# Fig nbsp xA Power coefficient calculated

Fig. 9. Power coefficient calculated directly.Figure optionsDownload full-size imageDownload as PowerPoint slide

Considering the wind rotor moment of inertia, it is more reasonable to analyze the power coefficient using the ratio of the total power output for a period of timeΔt to the total kinetic BIIE 0246 of air passing through the wind rotor in this period. Then, Equation (24) can be rewritten asequation(25)CP=(∫0t2Pgendt−∫0t1Pgendt+12Jrtωrt2 t=t2−12Jrtωrt2 t=t1)/(∫0t212ρπR2v13dt−∫0t112ρπR2v13dt)where t2 > t1, t2 − t1 = Δt, Jrt is wind rotor moment of inertia.

In Equation (25), the difference value of (∫0t2Pgendt−∫0t1Pgendt) denotes the total generator power output in the time interval Δt(=t2 − t1), the difference value of (1/2Jrtωrt2 t=t2−1/2Jrtωrt2 t=t1) denotes the change of the mechanical energy stored on the wind rotor in the time interval Δt. So the numerator in Equation (25) denotes the total energy captured by wind turbines from wind in the time interval Δt. The denominator denotes the total kinetic energy of air passing through the wind rotor in the time interval Δt.