Power limitations of transmission systems

Review of the Subject — Several independent studies have been made recently to determine the economies of a large, uniform power system. The two studies of more general interest were those conducted by the Department of the Interior, under the direction of W. S. Murray, for the Superpower Zone, and by F. G. Baum for the United States. Both of these investigations are available in published form. During the progress of the Superpower Survey, one of the longest transmission lines proposed was that extending 350 miles from the Niagara Falls Development to New York City. Under emergency conditions on this line, the power limit for the maximum amount of power was approached by two twin-circuit lower lines with three circuits carrying the emergency load. The maximum power limit would have been exceeded if two single-circuit tower lines had been employed, even though the transmission voltages and the total copper cross-section were the same as with the two twin-circuit lower lines. Similarly, several long, high-voltage lines will be required in a nation-wide system, especially through the middle western region as shown by Mr. Baum's report. The tendency to extensive transmission systems has emphasized the necessity of considering the factors which will limit the amount of power that can be transmitted any distance with the highest practical transmission voltage. On account of the transmission line characteristics, the power limits will be greater when the system is regulated by synchronous apparatus than when those such apparatus is used so that two power limits will be considered in this paper; first, for an unregulated system; and second, for a regulated system. However, while we are primarily interested in high-voltage systems in this paper, it should be kept in mind that these same methods of calculation may be applied to lower voltages in determining the power limitations of station tie lines. It is commonly accepted that different types of networks have certain power limitations. For example, a very simple case quite generally known is that of a simple resistance circuit in which the power delivered is a maximum when the resistance of the load is equal to that of the line. Another familiar case is that of the electric arc furnace where the maximum power occurs when the resistance of the furnace arc is equal to the reactance of the electric furnace leads. The general phenomenon of maximum power limit in circuits of fixed reactance and variable resistance or load has been recognized and Us theory worked out for numerous cases, such as short transmission lines, rotating machines, and transformers. A power transmission system may be regarded as a special type of network. Ordinarily it consists of long, high-tension transmission lines and apparatus connecting generating stations with distant load centers which may be either at the terminus or at intermediate points on the high-tension lines. In large systems, the high-tension lines may form a network similar to an ordinary local distribution system. Where synchronous condensers are not installed, the problem of the maximum amount of power which may be delivered through the system is similar to the simple resistance and reactance cases cited above in that additional load or shunt impedance simply alters the load and voltage in accordance with the relative impedances of the system. The employment of synchronous condensers at the load centers or along the transmission lines to alter the power factor and maintain the voltage at the load materially increases the maximum amount of power that may be desired over a given transmission network. The theoretical maximum amount of power however, cannoi be obtained under operating conditions because the synchronous equipment at the receiver drops out of step with the supply. Also, fluctuations in load will produce unstable conditions, which may accumulate sufficiently to cause the momentary swings in load to exceed the power limit, resulting in the receiver falling out of step with the supply at a lower load than it would under steady conditions. This is usually characterized as “hunting out of step.” In order to investigate the power limitations of a transmission system, it was necessary to rearrange and extend the present methods of transmission line calculations to make them more convenient for the study of the practical limit of maximum power. The method which has been found best adapted for this purpose is a development of the power circle diagram combined with the characteristic curves of the synchronous machines used to regulate the system. This power diagram has been mode applicable to all the types of transmission systems by including the transmission line, step-up and step-down transformers, series and parallel circuits, so that the most complex transmission system may be represented by a single equivalent set of transmission constants. A general discussion of the methods of calculation, the maximum power limits, the practical operating limit and illustrated examples is given in Part I of the paper, and the analytical development upon which the discussion is based is given in Part II