PE Electrical Electronics cheat sheet

Electrical and Computer: Electrical and Electronics

• Per-unit conversion: Z_pu = Z_actual / Z_base, with Z_base = V_base² / S_base (three-phase: V_base is line-to-line, S_base is three-phase). Per-unit impedance is identical on either side of an ideal transformer.

• Symmetrical components: I0 = (Ia + Ib + Ic)/3, I1 = (Ia + a·Ib + a²·Ic)/3, I2 = (Ia + a²·Ib + a·Ic)/3 with a = 1∠120°. Positive-sequence voltages are 120° apart; negative-sequence phase order is reversed; zero-sequence components are all in phase.

• Sequence networks: generator zero-sequence impedance is typically small (grounded wye) or infinite (ungrounded/delta); delta and ungrounded-wye transformer windings block zero sequence. Line-to-ground fault current = 3·I0 = 3·Vf / (Z1 + Z2 + Z0).

• Three-phase power: S = √3·V_LL·I_L for balanced loads; P = √3·V·I·cos θ, Q = √3·V·I·sin θ. Delta line current = √3 × phase current; wye line voltage = √3 × phase voltage.

• Transformer parameters from open-circuit and short-circuit tests: OC test (rated voltage, one side open) gives core loss, magnetizing branch, and turns ratio; SC test (rated current, low voltage) gives copper loss and series leakage impedance referred to the tested side.

• Induction motor: synchronous speed n_s = 120·f / P (rpm); slip s = (n_s − n_r)/n_s; rotor frequency = s·f. Torque is proportional to air-gap power divided by synchronous speed; breakdown torque occurs near s = R2/X2.

• DC machine: E_a = K·Φ·ω (or E_a = (P·Φ·n·Z)/(60·a)); developed torque T = K·Φ·I_a. Separately excited motor speed falls with load because armature resistance drop reduces E_a = V − I_a·R_a.

• Transmission line: characteristic impedance Z0 = √(L/C), propagation velocity v = 1/√(LC); a quarter-wave line transforms a short to an open. Reflection coefficient Γ = (Z_L − Z0)/(Z_L + Z0); VSWR = (1+|Γ|)/(1−|Γ|).

• Protection and grounding: inverse-time overcurrent coordination requires time-margin between upstream and downstream curves; a grounded system limits transient overvoltages and provides a low-impedance zero-sequence path. CT ratio error and saturation can cause relay misoperation during faults.