Three-Phase Power Fundamentals Flashcards

A set of flashcards covering complex power (S = VI*), per-phase vs total three-phase relationships, delta vs Y voltage/current relationships, power angle and impedance angle, and practical steps for calculating P, Q, and S in single- and three-phase configurations.

What is complex power S in terms of voltage and current?

S = V I, where V is the (complex) phase voltage and I is the complex conjugate of the phase current. S also equals P + jQ, with P real power and Q reactive power.

How are per-phase and three-phase powers related in a balanced system?

For a balanced three-phase system: Ptotal = 3 Pphase, Qtotal = 3 Qphase, and Stotal = 3 Sphase.

How do you compute per-phase apparent power from per-phase voltage and impedance?

Per-phase apparent power magnitude is |Sphase| = |Vphase|^2 / |Z|, since Iphase = Vphase / Z and Sphase = Vphase I_phase*.

What is power factor and how can you tell if it's leading or lagging?

Power factor PF = cos(theta), where theta is the angle between voltage and current. If theta > 0 (Q > 0), the current lags the voltage (lagging PF); if theta < 0 (Q < 0), the current leads (leading PF).

How do line voltage and phase voltage relate for delta and Y connections?

Delta: Vphase = Vline (each delta element sees the line voltage). Y: Vphase = Vline / sqrt(3) (phase voltage is line-to-neutral).

For a single-phase load connected to a three-phase source, what is the relationship between line current and phase current?

Line current equals phase current: Iline = Iphase, because the current through the single load is the line current.

What is the phase voltage when a three-phase source with line voltage V_line is Y-connected and the load is connected to one phase?

Vphase = Vline / sqrt(3).

What is the power angle theta and how is it determined in per-phase analysis?

Theta is the difference between voltage angle and current angle (theta = thetav − thetai). In balanced three-phase with a single-phase equivalent, theta also equals the impedance angle theta_z.

What is theta_z, the impedance angle, and how does it relate to theta?

Thetaz is the angle of the total per-phase impedance Z. The power angle theta equals thetaz in these analyses.

How do you compute the per-phase current from phase voltage and per-phase impedance?

Iphase = Vphase / Z.

How do you compute complex power from voltage and current using the conjugate of current?

S = Vphase Iphase*, i.e., multiply the phase voltage by the complex conjugate of the phase current.

What happens to theta and power factor when converting between single-phase and three-phase representations?

Theta and power factor do not change with conversion; magnitudes can scale with sqrt(3) factors depending on connection, but the per-phase angles stay consistent.

In a delta-connected load, what is the phase voltage and what voltage is applied across each phase?

Phase voltage equals line voltage; each delta element sees V_line across it.

In a Y-connected source with line voltage V_line, what is the phase voltage and phase current when the load is connected to one phase?

Phase voltage is Vline / sqrt(3); phase current is determined by Iphase = V_phase / Z.

What unit conventions are used for apparent power, real power, and reactive power, and what are their symbols?

Apparent power is in kVA (or VA), real power in kW (or W), reactive power in kVAR (or VAR).