Purpose of Instrument Transformers
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Safety: Isolate measuring instruments from high voltage circuits
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Convenience: Step down high currents and voltages to measurable levels
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Standardization: Provide standard secondary values (5A for CT, 110V for PT)
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Protection: Enable protection relay operation
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Metering: Facilitate accurate measurement in power systems
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Economic: Reduce size and cost of measuring instruments
Current Transformer (CT) - Basic Principle
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Function: Steps down primary current to secondary current
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Construction: Primary has few turns, secondary has many turns
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Connection: Primary in series with line, secondary connects to ammeter
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Turns Ratio: \(\dfrac{N_s}{N_p} = \dfrac{I_p}{I_s}\) (ideal condition)
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Standard Secondary: 5A or 1A
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Important: Secondary should never be open-circuited
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Magnetizing Current: \(I_m = I_p - \dfrac{N_s}{N_p}I_s\)
CT - Types and Construction
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Wound Type: Separate primary and secondary windings
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Bar Type: Single conductor acts as primary
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Window Type: No primary winding, cable passes through window
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Toroidal Type: Doughnut-shaped core, uniform flux distribution
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Core Material: High permeability silicon steel, grain-oriented
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Insulation: Paper, oil, or SF6 for high voltage applications
CT Equivalent Circuit
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Primary: Referred to secondary as \(I_p' = \dfrac{N_p}{N_s}I_p\)
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Magnetizing Branch: \(I_m = I_c + I_L\) (core loss + magnetizing current)
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Secondary: \(I_s = I_p' - I_m\)
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Burden: \(Z_b\) connected to secondary
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Leakage: Primary and secondary leakage reactances
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Resistance: Primary and secondary resistances
Potential Transformer (PT) - Basic Principle
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Function: Steps down primary voltage to secondary voltage
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Construction: Similar to power transformer but smaller rating
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Connection: Primary in parallel with line, secondary connects to voltmeter
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Turns Ratio: \(\dfrac{N_p}{N_s} = \dfrac{V_p}{V_s}\) (ideal condition)
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Standard Secondary: 110V or 100V
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Important: Secondary should never be short-circuited
PT - Types
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Electromagnetic Type: Conventional wound transformer
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Capacitor Voltage Transformer (CVT): Uses capacitive voltage divider
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Single Phase: For single phase or phase-to-ground measurements
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Three Phase: For three phase measurements
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Ferro-resonance Type: For very high voltage applications
CT Errors
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Ratio Error: \(\epsilon_r = \dfrac{K_n I_s - I_p}{I_p} \times 100\%\)
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Phase Error: \(\delta\) = phase difference between primary and secondary currents
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Causes: Magnetizing current, core losses, leakage flux
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Minimization: Low reluctance core, proper burden selection
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Saturation: Occurs at high fault currents, affects accuracy
Where \(K_n\) is nominal ratio = \(\dfrac{N_s}{N_p}\)
PT Errors
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Ratio Error: \(\epsilon_r = \dfrac{K_n V_s - V_p}{V_p} \times 100\%\)
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Phase Error: \(\delta\) = phase difference between primary and secondary voltages
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Causes: Magnetizing current, core losses, winding resistance
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Minimization: High permeability core, low burden
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Ferranti Effect: Secondary voltage may exceed primary in long lines
Where \(K_n\) is nominal ratio = \(\dfrac{N_p}{N_s}\)
Phasor Diagrams
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CT Phasor: \(I_p = I_s' + I_m\) where \(I_s' = \dfrac{N_s}{N_p}I_s\)
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Phase Error: \(\delta = \tan^{-1}\left(\dfrac{I_m \sin \phi}{I_p + I_m \cos \phi}\right)\)
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PT Phasor: \(V_p = V_s' + I_s Z_{eq}\) where \(V_s' = \dfrac{N_p}{N_s}V_s\)
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Error Reduction: Minimize magnetizing current and burden
Accuracy Classes
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CT Classes: 0.1, 0.2, 0.5, 1.0, 3.0, 5.0
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PT Classes: 0.1, 0.2, 0.5, 1.0, 3.0
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Meaning: Maximum permissible error at rated burden
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Metering: Classes 0.2, 0.5 for revenue metering
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Protection: Classes 5P, 10P for protection applications
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Special Classes: Class X for differential protection
Burden and VA Rating
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Burden: Total impedance of secondary circuit
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CT Burden: \(Z_b = \dfrac{V_s}{I_s}\) where \(V_s\) is secondary voltage
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PT Burden: \(Z_b = \dfrac{V_s^2}{VA}\) where VA is apparent power
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Standard Burdens: 2.5, 5, 10, 15, 30 VA
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Effect: Higher burden increases errors
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Power Factor: Burden power factor affects accuracy
Testing of Instrument Transformers
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Ratio Test: Verify turns ratio using bridge methods
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Polarity Test: Check instantaneous polarity markings
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Burden Test: Measure secondary circuit impedance
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Accuracy Test: Determine ratio and phase errors
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Insulation Test: High voltage and impulse tests
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Saturation Test: For CTs to find knee point voltage
CT Saturation and Knee Point
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Knee Point: Voltage at which 10% increase causes 50% current increase
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Saturation: Occurs when core flux density reaches maximum
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Effect: Severe ratio and phase errors during saturation
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Testing: Apply voltage to secondary, measure exciting current
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Applications: Critical for protection CT selection
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ALF: Accuracy Limit Factor = (Knee Point Voltage)/(Rated Burden Voltage)
Safety Considerations
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CT Secondary: Must never be open-circuited (causes dangerous voltages)
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PT Secondary: Must never be short-circuited (causes excessive current)
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Earthing: One point of secondary must be earthed
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Polarity: Proper polarity marking essential for measurements
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Short-circuiting: CT secondary terminals during maintenance
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Insulation: Adequate insulation levels for operating voltage
Applications
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Metering: Energy meters, power factor meters, demand meters
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Protection: Overcurrent relays, distance relays, differential relays
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Control: Automatic voltage regulators, load tap changers
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Monitoring: SCADA systems, power quality analyzers
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Measurement: Ammeters, voltmeters, wattmeters, varmeters
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Synchronization: Synchroscopes, synchronizing relays
Special Applications
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Multi-ratio CTs: Multiple secondary taps for different ratios
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Summation CTs: Combine currents from multiple circuits
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Bushing CTs: Built into equipment bushings
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Rogowski Coils: Air-core current sensors for high frequencies
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Optical CTs: Using Faraday effect for high voltage applications
Key Formulas for GATE
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CT Ratio: \(K_n = \dfrac{N_s}{N_p} = \dfrac{I_p}{I_s}\) (ideal)
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PT Ratio: \(K_n = \dfrac{N_p}{N_s} = \dfrac{V_p}{V_s}\) (ideal)
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Ratio Error: \(\epsilon_r = \dfrac{K_n \times \text{Secondary} - \text{Primary}}{\text{Primary}} \times 100\%\)
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Burden: \(Z_b = \dfrac{V_s}{I_s}\) (CT), \(Z_b = \dfrac{V_s^2}{VA}\) (PT)
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Phase Error: \(\delta = \tan^{-1}\left(\dfrac{I_m \sin \phi}{I_p + I_m \cos \phi}\right)\)
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Magnetizing Current: \(I_m = I_p - \dfrac{N_s}{N_p}I_s\)
Important Points for GATE
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CT secondary should never be open-circuited
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PT secondary should never be short-circuited
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Accuracy class indicates maximum permissible error
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Higher burden increases transformer errors
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Polarity marking is crucial for proper operation
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Standard secondary values: 5A (CT), 110V (PT)
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Phase error occurs due to magnetizing current
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Knee point voltage is critical for protection CTs
Numerical Problem Types
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Ratio Error Calculation: Given primary, secondary currents/voltages
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Phase Error Calculation: Using magnetizing current and burden
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Burden Calculation: From connected instrument specifications
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Accuracy Class Problems: Determining suitable class for application
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Saturation Analysis: Finding knee point and ALF
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Error Correction: Calculating true values from measured values