This document discusses testing, efficiency, and regulation of transformers. It describes how open circuit and short circuit tests are used to determine the parameters of an equivalent circuit model for a transformer. The open circuit test provides the magnetizing reactance and core loss resistance, while the short circuit test provides the winding resistance and leakage reactance. Transformer efficiency is defined and an expression is derived showing it depends on loading level and power factor. Maximum efficiency occurs when loading equals the ratio of core to copper losses. Regulation is also introduced but not defined. All-day efficiency accounts for varying loads over time to assess overall transformer performance.
To understand the basic working principle of a transformer.
To obtain the equivalent circuit parameters from Open circuit and Short circuit tests, and to estimate efficiency & regulation at various loads.
1. Transformer tests are conducted to determine the equivalent circuit parameters of a transformer and to evaluate its performance under various load conditions. Common tests include winding resistance, polarity, open circuit, short circuit, and load tests.
2. The load test is most important for determining the rated load and temperature rise of a transformer, but it is difficult to conduct with large transformers due to the need for a suitable load. Therefore, equivalent loss and phantom loading methods are commonly used to simulate full load testing.
3. Phantom loading uses two identical transformers connected back-to-back to simulate full load current flow without wasting real power. It subjects the transformers to full flux and current drawing conditions similar to actual loading.
OPEN CIRCUIT AND SHORT CIRCUIT TEST OF SINGLE PHASE TRANSFORMER|DAY7| BASIC E...Prasant Kumar
#Open_circuit_short_circuit_test of single phase transformer
#OC_SC_TEST OF TRANSFORMER
#Core loss and copper loss test of single phase transformer.
After going through this session you will be able to answer the following questions.
• Which parameters are obtained from O.C test?
• Which parameters are obtained from S.C test?
• What percentage of rated voltage is needed to be applied to carry out O.C test?
• What percentage of rated voltage is needed to be applied to carry out S.C test?
• From which side of a large transformer, would you like to carry out O.C test?
• From which side of a large transformer, would you like to carry out S.C test?
Aim of conduction transformer Open Circuit & Short Circuit test
To predict its performance without actual loading.
Determination of equivalent circuit parameters
To determine parameters of a transformer like voltage regulation and efficiency
Open circuit test is carried out to determine core loss and shunt parameters.
Open circuit test is carried out at rated voltage and rated frequency . During this test, rated flux is produced in the core .
To carry out open circuit test rated voltage at rated frequency is applied to LV side of the transformer and HV side is left opened as shown in the circuit diagram.
HV side is left opened because it is easier to arrange rated voltage supply on LV side because no load current which is quite small about 2 to 5% of the rated current.
Metering instrument connected at LV side are economical & always safer to work.
The voltmeter, ammeter and the wattmeter readings are taken and suppose they are Voc , Io and Poc respectively.
Strictly speaking the wattmeter will record the core loss as well as the LV winding copper loss. But the winding copper loss is very small compared to the core loss as the flux in the core is rated.
This experiment involves drawing the V and inverted V curves of a 3-phase synchronous motor under no-load and load conditions. The V curve shows the relationship between field current (I) and terminal voltage (V) of the motor. The inverted V curve shows the relationship between power factor and field current. Under normal excitation, the power factor is unity. Under-excitation results in lagging power factor while over-excitation results in leading power factor. The curves are drawn to determine the operating characteristics of the synchronous motor at different excitation levels.
This document discusses various tests performed on transformers to determine their electrical parameters and ratings. The key tests described are:
1. Winding resistance test to measure the resistance of transformer windings.
2. Polarity test to identify the primary and secondary polarities using AC or DC methods.
3. Open circuit test to determine core losses, magnetizing current, and core and leakage impedances with the secondary open.
4. Short circuit test to determine series branch parameters like copper and leakage impedances with the secondary shorted.
5. Load test to determine rated load and temperature rise under load, but it is difficult to implement for large transformers so equivalent loss methods are commonly used instead.
This technical report describes the design, simulation, construction and testing of a positive DC switch mode power supply with short circuit current limiting. The design was based on the SG3524 regulating pulse width modulator integrated circuit. Key measurements showed the circuit maintained a constant 8.5V output voltage and was able to supply 250mA of load current or go into current limiting mode during a short circuit. The efficiency was 74.5% and line and load regulation were both under 1%. While the design met its goals, the output ripple voltage was greater than intended due to a larger than expected filter capacitor being required.
A transformer is a static electrical device that transfers electrical energy between two or more circuits. A varying current in one coil of the transformer produces a varying magnetic flux, which, in turn, induces a varying electromotive force across a second coil wound around the same core. Electrical energy can be transferred between the two coils, without a metallic connection between the two circuits. Faraday's law of induction discovered in 1831 described the induced voltage effect in any coil due to changing magnetic flux encircled by the coil
This document describes an AC-DC matrix converter based on a Cockcroft-Walton voltage multiplier circuit. The converter uses a four bidirectional-switch matrix converter between an AC source and a CW circuit to provide high power factor, adjustable output voltage, and low output ripple. The matrix converter operates at two frequencies - one for power factor correction control and one to set the output frequency. Simulation results show the converter improves efficiency and power factor while reducing output voltage ripple compared to a conventional CW circuit. A 10V AC to 50V DC prototype was built and tested.
To understand the basic working principle of a transformer.
To obtain the equivalent circuit parameters from Open circuit and Short circuit tests, and to estimate efficiency & regulation at various loads.
1. Transformer tests are conducted to determine the equivalent circuit parameters of a transformer and to evaluate its performance under various load conditions. Common tests include winding resistance, polarity, open circuit, short circuit, and load tests.
2. The load test is most important for determining the rated load and temperature rise of a transformer, but it is difficult to conduct with large transformers due to the need for a suitable load. Therefore, equivalent loss and phantom loading methods are commonly used to simulate full load testing.
3. Phantom loading uses two identical transformers connected back-to-back to simulate full load current flow without wasting real power. It subjects the transformers to full flux and current drawing conditions similar to actual loading.
OPEN CIRCUIT AND SHORT CIRCUIT TEST OF SINGLE PHASE TRANSFORMER|DAY7| BASIC E...Prasant Kumar
#Open_circuit_short_circuit_test of single phase transformer
#OC_SC_TEST OF TRANSFORMER
#Core loss and copper loss test of single phase transformer.
After going through this session you will be able to answer the following questions.
• Which parameters are obtained from O.C test?
• Which parameters are obtained from S.C test?
• What percentage of rated voltage is needed to be applied to carry out O.C test?
• What percentage of rated voltage is needed to be applied to carry out S.C test?
• From which side of a large transformer, would you like to carry out O.C test?
• From which side of a large transformer, would you like to carry out S.C test?
Aim of conduction transformer Open Circuit & Short Circuit test
To predict its performance without actual loading.
Determination of equivalent circuit parameters
To determine parameters of a transformer like voltage regulation and efficiency
Open circuit test is carried out to determine core loss and shunt parameters.
Open circuit test is carried out at rated voltage and rated frequency . During this test, rated flux is produced in the core .
To carry out open circuit test rated voltage at rated frequency is applied to LV side of the transformer and HV side is left opened as shown in the circuit diagram.
HV side is left opened because it is easier to arrange rated voltage supply on LV side because no load current which is quite small about 2 to 5% of the rated current.
Metering instrument connected at LV side are economical & always safer to work.
The voltmeter, ammeter and the wattmeter readings are taken and suppose they are Voc , Io and Poc respectively.
Strictly speaking the wattmeter will record the core loss as well as the LV winding copper loss. But the winding copper loss is very small compared to the core loss as the flux in the core is rated.
This experiment involves drawing the V and inverted V curves of a 3-phase synchronous motor under no-load and load conditions. The V curve shows the relationship between field current (I) and terminal voltage (V) of the motor. The inverted V curve shows the relationship between power factor and field current. Under normal excitation, the power factor is unity. Under-excitation results in lagging power factor while over-excitation results in leading power factor. The curves are drawn to determine the operating characteristics of the synchronous motor at different excitation levels.
This document discusses various tests performed on transformers to determine their electrical parameters and ratings. The key tests described are:
1. Winding resistance test to measure the resistance of transformer windings.
2. Polarity test to identify the primary and secondary polarities using AC or DC methods.
3. Open circuit test to determine core losses, magnetizing current, and core and leakage impedances with the secondary open.
4. Short circuit test to determine series branch parameters like copper and leakage impedances with the secondary shorted.
5. Load test to determine rated load and temperature rise under load, but it is difficult to implement for large transformers so equivalent loss methods are commonly used instead.
This technical report describes the design, simulation, construction and testing of a positive DC switch mode power supply with short circuit current limiting. The design was based on the SG3524 regulating pulse width modulator integrated circuit. Key measurements showed the circuit maintained a constant 8.5V output voltage and was able to supply 250mA of load current or go into current limiting mode during a short circuit. The efficiency was 74.5% and line and load regulation were both under 1%. While the design met its goals, the output ripple voltage was greater than intended due to a larger than expected filter capacitor being required.
A transformer is a static electrical device that transfers electrical energy between two or more circuits. A varying current in one coil of the transformer produces a varying magnetic flux, which, in turn, induces a varying electromotive force across a second coil wound around the same core. Electrical energy can be transferred between the two coils, without a metallic connection between the two circuits. Faraday's law of induction discovered in 1831 described the induced voltage effect in any coil due to changing magnetic flux encircled by the coil
This document describes an AC-DC matrix converter based on a Cockcroft-Walton voltage multiplier circuit. The converter uses a four bidirectional-switch matrix converter between an AC source and a CW circuit to provide high power factor, adjustable output voltage, and low output ripple. The matrix converter operates at two frequencies - one for power factor correction control and one to set the output frequency. Simulation results show the converter improves efficiency and power factor while reducing output voltage ripple compared to a conventional CW circuit. A 10V AC to 50V DC prototype was built and tested.
The document discusses uncontrolled rectifiers, which provide a fixed DC output voltage from an AC supply using diodes. It describes single-phase half-wave and full-wave uncontrolled rectifiers with resistive and resistive-inductive loads. For a half-wave rectifier with resistive load, the average DC output voltage is half the peak AC input voltage. A full-wave rectifier doubles this output voltage by using two pairs of diodes to conduct during both half-cycles of the AC input. Rectifiers with resistive-inductive loads have more complex non-sinusoidal current waveforms that decay during the negative half-cycles.
This document summarizes a lab report on designing and testing an open loop buck converter circuit. The circuit was first designed and tested in simulations to ensure it met specifications. Key parameters like inductor and capacitor values were calculated. Simulation tests showed the output voltage met requirements when load current was varied and efficiency was above 75% at maximum load. Hardware was then implemented using the simulated design. Testing of the built circuit showed results matching simulations, with output voltage and current values meeting requirements when load was changed and dynamic voltage changes below 0.75V.
This document provides instructions for Laboratory 2 of an Electrical Engineering fundamentals lab manual. The lab focuses on voltage and current dividers, as well as Wheatstone bridges. Students are asked to complete pre-lab calculations and simulations to analyze voltage and current dividers, and open/short circuit conditions of a Wheatstone bridge. The objectives are to understand how voltage and current dividers work, validate formulas for output voltage and current, understand the impact of load resistors, and analyze Wheatstone bridges. Students will build divider circuits in lab and record measurements to compare to their pre-lab calculations and simulations.
An A.C. device used to change high voltage low current A.C. into low voltage high current A.C. and vice-versa without changing the frequency
In brief,
1. Transfers electric power from one circuit to another
2. It does so without a change of frequency
3. It accomplishes this by electromagnetic induction
4. Where the two electric circuits are in mutual inductive influence of each other.
This document describes the design of a non-ideal buck converter circuit. Key aspects include:
- The buck converter steps down the voltage from a 350V LiPo battery to 48V for a lead acid battery.
- Components are selected to handle non-idealities like resistance and voltage drops. These include a MOSFET, diode, inductor, and capacitor.
- Calculations are done to determine duty cycle, inductor value, and capacitor value based on specifications like output voltage, current, and power.
- A Pspice simulation is used to validate the circuit design and analyze performance considering component non-idealities.
Interleaved High Step-Down Synchronous Convertertheijes
For low output voltage, high output current systems applications, Synchronous switching power converters give better performance than non synchronous converters. This paper presents an interleaved synchronous buck converter which has low switch voltage stress with high conversion ratio. The input current can be shared among the inductors so that high reliability and efficiency can be obtained and ripples also reduced, the converter performance can be improved. Thus converter features automatic uniform current sharing characteristic of the interleaved phases without adding extra circuitry or complex control methods. Capacitors switching circuits are combined with interleaved four-phase buck converter for getting a high step-down conversion ratio without adopting an extreme short duty ratio. Synchronous rectifier technology is adopted to increase the converter efficiency. A 30V input voltage, 1.8V output voltage, circuit is simulated to verify the performance. The simulation is done in MATLAB/SIMULINK R2012a.
This manual consists of some important experiments of ac electrical machines.This is prepared by satish babu and lokesh.They are working as staff in usha rama college,telaprolu.
- The document describes the design, modeling, and simulation of a fuzzy logic controlled static VAR compensator (SVC) for a transmission line.
- An SVC uses thyristor-controlled reactors and fixed capacitors to continuously regulate the voltage of a transmission line by absorbing or producing reactive power.
- A fuzzy logic controller is designed to control the firing angle of the thyristors to maintain a constant voltage at the receiving end of the transmission line for different load conditions. Simulations are carried out to demonstrate the effectiveness of the fuzzy controlled SVC.
Abstract:-This paper deals with open loop study of fixed capacitor thyristor controlled reactor (FC-TCR) system simulation using Matlab/Simulink for various loading. The modelling of the FC-TCR is verified using the Matlab/Simulink. First power flow results are obtained and power profile have been studied for an uncompensated then results are compared with the results obtained after compensating using the FC-TCR.Its observed that current drawn by FC-TCR is varied by changing firing angle. In compensation without FC-TCR, load increases and power factor become less and in compensation with FC-TCR, load increases and power factor become near to the unity.Hence by providing compensation Voltage, power profile of system will be improved and system losses are reduced.
1) The document presents a technical summary of a power flow analysis for a system consisting of 5 generating stations providing power to a collector substation through a 34.5 KV cable.
2) An initial case with 0 load found no contingency violations, allowing further analysis. A case with assumed loads of 2.5 MVA for the wind turbine and 100 MVA for other equipment found 10 contingency violations.
3) Upgrading the transformer connecting the wind turbine to 25.5 MVA eliminated contingency violations and overloads, providing a solution to safely operate the system within equipment ratings.
IRJET- Simulation of Energization and De-Energization of Capacitor Banks and ...IRJET Journal
This document discusses simulation of transient overvoltages caused by energization and de-energization of capacitor banks in distribution systems. The key points are:
1. Energization of capacitor banks causes larger transient overvoltage peaks compared to de-energization. Peak voltages of 2.48 PU and currents of 2567 A were observed during energization.
2. Different mitigation techniques for transients were simulated, including pre-insertion resistors, inductors, and impedance. Pre-insertion impedance was found to be most effective at reducing transients.
3. Total harmonic distortion of voltages reached 35.34% during energization and 15.34% during de-energization without
This document provides a summary of a lecture on series RLC circuits. It begins with objectives of analyzing series RL, RC, and RLC circuits. It then derives the phasor diagrams for each circuit, showing voltage and current relationships. Key points covered include impedance, power factor, and phase angle calculations. Example questions are provided for reinforcement. The intended learning outcomes are for students to understand the concepts and phasor representations of series R, L, C circuits.
1.SINGLE PHASE HALF WAVE CONTROLLED CONVERTER WITH RESISTIVEINDUCTIVE LOAD
2 SINGLE PHASE FULLY CONTROLLED CONVERTER WITH RESISTIVEINDUCTIVE LOAD
3 SPEED CONTROL OF 3-PHASE SLIP RING (WOUND ROTOR) INDUCTION MOTOR
4 THYRISTORISED DRIVE FOR DC MOTOR WITH CLOSED LOOP CONTROL
5 THYRISTORISED DRIVE FOR PMDC MOTOR WITH SPEED MEASUREMENT & CLOSED LOOP CONTROL
6 SPEED MEASUREMENT OF PMDC MOTOR WITH CLOSED LOOP CONTROL
7 IGBT USING SINGLE 4 QUADRANT CHOPPER DRIVE FOR PMDC MOTOR WITH SPEED MEASUREMENT AND CLOSED LOOP AND CONTROL
8 SINGLE PHASE CYCLO CONVERTER BASED AC INDUCTION MOTOR CONTROLLER
9 THREE PHASE INPUT THYRISTORISED DRIVE 3HP DC MOTOR WITH CLOSED LOOP CONTROL
10 THREE PHASE INPUT IGBT DRIVE FOR 4 QUADRANT CHOPPER OF 3HP DC MOTOR WITH CLOSED LOOP CONTROL
This document provides instructions for testing the short-circuit impedance and load loss of transformers. The short-circuit voltage and loss show the transformer's performance and are important specifications. To measure: the HV windings are supplied while the LV windings are short-circuited, applying a current close to the rated current. Voltage, current and losses are measured in each phase. Losses are corrected to a reference temperature and separated into DC and AC components. Measurements are made at rated, maximum and minimum ranges.
Simulation and Experimental Verification of Single-Phase Pwm Boost -Rectifier...IRJET Journal
This document summarizes a simulation and experimental study of a single-phase PWM boost rectifier with controlled power factor. Key points:
- The rectifier uses IGBT transistors in a full bridge configuration to provide PWM control of input current and regulated DC output voltage.
- Simulation results in MATLAB show the rectifier can operate at unity power factor as well as leading and lagging power factors, with low harmonic distortion of input current.
- An experimental prototype was built using an Intel microcontroller to implement the control algorithm. Experimental waveforms verify unity power factor operation with sinusoidal input current.
Experimental simulation analysis for single phase transformer testsjournalBEEI
Transformer is one of main components in electrical power system which role to increase or reduce voltage. Characteristics of transformer would be vital to ensure the voltage is fully transferred. A single-phase transformer is a type of power transformer that utilizes single-phase alternating current, meaning the transformer relies on a voltage cycle that operates in a unified time phase. This article describes a workflow executed with Mat lab simulation and practical measurements for single-phase power transformer, no-load, short-circuit test and load test are achieved in this work. The test procedures are implemented on areal transformer (terco-type) which has a specification (1 KVA, 220/110 V, 50 Hz). Finally, the simulation results are appeared a proximately seminar from the practical results. The results indicated that the the technique and manner which presented in the current study can be depended as a miniproject in electrical technology mater for undergraduate studies.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
IRJET-Comparative Analysis of Rectangular and Square Column for Axial loading...IRJET Journal
This document describes the design and simulation of a Cockcroft-Walton voltage multiplier circuit to generate high voltage from a low input voltage. The circuit uses a ladder network of capacitors and diodes to multiply the input voltage in successive stages. The document discusses the design considerations for components based on expected output voltage and current. It also presents the simulation results showing the output voltage increasing with each stage up to 100kV at the final stage, along with the associated ripple voltage. The summary concludes that the designed circuit provides a small, low-cost way to generate high voltages for laboratory applications.
This document is an electrical machines lab manual containing experiments on various electrical machines and components used in engineering college. It provides details on 13 experiments including load tests on a single phase transformer, 3-phase squirrel cage induction motor, DC shunt generator, DC series motor, measurement of transformer coil coupling and resistance measurement techniques. The manual was prepared by three students and guided by an associate professor. It was created using LaTeX and various free Linux software and is licensed under a Creative Commons license.
This document provides information about transformer tests conducted at BEST Balıkesir Transformer Factory laboratories. It describes routine tests like winding resistance measurement, voltage ratio measurement and phase checking, as well as type tests and special tests. The routine tests section explains test procedures and equipment for various tests done on all transformers produced. These include impedance measurement, no-load loss tests, and tap changer tests. Type and special tests involve temperature rise testing, lightning impulse testing, and other advanced analyses. Laboratory equipment for performing over a dozen transformer tests is also listed.
U2 Thyristor open circuit troubleshooting 23_Jan_2019.pptxasprilla mangombe
The document summarizes troubleshooting done for a thyristor open circuit alarm on a power station unit. Actions taken included monitoring the exciter PLC and collecting raw data. Findings showed the alarm was occurring when either converter was in use, currents were balanced, and signals from two analogue input modules were lower. It was recommended to check the functionality of the DCCTs with a process calibrator.
The document discusses the Motorola HC11 microcontroller. It provides an overview of microcontrollers in general and describes some key features of the HC11, including its CPU core, addressing modes, instruction set, and programming. The HC11 has an 8-bit CPU, on-chip memory and peripherals, and supports various addressing modes and instruction types for arithmetic, logical, and program control operations. It is commonly used in embedded systems and products like appliances, thermostats, and industrial equipment.
The document discusses uncontrolled rectifiers, which provide a fixed DC output voltage from an AC supply using diodes. It describes single-phase half-wave and full-wave uncontrolled rectifiers with resistive and resistive-inductive loads. For a half-wave rectifier with resistive load, the average DC output voltage is half the peak AC input voltage. A full-wave rectifier doubles this output voltage by using two pairs of diodes to conduct during both half-cycles of the AC input. Rectifiers with resistive-inductive loads have more complex non-sinusoidal current waveforms that decay during the negative half-cycles.
This document summarizes a lab report on designing and testing an open loop buck converter circuit. The circuit was first designed and tested in simulations to ensure it met specifications. Key parameters like inductor and capacitor values were calculated. Simulation tests showed the output voltage met requirements when load current was varied and efficiency was above 75% at maximum load. Hardware was then implemented using the simulated design. Testing of the built circuit showed results matching simulations, with output voltage and current values meeting requirements when load was changed and dynamic voltage changes below 0.75V.
This document provides instructions for Laboratory 2 of an Electrical Engineering fundamentals lab manual. The lab focuses on voltage and current dividers, as well as Wheatstone bridges. Students are asked to complete pre-lab calculations and simulations to analyze voltage and current dividers, and open/short circuit conditions of a Wheatstone bridge. The objectives are to understand how voltage and current dividers work, validate formulas for output voltage and current, understand the impact of load resistors, and analyze Wheatstone bridges. Students will build divider circuits in lab and record measurements to compare to their pre-lab calculations and simulations.
An A.C. device used to change high voltage low current A.C. into low voltage high current A.C. and vice-versa without changing the frequency
In brief,
1. Transfers electric power from one circuit to another
2. It does so without a change of frequency
3. It accomplishes this by electromagnetic induction
4. Where the two electric circuits are in mutual inductive influence of each other.
This document describes the design of a non-ideal buck converter circuit. Key aspects include:
- The buck converter steps down the voltage from a 350V LiPo battery to 48V for a lead acid battery.
- Components are selected to handle non-idealities like resistance and voltage drops. These include a MOSFET, diode, inductor, and capacitor.
- Calculations are done to determine duty cycle, inductor value, and capacitor value based on specifications like output voltage, current, and power.
- A Pspice simulation is used to validate the circuit design and analyze performance considering component non-idealities.
Interleaved High Step-Down Synchronous Convertertheijes
For low output voltage, high output current systems applications, Synchronous switching power converters give better performance than non synchronous converters. This paper presents an interleaved synchronous buck converter which has low switch voltage stress with high conversion ratio. The input current can be shared among the inductors so that high reliability and efficiency can be obtained and ripples also reduced, the converter performance can be improved. Thus converter features automatic uniform current sharing characteristic of the interleaved phases without adding extra circuitry or complex control methods. Capacitors switching circuits are combined with interleaved four-phase buck converter for getting a high step-down conversion ratio without adopting an extreme short duty ratio. Synchronous rectifier technology is adopted to increase the converter efficiency. A 30V input voltage, 1.8V output voltage, circuit is simulated to verify the performance. The simulation is done in MATLAB/SIMULINK R2012a.
This manual consists of some important experiments of ac electrical machines.This is prepared by satish babu and lokesh.They are working as staff in usha rama college,telaprolu.
- The document describes the design, modeling, and simulation of a fuzzy logic controlled static VAR compensator (SVC) for a transmission line.
- An SVC uses thyristor-controlled reactors and fixed capacitors to continuously regulate the voltage of a transmission line by absorbing or producing reactive power.
- A fuzzy logic controller is designed to control the firing angle of the thyristors to maintain a constant voltage at the receiving end of the transmission line for different load conditions. Simulations are carried out to demonstrate the effectiveness of the fuzzy controlled SVC.
Abstract:-This paper deals with open loop study of fixed capacitor thyristor controlled reactor (FC-TCR) system simulation using Matlab/Simulink for various loading. The modelling of the FC-TCR is verified using the Matlab/Simulink. First power flow results are obtained and power profile have been studied for an uncompensated then results are compared with the results obtained after compensating using the FC-TCR.Its observed that current drawn by FC-TCR is varied by changing firing angle. In compensation without FC-TCR, load increases and power factor become less and in compensation with FC-TCR, load increases and power factor become near to the unity.Hence by providing compensation Voltage, power profile of system will be improved and system losses are reduced.
1) The document presents a technical summary of a power flow analysis for a system consisting of 5 generating stations providing power to a collector substation through a 34.5 KV cable.
2) An initial case with 0 load found no contingency violations, allowing further analysis. A case with assumed loads of 2.5 MVA for the wind turbine and 100 MVA for other equipment found 10 contingency violations.
3) Upgrading the transformer connecting the wind turbine to 25.5 MVA eliminated contingency violations and overloads, providing a solution to safely operate the system within equipment ratings.
IRJET- Simulation of Energization and De-Energization of Capacitor Banks and ...IRJET Journal
This document discusses simulation of transient overvoltages caused by energization and de-energization of capacitor banks in distribution systems. The key points are:
1. Energization of capacitor banks causes larger transient overvoltage peaks compared to de-energization. Peak voltages of 2.48 PU and currents of 2567 A were observed during energization.
2. Different mitigation techniques for transients were simulated, including pre-insertion resistors, inductors, and impedance. Pre-insertion impedance was found to be most effective at reducing transients.
3. Total harmonic distortion of voltages reached 35.34% during energization and 15.34% during de-energization without
This document provides a summary of a lecture on series RLC circuits. It begins with objectives of analyzing series RL, RC, and RLC circuits. It then derives the phasor diagrams for each circuit, showing voltage and current relationships. Key points covered include impedance, power factor, and phase angle calculations. Example questions are provided for reinforcement. The intended learning outcomes are for students to understand the concepts and phasor representations of series R, L, C circuits.
1.SINGLE PHASE HALF WAVE CONTROLLED CONVERTER WITH RESISTIVEINDUCTIVE LOAD
2 SINGLE PHASE FULLY CONTROLLED CONVERTER WITH RESISTIVEINDUCTIVE LOAD
3 SPEED CONTROL OF 3-PHASE SLIP RING (WOUND ROTOR) INDUCTION MOTOR
4 THYRISTORISED DRIVE FOR DC MOTOR WITH CLOSED LOOP CONTROL
5 THYRISTORISED DRIVE FOR PMDC MOTOR WITH SPEED MEASUREMENT & CLOSED LOOP CONTROL
6 SPEED MEASUREMENT OF PMDC MOTOR WITH CLOSED LOOP CONTROL
7 IGBT USING SINGLE 4 QUADRANT CHOPPER DRIVE FOR PMDC MOTOR WITH SPEED MEASUREMENT AND CLOSED LOOP AND CONTROL
8 SINGLE PHASE CYCLO CONVERTER BASED AC INDUCTION MOTOR CONTROLLER
9 THREE PHASE INPUT THYRISTORISED DRIVE 3HP DC MOTOR WITH CLOSED LOOP CONTROL
10 THREE PHASE INPUT IGBT DRIVE FOR 4 QUADRANT CHOPPER OF 3HP DC MOTOR WITH CLOSED LOOP CONTROL
This document provides instructions for testing the short-circuit impedance and load loss of transformers. The short-circuit voltage and loss show the transformer's performance and are important specifications. To measure: the HV windings are supplied while the LV windings are short-circuited, applying a current close to the rated current. Voltage, current and losses are measured in each phase. Losses are corrected to a reference temperature and separated into DC and AC components. Measurements are made at rated, maximum and minimum ranges.
Simulation and Experimental Verification of Single-Phase Pwm Boost -Rectifier...IRJET Journal
This document summarizes a simulation and experimental study of a single-phase PWM boost rectifier with controlled power factor. Key points:
- The rectifier uses IGBT transistors in a full bridge configuration to provide PWM control of input current and regulated DC output voltage.
- Simulation results in MATLAB show the rectifier can operate at unity power factor as well as leading and lagging power factors, with low harmonic distortion of input current.
- An experimental prototype was built using an Intel microcontroller to implement the control algorithm. Experimental waveforms verify unity power factor operation with sinusoidal input current.
Experimental simulation analysis for single phase transformer testsjournalBEEI
Transformer is one of main components in electrical power system which role to increase or reduce voltage. Characteristics of transformer would be vital to ensure the voltage is fully transferred. A single-phase transformer is a type of power transformer that utilizes single-phase alternating current, meaning the transformer relies on a voltage cycle that operates in a unified time phase. This article describes a workflow executed with Mat lab simulation and practical measurements for single-phase power transformer, no-load, short-circuit test and load test are achieved in this work. The test procedures are implemented on areal transformer (terco-type) which has a specification (1 KVA, 220/110 V, 50 Hz). Finally, the simulation results are appeared a proximately seminar from the practical results. The results indicated that the the technique and manner which presented in the current study can be depended as a miniproject in electrical technology mater for undergraduate studies.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
IRJET-Comparative Analysis of Rectangular and Square Column for Axial loading...IRJET Journal
This document describes the design and simulation of a Cockcroft-Walton voltage multiplier circuit to generate high voltage from a low input voltage. The circuit uses a ladder network of capacitors and diodes to multiply the input voltage in successive stages. The document discusses the design considerations for components based on expected output voltage and current. It also presents the simulation results showing the output voltage increasing with each stage up to 100kV at the final stage, along with the associated ripple voltage. The summary concludes that the designed circuit provides a small, low-cost way to generate high voltages for laboratory applications.
This document is an electrical machines lab manual containing experiments on various electrical machines and components used in engineering college. It provides details on 13 experiments including load tests on a single phase transformer, 3-phase squirrel cage induction motor, DC shunt generator, DC series motor, measurement of transformer coil coupling and resistance measurement techniques. The manual was prepared by three students and guided by an associate professor. It was created using LaTeX and various free Linux software and is licensed under a Creative Commons license.
This document provides information about transformer tests conducted at BEST Balıkesir Transformer Factory laboratories. It describes routine tests like winding resistance measurement, voltage ratio measurement and phase checking, as well as type tests and special tests. The routine tests section explains test procedures and equipment for various tests done on all transformers produced. These include impedance measurement, no-load loss tests, and tap changer tests. Type and special tests involve temperature rise testing, lightning impulse testing, and other advanced analyses. Laboratory equipment for performing over a dozen transformer tests is also listed.
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3. Contents
25 Testing, Efficiency & regulation 4
25.1 Goals of the lesson ………………………………………………………………….. 4
25.2 Determination of equivalent circuit parameters ……………………………………… 4
25.2.1 Qualifying parameters with suffixes LV & HV……………………………. 5
25.2.2 Open Circuit Test…………………………………………………………... 5
25.2.3 Short circuit test……………………………………………………………. 6
25.3 Efficiency of transformer…………………………………………………………….. 8
25.3.1 All day efficiency…………………………………………………………... 10
25.4 Regulation……………………………………………………………………………. 11
25.5 Tick the correct answer………………………………………………………………. 14
25.6 Solves the Problems …………………………………………………………………. 15
Version 2 EE IIT, Kharagpur
4. 25.1 Goals of the lesson
In the previous lesson we have seen how to draw equivalent circuit showing magnetizing
reactance (Xm), resistance (Rcl), representing core loss, equivalent winding resistance (re) and
equivalent leakage reactance (xe). The equivalent circuit will be of little help to us unless we
know the parameter values. In this lesson we first describe two basic simple laboratory tests
namely (i) open circuit test and (ii) short circuit test from which the values of the equivalent
circuit parameters can be computed. Once the equivalent circuit is completely known, we can
predict the performance of the transformer at various loadings. Efficiency and regulation are two
important quantities which are next defined and expressions for them derived and importance
highlighted. A number of objective type questions and problems are given at the end of the
lesson which when solved will make the understanding of the lesson clearer.
Key Words: O.C. test, S.C test, efficiency, regulation.
After going through this section students will be able to answer the following questions.
• Which parameters are obtained from O.C test?
• Which parameters are obtained from S.C test?
• What percentage of rated voltage is needed to be applied to carry out O.C test?
• What percentage of rated voltage is needed to be applied to carry out S.C test?
• From which side of a large transformer, would you like to carry out O.C test?
• From which side of a large transformer, would you like to carry out S.C test?
• How to calculate efficiency of the transformer at a given load and power factor?
• Under what condition does the transformer operate at maximum efficiency?
• What is regulation and its importance?
• How to estimate regulation at a given load and power factor?
• What is the difference between efficiency and all day efficiency?
25.2 Determination of equivalent circuit parameters
After developing the equivalent circuit representation, it is natural to ask, how to know
equivalent circuit the parameter values. Theoretically from the detailed design data it is possible
to estimate various parameters shown in the equivalent circuit. In practice, two basic tests
namely the open circuit test and the short circuit test are performed to determine the equivalent
circuit parameters.
25.2.1 Qualifying parameters with suffixes LV & HV
For a given transformer of rating say, 10 kVA, 200 V / 100 V, 50 Hz, one should not be under
the impression that 200 V (HV) side will always be the primary (as because this value appears
Version 2 EE IIT, Kharagpur
5. first in order in the voltage specification) and 100 V (LV) side will always be secondary. Thus,
for a given transformer either of the HV and LV sides may be used as primary or secondary as
decided by the user to suit his/her goals in practice. Usually suffixes 1 and 2 are used for
expressing quantities in terms of primary and secondary respectively – there is nothing wrong in
it so long one keeps track clearly which side is being used as primary. However, there are
situation, such as carrying out O.C & S.C tests (discussed in the next section), where naming
parameters with suffixes HV and LV become imperative to avoid mix up or confusion. Thus, it
will be useful to qualify the parameter values using the suffixes HV and LV (such as re HV, re LV
etc. instead of re1, re2). Therefore, it is recommended to use suffixes as LV, HV instead of 1 and
2 while describing quantities (like voltage VHV, VLV and currents IHV, ILV) or parameters
(resistances rHV, rLV and reactances xHV, xLV) in such cases.
25.2.2 Open Circuit Test
To carry out open circuit test it is the LV side of the transformer where rated voltage at rated
frequency is applied and HV side is left opened as shown in the circuit diagram 25.1. The
voltmeter, ammeter and the wattmeter readings are taken and suppose they are V0, I0 and W0
respectively. During this test, rated flux is produced in the core and the current drawn is the no-
load current which is quite small about 2 to 5% of the rated current. Therefore low range
ammeter and wattmeter current coil should be selected. Strictly speaking the wattmeter will
record the core loss as well as the LV winding copper loss. But the winding copper loss is very
small compared to the core loss as the flux in the core is rated. In fact this approximation is built-
in in the approximate equivalent circuit of the transformer referred to primary side which is LV
side in this case.
Open Circuit Test
HV
side
LV
side
Autotransformer
1-phase
A.C
supply
V
A
W
M L
S
Figure 25.1: Circuit diagram for O.C test
The approximate equivalent circuit and the corresponding phasor diagrams are shown in
figures 25.2 (a) and (b) under no load condition.
Version 2 EE IIT, Kharagpur
V0
(a) Equivalent circuit under O.C test
I0
X
m(LV)
Rcl(LV)
I0
Open
circuit
V0
I0
Im
Icl
θ0
θ0
(b) Corresponding phasor diagram
Figure 25.2: Equivalent circuit & phasor diagram during O.C test
6. Below we shall show how from the readings of the meters the parallel branch impedance
namely Rcl(LV) and Xm(LV) can be calculated.
Calculate no load power factor cos θ0 = 0
0 0
W
V I
Hence θ0 is known, calculate sin θ0
Calculate magnetizing current Im = I0 sin θ0
Calculate core loss component of current Icl = I0 cos θ0
Magnetising branch reactance Xm(LV) = 0
m
V
I
Resistance representing core loss Rcl(LV) = 0
cl
V
I
We can also calculate Xm(HV) and Rcl(HV) as follows:
Xm(HV) =
( )
2
m LV
X
a
Rcl(HV) =
( )
2
cl LV
R
a
Where, a = LV
HV
N
N
the turns ratio
If we want to draw the equivalent circuit referred to LV side then Rcl(LV) and Xm(LV) are to
be used. On the other hand if we are interested for the equivalent circuit referred to HV side,
Rcl(HV) and Xm(HV) are to be used.
25.2.3 Short circuit test
Short circuit test is generally carried out by energizing the HV side with LV side shorted.
Voltage applied is such that the rated current flows in the windings. The circuit diagram is
shown in the figure 25.3. Here also voltmeter, ammeter and the wattmeter readings are noted
corresponding to the rated current of the windings.
Short Circuit Test
HV
side
LV
side
Autotransformer
1-phase
A.C
supply
V
A
W
M L
S
Figure 25.3: Circuit diagram during S.C test
Suppose the readings are Vsc, Isc and Wsc. It should be noted that voltage required to be
applied for rated short circuit current is quite small (typically about 5%). Therefore flux level in
Version 2 EE IIT, Kharagpur
7. the core of the transformer will be also very small. Hence core loss is negligibly small compared
to the winding copper losses as rated current now flows in the windings. Magnetizing current
too, will be pretty small. In other words, under the condition of the experiment, the parallel
branch impedance comprising of Rcl(HV) and Xm(LV) can be considered to be absent. The equivalent
circuit and the corresponding phasor diagram during circuit test are shown in figures 25.4 (a) and
(b).
Xe(HV)
re(HV)
Therefore from the test data series equivalent impedance namely re(HV) and xe(HV) can
easily be computed as follows:
Equivalent resistance ref. to HV side re(HV) = 2
sc
sc
W
I
Equivalent impedance ref. to HV side ze(HV) = sc
sc
V
I
Equivalent leakage reactance ref. to HV side xe(HV) = ( ) ( )
2 2
e HV e HV
z - r
We can also calculate re(LV) and xe(LV) as follows:
re(LV) = a2
re(HV)
xe(LV) = a2
xe(HV)
where, a = LV
HV
N
N
the turns ratio
Once again, remember if you are drawing equivalent circuit referred to LV side, use
parameter values with suffixes LV, while for equivalent circuit referred to HV side parameter
values with suffixes HV must be used.
25.3 Efficiency of transformer
In a practical transformer we have seen mainly two types of major losses namely core and copper
losses occur. These losses are wasted as heat and temperature of the transformer rises. Therefore
output power of the transformer will be always less than the input power drawn by the primary
from the source and efficiency is defined as
VSC
ISC
Short
circuit
ISC
(a) Equivalent circuit under S.C test
ISC
θSC
(b) Correspondin
Parallel
branch
neglected
VSC
g phasor diagram
Figure 25.4: Equivalent circuit & phasor diagram during S.C test
Version 2 EE IIT, Kharagpur
8. η =
Output power in KW
Output power in Kw + Losses
= ( )
Output power in KW
25.1
Output power in Kw + Core loss + Copper loss
We have seen that from no load to the full load condition the core loss, Pcore remains
practically constant since the level of flux remains practically same. On the other hand we know
that the winding currents depend upon the degree of loading and copper loss directly depends
upon the square of the current and not a constant from no load to full load condition. We shall
write a general expression for efficiency for the transformer operating at x per unit loading and
delivering power to a known power factor load. Let,
KVA rating of the transformer be = S
Per unit degree of loading be = x
Transformer is delivering = x S KVA
Power factor of the load be = cos θ
Output power in KW = xS cos θ
Let copper loss at full load (i.e., x = 1) = Pcu
Therefore copper loss at x per unit loading = x2
Pcu
Constant core loss = Pcore (25.2)
(25.3)
Therefore efficiency of the transformer for general loading will become:
2
core cu
xS cos θ
η=
xS cos θ + P + x P
If the power factor of the load (i.e., cos θ) is kept constant and degree of loading of the
transformer is varied we get the efficiency Vs degree of loading curve as shown in the figure
25.5. For a given load power factor, transformer can operate at maximum efficiency at some
unique value of loading i.e., x. To find out the condition for maximum efficiency, the above
equation for η can be differentiated with respect to x and the result is set to 0. Alternatively, the
right hand side of the above equation can be simplified to, by dividing the numerator and the
denominator by x. the expression for η then becomes:
core
P
cu
x
S cos θ
η=
S cos θ + + x P
For efficiency to be maximum, d
dx (Denominator) is set to zero and we get,
or core
cu
P
d
S cos θ + + x P
dx x
⎛ ⎞
⎜ ⎟
⎝ ⎠
= 0
Version 2 EE IIT, Kharagpur
9. or 2
core
cu
P
+ P
x
− = 0
or x2
Pcu = Pcore
The loading for maximum efficiency, x = core
cu
P
P
Thus we see that for a given power factor, transformer will operate at maximum
efficiency when it is loaded to core
cu
P
P
S KVA. For transformers intended to be used continuously
at its rated KVA, should be designed such that maximum efficiency occurs at x = 1. Power
transformers fall under this category. However for transformers whose load widely varies over
time, it is not desirable to have maximum efficiency at x = 1. Distribution transformers fall under
this category and the typical value of x for maximum efficiency for such transformers may
between 0.75 to 0.8. Figure 25.5 show a family of efficiency Vs. degree of loading curves with
power factor as parameter. It can be seen that for any given power factor, maximum efficiency
occurs at a loading of x = core
cu
P
P
. Efficiencies ηmax1, ηmax2 and ηmax3 are respectively the maximum
efficiencies corresponding to power factors of unity, 0.8 and 0.7 respectively. It can easily be
shown that for a given load (i.e., fixed x), if power factor is allowed to vary then maximum
efficiency occurs at unity power factor. Combining the above observations we can say that the
efficiency is obtained when the loading of the transformer is x = core
cu
P
P
and load power factor is
unity. Transformer being a static device its efficiency is very high of the order of 98% to even
99%.
Power factor = 1
Power factor = 0.8
Power factor = 0.7
Degree of loading x
core
cu
P
x =
P
Efficiency
ηmax 1
ηmax 2
ηmax 3
Figure 25.5: Efficiency VS degree of loading curves.
25.3.1 All day efficiency
In the earlier section we have seen that the efficiency of the transformer is dependent upon the
degree of loading and the load power factor. The knowledge of this efficiency is useful provided
the load and its power factor remains constant throughout.
For example take the case of a distribution transformer. The transformers which are used
to supply LT consumers (residential, office complex etc.) are called distribution transformers.
For obvious reasons, the load on such transformers vary widely over a day or 24 hours. Some
times the transformer may be practically under no load condition (say at mid night) or may be
over loaded during peak evening hours. Therefore it is not fare to judge efficiency of the
Version 2 EE IIT, Kharagpur
10. transformer calculated at a particular load with a fixed power factor. All day efficiency,
alternatively called energy efficiency is calculated for such transformers to judge how efficient
are they. To estimate the efficiency the whole day (24 hours) is broken up into several time
blocks over which the load remains constant. The idea is to calculate total amount of energy
output in KWH and total amount of energy input in KWH over a complete day and then take the
ratio of these two to get the energy efficiency or all day efficiency of the transformer. Energy or
All day efficiency of a transformer is defined as:
ηall day =
Energy output in KWH in 24 hours
Energy input in KWH in 24 hours
=
Energy output in KWH in 24 hours
Output in KWH in 24 hours + Energy loss in 24 hours
=
Output in KWH in 24 hours
Output in KWH in 24 hours + Loss in core in 24 hours + Loss in the
Winding in 24 hours
=
core
Energy output in KWH in 24 hours
Energy output in KWH in 24 hours + 24 + Energy loss (cu) in the
winding in 24 hours
P
With primary energized all the time, constant Pcore loss will always be present no matter what is
the degree of loading. However copper loss will have different values for different time blocks as
it depends upon the degree of loadings. As pointed out earlier, if Pcu is the full load copper loss
corresponding to x = 1, copper loss at any arbitrary loading x will be x2
Pcu. It is better to make
the following table and then calculate ηall day.
Time blocks KVA
Loading
Degree of
loading x
P.F of load KWH output KWH cu
loss
T1 hours S1 x1 = S1/S cos θ1 S1 cos θ1T1
2
1
x Pcu T1
T2 hours S2 x2 = S2/S cos θ2 S2 cos θ2T2
2
2
x Pcu T2
… … … … … …
Tn hours Sn xn = Sn/S cos θn Sn cos θnTn
2
n
x Pcu Tn
Note that
1
n
i
i=
T
∑ = 24
Energy output in 24 hours =
1
n
i i
i=
S cos θ T
∑ i
Total energy loss = 2
1
24
n
core i cu i
i=
P + x P T
∑
allday
η = 1
2
1 1
n
i i i
i=
n n
i i i i cu i co
i= i=
S cos θ T
S cos θ T + x P T +24 P
∑
∑ ∑ re
Version 2 EE IIT, Kharagpur
11. 25.4 Regulation
The output voltage in a transformer will not be maintained constant from no load to the full load
condition, for a fixed input voltage in the primary. This is because there will be internal voltage
drop in the series leakage impedance of the transformer the magnitude of which will depend
upon the degree of loading as well as on the power factor of the load. The knowledge of
regulation gives us idea about change in the magnitude of the secondary voltage from no load to
full load condition at a given power factor. This can be determined experimentally by direct
loading of the transformer. To do this, primary is energized with rated voltage and the secondary
terminal voltage is recorded in absence of any load and also in presence of full load. Suppose the
readings of the voltmeters are respectively V20 and V2. Therefore change in the magnitudes of the
secondary voltage is V20 – V2. This change is expressed as a percentage of the no load secondary
voltage to express regulation. Lower value of regulation will ensure lesser fluctuation of the
voltage across the loads. If the transformer were ideal regulation would have been zero.
( )
20 2
20
Percentage Regulation 100
V -V
,% R =
V
×
For a well designed transformer at full load and 0.8 power factor load percentage
regulation may lie in the range of 2 to 5%. However, it is often not possible to fully load a large
transformer in the laboratory in order to know the value of regulation. Theoretically one can
estimate approximately, regulation from the equivalent circuit. For this purpose let us draw the
equivalent circuit of the transformer referred to the secondary side and neglect the effect of no
load current as shown in the figure 25.6. The corresponding phasor diagram referred to the
secondary side is shown in figure 25.7.
Approximate Equivalent Circuit referred to secondary
V20 V2 Z2
re2 xe2 S
S
I2
V20
C
D
F
O A
B
E
I2
θ2
θ2
θ2
V2
δ
I2 re2
I2 xe2
Figure 25.6: Equivalent circuit ref. to
secondary.
Figure 25.7: Phasor diagram ref. to
secondary.
It may be noted that when the transformer is under no load condition (i.e., S is opened),
the terminal voltage V2 is same as V20. However, this two will be different when the switch is
closed due to drops in I2 re2 and I2 xe2. For a loaded transformer the phasor diagram is drawn
taking terminal voltage V2 on reference. In the usual fashion I2 is drawn lagging V2, by the power
factor angle of the load θ2 and the drops in the equivalent resistance and leakage reactances are
added to get the phasor V20. Generally, the resistive drop I2 re2 is much smaller than the reactive
drop I2 xe2. It is because of this the angle between OC and OA (δ) is quite small. Therefore as per
the definition we can say regulation is
Version 2 EE IIT, Kharagpur
12. ( )
20 2
20
V -V OC -OA
R = =
V OC
An approximate expression for regulation can now be easily derived geometrically from
the phasor diagram shown in figure 25.7.
OC = OD since, δ is small
Therefore, OC – OA = OD – OA
= AD
= AE + ED
= I2 re2 cos θ2 + I2 xe2 sin θ2
So per unit regulation, R =
OC -OA
OC
= 2 2 2 2 2 2
e e
20
I r cos θ + I x sin θ
V
or, R = 2 2 2 2
2 2
20 20
e e
I r I x
cos θ + sin θ
V V
It is interesting to note that the above regulation formula was obtained in terms of
quantities of secondary side. It is also possible to express regulation in terms of primary
quantities as shown below:
We know, R = 2 2 2 2
2 2
20 20
e e
I r I x
cos θ + sin θ
V V
Now multiplying the numerator and denominator of the RHS by a the turns ratio, and further
manipulating a bit with a in numerator we get:
R =
2 2
2 2 2 2
2 2
20 20
( ) ( )
e e
I /a a r I /a a x
cos θ + s θ
aV aV
in
Now remembering, that 2 2
2 2 2 1 2
( / ) , ,
e e e 1
e
I a I a r r a x x
′
= = = and 20 20 1
aV V V
′
= = ; we get
regulation formula in terms of primary quantity as:
R = 2 1 2 1
2 2
20 20
e e
I r I x
cos θ + sin θ
V V
′ ′
′ ′
Or, R = 2 1 2 1
2 2
1 1
e e
I r I x
cos θ + sin θ
V V
′ ′
Neglecting no load current: R ≈ 1 1 1 1
2 2
1 1
e e
I r I x
cos θ + sin θ
V V
Version 2 EE IIT, Kharagpur
13. Thus regulation can be calculated using either primary side quantities or secondary side
quantities, since:
R = 2 2 2 2 1 1 1 1
2 2 2
20 20 1 1
e e e e
I r I x I r I x
cos θ + sin θ cos θ + sin θ
V V V V
= 2
Now the quantity 2 2
20
e
I r
V
, represents what fraction of the secondary no load voltage is
dropped in the equivalent winding resistance of the transformer. Similarly the quantity
2 2
20
e
I x
V
represents what fraction of the secondary no load voltage is dropped in the equivalent
leakage reactance of the transformer. If I2 is rated curerent, then these quantities are called the
per unit resistance and per unit leakage reactance of the transformer and denoted by ∈r and ∈x
respectively. The terms 2
20
rated e 2
I r
r V
∈ = and 2
20
rated e 2
I x
x V
∈ = are called the per unit resistance and per unit
leakage reactance respectively. Similarly, per unit leakage impedance ∈z,can be defined.
It can be easily shown that the per unit values can also be calculated in terms of primary
quantities as well and the relations are summarised below.
2 2 1
20 1
rated e rated e
r
1
I r I r
V V
∈ = =
2 2 1
20 1
rated e rated e
x
1
I x I x
V V
∈ = =
2 2 1
20 1
rated e rated e
z
1
I z I z
V V
∈ = =
where, 2 2
2 2
e e 2
e
x
= +
z r and 2 2
1 1
e e
z r x
= + 1
e .
It may be noted that the per unit values of resistance and leakage reactance come out to
be same irrespective of the sides from which they are calculated. So regulation can now be
expressed in a simple form in terms of per unit resistance and leakage reactance as follows.
per unit regulation, R = 2 2
r x
cos θ + sin θ
∈ ∈
and % regulation R = ( )
2 2 100
r x
cos θ + sin θ
∈ ∈ ×
For leading power factor load, regulation may be negative indicating that secondary
terminal voltage is more than the no load voltage. A typical plot of regulation versus power
factor for rated current is shown in figure 25.8.
HV LV LV HV HV LV LV HV
Lagging power factor
Leading power factor
% Regulation
6
4
2
-2
-4
-6
1
0.2 0.4 0.6 0.8 0.8 0.6 0.4 0.2
Figure 25.8: Regulation VS power Fig
factor curve.
ure 25.9: LV and HV windings in both
the limbs. Version 2 EE IIT, Kharagpur
14. To keep the regulation to a prescribed limit of low value, good material (such as copper) should
be used to reduce resistance and the primary and secondary windings should be distributed in the
limbs in order to reduce leakage flux, hence leakage reactance. The hole LV winding is divided
into two equal parts and placed in the two limbs. Similar is the case with the HV windings as
shown in figure 25.9.
25.5 Tick the correct answer
1. While carrying out OC test for a 10 kVA, 110 / 220 V, 50 Hz, single phase transformer
from LV side at rated voltage, the watt meter reading is found to be 100 W. If the same
test is carried out from the HV side at rated voltage, the watt meter reading will be
(A) 100 W (B) 50 W (C) 200 W (D) 25 W
2. A 20 kVA, 220 V / 110 V, 50 Hz single phase transformer has full load copper loss = 200
W and core loss = 112.5 W. At what kVA and load power factor the transformer should
be operated for maximum efficiency?
(A) 20 kVA & 0.8 power factor (B) 15 kVA & unity power factor
(C) 20 kVA & unity power factor (D) 15 kVA & 0.8 power factor.
3. A transformer has negligible resistance and has an equivalent per unit reactance 0.1. Its
voltage regulation on full load at 30° leading load power factor angle is:
(A) +5 % (B) -5 % (C) + 10 % (D) -10 %
4. A transformer operates most efficiently at 3
4 th full load. The ratio of its iron loss and full
load copper loss is given by:
(A) 16:9 (B) 4:3 (C) 3:4 (D) 9:16
5. Two identical 100 kVA transformer have 150 W iron loss and 150 W of copper loss at
rated output. Transformer-1 supplies a constant load of 80 kW at 0.8 power factor lagging
throughout 24 hours; while transformer-2 supplies 80 kW at unity power factor for 12
hours and 120 kW at unity power factor for the remaining 12 hours of the day. The all
day efficiency:
(A) of transformer-1 will be higher. (B) of transformer-2 will be higher.
(B) will be same for both transformers.(D) none of the choices.
6. The current drawn on no load by a single phase transformer is i0 = 3 sin (314t - 60°) A,
when a voltage v1 = 300 sin(314t)V is applied across the primary. The values of
magnetizing current and the core loss component current are respectively:
(A) 1.2 A & 1.8 A (B) 2.6 A & 1.5 A (C) 1.8 A & 1.2 A (D) 1.5 A & 2.6 A
Version 2 EE IIT, Kharagpur
15. 7. A 4 kVA, 400 / 200 V single phase transformer has 2 % equivalent resistance. The
equivalent resistance referred to the HV side in ohms will be:
(A) 0.2 (B) 0.8 (C) 1.0 (D) 0.25
8. The % resistance and the % leakage reactance of a 5 kVA, 220 V / 440 V, 50 Hz, single
phase transformer are respectively 3 % and 4 %. The voltage to be applied to the HV
side, to carry out S.C test at rated current is:
(A) 11 V (B) 15.4 V (C) 22 V (D) 30.8 V
25.6 Solve the Problems
1. A 30KVA, 6000/230V, 50Hz single phase transformer has HV and LV winding
resistances of 10.2Ω and 0.0016Ω respectively. The equivalent leakage reactance as
referred to HV side is 34Ω. Find the voltage to be applied to the HV side in order to
circulate the full load current with LV side short circuited. Also estimate the full load %
regulation of the transformer at 0.8 lagging power factor.
2. A single phase transformer on open circuit condition gave the following test results:
Applied voltage Frequency Power drawn
192 V 40 Hz 39.2 W
288 V 60 Hz 73.2 W
Assuming Steinmetz exponent n = 1.6, find out the hysteresis and eddy current loss
separately if the transformer is supplied with 240 V, 50 Hz.
3. Following are the test results on a 4KVA, 200V/400V, 50Hz single phase transformer.
While no load test is carried out from the LV side, the short circuit test is carried out from
the HV side.
No load test: 200 V 0.7 A 60 W
Short Circuit Test: 9 V 6 A 21.6 W
Draw the equivalent circuits (i) referred to LV side and then (ii) referred to HV side and
insert all the parameter values.
4. The following data were obtained from testing a 48 kVA, 4800/240V, 50 Hz transformer.
O.C test (from LV side): 240 V 2 A 120 W
S.C test (from HV side): 150 V 10 A 600 W
(i) Draw the equivalent circuit referred to the HV side and insert all the parameter
values.
(ii) At what kVA the transformer should be operated for maximum efficiency? Also
calculate the value of maximum efficiency for 0.8 lagging factor load.
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