No abstract

This study deals with the comprehensive modelling, analysis, and control of a DC microgrid (MG) in islanded mode. The proposed DC MG comprises a wind turbine, a photovoltaic (PV) source, battery storage, DC/DC source, and load side converters with DC loads. To this aim, a circuit‐oriented modelling of the whole system is developed. The PV source is modelled with a single‐diode electrical circuit. Afterward, a mathematical model of the system with state‐space representation was derived. A detailed analysis of PV system design is performed because the parameters of PV are appearing in the dynamic model of DC MG. For the purpose of controller development, the dynamic model of the DC MG, which is modelled by a non‐linear‐non‐affine eight‐order system, is linearized around an equilibrium point using the Jacobian matrix framework, while stability using eigenvalue is carried out showing that the stability is guaranteed under operating condition. Finally, for the first time, the state‐dependent Riccati equation (SDRE) technique is proposed to find the optimal regulation problem for the DC MG with non‐linear‐non‐affine dynamics. The numerical simulation studies first confirm the validity of the performed mathematical, then the effectiveness of the proposed non‐linear controller is evaluated under illumination and load change.

The discrete Fourier transform (DFT) is a powerful phasor estimation algorithm conventionally used in digital relaying applications. The DFT-based phasor estimation is usually accompanied by oscillatory error due to the presence of the decaying DC (DDC) components in fault current signals. Accordingly, two modified DFT-based phasor estimation algorithms are proposed in this paper. The proposed algorithms accurately estimate the exact fundamental phasor by extracting the DDC components using successive outputs of the conventional DFT algorithm. The performance of the proposed algorithms is validated by the mathematically generated and PSCAD-simulated signals and is compared with previous algorithms. The results demonstrate that the proposed algorithms in this paper are more robust than other ones. Moreover, they are applicable in the DFT algorithm with different data windows. INTRODUCTIONThe fundamental phasor estimation plays an important role in detecting, locating, and discriminating faults in power systems. There are a number of conventional phasor estimation algorithms, that include: discrete Fourier transform (DFT), least-square error (LSE), discrete wavelet transform (DWT), Kalman filters, discrete Hartley transform (DHT), and artificial neural networks (ANNs) [1][2][3][4]. The discrete Fourier transform (DFT) is a powerful phasor estimation algorithm, widely used in digital relaying applications due to its simplicity, accuracy, and speed. The DFT algorithm has a high capability to estimate the fundamental phasor of periodic sinusoidal signals. However, its performance is extremely influenced by non-periodic signals such as decaying DC components (DDCs), which are created in the current and voltage signals during fault conditions. This issue causes an undesired oscillating error in the estimated phasor, especially phase angle. Although this error decays after a certain period of time (depending on the time constant of the DDC component), it extremely reduces the speed and accuracy of decision-making in relays. The DDC component has two parameters, the initial value and time constant, which depend on fault inception angle and the value of pathway X ∕R ratio, respectively. Because the source impedance and line X ∕R ratio are so close to each other, the initial value ofThis is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

No abstract

No abstract