mining maximum demand may be very different. The following will, therefore, be confined largely to a consideration of most desirable intervals.

Variation in Demand Intervals

The Wright demand indicator installation used by several of the large companies answers very well for direct current installations of moderate size, but is found rather expensive for very large D. C. installations and unsatisfactory for alternating current because of the large rushes of current in the starting of A. C. motors. In direct current installations, for instance, the Wright demand indicators will, under most conditions, indicate about 85 per cent of the maximum in 5 minutes and the full maximum in 30 minutes. As this indicator has found rather wide application in several cities, the interval (one-half hour with a steady load) required to show the full maximum on this instrument naturally had some influence in fixing the width of peak over which the maximum was integrated in the sale of alternating current power.

It must be borne in mind that with a steady load there is no difference between a 5-minute and a one-hour peak. If the load is intermittent, the shorter interval will give the higher maximum demand. In making a schedule of rates for large consumers it is necessary, therefore, if the rate is to be a just one for all the users in a given class, that a fixed interval for maximum demand be established; that is, either the instantaneous, the one minute, the five minute, quarter hour, half hour, or the one hour.

If the entire output of a water power plant with long transmission lines is taken by a very few consumers, each taking large blocks of power, a short interval might be preferable.

Penalty for Poor Power Factor

In such cases it is also sometimes desirable to increase the charge to the consumer if the power factor of his load falls below a reasonable figure.

In such portions of our large cities, however, as are supplied by alternating current energy the maximum load almost invariably occurs between six and nine o'clock when it is almost exclusively lighting, and as a result the power factor is high at that time in the evening. The day load or motor load in above mentioned portions of these cities which naturally has a poor power factor is usually less

than one-half the evening load. The amount of copper in the distribution system is therefore not injuriously affected by the poor load factor in the daytime, and hence the cost to the central station company is not appreciably affected. Moreover, rotary condensers may be used in such particular sub-stations where the power factor is lower than desirable, thus insuring a high power factor on the generators, transmission lines and sub-stations, and then in the worst event only the distribution system would be affected. In dealing with large number of power consumers it is difficult enough to have them understand load factor, to say nothing of such a complicated matter as an equitable charge for low power factor. For these reasons the Central Station companies operating in large cities practically always charge for the maximum demand on the basis of true energy or watt-hour consumption and will also find many advantages in using a reasonably long interval.

Relative Advantages of Short and Long Demand Intervals

In order to separate more easily the relative advantages of short and long intervals in obtaining the maximum demand, it is well to consider a simple example-the sight reading of the dial of ordinary watt-hour meter by an observer. There are immediately apparent two causes of error: (1) the time of observation of the length of interval, and, (2) the value of the reading. Suppose the operator is allowed a leeway of ten seconds on either side of the exact time. The maximum error in five minutes would be approximately 6 per cent, while in one hour it would be less than 6-10 of 1 per cent. In the second place, assume that the meter has a constant of 1, is read directly in K. W. H. and is installed on a line using about 1 K. W. H. per minute. If the observer is allowed to interpolate to one-quarter of each division then there is a maximum possible error of 14 K. W. H. In five minutes this would introduce an error of 5 per cent, but in one hour only 4-10 of 1 per cent. The above illustration assumes a meter constant of one, and the percentage of error given should be increased correspondingly by the larger constant always necessary for a large consumer.

Another illustration of the advantage of using longer intervals. is an actual case in which power was sold to a large street railway system and metered on a number of transmission lines each delivering a coincident maximum demand of about 1800 kw. Originally one division of the lowest dial of the meter multiplied by the constant of the meter best fitted for the purpose which was on the

market at that time was something like 400 kw. This meant a maximum possible error of, say, 400 kw., which would have been prohibitive except that there were several lines used in the supply and also the average of several maxima was used. But even then the results were, of course, not satisfactory.

On the meters now in use by the same company on the very large number of railway lines delivering an aggregate of over 100,000 kilowatts one division of the first dial amounts to 1-100 kw., which, multiplied by the constant which is usually 4000, gives the value of the lowest division of the dial as 40 kw. The hourly reading is 40 kw. divided by 1800 kw. (the output for one hour) or a maximum possible error of 2.2 per cent. With a half-hour interval the error is the same, but the percentage is double-40 kw. divided by 900 kw., or 4.4 per cent. Similarly the quarter-hour error would be 8.8 per cent and the five-minute error 26.6 per cent.

In the railway business cited, hourly intervals are used and this possible error is reduced by using the average of several maxima. The maximum error of each hourly reading is 2.2 per cent. Taking the average of several cases, the error, according to the law of averages, would be only one-half of this, or 1.1 per cent, and the more we can average within practical limits the more this percentage of error will be reduced. For instance, using the average of six peaks would theoretically reduce the error of 2.2 per cent to .37 of 1 per cent.

The error in reading any integrating meter used in determining the maximum demand (and this error as shown above may be very large) would be a much smaller percentage of the total energy for a long period than for a short one; in fact, the error is inversely proportional to the interval.

Where more than one instrument is required to determine a particular customer's peak load the labor involved in computing the maximum is quite an item, as the output of all the meters for the intervals on which the contract is based must be added together to obtain the coincident maximum demand. If a 5-minute interval were used, the labor in computing the maximum would be practically 12 times as great as for the one hour. The longer interval is, of course, more favorable to the consumer with the intermittent load, as it does not penalize him for the short peaks. This feature appeals to the consumer as the primary or maximum demand charge is

usually the least intelligible to him, and the shorter the interval, the harder it is for him to understand. He realizes that the total kilowatt hours used bear some direct relation to the amount of work done, but the maximum demand, particularly if it be an instantaneous or very short interval demand, is not so well understood.

Relation Between One-Hour Peak and Various Shorter Peaks

In order to determine the relation between the one hour peak and the various shorter peaks some accurate observations, most of them very recent, were made on different classes of consumers, all but one of which are in or near Chicago, and are given in Table I:

In the two office buildings the maximum demands under each of the three different intervals include only the elevator and general power and do not include any of the lighting. An inspection of this five-minute power load curve indicates that four extraordinary peaks at 9:20, 9:40, 12:40 and 3:50 caused the large percentage of difference between the 5-minute and the 30-minute peak on the 19-story office building. Similarly one very unusual peak at 8:30 A. M. occurred on the 12-story office building.

An analysis of the data on the large department store given in Table I indicates that if the bills for a year had been rendered on a 5-minute peak the maximum demand on primary charge would have been 8.1 per cent greater than on the 30-minute peak actually

billed, but the total bills for the year would have been only 3 per cent greater on the 5-minute than on the 30-minute peak.

The difference between the 5-minute and 30-minute peak on the piano factory would have been 9 per cent in primary charge but only 3.8 per cent in the total charge. On the grain elevator the difference would have been 7.7 per cent in primary and 3.9 per cent in total charge.

Effect of Demand Interval on Rates

While none of the differences in the three cases analyzed or in most of those given in Table I are very large they show conclusively that the width of peak should always be taken into account in establishing rates for electric service. In other words, broadening the peak is equivalent to lowering the price.

The actual result on price of a given broadening of peak depends -First, on the amount of broadening, that is, from say 5 minutes to 30 minutes, and, secondly, on the steadiness or unsteadiness of load.

The percentage difference in total income between the results obtained from 5-minute and 30-minute intervals is relatively small and it is much better to take care of a small difference of this kind by a slight adjustment in making the original primary rates than to have any possibility of the most important customers feeling that the method used is not accurate enough and not fair to them in all cases. As an illustration, assume that there is 5 per cent difference in total bill between the 5-minute and the 30-minute method. The power company should not feel that it is giving away this difference by using the 30-minute readings. In making up a schedule of rates this 5 per cent should be taken into consideration by making the primary enough higher to compensate for this difference.

Some consideration of the size of the consumer and the question of diversity factor will be worth while in a study of the relative merits of long and short intervals, and as to whether to use one reading or the average of several readings. With either lighting or power, but especially with power, the more intermittent the load and the smaller the consumer, the greater will be the diversity factor.