Distance Protection Voltage and Current Calculations in the Test Room

In distance protection testing, an impedance relay is used to protect a line by calculating impedance using line current and voltage. The calculations in the distance room require injecting current and voltage proportional to the impedance of the relay. The training covers distance test calculations, along with proof for various fault types and testing methods. There are three common methods to calculate fault voltage and current for distance relay testing:

Constant Z-I Method

. Constant Z-I Method In this method, the fault current is considered constant, and the fault voltage is calculated by entering the impedance

In the Test Object window (Test Block), pay attention to the maximum test impedance (max(V)), which depends on the maximum test voltage displayed in the table for various fault types under the **Device Limits** section.

Constant Z-V Method

In this method, the fault voltage is considered constant, and the fault current is calculated by entering the impedance.

calculated by entering the impedance. In the Test Object window (Test Block), pay attention to the minimum test impedance (maxI), which depends on the maximum fault current displayed in the table for various fault types under the ‘Device Limits’ section.

Constant Source Impedance Method

In this method, neither voltage nor current is considered constant, but instead, the fault voltage is calculated using the source impedance (Zs) and the source factor (Ks). Information from the source may vary, but eventually, Ks and Zs are converted into usable values for calculations. All of this data is related to source impedance and is finally used in calculations.

In the next step, based on the chosen test method, fault current and voltage can be calculated in the ‘Distance Room’ under the ‘Setting’ tab, ‘Fault’ subsection, and ‘Test Model’ group. Click on the sliding field to select the desired mode.

Understanding the Concept of Source Impedance Ratio (SIR)

Consider a single-phase equivalent circuit of the network with a source or SV voltage. This network consists of the source impedance (Zs) up to the relay installation location and the line impedance (ZL), which the protection relay will monitor. The voltage measured by the relay is denoted as RV.

The system voltage seen by the relay is calculated using

the ratio between Zs and ZL, known as the ‘Source Impedance Ratio (SIR)’, which is represented by the following equation:

Also, using the following relationship, the voltage from the source to the short circuit level can be calculated asTherefore, the voltage measured by the relay during a fault depends on the SIR value and ultimately on the line impedance. Using the relationships for Ks and Zs, fault voltage and current can be calculated for the test.

Current and Voltage in Different Fault Types

So far, explanations have been provided regarding methods for impedance calculation. This section discusses the relationships of fault current and voltage in the software using the equivalent circuit for single-phase, two-phase, and three-phase faults

Single-Phase Fault:

The figure below shows the equivalent circuit of the line in the case of a single-phase fault. For calculating the current and voltage of the faulted phase and the other phases, methods such as constant current, constant voltage, and constant source impedance are used, with the calculations for each provided separately.

In Z-I Constant Method, the fault current (test current) is considered constant for all test points. Using the impedance and test current, the voltage is calculated as follows:

In Z-V Constant Method the fault voltage (test voltage) is fixed for all test points. Using the impedance and test voltage, the current is determined by:

In the Constant Source Impedance method, the fault current and voltage are calculated according to Kirchhoff's law as follows:

Proof of calculations in the Constant method:

. Two-Phase Fault

The equivalent circuit for a two-phase fault is shown below. For the faulted and healthy phases, methods like constant current, constant voltage, and constant source impedance are used, with each calculation presented separately

In Z-I Constant Method, the fault current remains constant across all test points and is the same for the two faulted phases but 180° out of phase. This results in the following relationships for current and voltage:

Proof of calculations in the Z-I constant method:

-In the Z-V constant method, the fault voltage for all test points is equal to the faulted two-phase line voltage (Vtest = V1N-V2N). Given the fault impedance, the line current and voltage are obtained from the following relationships:

Example: Two-Phase Fault (L1-L2) Assume a fault impedance of 1 ohm with an angle of 0° is used for testing. In this fault type, the angle between the line-to-line voltage and the corresponding current creates the desired impedance angle. The results for phase angles and magnitudes are:

In the Constant Source Impedance method, the fault current and voltage are obtained as follows according to Kirchhoff's law:

Three-Phase Fault

The equivalent circuit for a three-phase symmetrical fault is illustrated below. Faulted phase calculations are performed separately for constant current, constant voltage, and constant source impedance methods.

In Z-I Constant Method, fault current is fixed across all test points, and the fault voltage for all three phases is calculated using:

In the Z-V Constant Method the fault voltage is set equal to the phase-to-ground voltage for all test points. Fault currents for each phase are determined as:

In this method, both fault current and voltage are calculated using Kirchhoff's laws, considering the source impedance. The relationships for fault current and relay voltage are