Power System Analysis and Transmission Line Performance Flashcards

Vocabulary flashcards covering key definitions, formulas, ABCD parameters, and performance criteria for the Per Unit System and Transmission Line analysis.

Per Unit System

A system of calculation where any electrical quantity is expressed as the ratio of its actual value to a chosen reference value (base value) of the same quantity: $\text{Per Unit Value} = \frac{\text{Actual Value}}{\text{Base Value}}$.

Base Quantities

A set of four related electrical parameters—Base Power ($S_b$), Base Voltage ($V_b$), Base Current ($I_b$), and Base Impedance ($Z_b$)—used to normalize power system equations. Only two ($S_b$ and $V_b$) are chosen independently.

Base Impedance (Single-Phase)

The derived base impedance in a single-phase system, calculated using chosen independent bases $S_b$ and $V_b$ as $Z_b = \frac{V_b}{I_b} = \frac{V_b^2}{S_b}$.

Base Impedance (Three-Phase)

The derived base impedance in a balanced three-phase system, calculated using line-to-line base voltage ($V_{b(L-L)}$) and three-phase base apparent power (S_{b(3\text{\phi})}) as Z_b = \frac{V_{b(L-L)}^2}{S_{b(3\text{\phi})}}.

Base Conversion Formula

The formula used to convert a per-unit impedance from an old base system to a new base system: $Z_{p.u.(new)} = Z_{p.u.(old)} \times \left(\frac{V_{b(old)}}{V_{b(new)}}\right)^2 \times \frac{S_{b(new)}}{S_{b(old)}}$.

Per Unit Transformer Impedance

The per-unit leakage impedance of a transformer, which remains identical whether calculated from the primary side or the secondary side, provided base voltages on both sides match the voltage transformation ratio.

Short Transmission Line

A transmission line with a length up to $80\,km$, operating typically at voltages less than $20\,kV$, where line capacitance is neglected and resistance and inductance are modeled as lumped parameters.

Medium Transmission Line

A transmission line with a length between $80\,km$ and $160\,km$, where line capacitance is included as a lumped parameter (using Nominal T or Nominal $\pi$ models).

Long Transmission Line

A transmission line with a length above $160\,km$, where parameters (resistance, inductance, capacitance, conductance) are uniformly distributed along its entire length and analyzed using hyperbolic functions.

Transmission Efficiency

The ratio of active power received at the load (output power) to active power supplied at the sending end (input power): $\eta = \frac{P_{out}}{P_{in}} \times 100\% = \frac{P_{out}}{P_{out} + \text{Losses}} \times 100\%$.

Voltage Regulation

The change in receiving-end voltage magnitude when full load at a specified power factor is reduced to no load, keeping sending-end voltage and frequency constant: $\%VR = \frac{|V_{r(N.L.)}| - |V_{r(F.L.)}|}{|V_{r(F.L.)}|} \times 100\%$.

ABCD Parameters

Generalized generalized two-port network constants defining sending-end variables in terms of receiving-end variables: $V_s = A V_r + B I_r$ and $I_s = C V_r + D I_r$.

Symmetrical Two-Port Network Condition

The condition where a transmission line network looks identical from either terminal end, satisfied when $\mathbf{A = D}$.

Reciprocal Two-Port Network Condition

The condition satisfied by linear passive bilateral transmission lines, defined by the determinant equation $\mathbf{AD - BC = 1}$.

Short Transmission Line ABCD Parameters

The ABCD matrix parameters for a short transmission line: $A = 1$, $B = Z$ (total series impedance), $C = 0$, and $D = 1$.

Characteristic Impedance ($Z_c$)

The intrinsic impedance of a transmission line calculated as $Z_c = \sqrt{\frac{Z}{Y}} = \sqrt{Z_{oc} \times Z_{sc}}$, where $Z$ is per-unit-length series impedance and $Y$ is per-unit-length shunt admittance.

Condition for Maximum Voltage Regulation

The receiving-end lagging power factor angle condition under which voltage regulation of a short transmission line is maximized, occurring when $\phi_r = \theta = \tan^{-1}\left(\frac{X}{R}\right)$.

Condition for Zero Voltage Regulation

The receiving-end leading power factor angle condition under which voltage regulation of a short transmission line becomes zero, occurring when $\phi_r = \tan^{-1}\left(\frac{R}{X}\right)$.