EMF equation of an Alternator/AC Generator

EMF Equation of an Alternator/AC Generator

An alternator or AC generator (dynamo) is a gadget which converts mechanical Vitality to electrical vitality. When we supply the charging current by DC shunt generator through two slip rings (in ongoing alternators, they utilize electronic beginning framework rather than slip rings and commutators) because the field magnets are pivoting. remember that most alternators utilize a pivoting attractive field with a stationary armature.

At the point when the rotor turns, the stator conductors which are static in the event of alternator cut by attractive motion, they have instigated EMF delivered in them (as per Faraday's law of electromagnetic enlistment which expresses that if a conductor or loop joins with any evolving transition, there must be a prompted emf in it.

Note: We will examine the development, Working and Operation. Sorts of Alternators in subtleties in our next posts.EMF Equation of an Alternator and AC Generator

This incited EMF can be found by the EMF condition of the alternator which as pursues:

Lets,

P = No. of shafts

Z = No. of Conductors or Coil sides in arrangement/stage, for example, Z = 2T… Where T is the number of loops or turns per stage (Note that one turn or curl has two finishes or sides)

f = recurrence of actuated EMF in Hz

Φ = Flux per shaft (Weber)

N = rotor speed (RPM)

Kd= Distribution factor = Kd= Distribution factor for emf condition of alternator and air conditioning generator

Where Distribution factor = Kd =distribution factor

Kc or KP = Cos α/2

Whenever initiated EMF is accepted sinusoidal at that point,

Kf = Form factor = 1.11

In one upheaval of the rotor for example in 60/N seconds, every conductor is cut by a transition of ΦP Webers.

dφ = ΦP and furthermore dφ = 60/N seconds

at that point incited e.m.f per conductor ( normal) = EMF EQUATION OF AN ALTERNATOR OR AC GENERATOR… .. (I)

In any case, we realize that:

f = PN/120 or N= 120f/P

Putting the estimation of N in Equation (I), we get,

Normal estimation of EMF per conductor = EMF EQUATION OF AN ALTERNATOR∴ (N= 120f/P)

On the off chance that there are Z conductors in arrangement per stage,

at that point normal e.m.f per stage = 2 f Φ Z Volts = 4 f ΦT Volts … .. (Z=2T)

Likewise, we realize that;

Structure Factor= RMS Value/Average Value

= RMS value= Form factor x Average Value,

= 1.11 x 4fΦT = 4.44fΦT Volts.

(Note that is the very same condition as the EMF condition of the transformer)

What's more, the real accessible voltage per stage

= 4 Kc Kd f ΦT = 4 Kf Kc Kd f ΦT Volts.

Note: If alternator or AC generator is star associated as ordinarily the case, at that point the Line Voltage is √3 times the stage voltage as got from the above recipe

Winding Terminologies in an alternator

1. Conductor: The part of the wire, which is under the influence of the magnetic field and responsible for the induced emf is called the active length of the conductor. The conductors are placed in the armature slots.
2. Turn: A conductor in one slot, when connected to a conductor in another slot forms a turn. So Two conductors constitute a turn. 
3. Coil: As there is the number of turns, for simplicity the number of turns are grouped together to form a coil. Such a coil is called a multi-turn coil. A coil may consist of a single turn called a single turn coil.
4. Coil Side: Coil consists of many turns. Part of the coil in each slot is called coil side of a coil.
5. Pole pitch: It is centre to centre distance between the two adjacent poles. We have seen that for one rotation of the conductors, 2 poles are responsible for 360^o. electrical of emf, 4 poles are responsible for 720^o. electrical of emf and so on. So 1 pole is responsible for 180^o. electrical is also called one pole pitch. Practically how many slots are under one pole which is responsible for 180^o.electrical, are measured to specify the pole pitch.

          e.g. consider 2 poles, 18 slots armature of an alternator. Then under 1 pole, there are 18/2 i.e. 9 slots. so pole pitch is 9 slots or 180 degrees electrical. This means 9 slots are responsible to produce a phase difference of 180 degrees between the EMFs induced in different conductors.

        This number is  slots/pole is denoted as 'n'

                 Pole pitch = 180 degree electrical

                                   = slots per pole (number of  slots/P)=n

      6. Slot Angle (β): The phase difference contributed by one slot in degrees electrical is called slot angle β.

As slots per pole contribute 180-degree electrical which is denoted as 'n', we can write,

So, 1 Slot angle= 180 degree/n

means

   β=180 degree/n

In the above example,

   n= 18/2 =9, while β=180 degree/n = 20 degree

Note:- This means that if we consider an induced emf in the conductors which are placed in the slots which are adjacent to each other, there will exist a phase difference of β degree in between them. While if emf induced in the conductors which are placed in slots which are 'n' slots distance away, there will exist a phase difference of 180 degrees in between them.

Types of Armature winding of an AC machine

In general armature winding is classified as,

1. Single-layer and double-layer winding
2. Full pitch and short pitch winding
3. Concentrated and distributed winding

1. Single-layer and Double-layer winding- If a slot consists of only one coil side, the winding is said to be a single layer. This is shown in figure-

While there are two coil sides per slot, one at the bottom and one at the top the winding is called Double-layer winding.

A lot of space gets wasted in single layer hence in practice generally double layer winding is preferred.

2. Full pitch and short pitch winding- As seen earlier, one pole pitch is 180 degrees electrical. the value of 'n', slots per pole indicates how many slots are contributing 180-degree electrical phase difference. So if coil side in one slot is connected to a coil side in another slot which is one pole pitch distance away from the first slot, the winding is said to be full pitch winding and coil is called full pitch coil.

  For example in 2 poles, 18 slots alternator, the pole pitch is n= 18/2 =9 slots. So if coil side in slot No. 1 is connected to coil side in slot No. 10 such that two slots No. 1 and No. 10 are one pole pitch or n slots or 180 degrees electrical apart, the coil is called full pitch coil.

  Here we can define one more term related to a coil called coil span.

3. Coil Span- It is the distance on the periphery of the armature between two coil sides of a coil. it is usually expressed in terms of the number of slots or degrees electrical. So if the coil span is 'n' slots or 180 degrees electrical the coil is called full pitch coil. This is shown in figure-

     As against this if coils are used in such a way that coil span is slightly less than a pole pitch i.e. less than 180-degree electrical, the coils are called, Short pitched coils or fractional pitched coils. 

So in 18 slots, 2 pole alternator instead of connecting a coil side in slot No. 1 to slot No. 10, it is connected to a coil side in slot No. 9 or slot No. 8, the coil is said to be short pitched coil and winding is called short pitch winding. This is shown in figure-

Advantages of Short Pitch Coils-

In actual practice, short pitch  coils are used as it has the following advantages:

1. The length required for the end connections of coils is less i.e. inactive length of winding is less. so less copper is required. Hence economical.
2. Short pitching eliminates high-frequency harmonics which distort the sinusoidal nature of emf Hence waveform of an induced emf is more sinusoidal due to short pitching.
3. As high-frequency harmonics get eliminated, eddy current and hysteresis losses which depend on frequency also get minimized. This increases efficiency.

To be continued.....

Integral slot winding & fractional slot winding of AC machine

1. Integral slot winding-The value of slots per pole per phase decides the class of the winding.

m= Slots/Pole/Phase

Note-  When the value of m is an integer, then the winding is called integral slot winding.

Consider 2 pole, 12 slots alternator hence,

n= Slots/Pole =12/2 =6

Pole pitch= 180 degree = 6 slots

m= n/2 = 6//2 =3

As m is an integer, the type of winding is integral slot winding. This winding can be full pitch winding or short pitch winding.

Let, the winding is full pitch winding. For integral slot winding, coils of one coil group lying under one pole pair are connected in series. Thus the end of the first coil is connected to start of the next coil lying to the right of the first coil. The alternate coil groups must be reverse connected such that emf induced in them is addictive in nature.  Any slot contains the coil sides which belong to the same phase. Such a winding is shown in figure-

If the short pitch coils are used for integral slot winding then in each group of the slots per pole phase, the coil sides of different phases exist.

2. fractional slot winding- This is another class of winding which depends on the value of m.

Note-  The winding in which slots per pole per phase (m) is a fractional number is called fractional slot winding.

    In such a winding, the number of slots (S) must be divisible by 3. Thus slots per phase is an integer which is necessary to obtain symmetrical three-phase winding. But slots per pole (n) and slots per pole per phase (m) both are fractional. As n is a fraction, the coils cannot be the full pitch. Thus if there are 54 slots and 8 poles then the slots per pole n= 54/8 =6.75 hence coil span can be 7 or 6. Generally, short pitch coils are used. Such a fractional slot winding can be easily achieved with double layer winding.

    In a balanced three-phase winding, a basic unit under a pole pair (N and S) is repeated for remaining pole pairs where m is an integer. In fractional slot winding, they are reduced to an irreducible fraction by taking out the highest common factor in the number of slots and poles.

Let  S= Number of Slots
       P= Number of Poles

then for a 3 phase winding,

 The number k indicates the number of repeatable units and the number of possible parallel paths. The characteristics ratio indicates that there are Sk coils per phase distributed among Pk poles.

Thus the winding is to be considered only of Pk poles out of P poles and for other poles it is repeated.

Similarly, the winding arrangement is to be considered for Sk slots out of total S slots and for other slots it is repeated.

In a double layer winding, only the arrangement of the top layer is to be considered. This gets repeated in the bottom layer in which the corresponding coil sides are located one coil span away.

Advantages of Fractional slot winding-

The various advantages of fractional slot winding are-

1. Though appear to be complicated, easy to manufacture.
2. The number of armature slots (S) need not be an integral multiple of the number of poles (P)
3. The number of slots can be selected for which notching gear is available, which is economical
4. There is saving in machine tools.
5. High-frequency harmonics are considerably reduced.
6. The voltage waveform available is sinusoidal in nature.

Types of armature winding of an AC machine

3. Concentrated and Distributed Winding- In three-phase alternators, we have seen that there are three different sets of windings, each for a phase. So depending upon the total number of slots and number of poles, we have certain slots per phase available under each pole. This is denoted as'

m = Slots per pole per phase = n/number of phases
    = n/3 (generally number of phases is 3)

For example in 18 slots, 2 pole alternator we have

n= 18/2 = 9

and m =9/3=3

So we have 3 slots per pole per phase available. Now let 'x' number of conductors per phase are to be placed under one pole. And we have 3 slots per pole per phase available. But if all 'x' conductors per phase are placed in one slot keeping remaining 2 slots per pole per phase empty then the winding is called concentrated winding.

Note:-  So in the concentrated winding, all conductors or coils belonging to a phase are placed in one slot under every pole.

But in practice, an attempt is always made to use all the' slots per pole per phase available for distribution of the winding. So if 'x' conductors per phase are distributed amongst the 3 slots per phase available under every pole, the winding is called Distributed winding. So in a distributed type of winding all the coils belonging to a phase are well distributed over the' slots per phase, under every pole. Distributed winding makes the waveform of the induced emf more sinusoidal in nature. Also in concentrated winding due to a large number of conductors per slot, heat dissipation is poor.

Note:- So in practice, double layer, short-pitched and distributed type of armature winding is preferred for the alternators.

Example- Write the scheme of connections for a 3 phase, 1 layer stator lap winding of a synchronous machine having 6 poles and 36 slots.


Solution- P=6, 36 slots, n= Slots/pole =6

m= slots/pole/phase = n/3 =2, β= 180 degree/n = 30 degree

For full pitch coils if phase 1 say R starts in slot 1 then it must be connected in slot 7 so that coil span is 6 slots i.e. 6β degree i.e. 180 degrees. Thus the coils are full pitch coils.

  For distributed winding, both slots per pole per phase available are to be used. And all coils of one phase are to be in series. So from slot 7, connect it to coil in slot 2 for lap winding and the second end of slot 2 to coil in slot 8 and so on. After finishing all slots per pole per phase available under the first pair of poles connect the coil to slot 13 under next pole and the winding will be repeated thereon in a similar fashion. The starting end Rs and final end Rf for R phase is taken out finally. The connections for the R phase are shown in figure-

There must be a phase difference of 120 degrees between R and Y. Each slot contributes 30 degrees so the start of Y phase should be 120 degrees apart from Rs i.e. 4 slots away from Rs i.e. in slot 5. Similarly, the start of the B phase is further 120 degrees away from the Y phase i.e. 4 slots away from Ys i.e. in slot 9. Finally, all six ends Rs, Rf, Ys, Yf and Bs, Bf is brought out which are connected in star or delta to complete the winding.

What is Harmonized System?

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Harmonized Commodity Detailing and Coding Systems are commonly mentioned as "Harmonized Systems", or just "HS" is that the multipurpose international product nomenclature developed by the planet Customs Organization (WCO).

It consists of about 5,000 product groups; Each is identified by a six-digit code arranged during a legal and logical structure and supported by well-defined rules to realize a consistent classification.

 The system is used by more than 200 countries and economies as a basis for collecting data on tariffs and international trade. More than 98% of goods in international trade are classified according to their HR classification.

The HS contributes to the harmonization of customs and trade processes and to the exchange of undocumented trade data on such processes, thus reducing the costs of international trade.

Governments, international organizations and other privately owned purposes like internal taxation, national trading policy, control of controlled goods, rules of origin, shipping charges, shipping statistics, price monitoring, quota control, compilation at the national level Widely used by the region. Accounts, economic research and analysis. The HS is, therefore, a universal economic language and commodity code and an indispensable tool in international trade.

Harmonized systems are governed by the "International Convention on the Detailed Description and Coding of Harmonized Commodities". The official interpretation of the HS is given in the explanatory notes published by the WCO (5 volumes in English and French). Interpretative notes are also available online and on CD-ROM, as part of a database grouping all available HS tools, combining nomenclature information, classification opinions and compilation of explanatory notes, related alphabetical indicators and the Prospectus of the Harmonized Systems Committee. classification decisions are taken by the

Maintaining the HS is a priority for the WCO. This activity includes measures to ensure a similar interpretation of the HS and to update it from time to time in the light of technological developments and changes in business patterns. The WCO directs this process in the Harmonized Systems Committee (which represents the contracting parties to the HS Convention), which examines policy issues, decides on classification issues, settles disputes and amends explanatory notes. she exercises. The HS Committee also makes amendments that update the HR every 5-6 years.

What can we use for a single line diagram?

In electrical engineering, a one-phase diagram or single-line diagram (SLD) is a simplified notation to represent a three-phase power system.

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The one-line diagram has its greatest application in power flow studies. Electrical elements such as circuit breakers, transformers, capacitors, bus bars, and conductors are shown by standardizing schematic symbols. Instead of representing each of the three phases with a separate line or terminal, only one conductor is represented.

This is in the form of block diagram illustration illustration

The path for power flow between system entities. The elements on the diagram do not represent the physical shape or location of the electrical device, but a general convention is to arrange the diagram with the same left to right, top to bottom sequence

Represented switchgear or other equipment.

A high-line diagram can also be used to show a high-level view of a drain for a PLC control.

system.

The balanced system theory of three-phase power systems tells us that as long as the load on each of the three phases is balanced, we can consider each phase separately. In electrical engineering, this notion is often useful, and for all to consider

The three phases require more effort with very little potential benefit.

An important and often

• The exception is only an odd problem in one or two phases of the system.
• One-line diagrams are commonly used with other notable simplifications, such as per-unit system.
• A secondary advantage of using a one-line diagram is that the simple diagram leaves more
• Location for non-electric, such as economic, information to be included.

In unbalanced systems,

When using the symmetric components method, there are different one-line diagrams.

Each is designed for positive, negative and zero-sequence systems. This simplifies the analysis of unbalanced conditions of a polyphase system.

Electrical equipment for which there are different constraints

Different phase sequences are identified in the diagrams.

For example, a generator would normally have different positive and negative sequences.

Impedance and some transformer winding connections block zero-sequence currents.

The unbalanced system can be solved in three single line diagrams for each sequence and is interconnected to show how unbalanced components add to each part of the system.

What is (7.0) Ah and (20) hours in a 12 volt 7.0Ah / 20hr battery? How many amperes is the battery? I want to use it for two 12 volt motors.

The specification "7 Ah / 20 hours" states that the battery capacity, multiplied by the hour, is 7 Ah. However, there is a catch - the useful capacity of a lead-acid battery depends on the discharge rate, and the "20 H" part specifies that the 7 Ah portion only applies when the capacity is measured over a 20-hour period.

In other words: If you connect the battery to a load that draws 7/20 = 0.35 A, the battery will supply power for 20 hours, and the total capacity is actually 7 Ah.

However, if you draw 1A, you can expect 7 hours of usage, and you won't get that. Higher currents reduce capacity to some extent. You might also think that you can drag 7A for 1 hour, and that is far from the truth. At this high discharge rate, you may get half an hour, not 1 hour, of use.

The battery likely can supply the 7A safely (this is considered the "1C" discharge rate, as it is 1 times the capacity rating); Check the datasheet to make sure. Just not expected to last very long in that present

Like is it suitable for your motors, is there a peak current that can be pulled by the motors? How long do you want them to run before recharging the batteries? A battery of the size you are discussing will run toy-car shaped motors for a very long time. This can power the motors of a small robot for a few minutes. It would not be suitable for a lawnmower or golf cart at all.

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What is Corona effects in Electrical Transmission System?

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• Power transmission lines can produce small amounts of sound energy as a result of the corona.
• The corona is a phenomenon associated with all transmission lines. Under certain conditions, the localized electric field near the active components and conductors may produce a small electrical discharge or corona that causes the surrounding air molecules to ionize, or undergo minor local changes of electric charge.
• Utility companies try to reduce the amount of corona because the corona is a power loss in addition to low levels of results, and in extreme cases, it can damage system components over time.
• The corona occurs on all types of transmission lines, but it becomes more noticeable at higher voltages (345 kV and higher). Under fair weather conditions, audible noise from the corona is slight and rarely seen.
• During wet and moist conditions, droplets of water collect on the conductors and increase corona activity. Under these conditions, a hoarse or lukewarm sound can be heard in the vicinity of the line.
• The corona results in power loss. Electrical losses such as the corona result from operational inefficiencies and increase the cost of service for all ratepayers; A major concern in transmission line design is the lack of losses.

Source of corona:

• The amount of corona produced by a transmission line is a function of the voltage of the line, the diameter of the conductors, the location of the conductors in relation to each other, the line above sea level, the position and hardware of the conductors, and the local weather conditions. Electric current does not affect the amount of corona produced by a transmission line.
• The electric field gradient is largest on the surface of the conductor. Larger-diameter conductors have fewer electric field gradients on the surface of the conductor and, therefore, have fewer coronas than smaller conductors, all else being the same. The calumet was chosen to line the conductors chosen for larger diameters and to use two-conductor bundles. This reduces the ability to produce audible noise.
• Irregularities (such as nicks on the surface of the conductor and sharp edges on the scraper or suspension hardware) concentrate the electric field at these locations and thus increase the electric field gradient and consequent corona in these areas. Similarly, foreign objects on the conductor surface, such as dust or insects, can create irregularities on the surface that are a source for corona.
• The corona also grows at higher altitudes where the density of the atmosphere is lower than the sea level. Audible noise will vary with height. An increase in height of 1000 feet will result in an increase in audible noise of about 1 dB (A). At a height of 5000 feet, the audible noise will be 5 dB (A) compared to the same audio noise at sea level, which will be equal to everything else. The new Calumet for the Komanch 345 kV double circuit line was built with a height of 6000 feet.
• Rain, snow, fog, hoarseness, and condensation that accumulate on the surface of the conductor are also sources of surface irregularities that can increase corona. During fair weather, the number of these condensed water droplets or ice crystals is usually small and the corona effect is also small.
• However, during the wet season, the number of these sources increases (for example, due to standing raindrops on the conductor) and the corona effect is therefore greater.
• During wet or unscrupulous weather conditions, the conductor corona will produce the greatest amount of noise. However, the noise generated by the raindrops hitting the ground during heavy rains will usually be higher than the noise generated by the corona and thus mask the audible noise from the transmission line.
• The corona built on the transmission line can be minimized by the design of the transmission line and the selection of hardware and conductors used to construct the line. For example, the use of conductor hangers that are rounded instead of sharp edges and no bulging bolts with sharp edges will reduce the corona. Conductors themselves can be made and handled with larger diameters so that the conductor strands have a smooth surface without them. The transmission lines proposed here are designed to reduce corona generation.

Types of Corona:

There are three types of the corona.

• A glow discharge occurs at a gradient of about 20 kV RMS / cm. A glow discharge is light flashes from sharp points that do not produce objectionable RIV / TVI or produce any audible noise.
• At approximately 25 kV RMS / cm, a negative polarity "brush" discharge occurs. So named because the appearance is similar to the round ends of a bottle brush. Audible noise related to brushing corona is usually a continuous background type of hissing or frying noise.
• Approximately 30 kVrms / cm positive polarity plume is generated on a gradient of the corona; Hence its name is similar to a mango. When viewed in the dark, it has a concentrated stem that merges into the branches and purple, tree-like aura. The audible noise associated with the plum corona is a sharp snapping and hissing sound. The plume corona forms the important RIV / TVI.

These observations are based on fair weather conditions. In wet conditions, virtually all active electrodes will be in the corona of one form or another.

Many are under the impression that the dielectric strength of air is higher in dry conditions. That is not true. In fact, the dielectric strength of the air increases with an increase in moisture up to the dew point when moisture begins to condense on the surface of the insulator and other components of the line.

Physical parameters of corona:

• Corona is caused by ionization of the media (air) surrounding the electrode (conductor)
• The corona is a function of the starting voltage
• Corona onset is a function of relative air density
• Corona onset is a function of relative humidity

1. Corona and Electric Field

• The corona is not just a function of the electric field
• The corona is a function of the electric field on the surface of the electrode (conductor)
• The corona is also a function of the radius of curvature of the electrode (conductor).
• The corona is also a function of the rate of decay of the electric field away from the electrode (conductor).
• For the foregoing reasons, it is not correct to select a conductor with the smallest electric field on its surface.

2. Corona and Relative Air Density

• Corona has an inverse relationship with air density
• Standard line designs that perform well at sea level may have significant corona issues that are used on established lines in hilly areas

3. Corona and Humidity

• Corona has an inverse relationship with humidity at power frequencies
• Fairweather corona is more prevalent in low humidity environments

4. Corona is the dependent surface condition of conductors

• The corona is increased by irregularities on the surface of the conductor
• Irregularities include: dust, insects, burr and scratches and water droplets present on new conductors
• The corona will typically be higher on new conductors and will decrease to a steady-state value in about a year of service
• The corona rises considerably during the foul season.

Is the capacitor connected parallel to the fan or in series?

The ceiling fan has 2 windings. A winding consists of a capacitor that is permanently connected in series. This capacitor is located in the fan housing.

Most of the new ones have 2 capacitors on the switch which they are connected in series with the first capacitor located on the fan. They control fan speed through 3-speed switches.

Connecting the capacitor in series reduces capacitance thus slowing the fan run.

Fault finding signal. If Fab = N moves too slowly at high-speed setting then the capacitor in the fan body is faulty. If the fan runs fine at the high-speed setting but is not running properly at low and medium speeds, the problem is on the switch and there is a 2 capacitor pack on the switch. Switch (supplied to the fan) to pass this switch. If the fan runs fine at high speed then the fan is fine.

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