Distance Protection Basics

Visualizing Distance Protection: Mho Elements on an R-X Plot

Distance protection is a foundational concept in transmission line protection. Among the various elements used, the mho element is one of the most common and intuitive to understand when visualized on an R-X diagram. This blog post explores what mho elements look like on an R-X plot, how they are defined, and applies it to a specific case with real-world impedance values.

What Is a Mho Element?

A mho element is an impedance-based distance relay element that operates when the measured impedance from the relay location to the fault falls within a circle that passes through the origin on an R-X plot. The element is directional and typically used to detect faults within defined zones on a transmission line. It is especially effective in systems where speed and selectivity are essential.

Transmission Line Example

In this example:

• Line impedance (Z_line) = 0.2 + 0.8j Ω, or in polar form: 0.8246 ∠ 75.96° Ω

• Zone 1 reach = 80% of the line

• Zone 2 reach = 120% of the line

The magnitude of the line impedance is calculated as:

$$|Z_{line}| = \sqrt{R^2 + X^2} = \sqrt{0.2^2 + 0.8^2} = \sqrt{0.04 + 0.64} = \sqrt{0.68} \approx 0.8246 \Omega$$

The angle of the line impedance is:

$$\theta = \tan^{-1}\left(\frac{0.8}{0.2}\right) = \tan^{-1}(4) \approx 75.96^°$$

From this:

• Zone 1 reach: 0.8 × 0.8246 ≈ 0.6597 Ω

• Zone 2 reach: 1.2 × 0.8246 ≈ 0.9895 Ω

Defining the Mho Circle

Distance protection schemes typically include multiple zones with different time delays.

• Zone 1, covering approximately 80% of the protected line, is usually set to operate instantaneously with no intentional time delay to ensure the fastest possible clearing of faults within the majority of the line.

• Zone 2, which extends beyond the protected line into the next line section (typically 120% reach), has a delayed operation — usually in the range of 0.3 to 0.5 seconds. This delay helps coordinate protection with downstream relays.

The coordination of these timing settings is critical to ensuring proper selectivity and reliability in transmission-level protection.

Each mho element is represented as a circle on the R-X plot:

• It passes through the origin

• The center is located at half the reach point, i.e., Z_reach/2

• The radius is half the magnitude of the reach impedance

Computed as:

• Zone 1 circle center: (0.08, 0.32)

• Zone 2 circle center: (0.12, 0.48)

• Radii:

  • Zone 1: 0.6597 / 2 ≈ 0.3299 Ω

  • Zone 2: 0.9895 / 2 ≈ 0.4947 Ω

These settings result in two directional mho elements that align with the transmission line's impedance. The Zone 1 and Zone 2 angle is approximately 76°, indicating that the relay is tuned to detect faults in the forward direction along the transmission line.

Visualization

The R-X plot illustrates:

• Zone 1 (white circle) - reach: 0.6597 Ω

• Zone 2 (gray circle) - reach: 0.9895 Ω

• Transmission Line (white line) - impedance from the origin to (0.2, 0.8)

Both mho elements are directional and pass through the origin, which allows them to accurately detect forward faults while excluding reverse faults.

Final Thoughts

Mho elements offer an elegant visual and mathematical method to define distance protection zones. By plotting these circles on an R-X diagram, engineers gain intuitive insight into the coverage, selectivity, and operation of protective relays.

This type of visualization is particularly useful when configuring relays from vendors such as SEL, GE, or Siemens. A clear understanding of the mho element's geometry can enhance both reliability and speed of protection schemes across transmission systems. These visual tools are especially helpful for both seasoned protection engineers and those preparing for exams like the NCEES PE Power.