CHAPTER LXI
SYNCHRONOUS CONDENSERS
~Synchronous Condensers.~--A synchronous motor when sufficiently excited will produce a leading current, that is, when over excited it acts like a great condenser, and when thus operated on circuits containing induction motors and similar apparatus for the purpose of improving the power factor it is called a _synchronous condenser_.
Although the motor performs the duty of a condenser it possesses almost none of the properties of a stationary condenser other than producing a leading current, and is free from many of the inherent defects of a stationary condenser.
The relation of power factor to the size and efficiency of prime movers, generators, conductors, etc., and the value of synchronous condensers for improving the power factor is generally recognized.
Induction motors and other inductive apparatus take a component of current which lags behind the line pressure, and thereby lowers the power factor of the system, while a non-inductive load, such as incandescent lamps, takes only current in phase with the voltage and operates at unity power factor.
Since transformers require the magnetizing current, they may seriously affect the power factor when unloaded or partially loaded, but when operating at full load their effect is practically negligible.
The relative effect of fully loaded and lightly loaded induction motors on the power factor is indicated by the diagram, fig. 2,478. The magnetizing current is nearly constant at all loads and is wattless, lagging 90 degrees behind the impressed pressure, or at right angles to the current which is utilized for power.
In the figure, AB is the magnetizing component, which is always wattless, and CB the power component. The angle ACB gives the phase relation between voltage and current; the cosine of this angle CB ÷ AC is the power factor.
It is evident from the diagram that if the load be reduced, the side CB is shortened, and as AB is practically constant, the angle of lag ACB is increased. It therefore follows that the cosine of this angle, or the power factor is reduced.
The figure clearly shows the reason for the low power factor of induction motors on fractional loads and also shows that since the magnetizing current is practically constant in value, the induction motor can never operate at unity power factor.
With no load, the side CB (real power) is just sufficient to supply the friction and windage. If this be represented by DB, since AB remains constant, the power factor is reduced to 10 or 15 per cent. and the motor takes from the line about 30 per cent. of full load current. It therefore follows that a group of lightly loaded induction motors can take from the system a large current at exceedingly low power factor.
The synchronous motor when used as a condenser, as before stated, has the property of altering the phase relation between pressure and current, the direction and extent of the displacement being dependent on the field excitation of the condenser.
It can be run at unity power factor and minimum current input, or it can be over excited and thereby deliver leading current which compensates for the inductive load on other parts of the system. The synchronous condenser, therefore, can supply magnetizing current to the load on a system while the power component is supplied by the generators.
~Effects of Low Lagging Power Factors.~--Transformers are rated in kva. output; that is, a 100 kva. transformer is supposed to deliver 100 kw. at unity power factor at normal voltage and at normal temperatures; but, if the power factor should be, say .6 lagging, the rated energy output of the transformer would be only 60 kw. and yet the current and, consequently, the heating would be approximately the same as when delivering 100 kw. at unity power factor.
The regulation of transformers is inherently good, being for small lighting transformers about 1½ to 2 per cent. for a load of unity power factor, and about 4 to 5 per cent. at .7 power factor. Larger transformers with a regulation of 1 per cent. or better at a unity power factor load, would have about 3 per cent. regulation at .7 power factor.
Alternators also are rated in kva. output, usually at any value of power factor between unity and .8.
The deleterious effects of low power factor loads on alternators are even more marked than on transformers. These are, decreased kw. capacity, the necessity for increased exciter capacity, decreased efficiency, and impaired regulation.
Assume the case of a 100 kva. .6 power factor, 60 kw. output. It is probable that normal voltage could be obtained only with difficulty, unless the alternator was especially designed for low power factor service. The lagging power factor current in the armature sets up a flux which opposes the flux set up by the fields, and in consequence tends to demagnetize them, resulting in low armature voltage.
It is often impracticable, without the installation of new exciters, to raise the alternator voltage by a further increase of the exciting voltage and current. The field losses, and therefore the field heating of the alternator, when it is delivering rated voltage and current, are greater at lagging power factor than at unity. Increased energy input and decreased energy output both cause a reduction in efficiency.
The regulation at unity power factor of modern alternators capable of carrying 25 per cent. overload, is usually about 8 per cent. Their regulation at .7 power factor lagging is about 25 per cent. The effect of low power factor on the lines can best be shown by the following example:
EXAMPLE.--Assuming a distance of five miles and a load of 1,000 kw. and desiring to deliver this load at a pressure of about 6,000 volts, three phase, with an energy loss of 10 per cent., each conductor at unity power factor would have to be 79,200 c.m., at .9 power factor, 97,533 c.m., and at .6 power factor, 218,000 c.m. In other words, at the lower power factor of .6, the investment in copper alone would be 2.8 times as much.
If the same size of wire were used at both unity and .6 power factor lagging, the energy loss would be about 2.8 times the loss at unity power factor, or about 28 per cent. Low lagging power factor on a system, therefore, will generally mean limited output of prime movers; greatly reduced kilowatt capacity of generator, transformer and line; and increased energy losses. The regulation of the entire system will also be poor.
~Cost of Synchronous Condenser vs. Cost of Copper.~--Referring to the example given in the preceding paragraph, and calculating the necessary extra investment in copper with the .6 power factor load, and copper at 17 cents per pound, the result is that 29,292 pounds more copper is required than with the power factor of .9 which means a total extra investment in copper alone of $5,000 (29,292 × $.17). A synchronous condenser of sufficient capacity to accomplish the same result would cost about the same amount. It would therefore cost less to install the condenser because at the same time a considerably increased capacity would be obtained from the alternators, transformers, etc.
~Synchronous Condenser Calculations.~--In figuring on the installation of a condenser for correcting power factor troubles, a careful survey of the conditions should be made with a view of determining just what these troubles are and to what extent they can be remedied by the presence of a leading current in the system.
It is necessary to possess a thorough knowledge of the system, covering the generating capacity in energy and kva., average and maximum load, and power factor on the alternators, average and maximum load, and power factor on the feeders, system of distribution, etc.
The desirable location of a condenser is, of course, nearest the inductive load in order to avoid the transmission of the wattless current, but it often happens that a system is so interconnected that one large condenser cannot economically meet the conditions, in which case it may be better to install two or more smaller ones.
The question of suitable attendance should also be considered and, for this reason, it may be necessary to compromise on the location. When the location of the condenser has been decided upon and the load and power factor within its zone determined, the proper size of condenser to raise the power factor to a given value can be found as follows:
The method of procedure can best be explained by reference to a concrete case. Assume a load of 450 kw. at .65 power factor. It is desired to raise the power factor to .9. What will be the rating of the condenser?
Referring to the diagram, fig. 2,488, it is necessary to start with 450 kw. At .65 power factor, or 692 kva., this has a wattless lagging component of √(692² - 450²) = 525 kva. With the load unchanged and the power factor raised to .9, there will be 500 apparent kva., which will have a wattless component of √(500² - 450²) = 218 kva.
It is obvious that the condenser must supply the difference between 525 kva. and 218 kva., or 307 kva. A 300 kva. condenser would, therefore, meet the requirements.
If it be desired to drive some energy load with the condenser and still bring the total power factor to .9, proceed as indicated in fig. 2,489. Assume a total load of 150 kw. on the motor. As before, 450 kw. at .65 power factor, or 692 kva., with a wattless component of 525 kva.
The energy load will be increased from 450 to 600 kw. as indicated, and with the power factor raised to .9 there will be a kva. of 667 with a wattless component of √(667² - 600²) = 291.
There must be supplied 525 - 291 = 234 in leading kva.
The synchronous motor then must supply 150 kw. energy and 234 kva. wattless, which would give it a rating of √(150² + 234²) = 278 kva. at .68 power factor.
The standard 300 kva. condenser would evidently raise the power factor slightly above .9 power factor leading.
By reference to the chart, fig. 2,490, the size of the required condenser can be obtained direct without the use of the above calculation. The method of using this curve is as follows: Assume a load of say 3,000 kw. at .7 power factor and that it be desired to raise the power factor to .9. Run up the vertical line at 3,000 kw. to the .7 power factor line, and from there along the horizontal line to the margin and find a wattless component at this power factor of 3,000 kva., approximately. Again run up the 3,000 kw. vertical line to the .9 power factor line and from there along the horizontal line to the margin and find a wattless component of 1,500 kva. The rating of the condenser will then be 3,000 kva. - 1,500 kva. = 1,500 kva. This table of course can be used for hundreds of kilowatts as well.
For determining the rating of a synchronous motor to drive an energy load this curve is not so valuable, although it can be used in determining the wattless component direct in all cases where the energy component and power factor are known. Knowing this energy component and power factor or wattless component, the energy load can obviously be found by referring to the curved lines on the diagrams, the curve that crosses the junction of the vertical energy line and the power factor or wattless component line giving the total apparent kva.