AppC Ch9-DesignClac 8.9.10Chapter 9 Electrical DesignAppendix CDesign Calculations forElectrical Design2010 Edition SPU Design Standards and Guidelines9C-i

Appendix C Design Calculations9C-ii2010 Edition SPU Design Standards and Guidelines

AppC Ch9-DesignClac 8.9.10Chapter 9 Electrical DesignContentsAppendix C Design Calculations for Electrical Design . 11.1Introduction . 11.2Software . 11.3Calculation Matrix . 21.4Basic Requirements for Electrical Calculations . 41.5Basic Electrical Engineering Formulas . 41.5.1List of Symbols . 41.5.2Direct Current (DC) Formulas . 51.5.3Alternating Current (AC) Single Phase . 51.5.4Alternating Current (AC), Three-Phase . 51.5.5Motors . 61.5.6Power Factor Correction . 61.6Sample Calculations. 71.6.1Load . 71.6.2Generator Sizing . 71.6.3Conductor Size, General . 91.6.4Conduit Size and Fill. 131.6.5Motor Branch Circuit . 141.6.6Power Factor Correction Capacitors. 161.6.7Transformer Primary and Secondary Conductors . 181.6.8Voltage Drop. 201.6.9Short Circuit . 221.6.10 Lighting . 231.6.11 Grounding . 291.6.12 Cable Pulling Tension. 291.6.13 Equipment Heat Loads . 30List of TablesTable C-1 Calculations for Electrical Design . 2Table C-2 NEC References for Conductor Sizing . 9Table C-3 Coefficient of Utilization Zonal Cavity Method . 25Table C-4 Candlepower Distribution Curve . 27Table C-5 Losses in Electrical Equipment . 30List of ExamplesExample 1 Motors . 6Example 2 Conductor Size No. 1. 11Example 3 Conductor Size No. 2. 12Example 4 Conductor Size No. 3. 12Example 5 Conductor Size No. 3. 13Example 6 Conduit Size and Fill No. 1 . 13Example 7 Conduit Size and Fill No. 2 . 14Example 8 Motor Branch Circuit No. 1 . 15Example 9 Motor Branch Circuit No. 2 . 16Example 10 Power Factor No. 1 . 17Example 11 Power Factor Correction Capacitor No. 2 . 18Example 12 Transformer Primary and Secondary Conductors No. 1 . 182010 Edition SPU Design Standards and Guidelines9C-iii

Appendix C Design CalculationsExample 13 Transformer Primary and Secondary Conductors No. 2 . 19Example 14 Transformer Primary and Secondary Conductors No. 3 . 20Example 15 Feeder and Branch Circuits . 21Example 16 Short Circuit . 22Example 17 Lighting No 1: Lumen or Zonal Cavity Method . 24Example 18 Lighting No 2: Point by Point Calculation . 279C-iv2010 Edition SPU Design Standards and Guidelines

Chapter 9 Electrical DesignAppC Ch9-DesignClac 8.9.10APPENDIX CDesign Calculations for Electrical DesignThis appendix presents standards and guidelines for electrical design calculations for SPUprojects.1.1INTRODUCTIONDesign calculations establish minimum guidelines and requirements for generating electricalcalculations on projects. Electrical calculations should be made for all SPU projects that includeelectrical components and should be filed in the project notebook. Design calculations may bemade either manually or by SPU-approved computer programs. At a minimum, the followingtypes of calculations should be made where applicable: Load calculations Conductor sizing Conduit sizing Motor branch circuit sizing Power factor improvement Transformer primary and secondary circuit sizing Voltage drop Motor starting voltage dip Short circuit analysis Lighting levels Grounding in substations where step potentials are of concern Harmonic distortion analysis Cable pulling calculations Generator capability/motor starting.1.2SOFTWAREThe electrical design engineer must use only SPU-approved electrical analysis software. Theresults should be validated with a hand calculation or order of magnitude estimate. Some SPUapproved software tools are: SKM Power Tools for Windows (PTW) software. It includes a basic tool, DAPPER (loadcurrent, voltage drop, conductor sizing, etc) and several specialized tools such asHI WAVE (harmonic analysis) and CAPTOR (circuit breaker coordination and settings)2010 Edition SPU Design Standards and Guidelines9C-1

Appendix C Design Calculations Cummins Power Suite for sizing emergency generators CenterONE available from Rockwell Automation for laying out motor control centersSpreadsheets may also be used to perform basic electrical load calculations with programs suchas Microsoft EXCEL.1.3CALCULATION MATRIXProject calculations serve as formal documentation of the project electrical design. They mustcontain sufficient description and detail to communicate the design concept, assumptions, andjudgments associated with the design. Explanatory comments should be provided to assistreviewers and engineers who may use the calculations in the future.Table C-1 describes electrical calculation required for projects, tools to do the calculations, whois responsible for the calculations, and when they should be done.Table C-1Calculations for Electrical llLoad facility,switchgear,MCCLoad at each load center perNEC to determine bus,protective device & circuitsizeSKM PTWDAPPER,Spreadsheets,hand calcsXX30/ 60/90Load panelboardLoad on each panelboard perNEC to determine panel,circuit, and transformer sizeSKM PTWDAPPER,spreadsheetsXX60 and 90GeneratorsizingTo size engine generatorbased on critical run andstart loads.Cat, Kohler,Cummins, orother vendorsoftwareXX30/ 60/90Short CircuitAvailable fault current at eachbus to determine equipmentshort circuit/interruptingratingsSKM PTWDAPPER,Hand CalculationXXLightingTo determine fixturesneeded given desired lightlevel; also energy calculations(where req’d)AGI 32, Vendor,spreadsheetsXX60 and 90ConductorsizingTo size conductors per NECTables, hand calcsXX60 and 90Circuitbreaker andfuse sizingTo size circuit breakers andfuses per NECTables, hand calcsXX60 and 90ConduitFill/Tray SizeTo size conduit and cabletray per NECNEC Tables,Cablematic PlusXX60 and 90Voltage dropFor heavily loaded and/orlong circuits to confirmoperation within NECrecommendations (min)SKM PTWDAPPER,spreadsheets,hand calcsX60 and 90TransientMotorFor starting large motors(largest motor at each load9C-2SKM PTW TMS,hand calcs2010 Edition SPU Design Standards and GuidelinesReq’dCond2XXByEngr3ByCntr3XDesignPhase (%)30/60/90

Chapter 9 Electrical DesignAppC Ch9-DesignClac center) to determine if voltagedrop on motor starting ismagnitude to adversely impactother system equipment (e.g.20% voltage dip could makecontrol relays drop out. Manyare only designed to operate15% below rated voltage.)HarmonicDistortionAnalysisTo confirm operation withinIEEE 519 requirements (min) fornon-linear loadsSKM PTWHI WAVE, GEor other vendorsoftwareXXMultiplecircuitderatingFor more than 3 currentcarrying conductors in a conduitper NECNEC Tables,Cablematic PlusXX60 and 90AmbienttemperaturecircuitderatingFor higher than "normal"ambient temperatures--couldinclude heat from multiplecircuits in duct bankAMP CALC,NEC tablesXX60 and 90ProtectivedevicecoordinationTo minimize outages to smallestportion of system possibleSKM PTWCAPTORXXX90Cable PullingTo assure no damage to cablewhen pulled in conduit givenconduit size, distance and bends.Rq’d for medium-voltage &some large/long low-voltagePolywater orother vendorsoftwareXXX60, 90 dsgncheck;by cntrctrin ConstrbeforepullingArc-flashTo label gear regarding arc-flashhazard and PPE required. NECrequires label, not calcs.Reference NFPA 70E and IEEE1584.SKM PTW ArcFlash EvaluationXX90Power factorcorrectionTo size capacitors for singlemotor or systems.XXBattery/UPSsizingTo determine amp-hour basedon load and duration.XXX90, ConstrTransformerK-factorTo determine appropriate Kfactor for transformers withnon-linear loadsXXX90, ConstrVFDreflectivewaveFor motor distant from VFDXXX90, ConstrLightningProtectionStrikeDistanceMay be performance specifiedXXX60 and 90per NFPA 780Req’dAllReq’dCond2ByEngr3ByCntr3DesignPhase (%)X30/60/9060 and 901Suggested tools for use in SPU projects.Responsible party. Contractor-provided calculations may require design engineer-provided criteria.23Required conditionally: Required when applicable2010 Edition SPU Design Standards and Guidelines9C-3

Appendix C Design Calculations1.4BASIC REQUIREMENTS FOR ELECTRICALCALCULATIONSThe following are SPU basic requirements for electrical calculations:1. Non-computer generated calculations must be on standard calculations sheets with theheading completely filled out.2. Calculations generated by computer programs must conform with the followingprocedures:a. Include all heading information on each sheetb. Insert comments wherever possibly to clarify concepts and actions taken in thecomputer inputc. Provide clear documentation of electrical geometry, support conditions, loadapplication, and load requirementsd. Where practical, provide sketch of model indicting nodes, materials, connectivity,etc.e. Provide electronic copy on CD or other suitable device of analysis input and outputwith hard copy calculations.f.Provide manual checks of pertinent results (e.g. service size, main feeder voltagedrop) for computer generated output.1.5BASIC ELECTRICAL ENGINEERINGFORMULASThis section describes basic electrical engineering formulas for creating design calculations.1.5.1VIRXZWθeff9C-4List of Symbols-Voltage (volts)Current (amps)Resistance (ohms)Reactance (ohms)Impedance (ohms)Real Power (watts)- Phase angle whose cosine is the power factor- Efficiency2010 Edition SPU Design Standards and Guidelines

Chapter 9 Electrical DesignAppC Ch9-DesignClac Current (DC) FormulasBasic FormulasVoltsV IxRP V IPower in watts1.5.3P I2 RAlternating Current (AC) Single PhaseV denotes line to neutral voltage.Basic FormulasVoltsPower FactorV I Zpf cosθApparent PowerVA V x IReactive PowerVARS V x I x sin θW V x I x pfθ arctan(W/VARS)pf W/(V x I) W/VAReal PowerPhase AnglePower FactorVoltage Dropwhere:V 2 ( I R cos θ I X sin θ )dVd sinθ X 1.5.4voltage drop in circuitload reactive factorreactanceAlternating Current (AC), Three-PhaseV denotes line to line voltage.Basic FormulasApparent Power(kVA V I 3)kVA kW 2 kVAR 2Real PowerkW kVA cos θReactive PowerkVAR kVA sin θPhase Angleθ arctan Power Factorpf cos θ kW kVAR kWkVA2010 Edition SPU Design Standards and Guidelines9C-5

Appendix C Design CalculationsV 3 ( I R cos θ I X sin θ )dVoltage Dropwhere:Vd sinθ X 1.5.5voltage drop in circuitload reactive factorreactanceMotors1 horsepower (hp) 746 watts.Note: Motor hp rating relates to motor mechanical output. To determine motor input kVArequirements, the motor efficiency and power factor must be accounted for. In general, forpreliminary or rough load calculations, assume:1 kVA of electrical input power for 1 hp of motor.Example 1MotorsCondition: A motor control center with a total connected horsepower of 337 hp can be assumedto require 337 kVA of input power. This is a conservative value, particularly for larger motors.Torque (hp x 5250)/revolutions per minute (rpm)Fan hp (cubic feet per minute [cfm] x pressure)/(33000 x eff)Pump hp (gallons per minute [gpm] x head x specific gravity)/(3960 x eff)Motors (Single Phase)hp (V x I x eff x pf)/746Motors (3 phase)Synchronous Speed: ns (120)(Frequency)/(# of Poles)hp 1.5.6(V I 3 eff pf746)Power Factor CorrectionThe size of the capacitor needed to increase the power factor from pf1 to pf2 with the initialkVA given is: kVAR kVA 1 pf 2 pf / pf 1 pf 2 1122 9C-62010 Edition SPU Design Standards and Guidelines

Chapter 9 Electrical DesignAppC Ch9-DesignClac CALCULATIONSThis section presents sample calculations for electrical design.1.6.1LoadLoad calculations should be made using applicable sections of NEC Articles 220, 430, and othersections of the NEC. The following load calculations should generally be used for sizing: Feeder conductors and protective devices Transformers Panelboard and switchboard main busses Motor control center components Service entrance devices and conductorsLoad calculations must include all loads. They should be made by summing all of the loads (usingappropriate diversity factors allowed by NEC Article 220) that are connected to eachpanelboard, switchboard, and motor control center. An allowance must be made for future loadgrowth. The loads for each branch of the distribution system can then be summed back to theservice entrance equipment.1.6.2Generator SizingThe following information is intended to familiarize the design engineer with terms used bygenerator sizing software and underlying formulas.Generator single or multi-sets must be sized to supply maximum starting (SkVA), stead-staterunning (RkVA) and non-linear (GkW) demands of connected and future electrical equipment.Information critical to the sizing and selection of generator single or multi-sets include: Environmental conditions: elevation, temperature, indoor or outdoor Noise abatement requirements: mufflers, enclosure, silent models Fuel: diesel, gasoline, natural gas Fuel storage: skid mounted tank, day and remote tanks Cooling: liquid cooled radiator, forced air Voltage regulation: maximum allowable voltage dips Operation: prime, standby Voltage ratings: voltage,3-phase, 1-phase, solid grounded, delta, wye Connected loads: Linear, non-linear, power factor Load operation: Motor starting methods, single step, single step with diversity, multiplesteps of loading Future loads2010 Edition SPU Design Standards and Guidelines9C-7

Appendix C Design Calculations1.6.2.1Sizing Procedures for Generator Single or Multi-setsThe following is the sizing procedure for generator single or multi-sets:1. Prepare a load schedule.2. Enter individual load characteristics in software.3. Enter loads in step sequence in software.4. Have software calculate and select a generator set. It is a good practice to request averifying calculation from the preferred genset manufacturer. Generator Sizingeff EfficiencyFLA Full Load AmpsGkW Non-linear kW of connected load(s)LRA Locked Rollor AmpsRpf Running Power Factor of connected loads(s)RkVA Running kVA of connected load(s)RkW Running kW of connected load(s)Rpf Running power factor of connected load(s)Rmsf Reduced motor starting factorSkVA Starting kVA of connected load(s)SkW Starting kW of connected load(s)Spf Starting power factor of connected load(s) Equations1. Resistive Loads :SkVA RkVA SkW RkW2. Lighting Loads (except for HID): SkVA RkVA 3.HID Lighting Loads:SkWSpfRkWRpfSkVA 0.75 RkVASkW 0.75 RkW4. Motor Loads: SkVA ( NEMA Code Multiplier ) 5. Motor Loads (3-phase): SkVA LRA Vl l 9C-82010 Edition SPU Design Standards and Guidelines31000hp 746(eff Spf 1000)

Chapter 9 Electrical DesignAppC Ch9-DesignClac 8.9.10RkW 6.VFD:hp 746( eff 1000)RkW ( Drive Nameplate(hp ) 746( eff 1000)RkVA ( Drive Nameplate(hp ) 746( eff pf 1000)SkVA ( Drive Nameplate(kVA))eff7. VFD: GkW 2.0 RkWNote: This assumes a generator sizing factor of 2 unless otherwise known. Review informationon UPS as well.8. UPS: SkW (UPS Nameplate(kW ) BatteryCh arg ing ( kW ))( eff )RkW 9. UPS:(UPS Nameplate(kW ) BatteryCh arg ing ( kW ))effGkW (3 pulse) 2.50 RkWGkW (6 pulse) 1.40 RkWGkW (12 pulse) 1.15 RkW10. Reduced Voltage Motor Starting: SkVA SkVA Rmsf1.6.3Conductor Size, GeneralConductor sizes must be determined in compliance with the specific NEC articles noted below,and with due consideration of other factors, such as terminal ratings and voltage drop as shownon Table C-2.Table C-2NEC References for Conductor SizingGeneral Purpose Branch Circuits and FeedersArticle 220Service Entrance ConductorsArticle 230Motor CircuitsArticle 430Air Conditioning EquipmentArticle 440GeneratorsArticle 445Transformer (Primary and Secondary)Article 450Capacitor CircuitsArticle 4602010 Edition SPU Design Standards and Guidelines9C-9

Appendix C Design CalculationsIn this section, we will look at the general requirements for sizing conductors once thecalculated load current is known. This is a two-step process:1. The first step is to look at the temperature rating of the terminals and the ampacity ofthe conductor that could be used at a matching temperature rating.2. The second step is to look at the effect of ambient temperature and conductor deratingfactors on the ampacity of the conductor that results from where and how theconductors are installed.Insulation used to cover electrical wiring conductors is rated for the maximum temperature itcan withstand on a continuous basis. Standard ratings are 60 , 75 , 90 , and 105 C. The currentcarrying capability of a conductor is a function of: Cross-section of the conductor Insulation temperature rating Ambient temperature.The ampacity of a conductor of any size is increased as the rating of its insulation is increased.As the ambient temperature is increased, the ampacity of the conductor must be derated fromits ampacity at 30 C. A No. 6 copper conductor with 90 C insulation will be rated for a highercontinuous current than a No. 6 copper conductor with 60 C insulation. Because theUnderwriters Laboratories, Inc. (UL) places certain restrictions on the size and temperaturerating of conductor that can be used at its terminals, conductor size needs to be carefullydetermined.The UL tests for switchboards, panelboard, motor starters, and other equipment are made withwiring terminated on the equipment. The equipment is designed to take into account the heattransfer provided by these load-side conductors. If the conductor connected to a circuit breakeris smaller than the tested configuration, it will conduct less heat away from the circuit breaker.This will cause its thermal elements to operate at a lower temperature than with a largerconductor, even though the smaller conductor may be adequate based on the NEC tables forwire size at its insulation rating. For this reason, the UL listing for circuit breakers, and manyother types of equipment, is based on standard-size conductors. These standard sizes, in turn,are based on the NEC ampacity for a particular insulation temperature rating. UL uses thefollowing basic rule for circuit breakers: Circuit breakers through 125A:Use 60 C insulation ampacity Circuits breakers 150A and above:Use 75 C insulation ampacityHigher rated insulations may be used, but the conductors must be sized based on the lowerrated insulation. Of course, these are minimums, and larger wire may be used. Although this isthe basic rule, there are exceptions. Equipment where all terminations are rated for use with75 C wire has become widely available, and this is what we typically ask for in our specificationsfor all electrical equipment down through 120V panelboards. However, this is not universal, andwe must make sure that our wiring is sized appropriately. If you size all smaller circuits (through125A) based on 60 C wire, you will stay out of trouble.Paragraphs 210-19 and 215-2 of the NEC require that branch circuit and feeder conductors havean ampacity not less than the load to be served. NEC Paragraph 210-22 contains additionalinformation relative to branch circuit loads. Once branch circuit and feeder loads have been9C-102010 Edition SPU Design Standards and Guidelines

Chapter 9 Electrical DesignAppC Ch9-DesignClac 8.9.10determined using applicable sections of NEC Article 230 and other applicable articles, conductorsizes should then be determined using Tables 310-16 through 310-31 of the NEC. The fourexamples presented below are based on the ampacities presented in NEC Table 310-16, asmodified by the applicable correction factors for temperature and conduit fill.Example 2Conductor Size No. 1Conditions: Continuous load rated 43A served by a conduit containing only the conductors forthe load, running through a wet area that could have an ambient temperature as high as 42 C.Conductors are to be copper with type THHN/THWN insulation.Required ampacity per NEC paragraphs 210-16 and 210-22: Ampacity required continuous load x 125% or 53.75 ampsA No. 6 AWG copper conductor having an ampacity of 55 amps (with 60 C insulation) would bethe correct choice at the terminals of the circuit breaker serving the load. Note, however, thatNEC Table 310-16 applies only up to a maximum ambient temperature of 30 C.Where the ambient temperature exceeds the 30 C ambient temperature on which Table 310-16is based, the allowable ampacity of the conductor must be corrected using the correctionfactors at the bottom of Table 310-16, as required by NEC paragraph 310-10. Ampacity of No. 6 conductor (THHN/THWN wet, 75 C column) 65 amps Corrected ampacity 65 x correction factor (.82) 65 x .82 53.3 ampsBecause 53.75 amps is required, this conductor is not adequate. The next larger size conductorwill need to be used even though its ampacity was sufficient at the circuit breaker.If the circuit were being installed where the conductors would never be wet or whereconductors with insulation suitable for wet application at 90 C were being used, the 90 Ccolumn ampacity of the conductor could be used for determining the corrected ampacity of theconductor in the conduit. Ampacity of No. 6 conductor (THHN/THWN DRY, or THWN-2 or XHHW-2 wet, 90 Ccolumn) 75 amps Corrected ampacity 75 x correction factor (.87) 75 x .87 65.2 ampsThe No. 6 conductor would be adequate for this installation and could be protected by a 60-ampcircuit breaker even though its 60 C rating is only 55 amps. The 60-amp circuit breaker would beallowed by paragraph 240-3, which allows a conductor to be protected by the next larger sizeovercurrent device if the size of the device is 800 amps or less.2010 Edition SPU Design Standards and Guidelines9C-11

Appendix C Design CalculationsExample 3Conductor Size No. 2Conditions: The same load and ambient conditions as above, but with 6-phase conductors in thesame conduit. We already know that the No. 6 conductors are adequate at the terminals andthat they would not be adequate if the circuit were wet—unless the conductor insulation wererated 90 C, wet. Assume the conductors to be No. 6 THWN-2 insulation. Corrected ampacity 75 x correction factor (.87) 75 x .87 65.2 amps (Ampacity from 90 C column, corrected for temperature)Where more than three current-carrying conductors are contained in the same raceway, theampacity of the conductors must also be derated by the ampacity adjustment factor containedin Note 8 of NEC Tables 310-16 through 310-19. Corrected ampacity of six No. 6 conductors 65.2 x .8 52.2 ampsBecause 53.75 amps is required, this conductor is not adequate and the next larger sizeconductor will need to be used, even though its ampacity was sufficient at the circuit breaker.If the ambient temperature were reduced to below 40 C, the temperature correction factorwould be increased to .91, resulting in an increase in the conductor ampacity. Corrected ampacity 75 x .91 (temp. correction) x .8 (six conductors) 54.6 ampsAgain, the No. 6 THWN-2 conductor would be adequate for this installation and could beprotected by a 60-amp circuit breaker even though its 60 C rating is only 55 amps.Example 4Conductor Size No. 3Conditions: A feeder with 200A of noncontinuous load and 65A of continuous load to beinstalled in conduit in a wet area with an ambient temperature of 30 C or less. Required ampacity per NEC paragraph 220-10 noncontinuous load 1.25 x continuousload Or 200 1.25 x 65 281.25 ampsThe feeder overcurrent device would be sized at 300A because that is the next larger standardrating (see Article 240 of the NEC).The conductor ampacity requirement can be met by either one 300-kCM conductor or two 1/0conductors with THHN/THWN or XHHW insulation per phase.9C-122010 Edition SPU Design Standards and Guidelines

Chapter 9 Electrical DesignAppC Ch9-DesignClac 8.9.10Example 5Conductor Size No. 3Conditions: The same load as used in example No. 3, but the conduit is to be installed in a dryarea with an ambient temperature of 38 C. Required ampacity calculated above 281.25 amps. Ampacity of one 300-kCM THHN/THWN or XHHW conductor is 320 amps in a drylocation. Correction factor for 90 C conductors in a 38 C ambient temperature 0.91. Corrected ampacity 320 amps x 0.91 291.If the conductors were being installed in a wet location, the ampacity from the 75 C columnwould have to be used (refer to Table 310-13 for operating temperature), and the results wouldbe different—unless conductors with insulation rated 90 C, wet, such as THWN-2 or XHHW-2,are used. Note that, at the terminals, the ampacity of the conductors must be based on thetemperature rating of the terminals (either 60 C or 75 C); therefore, if the terminals are in ahigh-ambient-temperature area, this procedure must be modified.1.6.4Conduit Size and FillWhere conductors are installed in conduit, the conduit should be sized in accordance withTables 1 through 5A in Chapter 9 and Appendix C of the NEC, and all associated notes. Followingare two examples of how conduits can be sized under different circumstances.Example 6Conduit Size and Fill No. 1Conditions: Three 4/0 AWG conductors with XHHW insulation installed in rigid steel conduit (noseparate ground conductor).See NEC Table C8 for conduit size required for three 4/0 AWG conductors with XHHW insulation.The table would allow only two conductors to be installed in a 1-1/2-inch conduit and four to beinstalled in a 2-inch conduit; therefore, a 2-inch conduit is the correct choice.2010 Edition SPU Design Standards and Guidelines9C-13

Appendix C Design CalculationsExample 7Conduit Size and Fill No. 2Conditions: Three No. 4/0 phase conductors, one No. 1/0 neutral and one No. 2 equipmentground conductor to be instal

1. Non-computer generated calculations must be on standard calculations sheets with the heading completely filled out. 2. Calculations generated by computer programs must conform with the following procedures: a. Include all heading information on each sheet b. Insert comments wherever possibly to clarify concepts and actions taken in the