Visit Count: 615 Busbar Protection and CT Knee Point Voltage Whenever there is mal-operation or non-operation of busbar protection there is debate about CT saturation and CT knee point voltage. In this article, we check this fact mathematically and will also check the importance of busbar stabilizing resistance. It is true that nowadays most of the busbar protection schemes are replaced by numerical one; where stabilizing resistance is not required. However, the REF circuit is also just like the bus-bar protection circuit where still stabilizing resistance is required. This discussion is equally applicable to REF protection too To analyze the busbar protection circuit mathematically it is needed to model the CT properly. CT secondary current varies as per primary current but independent of the impedance connected across its secondary terminals. That means it is to be modeled as a constant current source. Converting Constant Current Source to Constant Voltage Source The constant voltage source model and constant current source model are represented in the following drawings. In terms of the electrical network analysis, they are called duals and one can be converted to another for network study. While converting the constant current model to a constant voltage model supply voltage would be Vs = I*Rp (i.e. in above circuit Vs = 5*500). Where Rp is the resistance in parallel with the constant current source and now the resistance in series with constant voltage Vs would be equal to Rp (see above circuit). Modelling the CT For example purpose, we will model a 400/1 A CT having its secondary winding resistance of 8 supplying relay of resistance 8 ohms and a knee point voltage of 450 Volts and magnetizing current specified as 100 mA at Vk/2. Form the above CT specifications, the value of Rp would be 225 V / 100 mA = 2250 Ohms. If the primary current of this CT is 240 Amp then the secondary current would be 0.6 Amp and hence the CT can be modeled as a voltage source of 0.6*2250 = 1350 V in series with the 2250 + 16 ohms resistance. Busbar protection circuit model Normal Operation With this background now we will go for our actual busbar protection modeling. Let us consider there are 3 feeders of CT ratio 1000/1 amp connected to the bus having loads as F1 = 300 Amp, F2 = 500 Amp, and F3 = 800 Amp. At the first stage, we will consider all CTs having approximate knee point voltage 700 V +/- 10% having a magnetizing current of 100 mA at Vk/2. Thus values of Rp would be 3500 +/- 10%. For modeling purpose let we choose these values as Rp1 = 3100, Rp2 = 3500 and Rp3 = 3300 ohms. Let the value of stabilizing current for busbar protection relay(87) is 300 ohms. Considering CT as a constant current source; the network model for this arrangement would be as shown in the following figure. Now if we replace constant current sources with equivalent constant voltage sources the network model would be as below. Now this network can be solved using mesh analysis (in college days very few of us might be solved it correctly) and with the help of Excel matrix inverse formula and current obtained are as below. Here is the screenshot of the Excel solution to these simultaneous equations. From these calculations, we can easily check that for balanced conditions current through the busbar relay is extremely less which agrees with our experience. Busbar protection circuit model External Fault + CT Knee Point Voltage Less Now we will see what happens if one of the CT knee point voltage is very less in case of outside bus zone fault. The constant current circuit would be as below. Note that we have considered a fault case. Thus currents through CT secondary would be 3 Amp, 5 Amp, and 8 Amp. Here is voltage source equivalent circuit and claculation part From these calculations, we can easily check that even if some CT has knee point voltage excessively less; current in the busbar differential relay is very limited for through fault. Conclusion It is NOT mean that we can use CT with less knee point volatge in busbar protection but only to indicate busbar protection operates for through fault ONLY WHEN ONE OF THE CT GET SATURATED. In this case too we can avoid relay maloperation by properly selecting its operating current setting and stablizing resistance. My friend Er. Vijay Katrale shared a simultenious equation calculator link for solving equations that link is given below. Insted of solving the equations by Excel sheet you can try by solving with the help of this calculator. https://play.google.com/store/apps/details?id=com.deep.smartcalculator Finaly we can conclude that busbar or REF relay does not mal-operates for through fault unless and untill CT get saturated (if all other circuit is OK) and properly selected series resistance avoides relay maloperation for through fault in case of CT saturation. You can download the respective excel file from here- CurrentInBusBarProtectionRelay.xlsx.