Electric Transmission of Water Power

by Alton D. Adams

The efficiency of the transmission is measured by the ratio of the energy delivered by the transformers at the receiving station for local distribution to the energy delivered by the generating plant to the transformers that supply energy to the line for transmission. If worked at full capacity the large transformers here considered would have an efficiency of nearly 98 per cent; but as they must work, to some extent, on partial loads, the actual efficiency will hardly exceed 96 per cent.

The efficiency of the line conductors rises on partial loads, and may be safely taken at 93 per cent for all of the energy transmitted, though it is only 90 per cent on the maximum load. The combined efficiencies of the two sets of transformers and the line give the efficiency of the transmission, which equals the product of 0.96 × 0.93 × 0.96, or almost exactly 85.7 per cent. In other words, the transformers at the water-power station absorb 1.17 times as much energy as the transformers at the receiving station deliver to distribution lines in the place of use.

Interest, maintenance, and depreciation of this complete transmission system are sufficiently provided for by an allowance of 15 per cent yearly on its entire first cost. As the total first cost of the transmission system was found to be $445,000, the annual expense of interest, depreciation, and repairs at 15 per cent of this sum amounts to $66,750.

In order to find the bearings of this annual charge on the cost of power transmission the total amount of energy transmitted annually must be determined. The 10,000 horse-power delivered by the system at the sub-station is simply the maximum rate at which energy may be supplied, and the element of time must be introduced in order to compute the amount of transmitted energy. If the system could be kept at work during twenty-four hours a day at full capacity, the delivered energy would be represented by the product of the numbers which stand for the capacity and for the total number of hours yearly.

Unfortunately, however, the demands for electric light and power vary through a wide range in the course of each twenty-four hours, and the period of maximum demand extends over only a small part of each day. The problem is, therefore, to find what relation the average load that may be had during the twenty-four hours bears to the capacity required to carry this maximum load. As the answer to this question depends on the power requirements of various classes of consumers, it can be obtained only by experience. It has been found that some electric stations, working twenty-four hours daily on mixed loads of lamps and stationary motors, can deliver energy to an amount represented by the necessary maximum capacity during about 3,000 hours per year. Applying this rule to the present case, the transformers at the sub-station, if loaded to their maximum capacity of 10,000 horse-power by the heaviest demands of consumers, may be expected to deliver energy to the amount of 3,000 × 10,000 = 30,000,000 horse-power hours yearly.

The total cost of operation for this transmission system was found above to be $66,750 per annum, exclusive of the cost of energy at the generating plant. This sum, divided by 30,000,000, shows the cost of energy transmission to be 0.222 cent per horse-power hour, exclusive of the first cost of the energy. To obtain the total cost of transmission, the figures just given must be increased by the value of the energy lost in transformers and in the line conductors. In order to find this value, the cost of energy at the generating plant must be known.

The cost of electrical energy at the switchboard in a water-power station is subject to wide variations, owing to the different investments necessary in the hydraulic work per unit of power developed. With large powers, such as are here considered, a horse-power hour of electrical energy may be developed for materially less than 0.5 cent in some plants. As the average efficiency of the present transmission has been found to be 85.7 per cent of the energy delivered by the generators, it is evident that 1.17 horse-power hours must be drawn from the generators for every horse-power hour supplied by the transformers at the sub-station for distribution. In other words, 0.17 horse-power hour is wasted for each horse-power hour delivered.

The cost of 0.17 of a horse-power hour, or say not more than 0.5 × 0.17 = 0.085 cent, must thus be added to the figures for transmission cost already found, that is, 0.222 cent per horse-power hour, to obtain the total cost of transmission. The sum of these two items of cost amounts to 0.307 cent per horse-power hour, as the entire transmission expense.

It may now be asked how the cost of transmission just found will increase if the distance be extended. As an illustration, assume the length of the transmission to be 150 instead of 100 miles. Let the amount of energy delivered by the sub-station, the loss in line conductors, and the energy drawn from the generating plant remain the same as before. Evidently the cost of the pole line will be increased 50 per cent, that is, from $70,000 to $105,000. Transformers, having the same capacity, will not be changed from the previous estimate of $150,000. If the voltage of the transmission remain constant, as well as the line loss at maximum load, the weight and cost of copper conductors must increase with the square of the distances of transmission. For 150 miles the weight of copper will thus be 2.25 times the weight required for the 100-mile transmission.

Instead of an increase in the weight of conductors a higher voltage may be adopted. The transformers for the two great transmission systems that extend over a distance of about 150 miles, from the Sierra Nevada Mountains to San Francisco Bay, in California, are designed to deliver energy to the line at either 40,000 or 60,000 volts, as desired. Though the regular operation at first was at the lower pressure, the voltage has been raised to 60,000.