University:
Kentucky State University
Course:
PHY 212 | General Physics II
Academic year:

2019
Views:

436

Pages:

11
Author:

Tyshawn Shaffer

Chapter #12: Polyphase Circuits: **Revision: Double Subscript Notation:** For voltages: * Instead of using +ve notations, we describe voltage difference by: * Vab: terminal (a) is at higher potential than terminal (b). Vab = -Vba * a | | | c | | | b Vab = Vac + Vcb * a | | | n | | | b Vab = Van + Vnb = Van - Vbn Vac = Van + Vnc = Van - Vcn Vbc = Vbn + Vcn = Vbn - Vcn For currents: * a | | | b Iab = -Iba * Iab; does it mean I1 or I2? * We always follow the shortest/the most direct path. (I1) * Icd; one to take? * Here we have to say Icd1 or Icd2. Icd = Icd1 + Icd2 **Poly-phase Systems** * a | | | b Two terminals! Vab ≠ 0 * a | | | n | | | b Three terminals! Vab = 0 **Single-phase:** * A | | | B * A, B - live terminals * N - neutral terminal * A | | | C * C - live terminal When: * α ≠ β ≠ γ: 3-phase, 4-terminals system * α = β ≠ γ: 2-phase * α = β = γ: 1-phase * |I_AN| = 135/2 K = 24.69 Arms * θ = -cos^(-1) (P.F) = -16.26° * I_AN = 24.69 ∠-16.26° Arms. * |I_AN| = 7/3 K = 20.334 Arms * θ = -cos^(-1) (0.85) = -31.788° * I_AN = 20.334 ∠-31.788° * Plug in A: 55.8 - j17.6 = 58.5 ∠-17.628° * Plug in (1): 22.6/3 = 0.9535 lagging. * P = (|I_AN|² * 3) + 0.1 = 1027.317 Watt. * V_AN = V_1 + V_2 = 135 ∠0° * = 140.59 ∠-0.718° * P.F. = 1027.317 / (140.59 * 58.5) = 0.9573 lagging. If Van is the reference, then: 1. Vbn = Vp ∠120° = Vp ∠120° (+ve / abc) sequence 2. Vcn = Vp ∠-120° = Vp ∠-120° (-ve / cba) sequence [Image of a three-phase system with phase voltages Van, Vbn, and Vcn] Vab = Van - Vbn Vbc = Vbn - Vcn Vca = Vcn - Van Vab = Vp - Vp(cos(-120) - jsin(-120)) Vab = Vp(1 + 1/2 + j√3/2) = √3Vp ∠30° V_L = √3 V_p * V_L: Line voltage * V_p: Phase voltage Line Voltage leads phase voltages by 30° (in +ve sequence) (abc) * Vab = √3 Vp ∠30° = √3 ∠30° Van * Vbc = √3 Vp ∠-90° = √3 ∠-90° Vbn * Vca = √3 Vp ∠-210° = √3 ∠-210° Vcn (cba) * Vab = √3 Vp ∠-30° = √3 ∠-30° Van * Vbc = √3 Vp ∠90° = √3 ∠90° Vbn * Vca = √3 Vp ∠210° = √3 ∠210° Vcn Default (if it is not mentioned) → +ve sequence.