The slide on Mathematical Modeling features two columns: the left explains wind power calculation via the formula \(P = 0.5 \rho A v^3 Cp\) and the DFIG dq model with stator/rotor voltage equations and flux linkages for control purposes. The right column details sub-synchronous resonance frequency computation as \(fr = \frac{1}{2\pi \sqrt{L{eq} C}}\) from an RLC circuit derivation, emphasizing its role in SSR analysis for DFIG wind systems.
Mathematical Modeling
| Wind Power and DFIG dq Model | Resonance Frequency Calculation |
|---|
| Wind power: $P = 0.5 \rho A v^3 Cp$, where $\rho$ is air density, $A$ rotor area, $v$ wind speed, $Cp$ power coefficient.
DFIG dq model: Stator voltage $v{ds} = Rs i{ds} + \frac{d\psi{ds}}{dt} - \omegas \psi{qs}$; rotor $v{dr} = Rr i{dr} + \frac{d\psi{dr}}{dt} + (\omegas - \omegar) \psi{qr}$. Flux linkages: $\psi{ds} = Ls i{ds} + Lm i{dr}$, etc. (Concise vector form for control.) | Sub-synchronous resonance frequency: $fr = \frac{1}{2\pi \sqrt{L{eq} C}}$, where $L{eq}$ is equivalent inductance (series/parallel of turbine, line, transformer), $C$ capacitance in series-compensated line.
Derivation from simplified RLC circuit: resonance at $\omega_r = 1/\sqrt{LC}$, converted to Hz. Critical for SSR analysis in DFIG systems. |
Source: Thesis: Damping of Sub-Synchronous Oscillation in DFIG-based Type 3 Wind System
Speaker Notes
Highlight key equations for wind power extraction, DFIG dynamics in dq-frame, and SSR resonance frequency. Emphasize derivations for control design.
