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Concept# Three-phase electric power

Summary

Three-phase electric power (abbreviated 3φ) is a common type of alternating current (AC) used in electricity generation, transmission, and distribution. It is a type of polyphase system employing three wires (or four including an optional neutral return wire) and is the most common method used by electrical grids worldwide to transfer power.
Three-phase electrical power was developed in the 1880s by several people. In three-phase power, the voltage on each wire is 120 degrees phase shifted relative to each of the other wires. Because it is an AC system, it allows the voltages to be easily stepped-up using transformers to high voltage for transmission and back down for distribution, giving high efficiency.
A three-wire three-phase circuit is usually more economical than an equivalent two-wire single-phase circuit at the same line to ground voltage because it uses less conductor material to transmit a given amount of electrical power. Three-phase power is mainly used directly to powe

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Usually, each phase of the direct reluctance motor is fed separately by its own inverter producing a squarewave phase current depending on the rotor position. In the present work, a star-connection of the three stator phases is used and the direct reluctance motor is fed by a three-phase switched inverter. The space phasor theory shows that three-phase sinewave currents can produce a constant electromagnetic torque. In this case, the rotating reference frame rotates at half of the rotor speed and in the opposite direction. This command strategy allows to reduce the stator deformation due to the electromagnetic radial force which is very high in this type of motor and which is mainly responsible for the acoustic noise. The electromagnetic torque control is realised by a sliding mode control of the three phase currents. In the rotating reference frame, it is possible to show that the eight commutation states of the switched inverter are placed around an ellipse in the complex plane of the derivatives of the space phasor of the phase current. A study of this ellipse has allowed to determine the maximal torque as a function of the speed for a given continuous voltage. It is important to insure that the torque reference will never exceed this limitation in order to avoid a pullout phenomenon, highly unwanted in the speed control. Despite the fact that the resolver inside the casing of the direct reluctance motor produces a small periodic error, it is accurate enough for the position measurement and to produce the three current references. However, the derivative of the position measurement provides a speed evaluation with such a ripple that the speed control cannot be outstanding. So, for the speed measurement, an additional laser rotary encoder is used. The experimental study in the steady-state mode of the speed control shows the presence of an electromagnetic torque ripple. This is a residual ripple caused by the dissimilarity between the stator poles teeth-shapes and the magnetic saturation effect. Although this torque ripple is rather low compared with the usual command strategy, two methods are proposed in order to compensate it. The first method is based on the use of a correction factor depending on the tooth angle. First, in steady-state conditions, the correction factor is stored off-line in a table. Then it is used in-line as a feedforward disturbance compensation. The second method of reducing the residual torque ripple consists in implementing an observer of variable disturbance. This is a disturbance observer able to determine the frequency content of the torque ripple. For instance, in order to observe the continuous component, the fundamental wave as well as the harmonics 2, 3, and 6, the observer must have ten poles. The main difficulty to deal with such an observer is the fact that each pole moves quickly as a function of the motor speed. So, in order to guarantee the observer stability over a large range of speed, the poles are located dynamically regarding to the motor speed by the way of a discontinuous adaptation of the feedforward coefficients. The theoretical study and the numerical simulation have allowed to formulate some criteria about the way of locating the poles. Experimental results confirm the efficiency of the observer of variable disturbance in order to reduce the electromagnetic torque ripple.

In the last years, static power converters have become widely used in various applications. They can be found in domestic applications, railways, urban and ship transport, and even in several industrial systems. Some of these applications require a high or medium voltage power supply that is easily adjustable while providing good spectral performances. To overcome the maximum blocking voltage limits of the main power switches, multilevel techniques and other new power conversion topologies have been developed. They are series/parallel associations of existing power semiconductors, and allow generating an output voltage with many levels. The number of power semiconductors needed in these topologies increases as the number of levels increases. The power converter circuit becomes more complex and its reliability decreases. This thesis focuses on three-phase multilevel converters based on a series connection of single phase inverters (partial cells) in each phase. It's shown that, feeding partial cells with unequal DC-voltages (asymmetric feeding), increases the number of levels of the generated output voltage without any supplemental complexity to the existing topology. Voltage resolution is increased through interpolating the generated output voltage phasor (three phase voltage in α-β frame). This is achieved by seeking the non redundant switching states of the power switches. The resultant converter can generate a very high resolution voltage phasor up to the possible maximum resolution. This approach is generalized for any number of partial cells. Each partial cell is fed through a three-phase diode rectifier, fed itself through the windings of a multi-secondary low frequency power transformer. From analytical expressions in continuous and discontinuous current conix duction modes, it is shown that, from a supply network point of view, a symmetrical multilevel converter has a smaller total harmonic distortion than an asymmetrical multilevel converter with the same number of partial cells per phase. An asymmetrical multilevel converter is not more interesting than a classical three-phase converter, but its total harmonic distortion is compatible to the recommended IEEE std 519-1992. It is also shown that the advantages of an asymmetric multilevel converter from a load point of view (generation of a high resolution voltage phasor, possibility to choose the number of redundant switching states, reduction of the number of power semiconductors for the same voltage resolution, flexibility for the DC-voltage feeding choice) and the advantages of a symmetrical multilevel converter from a supply network point of view (smaller total harmonic distorsion) can be combined. Simulation results and the experimental test setup showed the reliability of the suggested approach.

Willem Lambrichts, Mario Paolone

In this paper, we present an exact (i.e. non-approximated) and linear measurement model for hybrid AC/DC micro-grids for recursive state estimation (SE). More specifically, an exact linear model of a voltage source converter (VSC) is proposed. It relies on the complex VSC modulation index to relate the quantities at the converters DC side to the phasors at the AC side. The VSC model is derived from a transformer-like representation and accounts for the VSC conduction and switching losses. In the case of three-phase unbalanced grids, the measurement model is extended using the symmetrical component decomposition where each sequence individually affects the DC quantities. Synchronized measurements are provided by phasor measurement units and DC measurement units in the DC system. To make the SE more resilient to vive step changes in the grid states, an adaptive Kalman Filter that uses an approximation of the prediction-error covariance estimation method is proposed. This approximation reduces the computational speed significantly with only a limited reduction in the SE performance. The hybrid SE is validated in an EMTP-RV time-domain simulation of the CIGRE AC benchmark micro-grid that is connected to a DC grid using 4 VSCs. Bad data detection and identification using the largest normalised residual is assessed with respect to such a system. Furthermore, the proposed method is compared with a non-linear weighted least squares SE in terms of accuracy and computational time.

2022