## Power Quality and Generators, Part 8: Basic Calculations for Sizing Generators and the Impacts of Certain Loads

#### Editor's Note

This is the eighth installment in an ongoing series that will cover basic engineering and code issues for standby generators. In a subsequent column, the author will address grounding.

Once the starting kVA (sKVA), starting kW (sKW) and the alternator kW requirements are calculated by hand for generator sizing, these values are fed into sizing software to determine a particular manufacturer's recommended generator sizes. Although many generator simulation software programs are available, knowing the basics of generator sizing calculations will help the system designer understand the impact that certain loads and starting methods have on the ultimate size of the standby generator.

It is common for a system's sKVA - or its sKW and maximum allowable transient voltage drop-to determine the size of the generator. Motors can draw six times the full-load amps during startup. The motor's NEMA code letter, which identifies the starting kVA/hp, is a representation of the starting inrush current. The example below uses a NEMA "F" motor. Based on this letter code, the motor will draw approximately 5.3 kVA/hp. Using the following calculation for a 150 hp motor with 91% efficiency and 0.91 power factor, the motor will draw approximately 5.9 times the full-load current during motor starting:

#### Calculation #1

150 hp x 5.3 kVA/hp = 795 kVA = 956.6 amps @ 480 volt/3 phase (amps during startup)

(150 hp x 0.746 kW/hp) / 0.91 (efficiency) = 123.0 kW (running kW)

123.0 kW / 0.91 (power factor) = 135.1 kVA = 162.5 amps (represent full-load amps)

956.6 amps (during startup) / 162.5 A (full-load amps) = 5.9 (times full-load current)

High-efficiency motors can draw 10 or more times the full-load current. As a comparison, for a motor with a NEMA "K" rating (8.5 kVA/hp), the inrush current would have been significantly higher (9.4 times full-load current). The following calculation uses a 150-hp motor with 91% efficiency and 0.91 power factor:

#### Calculation #2

150 hp x 8.5 kVA/hp = 1,275 kVA = 1,534 amps @ 480 volt/3 phase (amps during startup)

(150 hp x 0.746 kW/hp) / 0.91 (Efficiency) = 123.0 kW (running kW)

123.0 kW / 0.91 (power factor) = 135.1 kVA = 162.5 amps (represent full-load amps)

1,534 amps (amps during starting) / 162.5 amps (full-load amps) = 9.4 (times full-load current)

This illustrates that the starting of motors can dramatically affect the inrush current and associated sKVA and the sKW required and may exceed the maximum sKVA or the sKW of a generator set that would otherwise be large enough to serve the steady state load. This could require an oversized generator set based solely on the motor starting requirements of the electrical system.

#### Examples of running capacity

To clarify this issue, I will use an example with the same load profile but with two different methods of motor starting. These simple examples will include lighting and miscellaneous loads as well as motor starting with an across the line starter in one example and a solid-state starter in another example.

#### Example #1: Motor with an across the line starter

**Motor Load: 150-hp motor, NEMA "F" with a 0.28 starting power factor**

Running power factor of 0.91 and an efficiency of 0.91.

NEMA Code Letter "F" = 5.3 kVA/hp

sKVA = 150 hp x 5.3 kVA/hp = 795 kVA

sKW = 795 kVA x 0.28 (starting power factor) = 222.6 kW

Running kVA = 123.0 kW / 0.91 (power factor) = 135.1 kVA

Running kW = (150 hp x 0.746 kW/hp) / 0.91 (Efficiency) = 123.0 kW

** Lighting Load: 75 kVA at 0.9 power factor **

sKVA = 75 kVA

sKW = 75 kVA x 0.9 power factor = 67.5 kW

Running kVA = 75 kVA

Running kW = 75 kVA x 0.9 power factor = 67.5 kW

**Miscellaneous Load: 50 kVA at 0.9 power factor**

sKVA = 50 kVA

sKW = 50 kVA x 0.9 power factor = 45 kW

Running kVA = 50 kVA

Running kW = 50 kVA x 0.9 power factor = 45 kW

**System Totals:**

sKVA = 795 + 75 + 50 = 920 kVA

sKW = 222.6 + 67.5 + 45 = 335.1 kW

Running kVA = 135.1 + 75 + 50 = 260.1 kW

Running kW = 123 + 67.5 + 45 = 235.5 kW

Alternator kW = 123 + 67.5 + 45 = 235.5 kW

Using one manufacturer's sizing software, the recommended generator set size is 350 kW. This is based on about a 20% transient voltage dip followed by a sustained recovery of 90% of rated voltage during starting. The generator would run at about 67% of capacity (Running kW = 236, Generator Capacity = 350 kW, 236 / 350 = 67.4%).

Large motors that are started with across-the-line starters fed by generators to allow for very low transient voltage drop during starting can require a greatly oversized generator set. In these cases the running capacity of the generator can be significantly lower than the rating of the generator set. It is critical to ensure that the running load represents at least 30% of the rated size of the generator set or wet stacking or carboning can occur.

#### Effectively sizing generators

#### Example #2: Motor will a solid-state starter with bypass contactor:

**Motor Load: 150-hp, NEMA "F" motor with a 0.28 starting power factor**

Running power factor of 0.91 and an efficiency of 0.91.

Soft Start set at a 300% full load ampere current limit. The current limiting range is typically between 150% and 600%. A 300% current limit reduces the starting kVA and starting kW by almost 50%.

sKVA, = (150 hp x 0.746 kW/hp) / 0.91 (efficiency) = 123.0 kW

123.0 kW / 0.91 (power factor) = 135.1 kVA = 162 amps @ 480-volt/
3 phase.

300 % current limit = 162 amps x 3 (3 x FLA) = 487 amps = 405 kVA

sKW = 405 kVA x 0.28 (starting power factor) = 113.4 kW

Running kVA = 123.0 kW / 0.91 (power factor) = 135.1 kVA

Running kW = (150 hp x 0.746 kW/hp) / 0.91 (Efficiency) = 123.0 kW

**Lighting Load:75 kVA at 0.9 power factor**

Starting kVA = 75 kVA

Starting kW = 75 kVA x 0.9 power factor = 67.5 kW

Running kVA = 75 kVA

Running kW = 75 kVA x 0.9 power factor = 67.5 kW

**Miscellaneous Load: 50 kVA at 0.9 power factor**

Starting kVA = 50 kVA

Starting kW = 50 kVA x 0.9 power factor = 45 kW

Running kVA = 50 kVA

Running kW = 50 kVA x 0.9 power factor = 45 kW

**System Totals:**

sKVA = 405+ 75 + 50 = 530 kVA

sKW = 113.4 + 67.5 + 45 = 225.9 kW

Running kVA = 135.1 + 75 + 50 = 260.1 kW

Running kW = 123 + 67.5 + 45 = 235.5 kW

Alternator kW = 123 + 67.5 + 45 = 235.5 kW

Using one manufacturer's sizing software, the recommended generator set size for this example is 275 kW. This is based on about a 20% transient voltage dip followed by a sustained recovery of 90% of rated voltage during starting. The generator would run at about 86% of capacity (Running kW = 236, Generator Capacity = 275 kW, 236 / 275 = 85.8%).

At this threshold, the engineer may want to specify the next larger generator set to allow for some future additional loads. It is clear from this example that reducing the sKW requirements of the motor with the use of current limiting starters can reduce the size of the required generator set.

The solid-state starter will cause voltage distortion across the alternator of the generator. This distortion is caused by the nonlinear way the silicon-controlled rectifiers (SCRs) in the solid-state starter draw current. The generators alternator may have to be oversized to compensate for this voltage distortion.

This issue can be avoided, as in the example above, by specifying a bypass contactor with the sold state starter. The bypass contactor closes after startup and the SCRs are only operating during the starting of the motor. If the solid-state starter does not have a bypass contactor, a rule of thumb is to add again the motor running kW to the running kW of the system. This calculation will estimate the total alternator kW.

See calculations below:

**Alternator kW with a bypass contactor: 235 kW****Alternator kW without a bypass contactor: 235 kW + 123 kW = 358 kW**

If the soft starter does not have a bypass contactor, the engineer must determine if a larger alternator is required. In our example above, the same 275-kW generator can handle either case (with and without a bypass contactor), but a larger alternator is required to handle the additional alternator kW if no bypass contactor is specified.

#### Critical parameters

In our example above, in the across-the-line starter situation, the sKW drove the requirement for the larger generator set. Below is a breakdown of some of the critical parameters for the different starting methods as well as the two generator set sizes noted above.

Three total generator set configurations have been noted below, one for 350 kW and two for 275 kW. The 275-kW generator set has been split into a smaller and a larger alternator. The parameters (sKVA,sKW, and alternator kW) noted under the three generator set configurations are the maximum the generator set can provide. The parameters noted under the form of motor starting are the requirements for the different system examples noted above with their associated form of motor starting configuration.

Several factors should be evaluated prior to determining the type of starting for motors within an electrical distribution system. These factors include, but are not limited to the following:

**Electrical system effects**from not providing some form of reduced voltage starting. How will the large inrush current affect the components in the electrical distribution system?**A cost analysis**of providing alternative forms of starting should be performed. It may be more cost effective to provide a solid state starter, or other form of reduced voltage starter, with a smaller generator set than to provide an across the line starter with a larger generator set.**All applicable utility or jurisdictional requirements**have to be evaluated during the design process of the generator standby system.

#### Reduced-voltage starting regulations

In addition, the system designer must be familiar with local codes and the serving electrical utility requirements. Many electrical utilities specify the largest system voltage drop during motor starting or specify the largest motor size that can be started with an across the line start.

For example, one of our local electrical utilities, Seattle City Light, indicates that "reduced starting current shall be required on all motors exceeding 15 hp nameplate rating, unless otherwise agreed to by the utility." Another serving utility in our area, Puget Sound Energy, indicates, "If the voltage dip exceeds 2%, the transformer size must be increased to reduce the dip to 2%. The customer is responsible for the difference in cost of the larger transformer."

When only the maximum allowable voltage dip is indicated as a requirement, the largest allowed motor without some form of reduced voltage starting will be based on the size and impedance of the serving utility transformer.

Another form of reduced-voltage starting is the variable-frequency drive. VFDs can reduce both sKVA and sKW. They draw load in a nonlinear fashion, similar to the solid-state starter, and will continue to draw loads in a nonlinear manner, as the frequency of the motor can be altered by control devices through the entire operation of the motor. The size of a generator set feeding a system with a VFD may have to be increased or may have to be fitted with an oversized alternator similar to that of a system feeding a soft start without a bypass contactor. The use of 12-pulse IGBTs (Insulated Gate Bipolar Transistor), (PWM) pulse width modulated drives and harmonic filtering can make the VFD more generator-friendly.

In addition, stepping the sequence of the loads within the requirements of the National Electric Code, Section 700 can greatly reduce the sizing of the generator set. Since larger generators are often required because of the peak kW or kVA on the system, stepping the loads long enough for the inrush of motors not to be simultaneous can reduce the ultimate size of the generator set required to feed the critical loads.

#### Articles in This Series

- Part 1: Sizing and Code Issues
- Part 2: The Effects of Harmonics
- Part 3: Complying with the Codes and Controlling Noise
- Part 4: Fuel Configurations for Standby Gensets
- Part 5: Paralleling Generators in Critical Applications
- Part 6: Generator Sizing and UPS
- Part 7: Commissioning, Training and Long-Term O&M Programs
- Part 8: Basic Calculations for Sizing Generators and the Impacts of Certain Loads
- Part 9: Design Criteria for Grounding
- Part 10: Generators and the 2005 NEC