Today, we will start explaining
the technical part for Power Factor
Correction Capacitors Sizing Calculations. We will explain the following topics:
 Applicable Standards for Power Factor Correction,
 Types of Loads,
 The Power Triangle,
 What is a power factor?
 Types of power factor
 Why utilities charge a power factor penalty?
 Billing Structure.
1 Applicable
Standards for Power Factor Correction

The design of the Low Voltage Power Factor Correction banks and accessories shall comply with the following standards:

2 Types
of Loads

1 According To Load Nature1
You can review our explanation for the Linear Electrical Loads in our article “Electrical Load Classification and Types – Part Two”
2 According To Load Nature2
You can review our explanation for the NoneLinear Electrical Loads in our article “Electrical Load Classification and Types – Part Three” and also in our article “Generators Sizing Calculations – Part Seven”

3 The Power Triangle

4 What is a power factor?

PF = P/S = KW/KVA
PF measures how effectively electrical power is being used. A high power factor signals efficient utilization of electrical power, while a low power factor indicates poor utilization of electrical power.
An ideal ratio is 1.0, thatis, a perfect match between power drawn from the network and useful power for the task. This is also known as unity power factor.

5 Types of power
factor


5.1 The Displacement
Power Factor

the above definition of the power factor is used only if there is no harmonics on the network. This is the case when pure sinusoidal (without harmonics) wave forms exist. In this case the power factor angle φ represents a phase shift or displacement between voltage and current. In this case the power factor will be called the displacement power factor and which can be measured with a power factor meter.

5.2 The Total power factor

Comparison between displacement and total power factor:
Displacement Factor = Cos Φ Distortion Factor = 1/ (1 + THD^{2}) Then, Total Power Factor= Cos Φ / (1 + THD^{2})

Also, you must be able to differentiate between two uses of power
factor expression:
 Power factor for Equipment,
 Power factor for consumer’s network.
5.3 Power Factor For Equipment

Examples for common Equipment Creating Poor Power Factor are listed in below:
Solution for Equipment Creating Poor Power Factor
If a single machine has a poor power factor, capacitors can be connected in parallel with the device, that is, connected to the live and the neutral terminals of the reactive device, so that they compensate for the poor power factor whenever the machine is switched on. This is a form of ‘fixed’ PFC which will be explained in detail later.

5.4 Power Factor For Consumer’s Network

Examples for consumer’s network with poor power factor are listed in below:
Solution for Consumer’s Network with Poor Power Factor

6 Why
utilities charge a power factor penalty?

With most power supply contracts the costs for electrical power comprise:
Now, if a facility has low power factor, Utilities must design their systems with oversized equipment to accommodate reactive current. In order to pass along the expense of the larger equipment required and the system losses from the flow of the reactive current, many utilities will charge their customers a penalty for low power factor as one of or combination of, the following:
There are a variety of means in which this penalty is calculated by the utility, for example:

7 Billing
Structure

Utility Bill
The more common ways utilities calculate electrical bills are as follows:

7.1 90% Billing Structure

Example#1: The following data for one facility KVA = 1000, KW = 800, KVAR = 600, PF = .80, calculate the facility billing using 90% Billing Structure. Solution: 90% of the KVA 1000 x 0.90 = 900 KVA
100% of the KW = 800 KW
So, the facility will pay demand rates on 900KVAThus the facility is paying a penalty on 100 KVA (1000 KVA produced – 900 KVA demand) of unproductive power. Correcting the facility’s Power Factor to 90% + will eliminate this penalty cost. 
7.2 100% KVA + 100% KW Billing Structure

With the same data from Example#1, calculate the facility billing using 100% KVA + 100% KW Billing Structure. Solution: 100% of the KVA 1000 = 1000 KVA
100% of the KW = 800 KW
Thus, Facility will pay demand costs on 1000 KVA + 800 KW = 1800, 
7.3
kVA
Billing

Example#3:
Solution:
Uncorrected original billing:
460 kVA × $4.75 = $2185 / month

7.4
kVA
Billing + KWH Billing

Assume the same conditions in Example#3 except that:
kVA demand charge:
$1.91 / kVA / month
Energy charge:
(112,400 kWh / month energy consumed)
$0.0286 / kWh (first 200 kWh / kVA of demand)
$0.0243 / kWh (next 300 kWh / kVA of demand)
$0.021 / kWh (all over 500 kWh / kVA of demand)
Solution:
kVA billing
460 kVA × $1.91 = $878.60
KWH billing
kWh = 112,400
460 × 200 = 92,000 kWh @ 0.0286 = $2631.20
balance only = 112,400 – 92,000 = 20,400 kWh @ $0.0243 = $495.72
total KWH billing = $2631.20 +$ 495.72 = $3126.92
Total billing = kVA billing + KWH billing = $878.60 + $3126.92 = $4005.52

7.5
KW
Demand Billing With Power Factor Adjustment

KW demand = KW × 0.90 / actual power factor
If power factor was 0.84, the utility would require 7% increase in billing, as shown in this formula:
KW demand = kW × 0.90/0.84 = 1.07 kW
Some utilities charge for low power factor but give a credit or bonus for power above a certain level as per the following:
Example#5:
Assume a 400 kW load, 87% power factor with the following utility tariff.
Demand charges:
First 40 kW @ $10.00 / kW monthly billing demand
Next 160 kW @ $ 9.50 / kW
Next 800 kW @ $ 9.00 / kW
All over 1000 kW @ $ 8.50 / kW
Solution:
At 87% power factor, there is no penalty.
So, utility billing will be :
Normal 400 kW billing demand
First 40 kW @ $10.00 = $ 400.00
Next 160 kW @ $ 9.50 = $1520.00
Bal. 200 kW @ $ 9.00 = $1800.00
Total 400 kW @ $3720.00 normal monthly billing
Example#6:
With the same 400 kW load, the power factor is only 81%.
Solution:
At 81% power factor, there will be a penalty.
In this example, the customer will pay an adjustment on:
kW demand = 400 × 0.90 / 0.81 = 444 billing kW demand
First 40 kW @ $10.00 = $ 400.00
Next 160 kW @ $ 9.50 = $1520.00
Next 244 kW @ $ 9.00 = $2196.00
Total 444 kW $4116.00 – $3495.00 = $621.00 x 12 = $7452.00

7.6
KVAR
Reactive Demand Charge

Example#7:
Assume a 400 kW load demand at 81% power factor.
Demand charge is:
$635.00 for the first 200 kW demand
$ 2.80 per kW for all addition
Reactive demand charge is:
$ 0.60 per kVAR in excess of 50% of kW demand
Solution:
Demand charge:
first 200 kW demand@ $635.00 = $635.00
200 kw addition @ $ 2.80 = $560.00
Total = $635.00 + $560.00 = $1195.00
Reactive demand charge
In this example, kW demand = 400 kW,
therefore 50% = 200 kVAR which will be furnished at no cost.
Cos Ø = PF = kW/kVA = 0.81
Tan Ø = = 0.724 = kvar/kW
kVAR = kW × Tan Ø = 400 × 0.724 = 289.6 kVAR
Because 200 kVAR is allowed, the excess kVAR is 89.6 (round to 90) x $0.60 = $54.00 per month billing for reactive demand.
Total billing = Demand charge + Reactive demand charge = $1195.00 + $54.00 = $1249.00

In the next article, we will continue explaining
the technical part for Power Factor Correction Capacitors Sizing Calculations. Please,
keep following.
The previous and related articles are listed in the below table:
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Glossary of Power Factor Correction Capacitors

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