Current Transformer Transient Performance Analysis

Current Transformer Transient Performance Analysis - Power System Protection

1. Current Transformer Transient Performance Analysis Explores the transient performance of CTs, analyzing how they respond during fault conditions Examines the critical issue of CT saturation. Understanding these dynamics is essential for proper relay performance and effective power system protection.

2. CT Steady State vs. Transient Performance As demonstrated in previous analysis, when burden impedance increases, the excitation current (I M ) requirement becomes larger, potentially pushing the CT into the saturation region of the BH curve. Once saturation occurs, the error becomes significant, affecting relay performance. Transient Performance Challenges During faults, the current undergoes a transition process before settling to a steady-state value. This transition period is critical as: Fault currents may be significantly high Currents may contain decaying DC components CTs may have residual flux in the magnetic core These factors can lead to saturation and significant distortions in the secondary output

3. Equivalent Circuit Model For transient analysis, we use the CT model shown in the image where: i 1 is the primary current referred to the secondary i 2 is the current going to the relay (burden) im is the magnetizing current divided into core loss component and flux component The primary current i 1 (t) during a fault can be expressed as: = 0 For t < 0 Where I max is the peak value of the sinusoidal steady-state fault current, T is the time constant associated with the fault current, and θ is the fault inception angle. CT Model for Transient Analysis Our goal is to determine the corresponding output current i2 that flows to the relay for a given input signal i1. This relationship is crucial for understanding how accurately the CT reproduces the primary current during transient conditions.

4. Mathematical Analysis of CT Transient Response To analyze the CT's transient response, we use Laplace transform techniques to derive expressions for the flux linkages (λ) and secondary current (i 2 ). Laplace Domain Expressions The primary current in Laplace domain: The voltage V2 across the core: Flux Linkages and Secondary Voltage Assuming a resistive burden (Lb=0) for assessment: Where τ is the time constant: These equations show that the CT's response depends on both its own parameters (Rc, Lm) and the burden (Rb, Lb). The time constant τ plays a crucial role in determining how the CT responds to transient inputs. In the circuit, i 2 = i 1 – (i f + i c ) The flux linkages of the core λ = L m I f

5. Time Domain Expressions for CT Response Flux Linkages (λ) where, tanϕ = ωτ Secondary Current (i2) These expressions reveal that the secondary current i 2 differs significantly from the primary current i 1 . Additional terms related to the time constants (τ and T) and phase angle (ϕ) affect the CT's output, potentially causing distortion in the reproduced current waveform. Using inverse Laplace transform, we can derive the time domain expressions for flux linkages (λ) and secondary current (i 2 ):

6. Example: CT Response to Transient Input Resulting Expressions Flux linkages: Secondary current: These expressions show that the CT's response includes exponential terms with different time constants and sinusoidal terms with phase shifts, resulting in a complex output that differs from the input waveform. Consider a CT with the following parameters: Core loss resistance Rc = 150 Ω Burden resistance Rb = 1 Ω Magnetizing inductance Lm = 0.01 H Primary current i 1 = 212.132sin( ωt -π) - 212.132e-20t Frequency f = 50 Hz Calculated parameters: T = 0.05 s (system time constant) τ = 0.01007 s (CT time constant) ωτ = 3.1636 ϕ = 72.458° = 1.2646 rad

7. CT Saturation Effects on Output Current The graph shows: Blue curve: Primary current (i1) with decaying DC component Red curve: Flux linkage (λ) Green curve: Theoretical secondary current (i2) without saturation Dotted line: Saturation threshold for the CT core Hatched portion: Actual secondary current with saturation effects Impact of Saturation: When the flux linkage exceeds the saturation threshold: The rate of change of flux ( dϕ /dt) approaches zero The induced EMF in the secondary becomes zero The output current (i 2 ) drops to zero during saturation periods The actual output current (hatched portion) shows significant distortion compared to the primary current With inductive burden, the expressions of i 2 and λ become more complex with additional time constants, potentially causing even more significant distortions in the output.

8. Factors Affecting CT Saturation Core Saturation is the most influencing factor that shapes the current transformer transient response. The DC component The primary time constant The remnant flux in the core Short circuit current magnitude CT turns ratio Magnetizing characteristics of the core Inductance and resistance of the burden and secondary Fault inception time

9. Factors Affecting CT Saturation Core Characteristics BH curve (hysteresis loop) across all four quadrants Residual flux in the magnetic core Magnetizing characteristics (Rc and Lm) Current Parameters DC component magnitude and time constant (T) Short circuit current magnitude (Imax) Fault inception angle (θ) CT Design CT turn ratio Secondary leakage impedance Air gap design (affects remanence) Burden Parameters Resistance of burden (Rb) Inductance of burden (Lb) Lead impedance CT Classifications Based on Remanence Flux 1 Higher Remanence CT No limit to remanent flux; magnetic core has no air gap. Remanent flux can be as high as 80% of saturation flux. 2 Low Remanence CT Small air gap in the magnetic core arrangement limits remanent flux to below 10% of saturation flux. 3 Non-Remanence CT Large air gap reduces remanent flux to negligible values, minimizing DC component influence. However, air gap decreases measuring accuracy.

10. Impact of Burden on CT Saturation The graphs compare CT performance with different burden values: Blue curve: Primary current referred to secondary Green curves: Secondary current with saturation Left graph: 0.5-Ω resistive burden Right graph: 2-Ω resistive burden Key Observations With a 0.5-Ω burden , the CT secondary current (green) shows some distortion compared to the primary current (blue), but still follows it reasonably well. With a 2-Ω burden , saturation becomes much more prominent , causing severe distortion in the secondary current (red). Conclusion Higher burden resistance (Rb) results in more severe saturation . In practical applications, the burden includes: Lead impedance Relay impedance Other accessories connected to the CT secondary Reducing the burden can significantly improve CT performance during transient conditions.

11. Impact on Relay Performance Effects on Overcurrent Relay Performance CT saturation can significantly impact relay operation: RMS value of the fundamental current is drastically reduced during saturation For IDMT (Inverse Definite Minimum Time) relays, this results in longer operating times In severe cases, the current may fall below pickup value, preventing fault detection Backup protection may operate before the primary protection Subsidence Current Issue When breaker poles open, trapped magnetic energy in the CT exciting branch produces a unipolar decaying current with a large time constant, potentially delaying breaker failure detection.

12. Mitigation Strategies Mitigation Strategies CT Design Improvements Select appropriate CT class based on application requirements (higher/low/non-remanence) Burden Reduction Minimize lead length and impedance; use relays with lower burden requirements Relay Algorithm Enhancements Implement saturation detection algorithms in digital relays System Design Considerations Account for CT limitations in protection scheme design