# Power System and Equipment Design Calculations

This article is about requirements and procedures for electrical system and equipment design calculations. Main keywords for this article are Power System IEC References, Power System and Equipment Design Calculations, Electrical Calculation Software, Electrical Load Summary, Load Flow Study, Short Circuit Study, Voltage Drop Calculations, Transient Stability Studies, Harmonic Analysis Power System, Power Factor Improvement Power System, Equipment and Cable Sizing, Transformer Capacity, Switchgear Rating, Battery and Charger Capacities, Cable Sizing.

## Power System IEC References

International Electrotechnical Commission (IEC)

60038 Standard Voltages
60059 Standard Current Ratings
60076 Power Transformers
60364 Low Voltage Electrical installations of Buildings
60909 Short circuit currents in three-phase a.c. Systems
60949 Calculation of thermally permissible short-circuit currents
60986 Short circuit ternperature limits of electric cables with rated voltages from 6 kV (Um-7,2 kV) up to 30 kV ) (Um=36 kV)
61800-2 Adjustable speed electrical power drive systems – Part 2: General requirements- Rating specifications for low voltage adjustable frequency a.c. power drive systems
61800-3 Adjustable speed electrical power drive systems – Part 3: EMC requirements and specific test methods.

## Electrical Calculation Software

• Electrical System calculations shall be made using a commercially available analysis program such as ETAP (Electrical Transient Analysis Program) by OTI (Operational Technology Incorporated), EDSA PALADIN DESIGNBASE (EDSA Micro Corporation).
• Calculations shall be made in accordance with IEC 60909.
• Calculation methods are related to the testing requirements for the equipment.
• Calculations for systems using IEC are different than for systems using ANSI/NEMA equipment. Some programs are capable of performing both type calculations but is important to select the appropriate mode of calculation.

## Sequence of Electrical Work

• Electrical system calculations for most projects are an iterative process. Sufficient data is not available at the beginning of a project to make final calculations. However, calculations must be made early in the project to properly specify the electrical equipment and to insure that use of large electrical drive motors is feasible.
• A number of preliminary calculations must be performed using various assumptions to arrive at an over-all one line diagram. Once the over-all one line diagram has been selected these calculations must be further refined using updated load estimates to allow procurement of major long-lead-time electrical equipment.
• As more information becomes available the calculations are updated and expanded to more detail levels to define the electrical equipment at the secondary level.
• The data base is continuously updated until at the completion of the project it accurately represents the as built electrical system.

• There are actually three different types of load summaries required: (1) Main (or utility) Load, (2) Essential or Stand-By Power and (3) UPS Power. Preparation of the main load summary and maintenance of an accurate data base is the major task. The other load summaries do not have as many loads or bus summaries.
• The load summary can be produced using a custom data base or spread sheet developed specifically for the project or the load summary tools contained in the master calculation package such as ETAP, EDSA, or PTW can be used. The load summary shall be electronically linked to the calculation data base such that single entry of data is required. It is preferred that the load summary be electronically linked with the mechanical equipment list and the electrical one line diagrams to permit single point data entry and insure consistency between these documents.
• The load summary shall contain the information and assumptions outlined below:
a. Equipment Number
b. Service
c. Status (operating or spare)
d. Mechanical Equipment Rated maximum kW and normal brake kW
e. Motor rated voltage, kW, efficiency and power factor at full, 3/4 and 1/2 load
f. Calculated motor load for mechanical equipment maximum and normal bake loads (kW, kVAR and kVA)
g. Utility factor
i. Lighting Load kW, kVAR and kVA
• Preliminary load estimates shall use motor nameplate rating in kW and shall assume a power factor of 0.85. As actual driven equipment loads and motor data become available, the motor loads shall be calculated from this data.
• Spare motors shall not be included in the overall total load. However, spare motors shall be included in the loads of buses, transformers, and feeders to which they contribute, in order to obtain the maximum operating load on individual equipment. When both the operating motor and its spare would contribute to the same load, if both were operating, only the operating motor shall be included in the load.
• Lighting and receptacle transformer operating loads shall be included at 80% of the transformer kVA rating. Substation transformers and load bus shall be sized to accommodate future load growth thus it is appropriate to include these loads at the initial design value.
• Intermittent short time loads such as motor operated valves shall not be included.

• A load flow study shall be run immediately after completion of data entry as a first check on the electrical system and to de-bug data in case errors were made. Once the system model has been confirmed, system load flow cases can be run or other calculations such as short circuit analysis can be started.
• The load flow study is used to confirm that voltages and loading on different elements of the system are within project parameters. For redundant systems the load flow shall be performed with one supply interrupted to insure that the system will operate satisfactorily in this condition.
• The load flow study provides information on the power factor of the circuits and buses of the electrical system.

## Short Circuit Study

• Short circuit studies shall be run to determine preliminary equipment rating and confirm required equipment ratings for purchase.
• The secondary of the 480 volt transformers shall be modeled with motor load equivalent to the kVA rating of the transformer.
• Buses with medium voltage motors shall be modeled with the actual motors at their nameplate rating plus additional motors to represent the capacity provided for future additions up to the maximum rating of the feeding transformer.
• Fault calculations for equipment selection shall be based on the system operating configuration that will result in the maximum available fault current.
• Standard transformers impedances shall be used; deviations must be approved by Company. Transformers shall be modeled with maximum allowed negative impedance tolerance.
• The utility supply to the plant shall be modeled as an infinite bus for short circuit calculations. (For motor starting the system shall modeled in its weakest configuration).#

## Voltage Drop Calculations

• Voltage drop calculations shall be made for both steady state and motor starting. As indicated above, the load flow study shall indicate steady state voltage at all buses.
• The allowable voltage drops are based on the use of transformer taps to maintain 100% voltage at the secondary terminals under normal loading conditions. Permissible steady state voltage drops shall be as follows:
a. Medium Voltage Distribution System. The total voltage drop to motors or unit substation transformers shall not exceed 5% under normal loading conditions.
b. Systems Rated 480 Volts and Below. The total voltage drop from the unit substation secondary terminals to the utilization equipment shall not exceed 5%.
• ‘Snap-shot’ voltage drop calculations are acceptable for most motors. Most calculation programs provide for this type calculation as an adjunct to the load flow; It calculates the voltage at the instant the switch is closed with out regard to any affect this lowering of the bus voltage might have on any other operating loads.
• For very large motors started on the bus with other motors, a transient stability program or dynamic motor starting program shall be employed to recognize the effect on and from all loads on the bus.
• The maximum acceptable voltage drops during motor starting are shown below. However in all cases Company must approve the permissible voltage drop limits for each project and approve individual calculations for motors larger than 2000 kW.
a. For motors on 480 volt bus with other loads, the maximum drop on the bus shall be 10%. The maximum drop to motor terminals shall be 15%.
b. For medium voltage motors on the same bus with other motors the maximum drop on the bus shall be 15%. The maximum drop to motor terminals shall 20%. If solid state control devices are used and the devices cannot accept 15% voltage drop, then the bus voltage drop shall be limited to 10%. The maximum voltage drop at an LV bus due to motor starting shall be restricted to 10%
c. For motors on captive transformers, the voltage drop at the bus supplying the captive transformer shall not exceed 10%. The voltage at motor terminals shall be at least 10% above the minimum value required to accelerate the load.

## Transient Stability Studies

• In general transient stability studies are not required for plants supplied from the utility grid unless in plant generation is to be operated in parallel with the utility, or as discussed for starting large motors. A transient stability study shall also be performed if a fast bus transfer scheme is to be utilized.
• Plants powered by one or more generators will require transient stability studies to insure that fault can be cleared quickly enough to maintain system stability.

## Re-acceleration Studies

• Reacceleration studies shall be purchased to determine the impact of automatically restarting designated process drive motors after a brief power interruption. Typically this control would permit the motors to restart over some time range. The minimum for the range would be the time required for the internal voltage to decay and the maximum would depend upon process considerations.
• The re-acceleration study is made to determine whether the motors can restarted simultaneously. If not, additional studies shall be made to establish group sizes and required time delay between groups.
• This study is a specialized motor starting study with the motors starting simultaneous, modeled as an equivalent single motor.

## Harmonic Analysis Power System

• Harmonic currents and voltages have undesirable affects on operation of the electrical power system including overheating of equipment and overvoltage failures. Aside from the undesirability from the owners standpoint, the utility generally has strict limits on harmonics since they flow back into the power grid.
• Harmonics are produced by rectifiers and frequency converters. The larger the loads are, the greater problem they create, so special attention must be given to large adjustable frequency drives and electrolytic process equipment.
• The normal practice is to require the supplier of the largest harmonic producing load to perform a harmonic study for the plant including all harmonic producing loads and calculating the affect on all buses.
• This study shall be done in accordance with IEC 61800-2.
• Harmonic filters can be installed to reduce the harmonics on the system. The design and supply of the filters if required are normally included with the harmonic study.
• Harmonic filters are of two types.
• One or more tuned reactor/capacitor filters tuned to just below the harmonics with the highest values. These are used mainly where there harmonic magnitudes are large.
• For small levels of harmonics, such as variable speed drives on 480 V motor control centers, programmable static harmonic filter are available. Placing the VFD at the 480 V level protects the equipment at that level, and reduces the harmonic impact on the step-down transformer.
• Harmonic Analysis study shall form an integral part of the studies when VFD is used with Power factor improvement/VAR compensation.
• Harmonic content calculations shall be performed for the entire distribution system and cancellation units shall be provided when equipment, building or plant exceeds the limits of IEC 61800-3.

## Power Factor Improvement Power System

• Power factor correction is important because low power factors increase voltage drop and sizes of cables, breakers, transformers, etc.; and may violate utility requirements or contracts.
• Early load flow studies can indicate if power factor correction may be needed. As soon as the need for correction is indicated, correction can be added to the study in the form of capacitors or utilization of synchronous motor operating with leading power factor.
• For detailed discussion of the application of capacitors for power factor improvement refer to article.
• As soon as synchronous motors are identified, their effect at both unity and leading power factor should be studied.
• It should be understood that the existence of synchronous motors does not necessarily guarantee that all power factor problems are resolved. The location and the size of the motor(s) will determine where and how much the motor improves the power factor.
• Once the system load has been firmed up, the load flow study will confirm that the desired correction has been obtained and the effect on bus voltages and equipment loading. The computer programs referenced in section above shall be used to run the load flow studies.
• Power factor improvement can be studied by changing the following system parameters:
a. Adding capacitors to the system at different locations
b. Changing an induction motor to synchronous motor
c. Changing the power factor on a synchronous motor
e. Changing the taps of a transformer
f. Changing the impedance of a transformer

## Equipment and Cable Sizing

Electrical equipment and cables shall be sized in accordance with the requirements of IEC 60038. In addition, the following shall be applied when determining equipment ratings and cable sizes. Following definitions to be used in equipment and cable sizing.

Eight Hour Maximum Demand

The eight hour maximum demand of loads is defined as the greatest rootmean-square value of the load during any eight hour period. It is the equivalent thermal aging load.

Fifteen Minute Maximum Demand

The fifteen minute maximum demand of loads is defined as the greatest average load which can occur for a fifteen minute period.

Firm load data is the load data derived from actual equipment performance characteristics and duty cycles.

The adjusted maximum demand based on firm load data is equal to 1.0 times maximum demand.

The load factor is to the ratio of the average load over a designated period of time to the peak load occurring in that period.

Demand Factor

The demand factor is the ratio of the maximum demand of a system, or part of a system, to the total connected load of the system, or part of the system, under consideration.

## Transformer Capacity

• An eight hour maximum demand (continuous plant load) shall be the basis for selection of transformer capacity.
• When synchronous motors with a leading power factor are connected to a bus, the resulting leading kVAR shall be considered when calculating the transformer kVA capacity.
• The initial design load connected to a transformer shall not exceed the following values of temperature rise according to IEC 60076-2 (reference ambient temperature 50 °C):
a. Top oil temperature rise 50K Average
b. Winding temperature rise 55K (for transformers identified as ON .. or OF ..)
• Power transformers shall be specified with 55 °C average winding temperature rise above ambient by resistance and 70 °C hottest-spot winding temperature above ambient at rated kVA.
Liquid-filled transformers installed as individual units supplying a radial type load, shall have self-cooled ratings sufficient to supply the following:                                                  a. In radial and primary selective substations, transformer self-cooled capacity shall be equal to or greater than 1.15 times the adjusted maximum demand
b. Peak demand of one-hour duration or less shall not exceed 110% of the transformer 55 °C self-cooled rating
c. The minimum transformer size for non-essential service shall be 750 kVA for units with a 480 V secondary and 3750 kVA for units with 4160 V and above secondary
d. The minimum transformer size for essential service (MCC) shall be 300 kVA for units with 480 V secondaries
• Secondary-Selective Systems
a. For a secondary selective system, if one transformer is out of service,  the remaining transformer shall have sufficient capacity at the highest temperature rise forced-cooled FA rating to serve the maximum designed load of both the buses with the bus-tie breaker closed.
b. The minimum transformer size shall be 1000 kVA for units with a low voltage secondary and 5000 kVA for units with a medium voltage secondary
• Captive transformers
Captive transformers for motors shall be thermally rated and mechanically braced for three repetitive motor starting duty cycles. kVA and impedance shall be selected for starting the motor and for limiting the voltage dip on the bus to which the transformer primary is connected.
• Transformer impedance shall be in accordance with IEC 60076-8, Power transformers – Application guide, except for the following:
a. To meet voltage drop limitations
b. To realize economics by the use of switchgear with lower interrupting ratings

## Switchgear Rating

• A 15 minute maximum demand shall be the basis for selecting switchgear continuous ratings.
• The main breaker and the main bus of the switchgear shall have a current rating equal to or greater than the highest current rating of the transformer that feeds the switchgear.
• Bus tie circuit breakers in secondary selective and spot network substations shall be interchangeable with the incoming breakers.
• Each feeder breaker shall have a continuous current rating equal to the higher of the 15 minute maximum of the feeder load or 100% of the full load currents plus 25% of largest motor current. Loads shall include any provisions for future loads.
• Circuit breakers used to control a single motor shall have a continuous rating at least equal to 1.25 times the motor full load current.
• Generator breakers shall have a continuous rating at least equal to 1.15 times the maximum continuous generator rating.
• Circuit breaker interrupting rating shall be adequate for the maximum short circuit level.
• Switchgear momentary rating shall be at least adequate for the maximum short circuit level, with estimated motor contribution, which would be expected when the transformer is loaded to its self cooled rated capacity.

## Motor Control Center (MCC) Bus Rating

1. Low Voltage MCCs (480 V ) shall have main bus current rating as per IEC 60059.
2. Medium Voltage MCCs (4160 V) shall have main bus current rating as per IEC 60059.

## Battery and Charger Capacities

• The 125 VDC systems supplies control power to switchgear, Excitation power backup for synchronous motors, MCC protective relays, annunciator, etc. The system is composed of dual, 100% redundant battery chargers and 125 VDC battery bank.
• The batteries are sized to provide power to trip the maximum number of breakers that might trip once, after supplying power to indicating lights, relays, etc. for four hours with both battery chargers off. An example would be a bus differential tripping the main breaker, the tie breaker, and all feeder breakers on one bus.
• Each battery is sized to recharge the fully discharged battery bank in 8 hours.

## Uninterruptable Power Supply Capacities

• The 125 VDC systems supplies control power to switchgear, excitation power backup for synchronous motors, MCC protective relays, annunciator, etc. The system is composed of dual, 100% redundant battery chargers and 125 VDC battery banks.
• The batteries for UPS shall be sized to deliver full rated output for 30 minutes operation in case of a single UPS system and 60 minutes (if there are two batteries each 30 minutes capacity) operation in case of parallel or dual redundant UPS system.
• The battery charger is sized to recharge the batteries in six hours while the UPS is carrying 100% load.

## Cable Sizing

• Cable sizing shall comply with IEC 60364, IEC 60949, IEC 60986. Conductor sizing shall take into account ambient temperature, continuous operating load, non-continuous loads, spared loads, spared loads, future loads, conduit fill, tray fill, tray covers, and other factors that may influence the allowable current rating.
• For all cables other than transformer feeders, the eight hour maximum demand shall be the basis for cable capacity calculation.
• Transformer feeders shall have a capacity not less than the transformer fancooled rating. When a feeder supplies more than one transformer, its rating shall be at least equal to the summation of the fan-cooled ratings of all secondary selective and spot network substations plus the self-cooled rating of all radial substation transformers supplied by the feeder.
• Lighting feeders feeding lighting panels shall have a capacity not less than the maximum demand of the load.
• Lighting and power wire and cable shall be derated under any of the following conditions:                                                                                                                                                                                                                                       a. Outdoor ambient temperature of 50 °C

b. More than three conductors in a raceway or cable
c. More than one cable in an underground duct bank or trench (search in PAKTECHPOINT for more details)
d. More than one cable in a cable tray
e. Cables shall be sized to limit voltage drop

• Motor branch circuit conductors shall be sized in accordance with IEC.
• Cable capacity for tray installation shall comply with the IEC including the effects of ambient temperature and solar radiation.
• Feeders rated above 600 volts shall be sized to withstand short circuit thermal stress without damage to the feeders. The maximum short circuit level of the supply, times a 1.25 safety factor, and the clearing time of the feeder protective device shall be used to determine this condition.
• Power cables in underground conduit banks shall be derated in accordance with the IEC standard in order not to exceed the conductor insulation temperature specified by the cable manufacturer. Cable capacity calculation shall take into account the applicable de-rating factors, such as for ambient temperature, soil thermal resistivity, depth of laying and grouped installation of cables.

a. For sizing of underground cables, use the following criteria:
Earth temperature = 35 °C
Earth thermal resistivity = 120 °C cm/W
Selected backfill thermal resistivity = 120 °C cm/W

• Cable sizing calculations shall include the 20% future cables installed in the top positions of the duct bank or trench. The rating shall be for the worst case location along the route, i.e., exiting the substation, approaching another duct bank, road crossing, etc.
• Medium and high-voltage cables shall be selected to coordinate with the maximum 1 second short circuit rating of the connected equipment.
• Medium-voltage feeders to load-center substations shall be sized for the maximum transformer rating. This size shall include the transformer rating obtainable by forced-air cooling.
• Services, feeders and branch circuits for power and lighting installations other than specified above shall be sized in accordance with the requirements of IEC.

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### 1 Response

1. May 6, 2020

[…] shall be performed for proper design of electrical power systems and equipment in this article Power System and Equipment Design Calculations. a. load data calculation. b. transformer sizing and selection. c. cable derating. d. load flow. e. […]

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