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Distance Protection Voltage and Current Calculations in the Test Room

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In distance protection testing, an impedance relay is used to protect a line by calculating impedance using line current and voltage

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The calculations in the distance room require injecting current and voltage proportional to the impedance of the relay

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The training covers distance test calculations, along with proof for various fault types and testing methods

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There are three common methods to calculate fault voltage and current for distance relay testing

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

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In the Test Object window (Test Block), pay attention to the maximum test impedance (max(V))

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which depends on the maximum test voltage displayed in the table for various fault types under the **Device Limits** section

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Constant Z-V Method

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

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calculated by entering the impedance. In the Test Object window (Test Block), pay attention to the minimum test impedance (maxI)

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which depends on the maximum fault current displayed in the table for various fault types under the ‘Device Limits’ section

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Constant Source Impedance Method

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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)

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). Information from the source may vary, but eventually, Ks and Zs are converted into usable values for calculations

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All of this data is related to source impedance and is finally used in calculations

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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

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, ‘Fault’ subsection, and ‘Test Model’ group. Click on the sliding field to select the desired mode

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Understanding the Concept of Source Impedance Ratio (SIR)

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Consider a single-phase equivalent circuit of the network with a source or SV voltage

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. 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

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 The voltage measured by the relay is denoted as RV.

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The system voltage seen by the relay is calculated using the ratio between Zs and ZL

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known as the ‘Source Impedance Ratio (SIR)’, which is represented by the following equation

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Also, using the following relationship, the voltage from the source to the short circuit level can be calculated asTherefore

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, the voltage measured by the relay during a fault depends on the SIR value and ultimately on the line impedance

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Using the relationships for Ks and Zs, fault voltage and current can be calculated for the test.

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Current and Voltage in Different Fault Types

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So far, explanations have been provided regarding methods for impedance calculation

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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

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Single-Phase Fault:

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The figure below shows the equivalent circuit of the line in the case of a single-phase fault

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For calculating the current and voltage of the faulted phase and the other phases

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methods such as constant current, constant voltage, and constant source impedance are used, with the calculations for each provided separately.

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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:

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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:

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

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Proof of calculations in the Constant method:

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. Two-Phase Fault

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The equivalent circuit for a two-phase fault is shown below

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For the faulted and healthy phases, methods like constant current, constant voltage, and constant source impedance are used, with each calculation presented separately

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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

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This results in the following relationships for current and voltage:

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Assume a fault impedance of 1 ohm with an angle of 0° is used for testing

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. In this fault type, the angle between the line-to-line voltage and the corresponding current creates the desired impedance angle

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The results for phase angles and magnitudes are:

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

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Three-Phase Fault

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The equivalent circuit for a three-phase symmetrical fault is illustrated below

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Faulted phase calculations are performed separately for constant current, constant voltage, and constant source impedance methods.

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

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In the Z-V Constant Method the fault voltage is set equal to the phase-to-ground voltage for all test points

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Fault currents for each phase are determined as:

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

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The relationships for fault current and relay voltage are