EXP. 1: Electric Power Measurement
AIM
The aim of this experiment is to understand the principle of electric power and the
method of power measurement. In this experiment, you will learn how to measure
power and power factor, and examine the power concept of single- and three-phase
load. Finally you need to determine the relations between the voltage and current
phasors and the power, and the solution for power-factor improvement.
INTRODUCTION
The measurement of power in a DC circuit can be carried out by simultaneous
measurements of voltage and current by using standard types of dc voltmeters and
ammeters. The product of the readings typically gives a sufficiently accurate measure
of dc power. If great accuracy is required, corrections for the power used by the
instruments should be made. In AC circuits the phase difference between the voltage
and current precludes use of the voltmeter-ammeter method unless the load is known
to be purely resistive. When this method is applicable, the instrument readings lead
directly to average power if the ac voltmeters and ammeters are capable of measuring
rms (root mean square) values.
The potential difference in volts between two points is equal to the energy per unit
charge (in joules/coulomb) which is required to move electric charge between the
points. Since the electric current measures the charge per unit time (in
coulombs/second), the electric power P is given by the product of the current i and the
voltage v ( joules/second = watts), as in Eq. (1).
P  vi
(1)
Alternate forms of the basic definition can be obtained by using Ohm's law, which
states that the voltage across a pure resistance is proportional to the current through
the element. This results in Eq. (2),
P  i2R 
v2
R
(2)
where R is the resistance, i is the current through and v is the voltage across the resistive
element. Other commonly used units for electromechanical systems is horsepower (1 hp =
746 W).
These fundamental expressions yield the instantaneous power as a function of time. In
the DC case where v and i are each constant, the instantaneous power is also constant.
In all other cases where v or i or both are time-varying, the instantaneous power is
also time-varying. When the voltage and current are periodic with the same
fundamental frequency, the instantaneous power is also periodic with twice the
fundamental frequency. In this case a much more significant quantity is the average
power, since in most cases the electric power is converted to some other physical
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form such as heat, mechanical power, or light. The rapid fluctuations of the power are
smoothed by the thermal or mechanical inertia of the output system.
There are three major power equations relating the three types of power to resistance,
reactance, and impedance (all use scalar quantities):
Figure 1: The three types of power to resistance, reactance, and impedance.
The following terms are used to describe energy flow in a system (and assign each
of them a different unit to differentiate between them):





Real power (P) or active power: watt [W]
Reactive power (Q): volt-ampere reactive [Var]
Complex power (S): volt-ampere [VA]
Apparent Power (|S|): The absolute value of the complex power S
Phase of Current (φ): The angle of difference (in degrees) between voltage
and current; Current lagging Voltage (Quadrant I Vector), Current leading
voltage (Quadrant IV Vector)
In Figure 2, P is the real power, Q is the reactive power (in this case positive), S is the
complex power and the length of S is the apparent power. Reactive power does not
transfer energy, so it is represented as the imaginary axis of the vector diagram. Real
power moves energy, so it is the real axis.
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Figure 2: The apparent power is the vector sum of real and reactive power.
EQUIPMENT
Digital Power Meter: WT210
Load: Light bulbs, varactor (Auto-transformer), single phase motor, three phase
motor.
LCR meter
EXPERIMENT
Step 1: Connect the light bulbs to the digital power meter and ask Lab demonstrator
to check the circuit connection before start your power measurement. Record all you
findings (voltage, current, different types of power, power factor), by conducting the
three measurements (one light bulb, the other light bulb, both light bulbs) and
compare the results with your calculation results.
Step 2: Repeat the measurements with the varactor connected in series with the light
bulbs, by choosing 50% and 100% of the varactor value.
Step 3: Calculate the values X and R for: one light bulb, the other light bulb, both
light bulbs, with and without the varactor in series. Record the values in a table (leave
some space on the right side for comparisons).
Step 4: Set the varactor to 0 and calculate the capacitor value to achieve a power
factor improvement 1 and enter the values into Figure 9.
Step 5: Connect the two 1-phase motors to the power meter and repeat the
measurements.
Step 6: Compare the findings of the motors, to each other, the type plate and to the
measurements from Step 2. Describe if the motors are resistive, reactive, complex….
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1. 3-Phase motor power measurements
In a 3-phase and 3-wire system, the active power supplied to a 3-phase load may be
measured by two single-phase power meter connected as shown in Figure 3. The total
power is equal to the sum of the two power meter readings. For balanced loads, if the
power factor is less than 100 percent, the instruments will give different readings.
Indeed, if the power factor is less than 50 percent, one of the power meters will give a
negative reading. In this case, the power of the 3-phase circuit is equal to the
difference between the two power meter readings. The two-power meter method gives
the active power absorbed whether the load is balanced or unbalanced. The following
equations can be used to calculate three phase power and angle.
Figure 3: 3-phase power measurement using two single-phase power meter
Apparent power supplied to the motor is
S  3VI
(3)
Active power supplied to the motor is
P  P1  P3
cos   P / S
(4)
Step 7: Conduct power measurements with the three phase motor (Figure 3) and
compare the findings with the type plate. How is the motor connected (star or delta)?
2. Power factor and angle
The angle of this “power triangle” as shown in Figure 2, graphically indicates the
ratio between the amount of dissipated (or consumed) power and the amount of
absorbed/returned power. It also happens to be the same angle as that of the circuit's
impedance in polar form. When expressed as a fraction, this ratio between true power
and apparent power is called the power factor for this circuit. Because true power and
apparent power form the adjacent and hypotenuse sides of a right triangle,
respectively, the power factor ratio is also equal to the cosine of that phase angle.
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The ratio between real power and apparent power in a circuit is called the power
factor. It's a practical measurement of the efficiency of a power distribution system.
For two systems transmitting the same amount of real power, the system with the
lower power factor will have higher circulating currents due to energy that returns to
the source from energy storage in the load. These higher currents produce higher
losses and reduce overall transmission efficiency. A lower power factor circuit will
have a higher apparent power and higher losses for the same amount of real power.
The power factor is 1 when the voltage and current are in phase. It is zero when the
current leads or lags the voltage by 90 degrees. Power factors are usually stated as
"leading" or "lagging" to show the sign of the phase angle, where leading indicates a
negative sign.
Purely capacitive circuits cause reactive power with the current waveform leading the
voltage wave by 90 degrees, while purely inductive circuits cause reactive power with
the current waveform lagging the voltage waveform by 90 degrees. The result of this
is that capacitive and inductive circuit elements tend to cancel each other out.
Example: Power factor improvement.
Figure 4 shows an example of power factor improvement.
Figure 4: Power factor improvement.
The power factor without parallel capacitor can be calculated as follow:
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Figure 5: Power factor calculation
Parallel capacitor corrects lagging power factor of inductive load, therefore the
apparent power can be reduced, as shown in Fig. 9.
Figure 6: Power factor correction.
Since we know that the (uncorrected) reactive power is 119.998 VAR (inductive), we
need to calculate the correct capacitor size to produce the same quantity of (capacitive)
reactive power. Since this capacitor will be directly in parallel with the source (of
known voltage), we'll use the power formula which starts from voltage and reactance:
Figure 7: Calculation of Capacitor.
The power factor for the circuit, overall, has been substantially improved. The main
current has been decreased from 1.41 amps to 994.7 milliamps, while the power
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dissipated at the load resistor remains unchanged at 119.365 watts. The power factor
is much closer to being 1:
Figure 8: Power factor improvement
3. Recommendation of power factor improvement
Reactive power flow on the alternating current transmission system is needed to
support the transfer of real power over the network. In alternating current circuits
energy is stored temporarily in inductive and capacitive elements, which can result in
the periodic reversal of the direction of energy flow. The portion of power flow
remaining after being averaged over a complete AC waveform is the real power,
which is energy that can be used to do work (for example overcome friction in a
motor, or heat an element). On the other hand the portion of power flow that is
temporarily stored in the form of electric or magnetic fields, due to inductive and
capacitive network elements, and returned to source is known as the reactive power.
AC connected devices that store energy in the form of a magnetic field include
inductive devices called reactors, which consist of a large coil of wire. When a
voltage is initially placed across the coil a magnetic field builds up, and it takes a
period of time for the current to reach full value. This causes the current to lag the
voltage in phase, and hence these devices are said to absorb reactive power.
A capacitor is an AC device that stores energy in the form of an electric field. When
current is driven through the capacitor, it takes a period of time for charge to build up
to produce the full voltage difference. On an AC network the voltage across a
capacitor is always changing – the capacitor will oppose this change causing the
voltage to lag behind the current. In other words the current leads the voltage in phase,
and hence these devices are said to generate reactive power.
Energy stored in capacitive or inductive elements of the network give rise to reactive
power flow. Reactive power flow strongly influences the voltage levels across the
network. Voltage levels and reactive power flow must be carefully controlled to allow
a power system to be operated within acceptable limits.
Regarding to your measurement results, if a capacitor and an inductor are placed in
parallel, then the currents flowing through the inductor and the capacitor tend to
cancel out rather than adding. Conventionally, capacitors are considered to generate
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reactive power and inductors to consume it. This is the fundamental mechanism for
controlling the power factor in electric power transmission; capacitors (or inductors)
are inserted in a circuit to partially cancel reactive power 'consumed' by the load. You
need to calculate the capacitor size (C=?) to produce the same quantity of reactive
power.
Figure 9: Calculation of capacitor value for power factor improvement
Reference:
[1] P. Schavemaker and L. V. D. Sluis, “Electrical Power System Essentials”, Wiley, 2009
[2] Tony R. Kuphaldt, Lessons In Electric Circuits, Volume II – AC, Sixth Edition, last update July 25,
2007
[3] Electric power - Wikipedia, the free encyclopedia.htm
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