Question

You are provided two bases: Vᴸᴺ​Bₐₛₑ​=100kV, IBₐₛₑ ​=1A, Calculate the three-phase power and Y-connected impedance bases: S³ϕBₐₛₑ ​ZγBₐₛₑ. Also calculate the actual power consumed by a component when Sₚᵤ​=Vₚᵤ​​(ₚᵤ​∗​)=∣0.75ₚᵤ​∣ej20∘(∣0.975ₚᵤ​∣ej5∘)∗ in VA.

Answer 1

The three-phase power base is 173205 VA and the Y-connected impedance base is 100000 Ω. The actual power consumed by the component is 0.75 VA.

Step-by-step explanation:

To calculate the three-phase power base (S³Bₑₙ), we need to use the formula S³Bₑₙ = √3 * VṓBₐ * IṓBₐ, where VṓBₐ is the voltage base and IṓBₐ is the current base. Plugging in the given values, we have S³Bₑₙ = √3 * 100kV * 1A = √3 * 100000V * 1A = √3 * 100000 VA = 173205 VA.

To calculate the Y-connected impedance base (ZγBₑₙ), we use the formula ZγBₑₙ = VṓBₐ / IṓBₐ. Plugging in the given values, we have ZγBₑₙ = 100kV / 1A = 100000 Ω.

To calculate the actual power consumed by the component, we need to multiply the apparent power (Sṓₚₔ) by the power factor (cos = 0.75θ). Plugging in the given values, we have Sṓₚₔ = |0.75θ| = 0.75 VA, where |0.75θ| represents the magnitude. Therefore, the actual power consumed by the component is 0.75 VA.