Power Definitions and the Physical Mechanism of Power Flow

Alexander Eigeles Emanuel

• Publisher: Wiley-IEEE Press
• Year: 2011
• Print ISBN: 9780470660744
• eBook ISBN: 9781119957287
• Edition: 1
• Topic: Technology & Engineering
• Subtopic: Quality Control in Engineering
• Index: Technology & Engineering

Professor Emanuel uses clear presentation to compare and facilitate understanding of two seminal standards, The IEEE Std. 1459 and The DIN 40110-2: 2002-11. Through critical analysis of the most important and recent theories and review of basic concepts, a highly accessible guide to the essence of the standards is presented.

Key features:

• Explains the physical mechanism of energy flow under different conditions: single- and three-phase, sinusoidal and nonsinusoidal, balanced and unbalanced systems
• Starts at an elementary level and becomes more complex, with six core chapters and six appendices to clarify the mathematical aspects
• Discusses and recommends power definitions that played a significant historical role in paving the road for the two standards
• Provides a number of original unsolved problems at the end of each chapter
• Introduces a new nonactive power; the Randomness power.

Power Definitions and the Physical Mechanism of Power Flow is useful for electrical engineers and consultants involved in energy and power quality. It is also helpful to engineers dealing with energy flow quantification, design and manufacturing of metering instrumentation; consultants working with regulations related to renewable energy courses and the smart grid; and electric utility planning and operation engineers dealing with energy bill structure. The text is also relevant to university researchers, professors, and advanced students in power systems, power quality and energy related courses.

1

Electric Energy Flow: Physical Mechanisms

Through valuation only is there value; and without valuation the nut of existence would be hollow. Hear it, ye creating ones!

—Fr. Nietzsche,Thus Spake Zarathustra

There are two schools of thought that help students visualize the flow of electric energy from source to load and grasp the basic relations among voltage, current, power, and energy. The first, and seemingly the simplest, explanation relies on the flow of electric charges represented in Fig. 1.1. We imagine a cylindrical conductor with a cross-sectional area A and length ℓ, containing uniformly distributed charged particles that carry a total electric charge q. The volume charge density is

(1.1)

When a voltage ν is applied between the ends of the conductive cylinder, a uniform electric field

(1.2)

is created within the conductor. The vector of this field is oriented parallel with the conductor. The interaction between the charged particles and the field E is causing their motion along the conductor. The force developed on the charged particles found within a thin slice of thickness dx, that holds the charge dq = ρ_vAdx is dF = Edq. The total force applied on the entire charge held by the cylinder is

(1.3)

Once this system reaches steady-state the voltage source will pump continuously a constant flow of charge in a closed loop. One may picture this flow as the effect of a mechanical pressure

Figure 1.1 Flow of uniformly distributed charges in a homogeneous conductor.

F/A = ℓ ρ_ν E = ρ_νν. This model leads us straight to the notion of work or energy. To side the total charge q a distance dx, consequent to the application of the force F, it is tantamount with doing the work

(1.4)

It may be assumed that the charged particles move with an average drift velocity u = dx/dt, proportional to the magnitude of the electric field, thus

(1.5)

where the constant K is known as the mobility of the particles, (m²/Vs). The elementary work dw is proportional to the drift velocity u. This fact becomes evident when (1.4) is written in the form

(1.6)

The drift velocity u = dx/dt is also hidden in the electric current expression

(1.7)

Substitution of (1.7) in (1.6) gives

(1.8)

During a time interval t = t₂ - t₁ the voltage source will generate the total energy

(1.9)

The rate of flow of the electric energy at a particular time is the electric power

(1.10)

From (1.7) and (1.5) we also obtain a simple deduction of Ohm’s law. The current

(1.11)

(1.12)

is the resistance of the conductor of length t and cross-sectional area A, and κ = ρ_v K is the specific conductivity of the observed conductive medium, (Ωm)^-1.

Finally, equations (1.10) and (1.11) lead to the well known expressions of electric power

(1.13)

The above explanation of power and energy flow appears in some introductory textbooks of physics and is favored by electrical engineers that deal with low frequency equipment. A major drawback of this rudimentary model becomes apparent when we try to explain situations where the energy is stored in, or transferred through, dielectrics immersed in alternating electromagnetic fields, Fig. 1.2.

Figure 1.2 Examples where the Energy is Transferred via Dielectric Material: (a) Capacitor. (b) Magnetic Coupling.

Figure 1.3 Poynting vector.

Engineers dealing with antennae, microwaves, and other high frequency applications long ago embraced a more advanced explanation based on a model loyal to the laws of storage, transmission, and dissipation of energy in any medium. Th...

Table of contents

• Cover
• Title
• Foreword
• Dedication
• Preface
• 1: Electric Energy Flow: Physical Mechanisms
• 2: Single-Phase Systems With Sinusoidal Waveforms
• 3: Single-Phase Systems with Nonsinusoidal Waveforms
• 4: Apparent Power Resolution for Nonsinusoidal Single-Phase Systems
• 5: Three-Phase Systems with Sinusoidal Waveforms
• 6: Three-Phase Nonsinusoidal and Unbalanced Conditions
• 7: Power Definitions for Time-Varying Loads
• 8: Appendices
• Index