--- title: "Knee point voltage and CT errors" subject: "Switchgear and Protection" chapter: 2 key: "semester_6/switchgear_and_protection:knee-point-ct-errors" source: https://www.bctengineer.com/q/semester_6/switchgear_and_protection/knee-point-ct-errors site: BCT Engineering --- # Knee point voltage and CT errors Switchgear and Protection · Chapter 2: Current and Potential Transformers - Asked in: 2080 Chaitra, 5 marks - Video: [Switchgear and Protection Course: Lecture 12c - Current Transformer Saturation](https://www.youtube.com/watch?v=U9QE8lF_PX4) — Dr. Ahmad Al-Subhi - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/switchgear_and_protection/knee-point-ct-errors - Whole chapter: https://www.bctengineer.com/md/semester_6/switchgear_and_protection/chapter-2 ## Question What do you mean by typical knee point voltage in relation to CT? Briefly explain the different errors of CT and its causes. ## Short answer Knee point voltage is the secondary e.m.f. at which a 10% increase causes a 50% rise in exciting current, marking the onset of saturation. CT errors include ratio error due to the loss component of exciting current, phase angle error from the magnetizing component, and composite error. High burden, saturation, and remanent flux are key causes. ## Answer #### Typical knee point voltage The **knee point voltage (Vk)** of a CT is the secondary e.m.f. at which a 10 % rise in voltage causes a 50 % rise in exciting current. It is the boundary between the linear part of the excitation curve and saturation. ```text Vs │ ______ saturation │ Vk ● │ / │ / linear (accurate) region └──────/──────────────── Ie ``` - Below Vk the CT transforms current accurately; above it the core saturates and secondary current is distorted and reduced. - A protective CT must have Vk higher than the voltage needed to drive the maximum fault current through its burden: Vk ≥ K·I_f(sec)·(R_ct + R_lead + R_relay). Typical values are a few hundred volts for protection CTs and much lower for metering CTs. #### Errors of CT and their causes An ideal CT has I_s = I_p / K_n exactly in phase opposition. In practice part of the primary ampere-turns is used to supply the exciting current I₀, causing errors. 1. **Ratio (current) error:** difference between actual and nominal ratio, `Current error % = (K_n·I_s − I_p) / I_p × 100` *Cause:* the loss component of I₀ (in phase with I_s) reduces I_s; also burden power factor. 2. **Phase angle error (phase displacement, β):** angle between the primary current and the reversed secondary current. *Cause:* the magnetising component of I₀ (in phase with flux) makes I_s lag/lead the ideal phasor. 3. **Composite error:** r.m.s. value of the difference between ideal and actual secondary current over a cycle, including harmonics caused by saturation (important for protective CTs). **Causes and factors increasing errors** - High exciting current due to poor core material or high flux density. - **High burden** (impedance of relays + leads) – requires more e.m.f., more flux, more I₀. - Burden power factor (inductive burden increases ratio error; resistive increases phase error). - **Saturation** due to high fault current or DC offset; **remanent flux** in core. - Low primary current (operating near ankle region, low permeability). - Frequency different from rated. Errors are reduced by using high-permeability cores (CRGO, nickel-iron), low flux density, low burden and turn compensation. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What mainly causes ratio error in a CT? A. Magnetising component only B. Frequency of primary C. Loss component of exciting current D. Remote breaker Answer: C. The loss component, in phase with I_s, reduces I_s. (Key point: Ratio error cause) 2. What mainly causes phase angle error? A. Magnetising component of exciting current B. Loss component only C. Fault current DC offset only D. CT ratio Answer: A. The magnetising component displaces I_s from the ideal phasor. (Key point: Phase error cause) 3. What is composite error? A. Difference in ratio only B. R.m.s. difference between ideal and actual secondary current over a cycle, including harmonics C. Phase angle only D. Burden VA mismatch Answer: B. It is the main specified error for protective CTs. (Key point: Composite error) 4. How does higher burden affect CT errors? A. It reduces errors B. It has no effect C. It only affects phase error D. It needs more e.m.f. and flux, so more exciting current and larger errors Answer: D. Greater burden increases I0 and errors. (Key point: Burden effect) ## Related in Switchgear and Protection - [Knee point voltage; measuring vs protective CT](https://www.bctengineer.com/question.md?key=semester_6%2Fswitchgear_and_protection%3Aknee-point-measuring-protective-ct) — Switchgear and Protection, chapter 2 - [Knee point voltage and CT selection](https://www.bctengineer.com/question.md?key=semester_6%2Fswitchgear_and_protection%3Aknee-point-ct-selection) — Switchgear and Protection, chapter 2 - [Different errors of CT](https://www.bctengineer.com/question.md?key=semester_6%2Fswitchgear_and_protection%3Aerrors-of-ct) — Switchgear and Protection, chapter 2 - [Need of instrument transformers; CT errors](https://www.bctengineer.com/question.md?key=semester_6%2Fswitchgear_and_protection%3Ainstrument-transformers-need-ct-errors) — Switchgear and Protection, chapter 2 - [CT purpose, phasor diagram and errors](https://www.bctengineer.com/question.md?key=semester_6%2Fswitchgear_and_protection%3Act-phasor-ratio-phase-error) — Switchgear and Protection, chapter 2 - [Causes of PT ratio and phase errors](https://www.bctengineer.com/question.md?key=semester_6%2Fswitchgear_and_protection%3Apt-ratio-phase-angle-error) — Switchgear and Protection, chapter 2 ## Related in other subjects - [Typical voltage levels and why three-phase](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Atypical-voltage-levels-three-phase) — Power System Analysis I, chapter 1 - [Typical power system with voltage levels](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Atypical-power-system-voltage-levels) — Power System Analysis I, chapter 1 - [Parseval's relation for CT periodic signals](https://www.bctengineer.com/question.md?key=semester_4%2Fsignals_and_systems%3Actfs-parseval) — Signals and Systems, chapter 2, asked 4×