Power Factor Correction Capacitors Sizing Calculations – Part Seventeen

In article” Power Factor CorrectionCapacitors Sizing Calculations – Part Fifteen” we indicated that The Main Components of PFC Panel are as follows:

1- The Main Components of PFC Panel

A Panel for power factor correction (PFC Panel) is constituted essentially from the following main components: A protective device; A switching device (contactor); One or more capacitors suitably connected; Resistors for capacitor discharge. A PF controller is used In case of an automatic PF compensation system to command switching in/off of the capacitors.

And we explained how to select the first three items (protective devices, contactors and capacitors) in the past article. Today we will explain the following:

• How to Select a Discharge Resistor,
• How to Calculate the Value of Discharge Resistor,
• How to Select Power Factor Controller,
• How to Calculate the Number of Physical Steps, Electrical Steps and Electrical Control.

Fourth: How to Select a Discharge Resistor

IEC Requirements for Discharge of capacitors When installing a capacitor, it is necessary to verify that when it is switched off it can discharge so that the presence of a voltage at its terminals will not be dangerous for people and things. In compliance with the Std. IEC 60252-2 for the power factor correction of motors discharge devices are not often required since the motor windings functioning as discharge resistances. When a discharge device is provided, it shall reduce the voltage at the capacitor terminals from the peak value of the rated voltage to a value of 50 V or less in the time of 1 min from the moment the capacitor is switched off. A discharge device may sometimes be specified, not for safety reasons, but to prevent electrical overstress on the capacitor: this may occur when a disconnected capacitor still charged is reconnected across another capacitor of different polarity. The Std. IEC 60364-5-55, clause 559.8) prescribes the use of discharge resistors for compensation capacitors having a total capacitance exceeding 0.5 μF (75/25 KVAR with star/delta connection at 400 V). Resistors have the purpose of nullifying, within a short time, the residual charge on the plates of the capacitor once it has been disconnected from the network. It is a good rule to provide discharge resistances for all the capacitors with power exceeding 0.5 KVAR, for whatever supply voltage. In compliance with the Std. IEC 60831-1 clause 22 ‘Each capacitor unit and/or bank shall be provided with a means for discharging each unit in 3 min to 75 V or less, from an initial peak voltage of √2 times rated voltage Un.’ Attention is drawn to the fact that in some countries smaller discharge times and voltages are required.

How to Calculate the Value of Discharge Resistor

The discharge resistance in a single-phase unit or in a phase of a poly-phase unit is given by: Where: R is the discharge resistance in ohms[Ω]; t is the discharge time from 2 Un to Ur, in seconds [s]; Un is the rated voltage in [V]; Ur is the admitted residual voltage in [V] (At the moment of energizing, the residual voltage must not exceed 10% of the rated voltage); k is a coefficient depending on the connection modality of resistors to capacitor units, see Fig-1; C is the capacitance of the capacitor bank in Farads [F]. To comply with the prescriptions of the Std. IEC 60831-1, t = 180 s and Ur = 75 V shall be put in the above formula. Fig.1

Fifth: How to Select Power Factor Controller

Function Of PF Controllers ABB RVT PF Controller PF controllers are microprocessor based controllers, which takes real time inputs from the network like the current input signal from the load current transformer and the Voltage tapped from the Bus, then calculate the KVAR required and produce switching commands to control the contactor ON/OFF of the capacitor steps. Intelligent control by PFC controllers ensures an even utilization of capacitor steps, minimized number of switching operations and optimized life cycle. The controller placed inside the panel shall have the reliability to withstand the operating temperature of at least 50 °C or more.

Difference Between Old And Modern PF Controllers C/k value is used in the setting of old generation Power Factor Controllers, however it is found rarely to be used in panels now. C/k value is a threshold value for switching On/Off the capacitor steps by the controller. C/k is the value obtained by dividing first step capacitor power “Q” to the current transformer ratio”K”. This setting shall be automatic or can be set manually.  The main features of the PF controller must include the following: Automatic C/k- value setting, Connection of different capacitor steps. Automatic detection and usage of optimum capacitor steps. Current measuring 10mA-5A, suitable for connecting CT x/1A and x/5A. Programmable capacitor switching delay Indication for over current Indication for low power factor Fan contact While Modern APFC controllers provide various additional functions like electrical data logging, self diagnostics and system health features and are capable of communication using standard protocols. Additional features can be chosen based on specific requirements of end user which are as follows: Four Quadrant operation Automatic phase reversal correction Various automatic trip conditions can be programmed – over current, over voltage Single phase measurement Various metering parameters like V, I, THD-V, Hz, KVAR, temp, PF etc.

PF Controller and Step Combinations The PF controllers continually measure installation reactive power and monitor on/off of capacitor steps in order to obtain the relevant power factor. Therefore, the capacitor steps are arranged in step combinations, these combinations will give many advantages like: Enabling accurate control, Reducing the number of compensation modules, Reducing Labor, Reducing financial costs. Meaning Of The Step Combinations For example, If we have (7) step PF controller, it will have one of the following step combinations Step Combination Meaning 1-1-1-1-1-1 etc. All steps have the same power as step no. 1 Step no. 1 is always the smallest 1-1-2-2-2-2 etc. The first two steps have the same power as step no. 1, but from step no. 3 onwards power is double. 1-1-2-3-3-3 etc. The first two steps have the same power as step no. 1, the 3rd step has twice the power and from step no. 4 onwards power is triple. 1-2-2-2-2-2 etc. From the 2nd step onwards power is twice that of step no. 1. 1-2-3-3-3-3 etc. The power of the 2nd step is twice that of step no. 1, and from step no. 3 onwards power is triple. 1-2-3-4-4-4 etc. The power of the 2nd step is twice that of step no. 1, the 3rd step triples in power, and from step no. 4 onwards power is quadruple. 1-2-4-4-4-4 etc. The power of the 2nd step is twice that of step no. 1, and from the 3rd step onwards power is quadruple. There are many other step combinations and in the same manner as above you can know the meaning of each step combinations, for example: 1.2.3.6.6.6 etc. 1.2.4.8.8.8 etc. The Control Programs Of The Step Combinations Control Program Features normal program (n) Suitable for all step types. Commonly used steps: 1.2.4.4.4.4 or 1.1.2.2.2.2 Linear sequence as from the 3rd step, the 1st two steps are used as adjustment steps (The controller always begins by energizing or tripping the 1st step, then the 2nd step). Circular program A (CA) Steps: 1.1.1.1.1.1., circular sequence. the 1st step energized will be the 1st step tripped Caution: this program only operates in optimum mode if the number of capacitor bank steps has been properly set. Circular program B (CB) Steps: 1.2.2.2.2.2., circular sequence as from the 2nd step, the 1st step is used as an adjustment step. the 1st step energized will be the 1st step tripped Caution: this program only operates in optimum mode if the number of capacitor bank steps has been properly set. Linear program (S) Steps: 1.1.1.1.1.1., linear sequence The last step energized is tripped 1st. Application: harmonic filtering. The below table shows the possible control programs for each type of step combinations: Step Combinations Possible Programs 1.1.1.1.1.1 CA/n/S 1.1.2.2.2.2 n 1.1.2.3.3.3 n 1.2.2.2.2.2 CB/n 1.2.3.3.3.3 n 1.2.3.4.4.4 n 1.2.4.4.4.4 n

Electrical Steps, Physical Steps And Electrical Control

Difference Between Electrical Steps, Physical Steps And Electrical Control 1- Physical Steps: They represent the Physical/real capacitor units seen by you inside the PFCC panel where their KVAR sum is equal to the total KVAR required for power factor correction and each physical step is tripped individually by a contactor. 2- Electrical Steps: they represent the KVAR power seen by the electrical installation according to the connected physical steps KVAR at  each time, so their total KVAR is varying according to the load variations of the installation and  their quantity =total KVAR required/smallest physical step KVAR. 3- Electrical Control: This is equal to the number of electrical step, multiplied by the power of step no. 1 which is always the smallest step. For example, if we need 100 KVAR for power factor correction of an installation, and we plan to get this 100 KVAR on 10 stages to give 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 KVAR as per the load variations. So, we have two case solutions as follows: Case solution#1:  Using 10 capacitors with 10 KVAR each to get the 100KVAR = 10 x 10 KVAR, in this case we say that the number of physical steps = the number of electrical steps. The step combination in this case will be 1.1.1.1.1.1.1.1.1.1 and this case called the physical steps method. Case solution#2:  Using 4 capacitors with ratings 10, 20, 30 and 40 KVAR to get the 100KVAR = 1 x 10KVAR + 1 x 20KVAR+ 1 x 30KVAR + 1 x 40KVAR, in this case we say that the number of physical steps = 4 and their step combination in this case is 1.2.3.4 and the number of the electrical steps will be 10 steps as follows: Electrical Steps Physical Steps number Rating (KVAR) 10 KVAR 20 KVAR 30 KVAR 40 KVAR 1 10 1 - - - 2 20 - 1 - - 3 30 - - 1 - 4 40 - - - 1 5 50 1 - - 1 6 60 - 1 - 1 7 70 - - 1 1 8 80 1 - 1 1 9 90 - 1 1 1 10 100 1 1 1 1 - = step disconnected & 1 = step in operation Case# 2 is called the electrical steps method. Comparing the two above case solutions, we will find the following: Case#1: physical steps method Case#2: the electrical steps method Number of used PFC panels 2 1 Number of used contactors 10 4 Number of used fuses 30 12 PF Controller used 10 output 4 output  So, using the electrical steps method gives the following advantages: Enabling accurate control, Reducing the number of compensation modules, Reducing Labor, Reducing financial costs.

How to Calculate the Number of Physical Steps, Electrical Steps and Electrical Control

The number of electrical step depends on: The number of PF controller outputs used, The chosen step combinations. Using the below table-1, you can find the number of electrical step. Table-1 Example#1: A capacitor bank made up of 7 physical steps: 1 of 30 kvar 6 of 60 kvar Find the used step combination, calculate the number of electrical steps and calculate the possible power for each electrical step? Solution: Steps unit power Step#1* 30 kvar = step#1x 1 Step#2 60 kvar = step#1x 2 Step#3 60 kvar = step#1x 2 Step#4 60 kvar = step#1x 2 Step#5 60 kvar = step#1x 2 Step#6 60 kvar = step#1x 2 Step#7 60 kvar = step#1x 2 Then , the Power factor controller step combinations = 1.2.2.2.2.2.2 7 physical steps = 7 contactors = 7 Outputs used And the Number of electrical step: 1+2+2+2+2+2+2 = 13 electrical steps * Step no. 1 is always the smallest Also, you can find the Number of electrical step from table-1 by look up for the column of 7 controller outputs with the row of step combination 1.2.2.2.2.2.2 which will give the Number of electrical step = 13 Electrical control: 13 times the power of step no. 1 = 13 x 30 kvar = 390 kvar The possible power for each electrical step will be as follows: possible power step (KVAR) 7 nos. Physical steps 30 60 60 60 60 60 60 30 1 - - - - - - 60 - 1 - - - - - 90 1 1 - - - - - 120 - 1 1 - - - - 150 1 1 1 - - - - 180 - 1 1 1 - - - 210 1 1 1 1 - - - 240 - 1 1 1 1 - - 270 1 1 1 1 1 - - 300 - 1 1 1 1 1 - 330 1 1 1 1 1 1 - 360 - 1 1 1 1 1 1 390 1 1 1 1 1 1 1 Operating cycle: - = step disconnected & 1 = step in operation Conclusion:  13 possible electrical steps, with only 7 physical steps which is the Optimized Solution. Example#2: Consider an APFC System of 250 kvar, calculate the number of electrical steps and calculate the possible power for each electrical step and Find the used step combination using the physical steps method and the electrical steps method? Solution: Using the physical step method: 10 physical steps will be used each 25 KVAR to get 250 KVAR = 10 steps x 25 KVAR Using physical steps method physical step KVAR 25 KVAR Number of physical steps 10 steps Total KVAR 25+25+25+25+25+25+25+25+25+25= 250 KVAR Used step combination 1.1.1.1.1.1.1.1.1.1 Number of used PFC panels 2 Number of used contactors 10 Number of used fuses 30 PF Controller used 12 output(step) possible power step (KVAR) 10 nos. Physical steps each 25 KVAR 25 25 25 25 25 25 25 25 25 25 25 1 - - - - - - - - - 50 1 1 - - - - - - - - 75 1 1 1 - - - - - - - 100 1 1 1 1 - - - - - - 125 1 1 1 1 1 - - - - - 150 1 1 1 1 1 1 - - - - 175 1 1 1 1 1 1 1 - - - 200 1 1 1 1 1 1 1 1 - - 225 1 1 1 1 1 1 1 1 1 - 250 1 1 1 1 1 1 1 1 1 1 Using the Electrical step method: 4 nos. electrical steps will be used with the following ratings 25, 50, 75, 100 KVAR. Using electrical steps method physical step KVAR 25, 50, 75, 100 KVAR Total KVAR 25+50+75+100= 250 KVAR Number of electrical steps total KVAR required/smallest physical step KVAR 250 KVAR / 25 KVAR = 10 steps Used step combination 1.2.3.4 Number of used PFC panels 1 Number of used contactors 4 Number of used fuses 12 PF Controller used 4 output(step) possible power step (KVAR) 4 nos. Physical steps 25 50 75 100 25 1 - - - 50 - 1 - - 75 - - 1 - 100 - - - 1 125 1 - - 1 150 - 1 - 1 175 - - 1 1 200 1 - 1 1 225 - 1 1 1 250 1 1 1 1 Conclusion High Labor, high cost: non-optimized solution when using the physical step method. Optimized Solution when using the electrical step method.

Notes for designing a capacitor bank with PF controllers When designing a capacitor bank, it is important to break down the total power Qt (KVAR) into several steps so as to ensure the best compromise between the number of steps and suitable regulation.so, first select the required number of electrical steps then Calculate the smallest physical capacitor unit = total KVAR required/ required number of electrical steps. The sum of the physical step power ratings must corresponds to the total reactive power. The maximum switching power of the contactors ≤ 60 kVAr at 400-440 V in order to switch the three-phase capacitors. Don’t exceed the maximum number of relay outputs the controllers can switch. For capacitor banks with few electrical steps, we recommend increasing the step switching times. It is possible to create physical steps > 60 kVAr via simultaneous control of 2 contactors, divided between 2 different capacitors, by the same controller relay output, to which it is essential to add a time delay of 1 second minimum. For Example: To create high-power capacitor banks > 1000 kVAr, a few 100 kVAr physical steps can be created by switching a 50 kVAr contactor-capacitor pairing twice at the same time. For the highest power ratings requiring steps > 18 steps. It is possible to use the same principle of physical steps > 60 kVAr by simultaneously controlling 2 contactors divided between 2 different capacitors using the same controller relay output, to which it is essential to add a long enough time delay (a minimum of several seconds).

In the next article, we will explain how to choose Cables for Power Factor Correction Capacitors. Please, keep following.

The previous and related articles are listed in below table:

Subject Of Previous Article	Article
Glossary of Power Factor Correction Capacitors	Power Factor Correction Capacitors Sizing Calculations – Part One
Types of Loads, The Power Triangle, What is a power factor? Types of power factor Why utilities charge a power factor penalty? Billing Structure.	Power Factor Correction Capacitors Sizing Calculations – Part Two
What causes low power factor? Bad impacts of low power factor, Benefits of Power Factor correction.	Power Factor Correction Capacitors Sizing Calculations – Part Three
How to make Power Factor Correction? Types of Power Factor Correction Capacitors Individual compensation	Power Factor Correction Capacitors Sizing Calculations – Part Four
Group compensation, Central compensation, Hybrid compensation. Summary for Power Factor Correction Capacitors Sizing Calculations Steps	Power Factor Correction Capacitors Sizing Calculations – Part Five
Step#1: Collect Monthly Billing Data Step#2: Make Some Preliminary Measurements For Current And Voltage	Power Factor Correction Capacitors Sizing Calculations – Part Six
Step#3: Fill the Economic Screening Worksheet	Power Factor Correction Capacitors Sizing Calculations – Part Seven
Step#4: Make Preliminary Measurements For Harmonics Step#5: Repeat the Economic Screening Worksheet Step#6: Compare the Savings with the Probable Cost of Capacitors' Installation Second: Design Phase Step#1: Performing a Detailed Plant Survey Step#1.A: Review the one line diagram Step#1.B: Take into consideration the loads that produce harmonics Step#1.C: collect sufficient data Inventory by using measuring instruments	Power Factor Correction Capacitors Sizing Calculations – Part Eight
Step#2: Select Economical Capacitor Scheme Step#3: Checking the "No Load" Voltage Rise Step#4: Select Capacitor Switching Options Step#5: Check the Harmonic Distortion and make Harmonic Mitigation Options Step#6: Use the Economic Screening Worksheet again	Power Factor Correction Capacitors Sizing Calculations – Part Nine
Power Factor Correction Capacitors Sizing Calculations Steps For New Designs	Power Factor Correction Capacitors Sizing Calculations – Part Ten
Factors Affecting The Rated KVAR For a Capacitor Calculation of the Capacitor KVAR Rating for Compensation at: 1-Transformer 2-Individual Motors	Power Factor Correction Capacitors Sizing Calculations – Part Eleven
3- Calculation Of The Capacitor KVAR Rating For Buildings And Power Plants(Group Compensation)	Power Factor Correction Capacitors Sizing Calculations – Part Twelve
Harmonics Effects On Power Factor Capacitors Harmonic Limits in Electric Power Systems (IEEE 519-2014) Options to Reduce Harmonics for PFCC Power Factor Compensation In Case Of Harmonics	Power Factor Correction Capacitors Sizing Calculations – Part Thirteen
Power Factor Correction Capacitors Calculators: 1- Arteche Reactive Power and Harmonic Resonance Point Calculator, 2- Eaton Power Factor Correction Calculator, 3- AccuSine Sizing Spreadsheet, 4- Square-D (Schneider Electric) Calculator.	Power Factor Correction Capacitors Sizing Calculations – Part Fourteen
The Main Components of PFC Panel How to select Circuit Breakers for PFC Panel How to select Fuses for PFC Panel How to select Contactors for PFC Panel	Power Factor Correction Capacitors Sizing Calculations – Part Fifteen
How to select a capacitor for PFC Panel and Capacitors’ rules Capacitor compensation with a detuned reactor How to Select a Detuned Reactor	Power Factor Correction Capacitors Sizing Calculations – Part Sixteen

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