Electric Power Principles (eBook)

Sources, Conversion, Distribution and Use

James L. Kirtley (Autor)

eBook Download: EPUB

2011 | 1. Auflage
404 Seiten
Wiley (Verlag)
978-1-119-95744-7 (ISBN)

Infos

This innovative approach to the fundamentals of electric power provides the most rigorous, comprehensive and modern treatment available. To impart a thorough grounding in electric power systems, it begins with an informative discussion on per-unit normalizations, symmetrical components and iterative load flow calculations.

Covering important topics within the power system, such as protection and DC transmission, this book looks at both traditional power plants and those used for extracting sustainable energy from wind and sunlight.

With classroom-tested material, this book also presents:

• the principles of electromechanical energy conversion and magnetic circuits;
• synchronous machines - the most important generators of electric power;
• power electronics;
• induction and direct current electric motors.

Homework problems with varying levels of difficulty are included at the end of each chapter, and an online solutions manual for tutors is available. A useful Appendix contains a review of elementary network theory.

For senior undergraduate and postgraduate students studying advanced electric power systems as well as engineers re-training in this area, this textbook will be an indispensable resource. It will also benefit engineers in electronic power systems, power electronic systems, electric motors and generators, robotics and mechatronics.

www.wiley.com/go/kirtley_electric

Professor James Kirtley is currently teaching a course on electric power systems to both undergaraduate and graduate students at MIT (Massachusetts Institue of Technology).  He has been a fellow of IEEE since 1990, was awarded the IEEE Third Millenium Medal   in 2000 and the Nikola Tesla Award in 2002. Since 2007 Professor Kirtley has been associate editor of IEEE Power Engineering Society’s Transactions on Energy Conversion. He lectures outside the university, writes exensively for journals and holds 23 patents. Amongst other areas, his research interests include electric ships, superconducting generator, intelligent monitoring of equipment and systems, and advanced motor/generator machines for kinetic energy storage systems.

Inhalt

Preface.

1 Electric Power Systems.

1.1 Electric Utility Systems.

1.2 Energy and Power.

1.3 Sources of Electric Power.

1.4 Electric Power Plants and Generation.

1.5 Problems.

2 AC Voltage, Current and Power.

2.1 Sources and Power.

2.2 Resistors, Inductors and Capacitors.

2.3 Problems.

3 Transmission Lines.

3.1 Modeling: Telegrapher's Equations.

3.2 Problems.

4 Polyphase Systems.

4.1 Three-Phase Systems.

4.2 Line-Line Voltages.

4.3 Problems.

5 Electrical and Magnetic Circuits.

5.1 Electric Circuits.

5.2 Magnetic Circuit Analogies.

5.3 Problems.

6 Transformers.

6.1 Single-phase Transformers.

6.2 Three-Phase Transformers.

6.3 Problems.

7 Polyphase Lines and Single-Phase Equivalents.

7.1 Polyphase Transmission and Distribution Lines.

7.2 Introduction To Per-Unit Systems.

7.3 Appendix: Inductances of Transmission Lines.

7.4 Problems.

8 Electromagnetic Forces and Loss Mechanisms.

8.1 Energy Conversion Process.

8.2 Continuum Energy Flow.

8.3 Surface Impedance of Uniform Conductors.

8.4 Semi-Empirical Method of Handling Iron Loss.

8.5 Problems.

9 Synchronous Machines.

9.1 Round Rotor Machines: Basics.

9.2 Reconciliation of Models.

9.3 Per-Unit Systems.

9.4 Normal Operation.

9.5 Salient Pole Machines: Two-Reaction Theory.

9.6 Synchronous Machine Dynamics.

9.7 Synchronous Machine Dynamic Model.

9.8 Statement of Simulation Model.

9.9 Appendix: Transient Stability Code.

9.10 Appendix: Winding Inductance Calculation.

9.11 Problems.

10 System Analysis and Protection.

10.1 The Symmetrical Component Transformation.

10.2 Sequence Impedances.

10.3 Fault Analysis.

10.4 System Protection.

10.5 Switches.

10.6 Coordination.

10.7 Impedance Relays.

10.8 Differential Relays.

10.9 Zones of System Protection.

10.10 Problems.

11 Load Flow.

11.1 Two Ports and Lines.

11.2 Load Flow in a Network.

11.3 Gauss-Seidel Iterative Technique.

11.4 Bus Admittance.

11.5 Example: Simple Program.

11.6 MATLAB Script for the Load Flow Example.

11.7 Problems.

12 Power Electronics and Converters in Power Systems.

12.1 Switching Devices.

12.2 Rectifier Circuits.

12.3 DC-DC Converters.

12.4 Canonical Cell.

12.5 Three-Phase Bridge Circuits.

12.6 High-Voltage DC Transmission.

12.7 Basic Operation of a Converter Bridge.

12.8 Achieving High Voltage.

12.9 Problems.

13 Induction Machines.

13.1 Introduction.

13.2 Induction Machine Transformer Model.

13.3 Squirrel-Cage Machines.

13.4 Single-Phase Induction Motors.

13.5 Induction Generators.

13.6 Induction Motor Control.

13.7 Doubly Fed Induction Machines.

13.8 Appendix 1: Squirrel-Cage Machine Model.

13.9 Appendix 2: Single-Phase Squirrel Cage Model.

13.10 Appendix 3: Induction Machine Winding Schemes.

13.11 Problems.

14 DC (Commutator) Machines.

14.1 Geometry.

14.2 Torque Production.

14.3 Back Voltage.

14.4 Operation.

14.5 Series Connection.

14.6 Universal Motors.

14.7 Commutator.

14.8 Compound Wound DC Machines.

14.9 Problems.

15 Permanent Magnets in Electric Machines.

15.1 Permanent Magnets.

15.2 Commutator Machines.

15.3 Brushless PM Machines.

15.4 Motor Morphologies.

15.5 Problems.

Index.

Textauszug

2

AC Voltage, Current and Power

The basic quantities in electric power systems are voltage and current. Voltage is also called, suggestively, ‘electromotive force’. It is the pressure that forces electrons to move. Current is, of course, that flow of electrons. As with other descriptions of other types of power, electric power is that force (voltage) pushing on the flow (current). In order to understand electric power, one must first solve the circuit problems associated with flow of current in response to voltage.

Most electric power systems, including all electric utility systems, employ alternating current. Voltages and currents very closely approximate to sine waves. Thus to understand the circuit issues it is necessary to prepare to analyze systems with sinusoidal voltages and currents. Robust and relatively easy to use methods for handling sinusoidal quantities have been developed, and this is the subject material for this chapter.

In this chapter we first review sinusoidal steady state notation for voltage and current and real and reactive power in single phase systems.

2.1 Sources and Power

2.1.1 Voltage and Current Sources

Consider the interconnection of two sources shown in Figure 2.1. On the right is the symbol for a voltage source. This is a circuit element that maintains a voltage at its terminals, conceptually no matter what the current. On the left is the symbol for a current source. This is the complementary element: it maintains current no matter what the voltage. Quite obviously, these are idealizations, but they do serve as good proxies for reality. For example, the power system connection to a customer’s site is a good approximation to a voltage source. And some types of generators interconnections to the power system, such as those from solar photovoltaic power plants and some types of wind turbines approximate current sources. So that the situation shown in Figure 2.1 is an approximation of the interconnection of a solar plant to the power system. If the voltage and current are both sine waves at the same frequency, perhaps with a phase shift, they could be represented as:

v = V cos ωt

i = I cos (ωt − ψ)

Figure 2.1 Current and voltage sources connected together

2.1.2 Power

Note that Kirchhoff’s Voltage and Current Laws (KVL and KCL), when applied here, specify that the voltage across the current source and the current through the voltage source are each specified by the other source. So power out of the current source is also power in to the voltage source. If the angle ψ is small so that the voltage and current are close to being in phase, the direction of positive power flow will be from the current source to the voltage source. That power flow will be:

p = vi = VI cos ωt cos (ωt − ψ)

Since cos a cos b = ½cos (a − b) + ½cos (a + b), that power flow is:

As will become clear shortly, it is possible to handle sine waves in a very straightforward way by using complex notation.

2.1.3 Sinusoidal Steady State

The key to understanding systems in the sinusoidal steady state is Euler’s relation:

ejx = cos x +j sin x

where e is the base for common logarithms (about 2.718).

From this comes:

ejωt = cos ωt + j sin ωt

and:

Re {ejωt} = cos ωt

If a voltage is a pure sine wave (that is, with no DC components or transients, it can be described as:

v(t) = V cos(ωt + ϕ) = Re {Vejϕejωt}

Figure 2.2 Voltage phasor

This is the real part of a complex exponential with continuously increasing phase angle. In this case the complex amplitude of the voltage is as shown in Figure 2.2:

V = Vejϕ

2.1.4 Phasor Notation

This sinusoidal voltage may be represented graphically as is shown in Figure 2.2. The magnitude of this ‘phasor’, V, is the length of the vector, while the phase angle ϕ is represented by a rotation of the vector about its origin. The instantaneous value of the voltage is equal to the projection onto the horizontal axis of the tip of a vector that is rotating with angular velocity ω that is at the position of the voltage phasor at time t = 0.

2.1.5 Real and Reactive Power

In a circuit such as that of Figure 2.1 in which there exists both voltage and current, as is represented by two phasors in Figure 2.3, voltage and current are:

Taking advantage of the fact that the real part of a complex number is simply one half of the sum of that number and its complex conjugate: Re{X} = ½(X + X*), one can see that instantaneous power is:

(2.1)

(2.2)

Figure 2.3 Voltage and current phasors

Figure 2.4 Instantaneous power with power factor of 0.8

This is illustrated in Figure 2.4. Note there are two principal terms here. One is for the real, or time-average power:

The other term has no time average, but represents power that is seemingly just ‘sloshing around’, or being exchanged between source and sink at twice the electrical frequency. This is reactive power:

and it plays a very important role in controlling voltage in electric power systems. Note that the apparent power is just the magnitude of real plus reactive power, assuming reactive is ‘imaginary’ in the real/imaginary number plane:

and

Here, real power is measured in watts (W), apparent power is measured in volt-amperes (VA) and reactive power is measured in volt-amperes reactive (VARs).

Figure 2.5 Resistor

2.1.5.1 Root Mean Square Amplitude

It is common to refer to voltages and currents by their root mean square (RMS) amplitudes, rather than peak. For sine waves the RMS amplitude is of the peak amplitude. Thus, if the RMS amplitudes are VRMS and IRMS respectively,

P + jQ = VRMSI*RMS

2.2 Resistors, Inductors and Capacitors

These three linear, passive elements can be used to understand much of what happens in electric power systems.

The resistor, whose symbol is shown in Figure 2.5 has the simple voltage–current relationship:

Since voltage and current are quite obviously in phase, when driven by a voltage source,

and complex power into the resistor is:

That is, the resistor draws only real power and reactive power at its terminals is zero.

The inductor, whose symbol is shown in Figure 2.6, has the voltage–current relationship:

Figure 2.6 Inductor

Figure 2.7 Capacitor

In sinusoidal steady state, this statement can be made using complex notation:

V = jωLI

This means that real plus reactive power is:

The inductor, then, draws reactive power (that is, the sign of reactive power into the inductor is positive), and for the ideal inductor the real power is zero. Of course real inductors have some resistance, so the real power into an inductor will not be exactly zero, but in most cases it will be small compared with the reactive power drawn. The inductor has reactance XL = ωL.

The capacitor, whose symbol is shown in Figure 2.7 has a voltage–current relationship given by:

Or, in complex notation:

I = VjωC

This means that complex (real plus reactive) power drawn by the capacitor is:

P +jQ = VRMSI*RMS = −j |VRMS|2ωC

The capacitor is a source of reactive power. As with the inductor, the capacitor draws little real power. The idealized capacitor sources reactive power and draws zero real power. The capacitor has reactance

2.2.1 Reactive Power and Voltage

Reactive power plays a very important role in voltage profiles on electric power systems. For that reason, it is useful to start understanding the relationship between reactive power and voltage from the very start. Consider the simple circuit shown in Figure 2.8. A voltage source is connected to a resistive load through an inductance. This is somewhat like a power system, where transmission and distribution lines are largely inductive. The voltage across the resistor is:

Figure 2.8 Power circuit

This is shown in abstract form in Figure 2.9. Quite clearly, the ‘receiving end’ voltage is less than the load voltage, and the inequality will increase as the load increases (meaning current through the inductor increases). Consider what happens, however, when a capacitance is put in parallel with the resistor, as shown in Figure 2.10.

The output voltage is:

2.2.1.1 Example

Suppose the voltage...

Produkt-Details

• Erscheint lt. Verlag: 5.7.2011
• Sprache: englisch
• Themenwelt: Technik ► Elektrotechnik / Energietechnik
• Schlagworte: Energie • Energietechnik • Energy • Power Technology & Power Engineering
• ISBN-10: 1-119-95744-3 / 1119957443
• ISBN-13: 978-1-119-95744-7 / 9781119957447