Appendix 9C: Design Calculations for Electrical Design, Exercises of Design Patterns

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SPU Design Standards and Guidelines November 2020 i

APPENDIX 9C

Design Calculations for Electrical Design

Appendix 9C Design Calculations for Electrical Design

Appendix 9C Design Calculations for Electrical Design

1. INTRODUCTION

This appendix presents standards and guidelines for electrical design calculations for SPU projects.

Design calculations establish minimum guidelines and requirements for generating electrical calculations on projects. Electrical calculations should be made for all SPU projects that include electrical components and should be filed in the project notebook. Design calculations may be made either manually or by SPU-approved computer programs. At a minimum, the following types 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

2. SOFTWARE

The electrical design engineer must use only SPU-approved electrical analysis software. The results should be validated with a hand calculation or order of magnitude estimate. Some SPU- approved software tools are:

• SKM Power Tools for Windows (PTW) software. It includes a basic tool, DAPPER (load current, voltage drop, conductor sizing, etc) and several specialized tools such as HI_WAVE (harmonic analysis) and CAPTOR (circuit breaker coordination and settings)
• Cummins Power Suite for sizing emergency generators
• CenterONE available from Rockwell Automation for laying out motor control centers

Spreadsheets may also be used to perform basic electrical load calculations with programs such as Microsoft EXCEL.

Appendix 9C Design Calculations for Electrical Design

3. CALCULATION MATRIX

Project calculations serve as formal documentation of the project electrical design. They must contain sufficient description and detail to communicate the design concept, assumptions, and judgments associated with the design. Explanatory comments should be provided to assist reviewers and engineers who may use the calculations in the future.

Table 9C-1 describes electrical calculation required for projects, tools to do the calculations, who is responsible for the calculations, and when they should be done.

Table 9C- Calculations for Electrical Design

Calculation Description Required Tools^1

Req’d All

Req’d Cond 2

By Engr^3

By Cntr^3

Design Phase (%) Load - facility, switchgear, MCC

Load at each load center per NEC to determine bus, protective device & circuit size

SKM PTW DAPPER, Spreadsheets, hand calcs

X X 30/ 60/

Load - panelboard

Load on each panelboard per NEC to determine panel, circuit, and transformer size

SKM PTW DAPPER, spreadsheets

X X 60 and 90

Generator sizing

To size engine generator based on critical run and start loads.

Cat, Kohler, Cummins, or other vendor software

X X 30/ 60/

Short Circuit Available fault current at each bus to determine equipment short circuit/interrupting ratings

SKM PTW DAPPER, Hand Calculation

X X X 30/60/

Lighting To determine fixtures needed given desired light level; also energy calculations (where req’d)

AGI 32, Vendor, spreadsheets

X X 60 and 90

Conductor sizing

To size conductors per NEC Tables, hand calcs X X 60 and 90

Circuit breaker and fuse sizing

To size circuit breakers and fuses per NEC

Tables, hand calcs X X 60 and 90

Conduit Fill/Tray Size

To size conduit and cable tray per NEC

NEC Tables, Cablematic Plus

X X 60 and 90

Voltage drop For heavily loaded and/or long circuits to confirm operation within NEC recommendations (min)

SKM PTW DAPPER, spreadsheets, hand calcs

X X 60 and 90

Transient Motor Starting

For starting large motors (largest motor at each load center) to determine if voltage drop on motor starting is magnitude to adversely impact other system equipment (e.g. 20% voltage dip could make control relays drop out. Many

SKM PTW TMS, hand calcs

X

Appendix 9C Design Calculations for Electrical Design

4. BASIC REQUIREMENTS FOR

ELECTRICAL CALCULATIONS

The following are SPU basic requirements for electrical calculations:

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 computer input

c. Provide clear documentation of electrical geometry, support conditions, load application, and load requirements

d. 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 output with hard copy calculations. f. Provide manual checks of pertinent results (e.g. service size, main feeder voltage drop) for computer generated output.

5. BASIC ELECTRICAL ENGINEERING

FORMULAS

This section describes basic electrical engineering formulas for creating design calculations.

5.1 LIST OF SYMBOLS

V - Voltage (volts) I - Current (amps)

R - Resistance (ohms) X - Reactance (ohms) Z - Impedance (ohms)

W Real Power ( watts)

θ - Phase angle whose cosine is the power factor

eff - Efficiency

Appendix 9C Design Calculations for Electrical Design

5.2 DIRECT CURRENT (DC) FORMULAS

Basic Formulas

Volts V = I x R

Power in watts

P V I

P I R

= ×

= 2 ×

5.3 ALTERNATING CURRENT (AC) SINGLE

PHASE

V denotes line to neutral voltage.

Basic Formulas

Volts V = I × Z

Power Factor pf=cos θ

Apparent Power =

Reactive Power =

VA V x I

VARS V x I x sin θ

Real Power W = V x I x pf

Phase Angle θ = arctan(W/VARS)

Power Factor pf = W/(V x I) = W/VA

Voltage Drop (^) V ( )

d =^2 ×^ I^ ×^ R^ ×^ cos^ θ+^ I^ ×^ X ×sinθ

where:

Vd = voltage drop in circuit

sin θ = load reactive factor

X = reactance

5.4 ALTERNATING CURRENT (AC),

THREE-PHASE

V denotes line to line voltage.

Basic Formulas

Apparent Power kVA =( V × I × 3 )

kVA = kW^2 + kVAR^2

Appendix 9C Design Calculations for Electrical Design

5.6 POWER FACTOR CORRECTION

The size of the capacitor needed to increase the power factor from pf 1 to pf 2 with the initial

kVA given is:

kVAR = kVA ×  − pf − pf pf − pf

6. SAMPLE CALCULATIONS

This section presents sample calculations for electrical design.

6.1 LOAD

Load calculations should be made using applicable sections of National Electrical Code (NEC) Articles 220, 430, and other sections 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 conductors

Load calculations must include all loads. They should be made by summing all of the loads (using appropriate diversity factors allowed by NEC Article 220) that are connected to each panelboard, switchboard, and motor control center. An allowance must be made for future load growth. The loads for each branch of the distribution system can then be summed back to the service entrance equipment.

6.2 GENERATOR SIZING

The following information is intended to familiarize the design engineer with terms used by generator sizing software and underlying formulas.

Generator single or multi-sets must be sized to supply maximum starting (SkVA), stead-state running (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

Appendix 9C Design Calculations for Electrical Design

• 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, multiple steps of loading
• Future loads

6.2.1 Sizing Procedures for Generator Single or

Multi-sets

The 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 a verifying calculation from the preferred genset manufacturer.

6.2.2 Definitions: Generator Sizing

eff = Efficiency

FLA = Full Load Amps

GkW = Non-linear kW of connected load(s)

LRA = Locked Rollor Amps

Rpf = 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 factor

SkVA = Starting kVA of connected load(s)

SkW = Starting kW of connected load(s)

Spf = Starting power factor of connected load(s)

6.2.3 Underlying Equations

1. Resistive Loads : SkVA = RkVA = SkW = RkW

Appendix 9C Design Calculations for Electrical Design

6.3 CONDUCTOR SIZE, GENERAL

Conductor 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 shown on Table 9C-2.

Table 9C- NEC References for Conductor Sizing

General Purpose Branch Circuits and Feeders Article 220 Service Entrance Conductors Article 230 Motor Circuits Article 430 Air Conditioning Equipment Article 440 Generators Article 445 Transformer (Primary and Secondary) Article 450 Capacitor Circuits Article 460

In this section, we will look at the general requirements for sizing conductors once the calculated 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 of the 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 derating factors on the ampacity of the conductor that results from where and how the conductors are installed.

Insulation used to cover electrical wiring conductors is rated for the maximum temperature it can withstand on a continuous basis. Standard ratings are 60°, 75°, 90°, and 105°C. The current- carrying 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 from its ampacity at 30°C. A No. 6 copper conductor with 90°C insulation will be rated for a higher continuous current than a No. 6 copper conductor with 60°C insulation. Because the Underwriters Laboratories, Inc. (UL) places certain restrictions on the size and temperature rating of conductor that can be used at its terminals, conductor size needs to be carefully determined.

The UL tests for switchboards, panelboard, motor starters, and other equipment are made with wiring terminated on the equipment. The equipment is designed to take into account the heat transfer provided by these load-side conductors. If the conductor connected to a circuit breaker is 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 larger

Appendix 9C Design Calculations for Electrical Design

conductor, even though the smaller conductor may be adequate based on the NEC tables for wire size at its insulation rating. For this reason, the UL listing for circuit breakers, and many other 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 the following basic rule for circuit breakers:

• Circuit breakers through 125A: Use 60°C insulation ampacity
• Circuits breakers 150A and above: Use 75°C insulation ampacity

Higher rated insulations may be used, but the conductors must be sized based on the lower rated insulation. Of course, these are minimums, and larger wire may be used. Although this is the basic rule, there are exceptions. Equipment where all terminations are rated for use with 75°C wire has become widely available, and this is what we typically ask for in our specifications for all electrical equipment down through 120V panelboards. However, this is not universal, and we must make sure that our wiring is sized appropriately. If you size all smaller circuits (through 125A) 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 have an ampacity not less than the load to be served. NEC Paragraph 210-22 contains additional information relative to branch circuit loads. Once branch circuit and feeder loads have been determined using applicable sections of NEC Article 230 and other applicable articles, conductor sizes should then be determined using Tables 310-16 through 310-31 of the NEC. The four examples presented below are based on the ampacities presented in NEC Table 310-16, as modified by the applicable correction factors for temperature and conduit fill.

Example 9C- Conductor Size No. 1

Conditions: Continuous load rated 43A served by a conduit containing only the conductors for the 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 amps

A No. 6 AWG copper conductor having an ampacity of 55 amps (with 60°C insulation) would be the correct choice at the terminals of the circuit breaker serving the load. Note, however, that NEC 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- is based, the allowable ampacity of the conductor must be corrected using the correction factors 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 amps

Because 53.75 amps is required, this conductor is not adequate. The next larger size conductor will 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 where conductors with insulation suitable for wet application at 90°C were being used, the 90°C

Appendix 9C Design Calculations for Electrical Design

The conductor ampacity requirement can be met by either one 300-kCM conductor or two 1/ conductors with THHN/THWN or XHHW insulation per phase.

Example 9C- Conductor Size No. 3

Conditions: The same load as used in example No. 3, but the conduit is to be installed in a dry area 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 dry location.
• 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 column would have to be used (refer to Table 310-13 for operating temperature), and the results would be 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 the temperature rating of the terminals (either 60°C or 75°C); therefore, if the terminals are in a high-ambient-temperature area, this procedure must be modified.

6.4 CONDUIT SIZE AND FILL

Where conductors are installed in conduit, the conduit should be sized in accordance with Tables 1 through 5A in Chapter 9 and Appendix C of the NEC, and all associated notes. Following are two examples of how conduits can be sized under different circumstances.

Example 9C- Conduit Size and Fill No. 1

Conditions: Three 4/0 AWG conductors with XHHW insulation installed in rigid steel conduit (no separate 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 be installed in a 2-inch conduit; therefore, a 2-inch conduit is the correct choice.

Example 9C- Conduit Size and Fill No. 2

Conditions: Three No. 4/0 phase conductors, one No. 1/0 neutral and one No. 2 equipment ground conductor to be installed in rigid metal conduit. Phase and neutral conductor insulation will be XHHW and the ground conductor will have TW insulation.

Because the tables in Appendix C of NEC are for situations where all conductors in a conduit are the same size, they cannot be used for this example. NEC Table 4, using appropriate conductor areas from NEC Table 5, must then be used.

Appendix 9C Design Calculations for Electrical Design

Table 9C- Total conductor area

Conductor size Area 4/0 XHHW 0. 1/0 XHHW 0.

2 TW 0.

Total Area = 3(.3197) + .1825 + .1333 = 1.275 square inches

Conduit size required:

Because more than two conductors that are not lead covered are being installed, the column for 40 % fill in NEC Table 4 can be used.

Select conduit with a usable area greater than 1.275 square inches; therefore, conduit size = 2 inch (40% of total area = 1.363 square inches).

Caution: Both Schedule 40 and Schedule 80 PVC have a smaller inside diameter than rigid metal conduit and thus will have a smaller total area. EMT also has a smaller inside diameter in the smaller sizes (2-inch and less). Conduits must be based on the conduit type having the smallest inside diameter allowed by the specifications for a project. Schedule 40 PVC has a smaller diameter than all other types of conduit, except Schedule 80 PVC, and its area could be used as a default value for most calculations.

6.5 MOTOR BRANCH CIRCUIT

NEC Article 430, Motors, Motor Circuits, and Controllers, covers the provisions for motors, motor circuits, and controllers. NEC Article 430 includes tables for motor full-load currents, which are the minimum values that can be used in determining sizes of motor branch circuits, motor feeders, short circuit and overcurrent device sizes and settings, and miscellaneous load calculations. Actual nameplate currents must be used if they are larger than the minimum values provided in the tables. The values in the tables should be increased for induction motors with full-load speeds of less than 1,200 rpm and for motors powered by solid-state drives. In addition, a table is provided for determining the maximum rating or setting of motor branch circuit, short circuit, and ground fault protective devices. NEC Article 440 contains special provisions that apply to the installation of air conditioning and refrigeration equipment and should be referred to for these applications.

The following calculations and the accompanying table are based on the applicable provisions of NEC Article 430 and are provided as a guide for performing motor branch circuit and feeder calculations and for sizing components for motor branch circuits as part of a design. The typical calculations required are demonstrated by the following examples.

Example 9C- Motor Branch Circuit No. 1

Conditions: Induction motor is rated 60 hp, 460V, 3-phase, Code letter G, 1,800 rpm continuous, and will be powered by a combination motor starter through a conduit system. All equipment and the conduit system are located in areas with ambient temperatures of 30°C or less.

Appendix 9C Design Calculations for Electrical Design

Example 9C- Motor Branch Circuit No. 2

Conditions: Determine the size of the feeder conductors and thermal magnetic circuit breaker feeding a motor control center that has a total connected motor load of 215A, with the 60-hp motor from Example 1 being the largest motor. In addition, there are 45A of continuous load and 65A of noncontinuous load. Conductors should be copper with type XHHW insulation installed in an area where the ambient temperature is less than 30°C.

Motor feeder conductors must be sized in accordance with applicable portions of Part B of NEC Article 430, and feeder breakers must be sized in accordance with applicable portions of Part E of NEC Article 430.

NEC paragraph 430-24 requires that the conductors supplying the motor control center have an ampacity sufficient for the motor load determined in accordance with NEC paragraph 430-24, plus the nonmotor load that would be determined in accordance with NEC Article 220. NEC paragraph 430-24 requires that the motor load used in this determination be equal to the sum of the full-load currents of all the motors in the group plus 25% of the highest rated motor.

The required ampacity of the conductors should be calculated as follows:

• Total motor load + 25% of largest motor FLA + noncontinuous load + 125% of continuous load or
• 215 + (.25 x 77) + 65 + (1.25 x 45) = 355 amps

Conductors may be either one 500 kCM or two No. 3/0 AWG per phase (one 500 kCM = 380 amps, two No. 3/0 = 400 amps).

NEC paragraphs 430-62 (a) and (b) cover the requirements for sizing the motor feeder short circuit and ground fault protection. Paragraph (a) covers the requirements for situations where spare capacity for future additions is not wanted or required. Paragraph (b) covers situations where spare capacity is to be provided and allows the feeder protective device size or setting to be based on the ampacity of the feeder circuit conductors.

For the above example, a 400-amp device would be selected. For the 400-amp device to be used to protect the 500-kCM conductors, NEC paragraph 240-3(b) needs to be used.

6.6 POWER FACTOR CORRECTION

CAPACITORS

Power factor correction capacitors are installed for either of the following reasons:

• To increase the measured power factor at the serving utility’s meter and reduce the power factor penalty being imposed by the utility. Power factor correction for this reason cannot be justified unless the serving utility actually has a power factor penalty in its rate schedule.
• To release additional capacity in feeder conductors.

Appendix 9C Design Calculations for Electrical Design

For example, a 3-phase load of 200 kW would be equal to 301A at 480V if the power factor were 80%, but it would be only 254A if the power factor were raised to 95%. This would release 47A of capacity for additional loads.

Article 460 of the NEC covers the installation of capacitors on electric circuits. Those calculations needed to determine the size of the capacitor required and the size of conductors required to connect the capacitors to their electric power supply are discussed in this section. Following are several examples to illustrate the required calculations:

Example 9C- Power Factor No. 1

Conditions: A load of 200 kVA exists at 480V with a power factor of 80%. Determine the amount of capacitors required to improve the power factor to 95%.

Power factor = Apparent power (kVA) ÷ Real power (kW)

By definition, the power factor is the cosine of the angle that exists between the real power and apparent power vectors.

The calculation to determine the amount of capacitance (measured in kVAR) should be made as follows:

kVAR at initial power factor = �(kVA)^2 – (kW)^2 ) = �(kVA)2 – (kVA X pf)

kVAR = �(200kVA)2 – (160kw)

kVAR = �40,000 – 25,600 = 120.0 kVAR

Because the real power of a load is not changed when the power factor is improved, we can use the known real power and desired power factor to calculate the new kVAR value in the vector triangle:

kVAR @ 95% power factor = �(kW ÷ pf)^2 – (kW)^2

kVAR = �(160 ÷ .95)^2 – (160)^2

kVAR = �(28,366 – 25,600) = 52.

Required kVAR for correction = 120 - 52.6 = 67.4 kVAR

Similar calculations can be made to determine the size of the capacitor required to improve the power factor of a single motor to a higher power factor. Tables are available from capacitor manufacturers to simplify the selection of these capacitors. Capacitors larger than the maximum size recommended by motor manufacturers must not be installed in order to avoid over- excitation of motor at no-load condition.

Example 9C- Power Factor Correction Capacitor No. 2

Conditions: Load is a 60-hp, 1,800-rpm motor operating at 480V, 3-phase. Capacitors rated 15 kVAR at 480V are being installed to improve the power factor. Determine the size of the conductor needed to meet the requirements of the NEC.