1. Ratio Error of Current Transformer and 10% Error Curve
The ratio error of a current transformer is also related to its secondary load impedance. For ease of calculation, the manufacturer provides the allowable secondary load impedance value Zen under m10 for each type of current transformer. The curve m10=f(Zen) is called the 10% error curve of the current transformer. Usually, the 10% error curve of a current transformer is determined by the manufacturer through experiments and is provided in the product manual. If it is not provided in the product manual, or after years of operation, when the characteristics of the current transformer need to be re-verified, the 10% error curve must be plotted through testing methods. Let Ki be the transformation ratio of the current transformer, and the primary current and secondary current have the relationship I2=I1/Ki. When Ki is constant (the power transformer I2 is not saturated), it is a straight line. When the iron core of the current transformer begins to saturate, it no longer maintains a linear relationship with I1/Ki, but instead takes the shape of the magnetization curve of the iron core. Relay protection requires that when the primary current I1 of the current transformer equals the maximum short-circuit current, its ratio error should be less than or equal to 10%. If the primary current I1 of the current transformer is such that the ratio error does not exceed 10%, then it is acceptable; if it exceeds, the ratio error is greater than 10%.
2. Method for Measuring the 10% Error Curve of Current Transformer
The direct method for measuring the 10% error curve of a current transformer is the secondary side current injection method. This method involves injecting current into the secondary side of the current transformer. The required power supply and equipment capacity are relatively small, and the results are the same as those obtained by the primary current method, making it easy to implement on-site. The following introduces the method of plotting the 10% error curve of a current transformer using the secondary side current injection method.
Collect data: protection device type, setting value, transformation ratio of the current transformer, wiring method, and the maximum fault current flowing through the current transformer.
Measure the DC resistance R2 of the secondary winding of the current transformer.
Calculate the secondary winding leakage reactance Z2: use the empirical formula: for oil-immersed LCCWD type, generally take Z2=(1.3～1.4)R2; for bushing-type LRD current transformers, generally take Z2=2R2. Use the current-voltage method to measure the maximum load impedance: at the root of the current transformer, use the current-voltage method to measure the impedances of the secondary circuits AB, BC, CA, and A0 phase. Note that the measurement wiring should preferably use the high internal resistance voltage method. For differential protection wiring, since during external faults only unbalanced current flows through the relay and the fault current does not flow through the relay, the differential relay coil should be short-circuited during actual measurement. The calculation formula is:
Either the low internal resistance current method or the high internal resistance voltage method can be used. During the test, attention should be paid to keeping the primary side of the current transformer open, disconnecting all loads on the secondary side before applying voltage, and increasing the voltage gradually from zero. Do not reduce the voltage and then increase it again midway, as this may cause the volt-ampere characteristic curve to be uneven due to the hysteresis loop, affecting the accuracy of the calculation. Generally, test up to 5A, and if there are special requirements, test until saturation.
Based on the U=f(I0) curve, determine the relationship between excitation voltage, excitation impedance, current multiple, and allowable load, and plot the 10% error curve. According to electrical theory, when the primary winding of the current transformer is open and voltage is applied to the secondary winding, the current flowing through the secondary winding is the excitation current of the current transformer. For different secondary windings of the same current transformer, under the same excitation current, the saturation degree of the iron core is different, which is reflected in the rate of change of magnetic flux dΦ/dt, and the induced electromotive force E0=W(dΦ/dt) generated in the winding is different (here E0 is approximately equal to the voltage value U2 on the secondary winding). For deeper saturation, dΦ/dt is small, and E0 is also small; for shallower saturation, dΦ/dt is large, and E0 is also large. According to the equivalent circuit diagram: E0=U2-I0Z2
When the ratio error of the current transformer is 10%, the excitation current I0 should be 10% of the primary current converted to the secondary side current I’1. That is, when I’1 is 100%, I0 is 10%, and I2 is 90%. Therefore, when the primary current is converted to the secondary side, it is 10 times the excitation current, and the secondary current is 9 times the excitation current. To ensure that the ratio error of the current transformer does not exceed 10%, the multiple of the primary current that the selected current transformer can withstand relative to the rated current should not be less than the values calculated by the following formulas:
Generator longitudinal differential protection: m10=(KkIkmax)/I1N
Ikmax: the maximum current flowing through the current transformer during external short circuit, which is equal to the short-circuit current at the generator outlet during a three-phase short circuit;
I1N: rated primary current of the current transformer;
Kk: reliability coefficient. Considering that relays with saturable current transformers are used in differential protection, the protection device is insensitive to the non-periodic component appearing in the short-circuit current at the initial moment of the short circuit; and when the reliability coefficient is taken as 2, the cross-section of the control cable needs to be greatly increased, which is uneconomical, so the reliability coefficient is taken as 1.3;
Transformer longitudinal differential protection, generator-transformer unit longitudinal differential protection: m10=(KkIkmax)/I1N
Ikmax: the maximum current flowing through the current transformer during external short circuit. For two-winding transformers and generator two-winding transformer units, when the power plant is connected to a large power system, the short-circuit current can be calculated assuming the system capacity is infinite. For three-winding transformers and generator three-winding transformer units, the short-circuit current is calculated based on various actual system capacity conditions;
Kk: reliability coefficient. Take 1.3; when relays without saturable current transformers are used, take 1.5.
Busbar longitudinal differential protection: m10=(KkIkmax)/I1N
Ikmax: the maximum current flowing through the current transformer during external short circuit. The short-circuit current needs to be calculated based on the actual current distribution in the power source branch lines;
Kk: reliability coefficient. Take 1.3; when relays without saturable current transformers are used, take 1.5.
