Lévy stable distribution and space-fractional Fokker–Planck type equation

The space-fractional Fokker–Planck type equation ∂p∂t+γ∂p∂x=-D(-Δ)α/2p(0<α⩽2) subject to the initial condition p(x,0)=δ(x) is solved in terms of Fox H functions. The solution as γ=0 expresses the Lévy stable distribution with the index α. From the properties of Fox H functions, the series representation and asymptotic behavior for the solution are also obtained. Lévy stable distribution as 0<α<2 describes anomalous superdiffusion and its diffusion velocity is characterized by xd∝(Dt)1/α

Conventional P-ω/Q-V Droop Control in Highly Resistive Line of Low-Voltage Converter-Based AC Microgrid

In low-voltage converter-based alternating current (AC) microgrids with resistive distribution lines, the P-V droop with Q-f boost (VPD/FQB) is the most common method for load sharing. However, it cannot achieve the active power sharing proportionally. To overcome this drawback, the conventional P-ω/Q-V droop control is adopted in the low-voltage AC microgrid. As a result, the active power sharing among the distributed generators (DGs) is easily obtained without communication. More importantly, this study clears up the previous misunderstanding that conventional P-ω/Q-V droop control is only applicable to microgrids with highly inductive lines, and lays a foundation for the application of conventional droop control under different line impedances. Moreover, in order to guarantee the accurate reactive power sharing, a guide for designing Q-V droop gains is given, and virtual resistance is adopted to shape the desired output impedance. Finally, the effects of power sharing and transient response are verified through simulations and experiments in converter-based AC Microgrid