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Electrical Energy Transmission

Consider the situation shown in Fig.1.The rate of electrical energy flow(power)from network A to network B is

fig1 Power transmission between two networks

Lowercase letters are used to indicate instantaneous valuesm, that is, that p, v, and I may vary with time. High power levels require high voltage and current values. For a given value of current, higher power flows may be obtained by increasing the voltage, and vice versa. Unfortunately, the existing technology sets practical upper limits onm allowable currents and voltages.

What are the limiting factors for current? We fabricate power conductors using materials with high conductivity, appropriate mechanical characteristics, and that are economical: aluminum is the most common choice, with copper used for some applications. The current-carrying capacity of a conductor is related to its maximum allowable current density and its cross=sectional area:

I

J

A

max

max

The maximum current density

J is determined by the maximum conductor

max

temperature that will not damage the conductor or its insulatinon system.

What are the limiting factors on voltage? The vundamental consideration is to provide electrical isolation(or insulation)between adjacent parts that can conduct current-that is, to confine current to the paths through which it waw intended to flow. When the voltage exceeds the breakdown strength for a given insulation system, undesirable conduction paths will be created and the system will be created and the system whll be either temporarily or permanently disabled. Fluid insulation tends to be “self-healing”(the system will recover from a breakdown if it is de-energized for a short time and then re-energized), whereas solid insulation is permanently damaged

by a breakdown.

The meaning lf “ground”is important; we quote from the IEEE Standard Dictionary of Electrical and Electronic Terms:

ground (earth)(electric system). A conducting connection, whether intentional or

accidental, by which an electric circuit or equipment is connected to the earth, or to some conducting body of relatively large extent that serves in place of the earth. Note:

It is used for establishing and maintaining the potential of the earth (or of the

conducting body) or approximately that potential, on conductors connected to it ,and for conducting ground current to and from the earth(or the conducting body).

We understand this to mean that at a given location in the power system,

accessible parts of power apparatus and earth constitute an equipotential surface when perfectly grounded. Insulation of conductors from ground is a basic problem.

Let us consider some different schemes for implementing the transmission line

indicated in Figure 1. For a fair comparison we select constrainst that all schemes must satisfy we allow any number of conductors to be used ,as long as each scheme

uses the same amount of conducting material, Given that networks A and B are

separated by a fixed physical length this means that in viewing the limes in cross section we must observe the same cross-sectional conducting area (A) for all schemes.

Also, we argue that no conductor shall carry current greater than that constrained by

some maximum current density

J.

We require that at least one conductor be grounded and shall refer to such a

conductor as the neutral, designated as “n”. If it is not required to conduct any

appreciable current, we will not include its cross-sectional area in A. This condition is achieved under certain symmetrical loading conditions, referred to as “balanced”

loading ,and can be maintained in a practical situation; therefore we allow all schemes

to ground exceed

V.It is assumed that the reader has a background in basic circuit 0

theory. The adjective “dc”, essentially means time invariant or constant with time.

Recall that the term“ac”, which historically stood for “alternating current “, in modern

usage means “sinusoidal steady state.”These terms are used to describe voltages and currents in time invariant (constant) steady-state and sinusoidal steady-state modes.

Transformers come in many sizes. Some power transformers are as big as a

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