Measurement of Electrical Parameters in Steam Turbine

As the generator is coupled with a steam turbine, we shall discuss the measurement of some Electrical parameters such as Voltage, Current, Power, Frequency, and Energy are the major parameters measured.

Voltage

• The other names for voltage are Potential Difference, Electromotive Force (EMF), and pressure of an electrical circuit.
• This voltage is measured with the help of a voltmeter.
• Voltmeters are standard items on switchboards and control panels.
• They are basically single-circuit elements therefore when three phases are to be indicated, either three instruments are used or one with a multipoint switch.
• The voltmeter is connected across the line and is a high-impedance one.
• The voltmeter ranges can be varied with high-value resistors connected in series; such resistors are called voltmeter multipliers.
• For high voltages, the Potential Transformer (PT) is connected to the main line called the primary, and the voltmeter is connected to the secondary.
• Voltmeters are normally of moving iron types.
• Moving coil meters can also be used but in conjunction with rectifiers.

Current

• The quantity of electrical current flowing through a circuit is measured by an ammeter.
• The low-impedance ammeter is connected in series with the line.
• Ammeters connected in parallel to the instruments are accommodated to various ranges with small value resistances.
• For the measurement of a very large current, these current transformers are connected to the main lines called primary, and the instruments are connected to their secondary.
• The Current Transformer (CT), is used to measure large currents.
• Normally the power line itself is considered as primary windings of the current transformer.
• The secondary windings are practically short-circuited by the measuring ammeters.
• Current Transformers convert the current to be measured into conveniently measurable secondary current preserving values and phases in proportion.
• Ammeters are almost identical to voltmeters, but for their input impedances and mode of connections.

Power (Active)

• The power of a direct current (always active) can be found in one ammeter and one voltmeter.
• Both voltage and current readings can be multiplied to get the required power.
• D.C. power can be measured by an Electro-dynamic wattmeter with a voltage coil and current coil.
• Instrument transformers are connected such that the voltage path is connected ahead of the current path.
• For safety reasons, the secondary of both transformers are connected to a common earth.
• Cosφ is the phase angle between the voltage and the current.
• For an alternating current circuit, the active power is given by P= V*I*Cosφ
• The active power for a 3φ phase system is the total of the three components.

For star connection, it is given by.

P = 3 Vp I cos φ

For delta connection, it is given by.

P= √3 V_L I cos φ

Where

V = RMS values of voltage

I = RMS values of current

P = Total power

Cosφ = Power Factor

V_p = Phase to neutral Voltage

V_L= Line Voltage

Some of the common methods used in power plants are

Three-wattmeter is the most accurate method with indications and mechanical adder having a common shaft.

Three-wattmeter Method (Three-phase three-wire system)

W_R+W_Y+W_B = (V_RC * I_R) + (V_YC * I_{Y) +} (V_BC * I_B)

W_R+W_Y+W_B = (V_RN * I_R) + (V_YN * I_{Y) +} (V_BN * I_B)

W_R+W_Y+W_B = P_R +P_Y+ P_B = Total Power

It is observed that the sum of the three individual wattmeter readings (W_R+W_Y+W_B) indicates the total power consumed by the load (P_R +P_Y+ P_B).

Three–Wattmeter Method (3φ 4-wire System)

W_R+W_Y+W_B   = (V_RC * I_R) + (V_YC * I_{Y) +} (V_BC * I_B)

W_R+W_Y+W_B = (V_RN * I_R) + (V_YN * I_{Y) +} (V_BN * I_B)

W_R+W_Y+W_B  = P_R +P_Y+ P_B

The total power consumed by load is given by the summation of three wattmeters.

Two Wattmeter Methods

• This is the most commonly used method for measuring three-phase power.
• It is useful for both balanced and unbalanced loads.
• The sum of two watt-meter readings will be equal to the total power consumed as given below.
• Power consumed by the load

P= V_RN * I_R + V_YN * I_Y + V_BN * I_B

Summation of wattmeter readings

W = W1 + W2

W = (V_RN -V_YN)* I_R + (V_BN – V_YN) * I_B

W = (V_RN * I_R) +(V_BN* I_B) + V_YN (-I_R – I_B)

By Kirchhoff’s law, we know that,  I_R+I_B+I_Y=0, or  I_R -I_B = I_Y

W₁+W₂= V_RN * I_R + V_YN * I_Y  + V_BN * I_B = P

For delta connection load

P = V_RB * I_R + V_YR * I_Y + V_BY * I_B

W₁ + W₂ = -V_YR * (I_R-I_Y) + V_BY *(I_B-I_R)

P= V_RB * I_R + V_YR * I_Y + V_BY * I_B

Where (V_YR + V_BY +V_RB = 0)

It can be proved that the total power

W₁ + W₂= 3*V*I*cos φ

W₁ – W₂ =√3*V*I*sin φ

 Hence,

tanφ = √3*[(W₁ – W₂)/(W₁ + W₂)]

Power factor Cosφ = Cos [tan^-1 {√3 ((W₁ – W₂)/ (W₁ + W₂))}]

Energy

• In terms of watt-hour or kilowatt-hour (kWh).
• The kWh is defined as the energy supplied or consumed at an average rate of 1 kilowatt for one hour.
• In commercial metering, 1 kWh is called 1 unit of energy.
• Energy meters are used for the measurement of energy.
• Energy meters have moving systems that revolve continuously, it deflects only through a fraction of a revolution
• In energy meters, the speed of revolution is proportional to the power and the total number of revolutions made by the meter moving system over a given period is proportional to the energy.
• The most commonly used energy meters are Induction type instruments.
• Such meters have lower friction and a higher torque/weight ratio.
• These meters are inexpensive but accurate.
• Constructional details of an induction type single phase energy meter are shown schematically in the Figure above
• The operating system consists of two electromagnets.
• The current coil is wound on the series magnet and the pressure coil is wound on the shunt magnet.
• Shading bands made of copper are used to bring the flux produced by the shunt magnet exactly in quadrature with the applied voltage.
• The moving system consists of a light aluminum disc mounted on a spindle.
• The disc is placed in the space between the series and shunt magnets.
• The disc is positioned such that it intersects the flux produced by both magnets.
• The deflecting torque on the disc is produced by the interaction between these fluxes and the eddy current they induce in the disc.
• As there is no control spring, continuous rotation is possible.
• The braking system consists of a permanent magnet positioned near the edge of the aluminum disc whose position is adjustable.
• When the braking torque becomes equal to the operating torque, the disc rotates at a steady speed.
• A registering system consisting of a train of reduction gears makes counting in numerical value possible.

Frequency

• Frequency meters are more convenient for most practical purposes.
• These indicate the generated power frequency.
• a vibrating reed frequency meter mainly consists of more thin steel strips called reeds arranged close electromagnet.
• The electromagnet is laminated and its winding is connected, in series with a resistance, across the supply whose frequency is to be measured.
• The external connection is the same as the voltmeter.
• The reeds are made with slight differences in that their natural frequencies are different.
• These reeds are arranged in ascending order of frequency from 47 cycles per second up to 53 cycles per second.
• The natural frequency of the first reed is 47 cycles per second, and the next reed is 47½ cycles per second, and so on.
• The magnetism of the electromagnet alternates with the supply frequency and exerts an attracting force when the meter is in use.
• The one whose natural frequency is matching with the supply frequency will vibrate appreciably showing the supply frequency.
• The flags at the top of the reeds are painted with the corresponding frequency so that one can read directly the frequency by observing the reed which is vibrating most.
• A great advantage of this type of meter is that its indications are independent of the applied voltage and waveforms.