By using some properties of driving-point functions and adopting an iterative circuit synthesis approach, the location, extent, and type of change introduced in a model winding could be identified, based on terminal measurements. In this study, a model winding was used. From knowledge of its measured shortcircuit and open-circuit natural frequencies, and pertinent winding data, an equivalent circuit was synthesized (called reference circuit). Next, changes were introduced at different locations in the model winding and its natural frequencies were measured. Corresponding to every new set of measured natural frequencies, a new circuit was synthesized (with topology remaining unchanged). A comparison of these circuits with the reference circuit revealed that a mapping could be established between changes introduced in the model winding and those predicted by the synthesized circuits. Many case studies are presented by considering continuous-disc and interleaved winding representations. Reasonably good results were obtained. Thus, localization of changes, based on terminal measurements, is shown to be a possibility. So, it is believed that these findings could be of some assistance in addressing the ultimate task of locating mechanical deformations in actual transformer windings.
The dynamics of an electrical network can completely be described from the knowledge of its poles and zeros. Computation of poles and zeros of the transfer function (TF) of a transformer winding, represented as a coupled ladder network, involves solution of a large-sized equivalent circuit. This paper presents a novel solution based on state space analysis approach. It is shown, how the linearly transformed state space formulation, together with algebraic manipulations, can become useful. In the proposed formulation, symbolic variables (i.e., Laplace variable,) are suitably manipulated, so as to render computations purely numerical. With this feature, there is practically no limit on the size of networks and topologies (including resistances to model losses) that can be represented. So, virtually any number of windings of a transformer can be considered, permitting a comprehensive analysis of winding behavior and its interactions, that was until now severely limited, by the simplifying assumptions imposed by existing methods.
For synchronization applications, synchronous reference frame (SRF) phase-locked loop (PLL) is widely deployed. Its performance is excellent when the input voltage consists of only fundamental positive sequence (FPS) component. If the grid voltage is unbalanced or polluted with harmonics and dc offset, its performance degrades. Many modifications were proposed to address this issue. However, the removal of dc offset and fundamental negative sequence (FNS) component without compromising the dynamic performance still remains a challenging task. To this end, this paper presents a rapid Type-1 SRF PLL scheme with preloop filtering stage for tracking the attributes of grid voltage FPS component. Fixed sampling period sliding discrete Fourier transform (SDFT) and instantaneous symmetrical components method are employed in the preloop stage. With this modification, the dc offset, harmonics and the FNS component are rejected and only the FPS component enters the PLL. As a result, transients vanish quickly. However, when the grid frequency drifts, SDFT causes amplitude and phase errors, and Type-1 PLL introduces a steady-state tracking error in phase. These errors are compensated with the help of an error correction criteria. Robustness and the improved transient response of the proposed scheme are demonstrated with an experimental study involving real-time controller board (dSPACE DS1104) and three-phase programmable power source.
A simple method is described for constructing physically realizable driving-point impedance function from measured frequency response data (i.e., magnitude and phase) on a model winding and a transformer. A unique feature of the proposed method is that it ensures the constructed rational function is always positive-real, thereby guaranteeing synthesis of a physically realizable network every time. This feature could not always be guaranteed by earlier methods. Hence, it was a limitation. The proposed method is demonstrated on a single-layer model winding and the measured terminal characteristics is converted to a lumped parameter ladder network, since this representation is naturally suited to establish a physical mapping between the actual winding and synthesized circuit. So, the need to guarantee physical realizability is evident. Proceeding further, the terminal characteristics of a 315-kVA, 11/6.9-kV transformer is measured and a rational function representation is obtained. However, its realization as a coupled ladder network requires some more work to be done. In summary, it is believed that this proposal is a step towards providing a solution for localization of deformation in actual transformer windings.
This study investigates the non-fragile sampled-data guaranteed cost control problem for a bio-economic singular Markovian jump system that is represented by the Takagi-Sugeno fuzzy model. The main intention of this study is to design a non-fragile sampled-data controller for the considered model to handle the issue of tax fluctuations by means of showing that the closed-loop system is regular, impulse free and stochastically finite-time bounded. Sampled-data controller is the one where the continuous system is controlled by the digital control algorithms. By introducing a proper Lyapunov-Krasovskii functional and using linear matrix inequality (LMI) approach, a new set of criteria is obtained in terms of LMIs for achieving the required result. More precisely, by solving LMIs, an upper bound for the cost function can be obtained. Finally, a simulation result is given to illustrate the effectiveness of the proposed control design.
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