report on the Power quality

Power Quality
Session 2014-2018 Yuvraj Singh
CHAPTER 1
INTRODUCTION TO POWER QUALITY
1.1 Electric Power Quality
Electric power quality, or simply power quality, involves voltage, frequency, and waveform.
Good power quality can be defined as a steady supply voltage that stays within the prescribed
range, steady ac. frequency close to the rated value, and smooth voltage curve waveform
(resembles a sine wave). In general, it is useful to consider power quality as the compatibility
between what comes out of an electric outlet and the load that is plugged into it. The term is
used to describe electric power that drives an electrical load and the load's ability to function
properly. Without the proper power, an electrical device (or load) may malfunction, fail
prematurely or not operate at all. There are many ways in which electric power can be of poor
quality and many more causes of such poor quality power. The electric power industry
comprises electricity generation (AC power), electric power transmission and ultimately
electric power distribution to an electricity meter located at the premises of the end user of
the electric power. The electricity then moves through the wiring system of the end user until
it reaches the load. The complexity of the system to move electric energy from the point of
production to the point of consumption combined with variations in weather, generation,
demand and other factors provide many opportunities for the quality of supply to be
compromised. While "power quality" is a convenient term for many, it is the quality of the
voltage rather than power or electric current that is actually described by the term. Power is
simply the flow of energy and the current demanded by a load is largely uncontrollable.
1.1.1 Introduction
The quality of electrical power may be described as a set of values of parameters, such as:

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 Continuity of service (Whether the electrical power is subject to voltage drops or
overages below or above a threshold level thereby causing blackouts or
brownouts)
 Variation in voltage magnitude (see below)
 Transient voltages and currents
 Harmonic content in the waveforms for AC power
It is often useful to think of power quality as a compatibility problem: is the equipment
connected to the grid compatible with the events on the grid, and is the power delivered by
the grid, including the events, compatible with the equipment that is connected?
Compatibility problems always have at least two solutions: in this case, either clean up the
power, or make the equipment tougher. The tolerance of data-processing equipment to
voltage variations is often characterized by the CBEMA curve, which give the duration and
magnitude of voltage variations that can be tolerated.
Fig 1- power qulity
Ideally, AC voltage is supplied by a utility as sinusoidal having an amplitude and frequency
given by national standards (in the case of mains) or system specifications (in the case of a
power feed not directly attached to the mains) with an impedance of zero ohms at all
frequencies.

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1.2 Power Quality Deviations
No real-life power source is ideal and generally can deviate in at least the following ways:
1.2.1 Voltage
 Variations in the peak or RMS voltage are both important to different types of
equipment.
 When the RMS voltage exceeds the nominal voltage by 10 to 80% for 0.5 cycle to 1
minute, the event is called a "swell".
 A "dip" (in British English) or a "sag" (in American English the two terms are
equivalent) is the opposite situation: the RMS voltage is below the nominal voltage by
10 to 90% for 0.5 cycle to 1 minute.
 Random or repetitive variations in the RMS voltage between 90 and 110% of nominal
can produce a phenomenon known as "flicker" in lighting equipment. Flicker is rapid
visible changes of light level. Definition of the characteristics of voltage fluctuations
that produce objectionable light flicker has been the subject of ongoing research.
 Abrupt, very brief increases in voltage, called "spikes", "impulses", or "surges",
generally caused by large inductive loads being turned off, or more severely by
lightning.
 "Under voltage" occurs when the nominal voltage drops below 90% for more than 1
minute. The term "brownout" is an apt description for voltage drops somewhere
between full power (bright lights) and a blackout (no power – no light). It comes from
the noticeable to significant dimming of regular incandescent lights, during system
faults or overloading etc., when insufficient power is available to achieve full
brightness in (usually) domestic lighting. This term is in common usage has no formal
definition but is commonly used to describe a reduction in system voltage by the
utility or system operator to decrease demand or to increase system operating
margins.
 "Overvoltage" occurs when the nominal voltage rises above 110% for more than 1
minute.

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1.2.2 Frequency
 Variations in the frequency.
 Nonzero low-frequency impedance (when a load draws more power, the voltage
drops).
 Nonzero high-frequency impedance (when a load demands a large amount of current,
then stops demanding it suddenly, there will be a dip or spike in the voltage due to the
inductances in the power supply line).
 Variations in the wave shape – usually described as harmonics at lower frequencies
(usually less than 3 kHz) and described as Common Mode Distortion or
Interharmonics at higher frequencies.
1.2.3 Waveform
 The oscillation of voltage and current ideally follows the form of a sine or cosine
function; however it can alter due to imperfections in the generators or loads.
 Typically, generators cause voltage distortions and loads cause current distortions.
These distortions occur as oscillations more rapid than the nominal frequency, and are
referred to as harmonics.
 The relative contribution of harmonics to the distortion of the ideal waveform is
called total harmonic distortion (THD).
 Low harmonic content in a waveform is ideal because harmonics can cause
vibrations, buzzing, equipment distortions, and losses and overheating in
transformers.
Each of these power quality problems has a different cause. Some problems are a result of the
shared infrastructure. For example, a fault on the network may cause a dip that will affect
some customers; the higher the level of the fault, the greater the number affected. A problem
on one customer‘s site may cause a transient that affects all other customers on the same
subsystem. Problems, such as harmonics, arise within the customer‘s own installation and

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may propagate onto the network and affect other customers. Harmonic problems can be dealt
with by a combination of good design practice and well proven reduction equipment.
1.2.4 Power Conditioning
Power conditioning is modifying the power to improve its quality. An uninterruptible power
supply can be used to switch off of mains power if there is a transient (temporary) condition
on the line. However, cheaper UPS units create poor-quality power themselves, akin to
imposing a higher-frequency and lower-amplitude square wave atop the sine wave. High-
quality UPS units utilize a double conversion topology which breaks down incoming AC
power into DC, charges the batteries, then remanufactures an AC sine wave. This
remanufactured sine wave is of higher quality than the original AC power feed. A surge
protector or simple capacitor or varistor can protect against most overvoltage conditions,
while a lightning arrester protects against severe spikes. Electronic filters can remove
harmonics.
1.2.5 Smart Grids And Power Quality
Modern systems use sensors called phasor measurement units (PMU) distributed throughout
their network to monitor power quality and in some cases respond automatically to them.
Using such smart grids features of rapid sensing and automated self healing of anomalies in
the network promises to bring higher quality power and less downtime while simultaneously
supporting power from intermittent power sources and distributed generation, which would if
unchecked degrade power quality.
1.2.6 Power Quality Compression Algorithm
A power quality compression algorithm is an algorithm used in the analysis of power quality.
To provide high quality electric power service, it is essential to monitor the quality of the
electric signals also termed as power quality (PQ) at different locations along an electrical
power network. Electrical utilities carefully monitor waveforms and currents at various
network locations constantly, to understand what lead up to any unforeseen events such as a
power outage and blackouts. This is particularly critical at sites where the environment and
public safety are at risk (institutions such as hospitals, sewage treatment plants, mines, etc.).

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1.3 Power Quality Challenges
Engineers have at their disposal many meters, that are able to read and display electrical
power waveforms and calculating parameters of the waveforms. These parameters may
include, for example, current and voltage RMS, phase relationship between waveforms of a
multi-phase signal, power factor, frequency, THD, active power (kW), reactive power
(kVAr), apparent power (kVA) and active energy (kWh), reactive energy (kVArh) and
apparent energy (kVAh) and many more. In order to sufficiently monitor unforeseen events,
Ribeiro et al. explains that it is not enough to display these parameters, but to also capture
voltage waveform data at all times. This is impracticable due to the large amount of data
involved; causing what is known the ―bottle effect‖. For instance, at a sampling rate of 32
samples per cycle, 1,920 samples are collected per second. For three-phase meters that
measure both voltage and current waveforms, the data is 6-8 times as much. More practical
solutions developed in recent years store data only when an event occurs (for example, when
high levels of power system harmonics are detected) or alternatively to store the RMS value
of the electrical signals. This data, however, is not always sufficient to determine the exact
nature of problems.
1.3.1 Raw data compression
Nisenblat etal. proposes the idea of power quality compression algorithm (similar to lossy
compression methods) that enables meters to continuously store the waveform of one or more
power signals, regardless whether or not an event of interest was identified. This algorithm
referred to as PQ Zip empowers a processor with a memory that is sufficient to store the
waveform, under normal power conditions, over a long period of time, of at least a month,
two months or even a year. The compression is performed in real time, as the signals are
acquired; it calculates a compression decision before all the compressed data is received. For
instance should one parameter remain constant, and various others fluctuate, the compression
decision retains only what is relevant from the constant data, and retains all the fluctuation
data. It then decomposes the waveform of the power signal of numerous components, over
various periods of the waveform. It concludes the process by compressing the values of at
least some of these components over different periods, separately. This real time compression
algorithm, performed independent of the sampling, prevents data gaps and has a typical
1000:1 compression ratio.

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1.3.2 Aggregated data compression
A typical function of a power analyzer is generation of data archive aggregated over given
interval. Most typically 10 minute or 1 minute interval is used as specified by the IEC/IEEE
PQ standards. A significant archive sizes are created during an operation of such instrument.
As Kraus et al. have demonstrated the compression ratio on such archives using Lempel–
Ziv–Markov chain algorithm, bzip or other similar lossless compression algorithms can be
significant. By using prediction and modeling on the stored time series in the actual power
quality archive the efficiency of post processing compression is usually further improved.
This combination of simplistic techniques implies savings in both data storage and data
acquisition processes.
1.4 POWER QUALITY
One of main problems regarding to electrified rail ways is power quality shortage that can
reduce other customers‘ usage efficiency below standards. Railway produced power
disturbances which can be classified as below:
1.4.1 Power Unbalance
Since electrified trains are single phase loads inherently, connection of these time varying (as
much as they are high speed) unbalance (as much as they are high power) loads to three
phase power system will lead to huge power unbalance. This problem has been facing
different solutions. Firstly some countries devoted a specific power system to their ERs and
made other customers isolated from power quality disturbances produced by railway. The
other solution is to use DC transmission systems for trains. This strategy is working and
different standard and a few not standard DC voltage levels are used to supply railway
system. In this approach railway is connected to a main power system trough an ACDC
rectifier and all of the power turbulences are cut off at a point of common coupling by this
high voltage rectifier. The other solution was to design railway train to work as AC load but
not necessarily with standard frequency of 50/60 Hz. There are different voltage levels for
this type of railway power feeding.
The solutions before power electronics viability for this level of voltage were limited to a few
balancing transformations in AC feeders namely: V transformer, Scott transformer and Le

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Blanc transformer all of them well compatible with simple single phase transformation in
capability of unbalance reduction.
Fig 1: Common traction system to grid configurations
Also to keep unbalance system within standard levels a strong network (high short circuit
duty) should be used at the voltages of 220kV, 115kV or 69kV at least.
1.4.2 Harmonic Distortion
There are speed drives, power conversion equipment or frequency converters that inject
harmonic in to railways suppling power system. These harmonics can disturb other power
systems or lead to high frequency electromagnetic fields incompatible with close equipment
as well as train signalling system. There are some classic solutions for harmonic distortion
reduction like third sequence harmonic eliminator transformers. An active power filter is a
modern solution for these problems such as unbalance, harmonic distortion and low power
factor problems.

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1.4.3 Flicke
As the train passes between two adjacent substations voltage sag may happen and affect other
customers electrical light performance so called flicker. There are some structural solutions
regarding to all of these challenges which are used in different countries. In Germany and
Sweden low frequency systems are used which are low frequency power system in Germany
and frequency conversion in Sweden. However in England, France, USA and Africa higher
voltages has reduced the problem in different manners which are connecting railway supply
system to main network in a high voltage point of common coupling or designing railway
system to work under a higher catenary voltage. All of abovementioned methods are relying
on a strong power system at the PCC to keep unbalance under 2% and harmonic distortion
within standard limits as well
1.5 ACTIVE POWER FILTERS
Considering power electronics facilities new frontiers opened to power quality compensation
solutions. Load unbalance can be attenuated by making controlled power transmission paths
between two or three single phases owing to power electronic switching circuits.
In 25 kV feeder characteristics are presented and reasons for power quality problems in
railway systems are mentioned, followed by brief description of methods for compensating
these shortage. Namely:
 Reducing the distance between 25kV supply substations.
 A higher fault level at each 25 kV supply station.
 Using static VAR compensator as voltage support at each supply point.
 More switching stations between each two adjacent substations to limit faults.
 Series capacitors either in substations or overhead wiring.
 Shunt connected capacitors either as circuit-breaker capacitors or reactive power
compensator.

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 Transformer type series regulators in the overhead line.
 On-load tap changing transformers installed for each substation.
 Paralleling feeders to share load between them and alleviate unbalance.
 Engineering the geometric configuration of feeders to reduce its series impedances.
 Single phase transition to distant stations at a higher voltage to decrease voltage loss.
 Paralleling of adjacent substations via the overhead line.
 Installing switching capacitors on board.
 Twining contact overhead lines to reduce inductance and resistance and increase the
line‘s current capacity.
 Unbalanced autotransformer voltage.
 Storage batteries connected by inverters to collect extra power and support overhead
line voltage.
1.5.1 Active Filters Structural Characteristics
In and power electronic compensators are designed, simulated and experimented to control
voltage form factor on 25 kV ERs. The presented active power filter in and the hybrid
(passive and active filters) multi level ones presented in and are shunt connected to solve both
harmonic distortion of 3rd
, 5th
and 7th
harmonics and low power factor. The shunt
compensator is installed at the end of overhead line and works regarding to the voltage which
senses at its connection point. In an algorithm to achieve high performance selective
harmonic extraction is revised. In same active filter as is deal as impedance connected to end
of feeder line. The paper is optimizing this impedance to find the most effective control
strategy for proposed active filter to achieve acceptable voltage pantograph along the whole
line. In another shunt connected active power compensator is presented that suppose to
compensate unbalance created by railway application on power system in addition to reactive
power required by traction motor. The method is upgrading a traditional Scott transformer
with a bidirectional inverter that can balance two output phases of Scott transformer by
transmitting a fraction of overloaded phase to under loaded one. By side the inverter

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compensates harmonics. has realized same but more advanced strategy for Shinkansen high
speed railway (HSR).
Fig 2: Scott transformer and DC/AC converter application for power balance in Railway system.
In hybrid active power filter (passive filter + active filter) configurations are classified and
modelled and their characteristics are tabulated (Table. 1) and explained. In addition the
problem of unbalanced harmonic distortion is mentioned. To solve this problem in an exact
way, positive, negative, and zero sequence harmonic compensation should de revised. A
novel configuration and control strategy is presented. In a power electronic system stabilizer
is utilised for HSR distribution system. The proposed method assesses relationship between
power loss and stability in railway supply system. The case study in is Korean HSR. It claims
that by reducing voltage drop through compensating reactive power system stability will
increase. The stabilizer produces required reactive power. In voltage switched capacitors are
applied to regulate voltage on a 25 kV railway system. uses a cheaper device (thyristor) in
comparison with mentioned references. As a drawback, compensation in this method can be
conducted in steps and not continuously. In addition thyristor is a source of harmonics
because of its low switching frequency. In a different compensating method is introduced
which adds a medium voltage level between main supply and railway lines. The compensator
which is a two phase inverter is connected to this medium voltage line and senses and then

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regulates this voltage.
1.5.2 Active Filter Equipped Power Systems Analysis
In a power system simulation has been directed to extract unbalance vulnerability of a test
network. According to voltage and current unbalance are related to train load and motion
conditions and power supply configuration. Classic methods of unbalance alleviation which
generally are 3 phase to 2 phase transformers are considered in this unbalance effect study (3
phase to 4 phase transformation for rail way application is proposed in). To compare different
railway load distribution effect four experiments with varying loads and different
arrangement has been prepared.
specifically focuses on active filter for tram. Unlike above mentioned active filters this one
acts as an input or series filter. In the mathematical technique of Diakoptics is applied for
railway system solutions. Diakoptics is to tear a given system into a number of independent,
then joining the solutions of separated parts together for the solution for complete problem. It
is a good idea for railway power system with indispensable characteristic of changing loads
and more identical: changing structure of under study railway system by its train‘s
movement. In harmonic analysis for Korean railway system has been implemented. To direct
this study an eight-port model for considered railway is defined and presented. In addition, to
certify proposed model simulations based on the model is compared with measurement in.
Further more amplification of harmonic by resonance in railway electrification system is
studied. In a mathematical approach to extract general control strategy for advanced 25kV-
50Hz ERs has been performed. The objective of nonlinear control is to attain current and
voltage balance in power system regardless of uncertainties and nonlinearities. In a purely
structural approach calculates the optimal positioning of RC-banks to reduce harmonic
distortion in a given railway network. Then Optimization is focused on R and C amounts to
alleviate harmonic amplification. In the case of Taipei MRT DC system is studied, focusing
on harmonic quantity and quality. In practical measurement method which is used in this
study is explained and measurements results are presented and compared with mathematical
predictions. Then parameters that can not be easily considered in mathematical harmonic
analyse methods are named and the difference they make is shown in measurement results. In
Olympic electric train is studied in the power quality point of view. Chargeable batteries are
used to improve power quality in case study system. In and probabilistic methods for load
flow in ER suppling power systems is suggested. They purpose to layout Probability density

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functions of voltage or power flow in certain point of the power system which indicates the
ranges of variations of these parameters. In traction unbalance problem is discussed and some
methodologies to analyse are presented. Then a new method is offered which is based on
sensing and compensating the negative sequence of three phase power supply. The point
about this idea is that multiple sources of unbalance do not interact because their effect on
negative sequence is additive and can be deal separately. In three level PWM inverter which
is used for the HSR traction drive is studied. The purpose is to analyses its harmonic current
characteristics in steady state mode. A comparison between a three level converter harmonics
with a pair of interlaced two level converters is presented and resulted to their equality in this
point of view. In a model of an auto transformer fed AC HSR is presented. Voltage
pantograph in HSR is more problematic because of fast change of load and structure by
train‘s movement has utilised its proposed model to introduce a generalized, multi rout, and
efficient method to solve complicated system of working HSR. In a mathematical work is
done to estimate voltage unbalance due to HSR power demands. Different main power supply
and feeder connections are considered and there potential to reduce unbalance is compared.
has suggested a rigorous way to evaluate voltage unbalance produced by single phase HSR
application on power system. This new method‘s results are compared with traditionally
formulas for unbalance estimation. In the case of Taiwan HSR is studied. Another study
concerning about unbalance estimation is presented in, which uses dynamic load estimation
(DLE) to predict railway produced unbalance. In this way an algorithm is illustrated which is
used to estimate dynamic load of Taiwan HSR and then foresee unbalance affect of this
changing load. In the regarding power system (Taipower) which -due to geographical
situations- is a longitudinal power system is studied to extract impact of HSR on such a
power system.
CHAPTER 2

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POWER SYSTEM
2.1 Electric Power System
An electric power system is a network of electrical components deployed to supply, transfer,
store, and use electric power. An example of an electric power system is the grid that
provides power to an extended area. An electrical grid power system can be broadly divided
into the generators that supply the power, the transmission system that carries the power from
the generating centers to the load centers, and the distribution system that feeds the power to
nearby homes and industries. Smaller power systems are also found in industry, hospitals,
commercial buildings and homes. The majority of these systems rely upon three-phase AC
power the standard for large-scale power transmission and distribution across the modern
world. Specialized power systems that do not always rely upon three-phase AC power are
found in aircraft, electric rail systems, ocean liners and automobiles.
2.2 History
That same year in London, Lucien Gaulard and John Dixon Gibbs demonstrated the
"secondary generator", namely the first transformer suitable for use in a real power system.
The practical value of Gaulard and Gibbs' transformer in 1881, two electricians built the
world's first power system at Godalming in England. It was powered by two waterwheels and
produced an alternating current that in turn supplied seven Siemens arc lamps at 250 volts
and 34 incandescent lamps at 40 volts. However, supply to the lamps was intermittent and in
1882 Thomas Edison and his company, The Edison Electric Light Company, developed the
first steam-powered electric power station on Pearl Street in New York City. The Pearl Street
Station initially powered around 3,000 lamps for 59 customers. The power station generated
direct current and operated at a single voltage. Direct current power could not be transformed
easily or efficiently to the higher voltages necessary to minimize power loss during long-
distance transmission, so the maximum economic distance between the generators and load
was limited to around half a mile (800 m),was demonstrated in 1884 at Turin where the
transformer was used to light up forty kilometers (25 miles) of railway from a single alternating

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current generator. Despite the success of the system, the pair made some fundamental mistakes.
Perhaps the most serious was connecting the primaries of the transformers in series so that active
lamps would affect the brightness of other lamps further down the line.
In 1885, Otto Titusz Bláthy (1860–1939) of Gang & Co.(Budapest) perfected the secondary
generator of Gaulard and Gibbs, providing it with a closed iron core, and thus obtained the
first true power transformer, which he dubbed with its present name. The same year, Bláthy
and two other engineers of the company set up the ZBD system (from their initials) by
implementing the parallel ac distribution proposed by British scientist R. Kennedy in 1883, in
which several power transformers have their primary windings fed in parallel from a high-
voltage distribution line. The system was presented at the 1885 National General Exhibition
of Budapest.
In 1885 George Westinghouse, an American entrepreneur, obtained the patent rights to the
Gaulard-Gibbs transformer and imported a number of them along with a Siemens generator,
and set his engineers to experimenting with them in hopes of improving them for use in a
commercial power system. In 1886, one of Westinghouse's engineers, William Stanley, also
recognized the problem with connecting transformers in series as opposed to parallel and also
realized that making the iron core of a transformer a fully enclosed loop would improve the
voltage regulation of the secondary winding. Using this knowledge he built the first practical
transformer-based alternating-current power system at Great Barrington, Massachusetts in
1886. Westinghouse would begin installing multi-voltage AC transformer systems in
competition with the Edison company later that year. In 1888 Westinghouse also licensed
Nikola Tesla's US patents for a polyphase AC induction motor and transformer designs and
hired Tesla for one year to be a consultant at the Westinghouse Electric & Manufacturing
Company's Pittsburgh labs.
By 1888, the electric power industry was flourishing, and power companies had built
thousands of power systems (both direct and alternating current) in the United States and
Europe. These networks were effectively dedicated to providing electric lighting. During this
time the rivalry between Thomas Edison and George Westinghouse's companies had grown
into a propaganda campaign over which form of transmission (direct or alternating current)
was superior, a series of events known as the "War of Currents". In 1891, Westinghouse
installed the first major power system that was designed to drive a 100 horsepower (75 kW)
synchronous electric motor, not just provide electric lighting, at Telluride, Colorado. On the

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other side of the Atlantic, Mikhail Dolivo Dobrovolsky of AEG and Charles Eugene Lancelot
Brown of Maschinenfabrik Oerlikon,uilt the very first long-distance (175 km, a distance
never tried before) high-voltage (15 kV, then a record) three-phase transmission line from
Lau fen am Neckar to Frankfurt am Main for the Electrical Engineering Exhibition in
Frankfurt, where power was used light lamps and move a water pump. In the US the AC/DC
competition came to the end when Edison General Electric was taken over by their chief AC
rival, the Thomson-Houston Electric Company, forming General Electric. In 1895, after a
protracted decision-making process, alternating current was chosen as the transmission
standard with Westinghouse building the Adams No. 1 generating station at Niagara Falls and
General Electric building the three-phase alternating current power system to supply Buffalo
at 11 kV.
Developments in power systems continued beyond the nineteenth century. In 1936 the first
experimental HVDC (high voltage direct current) line using mercury arc valves was built
between Schenectady and Mechanicville, New York. HVDC had previously been achieved
by series-connected direct current generators and motors (the Thury system) although this
suffered from serious reliability issues. The first solid-state metal diode suitable for general
power uses was developed by Ernst Presser at TeKaDe, Germany, in 1928. It consisted of a
layer of selenium applied on an aluminum plate. In 1957, a General Electric research group
developed a solid-state p-n-p-n switch device that was successfully marketed in early 1958,
starting a revolution in power electronics. In 1957, also Siemens demonstrated a solid-state
rectifier, but it was not until the early 1970s that solid-state devices became the standard in
HVDC, when GE emerged as one of the top suppliers of thyristor-based HVDC. In 1979, a
European consortium including Siemens, Brown Bovver & Cie and AEG realized the record
HVDC link from Cabora Bassa (Mozambique) to Johannesburg (South Africa), extending
more than 1,420 km and rated 1.9 GW at ±533 kV, that resorted to top performing 3.2-kV
thyristors, develped by AEG under GE‘s license, In recent times, many important
developments have come from extending innovations in the ICT field to the power
engineering field. For example, the development of computers meant load flow studies could
be run more efficiently allowing for much better planning of power systems. Advances in
information technology and telecommunication also allowed for remote control of a power
system's switchgear and generators.
2.3 Basics Of Electric Power

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Electric power is the product of two quantities: current and voltage. These two quantities can
vary with respect to time (AC power) or can be kept at constant levels (DC power). Most
refrigerators, air conditioners, pumps and industrial machinery use AC power whereas most
computers and digital equipment use DC power (the digital devices you plug into the mains
typically have an internal or external power adapter to convert from AC to DC power). AC
power has the advantage of being easy to transform between voltages and is able to be
generated and utilised by brushless machinery. DC power remains the only practical choice in
digital systems and can be more economical to transmit over long distances at very high
voltages (see HVDC).
The ability to easily transform the voltage of AC power is important for two reasons: Firstly,
power can be transmitted over long distances with less loss at higher voltages. So in power
systems where generation is distant from the load, it is desirable to step-up (increase) the
voltage of power at the generation point and then step-down (decrease) the voltage near the
load. Secondly, it is often more economical to install turbines that produce higher voltages
than would be used by most appliances, so the ability to easily transform voltages means this
mismatch between voltages can be easily managed. Solid state devices, which are products of
the semiconductor revolution, make it possible to transform DC power to different voltages,
build brushless DC machines and convert between AC and DC power. Nevertheless, devices
utilising solid state technology are often more expensive than their traditional counterparts, so
AC power remains in widespread use.
2.3.1 Balancing the grid
Plus losses should always equal the active power produced. If more power would be
produced than consumed the frequency would rise and vice versa. Even small deviations
from the nominal frequency value would damage synchronous machines and other appliances
One of the main difficulties in power systems is that the amount of active power consumed.
Making sure the frequency is constant is usually the task of a transmission system operator.
In some countries (for example in the European Union) this is achieved through a balancing
market using ancillary services.

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2.4 Components Of Power Systems
2.4.1 Supplies
All power systems have one or more sources of power. For some power systems, the source
of power is external to the system but for others it is part of the system itself—it is these
internal power sources that are discussed in the remainder of this section. Direct current
power can be supplied by batteries, fuel cells or photovoltaic cells. Alternating current power
is typically supplied by a rotor that spins in a magnetic field in a device known as a turbo
generator. There have been a wide range of techniques used to spin a turbine's rotor, from
steam heated using fossil fuel (including coal, gas and oil) or nuclear energy, falling water
(hydroelectric power) and wind (wind power).
The speed at which the rotor spins in combination with the number of generator poles
determines the frequency of the alternating current produced by the generator. All generators
on a single synchronous system, for example the national grid, rotate at sub-multiples of the
same speed and so generate electric current at the same frequency. If the load on the system
increases, the generators will require more torque to spin at that speed and, in a typical power
station, more steam must be supplied to the turbines driving them. Thus the steam used and
the fuel expended are directly dependent on the quantity of electrical energy supplied. An
exception exists for generators incorporating power electronics such as gearless wind turbines
or linked to a grid through an asynchronous tie such as a HVDC link these can operate at
frequencies independent of the power system frequency. Depending on how the poles are fed,
alternating current generators can produce a variable number of phases of power. A higher
number of phases leads to more efficient power system operation but also increases the
infrastructure requirements of the system.
Electricity grid systems connect multiple generators and loads operating at the same
frequency and number of phases, the commonest being three-phase at 50 or 60 Hz. However,
there are other considerations. This range from the obvious: How much power should the
generator be able to supply? What is an acceptable length of time for starting the generator
(some generators can take hours to start)? Is the availability of the power source acceptable
(some renewable are only available when the sun is shining or the wind is blowing)? To the
more technical: How should the generator start (some turbines act like a motor to bring

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themselves up to speed in which case they need an appropriate starting circuit) What is the
mechanical speed of operation for the turbine and consequently what are the number of poles
required? What type of generator is suitable (synchronous or asynchronous) and what type of
rotor (squirrel-cage rotor, wound rotor, salient pole rotor or cylindrical rotor
2.4.2 Loads
Power systems deliver energy to loads that perform a function. These loads range from
household appliances to industrial machinery. Most loads expect a certain voltage and, for
alternating current devices, a certain frequency and number of phases. The appliances found
in your home, for example, will typically be single-phase operating at 50 or 60 Hz with a
voltage between 110 and 260 volts (depending on national standards). An exception exists for
centralized air conditioning systems as these are now typically three-phase because this
allows them to operate more efficiently. All devices in your house will also have a wattage,
this specifies the amount of power the device consumes. At any one time, the net amount of
power consumed by the loads on a power system must equal the net amount of power
produced by the supplies less the power lost in transmission. Making sure that the voltage,
frequency and amount of power supplied to the loads is in line with expectations is one of the
great challenges of power system engineering. However it is not the only challenge, in
addition to the power used by a load to do useful work (termed real power) many alternating
current devices also use an additional amount of power because they cause the alternating
voltage and alternating current to become slightly out-of-sync (termed reactive power). The
reactive power like the real power must balance (that is the reactive power produced on a
system must equal the reactive power consumed) and can be supplied from the generators,
however it is often more economical to supply such power from capacitors. A final
consideration with loads is to do with power quality. In addition to sustained overvoltages
and undervoltages (voltage regulation issues) as well as sustained deviations from the system
frequency (frequency regulation issues), power system loads can be adversely affected by a
range of temporal issues. These include voltage sags, dips and swells, transient overvoltages,
flicker, high frequency noise, phase imbalance and poor power factor.[26]
Power quality issues
occur when the power supply to a load deviates from the ideal: For an AC supply, the ideal is
the current and voltage in-sync fluctuating as a perfect sine wave at a prescribed frequency
with the voltage at a prescribed amplitude. For DC supply, the ideal is the voltage not varying

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from a prescribed level. Power quality issues can be especially important when it comes to
specialist industrial machinery or hospital equipment.
2.4.3 Conductors
Conductors carry power from the generators to the load. In a grid, conductors may be
classified as belonging to the transmission system, which carries large amounts of power at
high voltages (typically more than 69 kV) from the generating centres to the load centres, or
the distribution system, which feeds smaller amounts of power at lower voltages (typically
less than 69 kV) from the load centres to nearby homes and industry. Choice of conductors is
based upon considerations such as cost, transmission losses and other desirable characteristics
of the metal like tensile strength. Copper, with lower resistivity than Aluminum, was the
conductor of choice for most power systems. However, Aluminum has lower cost for the
same current carrying capacity and is the primary metal used for transmission line
conductors. Overhead line conductors may be reinforced with steel or aluminum alloys.
Conductors in exterior power systems may be placed overhead or underground. Overhead
conductors are usually air insulated and supported on porcelain, glass or polymer insulators.
Cables used for underground transmission or building wiring are insulated with cross-linked
polyethylene or other flexible insulation. Large conductors are stranded for ease of handling;
small conductors used for building wiring are often solid, especially in light commercial or
residential construction. Conductors are typically rated for the maximum current that they can
carry at a given temperature rise over ambient conditions. As current flow increases through a
conductor it heats up. For insulated conductors, the rating is determined by the insulation. For
overhead conductors, the rating is determined by the point at which the sag of the conductors
would become unacceptable.
2.4.4 Capacitors And Reactors
The majority of the load in a typical AC power system is inductive; the current lags behind
the voltage. Since the voltage and current are out-of-phase, this leads to the emergence of an
"imaginary" form of power known as reactive power. Reactive power does no measurable
work but is transmitted back and forth between the reactive power source and load every
cycle. This reactive power can be provided by the generators themselves, through the
adjustment of generator excitation, but it is often cheaper to provide it through capacitors,
hence capacitors are often placed near inductive loads to reduce current demand on the power

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system (i.e., increase the power factor), which may never exceed 1.0, and which represents a
purely resistive load. Power factor correction may be applied at a central substation, through
the use of so-called "synchronous condensers" (synchronous machines which act as
condensers which are variable in VAR value, through the adjustment of machine excitation)
or adjacent to large loads, through the use of so-called "static condensers" (condensers which
are fixed in VAR value). Reactors consume reactive power and are used to regulate voltage
on long transmission lines. In light load conditions, where the loading on transmission lines is
well below the surge impedance loading, the efficiency of the power system may actually be
improved by switching in reactors. Reactors installed in series in a power system also limit
rushes of current flow, small reactors are therefore almost always installed in series with
capacitors to limit the current rush associated with switching in a capacitor. Series reactors
can also be used to limit fault currents. Capacitors and reactors are switched by circuit
breakers, which results in moderately large steps in reactive power. A solution comes in the
form of static VAR compensators and static synchronous compensators. Briefly, static VAR
compensators work by switching in capacitors using thyristors as opposed to circuit breakers
allowing capacitors to be switched-in and switched-out within a single cycle. This provides a
far more refined response than circuit breaker switched capacitors. Static synchronous
compensators take a step further by achieving reactive power adjustments using only power
electronics.
2.4.5 Power Electronics
Power electronics are semi-conductor based devices that are able to switch quantities of
power ranging from a few hundred watts to several hundred megawatts. Despite their
relatively simple function, their speed of operation (typically in the order of nanoseconds)
means they are capable of a wide range of tasks that would be difficult or impossible with
conventional technology. The classic function of power electronics is rectification, or the
conversion of AC-to-DC power, power electronics are therefore found in almost every digital
device that is supplied from an AC source either as an adapter that plugs into the wall as
component internal to the device. High-powered power electronics can also be used to
convert AC power to DC power for long distance transmission in a system known as HVDC.
HVDC is used because it proves to be more economical than similar high voltage AC
systems for very long distances (hundreds to thousands of kilometres). HVDC is also
desirable for interconnects because it allows frequency independence thus improving system

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stability. Power electronics are also essential for any power source that is required to produce
an AC output but that by its nature produces a DC output. They are therefore used by many
photovoltaic installations both industrial and residential. Power electronics also feature in a
wide range of more exotic uses. They are at the heart of all modern electric and hybrid
vehicles where they are used for both motor control and as part of the brushless DC motor.
Power electronics are also found in practically all modern petrol-powered vehicles, this is
because the power provided by the car's batteries alone is insufficient to provide ignition, air-
conditioning, internal lighting, radio and dashboard displays for the life of the car. So the
batteries must be recharged while driving using DC power from the engine a feat that is
typically accomplished using power electronics. Whereas conventional technology would be
unsuitable for a modern electric car, commutators can and have been used in petrol-powered
cars, the switch to alternators in combination with power electronics has occurred because of
the improved durability of brushless machinery. Some electric railway systems also use DC
power and thus make use of power electronics to feed grid power to the locomotives and
often for speed control of the locomotive's motor. In the middle twentieth century, rectifier
locomotives were popular, these used power electronics to convert AC power from the
railway network for use by a DC motor. Today most electric locomotives are supplied with
AC power and run using AC motors, but still use power electronics to provide suitable motor
control. The use of power electronics to assist with motor control and with starter circuits
cannot be overestimated and, in addition to rectification, is responsible for power electronics
appearing in a wide range of industrial machinery. Power electronics even appear in modern
residential air conditioners. Power electronics are also at the heart of the variable speed wind
turbine. Conventional wind turbines require significant engineering to ensure they operate at
some ratio of the system frequency, however by using power electronics this requirement can
be eliminated leading to quieter, more flexible and (at the moment) more costly wind
turbines. A final example of one of the more exotic uses of power electronics comes from the
previous section where the fast-switching times of power electronics were used to provide
more refined reactive compensation to the power system.

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2.5 Protective Devices
2.5.1 Power System Protection
Power systems contain protective devices to prevent injury or damage during failures. The
quintessential protective device is the fuse. When the current through a fuse exceeds a certain
threshold, the fuse element melts, producing an arc across the resulting gap that is then
extinguished, interrupting the circuit. Given that fuses can be built as the weak point of a
system, fuses are ideal for protecting circuitry from damage. Fuses however have two
problems: First, after they have functioned, fuses must be replaced as they cannot be reset.
This can prove inconvenient if the fuse is at a remote site or a spare fuse is not on hand. And
second, fuses are typically inadequate as the sole safety device in most power systems as they
allow current flows well in excess of that that would prove lethal to a human or animal. The
first problem is resolved by the use of circuit breakers devices that can be reset after they
have broken current flow. In modern systems that use less than about 10 kW, miniature
circuit breakers are typically used. These devices combine the mechanism that initiates the
trip (by sensing excess current) as well as the mechanism that breaks the current flow in a
single unit. Some miniature circuit breakers operate solely on the basis of electromagnetism.
In these miniature circuit breakers, the current is run through a solenoid, and, in the event of
excess current flow, the magnetic pull of the solenoid is sufficient to force open the circuit
breaker's contacts (often indirectly through a tripping mechanism). A better design however
arises by inserting a bimetallic strip before the solenoid this means that instead of always
producing a magnetic force, the solenoid only produces a magnetic force when the current is
strong enough to deform the bimetallic strip and complete the solenoid's circuit.
In higher powered applications, the protective relays that detect a fault and initiate a trip are
separate from the circuit breaker. Early relays worked based upon electromagnetic principles
similar to those mentioned in the previous paragraph, modern relays are application-specific
computers that determine whether to trip based upon readings from the power system.
Different relays will initiate trips depending upon different protection schemes. For example,
an overcurrent relay might initiate a trip if the current on any phase exceeds a certain
threshold whereas a set of differential relays might initiate a trip if the sum of currents
between them indicates there may be current leaking to earth. The circuit breakers in higher
powered applications are different too. Air is typically no longer sufficient to quench the arc

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that forms when the contacts are forced open so a variety of techniques are used. One of the
most popular techniques is to keep the chamber enclosing the contacts flooded with sulfur
hexafluoride (SF6) a non-toxic gas that has sound arc-quenching properties. Other techniques
are discussed in the reference.
The second problem, the inadequacy of fuses to act as the sole safety device in most power
systems, is probably best resolved by the use of residual current devices (RCDs). In any
properly functioning electrical appliance the current flowing into the appliance on the active
line should equal the current flowing out of the appliance on the neutral line. A residual
current device works by monitoring the active and neutral lines and tripping the active line if
it notices a difference. Residual current devices require a separate neutral line for each phase
and to be able to trip within a time frame before harm occurs. This is typically not a problem
in most residential applications where standard wiring provides an active and neutral line for
each appliance (that's why your power plugs always have at least two tongs) and the voltages
are relatively low however these issues do limit the effectiveness of RCDs in other
applications such as industry. Even with the installation of an RCD, exposure to electricity
can still prove lethal.
2.5.2 SCADA systems
In large electric power systems, Supervisory Control And Data Acquisition (SCADA) is used
for tasks such as switching on generators, controlling generator output and switching in or out
system elements for maintenance. The first supervisory control systems implemented
consisted of a panel of lamps and switches at a central console near the controlled plant. The
lamps provided feedback on the state of plant (the data acquisition function) and the switches
allowed adjustments to the plant to be made (the supervisory control function). Today,
SCADA systems are much more sophisticated and, due to advances in communication
systems, the consoles controlling the plant no longer need to be near the plant itself. Instead it
is now common for plants to be controlled with equipment similar (if not identical) to a
desktop computer. The ability to control such plants through computers has increased the
need for security—there have already been reports of cyber-attacks on such systems causing
Significant disruptions to power systems.

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2.5.3 Power Systems In Practice
Despite their common components, power systems vary widely both with respect to their
design and how they operate. This section introduces some common power system types and
briefly explains their operation.
2.5.4 Residential Power Systems
Residential dwellings almost always take supply from the low voltage distribution lines or
cables that run past the dwelling. These operate at voltages of between 110 and 260 volts
(phase-to-earth) depending upon national standards. A few decades ago small dwellings
would be fed a single phase using a dedicated two-core service cable (one core for the active
phase and one core for the neutral return). The active line would then be run through a main
isolating switch in the fuse box and then split into one or more circuits to feed lighting and
appliances inside the house. By convention, the lighting and appliance circuits are kept
separate so the failure of an appliance does not leave the dwelling's occupants in the dark. All
circuits would be fused with an appropriate fuse based upon the wire size used for that
circuit. Circuits would have both an active and neutral wire with both the lighting and power
sockets being connected in parallel. Sockets would also be provided with a protective earth.
This would be made available to appliances to connect to any metallic casing. If this casing
were to become live, the theory is the connection to earth would cause an RCD or fuse to trip
thus preventing the future electrocution of an occupant handling the appliance. Earthing
systems vary between regions, but in countries such as the United Kingdom and Australia
both the protective earth and neutral line would be earthed together near the fuse box before
the main isolating switch and the neutral earthed once again back at the distribution
transformer. There have been a number of minor changes over the year to practice of
residential wiring. Some of the most significant ways modern residential power systems tend
to vary from older ones include:
 For convenience, miniature circuit breakers are now almost always used in the fuse
box instead of fuses as these can easily be reset by occupants.
 For safety reasons, RCDs are now installed on appliance circuits and, increasingly,
even on lighting circuits.

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 Dwellings are typically connected to all three-phases of the distribution system with
the phases being arbitrarily allocated to the house's single-phase circuits.
 Whereas air conditioners of the past might have been fed from a dedicated circuit
attached to a single phase, centralised air conditioners that require three-phase power
are now becoming common.
 Protective earths are now run with lighting circuits to allow for metallic lamp holders
to be earthed.
 Increasingly residential power systems are incorporating micro generators, most
notably, photovoltaic cells.
2.5.5 Commercial power systems
Commercial power systems such as shopping centers or high-rise buildings are larger in scale
than residential systems. Electrical designs for larger commercial systems are usually studied
for load flow, short-circuit fault levels, and voltage drop for steady-state loads and during
starting of large motors. The objectives of the studies are to assure proper equipment and
conductor sizing, and to coordinate protective devices so that minimal disruption is cause
when a fault is cleared. Large commercial installations will have an orderly system of sub-
panels, separate from the main distribution board to allow for better system protection and
more efficient electrical installation. Typically one of the largest appliances connected to a
commercial power system is the HVAC unit, and ensuring this unit is adequately supplied is
an important consideration in commercial power systems. Regulations for commercial
establishments place other requirements on commercial systems that are not placed on
residential systems. For example, in Australia, commercial systems must comply with AS
2293, the standard for emergency lighting, which requires emergency lighting be maintained
for at least 90 minutes in the event of loss of mains supply. In the United States, the National
Electrical Code requires commercial systems to be built with at least one 20A sign outlet in
order to light outdoor signage. Building code regulations may place special requirements on
the electrical system for emergency lighting, evacuation, emergency power, smoke control
and fire protection.

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CHAPTER 3

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TRACTION SYSTEM
3.1 TRACTION
A part of traction system related papers are about traction motors. Other important part is
power converter which is strongly related to power electronic availabilities.
3.2 Traction Motor
A traction motor is an electric motor used for propulsion of a vehicle, such as an electric
locomotive or electric roadway vehicle. Traction motors are used in electrically powered rail
vehicles (electric multiple units) and other electric vehicles including electric milk floats,
elevators, conveyors, and trolleybuses, as well as vehicles with electrical transmission
systems (diesel-electric, electric hybrid vehicles), and battery electric vehicles.
3.2.1 Motor Types And Control
Direct-current motors with series field windings are the oldest type of traction motors. These
provided a speed-torque characteristic useful for propulsion, providing high torque at lower
speeds for acceleration of the vehicle, and declining torque as speed increased. By arranging
the field winding with multiple taps, the speed characteristic could be varied, allowing
relatively smooth operator control of acceleration. A further measure of control was provided
by using pairs of motors on a vehicle; for slow operation or heavy loads, two motors could be
run in series off the direct current supply. Where higher speed was desired, these motors
could be operated in parallel, making a higher voltage available at each and so allowing
higher speeds. Parts of a rail system might use different voltages, with higher voltages in long
runs between stations and lower voltage near stations where slower operation would be
useful. A variant of the DC system was the AC operated series motor, which is essentially the
same device but operated on alternating current. Since both the armature and field current
reverse at the same time, the behavior of the motor is similar to that when energized with
direct current. To achieve better operating conditions, AC railways were often supplied with

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current at a lower frequency than the commercial supply used for general lighting and power;
special traction current power stations were used, or rotary converters used to convert 50 or
60 Hz commercial power to the 16 2/3 Hz frequency used for AC traction motors. The AC
system allowed efficient distribution of power down the length of a rail line, and also
permitted speed control with switchgear on the vehicle. AC induction motors and
synchronous motors are simple and low maintenance, but are awkward to apply for traction
motors because of their fixed speed characteristic. An AC induction motor only generates
useful amounts of power over a narrow speed range determined by its construction and the
frequency of the AC power supply. The advent of power semiconductors has made it possible
to fit a variable frequency drive on a locomotive; this allows a wide range of speeds, AC
power transmission, and rugged induction motors without wearing parts like brushes and
commutators.
3.3 Transportation Applications
3.3.1 Road Vehicles
Traditionally road vehicles (cars, buses and trucks) have used diesel and petrol engines with a
mechanical or hydraulic transmission system. In the latter part of the 20th century, vehicles
with electrical transmission systems (powered from internal combustion engines, batteries or
fuel cells) began to be developed—one advantage of using electric motors is that specific
types can regenerate energy (i.e. act as a regenerative brake)—providing braking as well as
increasing overall efficiency.
3.3.2 Railways
Traditionally, these were series-wound brushed DC motors, usually running on
approximately 600 volts. The availability of high-powered semiconductors (thyristors and the
IGBT) has now made practical the use of much simpler, higher-reliability AC induction
motors known as asynchronous traction motors. Synchronous AC motors are also
occasionally used, as in the French TGV.

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3.4 Mounting of motors
Before the mid-20th century, a single large motor was often used to drive multiple driving
wheels through connecting rods that were very similar to those used on steam locomotives.
Examples are the Pennsylvania Railroad DD1, FF1 and L5 and the various Swiss Crocodiles.
It is now standard practice to provide one traction motor driving each axle through a gear
drive. Usually, the traction motor is three-point suspended between the bogie frame and the
driven axle; this is referred to as a "nose-suspended traction motor". The problem with such
an arrangement is that a portion of the motor's weight is unsprung, increasing unwanted
forces on the track. In the case of the famous Pennsylvania Railroad GG1, two bogie-
mounted motors drove each axle through a quill drive. The "Bi-Polar" electric locomotives
built by General Electric for the Milwaukee Road had direct drive motors. The rotating shaft
of the motor was also the axle for the wheels. In the case of French TGV power cars, a motor
mounted to the power car‘s frame drives each axle; a "tripod" drive allows a small amount of
flexibility in the drive train allowing the trucks bogies to pivot. By mounting the relatively
heavy traction motor directly to the power car's frame, rather than to the bogie, better
dynamics are obtained, allowing better high-speed operation.
3.4.1 Windings
The DC motor was the mainstay of electric traction drives on both electric and diesel-electric
locomotives, street-cars/trams and diesel electric drilling rigs for many years. It consists of
two parts, a rotating armature and fixed field windings surrounding the rotating armature
mounted around a shaft. The fixed field windings consist of tightly wound coils of wire fitted
inside the motor case. The armature is another set of coils wound round a central shaft and is
connected to the field windings through "brushes" which are spring loaded contacts pressing
against an extension of the armature called the commentator. The commentator collects all
the terminations of the armature coils and distributes them in a circular pattern to allow the
correct sequence of current flow. When the armature and the field windings are connected in
series, the whole motor is referred to as "series-wound". A series-wound DC motor has a low
resistance field and armature circuit. For this reason, when voltage is applied to it, the current
is high due to Ohm's law. The advantage of high current is that the magnetic fields inside the
motor are strong, producing high torque (turning force), so it is ideal for starting a train. The
disadvantage is that the current flowing into the motor has to be limited, otherwise the supply

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could be overloaded or the motor and its cabling could be damaged. At best, the torque would
exceed the adhesion and the driving wheels would slip. Traditionally, resistors were used to
limit the initial current.
3.5 Power Control
As the DC motor starts to turn, interaction of the magnetic fields inside causes it to generate a
voltage internally. This back EMF (electromotive force) opposes the applied voltage and the
current that flows is governed by the difference between the two. As the motor speeds up, the
internally generated voltage rises, the resultant EMF falls, less current passes through the
motor and the torque drops. The motor naturally stops accelerating when the drag of the train
matches the torque produced by the motors. To continue accelerating the train, series resistors
are switched out step by step, each step increasing the effective voltage and thus the current
and torque for a little bit longer until the motor catches up. This can be heard and felt in older
DC trains as a series of clunks under the floor, each accompanied by a jerk of acceleration as
the torque suddenly increases in response to the new surge of current. When no resistors are
left in the circuit, full line voltage is applied directly to the motor. The train's speed remains
constant at the point where the torque of the motor, governed by the effective voltage, equals
the drag - sometimes referred to as balancing speed. If the train starts to climb an incline, the
speed reduces because drag is greater than torque and the reduction in speed causes the back-
EMF to fall and thus the effective voltage to rise - until the current through the motor
produces enough torque to match the new drag. The use of series resistance was wasteful
because a lot of energy was lost as heat. To reduce these losses, electric locomotives and
trains (before the advent of power electronics) were normally equipped for series-parallel
control as well.
3.5.1 Dynamic Braking
If the train starts to descend a grade, the speed increases because the (reduced) drag is less
than the torque. With increased speed, the internally generated back-EMF voltage rises,
reducing the torque until the torque again balances the drag. Because the field current is
reduced by the back-EMF in a series wound motor, there is no speed at which the back-EMF
will exceed the supply voltage, and therefore a single series wound DC traction motor alone
cannot provide dynamic or regenerative braking. There are, however various schemes applied

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to provide a retarding force using the traction motors. The energy generated may be returned
to the supply (regenerative braking), or dissipated by on board resistors (dynamic braking).
Such a system can bring the load to a low speed, requiring relatively little friction braking to
bring the load to a full stop.
3.5.2 Automatic Acceleration
On an electric train, the train driver originally had to control the cutting out of resistance
manually, but by 1914, automatic acceleration was being used. This was achieved by an
accelerating relay (often called a "notching relay") in the motor circuit which monitored the
fall of current as each step of resistance was cut out. All the driver had to do was select low,
medium or full speed (called "series", "parallel" and "shunt" from the way the motors were
connected in the resistance circuit) and the automatic equipment would do the rest.
3.5.3 Rating
Electric locomotives usually have a continuous and a one-hour rating. The one-hour rating is
the maximum power that the motors can continuously develop over a one-hour period
without overheating the motors. Such a test starts with the motors at +25 °C (and the outside
air used for ventilation also at +25 °C). In the USSR, per GOST 2582-72 with class N
insulation, the maximum temperatures allowed for DC motors were 160 °C for the armature,
180 °C for the stator, and 105 °C for the collector.[3]
The one-hour rating is typically about
ten percent higher than the continuous rating, and limited by the temperature rise in the
motor. As traction motors use a reduction gear setup to transfer torque from the motor
armature to the driven axle, the actual load placed on the motor varies with the gear ratio.
Otherwise "identical" traction motors can have significantly different load rating. A traction
motor geared for freight use with a low gear ratio will safely produce higher torque at the
wheels for a longer period at the same current level because the lower gears give the motor
more mechanical advantage. In diesel-electric and gas turbine-electric locomotives, the
horsepower rating of the traction motors is usually around 81% that of the prime mover. This
assumes that the electrical generator converts 90% of the engine's output into electrical
energy and the traction motors convert 90% of this electrical energy back into mechanical
energy. Calculation: 0.9 × 0.9 = 0.81 Individual traction motor ratings usually range up
1,600 kW (2,144 hp). Another important factor when traction motors are designed or
specified is operational speed. The motor armature has a maximum safe rotating speed at or

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below which the windings will stay safely in place. Above this maximum speed centrifugal
force on the armature will cause the windings to be thrown outward. In severe cases, this can
lead to "birdnesting" as the windings contact the motor housing and eventually break loose
from the armature entirely and uncoil. Bird-nesting due to overspeed can occur either in
operating traction motors of powered locomotives or in traction motors of dead-in-consist
locomotives being transported within a train traveling too fast. Another cause is replacement
of worn or damaged traction motors with units incorrectly geared for the application. Damage
from overloading and overheating can also cause bird-nesting below rated speeds when the
armature assembly and winding supports and retainers have been damaged by the previous
abuse.
3.5.4 Cooling
Because of the high power levels involved, traction motors are almost always cooled using
forced air. Typical cooling systems on U.S. diesel-electric locomotives consist of an
electrically-powered fan blowing air into a passage integrated into the locomotive frame.
Rubber cooling ducts connect the passage to the individual traction motors and cooling air
travels down and across the armatures before being exhausted to the atmosphere.
3.6 Auxiliary systems
Is ―IEEE standard for passenger train auxiliary power systems interface‖, which describes
auxiliary power requirements as a standard. and are technical papers which list considerations
required in auxiliary power design to satisfy railway operator‘s requirements. In auxiliary
power configuration in whole train combined of motor cars and passenger cars is explained.
In a novel power control method suitable for auxiliary power supply system is presented,
which targets to achieve high reliability by redundancy. It keeps power factor of auxiliary
converters high. To avoid circulating currents between Auxiliary power converters, one of
them is controlling its power factor and others obey it. In the new topology of full-bridge
three-phase isolated DC/DC converter is suggested. The input DC voltage is inverted to
three-phase AC and then is rectified by a full-bridge rectifier. A new type of multi level
DC/DC converter designed for auxiliary power supply application is proposed in. The
proposed converter is based on half bridge converter. suggests some ideas to have more

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effective and efficient auxiliary equipments. Like fibre optic application in rolling stock
smart battery and charger control methods, etc. Introduces a specific prototype of auxiliary
power supply system, which has applied IGBT as high power switches. In an adaptive inverse
model controller is devised to compensate non-linearity and imperfections of components.
Switching strategy is a modified PWM to adapt duty cycle with nonlinear and non-ideal
system. In a two-switch high frequency flyback converter is developed to achieve ZVS. A
few modules of proposed converter can be paralleled for higher power. The input voltage of
dc/dc converter in is obtained from a fuel cell. The characteristic of this circuit is the
application of energy transfer from leakage inductance of transformer. Due to the fact that
auxiliary power despite of input voltage fluctuation has to provide a regulated voltage at
output, some papers around this purpose reviewed: In a phase modulated full-bridge
converter is improved to decrease output voltage harmonics and enhance it to show more
robustness against input voltage fluctuation. In a ZVS multi level resonant converter is
proposed as well as phase shift modulation is utilized. For ZVS, leakage inductance of
transformer is brought into play. In a novel AC three phase input DC output converter is
introduced. The previous circuit that the new one is based on is a three parallel full bridge
rectifiers followed by buck-boost converters, which proposed paper has merged rectifiers
together and uses a single buck boost converter. has presented a new scheme for switching
which decouples gate switching voltages from input voltage, and then it is a desirable
configuration for situations with varying input voltage.
3.7 Auxiliary Hydraulic System
An auxiliary hydraulic system delivers pressurized hydraulic fluid from a hydraulic pump to
operate auxiliary equipment or attachments. The addition of an auxiliary hydraulic system to
heavy construction equipment increases the versatility of the vehicle by allowing it to
perform additional functions with different attachments.
3.7.1 Usage
An auxiliary hydraulic system is needed to operate heavy construction attachments, such as:
 Hydraulic breakers
 Hydraulic brush cutters

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 Hydraulic compactors
 Hydraulic crushers
 Hydraulic grapples
 Hydraulic processors
 Hydraulic shears
 Hydraulic thumbs
 Hydraulic tilt bucket
 Hydraulic augers
3.7.2 Configuration
Depending upon the vehicle, whether an excavator a back-hoe or a front-end-loader, the
auxiliary hydraulic system may vary. Vehicle interface fittings, length from pump to
attachment and vehicle control systems require various configurations of an auxiliary
hydraulic system. Auxiliary hydraulic systems usually include external fluid fittings to
facilitate connecting and disconnecting the hydraulic fluid supply lines of the attachments to
the vehicles' hydraulic pump. They also usually include valves configured to control the
supply of hydraulic fluid through the fittings.
3.8 Auxiliary Power Unit
An auxiliary power unit (APU) is a device on a vehicle that provides energy for functions
other than propulsion. They are commonly found on large aircraft and naval ships as well as
some large land vehicles. Aircraft APUs generally produce 115 V alternating current (AC) at
400 Hz (rather than 50/60 Hz in mains supply), to run the electrical systems of the aircraft;
others can produce 28 V direct current (DC). APUs can provide power through single-
or three-phase systems.

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3.8.1 Transport Aircraft
The primary purpose of an aircraft APU is to provide power to start the main
engines. Turbine engines must be accelerated to a high rotational speed to provide sufficient
air compression for self-sustaining operation. Smaller jet engines are usually started by an
electric motor, while larger engines are usually started by an air turbine motor. Before the
engines are to be turned, the APU is started, generally by a battery or hydraulic accumulator.
Once the APU is running, it provides power (electric, pneumatic, or hydraulic, depending on
the design) to start the aircraft's main engines. To start, a jet engine requires pneumatic
rotation of the turbine, AC-electrical fuel pumps, and an AC-electrical "flash" that ignites the
fuel. As the turbine (behind the combustion chamber) is already rotating, the front inlet fans
are also rotating. After the ignition, both fans and turbine speed up their rotation. As
combustion stabilizes, the engine thereafter only needs the fuel to run at idle. The started
engine can now replace the APU when starting up further engines. During flight, the APU
and its generator are not needed because power is provided by the engines; in the rare event
of complete engine shutdown, the APU can be used to power critical computer systems and
flight controls, as was seen in the US Airways Flight 1549 water landing. It also allows the
cabin to be comfortable while the passengers are boarding before the aircraft's engines are
started. Electrical power is also used to run systems for preflight checks. Additionally, some
APUs are connected to a hydraulic pump, allowing crews to operate hydraulic equipment
(such as flight controls or flaps) prior to engine start. This function can also be used, on some
aircraft, as a backup in flight in case of engine or hydraulic failure. Aircraft with APUs can
also accept electrical and pneumatic power from ground equipment when an APU has failed
or is not to be used. Some airports reduce the use of APUs due to noise and pollution, and
ground power is used when possible. APUs fitted to extended-range twin-engine operations
(ETOPS) aircraft are a critical safety device, as they supply backup electricity and
compressed air in place of the dead engine or failed main engine generator. While some
APUs may not be startable in flight, ETOPS-compliant APUs must be flight-startable at
altitudes up to the aircraft service ceiling. Recent applications have specified starting up to
43,000 ft (13,000 m) from a complete cold-soak condition such as the Hamilton
Sundstrand APS5000 for the Boeing 787 Dreamliner. If the APU or its electrical generator is
not available, the aircraft cannot be released for ETOPS flight and is forced to take a longer
non-ETOPS route. APUs providing electricity at 400 Hz are smaller and lighter than their

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50/60 Hz counterparts, but are costlier; the drawback being that such high frequency systems
suffer from voltage drops.
3.8.2 History
During World War I, the British Coastal class blimps, one of several types of airship operated
by the Royal Navy, carried a 1.75 horsepower (1.30 kW) ABC auxiliary engine. These
powered a generator for the craft's radio transmitter and, in an emergency, could power an
auxiliary air blower. One of the first military fixed-wing aircraft to use an APU was the
British, World War 1, Supermarine Nighthawk, an anti-Zeppelin Night fighter. During World
War II, a number of large American military aircraft were fitted with APUs. These were
typically known as putt–putts, even in official training documents. The putt-putt on the B-29
Superfortress bomber was fitted in the unpressurised section at the rear of the aircraft.
Various models of four-stroke, Flat-twin or V-twin engines were used. The 7 horsepower
(5.2 kW) engine drove a P2, DC generator, rated 28.5 Volts and 200 Amps (several of the
same P2 generators, driven by the main engines, were the B-29's DC power source in flight).
The putt-putt provided power for starting the main engines and was used after take-off to a
height of 10,000 feet (3,000 m). The putt-putt was restarted when the B-29 was descending to
land. Some models of the B-24 Liberator had a putt–putt fitted at the front of the aircraft,
inside the nose-wheel compartment. Some models of the Douglas C-47 Skytrain transport
aircraft carried a putt-putt under the cockpit floor. The first German jet engines built during
the Second World War used a mechanical APU starting system designed by the German
engineer Norbert Riedel. It consisted of a 10 horsepower (7.5 kW) two-stroke flat engine,
which for the Junkers Jumo 004 design was hidden in the intake diverter, essentially
functioning as a pioneering example of an auxiliary power unit for starting a jet engine. A
hole in the extreme nose of the diverter contained a manual pull-handle which started the
piston engine, which in turn rotated the compressor. Two spark plug access ports existed in
the Jumo 004's intake diverter to service the Reidel unit's cylinders in situ, for maintenance
purposes. Two small "premix" tanks for the Riedel's petrol/oil fuel were fitted in the annular
intake. The engine was considered an extreme short stroke (bore / stroke: 70 mm / 35 mm =
2:1) design so it could fit within the intake diverter of jet engines like the Jumo 004. For
reduction it had an integrated planetary gear. It was produced by Victoria in Nuremberg and
served as a mechanical APU-style starter for all three German jet engine designs to have
made it to at least the prototype stage before May 1945: the Junkers Jumo 004, the BMW

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003, and the prototypes (19 built) of the more advanced Heinkel HeS 011 engine, which
mounted it just above the intake passage in the Heinkel-crafted sheetmetal of the engine
nacelle nose. The Boeing 727 in 1963 was the first jetliner to feature a gas turbine APU,
allowing it to operate at smaller airports, independent from ground facilities. The APU can be
identified on many modern airliners by an exhaust pipe at the aircraft's tail.
3.8.2.1 Sections
A typical gas turbine APU for commercial transport aircraft comprises three main sections:
3.8.2.2 Power section
The power section is the gas generator portion of the engine and produces all the shaft power
for the APU.
3.8.2.3 Load compressor section
The load compressor is generally a shaft-mounted compressor that provides pneumatic power
for the aircraft, though some APUs extract bleed air from the power section compressor.
There are two actuated devices: the inlet guide vanes that regulate airflow to the load
compressor and the surge control valve that maintains stable or surge-free operation of the
turbo machine.
3.8.2.4 Gearbox section
The gearbox transfers power from the main shaft of the engine to an oil-cooled generator for
electrical power. Within the gearbox, power is also transferred to engine accessories such as
the fuel control unit, the lubrication module, and cooling fan. In addition, there is also a
starter motor connected through the gear train to perform the starting function of the APU.
Some APU designs use a combination starter/generator for APU starting and electrical power
generation to reduce complexity. On the Boeing 787 more-electric aircraft, the APU delivers
only electricity to the aircraft. The absence of a pneumatic system simplifies the design, but
high demand for electricity requires heavier generators. Onboard solid oxide fuel cell (SOFC)
APUs are being researched.

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3.8.2.5 Manufacturers
Two main corporations compete in the aircraft APU market: United Technologies
Corporation (through its subsidiaries Pratt & Whitney Canada and Pratt & Whitney Aero
Power), and Honeywell International Inc.
3.8.2.6 Military aircraft
Smaller military aircraft, such as fighters and attack aircraft, feature auxiliary power systems
which are different from those used in transport aircraft. The functions of engine starting and
providing electrical and hydraulic power are divided between two units, the jet fuel
starter and the emergency power unit.
3.8.2.7 Jet fuel starter
A jet fuel starter (JFS) is a small turbo shaft engine designed to drive a jet engine to its self-
accelerating RPM. Rather than supplying bleed air to a starter motor in the manner of an
APU, a JFS output shaft is mechanically connected to an engine. As soon as the JFS begins to
turn, the engine turns; unlike APUs, these starters are not designed to produce electrical
power when engines are not running. Jet fuel starters use a free power turbine section, but the
method of connecting it to the engine depends on the aircraft design. In single-engine aircraft
such as the A-7 Corsair II and F-16 Fighting Falcon, the JFS power section is always
connected to the main engine through the engine's accessory gearbox. In contrast, the twin-
engine F-15 Eagle features a single JFS, and the JFS power section is connected through a
central gearbox which can be engaged to one engine at a time. On the F-15, the jet fuel starter
(JFS) is mated with a central gearbox (CGB). The CGB has extendable pawl shafts that
extend out to reach the aircraft mounted accessory drive (AMAD) mounted in front of each
engine. The AMAD is connected to the jet engine by the power takeoff (PTO) shaft. As the
engine accelerates to starting speed, the PTO shaft becomes the method to drive the AMAD
during flight. Once the aircraft engine has started and begins driving the AMAD, the pawl
shaft on the CGB returns to its retracted position and the JFS is shut down.
3.8.2.8 Emergency power unit
Emergency hydraulic and electric power are provided by a different type of gas turbine
engine. Unlike most gas turbines, an emergency power unit has no gas compressor or

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ignitors, and uses a combination of hydrazine and water, rather than jet fuel. When the
hydrazine and water mixture is released and passes across a catalyst of iridium, it
spontaneously ignites, creating hot expanding gases which drive the turbine. The power
created is transmitted through a gearbox to drive an electrical generator and hydraulic pump.
The hydrazine is contained in a sealed, nitrogen charged accumulator. When the system is
armed, the hydrazine is released whenever the engine-driven generators go off-line, or if all
engine-driven hydraulic pumps fail.
3.8.3 Airport Equipment
Many airports have adopted APUs as a solution to high fuel consumption. Much of the
equipment used to clean and clear runways will use an average of two or more gallons per
hour of diesel while idling. Adding an APU will provide power, heating and cooling as well
as hydraulic warming if necessary and can result in significant fuel and maintenance savings.
3.8.3.1 Spacecraft
The Space Shuttle APUs provided hydraulic pressure. The Space Shuttle had
three redundant APUs, powered by hydrazine fuel. They were only powered up for ascent, re-
entry, and landing. During ascent, the APUs provided hydraulic power for gimballing of the
Shuttle's three engines and control of their large valves, and for movement of the control
surfaces. During landing, they moved the control surfaces, lowered the wheels, and powered
the brakes and nose-wheel steering. Landing could be accomplished with only one APU
working. In the early years of the Shuttle there were problems with APU reliability, with
malfunctions on three of the first nine Shuttle missions.
3.8.3.2 Armor
APUs are fitted to some tanks to provide electrical power without the high fuel consumption
and large infrared signature of the main engine. As far back as World War II, the
American M4 Sherman was known to have had a small, piston-engine powered APU for
charging up the tank's batteries, a feature its Soviet-produced "partner" to the Lend-Lease
M4A2 diesel-engined Shermans the Red Army received — the Mikhail Koshkin-designed T-
34 tank, is not known to have had one.[19]
Both the M1 Abrams and variants of the Leopard
2 such as the Spanish and Danish variants carried the APU in the rear right hull section.
Succeeding versions of the M1 (M1A2 SEPv1, etc.) had different APUs, ranging from earlier

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ones stored in the turret bustle rack, to newer ones in the rear, left hand side of the hull
replacing a fuel cell. The British Centurion tank used an Austin A-Series inline-4 as its
auxiliary power unit. The Turkish self-propelled howitzer T-155 Fırtına uses a 2-stroke diesel
engine located at the rear right hull to supply power to fire control computers and turret
hydraulics.
3.8.3.3 Towed artillery
Many modern towed artillery pieces are fitted with internal combustion engines, primarily to
provide hydraulic power to aid in gun laying and to power flick rammers or other aids to
loading. These engines can also be used to provide limited battlefield mobility when
no artillery tractors are available.
3.9 Commercial vehicles
A refrigerated or frozen food semi trailer or train car may be equipped with an independent
APU and fuel tank to maintain low temperatures while in transit, without the need for an
external transport-supplied power source. In the United States, federal Department of
Transportation regulations require 10 hours of rest for every 11 hours of driving. When
stopped, drivers often idle their engines to provide heat, light, and power. Idling inefficiently
burns fuel and puts wear on engines. Some trucks carry an APU designed to eliminate these
long idles. An APU can save up to 20 US gallons (76 L) (Cat 600 – 10 hours downtime @ 2
gallons per hour idling) of fuel a day, and can extend the useful life of the main engine by
around 100,000 miles (160,000 km), by reducing non-productive run time. On some older
diesel engines, an APU was used instead of an electric motor to start the main engine. These
were primarily used on large pieces of construction equipment.
3.9.1 Diesel
The most common APU for a commercial truck is a small diesel engine with its own cooling
system, heating system, generator or alternator system with or without inverter, and air
conditioning compressor, housed in an enclosure and mounted to one of the frame rails of
a semi-truck. Other designs fully integrate the auxiliary cooling, heating, and electrical
components throughout the chassis of the truck. The APU generator engine is a fraction of

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the main engine's size and uses a fraction of the fuel; some models can run for eight hours on
1 US gallon (3.8 L) of diesel. The generator also powers the main engine's block and fuel
system heaters, so the main engine can be started easily right before departure if the APU is
allowed to run for a period beforehand. These units are used to provide climate control and
electrical power for the truck's sleeper cab and engine block heater during downtime on the
road as mandated by statewide laws for idle reduction.
3.9.2 Propane
A less common APU available for commercial diesel truck cabs and sleepers includes a
heating & cooling system, duplex 110 volt electrical power outlets inside and outside the cab.
These are all powered by a single propane fueled generator. With this system in place, it is no
longer necessary to use diesel fuel during rest and sleep periods in order to provide the air
condition/heating and appliance power for the driver. Delphi has said the 5 kW system for
Class 8 trucks will be released in 2012, at an $8000–9000 price tag that would be competitive
with other "midrange" two-cylinder diesel APUs, should they be able to meet those deadlines
and cost estimates.
3.9.3 Electric
Electric APU‘s have started gaining acceptance. These electric APU‘s use battery packs
instead of the diesel engine on traditional APUs as a source of power. The APU's battery
pack is charged when the truck is in motion. When the truck is idle, the stored energy in the
battery pack is then used to power an air conditioner, heater, and other devices
(television, microwave oven, etc.) in the bunk.
3.9.4 Fuel cells
In recent years, truck and fuel cell manufacturers have teamed up to create, test and
demonstrate a fuel cell APU that eliminates nearly all emissions and uses diesel fuel more
efficiently. In 2008, a DOE sponsored partnership between Delphi Electronics and Peterbilt
demonstrated that a fuel cell could provide power to the electronics and air conditioning of a
Peterbilt Model 386 under simulated "idling" conditions for 10 hours. Delphi has said the
5 kW system for Class 8 trucks will be released in 2012, at an $8000–9000 price tag that
would be competitive with other "midrange" two-cylinder diesel APUs, should they be able
to meet those deadlines and cost estimates.

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3.9.5 Other forms of transport
Where the elimination of exhaust emissions or noise is particularly important (such as yachts,
camper vans), fuel cells and photovoltaic modules are used as APUs for electricity
generation. APUs are installed on some diesel locomotives, allowing the prime mover to be
shut down during extended layovers. This provides power and heat to maintain air pressure,
provide battery charging and prevent the prime mover coolant from freezing.

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CHAPTER 4
INPUT VOLTAGE SOURCE
4.1 INPUT VOLTAGE SOURCE
A voltage source is a two terminal device which can maintain a fixed voltage.[1]
An ideal
voltage source can maintain the fixed voltage independent of the load resistance or the output
current. However, a real-world voltage source cannot supply unlimited current. A voltage
source is the dual of a current source. Real-world sources of electrical energy, such as
batteries, generators, and power systems, can be modeled for analysis purposes as a
combination of an ideal voltage source and additional combinations of impedance elements.
4.2 Ideal Voltage Sources
An ideal voltage source is a two-terminal device that maintains a fixed voltage drop across its
terminals. It is often used as a mathematical abstraction that simplifies the analysis of real
electric circuits. If the voltage across an ideal voltage source can be specified independently
of any other variable in a circuit, it is called an independent voltage source. Conversely, if the
voltage across an ideal voltage source is determined by some other voltage or current in a
circuit, it is called a dependent or controlled voltage source. A mathematical model of an
amplifier will include dependent voltage sources whose magnitude is governed by some fixed
relation to an input signal, for example.[2]
In the analysis of faults on electrical power
systems, the whole network of interconnected sources and transmission lines can be usefully
replaced by an ideal (AC) voltage source and a single equivalent impedance. The internal
resistance of an ideal voltage source is zero; it is able to supply or absorb any amount of
current. The current through an ideal voltage source is completely determined by the external
circuit. When connected to an open circuit, there is zero current and thus zero power. When
connected to a load resistance, the current through the source approaches infinity as the load

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resistance approaches zero (a short circuit). Thus, an ideal voltage source can supply
unlimited power.
No real voltage source is ideal; all have a non-zero effective internal resistance, and none can
supply unlimited current. However, the internal resistance of a real voltage source is
effectively modeled in linear circuit analysis by combining a non-zero resistance in series
with an ideal voltage source (a Thévenin equivalent circuit). A near to ideal voltage source
has been contemplated with a balanced post office box (PO box) network consisting of four
diodes sourced by a balanced supply from centre tapped transformer and capacitive filter with
ground open thus creating a positive and negative alternating reference level. If one of the
points of equal potential of the balanced PO box is supplied with a non ideal voltage source
the other point ( opposite ) raise to the same potential at virtual ground condition and this
raised voltage at this point of virtual ground creates an almost ideal constant voltage source.
Like ideal constant current source, an ideal constant voltage source causes nearly zero power
supplied to the load, hence reflection from load to source is minimum which causes much
better representation of waveform.
4.2.1 Comparison Between Voltage And Current Sources
Most sources of electrical energy (the mains, a battery) are modeled as voltage sources.
An ideal voltage source provides no energy when it is loaded by an open circuit (i.e. an
infinite impedance), but approaches infinite energy and current when the load
resistance approaches zero (a short circuit). Such a theoretical device would have a
zero ohm output impedance in series with the source. A real-world voltage source has a very
low, but non-zero internal resistance & output impedance: often much less than 1 ohm.
Conversely, a current source provides a constant current, as long as the load connected to the
source terminals has sufficiently low impedance. An ideal current source would provide no
energy to a short circuit and approach infinite energy and voltage as the load
resistance approaches infinity (an open circuit). An ideal current source has an infinite output
impedance in parallel with the source. A real-world current source has a very high, but
finite output impedance. In the case of transistor current sources, impedance of a
few megohms (at low frequencies) is typical. Since no ideal sources of either variety exist (all
real-world examples have finite and non-zero source impedance), any current source can be
considered as a voltage source with the same source impedance and vice versa. Voltage
sources and current sources are sometimes said to be duals of each other and any non ideal

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