Impedance

Impedance (Z) is the total opposition to alternating current flow in a circuit, expressed as a complex number Z = R + jX measured in ohms, where R is resistance and X is reactance. It is a fundamental parameter that governs how power systems behave under both normal and fault conditions.

Key Aspects of Impedance:

• Real and Imaginary Components: The real part (resistance) dissipates energy as heat, causing I²R losses in conductors and windings. The imaginary part (reactance) stores and releases energy in magnetic and electric fields, causing current and voltage to be out of phase.
• Voltage Drop: Voltage drop along a transmission line or through a transformer is directly determined by the current flowing through the element's impedance, making it a key factor in voltage regulation.
• Fault Current: During short circuits, the total impedance between the source and the fault point determines the magnitude of fault current, lower impedance means higher fault current. Transformer impedance (often quoted as Z%, e.g. 6%) directly limits fault current through the device.
• Per-Unit Normalization: For analysis across multi-voltage networks, impedance is normalized using Z_base = V_base² ÷ S_base, which eliminates transformer turns ratios from calculations and allows direct comparison of elements at different voltage levels.
• Mathematical Forms: Impedance is expressed in rectangular form (R + jX) for series element addition, or polar form (|Z|∠θ) for multiplication and division, the angle θ determines the power factor of the element.
• Critical Input Data: Impedance values for every transmission line and transformer are required inputs for power flow, short-circuit, stability, and protection coordination studies.