System Unbalance Research Articles

Analysis of unbalanced polyphase networks by the method of phase co-ordinates. Part 1: System representation in phase frame of reference

The analysis of unbalanced-power-system problems depends usually on transformation methods by which the primary or phase quantities are substituted by, for example, symmetrical-component quantities. These transformations have had computational advantages in the past, but with the use of the digital computer, they no longer appear to be necessary. Investigations into system-unbalance problems and their solution using only the actual system phase voltages, currents and impedances show that a major difficulty concerns the representation of transformers. In this paper the principles of transformer models in phase co-ordinates are derived and applied to the development of the phase equivalent circuits of a number of balanced and unbalanced polyphase multiwinding transformers. The basic element of these equivalent circuits is shown to be a symmetrical lattice network that is bilinear in all cases except for quadrature boosting transformers. With these equivalent circuits and with the phase representations of the transmission lines, generators and other system components it is then possible to solve unbalanced polyphase network problems entirely in phase co-ordinates, retaining symmetrical components only as measures of system unbalance.

Circulating Currents in Paralleled Untransposed Multicircuit Lines: I - Numerical Evaluations

The current unbalance in a 50O-kV double-circuit and a 138-kV triple-circuit, paralleled and untransposed transmission line is analyzed comprehensively. This paper establishes that the magnitudes of individual circuit current unbalances due to currents circulating between the paralleled circuits are more significant than the net through system unbalance. Since the former were not considered in previous investigations, the criteria established there for proper phase configurations is shown in this paper to lead to maximum circulating current unbalance. The influence of series capacitor line compensation is also shown and the ramifications of these unbalances are discussed and evaluated on a present worth of annual loss basis.

Circulating Currents in Paralleled Untransposed Multicircuit Lines: II - Methods for Estimating Current Unbalance

The current unbalance in a 500-kV double-circuit and a 138-kV triple-circuit, paralleled and untransposed transmission line is analyzed comprehensively. This paper establishes that the magnitudes of individual circuit current unbalances resulting from currents circulating between the paralleled circuits are more significant than the net through system unbalance. Since the former were not considered in previous investigations, the criteria established there for proper phase configurations is shown in this paper to lead to maximum circulatimg current unbalance. The influence of series capacitor-line compensation is also shown and the ramifications of these unbalances are discussed and evaluated on a present worth of annual loss basis.

Analysis and synthesis of feedback control systems for the automatic balancing of rotating shaft systems

Automatic balancing is considered as a true feedback control problem, rather than as an automated sequence of separate operations. An adjustable correction mass must be positioned relative to a rectangular coordinate system rotating with the shaft such as to counterbalance the inherent system unbalance. This approach widens the scope of automatic balancing to include systems of which the unbalance conditions may change with time, for example, the rotor of a pump handling a fluid with some abrasive material. Transfer functions with complex coefficients provide a natural basis for the analysis of this type of system, and should be useful also for the study of rotating fields in general. The root-locus technique is applied for system synthesis, using these “complex transfer functions”. The control system is multivariable because the rotating system consists of a light flexible shaft, with more than one mass with unbalance fixed along its length. Neither the system inputs (the inherent unbalances) nor the errors (the resulting unbalances) are accessible for direct measurement, and the control tends to be quite sensitive to errors in the mathematical model. Diagonalization in terms of the orthogonal modes is proposed as a basis for synthesis in order to overcome these restrictions, and to obtain relatively simple subsystems.

Continuous Automatic Balancing of Rotating Systems

An automatic balancing system with continuous operation is proposed, based on the use of correction masses which are continuously adjustable relative to the rotating system. A feedback control system positions these masses so as to counterbalance the inherent system unbalance. This application of feedback control principles reduces the dependence upon accuracy of calibration. A major advantage is that systems with time-varying unbalance conditions, due to wear or foreign material, can be rebalanced without interrupting operation. The application to single-mass and multiple-mass systems will be discussed, including the special considerations necessitated by operation near critical speeds.

A Variable-Radio-Frequency-Follower System

This paper deals with a new follow-up or servo system for amplification of mechanical forces and remote positioning. The system described makes use of variable radio frequencies representative of the respective positions of system leader and follower. Two parallel-resonant circuits are provided, one of which is the frequency-determining circuit of an oscillator, while the other is the balance-frequency-determining circuit of a balanced-frequency discriminator. One of the circuits can be tuned by the leader, while the other is tuned by the follower; or, one of the circuits can be tuned by both leader and follower. System balance is reached when both circuits are tuned to the same frequency. Of the possible variety of system modifications, four significant types are described with their particular applications. The system provides for low-frequency keying of the radio-frequency signal before application to the frequency discriminator, in order to obtain a low-frequency-discriminator output signal of one phase or opposite phase, depending upon the direction of system unbalance. For system balance no discriminator output signal is produced. The low-frequency signal is used to control a two-phase induction motor driving the follower. System design considerations and performance data are given. Wide-band frequency-discriminator tuning is discussed with respect to constant system sensitivity. Experimental and production models are described.