Space Phasor Research Articles

Power Systems Monitoring and Control by Space Phasors

A complex space phasor is continuously formed by any three given time dependent real quantities, whose sum at any point in time is zero. Therefore, a space phasor represents unambiguously the heteropolar dynamic state of a three-phase quantity, e.g. for power systems monitoring and control.After a short introduction, various new developed measuring devices utilizing space phasors are described. In monitoring the three-phase voltage state in a network node or amperage state in a network branch, the undesired asymmetries and harmonics may be suppressed by special modal algorithms. Their fast versions of direct type need not more than 4 samples within 8 milliseconds, their more precise versions of Fourier-or Kalman-type require at least one period of 50 or 60 Hz. In a similar way the instantaneous heteropolar active and reactive power in a branch can be determined. In case of jeopardized stability the three-phase instantaneous frequency of a power system is of interest, whereby electromagnetical disturbances must be eliminated. For this purpose a three-phase dynamic frequency-meter has been developed, including an observer based filter for the separation of the slow aperiodic frequency components from the faster swinging components. Furthermore, the direction of harmonic currents caused by power converters or other harmonic generators can be best detected by filtering the space phasor. Finally an elastic firing control of power converters based on measured space phasor voltages is investigated and proposed for improving the stability of three-phase power systems energized by high voltage direct current transmission.With the new methods of digital signal processing the three-phase monitoring and control technic becomes a space phasor technic.

Space-phasor model of a three-phase induction motor with a view to digital simulation

A general mathematical model of a three-phase symmetrical induction motor is presented with space phasors of current, voltage and flux linkages defined according to the corresponding phase quantities. The model is compact and facilitates conversion from one coordinate system to another; it is applicable to investigation of transient phenomena involved in symmetrical or asymmetrical supply by voltage inverters, and permits definition of a torque angle. A most general model is introduced covering the whole family of space-phasor models. By means of several such models digital simulations have been carried out and results are reported.

NON-TRANSFORMATIONAL MATRIX ANALYSIS OF ELECTRICAL MACHINERY

ABSTRACT The general theory of electrical machines based on space phasor representation of space waves is explained. Harmonics of both the winding distribution and air-gap irregularities are taken into account for any winding asymmetry. Complex winding factors, symmetrical components of instantaneous values, and the winding inductances referring to the air-gap field are obtained during derivation of equation without the use of transformations. All quantities involved are physically defined. The method represents a common basis for analysis and design.

Time-dependent vector functions in electromechanical energy conversion and related low frequency phenomena Part I. Fundamentals

The paper is based on the mathematical concept of a vector as an element of a linear space whose most common geometric representation is a straight line with specific length and direction. Inherent in this definition is the fact that the concept of a vector is more general than just a straight line with specified length and direction. The term vector is used in this general context in this presentation and goes beyond such particular cases as conventional space vectors ( $$\bar B, \bar D$$ , etc.) and phasors (single frequencyLaplace-transform solutions). Time dependent vectors describing certain integral properties of electromagnetic devices have been used for a long time. Despite their attractivness their usage was rather limited and in a sense isolated. The most widely used field is tensor analysis where the functions relating the vectors have to be, by definition, linear. Some other approaches assume sinusoidally distributed windings, current sheets, radial $$\bar H$$ fields, etc.; all of these drastically idealize the physical picture. No successful attempt has been made in the past to relate directly the terminal properties of devices to the behaviour of the electromagnetic field itself and to relate them toMaxwell's equations without imposing any restriction on the system. The present paper proves that there is a simple mathematical discipline which handles simultaneously and directly the phenomena of the entire electromagnetic field and the terminal performance of electromagnetic devices. This mathematical technique is vectorarithmetic and vector-analysis. The foundation of this treatment uses onlyMaxwell's first two equations and energy relations; thus, unrestricted in any way, it can handle all problems involving the macroscopic electromagnetic field. With this approach some of the old concepts can be revaluated. It turns out, for example that circuits such as equivalent circuits widely used in electric machinery (which describe in the time domain the single-frequency steady state behaviour of one phase) become circuits describing entire machines under far more general operational conditions; as a result parametric amplification techniques, etc., may be directly applied to electric machines and other devices. It is shown in the paper that tensor analysis is more general than usually claimed. The importance of eigenvector transformations is also emphasized. Examples accompanying this introduction to the vector approach are well known problems this is done to demonstrate that most classical problems can be solved directly and with very little effort by using vector functions. Some topics beyond the terms of references set by the title are also discussed and indication is given that network theory, system theory, high frequency devices, etc. all have the same common basis and as such are special cases within this general vector method.