Two Watt Meter Method For Power Measurement

Two watt meter method is used for measuring power in 3 phase 3 - wire star or delta connected systems either with balanced or unbalanced load. Let us discuss two watt meter method for 3 phase power measurement  with star and delta connection in detail.

Measurement of power by two watt meter method in star connection:

In this method we use two watt meters and the current coils of these watt meters are connected in series with two lines and potential coils are connected across these two lines  and load is connected in star as shown in the following figure.

From figure

The instantaneous current flowing through the watt meter W1 is Ir

The voltage across the potential coil of watt meter W1 is

Instantaneous power measured by the watt meter, W1 is given by,

The instantaneous current flowing through the watt meter W2 is Iy

The voltage across the potential coil of watt meter W2 is
Instantaneous power measured by the watt meter, W2 is given by
The total 3 phase power will be sum of power measured by watt meters W1 and W2

Adding equations 1 and 2 we get following results.

Where P is the total 3 phase power consumed by load.

Measurement of power by two watt meter method in delta connection:

In this method also we use two watt meters and the current coils of these watt meters are connected in series with two lines and potential coils are connected across these two lines and load is connected in delta as shown in the following figure.

The instantaneous current flowing through the watt meter W1 is,

The voltage across the potential coil of watt meter W1 is Erb

Instantaneous power measured by the watt meter, W1 is given by,

The instantaneous current flowing through the watt meter W2 is,
The voltage across the potential coil of watt meter W2 is Eyb

Instantaneous power measured by the watt meter, W2 is given by,
The total 3 phase power will be sum of power measured by watt meters W1 and W2

Adding equations 3 and 4 we get following results.

Where P is the total 3 phase power consumed by load.

Note : The power measured by watt meter is average power because of the inertia of their moving system.

In this post we have discussed about measurement of three phase power using two watt meter method.

Electrical Bus - Bar And Types Of Bus - Bar Arrangements And Its Advantages And Disadvantages

What is a bus bar?

A bus - bar is a conductor or group of conductors and it collects electric energy from incoming feeders and distributes them to outgoing feeders. So bus - bar is a junction where all incoming and out going currents meet. Bus - bar is generally made up of aluminium but not with copper because aluminium has special characters like higher conductivity, lower cost, excellent corrosion resistance, etc.

Criteria For Choosing Type Of Bus - Bar Arrangement:

We have different types of bus - bar arrangements we need to choose the required arrangement. This depends on various factors such as

1. System voltage.
2. Position of a substation in the system.
3. Reliability of supply.
4. Flexibility.
5. cost.
6. Availability of alternative arrangements if outage of any of the apparatus happens.
7. Bus - bar arrangement should be simple and easy to maintain.
8. In case of load - growth there must be possibility to extend the system to meet the load requirements.
9. The installation should be as economical as possible, keeping in view about the needs and continuity of supply.

Types Of Bus - Bar Arrangements:

1. Single bus-bar arrangement.

2. Single bus-bar arrangement with bus sectionalized.

3.Double bus arrangement.

4. Double bus double breaker arrangement.

5. One and a half Breaker arrangement.

6. Main and transfer bus arrangement.

7. Double bus system with bypass isolators.

8. Ring main arrangement.

9. Mesh arrangement.

Let us see each of bus - bar arrangements in detail now.

Note: Through outgoing feeders power is supplied to loads.

Single bus - bar arrangement:

This single bus - bar arrangement consists of only one bus - bar and all the incoming feeders and outgoing distributors are connected to this bus - bar only. All the fuses, circuit breakers, generators and transformers are connected to this as shown in the following figure.

Advantages of single bus - bar arrangement:

1. It is easy in operation.

2. Initial cost s less.

3. Requires less maintenance.

Disadvantages of single bus - bar arrangement:

1. When damage occurs then there will be whole interruption of power supply.

2. Flexibility and immunity are very less.

Single bus - bar arrangement with bus sectionalized:

In  single bus-bar arrangement with bus sectionalized we divide a single bus - bar into two sections with the help of a circuit breaker and isolator switches and load is distributed equally among both sections as shown in the following figure:

Advantages of sectionalized single bus - bar arrangement:

1. As we are using circuit breaker to divide a bus - bar into two sections fault on one section will not interrupt power supply on the other section only few loads will have lac of power supply.

2. The fault level can be reduced by adding a current limiting reactor.

Disadvantages of sectionalized single bus - bar arrangement:

1. We are using extra isolators and circuit breakers so that the cost will be high.

Double bus arrangement:

Double bus arrangement has two bus bars and the incoming feeders and outgoing feeders are connected in parallel to both buses with the help of isolators. By closing the isolator switch we can connect the feeders either to bus - bar 1 or to bus - bar 2 . We can divide the load among two buses with the help of isolator switches by closing the isolator switch that is connected to bus - bar 1 and feeder the load can be connected to bus - bar 1 and by closing the isolator switch connected to bus - bar 2 and feeder the load gets connected to bus - bar 2.  This can be shown in following figure:

We have a bus coupler breaker which is used for bus transfer operation. When we need to transfer load from one bus to other bus we need to close the bus coupler first and then close isolators of the associated bus to which load is to be connected and open the isolator switch coupled to fault bus and then open the bus coupler breaker.

1. It has greater flexibility.

2. During fault conditions there is no interruption of power supply to load.

1. We cannot transfer load from one bus to other bus without interruption of power supply for few minutes.

Double bus double breaker arrangement:

In double bus double  breaker arrangement we connect a feeder in parallel to both buses with the help of two circuit breakers and isolator switches instead of bus coupler as shown in the following figure:
Here we energize both the feeders and divide feeders among both the buses but we can connect desired feeder to desired bus at any time for this purpose we need to close the isolator and then circuit breaker associated with the required bus - bar and later open the circuit breaker and then isolator from which is has to be disconnected.

Advantages of double bus double breaker system:

1. During fault conditions load can be transferred to one bus so there will not be interruption in power supply.

2. Here we are not using a bus coupler so there will not be much delay in power supply while closing circuit breaker to transfer load from one bus to other bus.

3. High flexibility.

Disadvantages of double bus double breaker system:

1. The number of circuit breakers used are high so cost is very high.

2. Maintenance cost will also be high.

So this type of arrangement is used very rare.

One and a half breaker arrangement:

Because of high cost of double bus double breaker arrangement we use one and a half breaker arrangement. Here the two feeders are fed through their corresponding bus - bars and these two feeders are coupled by a third circuit breaker called tie - breaker as shown in the following figure:
During normal conditions all the three circuit breakers are closed and the both circuits operate in parallel and power is fed to feeders from the two bus - bars. If fault occurs on one bus bar then  with the help of second  bus - bar feeder circuit breaker and tie breaker power is fed to feeders. This means each feeder breaker has to be rated to feed both feeders which are coupled by tie breaker.

Advantages of one and a half breaker system:

1. There will be no interruption of power in case of fault because all the feeders can be transferred to other healthy bus immediately.

3. Cost is less compared to double bus double breaker arrangement.

Disadvantages of one and a half breaker system:

1. This arrangement is complicated because during fault two circuit breakers are to be opened.

2. Maintenance cost is high.

Main and transfer bus arrangement:

In main and transfer bus arrangement we have two buses one is main bus and the other is transfer bus. With the help of isolator switches it is connected to the transfer bus which are called bypass isolators and with the help of circuit breakers and isolator switches it is connected to the main bus. There is also bus coupler as shown in the following figure:

In normal conditions the feeders are fed through main bus but during fault conditions load is transferred to the transfer bus. In order to transfer load from main bus to transfer bus we need to close the bus coupler first and then close by pass isolators of feeder to be connected to transfer bus and open the isolator switch of feeder coupled to main bus and then open the bus coupler breaker.

Advantages of main bus and transfer bus system:

1. No interruption of  power supply because in case of fault load can be shifted to transfer bus.

2. Load can be divided into two groups since they can be feed from either of the buses.

Disadvantages of main bus and transfer bus system:

1. Two bus - bars are used which increases the cost.

Double bus arrangement with by pass isolators:

Double bus system with bypass isolators is combination of double bus system and main and transfer bus system. Here the feeders are connected to both the buses with the help of isolators during fault conditions loads can be transferred to healthy bus by closing isolators of feeders associated to healthy bus and opening isolators of feeders associated to faulty bus. The connection diagram is given below:
A bus coupler is also provided so while transferring load to healthy bus close the bus coupler breaker first and close the isolator of feeder to which it has to be transferred and open the isolator switch of feeder coupled to fault bus and then open the bus coupler breaker.

Advantages of double breaker system with by pass isolators:

1. No interruption of  power supply because in case of fault load can be shifted to transfer bus.

2. Load can be divided into two groups since they can be feed from either of the buses.

Disadvantages of double breaker system with by pass isolators:

1. cost is high as we are using two bus bars and extra isolator switches.

2. Complex in nature.

Ring main arrangement:

Ring main arrangement provides double feed to each feeder circuit. Here the end of the bus bars is returned upon themselves to form a ring. Hence it is called main ring arrangement. This arrangement is shown in the following figure:
Here if one circuit beaker is damaged it is opened and the feeder can be supplied from the other circuit breaker which is near to it.

1. Since each feeder is fed from two circuit breakers even if fault occurs in one system the feeder can be fed from other system so there will be no interruption of power supply under fault conditions.

2.The effect of fault is localized to that section alone and the rest of the section continues to operate normally.

1. There will be difficulty to add  any new circuit in the ring.

Mesh arrangement:

In mesh arrangement between the mesh formed by bus bars circuit breakers are installed as shown in the following figure:
From the node point of mesh circuit is tapped. We need to open two circuit breakers when the fault occurs so that protection can be obtained but switching is not possible.

1. Provides protection against fault.

2. For substations having large number of circuits this arrangement is suitable.

1. It doesn't provide switching facility.

2. Not suitable for all type of substations.

These are the different sub station layouts or bus bar arrangements.

In this post we have learnt about electrical bus -bar and types of bus - bar arrangements and its advantages and disadvantages.

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Star - Delta Starter

To start a large induction motor we use star - delta starter because large induction motors(cage type) with delta connected stator when started directly on line it produces large starting current surges which causes fluctuations in voltage on supply line. To prevent this we run induction motor at reduced voltage at the start of induction motor and later on after getting require speed we operate induction motor at full supply voltage for this purpose we use star delta starter.

Working Principle Of Star - Delta Starter:

As discussed above to reduce fluctuations in voltage on supply line we need to reduce starting surge currents so we need to reduce the voltage at the start of induction motor for this purpose we firstly connect the stator windings of induction motor in star connection and later on we connect the stator windings in delta to operate at full supply voltage. See the below circuit diagram how the star - delta starter is connected to induction motor.

Connection diagram of star - delta starter:

 star delta starter control circuit diagram
During start position of switch the stator windings are connected in star as shown in the following figure.

Now the induction motor gradually picks up it's speed. When the speed becomes 80 percent of its rated speed then the switch moves to run position as a result stator windings get connected in delta as shown in the below figure.

Theory And Calculations Of Star - Delta Starter:

To understand how voltage is reduced by star connection of stator windings see the below calculations.

In star connection the phase voltage is 1/√3 times of line voltage as the torque is directly proportional to square of voltage applied the torque is reduced to 1/3 times than the torque produced by starting with direct delta connection.

Let,

VL be the line voltage.

V1 is the phase voltage.

Istyp be  starting current per phase when the stator windings are connected in star.

Istyl is the starting line current when the stator windings are connected in star.

IstΔp is the starting current per phase by direct switching with the stator windings connected in delta

IstΔl is the starting line current by direct switching with the stator windings in the delta.

IscΔp is the short circuit phase current by direct switching with the stator windings in the delta.

Ze10 is the standstill equivalent impedance per phase of the motor, referred to the stator

In star connection,  line current will be equal to phase current.
In delta connection, the line current is equal to the √3 times of the phase current. so we get,

This shows that with star delta starter, the starting current from the main supply is one-third of that with direct switching in the delta.
This shows with star delta starter, the starting torque is reduced to one-third of the starting torque obtained with the direct switching in the delta.
Here,
IflΔp is the full load phase current with the winding connected in delta. But
So the above equations show how voltage and torques are reduced with star delta starter than direct delta starting.

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Electrical Braking Of DC Motor

We have two types of braking they are mechanical braking and electrical braking. We prefer electrical braking to stop a dc motor rather than mechanical braking because electrical braking has more advantages than mechanical braking they are mentioned below:

Advantages of electrical braking over mechanical braking:

1. Electrical braking is fast and effective than mechanical braking

2. Electrical braking doesn't involve high maintenance cost unlike mechanical braking. In mechanical braking we need to replace break shoes periodically which involves high maintenance cost.

3. Amount of heat generated in electrical braking is very much less than that of heat produced due to mechanical braking. This heat produced in mechanical braking at brake shoes leads to failure of brakes.

4. In electrical braking a part of electrical energy is returned to supply which helps in reducing the running cost.

5. Using electric braking the capacity of the system like higher speeds, heavy loads can be increased which cannot be obtained through mechanical braking.

Because of the above advantages we use electrical braking to stop dc motor instead of using mechanical braking.

Now let us see about electrical braking in detail.

Types of electrical braking :

There are three types of electrical braking. They are:

1.Regenerative Braking.

2.Dynamic Braking or rheostatic braking.

3.Plugging.
Here let us see how electrical braking is applied to stop dc shunt motor and dc series motor.

Electrical braking of dc shunt motor:

Each of the three electrical braking methods to stop dc shunt motor are discussed clearly below.

Regenerative braking of dc shunt motor:

In this type of braking if the load on the dc shunt motor increases the speed of motor above the no load speed at constant excitation then the back emf (Eb)produced will be greater than the supply voltage at this stage dc shunt motor acts as generator since the motor armature current reverses its direction. So now it supplies power to the line. Due to reversal of direction of armature current as Eb  > V, armature torque is reversed and speed falls until Eb  becomes less than V so the motor doesn't completely stop in regenerative braking only speeds above no load speeds are decreased and controlled. Regenerative braking is clearly shown in the following figure.

Dynamic braking or rheostatic braking of dc shunt motor:

In dynamic braking we disconnect the armature of dc motor from the supply and connect a resistor to it while the field is connected to the supply as shown in the following figure.
As the armature is disconnected from the supply and connected as shown above now it acts as generator and kinetic energy stored in rotating parts and connected load is converted into electrical energy and is dissipated through rheostat as heat energy and dc shunt motor stops. This is not an efficient method because all the generated energy is dissipated as heat energy.

Plugging of dc shunt motor:

In this method the terminals of the armature of dc motor or supply polarity is reversed. So the torque direction gets reversed and hence back emf Eb and supply voltage V will be in the same direction. So now voltage will 2V which involves high inrush current to prevent this we add a resistance as shown in the following figure.
Now the motor speed decreases slowly and stops, at this point an external device is required to cut off supply as soon as motor comes to rest.Plugging gives greater braking torque as compared to rheostatic braking or dynamic braking.

Electrical braking of dc series motor:

Each of the three electrical braking methods to stop dc series motor are discussed clearly below.

Dynamic braking or rheostatic braking of dc series motor:

In this the armature is disconnected from the supply and current through the armature reverses its direction and field remains connected to the supply. Care should be taken such that current direction through field doesn't changes for this purpose we reverse the field .Now dc series motor acts as dc series generator. This can be shown in the following figure.
Now the kinetic energy stored in rotating parts and connected load is converted to electrical energy and dissipated through rheostat as heat and dc series motor stops.

Plugging of dc series motor:

In this method terminals of the armature or supply voltage are reversed and a resistance is added to control magnitude of braking torque. By this dc series motor stops. The figure is shown in the following diagram.Plugging gives greater braking torque as compared to rheostatic braking or dynamic braking.

Regenerative braking of dc series motor:

Regenerative braking with dc series motor is not possible because increasing in excitation causes decrease in speed. Back e.m.f Eb cannot be greater than supply voltage.So regenerative braking is not possible with dc series motor to make it possible we need to connect dc series as shunt motor. For traction motors regenerative braking is done by special arrangement as shown in the following figure. Using series motors for regenerative braking the fields must be excited separately and use stabilizing circuits. The figure shown below gives connections for regenerative braking on dc series motor.

By connecting in this way back e.m.f Eb can be made greater than V and can be run as generator and torque gets reversed and speed falls till Eb becomes less than V. Hence in this way regenerative braking is done on dc series motor.

In this post we have discussed about electrical braking of dc series and dc shunt motor.

Torque Equation And Torque - slip Characteristics Of Three Phase Induction Motor

Torque - slip characteristics shows the variation of torque of 3- phase induction motor with the change in slip of  that three phase induction motor.

To understand the torque - slip characteristics let us first derive torque equation under running conditions of three phase induction motor.

Torque equation under running conditions of 3 phase induction motor:

Let us see derivation for torque equation of 3 phase induction motor.

We know that,

Torque  T = Er Ir cosϕ2 or T ∝ ϕ Ir cosϕ2

Here Er = rotor e.m.f / phase under running conditions.
Ir = rotor current / phase under running conditions.

And Er = s E2

Ir = Er / Zr

Zr can be calculated from the following figure by applying pythogerous theorem.

Now we get

From figure we get,

Where S is slip which is defined as ratio of difference between synchronous speed and actual speed of rotor.

When the speed changes slip changes as a result torque also changes. Also the equation clear shows that torque changes with respect to change in slip but is not always directly proportional it always depends on the value of slip that is whether the slip value is low , medium or high. Now let us see this in detail.

Relation between torque and slip of a 3 phase induction motor:

Now let us see how torque changes with low , medium and high values of slip in detail.

Slip less than zero ( s < 0):

If the slip is less than zero it will be in generating mode. As in this mode both torque and slip are negative it should be driven by prime mover so it acts as induction generator as is it used mechanical energy and converts into electrical energy. Generally this mode of operation is not used because if the induction machine is used as generator it requires high amount of reactive power to be supplied which is expensive again.

Slip is between zero and one ( 0 < s < 1 ):

From torque equation we have torque as
T =

At s=0, T will be zero so the curve starts from origin.

Now at speeds close to synchronous speed the value of sX2 is small and an be ignored. so now torque T becomes

T ∝ s / R2

If R2 is constant the we have

T ∝ s so the torque graph will be approximately a straight line for low values of slip.

As slip increases torque also increases and becomes maximum when slip s = R2 / X2. To know how at maximum torque slip is R2 / X2 see the following derivation.

Condition for maximum torque:

We know torque is given by,

Now differentiate above expression with respect to slip s and equate the expression to zero.

Put Y = 1/T for making calculation simpler we get,

So we get at maximum torque slip is s = R2/X2.

The torque at this point is called breakdown torque or pull-out torque.

Now if the slip increases further by increasing the load then R2 can be ignored. So for large values of slip we get torque as

T ∝ 1/s.

So in this region the torque slip characteristics is a rectangular hyperbola. This can be seen in the following figure.

In this mode 3 phase induction machine will be in motoring mode. At no load slip will be zero and at full load slip will be 1.

Slip greater than one ( S > 1 ):

This mode is called breaking mode. In this mode the supply voltage polarities are changed as a result motor rotates in reverse direction an stops. This help to stops the induction machine in very short time.

The overall torque - slip characteristics of 3 phase induction motor is shown in the following figure.

Today we have learnt about torque equation of 3 phase induction motor and torque slip characteristics of 3 phase induction motor.

Instrument Transformers

Definition of Instrument Transformer

In heavy currents and high voltage a.c. circuits, the measurement can not be done by using the method of extension of ranges of low range meters by providing suitable shunts. In such conditions, specially constructed accurate ratio transformers called instrument transformers. These can he used, irrespective of the voltage and current ratings of the a.c. circuits. These transformers not only extend the range of the low range instruments but also isolate them from high current and high voltage a.c. circuits. This makes their handling very safe. These are generally classified as

(i) current transformers and (ii) potential transformers.

Current Transformers (C.T.) Construction:

The large alternating currents which can not be sensed or passed through normal ammeters and current coils of watt meters, energy meters can easily be measured by use of current transformers along with normal low range instruments.

A transformer is a device which consists of two winding's called primary and secondary. It transfers energy from one side to another with suitable change in the level of current or voltage. A current transformer basically has a primary coil of one or more turns of heavy cross-sectional area. In some, the bar carrying high current may act as a primary. This is connected in series with the line carrying high current.

The secondary of the transformer is made up of a large number of turns of fine wire having small cross-sectional area. This is usually rated for 5 A. This is connected to the coil of normal range ammeter. Through this ammeter we can note down the value of current flowing through the secondary winding of current transformer. Symbolic representation of a current transformer is as shown in the figure.

Working of a current transformer and C.T Ratio:

A combination of current transformer and ammeter helps us to find out the higher values of current flowing through line. As discussed we step down the value of line current by increasing the turns in secondary winding. This shows that there is inverse relation between between primary and secondary current and the number of turns of primary and secondary. We connect an ammeter to the secondary winding of current transformer to get secondary current which is shown in the following figure.

So now we can calculate the value of current through line or primary current from the C.T ratio.

Where,
Np is number turns of primary winding.
Ns is number turns of secondary winding.
Ip is current through primary winding.
Is is current through secondary winding.

Potential Transformers (P.T) Construction:

The large alternating currents which can not be sensed or passed through normal voltmeters and voltage coils of watt meters, energy meters can easily be measured by use of potential transformers along with normal low range instruments.

A potential transformer has two winding's namely primary and secondary. Primary winding has large number of turns and it is connected in parallel to the line(between line and ground) whose voltage is to be measured. Now the secondary has less number of turns. This is usually rated to 110 V and is connected directly to voltmeter. Through this voltmeter we can note down the value of voltage across the secondary winding of potential transformer.Symbolic representation of a potential transformer is as shown in the figure.

Working of a potential transformer and P.T Ratio:

A combination of potential transformer and voltmeter helps us to find out the higher values of potential across the line. As discussed we step down the value of primary voltage by decreasing the turns in secondary winding. This shows that primary and secondary voltage and the number of turns of primary and secondary are directly proportional.We connect an voltmeter across the secondary winding of potential transformer to get secondary voltage which is shown in the following figure.

So we can calculate the value of line voltage or voltage across the primary of potential transformer from the P.T ratio
Where,
Np is number turns of primary winding.
Ns is number turns of secondary winding.
Ip is current through primary winding.
Is is current through secondary winding.

In this post we have learnt about instrument transformers namely current transformer and potential transformer.