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Maximum power factor of three phase receiver
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[QUOTE="gruba, post: 5475905, member: 540949"] [B]EDITED:[/B] Last line: [tex]\underline{Z_3}=\underline{Z_2}+jX_L=\underline{Z_2}+j20=\frac{300+j160(3−2⋅10^4C+25⋅10^6C^2)}{2⋅10^8C^2−6⋅10^4C+9}\Omega=\frac{20(15+j8(3−2⋅10^4C+25⋅10^6C^2))}{2⋅10^8C^2−6⋅10^4C+9}\Omega[/tex] Power factor can be expressed by [itex]\cos\phi=\frac{\mathfrak{R}(\underline{S})}{\sqrt{P^2+Q^2}}[/itex] where [itex]\underline{S}[/itex] is complex apparent power, [itex]P[/itex] is active and [itex]Q[/itex] is reactive power. Power factor has a maximum value when reactive power tends to zero. Since we know only the impedance, we can look at the imaginary part of impedance [itex]Z_3[/itex]. If we introduce a function [tex]f(C)=\frac{160(25\cdot 10^6C^2-2\cdot 10^4C+3)}{2⋅10^8C^2−6⋅10^4C+9}[/tex], minimum value of [itex]f(C)[/itex] is [itex]\frac{-40}{3}[/itex] at [itex]C=3\cdot 10^{-4}F.[/itex] So, maximum power factor is for [itex]C=0.0003F[/itex]. [B]Question[/B]: Is this correct? [/QUOTE]
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Maximum power factor of three phase receiver
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