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Electric Power Systems: Analysis and Control / Edition 1

Electric Power Systems: Analysis and Control / Edition 1

by Fabio Saccomanno


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Product Details

ISBN-13: 9780471234395
Publisher: Wiley
Publication date: 02/07/2003
Series: IEEE Press Series on Power Engineering Series , #15
Pages: 744
Product dimensions: 6.40(w) x 9.39(h) x 1.51(d)

About the Author

FABIO SACCOMANNO received his masters degree in electrical engineering from the University of Genoa, Italy, where he is a full professor of Automatic Controls, and is a lecturer on the automation of power systems. Previously, he was involved in design and research in the electric power industry, first with a utility of the Edison Group in Northern Italy, and then as a research manager at the Automatics Research Center of the Italian Electricity Board (ENEL). He is an internationally recognized expert with extensive practical experience in the areas discussed in this book.

Read an Excerpt

Electric Power Systems

Analysis and Control
By Fabio Saccomanno

John & Wiley Sons

ISBN: 0-471-23439-7

Chapter One



1.1.1 Electric power can be easily and efficiently transported to locations far from production centers and converted into desired forms (e.g., mechanical, thermal, light, or chemical).

Therefore, electric power can satisfy the requirements of a variety of users (e.g., factories, houses, offices, public lighting, traction, agriculture), widely spread around the intended territory.

On the other hand, it is generally convenient to concentrate electric power generation into a few appropriately sized generating plants. Moreover, generating plants must be located according to both technical and economic considerations. For example, the availability of water is obviously of primary concern to hydroelectric power plants as well as the availability of fuels and cooling water to thermoelectric power plants. General requirements-about primary energy sources to be used, area development planning, and other constraints, e.g., of ecological type-must also be considered.

Consequently, the network for electric power transportation must present a branched configuration, and it can be required to cover large distances between generation and end-users. Moreover, the possible unavailability of some generating units orinterconnection lines could force electric power flows to be routed through longer paths, possibly causing current overloads on interconnection lines.

These considerations make it preferable to have a network configuration sufficiently meshed to allow greater flexibility in system operation (as an adequate rerouting when encountering partial outages) thus avoiding excessive current flows in each line and limiting voltage dips and power losses to acceptable levels.

1.1.2 As it is widely known, electric power is produced, almost entirely, by means of synchronous three-phase generators (i.e., alternators) driven by steam or water turbines. Power is transported through a three-phase alternating current (ac) system operated by transformers at different voltage levels.

More precisely:

Transportation that involves larger amounts of power and/or longer distances is carried out by the "transmission" system, which consists of a meshed network and operates at a very high voltage level (relative to generator and end-user voltages). This system ensures that at the same transmitted powers the corresponding currents are reduced, thereby reducing voltage dips and power losses.

Power transportation is accomplished through the "distribution" system, which also includes small networks of radial configuration and voltages stepped down to end-user levels.

The use of ac, when compared with direct current (dc), offers several advantages, including:

transformers that permit high-voltage transmission and drastically reduces losses;

ac electrical machines that do not require rotating commutators;

interruption of ac currents that can be accomplished in an easier way.

Moreover, the three-phase system is preferable when compared with the single-phase system because of its superior operating characteristics (rotating field) and possible savings of conductive materials at the same power and voltage levels.

For an ac three-phase system, reactive power flows become particularly important. Consequently, it is also important that transmission and distribution networks be equipped with devices to generate or absorb (predominantly) reactive power. These devices enable networks to adequately equalize the reactive power absorbed or generated by lines, transformers, and loads to a larger degree than synchronous machines are able.

These devices can be static (e.g., inductive reactors, capacitors, static compensators) or rotating (synchronous compensators, which can be viewed as synchronous generators without their turbines or as synchronous motors without mechanical loads).

Furthermore, interconnection between different systems-each taking advantage of coordinated operation-is another important factor. The electrical network of the resulting system can become very extensive, possibly covering an entire continent.

1.1.3 The basic elements of a power system are shown in Figure 1.1. Each of the elements is equipped with devices for maneuvering, measurement, protection, and control.

The nominal frequency value is typically 50 Hz (in Europe) or 60 Hz (in the United States); the maximum nominal voltage ranges 20-25 kV (line-to-line voltage) at synchronous machine terminals; other voltage levels present much larger values (up to 1000 kV) for transmission networks, then decrease for distribution networks as depicted in Figure 1.1.

Generation is predominantly accomplished by thermal power plants equipped with steam turbines using "traditional" fuel (coal, oil, gas, etc.) or nuclear fuel, and/or hydroelectric plants (with reservoir or basin, or fluent-water type). Generation also can be accomplished by thermal plants with gas turbines or diesel engines, geothermal power plants (equipped with steam turbines), and other sources (e.g., wind, solar, tidal, chemical plants, etc.) whose actual capabilities are still under study or experimentation.

The transmission system includes an extensive, relatively meshed network. A single generic line can, for example, carry hundreds or even thousands of megawatts (possibly in both directions, according to its operating conditions), covering a more or less great distance, e.g., from 10 km to 1500 km and over. The long lines might present large values of shunt capacitance and series inductance, which can be, at least partially, compensated by adding respectively shunt (inductive) reactors and series capacitors.

The task of each generic distribution network at high voltage (HV), often called a "subtransmission" network, is to carry power toward a single load area, more or less geographically extended according to its user density (e.g., a whole region or a large urban and/or industrial area). The power transmitted by each line may range from a few megawatts to tens of megawatts.

Electric power is then carried to each user by means of medium voltage (MV) distribution networks, each line capable of carrying, for example, about one megawatt of power, and by low voltage (LV) distribution networks. To reduce the total amount of reactive power absorbed, the addition of shunt capacitors might be helpful ("power factor correction").

Reactor and capacitor types can be fixed or adjustable (through the use of switching devices); the adjustment increases the networks' operation flexibility and may be realized before ("no-load") or even during operation ("under-load", or "on-load").

To further improve system behavior, controlled compensators (synchronous and/or static ones) may be added in a shunt configuration at proper busbars of HV (transmission and subtransmission) networks. Tap-changing transformers, which are controllable under load, are also adopted, mostly at the HV to MV transformation, sometimes between HV transformations. While at the MV/LV transformation, the use of tap-changing transformers, set up at no load, can be sufficient.

Moreover, some transmission lines are equipped with series "regulating" transformers, by which a range of voltage variations (both in magnitude and phase)-particularly useful to control line power flows-can be achieved.

More recently, the so-called FACTS (Flexible AC Transmission Systems) have also emerged; these equipments recall and integrate the above-cited functions, providing controlled injections of active and reactive powers, through the use of high-performance electronic devices.

The possibility of adopting direct current links, by using controlled converters (i.e., rectifiers and inverters) at line terminals, also must be discussed. This is particularly helpful with very long distances and/or with cable connections (e.g., sea-crossing connections); that is, when the ac option would prevent voltage variations within given ranges at the different locations or the synchronism between connected networks.

Finally, the interconnections between very large systems (e.g., neighboring countries) are generally developed between their transmission networks. Similar situations involving a smaller amount of power can occur, even at the distribution level, in the case of "self-generating users" (e.g., traction systems, large chemical or steel processing plants, etc.), which include not only loads in the strict sense but also generators and networks.


1.2.1 A proper definition of the generic steady-state (or equilibrium) operating condition (i.e., the "working point" at which the system may be required to operate) refers to a well-defined mathematical model of the system itself, as discussed in detail in the following chapters. The present section is limited to a general definition at this preliminary stage.

Let us assume that the "configuration" and the system parameters are constant, as well as the external variables which define, together with parameters concerning users, each load requirement (e.g., braking torques externally applied to electromechanical users). Let us also assume that the three-phase electrical part of the system is "physically symmetrical." Moreover, we may assume that the electrical part of the system is linear with regard to the relationships between phase voltages and currents, thus allowing sinusoidal operations of phase variables without waveform distortions or production of harmonics.

Note however that, in this concern, the presence of nonlinearities also may be assumed, provided they can be simply translated into nonlinear time-invariant relationships between (voltage and current) Park's vectors, as specified in Section 5.6.1.

We will say that the system is in equilibrium operation if (and only if):

excitation voltages of synchronous machines are constant;

all synchronous machine shafts rotate at the same electrical speed ("synchronous" operation), so that electrical angular shifts among rotors are constant;

such speed is constant.

Under the above-mentioned conditions, each three-phase set of the emfs applied to the electrical part of the system results in a positive sequence sinusoidal set, at a frequency equal to the electrical speed of the synchronous machines; the same applies for voltages and currents at any generic point inside the electrical network. More precisely, the frequency of these sets, which comes from the synchronous motion of the machines, can be given the name of "network" frequency because of its common value at every point of the network.

The following important consequences apply:

by using the Park's transformation (see Appendix 2) with a "synchronous" reference (i.e., rotating at synchronous speed), both voltages and currents at any generic point of the network are represented by constant vectors;

active and reactive powers at any point of the network are constant, as well as active powers generated by alternators; consequently, the driving powers also must be constant, otherwise a variation in machines' speeds would result.

The definition of the steady-state condition is both useful and appropriate, as it can be transformed, by means of the Park's transformation, into an operating condition characterized by constant values. The definition also has practical aspects, as the synchronous operation at a given speed can be viewed (at ideal operating conditions and once stability conditions are satisfied) as a result of the "synchronizing" actions between the machines and the frequency regulation (see also Sections 1.3 and 1.6).

The generic equilibrium operation is determined by:

system configuration and parameters,

load requirements,

network frequency,

synchronous machine excitation voltages,

synchronous machine (electrical) angular shifts.

Note that, once all the N excitation voltages and the (N - 1) angular shifts are known (where N is the number of synchronous machines), the N vectors corresponding, through the Park's transformation, to the synchronous machine emfs in equilibrium conditions, can be directly deduced, both in magnitude and phase, by assuming an arbitrary reference phase.

However, for a better characterization of the steady-state, one could specify the value of other (2N - 1) scalar variables, as detailed in Chapter 2.

For example, instead of excitation voltages, it is usually preferable to specify the terminal voltage values (magnitude) of all synchronous machines, as these values are of paramount importance for the system operation (and are under the so-called "v/Q control"; see Section 1.3).

Similarly, it is preferable to specify, instead of angular shifts:

all active powers of generating plants except one, that is, the active power generation dispatching: this distribution is, in fact, important for system operation (and is related, with frequency regulation, to the "f/P control"; see Section 1.3);

mechanical powers generated by synchronous motors and compensators; powers can be considered known for motors based on actual loading conditions, whereas powers for compensators can be neglected, as their value is only equal to mechanical losses at the given speed.

1.2.2 Nevertheless, the equilibrium operation previously defined corresponds to, with regard to voltage and current behavior, an ideal situation which in practice can be only approximately achieved.

Regarding the above-mentioned hypotheses (and assuming that stability holds), the most important reasons for deviation from the ideal behavior are:

network configuration variations, in proximity to loads: for example, frequent inserting and disconnecting operations of loads, or opening and closing operations of distribution networks due to local requirements or operation of protection systems (e.g., with stormy weather);

load variations: for example, those caused by intermittent operating cycles (traction systems, rolling mills, tooling machines, excavators, welding machines, etc.);

the physical dissymmetries of the electrical part of the system: for example, in lines, transformers, and mostly in loads (as single-phase loads), which can be amplified by anomalous connections (e.g.,


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Table of Contents




1. Introduction to the Problems of Analysis and Control of Electric Power Systems.

2. Configuration and Working Point.

3. Frequency and Active Power Control.

4. Dynamic Behavior of the Synchronous Machine.

5. Dynamic Behavior of Network Elements and Loads.

6. Voltage and Reactive Power Control.

7. The Synchronous Machine Connected to an Infinite Bus.

8. Electromechanical Phenomena in a Multimachine System.

Appendix 1: Transformation to Symmetrical Components.

Appendix 2: Park's Transformation.

Appendix 3: Elementary Outline of the Automatic Control Theory.



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