--- title: "CT purpose, phasor diagram and errors" subject: "Switchgear and Protection" chapter: 2 key: "semester_6/switchgear_and_protection:ct-phasor-ratio-phase-error" source: https://www.bctengineer.com/q/semester_6/switchgear_and_protection/ct-phasor-ratio-phase-error site: BCT Engineering --- # CT purpose, phasor diagram and errors Switchgear and Protection · Chapter 2: Current and Potential Transformers - Asked in: 2073 Magh, 1+3 marks - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/switchgear_and_protection/ct-phasor-ratio-phase-error - Whole chapter: https://www.bctengineer.com/md/semester_6/switchgear_and_protection/chapter-2 ## Question What is the purpose of a CT? Draw a phasor diagram and explain briefly what are the ratio and phase angle error of CT? ## Short answer A CT steps down high line current for safe measurement and relaying, providing isolation. Ratio error is the percentage difference between nominal and actual ratios, caused by the loss component of exciting current. Phase angle error is the small angle β between primary current and reversed secondary current, due to the magnetizing component. ## Answer #### Purpose of a CT A current transformer steps down a high line current to a standard low value (1 A or 5 A) for meters and relays, and isolates them from the high-voltage circuit, so that standard low-rated instruments can be used safely. #### Phasor diagram of CT ```text Flux Φ is the reference (horizontal). −E_s −n·I_s ▲ ▲ ▲ I_p │ δ ╱ β ╱ │ ╱ ╱ │ ╱ ╱ │ ╱ ╱ │ ╱ ╱ _ ─▶ I₀ │╱ ╱_ ─ α O──────────────────► Φ I_m = I₀ cos α (along Φ), I_w = I₀ sin α (⊥ Φ) E_s lags Φ by 90°; I_s lags E_s by δ. I_p = (−n·I_s) + I₀ (phasor sum) ``` Where: Φ = core flux, E_s = secondary induced e.m.f., I_s = secondary current (lags E_s by the burden angle δ), −n·I_s = reversed secondary current referred to the primary, I₀ = exciting current, leading Φ by α, = I_m (magnetising, in phase with Φ) + I_w (loss, leading Φ by 90°), n = turns ratio N_s/N_p. The primary current I_p is the phasor sum of the reversed secondary current (n·I_s) and the exciting current I₀. Because of I₀, I_p is neither exactly n·I_s in magnitude nor exactly in phase with it; the reversed secondary current leads I_p by the small angle β. #### Ratio error The actual ratio R = I_p/I_s differs from the nominal ratio K_n: ```text R ≈ n + I₀ sin(δ + α) / I_s Ratio error (%) = (K_n − R) / R × 100 ``` It arises mainly from the loss component of I₀ and depends on the burden. #### Phase angle error β is the angle between I_p and the reversed I_s: ```text β ≈ (180/π) · I₀ cos(δ + α) / (n·I_s) degrees ``` It arises mainly from the magnetising component I_m. It is important for wattmeters, energy meters and directional relays. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What is the purpose of a CT? A. Step down line current to 1 A or 5 A and isolate meters and relays B. Step up current C. Convert AC to DC D. Store energy Answer: A. CTs allow safe standard low-rated instruments. (Key point: Purpose of CT) 2. What is the phasor relation in a CT? A. I_p = n I_s exactly B. I_p is the phasor sum of reversed n.I_s and I0 C. I_p = I0 only D. I_p = I_s - I0 in phase Answer: B. I0 causes magnitude and angle differences. (Key point: Phasor relation) 3. What are the components of I0? A. I_m leads flux; I_w in phase B. Both in phase with I_s C. Magnetising I_m (in phase with flux) and loss I_w (leads flux by 90 deg) D. Both zero Answer: C. Per the phasor description. (Key point: Components of I0) 4. How is phase angle error beta defined? A. Angle between flux and E_s B. Angle between I_s and I0 C. Burden angle D. Angle between I_p and reversed I_s Answer: D. It is the displacement of the reversed secondary current. 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