C. N. Weygandt

Integrals Required for Computing the Energy of H3 and of H3

Some of the difficult integrals required for the variational method calculation of the energy of the triatomic hydrogen molecule and positive ion were evaluated with the aid of the differential analyzer. The integral ∫ 0πexp (−B(1−A cos θ)12)dθ is tabulated for a complete range of the parameters, A and B. The integral K(c,ab)=(1/π) ∫ rc−1exp(−ra−rb)dτ is tabulated for many configurations of the three electrons or nuclei: a, b, and c. Numerical tables are given of all of the integrals occurring in the Sugiura treatment of the ground state of H2. The values of all of the other integrals used in the calculation of the energy of H3 and of H3+ are given. It is expected that these tables will be useful for many problems of molecular quantum mechanics.

Transient Characteristics of Current Transformers During Faults

THE factors involving current-transformer performance that affect the operation of protective equipment have recently received considerable attention.1–3 The fact that the transient performance may be greatly different from the steady-state performance has been recognized, but little quantitative data on transient performance have been published. Data from oscillograph records of tests and from approximate analytical methods have definitely indicated the magnitudes of the expected steady-state errors and at the same time conveyed the thought that the transient errors would be very much larger. This paper presents some of the results of a study of current-transformer transient performance that has been made on the differential analyzer with the effects of transformer saturation more accurately considered.

Control of Tie-Line Power Swings

THE object of this paper is to present the results of an analytical study of tie-line power control. This study was made as a logical development of the general subject of power system control. Previous work1,2 has indicated the general requirements of the prime-mover speed governors and the desirability of supplementary control to insure proper load division, frequency, and time. The general requirements of supplementary controls are given in the companion paper3 by Crary and McClure. In most cases these controls are satisfactorily obtained as rather slow corrective adjustments to the speed-governor mechanisms, but for certain types of load a more active tie-line load controller, which will tend to suppress transient load swings also, may be required. An example of this is a rapidly varying load, such as a strip mill supplied from local generation as well as from a tie to a larger power system, in which it may be desirable to keep the load variations off the tie line as much as possible.

Overvoltages Caused by Unbalanced Short Circuits Effect of Amortisseur Windings

IN CASE of unbalanced faults on power systems, the voltage on the unfaulted phase or phases may often reach very high values. There may be an overvoltage caused by the short circuit itself and a further overvoltage caused by the clearing of the fault. In the present paper only the first type will be discussed. These unfaulted phase overvoltages may vary widely with the type of fault, the system constants and arrangement, and the kinds of synchronous machines affected. However, in faults not involving ground the presence of overvoltages depends on the fact that the synchronous machines supplying the fault current are not electrically symmetric-rotor machines. Thus, these overvoltages may be largely eliminated or reduced by a properly designed amortisseur winding. Even in case of overvoltages caused by faults involving ground there is a considerable reduction with such an amortisseur winding.

Synchronous Starting of Generator and Motor

A SYNCHRONOUS motor, generator, or condenser can be started from rest, by means of shaft torque, induction-motor (amortisseur winding) torque, or synchronizing torque. This paper presents data on the last method of starting. The system studied consists of a prime mover driving a synchronous generator, and a synchronous machine driven electrically by the generator. The whole system is started from rest by means of torque applied to the generator shaft, the motor being accelerated to normal speed by the synchronous torque developed. The performance of such a system was determined both by tests on several machines and by calculations with the aid of the differential analyzer at the University of Pennsylvania, and limiting conditions and criteria for successful starting were found in terms of the various pertinent system parameters. In a few cases a system consisting of a generator and two motors was studied.

Double-Line-to-Neutral Short Circuit of an Alternator

Starting with R. H. Parks formulas for the flux linkages of an ideal synchronous machine, the case of a fault from 2 line terminals of a generator to neutral is treated in a manner similar to that used by Doherty and Nickle for other unsymmetrical faults. Expressions are given for the armature currents in the faulted phases and for the main field current, at any time after the short circuit. An expression for the voltage across the open phase a short time after the fault is also developed.

A Method for Optimization of Nonlinear System Response

If the transient response of the error between the input and the output of a given nonlinear system is known to be asymptotically stable, and if it is desired that this response should follow some model response, the proposed method can be used to compute the optimum values of the adjustable parameters of this system. For using this method, the solution of the nonlinear differential equation governing the system need not be known. The method does not require the incorporation of a physical model for generation of the model response. In some cases, it is not required to know the nonlinearity in explicit analytical form but just the graphical form is enough. The method is applicable to time-invariant noiseless continuous systems subjected to deterministic inputs. Application of the method is illustrated by working out examples. Analog computer plots of the model and optimum responses are presented in every case.