This document provides an overview of AC power calculations. It introduces concepts like instantaneous power, average power, reactive power, and power factor. It discusses how to calculate average power for resistive, inductive, and capacitive circuits. It explains that average power is zero for purely inductive and capacitive circuits. The document also covers calculating power for a complex load, and defines true power, reactive power, and apparent power in terms of the load's resistance and reactance.
Any periodic variation of current or voltage where the current (or voltage), when measured along
any particular direction goes positive as well as negative, is defined to be an AC quantity.
Sinusoidal AC wave shapes are the ones where the variation (current or voltage) is a sine function
of time.
BEF 23803 - Lecture 7 - Complex Power Calculation.pptLiewChiaPing
This document summarizes the calculation of complex power for resistive, inductive, and capacitive circuits. It defines complex power as the product of the conjugate of the current and voltage. For a resistive circuit, only active power is consumed, with no reactive power. An inductive circuit consumes only reactive power, with no active power. A capacitive circuit also consumes only reactive power, but the reactive power value is negative. Worked examples are provided for calculating complex power for each type of circuit.
The document discusses regulated DC power supplies and their components. It explains that a regulated DC power supply consists of a step-down transformer, rectifier, filter, and voltage regulator. The transformer steps down AC voltage, the rectifier converts it to DC, the filter smooths the output, and the regulator sets the output to a fixed voltage. It then discusses half-wave and full-wave rectifiers in detail, deriving their key parameters such as DC output voltage and current, ripple factor, and efficiency.
The document summarizes the key components and operation of a regulated DC power supply. It consists of a step-down transformer, rectifier, filter, and voltage regulator. The transformer steps down AC voltage, the rectifier converts it to DC but with variation, the filter smooths the output, and the regulator sets the output to a fixed voltage. Rectifiers are then discussed in more detail, including half-wave and full-wave rectifiers. Key rectifier parameters like DC output voltage and current, ripple factor, and efficiency are defined. Half-wave rectifier operation and analysis is explained through derivations of these parameters.
The document provides an overview of phasor analysis for power systems. It discusses:
1) Representing AC voltages and currents as phasors using Euler's identity, which allows simplifying the analysis of constant frequency AC systems.
2) The advantages of phasor analysis for representing impedances of components like resistors, inductors, and capacitors.
3) Examples of calculating real and reactive power in circuits using phasor representations and the power triangle.
4) Applications of reactive power compensation to reduce line losses and current.
The document discusses power analysis of AC circuits. It defines instantaneous power as the product of instantaneous voltage and current at a point in time. Average power is defined as the average of instantaneous power over one period. Average power is important because power meters measure average power. For a sinusoidal voltage and current, average power is equal to one-half the product of the rms voltage and current multiplied by the cosine of the phase difference between voltage and current. Resistive circuits absorb power continuously, while reactive circuits absorb no average power. The document provides examples of calculating instantaneous and average power in AC circuits.
1) Power in DC circuits is measured as P=VI watts. In AC circuits, instantaneous power varies over each cycle but average power is measured by integrating over a full cycle.
2) An electrodynamometer wattmeter works by measuring the torque produced by the interaction between fixed and moving coils. The deflection is proportional to power.
3) Power in polyphase systems can be measured using the three wattmeter method or two wattmeter method depending on the circuit configuration and whether the load is balanced. Corrections may be needed due to phase angle errors in current and potential transformers.
1. The document discusses several important network theorems including Kirchhoff's laws, Thevenin's theorem, maximum power transfer theorem, superposition theorem, and the growth and decay of charge and current in RC and LR circuits respectively.
2. Kirchhoff's laws include Kirchhoff's current law (KCL) and Kirchhoff's voltage law (KVL). KCL states the sum of currents at a node is zero, and KVL states the algebraic sum of voltages in a closed loop is zero.
3. Thevenin's theorem states any linear network can be reduced to a single voltage source in series with a resistance, with the Thevenin voltage and resistance values defined.
Any periodic variation of current or voltage where the current (or voltage), when measured along
any particular direction goes positive as well as negative, is defined to be an AC quantity.
Sinusoidal AC wave shapes are the ones where the variation (current or voltage) is a sine function
of time.
BEF 23803 - Lecture 7 - Complex Power Calculation.pptLiewChiaPing
This document summarizes the calculation of complex power for resistive, inductive, and capacitive circuits. It defines complex power as the product of the conjugate of the current and voltage. For a resistive circuit, only active power is consumed, with no reactive power. An inductive circuit consumes only reactive power, with no active power. A capacitive circuit also consumes only reactive power, but the reactive power value is negative. Worked examples are provided for calculating complex power for each type of circuit.
The document discusses regulated DC power supplies and their components. It explains that a regulated DC power supply consists of a step-down transformer, rectifier, filter, and voltage regulator. The transformer steps down AC voltage, the rectifier converts it to DC, the filter smooths the output, and the regulator sets the output to a fixed voltage. It then discusses half-wave and full-wave rectifiers in detail, deriving their key parameters such as DC output voltage and current, ripple factor, and efficiency.
The document summarizes the key components and operation of a regulated DC power supply. It consists of a step-down transformer, rectifier, filter, and voltage regulator. The transformer steps down AC voltage, the rectifier converts it to DC but with variation, the filter smooths the output, and the regulator sets the output to a fixed voltage. Rectifiers are then discussed in more detail, including half-wave and full-wave rectifiers. Key rectifier parameters like DC output voltage and current, ripple factor, and efficiency are defined. Half-wave rectifier operation and analysis is explained through derivations of these parameters.
The document provides an overview of phasor analysis for power systems. It discusses:
1) Representing AC voltages and currents as phasors using Euler's identity, which allows simplifying the analysis of constant frequency AC systems.
2) The advantages of phasor analysis for representing impedances of components like resistors, inductors, and capacitors.
3) Examples of calculating real and reactive power in circuits using phasor representations and the power triangle.
4) Applications of reactive power compensation to reduce line losses and current.
The document discusses power analysis of AC circuits. It defines instantaneous power as the product of instantaneous voltage and current at a point in time. Average power is defined as the average of instantaneous power over one period. Average power is important because power meters measure average power. For a sinusoidal voltage and current, average power is equal to one-half the product of the rms voltage and current multiplied by the cosine of the phase difference between voltage and current. Resistive circuits absorb power continuously, while reactive circuits absorb no average power. The document provides examples of calculating instantaneous and average power in AC circuits.
1) Power in DC circuits is measured as P=VI watts. In AC circuits, instantaneous power varies over each cycle but average power is measured by integrating over a full cycle.
2) An electrodynamometer wattmeter works by measuring the torque produced by the interaction between fixed and moving coils. The deflection is proportional to power.
3) Power in polyphase systems can be measured using the three wattmeter method or two wattmeter method depending on the circuit configuration and whether the load is balanced. Corrections may be needed due to phase angle errors in current and potential transformers.
1. The document discusses several important network theorems including Kirchhoff's laws, Thevenin's theorem, maximum power transfer theorem, superposition theorem, and the growth and decay of charge and current in RC and LR circuits respectively.
2. Kirchhoff's laws include Kirchhoff's current law (KCL) and Kirchhoff's voltage law (KVL). KCL states the sum of currents at a node is zero, and KVL states the algebraic sum of voltages in a closed loop is zero.
3. Thevenin's theorem states any linear network can be reduced to a single voltage source in series with a resistance, with the Thevenin voltage and resistance values defined.
This document section describes alternating current (AC) circuits containing a single circuit element: resistor, inductor, or capacitor, connected to an AC voltage source. For a resistive circuit, the current and voltage are in phase. For an inductive circuit, the current lags the voltage by 90 degrees. For a capacitive circuit, the current leads the voltage by 90 degrees. The document defines important concepts such as reactance, impedance, and phasor diagrams for analyzing AC circuits.
This document discusses Ohm's law and basic circuit concepts. It defines key terms like voltage, current, resistance, power, and energy. It explains that voltage is directly proportional to current based on Ohm's law. Circuits can be connected in series or parallel, and examples show how to calculate current, voltage, resistance, and power in different circuit configurations using Ohm's law.
The document discusses alternating current (AC) circuits containing resistors, inductors, and capacitors. It explains how to analyze such passive AC circuits to determine current, voltage, power dissipation, and resonance. It also describes how capacitance transducers can be used to measure displacement by utilizing the operation of capacitors in an AC circuit. After studying this unit, the reader should be able to analyze various AC circuits containing combinations of R, L, and C components and understand the use of capacitance transducers.
Electrical Engineering is the Branch of Engineering. Electrical Engineering field requires an understanding of core areas including Thermal and Hydraulics Prime Movers, Analog Electronic Circuits, Network Analysis and Synthesis, DC Machines and Transformers, Digital Electronic Circuits, Fundamentals of Power Electronics, Control System Engineering, Engineering Electromagnetics, Microprocessor and Microcontroller. Ekeeda offers Online Mechanical Engineering Courses for all the Subjects as per the Syllabus. Visit : https://ekeeda.com/streamdetails/stream/Electrical-and-Electronics-Engineering
This document discusses alternating current (AC) circuits. It begins by describing how an alternating electromotive force (EMF) is generated using a coil rotating in a magnetic field. Equations are provided showing that both the induced EMF and current vary as sine functions. Common terms used in AC circuits like cycle, frequency, phase, and root mean square (RMS) value are defined. Phasor diagrams are introduced to represent AC quantities in terms of magnitude and direction. Derivations of average and RMS values are shown. Finally, a purely resistive AC circuit is analyzed, showing the current is in phase with voltage and both follow sine waves. Power calculations are also demonstrated.
The document discusses AC power concepts including real power, reactive power, and apparent power. It defines real power as power dissipated in resistance, reactive power as power exchanged between reactive components like inductors and capacitors, and apparent power as total power flowing in a circuit. Real power is calculated using resistance, reactive power using reactance, and apparent power using impedance. A power triangle is used to show the relationships between real, reactive, and apparent power components of AC power. Several examples are provided to demonstrate calculating power values in AC circuits.
Electrical Engineering is the Branch of Engineering. Electrical Engineering field requires an understanding of core areas including Thermal and Hydraulics Prime Movers, Analog Electronic Circuits, Network Analysis and Synthesis, DC Machines and Transformers, Digital Electronic Circuits, Fundamentals of Power Electronics, Control System Engineering, Engineering Electromagnetics, Microprocessor and Microcontroller. Ekeeda offers Online Mechanical Engineering Courses for all the Subjects as per the Syllabus Visit : https://ekeeda.com/streamdetails/stream/Electrical-Engineering
Experimental verification of network theorems, ugc practical physics s_paulspaul15
This document describes an experiment to verify several network theorems including Thevenin's theorem, Norton's theorem, superposition theorem, and the maximum power transfer theorem. The experiment uses a Wheatstone bridge circuit with resistors R1-R4 and a voltage source. Measurements are taken at various load resistances RL and graphs are plotted to experimentally determine the Thevenin resistance Rth, Thevenin voltage Vth, Norton current In, and maximum power transfer. Direct measurements are also taken and compared to theoretical calculations to verify the network theorems.
The document provides an overview of topics related to electrical circuits and electromagnetism including:
1) Definitions of key circuit elements and analysis techniques like Kirchhoff's laws, superposition theorem, and Thevenin's theorem.
2) Concepts in electromagnetism including Biot-Savart law, Ampere's law, Faraday's law, and magnetic circuits.
3) Analysis of AC circuits including waveform properties, phasor representation, and resonance in RLC circuits.
1. Alternating current is an electric current whose magnitude and direction periodically revers. It can be expressed by the equation I = I0 sinωt, where I0 is the peak value and ω is the angular frequency.
2. When alternating current flows through a pure resistor, the current is in phase with the applied voltage. There is no phase difference. However, when it flows through a pure inductor, the current lags the applied voltage by 90 degrees.
3. Root mean square (RMS) value is a useful parameter for alternating current and voltage. It is defined as the square root of mean of the squares of instantaneous values over one complete cycle. The RMS value of a sinusoidal current
Alternating Current Circuits And Electromagnetic WavesSarah Pollard
This document provides an overview of alternating current (AC) circuits and electromagnetic waves. It begins by introducing the characteristics of AC circuits containing resistors, capacitors, or inductors connected to an AC voltage source. It describes how resistors allow current to flow in phase with voltage, while capacitors cause voltage to lag current by 90 degrees. Inductors cause current to lag voltage by 90 degrees. The document then discusses electromagnetic waves, their properties, and their spectrum. It covers Maxwell's and Hertz's work validating electromagnetic wave theory. The key concepts covered are AC circuits, resistors, capacitors, inductors, resonance, transformers, electromagnetic waves, and the electromagnetic spectrum.
This document discusses single-phase and three-phase rectifiers. It describes how a single-phase half-wave rectifier works by only allowing current to flow during one half of the AC cycle. Waveforms are provided for the voltage and current. When an inductive load is used, the current remains continuous. Performance parameters for rectifiers include efficiency, form factor, ripple factor, and total harmonic distortion. Three-phase bridge rectifiers are also covered.
BEF 23803 - Lecture 8 - Conservation of Complex Power.pptLiewChiaPing
This document discusses power factor correction in electrical circuits. It provides an example of a circuit with a 600V load consuming 120kW of real power and 160kVAr of reactive power. Without correction, the supply current lags the voltage by 51.3 degrees and has a magnitude of 333.3A. To achieve unity power factor, a compensating capacitor would be added to cancel the 160kVAr of reactive power, reducing the supply current. The worked example calculates the uncorrected and corrected supply currents to demonstrate the benefit of power factor correction.
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.
1. This document discusses sinusoidal steady-state analysis of AC circuits. It describes transforming circuits to the phasor domain, solving using techniques like mesh/nodal analysis, and transforming results back to the time domain.
2. It provides the impedance equations for resistors, inductors, and capacitors in the phasor domain. It also defines admittance and its real and imaginary parts.
3. The document presents several example circuit problems and solves them using techniques like mesh analysis, nodal analysis, superposition, Thevenin's theorem, and source transformations.
Variable Voltage Source Equivalent Model of Modular Multilevel ConverterIJRES Journal
The structures of modular multilevel converter module (MMC) are very complex, and the
numerous sub-modules and output level number bring difficulties for the analysis and simulation. In this paper,
assuming the sub-capacitor voltage instantaneous value of a single arm is the same value, the switching
frequency of the switch is much higher than the output voltage frequency, the system harmonics were ignored,
the system state equations are deduced about the intermediate variables as circulation current and the capacitor
voltage between the upper and lower arms. On this basis, a variable voltage source continuous equivalent
model is proposed, which may replace the system physical simulation model with the actual simulation study. At
the same time, the model reflects the relationship between the output voltage and circulation current,which
provide a way to analyze the formation mechanism of circulation and the capacitor voltage fluctuations, and
make system analysis simple and intuitive. The simulation results validate that this continuous model is
rationality and correctness.
This chapter provides complete solution of of first, Second order differential equations of series & parallel R-L, R-C, R-L-C circuits, bu using different methods.
The MATLAB File by Akshit Jain .pdf on .Akshit Jain
"Unlock the Power of Data Analysis and Computational Modeling with this MATLAB File!
This MATLAB file is a versatile tool designed to revolutionize your data analysis and computational modeling processes. Whether you're a scientist, engineer, researcher, or student, MATLAB empowers you to tackle complex problems with ease.
With an intuitive interface and robust functionality, this file enables you to manipulate, visualize, and interpret data with precision. From statistical analysis and signal processing to machine learning and optimization, MATLAB offers a comprehensive suite of tools to meet your diverse needs.
Additionally, this file provides access to a vast library of built-in functions and toolboxes, allowing you to customize and extend its capabilities to suit your specific requirements. Whether you're analyzing experimental data, simulating dynamic systems, or developing algorithms, MATLAB empowers you to turn your ideas into reality.
Experience the power and versatility of MATLAB today and unlock new possibilities in data analysis and computational modeling!"
This document summarizes inverters and their operation. It begins with an introduction that defines inverters as devices that convert DC to AC power by switching the DC input voltage in a predetermined sequence. It then discusses the basic principles of inverters including single-phase half-bridge and full-bridge inverter circuits. Fourier series analysis is introduced as a tool to analyze the output waveforms of inverters in terms of harmonic components. The document concludes with a discussion of total harmonic distortion as a measure of output waveform quality.
chapter_1 Intro. to electonic Devices.pptLiewChiaPing
The document discusses power electronics concepts and devices. It begins with an introduction to power electronics and outlines various power electronic converters including controlled rectifiers, choppers, inverters, cycloconverters, and AC voltage controllers. It then discusses applications of power electronic converters in various industries. The document also describes several power semiconductor devices used in power electronics, such as power diodes, transistors, MOSFETs, IGBTs, thyristors, GTOs, and IGCTs. It covers the characteristics, ratings, and drive circuits of these devices.
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This document section describes alternating current (AC) circuits containing a single circuit element: resistor, inductor, or capacitor, connected to an AC voltage source. For a resistive circuit, the current and voltage are in phase. For an inductive circuit, the current lags the voltage by 90 degrees. For a capacitive circuit, the current leads the voltage by 90 degrees. The document defines important concepts such as reactance, impedance, and phasor diagrams for analyzing AC circuits.
This document discusses Ohm's law and basic circuit concepts. It defines key terms like voltage, current, resistance, power, and energy. It explains that voltage is directly proportional to current based on Ohm's law. Circuits can be connected in series or parallel, and examples show how to calculate current, voltage, resistance, and power in different circuit configurations using Ohm's law.
The document discusses alternating current (AC) circuits containing resistors, inductors, and capacitors. It explains how to analyze such passive AC circuits to determine current, voltage, power dissipation, and resonance. It also describes how capacitance transducers can be used to measure displacement by utilizing the operation of capacitors in an AC circuit. After studying this unit, the reader should be able to analyze various AC circuits containing combinations of R, L, and C components and understand the use of capacitance transducers.
Electrical Engineering is the Branch of Engineering. Electrical Engineering field requires an understanding of core areas including Thermal and Hydraulics Prime Movers, Analog Electronic Circuits, Network Analysis and Synthesis, DC Machines and Transformers, Digital Electronic Circuits, Fundamentals of Power Electronics, Control System Engineering, Engineering Electromagnetics, Microprocessor and Microcontroller. Ekeeda offers Online Mechanical Engineering Courses for all the Subjects as per the Syllabus. Visit : https://ekeeda.com/streamdetails/stream/Electrical-and-Electronics-Engineering
This document discusses alternating current (AC) circuits. It begins by describing how an alternating electromotive force (EMF) is generated using a coil rotating in a magnetic field. Equations are provided showing that both the induced EMF and current vary as sine functions. Common terms used in AC circuits like cycle, frequency, phase, and root mean square (RMS) value are defined. Phasor diagrams are introduced to represent AC quantities in terms of magnitude and direction. Derivations of average and RMS values are shown. Finally, a purely resistive AC circuit is analyzed, showing the current is in phase with voltage and both follow sine waves. Power calculations are also demonstrated.
The document discusses AC power concepts including real power, reactive power, and apparent power. It defines real power as power dissipated in resistance, reactive power as power exchanged between reactive components like inductors and capacitors, and apparent power as total power flowing in a circuit. Real power is calculated using resistance, reactive power using reactance, and apparent power using impedance. A power triangle is used to show the relationships between real, reactive, and apparent power components of AC power. Several examples are provided to demonstrate calculating power values in AC circuits.
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Experimental verification of network theorems, ugc practical physics s_paulspaul15
This document describes an experiment to verify several network theorems including Thevenin's theorem, Norton's theorem, superposition theorem, and the maximum power transfer theorem. The experiment uses a Wheatstone bridge circuit with resistors R1-R4 and a voltage source. Measurements are taken at various load resistances RL and graphs are plotted to experimentally determine the Thevenin resistance Rth, Thevenin voltage Vth, Norton current In, and maximum power transfer. Direct measurements are also taken and compared to theoretical calculations to verify the network theorems.
The document provides an overview of topics related to electrical circuits and electromagnetism including:
1) Definitions of key circuit elements and analysis techniques like Kirchhoff's laws, superposition theorem, and Thevenin's theorem.
2) Concepts in electromagnetism including Biot-Savart law, Ampere's law, Faraday's law, and magnetic circuits.
3) Analysis of AC circuits including waveform properties, phasor representation, and resonance in RLC circuits.
1. Alternating current is an electric current whose magnitude and direction periodically revers. It can be expressed by the equation I = I0 sinωt, where I0 is the peak value and ω is the angular frequency.
2. When alternating current flows through a pure resistor, the current is in phase with the applied voltage. There is no phase difference. However, when it flows through a pure inductor, the current lags the applied voltage by 90 degrees.
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This document provides an overview of alternating current (AC) circuits and electromagnetic waves. It begins by introducing the characteristics of AC circuits containing resistors, capacitors, or inductors connected to an AC voltage source. It describes how resistors allow current to flow in phase with voltage, while capacitors cause voltage to lag current by 90 degrees. Inductors cause current to lag voltage by 90 degrees. The document then discusses electromagnetic waves, their properties, and their spectrum. It covers Maxwell's and Hertz's work validating electromagnetic wave theory. The key concepts covered are AC circuits, resistors, capacitors, inductors, resonance, transformers, electromagnetic waves, and the electromagnetic spectrum.
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BEF 23803 - Lecture 8 - Conservation of Complex Power.pptLiewChiaPing
This document discusses power factor correction in electrical circuits. It provides an example of a circuit with a 600V load consuming 120kW of real power and 160kVAr of reactive power. Without correction, the supply current lags the voltage by 51.3 degrees and has a magnitude of 333.3A. To achieve unity power factor, a compensating capacitor would be added to cancel the 160kVAr of reactive power, reducing the supply current. The worked example calculates the uncorrected and corrected supply currents to demonstrate the benefit of power factor correction.
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.
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3. The document presents several example circuit problems and solves them using techniques like mesh analysis, nodal analysis, superposition, Thevenin's theorem, and source transformations.
Variable Voltage Source Equivalent Model of Modular Multilevel ConverterIJRES Journal
The structures of modular multilevel converter module (MMC) are very complex, and the
numerous sub-modules and output level number bring difficulties for the analysis and simulation. In this paper,
assuming the sub-capacitor voltage instantaneous value of a single arm is the same value, the switching
frequency of the switch is much higher than the output voltage frequency, the system harmonics were ignored,
the system state equations are deduced about the intermediate variables as circulation current and the capacitor
voltage between the upper and lower arms. On this basis, a variable voltage source continuous equivalent
model is proposed, which may replace the system physical simulation model with the actual simulation study. At
the same time, the model reflects the relationship between the output voltage and circulation current,which
provide a way to analyze the formation mechanism of circulation and the capacitor voltage fluctuations, and
make system analysis simple and intuitive. The simulation results validate that this continuous model is
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This chapter provides complete solution of of first, Second order differential equations of series & parallel R-L, R-C, R-L-C circuits, bu using different methods.
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This MATLAB file is a versatile tool designed to revolutionize your data analysis and computational modeling processes. Whether you're a scientist, engineer, researcher, or student, MATLAB empowers you to tackle complex problems with ease.
With an intuitive interface and robust functionality, this file enables you to manipulate, visualize, and interpret data with precision. From statistical analysis and signal processing to machine learning and optimization, MATLAB offers a comprehensive suite of tools to meet your diverse needs.
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Experience the power and versatility of MATLAB today and unlock new possibilities in data analysis and computational modeling!"
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This document summarizes inverters and their operation. It begins with an introduction that defines inverters as devices that convert DC to AC power by switching the DC input voltage in a predetermined sequence. It then discusses the basic principles of inverters including single-phase half-bridge and full-bridge inverter circuits. Fourier series analysis is introduced as a tool to analyze the output waveforms of inverters in terms of harmonic components. The document concludes with a discussion of total harmonic distortion as a measure of output waveform quality.
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So in summary, it
1) DC-DC converters control the output voltage by converting the unregulated DC input voltage to a regulated DC output voltage. Switching regulators have near zero power loss by rapidly opening and closing a switch to transfer power from input to output in pulses.
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This document discusses overcurrent protection and radial system protection. It describes different types of overcurrent relays, including instantaneous and time-delay relays. Instantaneous relays trip immediately when current exceeds the pickup setting, while time-delay relays introduce an intentional delay based on how many times the pickup current is exceeded. The document includes examples of selecting settings for time-delay relays in a radial power system to coordinate protection among circuit breakers while maintaining a minimum coordination time interval between devices.
Here are the key steps and settings for the distance relay protection of the transmission line:
- Zone 1 reach is set to 80% of Line 1-2 impedance for fast tripping of faults close to the relay location.
- Zone 2 reach is set to 120% of Line 1-2 impedance to cover faults beyond the far end of Line 1-2 up to Bus 2.
- Zone 3 reach covers 100% of Line 1-2 plus 120% of the longer of Lines 2-3 and 2-4 to coordinate with downstream relays.
The settings determined for zones 1, 2 and 3 are 4.05∠80.9°Ω, 6.08∠80.9
This document discusses distance protection in power systems. It begins by introducing system protection and explaining why it is needed to protect systems from short circuits. It then describes the typical components of a protection system including instrument transformers, relays, and circuit breakers. Current transformers and voltage transformers are explained in detail, including their purposes, characteristics, and how they are used to scale down high voltages and currents for relay operation. Examples are provided to demonstrate how to evaluate current transformer performance.
BEF43303_-_201620171_W8 Power System Stability.pdfLiewChiaPing
This document discusses power system stability analysis and protection. Section 8.1 applies the equal-area criterion to determine stability limits for a sudden increase in power input. The maximum additional power that can be applied without losing stability is found by ensuring the accelerating and decelerating energy areas are equal. Section 8.2 applies the same technique to determine critical clearing times and angles for temporary three-phase faults on transmission lines connecting a generator to an infinite bus. The power-angle curve shifts during a fault, and stability is lost if the angle increases too much before fault clearing. Examples calculate critical clearing parameters for specific generator and line configurations.
BEF43303_-_201620171_W7 Power System Stability.pdfLiewChiaPing
This document provides an overview of power system stability analysis and the transient stability equal area criterion. It introduces steady-state and transient stability, defines the swing equation that describes the relative motion of a generator rotor during a disturbance, and presents synchronous machine models used for stability studies. It also explains the equal area criterion method for determining transient stability of a single machine connected to an infinite bus system by equating the accelerating and decelerating energy areas on the generator's power-angle curve.
BEF43303_-_201620171_W6 Analysis of Fault.pdfLiewChiaPing
This document discusses the analysis of balanced and unbalanced faults in power systems. It covers the modeling and calculation of fault currents for single line-to-ground, line-to-line, and double line-to-ground faults using symmetrical components. Equivalent circuits are presented for each type of fault. An example problem is also given to calculate fault currents for different fault types using given system data and a simple one-line diagram.
BEF43303_-_201620171_W5 Analysis of fault.pdfLiewChiaPing
The document discusses sequence impedances and fault analysis of power systems. It covers:
- Sequence impedances of equipment like loads, transmission lines, synchronous machines and transformers.
- How to derive the positive, negative and zero sequence impedance matrices.
- Representing the system using sequence networks that allow independent analysis of each sequence.
- Examples of analyzing single line to ground, line to line and other faults using the sequence impedance approach. Diagrams of sequence networks are provided for different fault conditions.
BEF43303_-_201620171_W4 Analysis of Balance and Unbalance Fault.pdfLiewChiaPing
This document discusses the analysis of balanced and unbalanced faults in power systems. It introduces balanced three-phase faults and various types of unbalanced faults. The key aspects covered include:
- Determining bus voltages and line currents during different fault types for protection and rating equipment.
- Generator behavior during sub-transient, transient, and steady-state periods of a fault.
- Calculating fault current, bus voltages, and line currents using bus impedance matrix methods for examples of three-phase faults on different buses.
- Definitions and calculations related to short-circuit capacity and symmetrical components analysis for unbalanced faults.
BEF43303 - 201620171 W3 Power Flow Analysis.pdfLiewChiaPing
The document describes power flow analysis and the Gauss-Seidel method for solving power flows. It discusses:
1) Power flow equations relating voltage, current, real and reactive power at each bus.
2) The Gauss-Seidel method iteratively solves these nonlinear equations to determine voltage phasors and power flows.
3) Line flows and losses are then calculated using the bus voltages and currents based on admittance matrices.
Examples and tutorials demonstrate applying the method to simple systems.
BEF43303 - 201620171 W2 Power System Analysis and Protection.pdfLiewChiaPing
The document discusses the bus admittance matrix formulation for power flow analysis. It explains how to convert a power system represented by impedances to one represented by admittances. The node-voltage equations are then expressed in matrix form using the bus admittance matrix. Tutorial examples demonstrate how to obtain the bus admittance matrix for given power systems by inspection and converting impedances to admittances.
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UPRAHUL
This Dissertation explores the particular circumstances of Mirzapur, a region located in the
core of India. Mirzapur, with its varied terrains and abundant biodiversity, offers an optimal
environment for investigating the changes in vegetation cover dynamics. Our study utilizes
advanced technologies such as GIS (Geographic Information Systems) and Remote sensing to
analyze the transformations that have taken place over the course of a decade.
The complex relationship between human activities and the environment has been the focus
of extensive research and worry. As the global community grapples with swift urbanization,
population expansion, and economic progress, the effects on natural ecosystems are becoming
more evident. A crucial element of this impact is the alteration of vegetation cover, which plays a
significant role in maintaining the ecological equilibrium of our planet.Land serves as the foundation for all human activities and provides the necessary materials for
these activities. As the most crucial natural resource, its utilization by humans results in different
'Land uses,' which are determined by both human activities and the physical characteristics of the
land.
The utilization of land is impacted by human needs and environmental factors. In countries
like India, rapid population growth and the emphasis on extensive resource exploitation can lead
to significant land degradation, adversely affecting the region's land cover.
Therefore, human intervention has significantly influenced land use patterns over many
centuries, evolving its structure over time and space. In the present era, these changes have
accelerated due to factors such as agriculture and urbanization. Information regarding land use and
cover is essential for various planning and management tasks related to the Earth's surface,
providing crucial environmental data for scientific, resource management, policy purposes, and
diverse human activities.
Accurate understanding of land use and cover is imperative for the development planning
of any area. Consequently, a wide range of professionals, including earth system scientists, land
and water managers, and urban planners, are interested in obtaining data on land use and cover
changes, conversion trends, and other related patterns. The spatial dimensions of land use and
cover support policymakers and scientists in making well-informed decisions, as alterations in
these patterns indicate shifts in economic and social conditions. Monitoring such changes with the
help of Advanced technologies like Remote Sensing and Geographic Information Systems is
crucial for coordinated efforts across different administrative levels. Advanced technologies like
Remote Sensing and Geographic Information Systems
9
Changes in vegetation cover refer to variations in the distribution, composition, and overall
structure of plant communities across different temporal and spatial scales. These changes can
occur natural.
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...PECB
Denis is a dynamic and results-driven Chief Information Officer (CIO) with a distinguished career spanning information systems analysis and technical project management. With a proven track record of spearheading the design and delivery of cutting-edge Information Management solutions, he has consistently elevated business operations, streamlined reporting functions, and maximized process efficiency.
Certified as an ISO/IEC 27001: Information Security Management Systems (ISMS) Lead Implementer, Data Protection Officer, and Cyber Risks Analyst, Denis brings a heightened focus on data security, privacy, and cyber resilience to every endeavor.
His expertise extends across a diverse spectrum of reporting, database, and web development applications, underpinned by an exceptional grasp of data storage and virtualization technologies. His proficiency in application testing, database administration, and data cleansing ensures seamless execution of complex projects.
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Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
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This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
বাংলাদেশের অর্থনৈতিক সমীক্ষা ২০২৪ [Bangladesh Economic Review 2024 Bangla.pdf] কম্পিউটার , ট্যাব ও স্মার্ট ফোন ভার্সন সহ সম্পূর্ণ বাংলা ই-বুক বা pdf বই " সুচিপত্র ...বুকমার্ক মেনু 🔖 ও হাইপার লিংক মেনু 📝👆 যুক্ত ..
আমাদের সবার জন্য খুব খুব গুরুত্বপূর্ণ একটি বই ..বিসিএস, ব্যাংক, ইউনিভার্সিটি ভর্তি ও যে কোন প্রতিযোগিতা মূলক পরীক্ষার জন্য এর খুব ইম্পরট্যান্ট একটি বিষয় ...তাছাড়া বাংলাদেশের সাম্প্রতিক যে কোন ডাটা বা তথ্য এই বইতে পাবেন ...
তাই একজন নাগরিক হিসাবে এই তথ্য গুলো আপনার জানা প্রয়োজন ...।
বিসিএস ও ব্যাংক এর লিখিত পরীক্ষা ...+এছাড়া মাধ্যমিক ও উচ্চমাধ্যমিকের স্টুডেন্টদের জন্য অনেক কাজে আসবে ...
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...Dr. Vinod Kumar Kanvaria
Exploiting Artificial Intelligence for Empowering Researchers and Faculty,
International FDP on Fundamentals of Research in Social Sciences
at Integral University, Lucknow, 06.06.2024
By Dr. Vinod Kumar Kanvaria
Walmart Business+ and Spark Good for Nonprofits.pdfTechSoup
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Answers about how you can do more with Walmart!"
A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.
How to Add Chatter in the odoo 17 ERP ModuleCeline George
In Odoo, the chatter is like a chat tool that helps you work together on records. You can leave notes and track things, making it easier to talk with your team and partners. Inside chatter, all communication history, activity, and changes will be displayed.
2. The objective of this lecture is to introduce AC power.
Lecture Objective
3. 1. Understand the meaning of instantaneous and average
power,
2. master AC power notation, and compute average power,
and reactive for AC circuits
3. Compute the power factor of a complex load.
LEARNING OUTCOMES
After completing this course you will be able to:
4. AVERAGE POWER CALCULATIONS
i. the two-port network is linear and contain no energy
sources,
ii. the two-port network is excited by a sinusoidal input,
v(t) = Vmcost
iii. The terminal voltage v(t) and terminal current i(t) have
reached their steady state values.
i(t)
v(t)
Linear
network
Consider the two-port network shown in the figure below. We
assume that :
5. We wish to calculate:
1. Active power consumed by the network
2. Reactive power consumed by the network
3. Power factor at the input terminals of the network.
AVERAGE POWER CALCULATIONS
6.
t
V
t
v m
sin
)
(
t
I
R
t
V
R
t
v
t
i m
m
sin
sin
)
(
)
(
Let the terminal voltage v(t) be given by
the expression
where Im =Vm/R is the peak current.
Power Absorbed by Resistive Circuit
Consider a resistive circuit with a terminal
resistance R. i(t)
v(t)
Linear
circuit
Linear resistive circuit
Ohm’s law requires that the terminal current i(t) be related to
voltage v(t) and resistance R via the equation
7. Then, instantaneous power supplied to the circuit is
t
I
V
t
I
V
t
I
V
t
t
I
V
t
i
t
v
t
p
m
m
m
m
m
m
m
m
2
2
cos
2
2
2
1
1
cos
2
1
2
1
2
cos
1
2
1
sin
sin
)
(
)
(
)
(
Power Absorbed by Resistive Circuit
8. Further simplifications give us
Power Absorbed by Resistive Circuit
t
V
p m
m
2
cos
1
I
2
1
(t)
Therefore,
t
I
V
t
I
V
t
I
V
t
p
m
m
m
m
m
m
2
cos
1
2
2
2
2
cos
1
1
cos
1
)
( 2
10. From the plot, we note the following:
1. p(t) has two components: a constant component, and a
time-varying component,
2. p(t) is always positive.
rms
rms
m
m I
V
I
V
P
2
1
The constant component is the average power consumed by
the circuit. Thus, average power consumed by the circuit is
11. t
I
t
i m
sin
)
(
Let
Power Absorbed by a Purely Inductive Circuit
i(t)
v(t)
Linear
circuit
Consider an inductive circuit of inductance L.
Then, for an inductor,
t
V
t
LI
t
I
dt
d
L
dt
di
L
t
v
m
m
m
cos
cos
sin
)
(
where m
m LI
V
12. Instantaneous power supplied to the circuit is
t
I
V
t
t
V
I
t
V
t
I
t
i
t
v
t
p
m
m
m
m
m
m
2
sin
2
1
cos
sin
cos
sin
)
(
)
(
)
(
14. From the plot, we note the following:
1. p(t) is equally both positive and negative; i.e. power is
circulating.
2. p(t) has no constant component. Thus, the average
power consumed by the purely inductive circuit element
over one cycle of the supply voltage is zero. That is,
0
P
15. t
V
t
v m
sin
)
(
Let
Power Absorbed by a Purely Capacitive Circuit
i(t)
v(t)
Linear
circuit
Consider a purely capacitive circuit of capacitance C.
Then, for a capacitor,
t
I
t
CV
t
V
dt
d
C
dt
dv
C
t
i
m
m
m
cos
cos
sin
)
(
where
2
m
m CV
I
16. Instantaneous power supplied to the circuit is
t
I
V
t
t
V
I
t
I
t
V
t
i
t
v
t
p
m
m
m
m
m
m
2
sin
2
1
cos
sin
sin
cos
)
(
)
(
)
(
18. From the plot, we note the following:
1. p(t) is equally both positive and negative, power is
circulating.
2. p(t) has no constant component. Thus, the average
power consumed by the purely capacitive circuit element
over one cycle of the supply voltage is zero. That is,
0
P
19. Power absorbed by a Reactive Circuit
Consider a linear AC circuit of terminal impedance Z. Let the
the circuit be excited by a sinusoidal source, v(t) = Vmcos(ωt),
as shown in the figure below. Assume that the impedance Z
causes the terminal current i(t) to lag behind the terminal
voltage by an angle . For a linear circuit we can write
i(t)
v(t)
Linear
circuit
where Im is the amplitude of the terminal
current.
t
I
t
i m cos
)
(
20. Instantaneous power dissipated by a circuit element is
given by the product of the instantaneous voltage and
current:
The above equation can be further simplified with the aid of
trigonometric identities to yield
where θ is the difference in phase between voltage and current.
t
I
V
I
V
t
p m
m
m
m
2
cos
2
cos
2
)
(
t
t
I
V
t
i
t
v
t
p m
m cos
cos
)
(
)
(
)
(
21. The equation shows that the instantaneous power dissipated
by an AC circuit element is equal to the sum of an average
component:
and a sinusoidal component
oscillating at a frequency double that of the original source
frequency.
cos
2
m
mI
V
t
I
V m
m
2
cos
2
22. A plot of the instantaneous and average power is shown below.
23. The average power can be obtained by integrating the
instantaneous power over one cycle of the sinusoidal signal.
cos
2
2
cos
2
1
cos
2
1
)
(
1
0
0
0
m
m
av
T
m
m
T
m
m
T
av
I
V
P
dt
t
I
V
T
dt
I
V
T
dt
t
p
T
P
since the second integral is equal
to zero and cos(θ) is a constant.
Therefore,
24. The same analysis can be also be carried out in the phasor
domain. In the phasor domain, the terminal current and
terminal are given by
I
V
Linear
circuit
j
m
j
m
e
I
I
e
V
V
0
The impedance of the circuit element is defined by the phasor
voltage and current to be
j
j
m
m
j
m
j
m
Ze
e
I
V
e
I
e
V
I
V
Z
0
where
m
m
I
V
Z
25. The expression for the average power also be represented
using phasor notation, as follows:
cos
2
1
cos
2
1 2
2
Z
I
Z
V
P m
m
av
It may be expanded using trigonometric identities to obtain
the following expressions:
cos
2
1
cos
2
1 2
2
Z
I
Z
V
P m
m
av
In terms of rms values, we have
cos
cos 2
2
Z
I
Z
V
P rms
rms
av
26. It may be expanded using trigonometric identities to obtain
the following expressions:
Recall the expression for the instantaneous power given
below
True, Reactive, and Apparent power
t
I
V
I
V
t
p m
m
m
m
2
cos
2
cos
2
)
(
t
Z
I
t
Z
I
t
t
Z
I
t
t
Z
V
t
p
rms
rms
rms
rms
2
sin
sin
2
cos
1
.
cos
2
sin
.
sin
2
cos
.
cos
cos
2
sin
sin
2
cos
cos
cos
)
(
2
2
2
2
27. Now, from the impedance triangle, we have
where R and X are the resistive and reactive components of
the load impedance, respectively. On the basis of this fact, it
becomes possible to write the instantaneous power as
R
Z
cos
X
Z
sin
and
t
X
I
t
R
I
R
I
t
X
I
t
R
I
t
p
rms
rms
rms
rms
rms
2
sin
2
cos
.
2
sin
2
cos
1
.
)
(
2
2
2
2
2
Z
X
R
28. The physical interpretation of this expression for the
instantaneous power is as follow:
Instantaneous power dissipated by a complex load consists
of the following three components:
1. An average component, which is constant; this is called the
average power and is denoted by the symbol Pav:
where R = Re[Z].
R
Irms
2
av
P
29. 2. A time-varying (sinusoidal) component with zero
average value that is contributed by the power
fluctuations in the resistive component of the load
and is denoted by PR(t):
t
P
t
R
I
t
p av
rms
R
2
cos
.
2
cos
.
)
( 2
3. A time-varying (sinusoidal) component with zero
average value, due to the power fluctuation in the
reactive component of the load and denoted by
pX(t):
t
Q
t
X
I
t
p rms
2
sin
2
sin
)
( 2
where X = Im [Z] and Q is called the reactive power.
30. 1. Since reactive elements can only store energy and not
dissipate it, there is no net average power absorbed by X.
2. Since Pav corresponds to the power absorbed by the load
resistance, it is also called the real power, measured in
units of watts (W). On the other hand, Q takes the name
of reactive power, since it is associated with the load
reactance. The units of Q are volt-amperes reactive, or
VAR.
3. The combination of reactive power and true power is
called apparent power, and it is the product of a circuit's
voltage and current, without reference to phase angle.
Apparent power is measured in the unit of Volt-Amps (VA)
and is symbolized by the capital letter S.
Notes
31. There are several power equations relating the three types of
power to resistance, reactance, and impedance (all using
scalar quantities):
Summary
32. Worked Example
Compute the power absorbed (i) by R, (ii) by L.
Solution
V
o
s
S t
v
P
V 15
20
)
(
12
10
120
100 3
j
j
L
j
35. 4.327 A peak
120 V peak
234.1 W average
The plot shows:
1. Power flows from the supply into the load for only a part of the
cycle! For a portion of the cycle, power actually flows back to
the source from the load!
2. There is reactive power in the circuit.
A plot of the voltage and current waveforms is shown in the
figure below.
36. Worked Example
For the circuit below, compute :
(i) true power absorbed by the load
(ii) reactive power consumed by the load
(iii) apparent power supplied by the source
38. A 10 resistor and a capacitive reactance of 20 are
connected in series to a 240 V supply. Calculate the apparent
power, the true power and the reactive power supplied by the
source.
Worked Example
Solution
39. Solution
Impedance seen by the source
4
.
22
20
10 2
2
2
2
C
X
R
Z
A
7
.
10
4
.
22
240
Z
V
I S
Current flowing through the circuit
40. Apparent Power supplied to the load
VA
2570
7
.
10
240
VI
S leading
True power supplied to the load is the power consumed by
the resistor R.
W
1145
10
7
.
10
cos
2
1 2
2
2
R
I
Z
I
P rms
m
av
Reactive power supplied to the load is the power consumed
by the capacitance C.
VAR
2290
20
7
.
10
sin
2
1 2
2
2
C
rms
m X
I
Z
I
Q
41. Exercise
Calculate voltage drop across each element, the
apparent power, the true power and the reactive
power supplied by the source. Given : vS(t) =
1002cos1000t
42.
20
10
20
1000 3
L
XL
10
10
100
1000
1
1
6
C
XC
Impedance seen by the source
14
.
14
10
10 2
2
2
2
C
L X
X
R
Z
A
07
.
7
14
.
14
100
Z
V
I S
Current flowing through the circuit
Solution
43. Solution
Voltage drop across each element:
V
7
.
70
10
07
.
7
IR
VR
V
4
.
141
20
07
.
7
L
L IX
V
V
7
.
70
10
07
.
7
C
C IX
V
Apparent power supplied to circuit elements by the voltage
source
VA
707
100
07
.
7
S
IV
S
44. True power supplied to the load is the power consumed by
the resistor R.
W
500
10
07
.
7 2
2
R
I
P rms
av
Reactive power supplied to the load is the power consumed
by the inductor and the capacitance.
VAR
500
10
07
.
7
sin
2
1 2
2
2
C
L
rms
m X
X
I
Z
I
Q
Solution
45. Calculate the total active and reactive powers supplied by the source
to the resistors.
Worked Example
46. The total impedance seen by the source is
Solution
o
j
j
Z 62
.
20
69
.
12
6
8
//
4
10
Z
47
.
4
877
.
11 j
Z
In rectangular form,
47. Total active supplied by the source is equal to the active
power consumed by the real part of the load.
W
4533
69
.
12
9
.
18
Re 2
2
Z
I
P rms
av
Reactive power supplied to the load is the power consumed
by the capacitance C.
VAR
2143
6
9
.
18
sin
2
1 2
2
2
C
rms
m X
I
Z
I
Q
Solution
Current supplied by the source to the load is
A
9
.
18
69
.
12
240
Z
V
I S
rms
48. Power Factor
The ratio of the real power to the apparent power is called
the power factor (pf).
S
P
power
apparent
power
real
(p.f.)
factor
Power
m
m
m
m
I
V
2
1
cos
I
V
2
1
cos
.
.
f
p
I
V -
where
Therefore,
49. Calculate the power factor seen by the source and the average power
supplied by the source.
Worked Example
50. The total impedance seen by the source is
Solution
o
j
j
Z 62
.
20
69
.
12
6
8
//
4
10
Z
47
.
4
877
.
11 j
Z
In rectangular form,
51.
cos
.
.
S
P
f
p
Z
X
R
When we have reduced the load seen by the source into one
equivalent impedance, , then the power factor of the load is
simply equal to the cosine of the angle in the impedance triangle.
That is,
Note
Z
Linear
network
I
V
Z
Therefore, power factor of load is
cos
.
.
2
2
2
2
2
Z
R
X
I
R
I
R
I
S
P
f
p
Hence, for the circuit given
936
.
0
62
.
20
cos
.
.
o
f
p
52. To determine whether the current is leading or lagging the source
voltage, we recall that
Z
I
V
By setting , we obtain
o
I
I 0
o
o
o
IZ
Z
I
Z
I
V 62
.
20
62
.
20
0
This result tells us that phasor V is leading phasor I by 20.62o. More
usually, we say that phasor I is lagging phasor V by 20.62o.
936
.
0
62
.
20
cos
.
.
o
f
p
Hence, for the circuit given
lagging
53.
Z
I
P m
Re
2
2
Average power supplied by the source to the load is
118
877
.
11
152
.
3
Re 2
2
Z
I
P
In terms of rms values, we can write
Load current is
A
o
o
s
Z
V
I 62
.
20
252
.
31
62
.
20
60
.
12
0
40
Therefore,
W
118
877
.
11
152
.
3 2
P
54. Why is electrical apparatus is rated in VA instead of watts ?
The calculations above show both loads dissipate 120 kW, but the
current rating of generator (b) is exceeded because of the power
factor of its load.
VA Rating of Electrical Apparatus
55. Summary
In this study unit we have looked at
1. Active power
2. Reactive power
3. Apparent power, and
4. Power factor