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maximum-demand in kilowatts, and in consequence Wh the energy consumed in kilowatt-hours,
A W + B Wh
h which is of the same form as equation (2).
Thus a Manchester-Hopkinson maximum-demand system is equivalent to a Wright maximum-demand system when the fixed rate per kilowatt is A = H (P1 – P2) and the kilowatthour rate is B = P..
Thus a Wright system in which H = 83h per month, P,= 5 cents. P,=2 cents is equivalent to a Manchester-Hopkinson maximum-demand system, in which there is a charge of $2.49 per kilowatt-month of maximun-demand and 2 cents per kilowatt-hour required, with the only difference that the Wright system cuts off the top portion of the curve in the first hour's use.
In Fig. I the dotted portion of the curve belongs to a Manchester-Hopkinson system and the portion in full line is common to both systems.
Hence the question arises as to which is the most convenient form of the two to give to our schedule of rates. The Manchester-Hopkinson is the simplest and the clearest; so many kilowatts are indicated by the maximum-demand indicator, and so many times $2.49 have to be paid; so many kilowatt-hours so many times 2 cents.
On the other hand, the customer appreciates very quickly what is the influence of his maximum-demand. With the Wright system he does not realize it so clearly, as there is involved in it the complication of a quantity very difficult to conceive, namely, the hour's use per kilowatt.
Sellers of electricity are afraid that a Manchester-Hopkinson system is too complex for most consumers. I believe, however, that once they are persuaded that the two systems are virtually alike, they will have no objections to raise. The only difference is that with the Wright system, for the first H hours one must pay a simple meter rate, while with the Manchester-Hopkinson system he pays a larger sum. This is, however, thoroughly justified, and, secondly, is not a serious objection, as with motor service the time H is normally always reached. For these reasons I incline to the Manchester-Hopkinson method.
Now we come to a second point: The most convenient maximum-demand indicators are ammeters. With these no inconveniences are experienced when direct current is used: but when use is made of alternating current, as is the case in Italy, where the electrical energy is generally three-phase and has, of course, a power-factor lower than unity, the current indicators represent a real drawback. In fact, the power must be determined in kilowatts and not in kilovolt-amperes, and it is necessary to multiply the indications of the instrument by the value of the voltage and by a certain power-factor which is supposed to be the right one. Such a method engenders discussions and disagreements, and to get over the difficulty, at least with reference to the power-factor, the changes in the voltage being only small, the best way is to determine the maximum-demand in kilovolt-amperes, which coincides with a rational principle. In fact, what count in maximum-demand in an alternating-current system are the amperes and not the kilowatts. The overload of the generators, transformers and cables is limited by the current. It is right, therefore, to fix the maximumdemand in kilovolt-amperes.
On the other hand, the cost of production is really proportional to the true energy, consequently it is rational to make the fixed rate B so much per kilowatt-hour.
It may appear that such a double assumption would give rise to a non-homogeneous result; but this is not the case, as, practically, it is the same as assuming a conventional value for the power-factor.
It may be further objected that it is not right to apply the same value of the power-factor to all values of the maximumdemand. I will show later that this objection also can easily be met. Anyhow, the substitution of the kilovolt-ampere for the kilowatt will tend to better the power-factor of the distribution.
Let us come back to the curve of coefficient C.
In Fig. 2 I have drawn the curve A, which is derived from the first rates charged in the schedule applied in Milan. In this curve are represented the ratios of the first prices for different values of power to the first price for one kilowatt. I must here remind you that the origin and object of this curve was to meet competition. Hence it is a curve for the special case of Milan. The curve representing B is an hyperbola whose equation is
which is quite near to curve A. Thus the substitution of the hyperbola B for the empirical curve A can be made without altering the results in any marked way. In any event, it will be noted that the function C=f (M) may be of the form of the expression (4), this is,
which is a fairly simple expression.
Of course the values of m, n and q are to be arranged for each different case in order to meet different local conditions.
I now wish to show you how the law of variation of the power-factor can be incorporated in the schedule.
First of all, if P were the fixed charge for one kilowatt of maximum-demand and the fixed charge per kilowatt-hour, admitting for the power of one kilowatt a cos 0 = 3, the fixed charge per kilovolt-ampere ought to be
while Q, the fixed charge per kilowatt-hour, will remain the same.
Now, suppose we are starting from curve B, in which the abscissæ are true kilowatts and we want to apply a conventional power-factor in order to have a coefficient curve for the kilovoltamperes.
As these curves represent ratios of each price to the fundamental price, if a single value of the power factor were used for any power, curve B would be correct either for kilowatts or for kilovolt-amperes; but if the power-factor is considered variable, following a certain law, we can alter the ordinates of curve B in proportion to the ratio of each value of the power-factor, to its value for one kilovolt-ampere.
The result will be the curve shown as C in the diagram, Fig. 2, and is naturally higher than B, of which the equation is
4.44 y =
x + 5.2 In conclusion, this method of charging, which I should call the double sliding scale method, is applied by installing with each customer a volt-ampere and a maximum-demand indicator, the readings of which are taken at periods corresponding to the billing periods, the bills being made up in the following manner:
(1) By charging a fixed rate A for each kilovolt-ampere of maximum demand.
(2) By charging a fixed rate B for each kilowatt-hour.
Kilovolt-amperes XA + kilowatt-hours x B= S by a coefficient C from a special coefficient curve, preferably prepared with a simple formula.
Of course the values A, B and the curve of coefficients must be worked out in accordance with local conditions, cost of energy, and all the ordinary items which are to be taken into consideration in planning any method of charging.
DISCUSSION MR. FERGUSON: At one of the meetings of the executive committee of the association during the past year, I suggested to President Williams the advisability of having a discussion at this convention to ascertain the necessity for obtaining some meter that would measure the true energy on polyphase system for general service, not for large consumers, but for general motor service, and the president asked me if I would provoke such discussion at this convention. I notice in this paper of Mr. Semenza that he brings out some of the points I intended to bring out at the convention, but he has viewed them from a somewhat different standpoint.
This whole subject of charging for alternating power service is very important at the present time. The use of alternatingcurrent service for industrial power is growing tremendously all over the country, especially in the large cities and in sections of the country where water-power is available; but at the present time it is difficult to deal with the customers on a differential system, owing to lack of an inexpensive demand meter to measure the true energy of the polyphase service delivered to the consumer. If you are selling on flat rate per kilowatt or horse-power per year, of course there is nothing to consider; but there are some of us who believe that, at least where steam is the source of supply, a flat rate per kilowatt or horse-power per year is not the correct system, and the differential system should be used in order to avoid difficulties with our customers in making relative comparisons of their costs. If we sell on a differential system every one pays on exactly the same basis. The difficulty is that we have no means of measuring the maxi