If the transformer winding resistances and reactances are expressed in pu value, then

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Examoogle · Accepted Answer

Option D: $R_1(pu) = R_2(pu)$ and $X_1(pu) = X_2(pu)$

Explanation & Concepts:
In a transformer, the per-unit (pu) values of impedance parameters like resistance and reactance are the same when referred to either the primary or secondary side. This is because per-unit normalization is specifically designed to eliminate the effect of the transformer's turns ratio $a$ by normalizing against the respective side's base values.

Working Principle: The per-unit value is defined as the ratio of actual value to base value: $Z_{pu} = \frac{Z_{actual}}{Z_{base}}$. When referring parameters from the secondary to the primary, the actual resistance $R_2$ is multiplied by $a^2$, and the base impedance $Z_{base,2}$ is also multiplied by $a^2$ when referred to the primary base. Consequently, the factor $a^2$ cancels out, leading to identical per-unit values regardless of the side of reference.

Key Formulas: $Z_{pu} = \frac{Z_{\Omega} 	imes (MVA)_{base}}{(kV)_{base}^2}$ — Per-unit impedance calculation formula; $R_{1(pu)} = R_{2(pu)}$ — Equality of pu resistance; $X_{1(pu)} = X_{2(pu)}$ — Equality of pu reactance

Key Points: Per-unit system normalizes parameters to a common base.; The turns ratio $a$ does not affect per-unit values.; This simplifies multi-winding transformer analysis in power systems.; Calculations become independent of voltage levels.

Advantages: Eliminates the need for turns ratio calculations.; Simplifies power system network analysis.; Values of machines are typically within a narrow range regardless of rating.

Disadvantages: Requires careful selection of consistent base values.; Does not account for inherent saturation in high-precision modeling.

Applications: Short circuit studies.; Power flow analysis in multi-bus systems.; Transformer impedance matching.

Additional Info: The per-unit system is the industry standard for analyzing interconnected power systems consisting of various transformers and transmission lines.. Option A, B, and C are incorrect because they imply dependence on the side of reference, which contradicts the fundamental property of the per-unit system.

Answer: D is correct — The per-unit impedance (resistance and reactance) of a transformer is a constant value independent of whether it is referred to the primary or secondary side.

Exam Tip: Always convert actual ohms to per-unit values before performing fault calculations; it reduces algebraic complexity significantly and prevents errors involving the transformer turns ratio.

Examoogle · Answer

Option A: $R_1(pu) = R_2(pu)$ and $X_1(pu) 
eq X_2(pu)$

Examoogle · Answer

Option B: $R_1(pu) 
eq R_2(pu)$ and $X_1(pu) = X_2(pu)$

Examoogle · Answer

Option C: $R_1(pu) = 0.5R_2(pu)$ and $X_1(pu) = 0.5X_2(pu)$

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