Principle of Current Differential Protection

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1. **Basic Concept**
Current differential protection is a protection principle based on Kirchhoff's Current Law (KCL). Kirchhoff's Current Law states that the sum of currents flowing into any node in a circuit is equal to the sum of currents flowing out of that node. For protected components in a power system (such as transmission lines, transformers, etc.), during normal operation and in the case of external faults, the vector sum of currents flowing into and out of the protected component is approximately zero; while when a fault occurs inside the protected component, this current vector sum is no longer zero.

2. **Principle of Current Differential Protection for Transmission Lines**
- **Normal Operation and External Fault Conditions**:
Suppose current transformers (CTs) are installed on both sides of a transmission line to measure the currents on both sides of the line. During normal operation, according to Kirchhoff's Current Law, the magnitude of the current flowing into one side of the line is equal to the magnitude of the current flowing out of the other side. For example, for a simple transmission line transmitting power from busbar A to busbar B, during normal operation, the current \(I_{A}\) measured by the CT on the side of busbar A and the current \(I_{B}\) measured by the CT on the side of busbar B satisfy \(I_{A}+I_{B} = 0\) (here, the direction of the current is considered, with the current flowing into the line defined as positive and the current flowing out of the line defined as negative). When a fault occurs outside the line (such as on an adjacent line), this relationship still holds. This is because the fault current does not flow into the protected line but flows through other paths.
- **Internal Fault Conditions**:
When a fault occurs inside the protected transmission line, a short-circuit current will be generated at the fault point. At this time, the currents measured by the CTs on both sides no longer satisfy the above balance relationship. For example, when a three-phase short-circuit fault occurs in the middle of the line, assuming the short-circuit current is \(I_{k}\), the current \(I_{A}\) measured by the CT on the side of busbar A and the current \(I_{B}\) measured by the CT on the side of busbar B satisfy \(I_{A}+I_{B}=I_{k}\). The differential protection device will detect this unbalanced current (differential current). When the differential current exceeds the set operating threshold, the protection device will operate, trip the circuit breakers on both sides of the line, and remove the faulty line from the power system.

3. **Principle of Current Differential Protection for Transformers**
- **Normal Operation and External Fault Conditions**:
For transformers, CTs are also installed on each side. During normal operation, according to the principle of electromagnetic induction of transformers and Kirchhoff's Current Law, there is a certain relationship among the currents on each side of the transformer. Taking a two-winding transformer as an example, assuming the primary side current of the transformer is \(I_{1}\), the secondary side current is \(I_{2}\), and the transformation ratio of the transformer is \(n\), under ideal conditions, \(I_{1}+(-nI_{2}) = 0\) (here, the direction of the current is considered, with the current flowing into the primary side defined as positive and the current flowing out of the secondary side defined as positive, and the influence of the transformation ratio is taken into account). When a fault occurs outside the transformer, this relationship basically remains unchanged.
- **Internal Fault Conditions**:
When a fault occurs inside the transformer (such as inter-turn short-circuit of windings, phase-to-phase short-circuit, etc.), the current balance relationship on each side of the transformer is broken. For example, when an inter-turn short-circuit occurs in the primary winding of the transformer, the primary side current \(I_{1}\) and the secondary side current \(I_{2}\) no longer satisfy the above balance relationship, and a differential current will be generated. When the differential protection device detects that this differential current exceeds the operating threshold, it will operate, trip the circuit breakers on each side of the transformer, and protect the transformer.

4. **Factors Affecting the Correct Operation of Current Differential Protection and Countermeasures**
- **Errors of Current Transformers**:
During the process of measuring current, CTs will have ratio errors and phase angle errors. The ratio error refers to the difference between the actual transformation ratio and the nominal transformation ratio of the CT, and the phase angle error refers to the phase difference between the secondary current vector and the primary current vector of the CT. During external faults, these errors may cause the differential current to be non-zero, which may lead to misoperation of the protection. To reduce the impact of CT errors, high-precision CTs can be used, and appropriate compensation algorithms can be adopted in the protection device to correct CT errors.
- **Generation of Unbalanced Currents**:
Due to the influence of factors such as the exciting current of the transformer and the distributed capacitance current of the line, unbalanced currents will be generated. For example, during the normal operation of the transformer, the exciting current will generate an unbalanced current in the differential circuit. To avoid misoperation of the protection caused by unbalanced currents, it is necessary to reasonably set the operating threshold of the differential protection and adopt the braking characteristic. The braking characteristic means that the operating current of the differential protection increases with the increase of the braking current (usually taking the maximum unbalanced current that may be generated during external faults), so that it can reliably brake during external faults to prevent misoperation and operate sensitively during internal faults.
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