Rubber bands- they can be stretched by our hands. Ever wondered how other materials such iron, copper, superconductors etc. could be stretched? A universal testing machine (UTM), also known as a universal tester, materials testing machine or materials test frame, is used to test the tensile strength and compressive strength of materials. The "universal" part of the name reflects that it can perform many standard tensile and compression tests on materials, components, and structures.

-project and article contributed by Shantanu Bhosale, EEE, VNIT, Nagpur.

State Estimation:

It is a process where the state of the power system is estimated.All the telemetry values of power flow, voltage levels are considered.These values are used to calculate the phase angle of the voltage which helps in determination of the power flow between two nodes in the power system as the power flow is directly proportional to sine of that angle.

The power flow monitoring is important for the power system as any kind of overloading on the lines can lead to cascade tripping and can also lead to black out.

Even after getting acquainted to the various concepts related to electrical engineering, there is always one important concept which most electrical engineers, including me, tend to forget. What exactly is reactive power? What is power factor? Why is it so damn important? What do you actually mean by lag and lead? So this discussion would be an informative recap into the basics.

Disclaimer: You could find this highly descriptive, but a short circuit is the only thing ‘short’ in Electrical Engineering. :P

India has one of largest electrical networks in the world. Different types of sources and load are feeding and consuming power from this massive mesh called the NATIONAL GRID. All the sources are connected in parallel. Parallel operation of the generators improves the reliability of the power system by allowing the isolation of few generators for maintenance or under fault condition without any loss of load.

Maximum percentage of power generation is done by Coal based and hydro-based power plants which use synchronous generators as the generating unit. Wouldn't it be interesting to understand how these power plants control the flow of power and maintain such a large network where there is so much variation of load time to time. Let’s become adept over it.

To begin with lets analyze two synchronous generators working in parallel and observe how various circuit parameters are affected. There are two ways how the generating unit control the power flow to the grid:

•  Adjusting the Driving Torque
• Adjusting the Excitation Voltage

In this post we shall discuss just the affect of change of driving torque on various parameters.

NO LOAD OPERATION:

Let us consider two alternators connected in parallel and are unloaded. With respect to external circuit, both the emfs of generators are in phase and with respect to the local circuit they are in phase opposition.

   

Driving torque can be varied by controlling the gate openings of the hydro turbines or by throttle openings of steam turbine. In this article, we have considered cylindrical rotor generator but the results are equally relevant to salient pole generator too.          

If we increase the driving torque of generator 1, then speed increases and generator 1 emf (E_f1)  gets ahead of generator 2 emf (E_f2) there by a resultant emf (E_c) appears. Due to this resultant emf, E_c a circulating current I_c (fig i) flows which lags E_c by almost 90^.  (as the value of resistance is too small compared to the reactance of the machine). This current flows out of gen 1 nearly in phase with it’s emf E_f1 and enters gen 2 in near phase opposition with E_f2. Thus Gen 1 produces power (=E_f1I_c) as a generator and supplies it to Gen 2  which acts as a motor. This would thus retard the faster machine and accelerates the slower one, finally leading to auto equalization of speed.
  

It is necessary that the machines impedance shouldn’t be purely resistive. If they are purely resistive, then the circulating current would be in phase with E_c      (fig ii) and thereby both will act as generator. There would be no tendency of auto equalization of speed. It implies that there would be frequency mismatch leading to power surges and harmonics.

ON LOAD:

The load current I_L = I_a1 + I_a2 (can be seen in the circuit beside).  Increasing the driving torque would result a change in the amount of load shared, the currents I_a1 and I_a2 and respective power factors. Howsoever, the load current I_L remains constant. First, we’ll see how load sharing varies.
On load operation depends upon the speed-load characteristics of the alternator. Generally these characteristics are not linear. Hence a governor mechanism is used to make them linear as in the figure beside.

If we increase the driving torque of Gen1, speed increases and the speed-load curve shifts upwards indicating the increase in speed. Obviously decreasing the driving torque would shift the characteristics downwards. 

Consider the two generators are supplying to a load P_L (=P₁+P₂ initially). Now if we increase the driving torque of gen1. It’s speed-load characteristics shift upwards. In order to maintain the frequency (as the load is constant) the driving torque of gen2 should be decreased. Thus the dotted lines in the figure indicate the speed load characteristics of both the generators and the line2 indicates the frequency of the constant load. Thus the load shared by gen1 increases to P₁’ and the load of gen 2 decreases to P₂’ but to the end the sums of loads shared by both the generators would be constant and equal to the total load P_L.
Now let us see how the currents and power factors of each generator is effected.

At first assume that E_f1= E_f2 and therefore Ia₁=Ia₂ and the load shared will be equal.

Now increase the driving torque of gen 1 which increases the speed and frequency and thereby increasing the power angle δ to δ1 and the power increases to P₁’.

                                     

 The driving torque of gen2 is now decreases in order to supply to the load at constant frequency. E_f2 decreases and power angle also decreases to δ2 and the power decreases to P₂’.

More over, this change in the emfs will lead to a resultant emf E_c. Hence,  a circulating current flows which lags E_c almost 90^.. This current adds up to I_a1 and hence current through gen 1 increases (indicating that the load shared by this gen has increased). The power factor angle decreases thereby improving the power factor. The current I_c reduces the current from gen 2 and there by indicating that the load shared by this gen is reduced. The power factor angle increases and thereby decreasing the power factor.

Thus we can conclude that, by increasing the driving torque on load increases the load shared, current and also improves the power factor.

Potier triangle method is helpful in obtaining the voltage regulation of synchronous machines. It gives the value of potier reactance and the armature mmf (reaction) by drawing a series of curves on experimental basis.

Potier reactance is the air gap reactance (leakage reactance) of the synchronous machine at full load (rated voltage and current of armature).

Circuit Diagram For Determination of Portier Reactance

Working of a 3 phase Induction Motor

The induction motor works on the principle of Induction and hence the name Induction Motor. The rotating magnetic field produced by the stator cuts through the conductors of the rotor and hence induces voltage. The induced voltage circulates current in the windings of the rotor since the ends of the rotor are short circuited. Current carrying conductor experiences force when placed in a magnetic field. As a result the motor rotates.

What is important for an induction motor to works is a Rotating magnetic field. What is actually a rotating field?

I shall try to explain that through slides of images.

A 3-phase supply consist of same magnitude emf displaced by 120 degrees. Corresponding flux produced are also displaced by 120 degrees. Let us draw these wave forms and find there find their resultant sum for different angles. We find that the resultant of the 3 flux waveform always remain constant for any value of theta. When we plot this magnitude vs. theta graph in polar form we get a rotating magnetic field which is rotating with an angular frequency omega.

Consider the flux produced by the stator is rotating in clockwise direction. Since there is change of flux, there will be induction of voltage. The direction of the current flowing will be such that it opposes the cause of it that is the relative displacement of the flux and conductor. Hence the rotor will rotate in same direction. So 3 phase induction motor is a self-starting motor.


The rotor will always try to make the relative speed to 0 but will not be able to achieve that. As it reaches the Synchronous speed there will be no relative speed and hence no current and no torque. Hence 3 phase induction motor is also called asynchronous motor. However the average speed of the rotor remains almost constant.

Transformer is one of the most essential equipment in a power system. It transfers the electrical energy between two circuits linked magnetically through electromagnetic induction and hence the name transformer.

Transformer require an AC supply for its functioning. Alternating current flowing through the primary winding creates an alternating flux which links the secondary through a magnetic core. Due to changing flux, emf is induced in the secondary winding. The ratio of voltage appearing across the primary and secondary depends upon their turn ratio, being more specific on the transformation ratio.

This was something too basic which I needed to discuss before I take up the more important topic – Harmonics in transformer.

The first question what comes in mind is why will harmonics be produced after all. When we are supply of constant frequency f how can we hope to get multiple frequency? The reason is the B-H curve of the magnetic core through which the flux flows which leads to the production of harmonics.

First of all let me clear what is commutation process. Process of reversal of current through the coil during the short circuit condition is called Commutation.



Let us consider a few commutation segments and see process of reversal of current in the coil step by step. Suppose the dc motor to rotating in anticlockwise direction. Observe the direction of current through the coil 3 during the process of commutation. Initially when the coil 3 (commutator segment 4) is under the S pole the current I_c through it is in clockwise direction and through the brush is 2I_c as can be easily deduced from the figure. The brush is in contact with commutator segment 4 completely.



As the motor rotates, brush comes in contact with the CS-5. Total current through the brush remains same but the contribution of C-3 changes to I₅ from I_c . Rest of the current goes through the coil.



On further rotation half of the CS-5 comes in contact with the brush , thus there is equal contribution from CS-4 and CS-5 to the brush. Notice the current through the coil 3 will become 0. This is a short circuit condition. If there is even a small amount of induced voltage, it would result in large current through the coil thus damaging the winding.



Further rotation brings majority of the current to brush through CS-5. And the direction of the current in the coil 3 has reversed.

One of the most interesting phenomena that occurs in a DC Motor is armature reaction. Current flowing through the armature creates its own magnetic flux called the armature flux. The action of this armature flux on the main flux set up by the field is known as armature reaction. Let us explain this through a series of diagrams. The excitation of field winding sets up magnetic flux from North Pole to South Pole. When the current flows through the armature winding, the direction of current under one pole face is same and opposite to that of other. It can be clearly seen that the resultant armature flux strengthens the main flux on the top left and bottom right side and weakens it on the other. The resultant flux in the armature region is as shown.