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MEASURING ELECTRICAL

ENERGY

PRINCIPLES OF MEASUREMENTS

ANALOG POWER METERS

DIGITAL METERS

Electrical Power in Resistive Loads

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The product of voltage and current, P, varies during the

sinusoidal cycle

Electrical Power in Resistive Loads

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v(t) = Vmaxcos(t) i(t) = Imaxcos(t) p(t) = VmaxImaxcos2(t)

cos2x = 0.5(1+cos(2x) p(t) = 0.5 VmaxImax(1+cos(2t))

The average power in one cycle of AC voltage and current

applied to the load is

and

and

Electrical Power in Reactive Loads

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v(t) = Vmaxcos(t)

i(t) = Imaxcos(t+)

p(t)=VmaxImaxcos(t)cos(t+)

Electrical Power in Reactive Loads

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i(t) = Imaxcos(t+)

Voltage (V)

Current (A)

Phase angle

(degrees)

p=VmaxImaxcos(t)cos(t+ )

cos(t)cos(t+ )=0.5cos()(1+cos(2t)) – 0.5sin()sin(2t))

P = IrmsVrmscos()

pF = cos( ) real average power

divided by apparent power, pF = P/VA

Active power (W)

Apparent power

(VA) Reactive power

(VARs)

The maximum is called the

apparent power or volt-ampere (VA)

Monitoring voltage, current, and power

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The apparent power (VA) is the one generated and transmitted to

the loads. Two parts:

•one converted to real work, expressed in watts and

•one stored in the electromagnetic fields; called the reactive

power expressed in reactive Volt-Amperes (VARs).

How

much is

pF and

VAR?

Distribution of Electricity • The transmission and distribution of alternating current electricity typically ranges from

100 volts for residential consumers to 500,000 volts or greater for transmission lines. The frequency is usually 50 or 60 Hz but other frequencies (400 Hz in ships for example) are sometimes used.

• There are several schemes used worldwide for distribution of electricity to the customers. The power and energy measurements vary among them. The commonly used ones:

• Single phase 2-wire: a common residential service in many parts of the world which provides a single voltage, usually 100 to 240 volts.

• Single phase 3-wire: a common residential in North America which provides 2 voltages, 120 volts and 240 volts.

• Polyphase 3-wire network: common in apartment building where it provides 120 volts and 208 volts.

• Polyphase 3-wire delta: generally used in industrial operations or for a single phase motor load such as water pumping station.

• Polyphase 4-wire delta: sometimes used in supplying electricity to sparely populated rural areas. It is an economical way of providing a combination of single phase 3-wire service and a limited supply of polyphase power.

• Polyphase 4-wire wye: commonly used for industrial and commercial operations. It is widely used for electricity distribution systems, where it is transformed to other suitable service configurations.

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Metering Electricity

• Active power, reactive power and volt-ampere are commonly measured

• Maximum or peak power is used to determine the capacity of the generator and transmission system.

• Average power taken by the load in a given time interval indicates the power demand. – Watt (W) meter: measures active electrical power, normally displayed as kW.

– Reactive Volt-Ampere (VAR) meter: measures reactive electrical power, normally displayed as kVAR.

– Volt-Ampere (VA) meter: measures apparent electrical power, normally displayed as kVA.

• Energy is measured by energy meters and generally used for billing – Watt hour (Wh)meter: measures active electrical energy, integrating active

electrical power with respect to time; watts x time(in hours), normally displayed as kWh.

– VAR hour (VARh) meter: measures reactive electrical energy, integrating reactive electrical power with respect to time, normally displayed as kVARh.

– VA hour (VAh) meter: measures apparent electrical energy, integrating apparent electrical power with respect to time, normally displayed as kVAh.

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Electricity Metering Circuits

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Power meter

connection for a

single phase 2-wire

connection

Wattmeter

connection for a

three phase, 4-

wire wye service

Electricity Measuring Devices

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Fundamental

elements of an

electricity meter

•Electromechanical meters

•Electronic meters

Electromechanical meters

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1. Current coil

2. Voltage coil

Mechanical Watt-hours meter

Mechanical means for measuring Watt-Hours are usually centered around the concept of the motor:

1. build an AC motor that spins at a rate of speed proportional to the instantaneous power in a circuit, then have that motor turn an “odometer” style counting mechanism to keep a running total of energy consumed.

2. The “motor” used in these meters has a rotor made of a thin aluminum disk, with the rotating magnetic field established by sets of coils energized by line voltage and load current so that the rotational speed of the disk is dependent on both voltage and current.

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1. Voltage coil - many turns

of fine wire encased in

plastic, connected in

parallel with load.

2. Current coil - three turns

of thick wire, connected

in series with load.

3. Stator - concentrates and

confines magnetic field.

4. Aluminium rotor disc.

5. rotor brake magnets.

6. spindle with worm gear.

7. display dials - note that

the 1/10, 10 and 1000

dials rotate clockwise

while the 1, 100 and

10000 dials rotate

counter-clockwise

Electronic meters

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•Analog multiplying

•Mark-space amplitude or time division multiplexing

•Hall effect

•Transconductance

•Digital sampling

Electrical power transducer with an

analog multiplying device

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Time Division Multiplexer (TDM)

Transducer

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Time Division Multiplexing(TDM)

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V2 = k2I

T1 – T2 = k1V1

The average value of V2 is V2A = k2I(T1-T2)/(T1+T2) = k1k2IV/(T1+T2)

Power to DC voltage converter using pulse-width pulse-height multiplier

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Waveforms for

Analog

computation type

wattmeter (TDM)

General features of TDM method

• Good cost to accuracy ratio

• Excellent linearity and reliability

• Performance under distortion is limited

• Direct measurement limited to watts / vars

• Calibration is necessary

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Hall Effect

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Voltage is proportional to current

and strength of the perpendicular

magnetic field

A Hall probe contains a semiconductor crystal

such as indium antimonide, mounted on an

aluminum backing plate, and encapsulated in the

probe head

Hall effect sensors in measuring

electrical power

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Hall effect power sensor measures instantaneous power

vH(t) =RHi(t)B(t) RH = Hall constant, vx(t) = ai(t) and ix(t) = bB(t)

Advantages of Hall effect method

• Analog watt transducers including Hall effect provide good accuracy even with distorted wave shapes, discontinuity, or where there is poor frequency regulation.

• General features of this method can be summarized as – Very cost effective

technology

– Can measure Watt /VARs, but not VA

– Linearity less than TDM technology

– Excellent response for harmonic content

– Susceptible to large temperature changes. 22

Bias

Resistor

Hal

l S

enso

r

Integration/

calibration Register

Module

Indicator

LED

Magnetic

Core

Iline

Vline

Transconductance

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I0

GT(V2 – V1)

V1

V2

G0 Rd

Having Vi = (V1 – V2)

•An ordinary transistor type differential amplifier can also work:

•The secondary current from the meter transformer is converted to a voltage and

applied the bases of the two transistors.

•The line voltage is applied between the collectors and emitters of the transistors.

•A potential difference between the two collectors is generated. This voltage is the

product of the line voltage and line currents and therefore proportional to the line

power.

•Excellent cost to accuracy ratio

•Requires four quadrant amplifier for superior performance under varying power factors

and harmonic distortions.

CA 3080

Digital sampling

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u(t): instantaneous

voltage value at time t

i (t) instantaneous

current value at time t

u (k): instantaneous

voltage value at kth

sample

i (k) instantaneous

current value at kth

sample

T : cycle

Waveforms for digital sampling

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An example of Semi-Digital Type:

Yokogawa 2533E

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An example of a Full-Digital

Type: Yokogawa WT 2030

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Review of Digital Sampling

• Only technology that does not use analog values of voltage and current. – analog values of voltage and currents are converted to digital data prior to

any multiplication taking place.

– A group of sample includes a sample of voltage and current on each of the three lines.

– Two consecutive cycles have samples that are 34 microseconds apart, this is called sample migration and ensures that each group of samples is not taken at an identical point during the cycling of the signal.

• Most inaccuracies can be fully compensated algorithmically eliminating the need for any physical calibration of the meter.

• Not very cost effective technology for single phase residential compared to TDM, Hall effect and transconductance technologies.

• When measured with digital sampling type instrumentation, the powerful micro-processors can run statistical routines to reveal computed data, oriented to particular customer requirements.

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Advantages and disadvantages of

Digital Sampling

Advantages:

• Ability to handle complex billing rates

• Increased accuracy

• Ability to measure various quantities, one device

• Ability to collect meter data remotely

• Ability to program meter remotely

• Have time saving features

• Ability to measure all four quadrants

Disadvantages:

• More sophisticated testing

apparatus required

• More accurate reference

standards required

• More advanced training is

required.

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