Daniel K. Reitan

Calculation of the Electrical Capacitance of a Cube

The basic theory of calculation of the capacitance of a given geometrical configuration by the use of subareas is advanced and applied to solve the long‐standing problem of the accurate evaluation of the capacitance C of a cube of side a. The best previously published determination is 0.62211a<C<0.71055a. The value obtained of C≈0.655a esu is both a lower limit and very close to the exact value.

Improvement of Power System Transient Stability Using Optimal Control: Bang-Bang Control of Reactance

The problem of restoring a power system to its initial steady state in minimum time after a transient disturbance is identified as a minimum time problem in optimal control theory. The optimal control obtained to achieve this objective, by use of Pontryagins maximum principle, is bang-bang control of line reactance. The implementation of this scheme on a simple power system model is shown, along with numerical results.

Accurate Determination of the Capacitance of Rectangular Parallel‐Plate Capacitors

The basic theory of calculation of the capacitance of a parallel‐plate capacitor by the method of subareas is advanced. This method enables accurate approximation of the long‐standing problem of the accurate evaluation of the capacitance of a rectangular parallel‐plate capacitor. A universal curve enabling rapid determination of the capacitance of the commonly used square‐plate capacitor of side a is given.

Modification of the bus impedance matrix for system changes involving mutual couplings

A direct method is presented for modification of the bus impedance matrix using a well-known building algorithm. The simplicity and generality of the method are demonstrated in two numerical examples.

Calculation of the Capacitance of a Circular Annulus by the Method of Subareas

1. The basic theory of approximate calculation by the use of subareas of the capacitance of a plane area and of the distribution of charge density over it is outlined. 2. The method of subareas is employed to obtain an accurate value for the capacitance of an annulus of ratio of outer to inner radius of ro/ri=1.5. 3. The fourth approximation to the capacitance of a specified circular disk, as calculated by the method of subareas, is found to be in good agreement with the known exact value. As a circular disk is an annulus of ratio of radii ro/ri=∞, it is to be concluded that the fourth approximation for the much narrower annulus of ratio 1.5 is very nearly the exact value. This conjecture is substantiated by the curve of Figure 3. 4. Comparison in Figure 6 of the charge distribution on a circular disk as determined both from the known equation and by the method of subareas indicates that calculation of charge distribution by use of subareas affords a good approximation to the actual distribution. Accordingly, the charge distribution of Figure 7 for the much narrower annulus is to be considered as a close approximation to the actual distribution. 5. The universal curve of Figure 8 yields the capacitance of an annulus of any stated ratio of external to internal radii.

Pontryagin's maximum principle aids transient stability: Bang-bang control of reactance

Application of Pontryagins maximum principle to the problem of restoring a power system to its steady-state operating point in minimum time after a transient disturbance is discussed. A new mode of control is presented.

Optimal control of transients in a power system

This letter investigates optimal control of transients in a nonlinear power system by means of the new approach of bang-bang control of reactance. The generality and utility of this control process are discussed and computational results are presented for a specific case.

A Method of Improving Transient Stability by Bang-Bang Control of Tie-Line Reactance

This paper presents a new approach to the problem of improvement of transient stability of a power system by means of optimal control of transients and is in continuation of the work reported in a previous paper.1 Essentially the system state is transferred from that at the beginning of the transient to a post-transient steady state in a nonoscillatory manner by means of a bang-bang control, thereby contributing significantly to the improvement of transient stability. A power system model with two interconnecting tie-lines is considered. It is shown that the control process may be implemented with two intermittent duty series capacitors or a capacitor and a reactor. Results of the synthesis of the optimal controllers and evaluation of realistic indices of performance are presented along with practical considerations.

Parallel Operation of AC and DC Power Transmission

A preliminary account has already been given of the EHV composite ac-dc study initiated last year at the University of Wisconsin [1]. This paper presents additional results obtained in the study of parallel EHV ac-dc power transmission in a basic 2-machine equivalent system. The consequences of 3-phase faults on inverter commutation are evaluated, and circumstances leading to inverter commutation failure (shoot-through) are made clear for various conditions of initial loadings and faulting. The consequences of inverter shoot-through onsystem stability are also evaluated for the 2-machine case. The characteristics of the control arrangement for a dc line are expected to be of special significance in determining the final overall performance of composite ac-dc systems.

A new method using the bus-impedance matrix model for short-circuit calculations

The bus-impedance matrix is a familiar tool in short-circuit calculations in power networks. This letter offers a new method of employing this Zbusmatrix and shows a numerical sample case. The method has tutorial significance and is applicable to the usual types of short circuits including simultaneous faults.