C.
9 Power Factor Correction Calculation
C.9.1 Introduction
The distribution authority is responsible for the production and transmission of the
reactive power required by the user installations, and therefore has a series of further
inconveniences which can be summarized as:
- Oversizing of the conductors and of the components of the transmission lines;
- Higher Joule-effect losses and higher voltage drops in the components and lines.
The same inconveniences are present in the distribution installation of the final user.
The power factor is an excellent index of the size of the added costs and is therefore
used by the distribution authority to define the purchase price of the energy for the final
user
The ideal situation would be to have a cosφ slightly higher than the set reference so as
to avoid payment of legal penalties, and at the same time not to risk having, with a
cosφ too close to the unit, a leading power factor when the power factor corrected
device is working with a low load.
The distribution authority generally does not allow others to supply reactive power to
the network, also due to the possibility of unexpected overvoltages.
Power capacitors provide many benefits.
- Reduced electric utility bills
- Increased system capacity
- Improved voltage
- Reduced losses
C.9.2 Reactive Power Calculation
In the case of a sinusoidal waveform, the reactive power necessary to pass from one
power factor cosφ1 to a power factor cosφ2 is given by the formula:
Qc = Ql – Qs = P.(tanφ1 – tanφ2) = P. Kc
See fig. (1)
Where:
P is the activate power (kw) = x V x I x Cos 1
QL are the reactive power and the phase shifting before power factor correction
(KVAR)
QS are the reactive power and the phase shifting after power factor correction;
(KVAR)
QC is the reactive power for the power factor correction (KVAR).
KC deference between tanφ1 and tanφ2 from (table -1)
Fig. (1)
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CONSULTANT ENGINEER / MOHAMED OSMAN AL SHAFEY
For Different Values of the Power Factor before and after the Correction
Table (1): Factor Kc
Kc Cosφ2
Cosφ1 0.80 0.85 0.90 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1
0.60 0.583 0.714 0.849 0.878 0.907 0.938 0.970 1.005 1.042 1.083 1.130 1.191 1.333
0.61 0.549 0.679 0.815 0.843 0.873 0.904 0.936 0.970 1.007 1.048 1.096 1.157 1.299
0.62 0.515 0.646 0.781 0.810 0.839 0870 0.903 0.937 0.974 1.015 1.062 1.123 1.265
0.63 0.483 0.613 0.748 0.777 0.807 0.837 0.870 0.904 0.941 0.982 1.030 1.090 1.233
0.64 0.451 0.581 0.716 0.745 0.775 0.805 0.838 0.872 0.909 0.950 0.998 1.058 1.201
0.65 0.419 0.549 0.685 0.714 0.743 0.774 0.806 0.840 0.877 0.919 0.966 1.027 1.169
0.66 0.388 0.519 0.654 0.683 0.712 0.743 0.775 0.810 0.847 0.888 0.935 0.996 1.138
0.67 0.358 0.488 0.624 0.652 0.682 0.713 0.745 0.779 0.816 0.857 0.905 0.966 1.108
0.68 0.328 0.459 0.594 0.623 0.652 0.683 0.715 0.750 0.787 0.828 0.875 0.936 1.078
0.69 0.299 0.429 0.565 0.593 0.623 0.654 0.686 0.720 0.757 0.798 0.846 0.907 1.049
0.70 0.270 0.400 0.536 0.565 0.594 0.625 0.657 0.692 0.729 0.770 0.817 0.878 1.020
0.71 0.242 0.372 0.508 0.536 0.566 0.597 0.629 0.663 0.700 0.741 0.789 0.849 0.992
0.72 0.214 0.344 0.480 0.508 0.538 0.569 0.601 0.635 0.672 0.713 0.761 0.821 0.964
0.73 0.186 0.316 0.452 0.481 0.510 0.541 0.573 0.608 0.645 0.686 0.733 0.794 0.936
0.74 0.159 0.289 0.425 0.453 0.483 0.514 0.546 0.580 0.617 0.658 0.706 0.766 0.909
0.75 0.132 0.262 0.398 0.426 0.456 0.487 0.519 0.553 0.590. 0.631 0.679 0.739 0.882
0.76 0.105 0.235 0.371 0.400 0.429 0.460 0.492 0.526 0.563 0.605 0.652 0.713 0.855
0.77 0.079 0.209 0.344 0.373 0.403 0.433 0.466 0.500 0.537 0.578 0.626 0.686 0.829
0.78 0.052 0.183 0.318 0.347 0.376 0.407 0.439 0.474 0.511 0.552 0.599 0.660 0.802
0.79 0.026 0.156 0.292 0.320 0.350 0.381 0.413 0.447 0.484 0.525 0.573 0.634 0.776
0.80 0.130 0.266 0.294 0.324 0.355 0.387 0.421 0.458 0.499 0.547 0.608 0.750
0.81 0.104 0.240 0.268 0.298 0.329 0.361 0.395 0.432 0.473 0.521 0.581 0.724
0.82 0.078 0.214 0.242 0.272 0.303 0.335 0.369 0.406 0.447 0.495 0.556 0.698
0.83 0.052 0.188 0.216 0.246 0.277 0.309 0343 0.380 0.421 0.469 0.530 0.672
0.84 0.026 0.162 0.190 0.220 0.251 0.283 0.317 0.354 0.395 0.443 0.503 0.646
0.85 0.135 0.164 0.194 0.225 0.257 0.291 0.328 0.369 0.417 0.477 0.620
0.86 0.109 0.138 0.167 0.198 0.230 0.265 0.302 0.343 0.390 0.451 0.593
0.87 0.082 0.111 0.141 0.172 0.204 0.238 0.275 0.316 0.364 0.424 0.567
0.88 0.055 0.084 0.114 0.145 0.177 0.211 0.248 0.289 0.337 0.397 0.540
0.89 0.028 0.057 0.086 0.117 0.149 0.184 0.221 0.262 0.309 0.370 0.512
0.90 0.029 0.058 0.089 0.121 0.156 0.193 0.234 0.281 0.342 0.484
Table (1)
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CONSULTANT ENGINEER / MOHAMED OSMAN AL SHAFEY
C.9.3 Where to install correction capacitors
Individual capacitor units (A) Fixed and automatic capacitor
banks (B)
Definition Located directly at the - fixed capacitor banks – individual
inductive load (Motor in most capacitors racked in a common
case) enclosure with no switching or
stepping capability
- Automatic capacitor banks
individual capacitor racked in a
common enclosure with switching
and stepping capability.
Advantages 1. Increasing distribution 1. More economical reduces the
system capacity, improve utility power bills or reduce the
power consumption current in primary feeders
2. Stabilized voltage levels 2. Low installation cost
3. Lower losses, line losses 3. Switching – Automatic capacitor
are reduced banks can switch all or part of
4. Capacitor & load can be capacitance automatically
switched ON/OFF together depending on load
5. Extra switching not requirements.
required.
6. Easier selection for the
capacitor needed for each
motor
C.9.4 Choice of Protection Devices, Capacitors and Damping Reactor in P.F.C Panel
For capacitors, the current is a function of:
The applied voltage and its harmonics
The capacitance value
The nominal current (In) of a 3-phase capacitor bank is equal to:
Q
In= (A)
Vn
- Q: Kvar rating
- Vn: Phase-to-phase
Voltage (Kv)
C.9.4.1 Capacitor to be with the following specs. Refer to Standard IEC 60831-1 and 2
- Continuous rated volt 130% from the nominal voltage.
- 110 rated current from nominal current.
- UL listed.
- CSA approval.
- 0.5 watt losses per one KVAR.
- Non flammable insulation with ambient temperature. 50oC.
- Shunt resistor to discharge the value of (Capacitor) to be 50V during 1min.
- Dry type.
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CONSULTANT ENGINEER / MOHAMED OSMAN AL SHAFEY
C.9.4.2 Rated current for main circuit breaker. Contactor to be 130% from minimal current at
50oC. for (long time delay setting) and (10 In) for (short time delay setting) to
withstand inrush current. Contactor to be AC-4 category. (According to BS 60947)
C.9.4.3 Thermostat to be installed inside panel with ventilation fans to work automatically in
case of exceeding temperature.
C.9.4.4 Power factor correction panel (To be comply with IEC 61439 and IEC 61912) and
should include damping reactor with enough reactance before capacitor in services
connection in this case capacitor and services connected reactor must have a turning
frequency below the lowest critical order of harmonic which is usually the 5 th see
attached Figure (2).
On 50/60 HZ systems, these damping reactors should be used to make harmonic
order approximately mid-way between 3rd and 5th harmonics.
S.L.D. FOR ONE STEP OF CAPACITOR BANK
Fig. (2)
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CONSULTANT ENGINEER / MOHAMED OSMAN AL SHAFEY
