This paper proposes a new reference frame, namely Reduced Reference Frame (RRF), specially suited for unbalanced three-phase four-wire systems which improves the performance of the classical Fortescue, Clarke and Park transformations. The RRF transfomation allows to represent any unbalanced three-phase sinusoidal magnitude with just two components even if the zero-sequence component is present. For doing so, the RRF transformation takes into account that the abc space-vector trajectory of the transformed three-phase sinusoidal magnitude is always within a plane. The geometric properties of this trajectory are considered for outlining a general classification of the transformation depending on the input voltages and an adequate reference frame within the plane. Then, a step-by-step procedure for computing the transformation matrix is detailed. Once the voltages and currents are transformed into the RRF, it is proposed a power theory which allows to compute the instantaneous active and reactive powers. The paper includes two simulations and an experimental validation through a real-time application to highlight the benefits of the proposal. The paper closes with the main conclusions and some future research lines where this transformation can be applied.INDEX TERMS coordinate transformation, reference frame, three-phase four-wire systems, unbalanced power systems.
The increased penetration of Distributed Renewable Energy Sources (DRES) has posed several challenges into the electric power systems, the most important of which is the instability caused by the intermittent and stochastic nature of the primary sources (wind, sun). Since the System Operators have started to specify limits for the restriction of the Ramp-Rate (RR) at the Point of Common Coupling (PCC) of the DRES with the grid, several algorithms have been proposed to mitigate the power fluctuations using energy storage systems (ESS). Some drawbacks are: high computational effort in the calculation of RR, increased ESS size/decreased ESS operational life, etc. In this paper a new RR Limitation (RRL) algorithm is proposed to address gaps in the current state-of-the-art. This algorithm is based on the two-point calculation of RR and is performed considering the connection of a Supercapacitor (SC) at the DC-link of a DRES converter. The relationship between the SC voltage and the degree to which the RRL is achieved is established, which is something missing from the current state of the art and is essential if the RRL is to be treated as a new tradeable AS. The RR control is validated in a real experimental testbed. Finally, this control is modelled in Simulink in order to perform investigations on the influence that several parameters have on the achieved RRL at the DRES PCC. This is important, since the evaluation of the RRL impact at DRES level will allow for further investigations to evaluate the RRL impact at distribution system level and defer costs related to the installation of large-scale ESS.
Three-phase four-wire systems require a reference frame similar to that used in 3-phase 3-wire system configurations that allow them to be easily analysed, modelled and controlled. A new reference frame called Reduced Reference Frame (RRF) was presented by the authors in a previous work to satisfy these objectives. This is based on the locus of the voltage space vector which is used to perform a transformation applied to 3-phase 4-wire systems. This paper uses the proposed RRF to demonstrate the benefits of this transformation under different conditions of load or voltage imbalance. To this end, the different types of imbalances considered are studied by comparing the results in the classical αβγ axes, the so-called mno-transform specifically developed for 3-phase 4-wire systems and the RRF coordinates. In addition, a theoretical identification of some types of imbalances is done comparing the simulation results and the fundamentals of the RRF.INDEX TERMS Coordinate transformation, reference frame, three-phase four-wire system, unbalanced power system.
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