The knee point voltage (KPV) of a current transformer is a critical parameter that defines the boundary between the linear and saturated regions of the CT's magnetizing characteristic. It represents the maximum secondary voltage at which the CT can operate while maintaining a substantially linear relationship between the applied voltage and the excitation current. Beyond the knee point, small increases in voltage cause large increases in excitation current, and the CT's ability to accurately transform current is severely compromised.
The knee point voltage is formally defined as the voltage at which a 10% increase in the applied voltage causes a 30% to 50% increase in secondary current. This definition is specified in IEC standards and provides a standardized method for characterizing the onset of saturation. According to the IEC standard, the knee point is defined as the point at which a voltage increase of 10% causes a current increase of 50%. This definition allows engineers to compare CTs from different manufacturers on a consistent basis.
The knee point voltage is determined by the magnetic properties of the CT core and the number of secondary turns. A larger core with higher saturation flux density and more secondary turns will have a higher knee point voltage. The knee point voltage is typically measured by applying a variable AC voltage to the secondary winding with the primary open-circuited and recording the excitation current at each voltage level. The resulting excitation curve shows a linear region at low voltages, a transition region (the knee), and a saturated region at high voltages.
In protection applications, the knee point voltage is of particular importance. Protection CTs must maintain their accuracy during fault conditions when primary currents can reach many times the rated value. The secondary voltage during a fault is determined by the product of the secondary current and the total secondary burden. If this voltage exceeds the knee point voltage, the CT will saturate and the secondary current will not accurately represent the primary fault current. This can cause protective relays to fail to operate or to operate with excessive delay.
The required knee point voltage for a protection application depends on the specific protection scheme and the system parameters. For differential protection, the knee point voltage must be high enough to ensure stability during through-fault conditions. The required knee point voltage is typically calculated using the formula: VK ≥ 2 × VS, where VS is the stabilizing voltage. This ensures that the CT can drive the necessary current through the relay circuit during an internal fault while remaining stable during external faults.
The knee point voltage can be calculated from the CT's rated data using empirical formulas. One common formula is: VKP = (R1 + Prated/Irated) × n × Irated, where R1 is the secondary winding resistance, Prated is the rated burden, Irated is the rated secondary current, and n is the accuracy limit factor. This formula provides an estimate of the knee point voltage based on the CT's nameplate data and can be used for preliminary design calculations.
For a typical protection CT with a 15 VA, 5P10 rating, the estimated knee point voltage can be calculated as: VK = (VA × ALF / In) + (ALF × In × Rct), where VA is the rated burden, ALF is the accuracy limit factor, In is the rated secondary current, and Rct is the secondary winding resistance. Using the values from this example: VK = (15 × 10 / 5) + (10 × 5 × Rct) = 30 + 50 × Rct. For a CT with a secondary winding resistance of 0.5 Ω, the estimated knee point voltage would be 30 + 25 = 55 V.
The knee point voltage is closely related to the accuracy limit factor (ALF). The ALF specifies the multiple of rated primary current at which the CT must still maintain its specified accuracy. A CT with a high ALF must have a high knee point voltage to support the high secondary current that flows during fault conditions. The relationship between ALF and knee point voltage is approximately linear, assuming constant burden and winding resistance.
In practice, the knee point voltage is verified during CT testing to ensure that the CT meets its specifications. The test involves applying a variable voltage to the secondary winding and measuring the excitation current at each voltage level. The knee point is identified from the excitation curve as the point where the curve begins to deviate from linearity. A CT with an abnormally low knee point voltage may indicate core damage, incorrect core material, or winding problems.
The knee point voltage also has implications for CT safety. If the secondary circuit is opened while primary current flows, the voltage across the open secondary can rise to dangerous levels, limited only by the knee point voltage and the core saturation characteristics. This is why the secondary circuit of a CT must never be opened while primary current is flowing. The high voltage that appears at the secondary terminals can endanger personnel and damage equipment.
In summary, the knee point voltage is a fundamental parameter that characterizes the saturation behavior of a current transformer. It defines the boundary between linear and saturated operation and is essential for ensuring that protection CTs perform reliably during fault conditions. Proper selection of the knee point voltage-based on the application requirements and system parameters-is essential for reliable protection system operation.