and the neutral conductor.

In the three-wire circuit, Fig. 2, let A, B, D t C be the outside legs, E the neutral conductor, and b and c translating devices.

When the currents in A B and D C are equal no current flows in E ; when they are unequal E carries the difference positive or negative. The energy flowing on each side of the system can be measured by two two- wire meters, or one three- wire meter. In either case, the series coils carry the varying amperes of each side of the system, while the shunt field coils are energized proportionately to the voltage of the system.

If two two-wire meters be used, the same connections are made as in a two-wire system. If a three-wire meter be used, the two series fields are superposed to form a resultant field proportional to the current flowing in both sides of the system. The torque due to this resultant field and the field set up by the potential circuit operates the meter in such a manner as to record the total energy passing in the three-wire circuit.

A form of meter which is not manufactured commercially, so far as the author is aware, can be constructed to measure the total energy flowing in a three-wire circuit by placing one series coil of an ordinary three-wire meter in one outside leg of the circuit and a coil of half the number of turns in series with the neutral. The power registered is multiplied by two.

To illustrate, suppose A B, Fig 2, to carry 50 amperes, positive, and D C 25 amperes, negative, then the neutral wire, E, carries 25 amperes, negative. As the neutral field coil has half the number of turns, the sum of the magnetizations of the series fields is equal in effect to a positive current of 37.5 amperes. Twice this amount is 75 amperes, or the same as the series fields of the ordinary three- wire meter would carry in the example given.

The PR losses in the fields of a meter at full load reach an appreciable amount, but at light loads are not of much consequence, hence, in the form of meter just given, on a properly balanced three-wire service the PR losses would be halved as the neutral would carry no current. On unbalanced loads the loss in this form of meter would be reduced by some quantity varying between the limits of $ and — J, so that an average saving in PR losses in the field coils for any meter would be 12 \ per cent. In reality this would be much larger, as any serious unbalancing would scarcely take place except at light loads, when the PR losses are negligible.

The shunt field coil, where a single meter is employed, can be fed from across the outside or between the neutral and one outside. In either arrangement, unless the voltage be equal on both sides of the system, an error is introduced into the record proportional to the difference of voltage existing. To obtain a true record, if the voltage be unequal, it is necessary to employ two two-wire meters or a three-wire meter having two armatures fed respectively from each side of the system.

The latter arrangement amounts to the combining of two meters under one cover, resulting in a clumsy and expensive device. In commercial practice the voltage on one side of a three-wire distributing system is usually maintained about equal to that on the other; the errors resulting from inequalities of the sides supposedly balance, so that it is the usual practice to meter with a three-wire meter with the shunt field coils fed between the two outsides or between one outside and neutral.

In meters of the class described, the torque urging the rotary part at any given moment is proportional to the energy of the current at that moment, while, to record correctly, the speed must be proportional to the energy, and, consequently, to the torque. This result is secured by providing a breaking device in which the resistance offered to rotation is proportional to the speed.

This brake may be of various constructions, but the usual form is that of a conducting non-magnetic metallic disk revolving between the poles of a permanent magnet. The eddy currents generated in the disk, by their reaction on the permanent magnetic field, exert a resistance to movement which varies in amount proportionately to the speed of the torque exerted by the moving member to which the disk is fixed. Hence, the power necessary to generate the eddy currents becomes proportional to the torque •exerted on the moving member or the watts passing in the circuit. Other forms of brakes are employed, such as fans and liquid brakes, but they have given place in the latest types of meters to the now universal magnetic brake.

F

CHAPTER II. Measurement of Power in Alternating Current Circuits

In passing to the measurement of alternating currents, simple two and three-wire non-inductive single-phase circuits will be first considered.

The power flowing in a non-inductive two-wire circuit is at any instant the product of the instantaneous values of the current and voltage. To get the mean power the in-

Fig. 3.

stantaneous values must be integrated through a complete cycle. Graphically we may represent such a power as in Fig. 3 , wherein e represents the sine wave of varying voltage values for a single period and i the varying ampere values for the same period in phase with the voltage. The curve p then represents the varying power values, and is obtained by multiplying the corresponding ordinates of the voltage and current curves.

The product of the mean effective volts and amperes gives the mean effective watts passing in the circuit or the mean value of the power curve p, hence, for all non-in-

•

ductive circuits, Pe= true watts.

If the current flowing in curve i be passed through a coil of wire and another coil be energized by a current proportional to and varying with the voltage curve e, the two coils, if so placed, will form a resultant magnetization for any instant of time proportional to the product of the instantaneous values of e and i or the watts passing in the circuit.

If a movable member or armature be provided, of such character that it is moved by the operation of this resultant magnetization in such manner that its speed is proportional to the watts passing in the circuit, a record of the power passing is obtained. In recording the flow of alternating current energy this principle has been used in the development of two classes of meters, which for convenience are styled inductive and non-inductive.

A non-inductive meter can be used for either direct or alternating current. A familiar type is the Thomson recording wattmeter. In this type of meter the field coils are in series with the current flowing, the shunt field coils are energized proportionately to the voltage of the circuit, and the torque exerted on the armature is for any instant proportional to the product of the instantaneous values of the current and E. M. F., hence the mean torque is proportional to the product of effective volts by effective amperes, or the true watts passing in the circuit.

The method of connecting this meter is the same as on direct current circuits, and, in fact, is interchangeable without recalibration, the error being for practical purpose inappreciable.

The induction me;ter is either a " current' ' meter or wattmeter, and operates by means of a " shifting " field acting on a closed secondary armature, the eddy currents induced in the armature reacting on the shifting or rotating field in such manner as to produce a torque proportional to the energy or current passing, according to whether it is a " current " or wattmeter.

A well-known type of current meter is the Shallenberger in which the series current passes through a primary coil set at an angle with a closed secondary within it, the plane of the two magnetizations being at a like angle and differing in phase. Mounted in inductive relation is a thin disk armature in which eddy currents are generated by the shifting or rotating field. The reaction of these resultant fields tends to revolve the armature, the torque being proportional to the square of the current.

A fan brake, whose retarding effect increases as the square of the speed, is attached to the spindle on which the armature is carried, and enables the meter to record the current flowing.

In the wattmeter, of which there are many types, the series and shunt field coils are wound in inductive relation to a movable closed secondary or armature in which eddy currents are induced proportional to the magnetizations set up in the series and shunt field coils. The shunt field coils are displaced in phase from the series coils by having a reactance placed in series with them, the magnetizations thus creating a shifting or rotating resultant field.

The field set up by the induced eddy currents in the revolving secondary lags behind the resultant field set up by the series and shunt field coils, creating a torque on the secondary which is proportional to the square of the energy flowing. The providing of a brake, whose retarding force varies as the square of the speed, enables the energypassing to be obtained from the speed of the revolving spindle to which the armature is attached. There are many variations and different arrangements of the foregoing general principles.

The power passing in an inductive single-phase circuit may be graphically illustrated by Fig. 4, wherein the current lags behind the voltage by 6o°.

Fig. 4.

The resultant power curve p represents the watts passing

€ t

in the circuit, and is written Pe=* — cos. S angle of lag.

The power passing in an alternating circuit at any instant is equal to the product of the instantaneous values of the current and voltage, etc. (see American Electrician, March, 1902), and acts as a generator for a portion of each period, the useful power being the difference between positive and negative values of the curve p.

The resultant torque, therefore, exerted on the coils of a meter in circuit with an inductive load is not proportional to the product of the virtual volts and virtual amperes as measured by an indicating instrument, but to this product multiplied by the power factor of the circuit; the power factor is the ratio between the true and apparent watts.

In the metering of three-wire single-phase systems, inductive or non-inductive, the same general principles outlined in the foregoing hold true.

Multiphase systems are a combination of single-phase systems differing in phase from each other, and are used in distributions for light and power owing to the ease with which motors can be operated thereon.

The systems in general use are the quarter-phase and three-phase, the former composed of two single-phase circuits differing by 90 and distributed by either four or three-wires, the latter of three single-phase circuits differing by 120 and distributed by either four or three-wires.

The quarter-phase system, employing four wires for its distribution, is metered exactly as two separate single-phase circuits would be, the total power in the two-phases being the sum of the Energy components of each phase. When the two phases are balanced, that is, have the same amount of energy passing in each phase, it is only necessary to meter one phase and multiply the result by two to get the total amount of energy passing. When the phases are unbalanced, that is, have different loads on each phase, two meters are necessary, one in each phase, to register the energy passing.

In the commercial distribution of this system it is the usual practice to take a lighting circuit into a customer's premises from one phase only and a power circuit from both phases. The motor furnishes a balanced load and needs only one meter and the lights one meter. In this way, by loading up the phases equally, the number of meters needed for metering the lights can be kept down to one meter per customer.

When three wires are used in the distribution of two-phase currents, one wire acts as a common return for the

AMERICAN METER PRACTICE.

other two, and the instantaneous value of the current on the common return at any instant is the algebraic sum of the instantaneous values of the currents of each phase.

The virtual resultant value would be the hypothenuse of a right triangle which would represent the current in phase and value. The resultant voltage is found in the same way, hence the virtual watts would be the product of the resultant current by the resultant voltage for a non-inductive circuit.

As an example, suppose we have a two-phase system carrying 10 amperes in each phase at a voltage of ioo v.,

10 Amp.

ICO. v.

Fig. 5.

Fig. 6.

the triangle of the current values, Fig. 5, would give a resultant amperage of 14.14, the triangle of the voltage values, Fig. 6, gives a resultant voltage of 141. 4 volts. The total watts passing in the circuit is the product of these two resultants, or a watt value of 2,000 watts.

Calculating the watts separately for each phase we have 10 amp., x 100 v. = 1000 watts (1) 10 amp., x 100 v. = 1000 " (2)

2000 watts which is the same as the above.

MEASUREMENT OF POWER.

The resultant voltage and resultant amperes being the same in phase when the load is balanced, a meter, Fig. 7 , with its series field coils placed in the common return and

'V'WW

Fig. 7.

its shunt field coils energized by the resultant voltage of the system, would give the true power passing in the circuit.

When the load is unbalanced the resultant ampere value leads or lags behind the resultant voltage of the system and may be displaced in phase either way by 45 on non-inductive load. The true power in the circuit is then obtained by multiplying by the cosine of angle of lag or lead.

Fig. 8.

As a wattmeter records the product of the instantaneous values and not the maximum values of current and voltage, the record is a true one of the energy passing in the circuit.

AMERICAN METER PRACTICE.

This connection, Fig. 7, will not record the true power passing on an unbalanced inductive circuit, as an angle of lag or lead of 45 could give a wattless register, allowing 70 per cent, of the energy passing to remain unrecorded. On balanced circuits, however, feeding induction motors, this connection readily takes the place of the two meters shown in Fig. 8, where the series field coils are connected in the outside legs of the circuit and the potential circuit fed between the given leg in the meter and the common return.

When the induction type of meter is used, the potential circuit is so connected as to differ in phase from the

A

Fig. 9.

series field circuit by 90 , hence in Fig. 8 the potential circuit for each meter would be fed from the given leg in the meter to the other outside. This is the connection most commonly used in metering two-phase circuits. The elements of two meters are often combined under one cover to act on a common armature.. The elements are connected in the same manner as though they were separate meters, and need not be further elaborated.

MEASUREMENT OF POWER.

Three-phase circuits are connected in "star" or "delta" grouping; the former sometimes uses four wires in the distribution while the latter is always distributed by means of three wires.

In Fig. 9, the "star" grouping with common centre at o is shown, the voltage of the three legs being represented in intensity and phase by the lines a, b, c. The resultant voltage of such a system for any instant of time may be found graphically by producing the single-leg of opposite sign to the other two backwards, and finding the resultant by the parallelogram of forces. The diagonal will represent in sign and phase the resultant of the voltage on the three legs. In Fig. io the resultant is ^3 times the voltage of one phase and leading it by 30 . If one phase be selected as the leading one, the resultant voltage will be found to be always leading it by 30 . In the same Fig. 10 in a balanced circuit the current will have a resultant coinciding with the voltage resultant, and the product of the two resultants will, for non-inductive load, represent the true power passing.

The algebraic sum of the resultants of the voltage taken consecutively between the three legs of a system will equal for any instant the resultant positive or negative value of the voltage at that instant. Likewise, the resultant of the current flowing for any instant is the algebraic sum of the three resultant currents of the system found in like manner. Therefore, the current passing over any two legs of a three-wire three-phase circuit is the algebraic sum of the three resultant currents of the system, hence the power passing in the circuit is the product of the resultant current and voltage. The algebraic product of two minus quantities is always a plus quantity, hence the power passing is always positive in character on non-inductive circuits. On inductive circuits, where the current leads or lags behind the voltage, a minus quantity of current flows for a portion of each period.

Some simple rules deduced from the above may be of service in readily computing the energy passing in polyphase systems.

In "star" or "Y" connected systems, or any system employing a common neutral, the resultant voltage is equal to the effective voltage X y/m, w> being the number of phases. The resultant amperes flowing in any system is the average of the sum X \/m- The energy passing is, therefore, the common resultant voltage X common resultant amperage X cos. <p or lag angle. Suppose, for example, the amperes in the different legs of a three-phase unbalanced system are 10, 20 and 30 respectively, and the effective volts of the circuit, taken with regard to a common neutral point or conductor, 100 volts. The average value of the amperes is 20, and the resultant is 20 X \J 3 = 34-6 amperes. The resultant voltage is 100 X V3"" *73 v °l ts - The cosine of angle of lag <p is taken as .5, corresponding to an angle of 6o°.

The energy passing in such a circuit is 34.6 amperes X 173 volts X .5 = 3000 watts. The same result is obtained by taking each leg separately, multiplying amperes X effective volts X cosine <p — 60 amperes X 100 V. •5 X3°°o watts.