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Evolution and monotonicity for a class of quantities along the Ricci-Bourguignon flow
Farzad Daneshvar,Asadollah Razavi 대한수학회 2019 대한수학회지 Vol.56 No.6
In this paper we consider the monotonicity of the lowest constant $\lambda^{b}_{a}(g)$ under the Ricci-Bourguignon flow and the normalized Ricci-Bourguignon flow such that the equation \begin{equation*} -{\rm \Delta} u + au\log u + bRu= \lambda^{b}_{a}(g) u \end{equation*} with $\int_M u^2\, {\rm dV}=1,$ has positive solutions, where $a$ and $b$ are two real constants. We also construct various monotonic quantities under the Ricci-Bourguignon flow and the normalized Ricci-Bourguignon flow. Moreover, we prove that a compact steady breather which evolves under the Ricci-Bourguignon flow should be Ricci-flat.
EVOLUTION AND MONOTONICITY FOR A CLASS OF QUANTITIES ALONG THE RICCI-BOURGUIGNON FLOW
Daneshvar, Farzad,Razavi, Asadollah Korean Mathematical Society 2019 대한수학회지 Vol.56 No.6
In this paper we consider the monotonicity of the lowest constant ${\lambda}_a^b(g)$ under the Ricci-Bourguignon flow and the normalized Ricci-Bourguignon flow such that the equation $$-{\Delta}u+au\;{\log}\;u+bRu={\lambda}_a^b(g)u$$ with ${\int}_{M}u^2dV=1$, has positive solutions, where a and b are two real constants. We also construct various monotonic quantities under the Ricci-Bourguignon flow and the normalized Ricci-Bourguignon flow. Moreover, we prove that a compact steady breather which evolves under the Ricci-Bourguignon flow should be Ricci-flat.
Power Swing Detection Using rms Current Measurements
Behrooz Taheri,Farzad Razavi 대한전기학회 2018 Journal of Electrical Engineering & Technology Vol.13 No.5
During a power swing, distance relays may mistakenly spread fault throughout the power grid, causing a great deal of damage. In some cases, such mistakes can cause global outages. For this reason, it is critical to make a distinction between power swings and faults in distance relays. In this paper, a new method is proposed based on RMS measurement to differentiate between faults and power swings. The proposed method was tested on two standard grids, demonstrating its capability in detecting a power swing and simultaneous fault with power swing. This method required no specific configurations, and was independent of grid type and zoning type of distance relays. This feature in practice allows the relay to be installed on any grid with any kind of coordination. In protective relays, the calculations applied to the microprocessor is of great importance. Distance relays are constantly calculating the current RMS values for protection purposes. This mitigates the computations in the microprocessor to detect power swings. The proposed method was able to differentiate between a fault and a power swing. Furthermore, it managed to detect faults occurring simultaneously with power swings.
Power Swing Detection Using rms Current Measurements
Taheri, Behrooz,Razavi, Farzad The Korean Institute of Electrical Engineers 2018 Journal of Electrical Engineering & Technology Vol.13 No.5
During a power swing, distance relays may mistakenly spread fault throughout the power grid, causing a great deal of damage. In some cases, such mistakes can cause global outages. For this reason, it is critical to make a distinction between power swings and faults in distance relays. In this paper, a new method is proposed based on RMS measurement to differentiate between faults and power swings. The proposed method was tested on two standard grids, demonstrating its capability in detecting a power swing and simultaneous fault with power swing. This method required no specific configurations, and was independent of grid type and zoning type of distance relays. This feature in practice allows the relay to be installed on any grid with any kind of coordination. In protective relays, the calculations applied to the microprocessor is of great importance. Distance relays are constantly calculating the current RMS values for protection purposes. This mitigates the computations in the microprocessor to detect power swings. The proposed method was able to differentiate between a fault and a power swing. Furthermore, it managed to detect faults occurring simultaneously with power swings.
Power Swing Detection in Parallel Transmission Lines Connected to Wind Farms Employing del2sg Method
Abniki Hassan,Samsi Mostafa Hajati,Taheri Behrooz,Razavi Farzad 대한전기학회 2023 Journal of Electrical Engineering & Technology Vol.18 No.4
A power system is reliable when it could satisfy consumer demand with desirable continuity and specific voltage quality. However, because of the ever-rising energy demand, power systems are becoming more complex. Moreover, environmental problems have aroused interest in the application of wind turbines in power networks. These items have caused the requirement for better and more sophisticated protection methods to upgrade the system reliability to be highly felt. In addition to accurate and timely detection of faults and quick disconnection of the defective part, modern protection systems have to be able to avoid faults as soon as possible and to maintain the stability of the system as well. Therefore, a power swing detection technique based on del2SG and IEC-61850 communication protocol was proposed in this article. At first, the challenges that distance relays face due to simultaneous faults with power swing are investigated in power systems connected to wind turbines. Afterward, different types of power swings and their characteristics are explained. The last step also investigates the performance of the proposed method during a power swing and simultaneous faults in the power network connected to a wind turbine, and without wind turbines. The simulation results demonstrate that the proposed method has a precise operation to detect various types of power swings and simultaneous faults in both examined networks. The comparison results between the conventional power swing detection methods and the proposed approach in this article show the superiority of the proposed method.