US2222925A - Calculator - Google Patents

Description

Nov. 26, 1940. WEST 2,222,925

CALCULATOR Filegl Aug. 29, 1939 5 Sheets-Sheet 1 FIG um? FIGURE II INVENTOR 4 68? P ATTORNEY A. P. WEST CALCULATOR v 5 Sheets-Sheet 2 Filed Aug. 29, 1939 M bSwt L 5k?) hsivvv rip Q n INVENTOR fli/ml 2 5 6 BY ATTORNEY Nov. 26, 1940. A. P. WEST CALCULATOR Filed Aug. 29, 1959 5 Sheets-Sheet 3 FIGUl-Tf 4 FIGURE 3 iNVENTOR ATTOREY A. P. WEST CALCULATOR Nov. 26, 1940.

Filed Aug. 29, 1959 5 Sheets-Sheet 4 Y FIGURE 5 FIGURE 7 FIGURE 5 INVENTOR JrezZ I? %es7. BY

ATTORNEY Nam 26, 1940.

CALCULATOR Filed-Aug. 29, 1939 5 Sheets-Sheet 5 FIGURE 5* imam? .INVENTOR vidual feeders emanating from substations other Patented Nov. 26, 1940 UNITED STATES PATENT OFFICE 11 Claims.

My invention relates to calculators, and particularly to a calculator designed for use incalculating allowable circuit loading, voltage regulation, for circuit scheduling purposes; and for voltage regulation improvement on power distribution circuits serving all types of loads met with in the public utility business, as, for instance, loads for residences, business ofiices, street lighting' playgrounds, athletic fields, tennis courts; and for advertising, decorative, andindustrial purposes. i

' The primary object of all Voltage regulation is either to supply a constant and predetermined voltage at the load, or to vary the voltage as the nature of the load may require.

Continuity of service is generally recognized as the "prime requisite in'the distribution of electric energy; and the quality of the service is next in importance. The valueof accurate voltage control naturally varies for different applications of power, and is probably at a maximum in incandescent lighting;

Power used for illumination comprises the bulk of all power sold today. The illumination obtained from the'incandescent lamp is affected to a greater extentby changes in voltage than is the performance of other electrical devices. The candle-power output of thelamp, in percent of rated candle-power, is the criterion by which the quality of the service is judged.

How important voltage, regulation is, in the casefof the Mazda lamp for instance, will be understood when it is noted that a one percent change in voltage will produce a three and one half percent change in candle-power; and that for each one per cent increase in applied voltage there is an increase of oneand six tenths percent in the power'consumed by the lanip.

The economy of generating electric power by the use of large generating units in generating stations of great capacities, and in distributing the power at high voltages, is generally recognized. By "controlling the voltage of the indieconomies are possible. By controlling the bus voltage of the substation, or by regulating the voltage'bf its individual feeders, a number of substations canbe supplied by a single transmis sion circuit. Economies can also beelfected by net-working or interconnecting power transmissionci'rcuits. I

In areas" inavhich the electric load is'increasing from year to year, utilities are confronted with the problem of voltage regulation improvement.

This improvement can be. accomplished by the use of voltage regulators, or by an increase in the size of the line copper. The choice between voltage regulators to compensate for the voltage drop in a feeder, and an increase in the section of the line copperto decrease the drop, depends on the relation between the cost of the regulator and of the regulator and linelosses, and the cost of tlie additional line copper (sufficient to decrease the line drop to an allowable amount) plus the line loss.

Constant voltage can be maintained at the circuit load center by means of a regulator; but constant voltage at that point cannot be maintained by any increase in line copper.

We are concerned with certain problems. in efiiciently operating a power distribution system. The first problem confronting us is transformer impedance volts drop or transformer regulation, at our power distributing stations, commonly called substations. Next we are concerned about impedance "volts drop (Z1) in our distribution system conductors; most of which occursin the express feeder portion of the circuit. An express feeder is' that portion of the circuit betweenthe substation and point on the distribution circuit at which some distribution customer load is being supplied with electric service. The voltage drops in the individual distribution system transformers are of some concern to us; as is also the voltage 0 drop in the secondary conductors serving the individual customers. With the advent of large pumping stations in strictly residential areas, and with the growth of air-conditioning load in the newly developed community theatre, the control of motor starting current to a value which will not produce perceptible voltage flicker to other customers on the circuit, and which will allow sufficient static and starting motor torque, has become of importance. Another problem that is becoming of growing importance isthe application of capacitors to power distribution systems for purposes of absorbing reactive Kva.

The object of my invention is to solve these and other problems which arise in connection with the efficient operation of a power distribution system. The design of my calculator is based upon the solution of these problems by vector methods. 7

In the following explanation of my instrument and its uses, 1 make use of'certain well known symbolsj for instance-RI to represent resistance volts drop; XI to represent reactance volts drop; ZI to represent impedance volts drop; pi. to represent powcr factor; XX to represent the horizontal reference line through a center; YY to represent the vertical reference line through the center; to represent per cent. Also Es for voltage at sending station; E: voltage at receiving station; cos for the substation power factor, and cos p for the relative power factor at the end of the express feeder.

In the drawings which accompany and form a part of this specification:

Figure 1 shows my instrument as it is arranged for the solution of line drop problems in express feeders;

Figure 2 shows the instrument arranged for the solution of transformer impedance drop problems;

Figures 3 to 8 inclusive show parts of the instrument;

Figure 9 shows the development of the completed part shown in Figure 4;

Figure 10 is a table used in the development of the part shown in Figure 4; and Figure 11 shows a vector solution of the problem set up in Figure 1.

In Figure l, the numeral I indicates a baseboard, in which is cut a straight slot 2, substantially parallel with the edge of the board I. A semicircular protractor 3 is slidably mounted on the base-board I, having on its back two lugs, 4, one on either side of the center of the protractor scale, and engaging in the slot 2 to guide the movement of the protractor. On 3 is drawn a circular scale l0, whose axes intersect at the center 5,- and whose horizontal axis or XX line is parallel with the center line of the slot 2 in board I. A pivot pin 6, which is shown in detail in Figure 7, passes through the center 5 and through the slot 2. After adjustment by sliding along the slot. protractor 3 is held in place on the board by the tightening of the nut 1, which may be screwed up against the back of the board.

On this pin 6, when the instrument is completely assembled, are also pivoted the chart 9, shown in detail in Figure 4; the chart 35, shown in detail in Figure 5; and the scale 40, shown in detail in Figure 6.

A straight-edged scale 20 is pivoted on a fixed pin 2|, the center of which is set in line with the XX line of scale Ill. The pivot on scale 20 is on the zero mark. On this scale 20 I have slidably mounted another protractor 25 (see Figures 1 and 8).

The scale I0 is graduated in terms of power factor. This graduation is determined by converting the angle of displacement from the YY line or vertical axis of the protractor into p. f. by the formula cos 0 p. f. On the left of the YY line the graduations are for lagging p. f.; and on the right of the YY line they are for leading p. f. Unity p f. is represented at the intersection of the YY line with the scale Ill. The intersection of the X-X line with the scale In represents zero p. f.

The chart 9, which is also pivoted on the pin 6, is shown in detail in Figure 4. On this chart the radial lines represent the directions of the Z1 volts drop vectors, encountered in the solution of voltage drop problems in express feeders, for all wire sizes commonly used in commercial practice. The development of these ZI vectors is shown in Figures 9 and 10, to which I refer.

In commercial practice overhead conductors for B-phase circuits are usually constructed so that their effective spacing is 22.6 inches or 53 inches. The effective conductor spacing is determined from the formula in which D is the effective spacing in inches; A is the A-phase conductor, B is the B-phase conductor, C is the C-phase conductor; AB is the spacing between conductors A and B, BC the spacing between conductors B and C; and AC the spacing between conductors A and C. This formula applies to conductors arranged in horizontal or in triangular spacing, From this we can develop the fact that in 22.6 inch horizontal effective spacing, the spacing AB is 14.5 inches, the spacing BC is 14.5 inches, and the spacing AC is 29 inches. Likewise, in the effective spacing of 53 inches, AB is 29 inches, BC is 59 inches, and AC is 88 inches. These two spacings are the standard spacings mostly used in the construction of 2.3 KV 3-phase circuits in the United States.

The directions taken by these ZI volts drop vectors in relation to the XX and YY lines are determined as follows: for the 4/0 stranded conductor (see Figure 10) V3 RI and V3 XI values in terms of volts were determined for 100,000 ampere-feet. (For 100,000 I hereinafter use 10.)

V3 RI for 10 ampere-feet in a 4/0 stranded conductor=8.92 resistance volts drop (see table in Figure 10) and the V3 XI for 10 ampere-feet for the same conductor is 18.98 reactance volts drop. We set off 8.92 resistance volts drop on the XX line (Figure 9), and 18.98 reactance volts drop on the Y-Y line; and from these points on the Y--Y and XX lines we draw rectangular coordinates. Then through the intersection of these coordinates a line is drawn to the origin, or center of the chart. This line is the Z1 vector for 4/0 stranded conductor. The ZI vectors for the remaining wire sizes in Figure 9 are plotted in the same way.

In my instrument all scales having the same class of graduations are graduated in like units or in multiples thereof.

The length of the ZI vectors in Figures 4 and 9 are approximately 860 volts long; this figure being near the limit of voltage drops to be considered.

In the arrangement of this chart 9 (Figure 4) the Z1 volts drop vectors for an effective spacing of 22.6 inches are plotted in the third quadrant; and those for an effective spacing of 53 inches are plotted in the fourth quadrant. I speak of the third quadrant or of the fourth quadrant to indicate the quadrant to the left or to the right of the Y reference line on chart 9. There is no question of positive or of negative quantities. As will be explained later in this specification, both sets of vectors are actually plotted on the left of the Y reference line.

In the table (Figure 10) the V3 RI and V3 XI values for 10 ampere-feet were calculated for the conductors enumerated on the table in Fig ure 10 for effective spacings of 22.6 inches and 53 inches.

On the chart 9, Figure 4, each vector representing a conductor size is divided into spaces; the unit space on each vector representing the Z1 drop which would be created by 10 amperefeet in a circuit. The lengths of these unit spaces will increase as the conductors become smaller because the drop will increase as the wire section decreases.

If we now connect the divisions, on the several vectors, representing the-Z1 drop for a given circuit load, we develop a load-drop-line, which line will give at a glance the ZI drop for each wire size. In Figure 4 the load-drop-line g-h gives at its intersection with the several vectors the phase to phase volts drop in each of the circuit wire sizes represented, for a circuit load of 20 10 ampere feet. On the chart 9 the loaddrop-lines are 10 ampere-feet apart.

The ZI vectors in the fourth quadrant of chart 9 are arranged for an effective spacing of 53 inches. For the sake of simplicity, and to reduce the number of parts, as will be understood later, in the fourth quadrant the wire sizes are arranged in the same order as: in the third quadrant. If the drawing be held in such a posi tion that the XX line becomes the Y-Y line, and the Y-Y line becomes the XX line, we shall see that the load-drop-lines for the 53 inch eifective spacing are developed in the same manher as are the load-drop-lines for the 22.6 inch eifective spacing. The old YY line being short for use as the new XX line, for convenience in reading with the protractor 25 I have extended the body of the chart 9, as at l6, and I have produced the new XX line on this extension. as at [1.

Referring to Figure 1: the straight-edged scale 20 is pivoted at 2!, this pivot being exactly in line with the XX line of protractor 3, and also in line with the graduated edge 22 of the scale, and on the zero mark. The graduations are in volts. The zero of the scale is at the pivot 2|. The graduation shown in the drawing is from 1500 to 3000 volts, in units of 10 volts each. These volts are sending and receiving volts. For the sake of clearness in the drawings, only a small section of this graduated scale has been graduated in the smaller units, as at 23.

'40' Referring again to Figure 1: 25 is a protractor,

shown in detail in Figure 8. Along the lower part of this protractor there is arranged a slot 26, with loops 2'! through which the straight-edged scale 20 is passed. The scale is a neat fit in the slot; with just enough play between them to allow the protractor to slide on the scale. The upper edge of the slot 26, which coincides with the graduated edge of the scale 20, is taken as an XX line of reference; and from a point about the middle of its length a YY line is erected at right angles to this XX line. Taking the intersection of these two reference lines as center, the are 30 is described. This arc is graduated in terms of power factor; these graduations being developed as in the case of scale [0. The arc is drawn in the second quadrant, to read relative power factor for the problems based on an effective spacing of 22.6 inches. It will be seen that by exchanging the relative positions of the XX and YY lines on chart 0 I am able to read relative power factor on the same second quadrant for problems based on an effective spacing of 53 inches. By using the chart 9 and the protractor 25 in this way, my instrument is made simpler in its construction. This will be understood when we consider the problem set up on the instrument as shown in Figure 1.

For working transformer problems I use the scale 3, the protractor 20, with the chart 35 and scale 00, as shown in Figure 2. Chart 65 and scale 40 are shown in detail in Figures 5 and 6 respectively. In chart 35 the XX line is divided in ohms resistance; and the YY line is divided in ohms reactance. The smallest divi- 75 sion is one-tenth of an ohm; and the graduations extend to three ohms. One division, or one-tenth of an ohm, is equivalent in length to thirty volts on scale 20.

Scale 40 is a straight edged scale, with the graduated edge il in line with the center of the pivotal hole at 42. Through this hole scale 40 is pivoted to the chart 35 at the intersection of its XX and YY lines; and both are pivoted on the pin 6 with the protractor 3 and the scale 20. The graduations on the scale 40 are in volts, as in scale 20; except that the volts on scale 40 are ZI volts. The zero of the scale is at the pivot, and the scale extends to 850 volts, and for con- Venience in units of volts each.

Referring now to Figure 1: the instrument is set up to solve an express feeder voltage drop problem. For the sake of example let us take the following problem: a 3-phase 4/0 express feeder, 6666.6 circuit feet long, serves a distribution load of 300 amperes per phase with a power factor of .80, measured at the substation. The distribution system is a 2.3KV 3-phase delta system. The output substation voltage is 2350 volts. The effective conductor spacing is 22.6 inches. Determine the receiver voltage at the end of the express feeder; and the relative p. f. at the end of the express feeder.

First, scale 20 is placed in such a position that its graduated edge passes through the center of pivot 0. Then slide protractor 3 in the slot 2 until its center or pivotal point is directly wider the graduation representing 2350 volts on scale 20. Protractor 3 is then clamped in position. Chart 0 is then rotated until its Y-Y line is directly over .80 p. f. on protractor 3. Now multiply the current by the distance in circuit feet, and we have 300 amperes 6666.6 circuit feet: 2,000,000 or 20 X 10 ampere-feet. Now swingthe scale 20 downward until its graduated edge passes through the 4/0 wire size vector at the 20 X 10 division; that is at 20 X 10 ampere-feet; and read at the point of intersection, on scale 20, 1996 receiver volts. This is the voltage at the receiver end of the express feeder.

We also wish to determine the relative D. f. Holding protractor chart 9, and scale 20 in position, as developed above, slide the protractor 26 on the scale arm 20 until its Y-Y line coincides with the intersection of the XX line of chart 0 and the graduated edge of scale 20. This intersection is indicated by the letter c. The relative p. f. is now read on the graduated are on the protractor 25, at the point of its intersection with the X-X line of chart 2. The reading, in relative power factor is .858.

The ordinary vector solution of this problem is shown in Figure 11. In this figure the points a, b, and c are the points a, b, and c in Figure 1}. The point 0 in Figure 11 is the pivot 0- in Figure 1. In Figure 11 the angle 5 is the angle representing .858 power factor on the protractor 25 in Figure 1.

The vector diagram is constructed as follows:-the line o'a' is laid down to represent the substation voltage. o'I is drawn at an angle to the line o'a, the said angle being the angle whose cosine is represented by the p. f. at the substation. Through a draw the line XX parallel to o'I; then draw YY through point a perpendicular to X-X and o'I produced. From tables we determine that the R (resistance) per 1000 feet of 4/0 copper conductor is 0.0515 ohms; and the X (reactance) per 1000 feet of 4/0 copper conductor is 0.1097 ohms. In the problem stated I equals 300 amperes; and the circuit length is 6666.6 feet. We have:

We also have:

V3 XI= /3 .1097 6666.6/1000 X 300 :380 volts drop.

On Figure 11: from a lay off on the YY line 380 volts of XI drop. Then at the end of the XI vector on YY, at 380 volts, draw a perpendicular to the left of YY. Lay off on this vector line 178.2 volts of RI drop. Call the end of this vector b. Connect b and a by a line. This line b'-a' is the Z1 volts drop, which equals /RI +XI To complete the arithmetical equation; 21 volts drop=\/1'78.2 +380 :40O volts.

Connect 0 to b. The length of this line o'b' represents the receiver voltage, or 1996 volts.

Now we wish to determine the relative p. f. Note that the substation p. f. is equal to the cosine of 0, which is the angle between o--I and o'a'. Note also that the relative p. f. at the end of the express feeder is equal to the cosine of 6, which is the angle between o'I and o'b. Produce line o'-b until it intersects X-X in 0'. Then, because line o'I is parallel to the line X-X, the angle 10 b equals the angle between X-X and o'c. This is the angle which, measured by the protractor 25 in Figure 1, is .858 power factor.

Referring now to Figure 2: the protractor 3 as before is slidable on the base I, being guided by the lugs 4 on its back engaging in the slot 2. The chart 35 is pivoted by its center to the center of the protractor 3. On the same pivot, scale 40 is pivoted. Chart 35 and scale 43, have already been described in detail.

The problem set up in Figure 2 is as follows: a 25 Kv-a 2400/ 120-240 volt distribution transformer, whose equivalent secondary resistance is .0329 ohm, and whose equivalent secondary reactance is .0256 ohm, is serving a load of 75 Kv-a at a relative transformer p. f. of .95. The noload voltage on the transformer secondary side is 237.0. Our problem is to determine the voltage drop in the transformer in per cent of its secondary no-load terminal voltage. We proceed as follows:

We determine the full load secondary output current at the transformer. This equals 25000 volt-amperes divided by 240 volts; or 104.1 amperes.

To determine the equivalent secondary Z of the transformer: Z equals /R +X equals /.0329 +.0256 equals .0416 ohm.

The ZI at the above load is or 13.02 volts.

Referring to the instrument in Figure 2: bring scale 20 to its horizontal position, its graduated edge cutting the center of the pivot of protractor 3; slide protractor 3 until its center rests on 237 volts on scale 20. (In the drawings, Figure 2, the center of protractor 3 actually rests on 2370 on scale 20; that is, on 237x10.) Rotate chart 35 until its YY line is on .95 p. f. on protractor 3. Now rotate the Z1 volts vector scale 40 until its edge passes through a point, the coordinates of which are determined by laying off on the R and on the X lines on chart 35, respectively, multiples of the equivalent secondary resistance and of the equivalent secondary reactance found above; namely .0329 ohm and .0256 ohm; and by drawing perpendiculars to the R and X lines through these points. This determines the direction of the Z1 volts vector relative to the secondary noload terminal voltage.

Now read 13.02 volts, or the Z1 volts drop in the transformer, on scale 40. Bring scale 20 up until its edge coincides with 13.02 volts on scale 40, and read on scale 20, at the intersection, 224.4 volts. This is the secondary terminal voltage when supplying '75 Kv-a of load.

The arithmetical voltage drop in the transformer is 237224.4=12.6 volts; and

voltage drop in the transformer.

I have described my instrument and its operation as shown in Figure 2 for solving distribution transformer problems. The instrument can be used in exactly the same way for solving substation transformer problems.

In the table shown in Figure 10, the seven columns taken in order give the following: (1) Wire sizes used in commercial practice; (2) Resistance in ohms for 1000 feet for each size of conductor; (3) Reactance per 1000 ft. for each size for an effective spacing of 22.6 inches; (4) the same for an effective spacing of 53 inches; (5) the 3 RI for 10 ampere-feet for each wire size; (6) the V3 XI for 10 ampere-ft. for each size of conductor for 22.6 inch effective spacing; and (7) the /3 XI for 10 ampere-feet for each size of conductor for 53 inches effective spacing.

Either the voltage scale 20 or the protractor 3 may be made adjustable towards the other to adjust the distance between the zero of the scale and the center of the protractor.

Note that the chart 35 shown on Figure 2 may be drawn on the same chart 9 shown on Figure 1. Their being on separate pieces of the instrument is only a matter of convenience, and for ease in reading. I prefer to make my parts of transparent material.

I claim:

1. In an instrument of the class described: a voltage scale pivoted at its zero; a protractor on which are constructed X-X and YY reference lines, set with its XX line in line with the pivot of the said voltage scale, the said protractor having also constructed upon it a circular arc whose center coincides with the intersection of the said X-X and YY reference lines, and which are is graduated in terms of power factor; and a chart on which are constructed X-X and YY lines and which is pivoted at the intersection of its X-X and YY lines to the center of the protractor, the said chart having plotted upon it impedance volt-s drop vectors for wire sizes for a selected effective spacing.

2. In an instrument of the class described: a voltage scale pivoted at its zero; a protractor on which are constructed X-X and YY reference lines, set with its X-X line in line with the pivot of the said voltage scale, the said protractor having also constructed upon it a circular arc whose center coincides with the intersection of the said XX and YY reference lines, and which are is graduated in terms of power factor; means for adjusting the length of the line between the zero point of the voltage scale and the center of the protractor; and a chart on which are constructed X-X and YY reference lines and which is pivoted at. the intersection of its reference'lines to the'ce'nter' of the protractor; the said chart having plotted upon it'impedance volts dropvectors for wire sizes for a selected effective spacing' U 3. In an instrument of the class described: a voltage scale pivoted at its zero; a protractor on which are constructed- Xv -X and YY reference lines, set with'its 'XX line in line with the pivot, of the voltage scale,the said protractor having also constructed upon it a circular arc whose center coincides with the" intersection of the said XX and Y-Y reference lines, and which are is graduated in terms of power factor; means for adjusting the distance between the zero point of the voltage scale and the center of the protractor; and a chart on'which are constructed X-X and Y-QY reference lines and which is pivoted at the intersection of its reference lines to the center of the protractor, the said chart having plotted upon it impedance volts drop vectors for err several wire sizes and for a selected effective spacing, and plotted upon the vectors a series of IOad drOp-Iines giving at their intersections with the vectors the phase to phase volts drop in each of the circuit wires represented by the several vectors.

4. In an instrument of the class described: a voltage scale pivoted at its zero; a protractor on which are constructed XX and YY reference lines, set with itsX--X line in line with the pivot of the said voltage scale, the said protractor having also constructed upon it a circular arc whose center coincides with the intersection of the said X--X and YY reference lines, and which arc is graduated in terms of lagging power factor and in terms of leadingpower factor; means for adjusting the distance between the zero point of the voltage scale and the center of the protractor; and a chart on which are constructed XX and Y-Y lines and which is pivoted at the intersection of its reference lines to the center of the protractor, the said chart having plotted upon it impedance volts drop vectors for several wire sizes and for a selected effective spacing.

5. In an instrument of the class described: a voltage scale pivoted at its zero; a protractor on which are constructed XX and YY reference lines, set with its X-X line in line with the pivot of the voltage scale, the said protractor having also constructed upon it a circular arc whose center coincides with the intersection of the said X-X and Y-Y reference lines, and which are is graduated in terms of power factor lagging and leading; means for adjusting the distance between the zero point of the voltage scale and the center of the protractor; and a chart on which are constructed XX and Y-Y reference lines and which is pivoted at the intersection of its reference lines to the center of the protractor, the said chart having plotted upon it impedance volts drop vectors for wire sizes and for a selected effective spacing, and also plotted upon the vectors load-drop-lines giving at their intersections with the vectors the. phase to phase volts drop in each of the circuit wires represented by the several vectors.

6. In an instrument of the class described: a voltage scale pivoted at its zero; a protractor on which are constructed XX and YY reference lines, set with its XX line in line with the pivt of the Voltage scale, the said protractor having also constructed upon it a circular arc whose center coincides with the intersection of the said XX and YY reference lines, and which are is graduated in terms of power factor; a chart on which are constructed XX and YY lines and which: is pivoted at the intersection of its XX and Y-Y lines to the center of the protractor, the said chart having plotted upon it impedance volts drop vectors for wire sizes for a selected eifective spacing; and a second protractor slidalbly mounted on the voltage scale, the said second protractor being graduated in terms of power factor arranged to indicate relative power factor when associated with the X-X line of the said chart.

'7. In an instrument of the class escribed: a voltage scale pivoted at its zero; a protractor on WhlCl'l are constructed X-X and YY reference lines, set with its X-X line in line with the zero of the voltage scale, the said protractor having also constructed upon it a circular arc Whose center coincides with the intersection of the said X-X and YY reference lines, and which are is graduated in terms of power factor; means for adjusting the voltage scale with reference to the center of the protractor; a chart on which are constructed XX and Y--Y lines, and which is pivoted at the intersection of its XX and YY lines to the center of the protractor, the said charthaving plotted upon it an impedance volts drop vector for a wire size; and a second protractor slidably mounted on the voltage scale with its X-X line coincident with the graduated edge of the voltage scale, the said second protractor being graduated in terms of power factor to read relative power factor in association with the X--X line of the said chart.

8. In an instrument of the class described: a voltage scale pivoted at-its zero; a protractor on which are constructed X-X and YY lines, set with its X--X line in line with the zero of the voltage scale, the said protractor having also constructed upon it a circular arc whose center coincides with the intersection of the said XX and Y--Y reference lines, and which are is graduated in terms of power factor lagging and leading; means for adjusting the distance between the zero point of the voltage scale and the center of the protractor; a chart on which are constructed an I X line and a YY line and which is pivoted at the intersection of its XX and Y-Y lines to the center of the protractor, the said chart having plotted upon its impedance volts drop vectors for wire sizes for selected eifective spacings; and a second protractor graduated in terms of power factor and arranged with its X-X line movable along the edge of the voltage scale so that its power factor scale may be associated with the said chart to read relative power factor.

9. in an instrument for determining the receiver voltage and the relative power factor at the end of an express feeder; a voltage scale pivoted at its zero point; a protractor having constructed upon it an XX line and a YY line, the X-X line being in line with the zero of the voltage scale, the said protractor having also constructed upon it a circular arc whose center coincides with the intersection of the said XX and Y-Y lines, and which are is graduated in terms of power factor leading on the right of its Y--Y line and in terms of power factor lagging on the left of its Y-Y line; means for moving the protractor to bring its center to the graduation on the voltage scale representing the output substation voltage; a chart having X-X and Y-Y lines pivoted at its center to the center of the protractor and rotatable on its pivot to bring its YY line to the substation power factor on the protractor scale, the said chart having plotted upon it ZI vectors for selected wire sizes and on the vectors voltage drop for various loads; and a second protractor graduated in power factor with its XX line coincident with and slidable along the voltage scale; so arranged with each other that when the center of the first protractor is brought to the graduation on the voltage scale representing the substation voltage, the chart is rotated to bring its YY line to intersect the protractor scale at the figure representing the substation power factor, and the voltage scale is rotated on its pivot to bring its scale into intersection with the Z1 vector on the chart at the point representing the voltage drop due to load the said vector will then intersect the voltage scale at the receiver voltage at the end of the express feeder, and also so that when the center of the second protractor is brought into coincidence with the intersection of the voltage scale and the XX line of the chart the XX line of the chart will indicate on the scale of the second protractor the relative power factor at the end of the express feeder.

10. In an instrument of the class described: a voltage scale pivoted at its zero point; a Drotractor having XX and YY lines and having its XX line in line with the zero of the voltage scale, the said protractor having also constructed upon it a circular arc whose center coincides with the intersection of the said XX and YY lines, and which arc is graduated in terms of power factor; means for adjusting the distance between the zero point of the voltage scale and the center of the protractor; a chart having XX and YY lines and which is pivoted at its center to the center of the protractor, the said chart being divided on its XX line in terms of ohms resistance and on its YY line in terms of ohms reactance and having upon its surface intersecting lines erected on the said divisions; and a second voltage scale pivoted at its zero point to the center of the chart and graduated to read 21 volts drop at the intersections of the lines erected on the XX and YY lines, and so arranged with respect to the first voltage scale that if the first voltage scale be now rotated on its pivot to bring it into intersection with the second voltage scale at the 21 volts drop reading, the scale indication on the first voltage scale at its intersection with the second voltage scale will be the secondary terminal voltage, when used for solving transformer problems.

11. In a calculator for solving electrical power distribution problems: means for combining vectors of proper length and direction to obtain the desired result comprising a sending and receiving voltage scale; a protractor having constructed upon it XX and YY lines, and also having constructed upon it a circular arc whose center coincides with the intersection of the said XX and YY lines, and which are is graduated in terms of power factor and which protractor is associated with the voltage scale to indicate sending voltage; a vector chart representing impedance volts drop for wire sizes for selected spacings and divided for voltage drop at given loads, and arranged to indicate receiver voltage on the voltage scale; and a second protractor graduated in terms of power factor and associated with the chart and with the voltage scale to read relative power factor at the receiving voltage.

ALFRED P. WEST.

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