Introduction:
Positive, negative, and zero sequence impedances are used to study the behavior of three-phase electrical systems under unbalanced conditions. Each sequence impedance represents the impedance seen by the respective sequence component in the system.

Explanation:
In a three-phase power system, the positive, negative, and zero sequence components represent the symmetrical components of the system. The positive sequence represents the balanced condition, while the negative and zero sequences represent the unbalanced conditions.

Transmission Lines:
In a transmission line, positive, negative, and zero sequence impedances are not equal. This is because transmission lines are typically designed to have different characteristics for each sequence component. For example, the positive sequence impedance is lower than the negative sequence impedance in order to provide better performance under normal balanced conditions.

Alternator:
In an alternator, positive, negative, and zero sequence impedances are also not equal. The positive sequence impedance is typically lower than the negative sequence impedance to ensure stable operation under normal balanced conditions.

Transformer:
In a transformer, the positive, negative, and zero sequence impedances are equal. This is because transformers are designed to have symmetrical characteristics for each sequence component. The equal sequence impedances ensure that the transformer operates efficiently and reliably under both balanced and unbalanced conditions.

Conclusion:
In summary, the positive, negative, and zero sequence impedances are equal for transformers, while they are not equal for transmission lines and alternators. Transformers are specifically designed to have symmetrical characteristics for each sequence component, while transmission lines and alternators are designed with different characteristics for each sequence component to ensure optimal performance under various operating conditions.