One of the most basic calculations for any power system, and arguably the least understood and most misrepresented, is the calculation of available fault current. The effort of calculating fault currents flexes the basics of math and engineering. This article is not going to get into the details of the calculation; instead, we’ll have a high-level discussion to provide a general understanding of how that number is obtained. The mechanics of the calculations may be a good topic for a future article. We’ll also discuss how this relates to the NEC, especially NEC-2011 Section 110.24, Available Fault Current.

**Short Circuit Study – A Basic Power System Tool**

A system short circuit study is just one of many performed on power systems. Studies are performed for new and existing power systems, a few of which are described below:

* Short Circuit: *Determine the magnitude of the prospective currents flowing throughout the power system at various time intervals after a fault occurs. The information is used to select fuses, breakers, and switchgear ratings in addition to setting protective relays.

* Load Flow:* A system planning tool that determines voltage, current, active, and reactive power and power factor for a power system.

* Coordination: *Coordination studies select or verify the clearing characteristics of devices such as fuses, circuit breakers, and relays used in the protection scheme.

* Power System Stability: *The ability of a power system, containing two or more synchronous machines, to continue to operate after a change occurs on the system. This is a measure of its stability.

* Harmonic Analysis:* A study of power system harmonics to avoid control/computer system interferences, heating of rotating machinery and overheating/failure of capacitors. Predicts distortion levels of harmonic producing loads or capacitor banks.

* Motor Starting:* A study to help ensure the starting of large motors and continuous running of motors in the system operate without experiencing problems including

- Failing to accelerate up to running speed
- Stalling from excessive voltage drops
- Under voltage operating during motor starting
- Voltage dips causing objectionable flicker in the lighting system

These studies help achieve the goals that the design engineer sets for the power system. The power system engineer must evaluate initial and future system performance, reliability, safety, and ability to grow with production and/or operating requirements. Studies such as these are critical in the design process as well as throughout the life of the facility.

**Types of Fault Current**

There are a few important parameters that help define the electric power system; available fault current is one of those critical data points used in any and all of the following manners:

* Interrupting ratings*: The overcurrent protective devices must be able to interrupt the maximum available fault current.

* Selective coordination*: Time Current Characteristic (TCC) Curves are usually overlaid with each other to determine selective coordination. The available fault current is an important data point on these curves.

* Arc flash*: IEEE 1584 and NFPA 70E require fault current and clearing time to calculate arc flash values.

* Equipment ratings*: Fault current and time help determine withstand ratings of electrical equipment. The equipment has to be able to safely deliver this faulted current until it is cleared by an overcurrent protective device.

There are four types of faults that can occur in a power system. The engineer will have to consider more than just one fault current calculation to ultimately arrive upon a maximum value at any one point in the power system. The following are types of faults that can occur:

- Three-phase grounded or ungrounded faults
- Phase-to-phase (line to line) ungrounded faults
- Phase-to-phase ground (double line to ground) faults
- Phase-to-ground (single line to ground) faults

One of the first of many assumptions to be made during a fault study is that the above mentioned faults are bolted. This removes the arcing impedance that is normally a part of the circuit and yields a maximum available fault current. The three-phase ungrounded bolted fault is usually mistakenly assumed to be the maximum fault current when in all actuality the single phase-to-ground fault often produces a greater fault current under certain circumstances;

- when associated generators have solidly grounded neutrals or low-impedance neutral impedances
- on wye-grounded side of a delta-wye grounded transformer

In general, the power systems engineer will calculate a maximum and minimum fault current for a given distribution system. The maximum fault current is calculated on the following assumptions:

- all generators are in service (connected to the system and running);
- the fault is a bolted fault (fault impedance is zero);
- the load is a maximum (your on-peak load. Motors which contribute fault current will be connected and add to the total fault value.)

A minimum fault current is also calculated applying the following assumptions:

- The number of generators connected is minimum
- The fault is not a bolted fault (Fault impedance is not zero. A value between 30 and 40 ohms is commonly used.)
- The load is a minimum (off-peak load. Motors which contribute fault current will not be connected.)

Maximum and minimum fault currents will be used in different ways. Maximum fault currents help determine the required interrupting capacities of overcurrent protective devices. Minimum fault currents are used in coordinating operations of overcurrent devices, re-closers and relays.

### The One-line Diagram

One of the first steps a power systems engineer will take is to secure an accurate up-to-date one-line diagram. New and existing construction projects present challenges to the power systems engineer. Let’s first talk about existing facilities. We have all seen one-line diagrams before, but I would say that probably very few of those have been accurate and up-to-date. The first short-circuit study of my career was for an existing industrial facility. After obtaining what was professed to be the latest accurate one-line diagram, my mentor advised a walk down of the facility. I approached that task as anyone who had the latest accurate one-line diagram in his hands would — with very little enthusiasm and feeling as if this task was a waste of time.

First visit: Main switchgear. Uneventful, it was exactly what I expected. The engineer, during a walk down, records breaker ratings and trip unit settings. Manufacturer and model numbers are very important as well. After visiting the main switchgear, it was off to visit all of those big grey boxes that you would expect to find throughout the facility. I spent an abnormal amount of time trying to find a particular MCC which proved quite illusive. After pulling floor plans, I asked questions to ensure I was in the right area. I walked that area of the plant more than once and asked an electrician for help finding a few MCCs highlighted on my drawings. He reviewed the drawings and grinned as he informed me that they had removed that equipment quite a few years ago. “You’re huntin’ a ghost, son” were his exact words.

He showed me various errors on the drawings and my efforts morphed into updating them — at least enough for me to recreate the one-line diagram at my desk. Some equipment was replaced and new equipment was installed. That’s the day I learned that an accurate updated one-line diagram is not only key to a successful short-circuit study but a rare item for some existing plants.

Missing motors and other equipment could put your calculated fault current numbers high or low depending upon the differences between paper and reality. Numbers that are high will make an expensive solution that is more than what is needed to get the job done and numbers that are low could create unsafe applications with equipment that is undersized for the job at hand.

New construction, you would think, would have the accurate up-to-date one-line diagram issue in the bag. Guess again. The challenge here is the lack of accurate information until the “as-builts” are completed. Conductor lengths are estimates and the loads you show may or may not be what actually makes it into the facility. The one-line diagram will be continuously changing as the project is being constructed.

There’s no walk down for a facility that is not there and no name plates to review. The challenge is to specify and purchase equipment based on estimated lengths of conductors and equipment with generic manufacturer data. The one-line diagrams should be updated based on as-built drawings to ensure accuracy. Updating drawings can be a laborious project but one that is very important to ensure systems analysis studies are as accurate as possible. It is one of the last tasks of the project and sometimes one of those that falls off the radar screen. The engineer will be making assumptions and using rules of thumb for many different aspects of the power system but conductor lengths, transformer impedances and other electrical equipment data that can be accurately included in systems studies should be reflected as such. This requires updated and accurate one-line diagrams.

Even with accurate one lines, the power systems engineer will make assumptions in calculating fault currents. Engineering judgment is used to estimate loads and impedances. You’ll learn more of these assumptions as we take the next step in this process, the impedance diagram.

### Impedance Diagram

If you thought putting together an accurate one-line diagram was difficult, you haven’t created an impedance diagram. Once you have an accurate one-line, the engineer of today will enter data in software applications that perform all of the necessary calculations. But it is not as simple as it sounds; the details of impedances for each of the components must be addressed. This step is critical for your calculations. Short circuit studies are based on the following very familiar equations.

V = IR (Eq-1)

I = V/R (Eq-2)

The impedance diagram is the tool that will give you the denominator in equation Eq-2. Electrical components are comprised of a real and reactive component for their impedance. Not too many electrical components are purely resistive. So the R value above, Resistance, is broken down into a real and reactive component usually expressed as Z shown below:

Z = R + JX (Eq-3)

The X in this equation is there due to the capacitive and reactive nature of electrical components. The above equations can be re-written as follows:

V = I (R + jX) (Eq-4)

I = V / (R + jX) (Eq-5)

The impedance diagram is an effort that takes all of the electrical components and replaces them with their equivalent R + JX. A single line equivalent is created with all R+jX’s in place of the electrical components. This sounds much simpler than it is. The challenge is on a component- or equipment-by-equipment basis. Some of the major components that require research include the following:

- Utility
- Conductors / Busway
- Motors (Induction / Synchronous)
- Generators (Induction / Synchronous)
- Reactors
- Transformers

As noted above, even the utility will be represented as impedance. Even if the utility only provides available fault current, the engineer will convert that number into impedance for the calculations. But not all electrical device impedances are included. For example, impedances of breakers and fuses and other overcurrent protective devices are omitted and considered to be negligible. Conductor impedance data is readily available either from IEEE documents or NFPA 70. These numbers are usually given on an Ohms/1000Ft basis and not something that changes for each roll of conductor that you receive.

Transformer impedances on the other hand may not be the same as what you see in manufacturer’s literature when it arrives on-site. The impedance numbers found on the nameplate are calculated for each transformer when it is made. The data found in manufacturers marketing literature are usually minimum values that the engineer uses as assumptions for new construction projects and yield higher fault currents than what will be expected when the actual transformer and impedance data is used. In addition, transformer nameplates will usually only include the %Z and not the X/R ratio that is required to separate the Z into real and reactive components. Large transformers may have that additional test data but smaller transformers typically do not. The engineer often assumes the resistance is negligible and uses the number on the nameplate as X.

Similar issues arise for motors and generators. IEEE documents do provide resources to help estimate X/R ratios and other values for various electrical equipment. The engineer may leverage these resources as required.

The impedance of rotating machines is not a simple value but is rather complex and variable with time. Machines will have different values of impedance that are used in calculations for various reasons. You may recognize the following:

**X”d – Subtransient Reactance:** Used to determine current during the first cycle after a fault occurs. This is usually the smallest reactance yielding the largest contribution of fault current.

**X’d – Transient Reactance:** This impedance is used for calculations around 0.1 seconds. It helps calculate the current after several cycles at 60 Hz.

**Xd – Synchronous Reactance:** The impedance used for calculating currents above from .5 to 2 seconds. These currents determine the current flow after a steady-state condition.

Detailed data may or may not be readily available and assumptions may be needed to represent rotating machines in the system modeling. Again, engineering judgment and IEEE documents help provide those rules of thumb necessary to get you in the ballpark with respect to short circuit numbers. These documents and other similar documents provide industry standard assumptions that help fill in the gaps of information.

In most cases, the assumptions made are conservative in that a higher than actual fault current is a result. In most cases the higher fault current is the worse condition. But this is not always the case as such calculations as arc flash require lower available fault currents to produce longer clearing times which result in higher energy values. Smaller rotating machines will have less available data from the manufacturer as standard. Large motors will have the most detail as more data is necessary for protection schemes they require. These are larger investments for a facility and hence more detail around motor and generator performance is provided to help protect this investment. Again, this data is not something that you will find in marketing or engineering generic literature. This data is specific to the motor that was manufactured.

### Short Circuit Calculation / Closing

Once the impedance diagram is created, most of the hard work has been achieved. The rest of the work is a process of mathematical equations that reduce the impedance diagram into a voltage source and impedance (Thévenin Equivalent) to calculate fault current by the equation above. The important work and most laborious efforts are made when constructing an accurate one-line diagram and its equivalent impedance diagram.

Calculating fault currents is more of an art than it is a science. The values calculated are the best possible numbers available based on nameplate data, engineering assumptions and the use of sophisticated software programs. The use of available fault currents must be done so with an understanding of the number being used and what it represents. Arriving upon a maximum fault current is a journey for the engineer during which time the power system is thoroughly investigated. The result of this effort can be easily misapplied when care is not taken.

As always, keep safety at the top of your list so that you and those that work around you live to see another day.