Impedance-Based Fault Location | A Step-by-Step Guide
Impedance-based fault location is widely used throughout the power transmission and distribution industry. In fact, for most numerical relays, one-ended impedance-based fault location always comes as a standard feature.
Why?
It is because most numerical relays can measure voltages and currents.
In our previous article, we presented the derivation of the impedance equations using symmetrical fault analysis. We showed that the impedance to fault can be calculated in terms of the measured voltages and currents. The following table summarizes the apparent impedance equation for different fault types.
In this article, we will present one-ended impedance-based fault location methods commonly used in the industry. Basic principles will be laid-out and a step-by-step calculation will be presented. The voltages and currents, and all other necessary information to be used throughout the calculation process will be based on a simple ETAP model.
Apparent Impedance General Equation
One-ended impedance-based fault location methods are based on the analysis of the network as shown in figure 1.
As with how we derived the apparent impedance equations for different fault types, the derivation of the general equation for one-ended impedance-based fault location is pretty straightforward.
The derivation is based on Kirchhoff’s Voltage Law (KVL).
The general equation for the impedance-based fault location as shown above is actually the apparent impedance seen by the relay. As discussed in our previous article “Distance Relaying Fundamentals | What is Apparent Impedance?“, apparent impedance is the impedance calculated in terms of the measured voltages and currents. In the above equation, the measured voltage and current are represented by ‘VR‘ and ‘IR‘, respectively.
Notice that the apparent impedance seen by the relay is the sum of the line impedance and fault resistance. The objective here is to solve for ‘m‘ which is the per-unit distance to fault i.e. the distance to the fault divided by the total line length. With the available information on the positive-sequence impedance of the line, ‘Z‘, the challenge is to find the value of the fault resistance ‘RF‘ and the current ‘IF‘ or to find a way to eliminate them from the equation. In the following section, the two most basic one-ended impedance-based fault location methods are discussed.
One-Ended Impedance-Based Fault Location Methods
Simple Reactance Method
The Simple Reactance method, as the name suggests, considers only the reactance in the impedance calculation. This is done by assuming that the fault currents ‘IF‘ and ‘IR‘ are in-phase, and taking only the imaginary component of the whole equation thus eliminating the fault resistance term.
From the above equation, with fault currents ‘IF‘ and ‘IR‘ in-phase, the resistance term is a real quantity. Taking the imaginary a component and solving for ‘m‘,
Simple as it is but the Simple Reactance method suffers when fault currents ‘IF‘ and ‘IR‘ are not in-phase. This happens due to system load.
Takagi Method
The Takagi method improves upon the Simple Reactance method by considering the load current. In this method, the load current (pre-fault condition) is subtracted from the fault current ‘IR‘ such that the resulting quantity is approximately equal to and in-phase with ‘IF‘. We will call this quantity ‘IF_sup‘.
By multiplying the KVL equation by the conjugate of ‘IF_sup‘, the resistance term becomes a real value.
Taking the imaginary a component and solving for ‘m‘,
The Takagi method may have improved upon the Simple Reactance method however, it requires the pre-fault information in addition to the fault data. In most numerical relays, if not all, pre-fault information is readily available.
The success of the Takagi method lies in the assumption that load currents stay relatively constant before and during a fault.
Step-by-Step Calculation
We will start the calculation process by creating a system model using ETAP software where faults will be simulated. The fault information from the simulation will be used in the fault location calculation.
Transmission Line Impedance Parameters:
R1 = 3.72723 ohms
X1 = 20.6122 ohms
R0 = 13.5151 ohms
X0 = 62.0961 ohms
From this network, a single line-to-ground fault at Bus2 will be simulated. The voltages and currents at Bus1 will be used to represent ‘VR‘ and ‘IR‘, respectively.
As discussed in our previous article “Distance Relaying Fundamentals | What is Apparent Impedance?“,
it is very important to identify the fault type prior to conducting apparent impedance calculations.
In manual calculations, the choice of the equation for an A-ground fault will depend on the available information. Based on Table 1, for an A-ground fault, the following equation will be used.
From the above equation and the fault information from the simulation, the relay measured values, ‘VR‘ and ‘IR‘, are determined.
In solving for ‘IR‘, the zero-sequence current, ‘3I0‘, is equal to the current ‘IRA‘ since a radial system without load was utilized as the network model. This was done to simplify the calculation process. However, in actual systems, it should be noted that ‘3I0‘ may have a different value from the measured current ‘IRA‘.
From the transmission line model, we will use the positive sequence impedance.
Now that we have ‘VR‘, ‘IR‘, and ‘Z‘, we ready to solve the fault location using the methods that we have discussed.
Fault Location Solution Using the Simple Reactance Method
Using the equation for Simple Reactance method to solve for ‘m‘,
By multiplying ‘m‘ by the transmission line length of 50 km, we can get the estimated fault location of 50.02 km.
Fault Location Solution Using the Takagi Method
The first step in this method is to calculate the superposition current, ‘IF_sup‘.
Since we used an unloaded network in our simulation, ‘IF_sup‘ is equal to ‘IR‘. Solving for m,
By multiplying ‘m‘ by the transmission line length of 50 km, we can get the estimated fault location of 50.01 km.
At this point, we have shown the step-by-step fault location calculation of the two most basic methods. There are other impedance-based methods available and choosing from among these depends on the system conditions and fault scenarios. If you are interested in learning more, the following references should help you dive deep into fault location topics.
References
[1] Das, Swagata & Santoso, Surya & Gaikwad, Anish & Patel, Mahendra, “Impedance-based Fault Location in Transmission Networks: Theory and Application,” IEEE Access. 2. 1-1. 10.1109/ACCESS.2014.2323353, January 2014.
[2] F. Calero, “Distance Elements: Linking Theory with Testing,” Schweitzer Engineering Laboratories, Inc., August 2009.
[3] K. Zimmerman, and D. Costello, “Impedance-Based Fault Location Experience,” Schweitzer Engineering Laboratories, Inc., July 2010.
[4] M. Ibrahim, “Case Studies Related to Overhead Transmission-Line System Disturbances,” in Disturbance Analysis for Power Systems, IEEE, 2012, pp.461-570, DOI: 10.1002/9781118172094.ch6.
[5] G. Pradeep Kumar, “Transmission Line Protection,” notes on Power System Protection Training, Visayan Electric Company, Cebu City, Philippines, 2016.
