Lamp color temperature is rated in Kelvin degrees, and the term is used to describe the “whiteness” of the lamp light. In incandescent lamps, color temperature is related to the physical temperature of the filament.

In fluorescent lamps where no hot filament is involved, color temperature is related to the light as though the fluorescent discharge is operating at a given color temperature. The lower the Kelvin degrees, the “warmer” the color tone. Conversely, the higher the Kelvin degrees, the “cooler” the color tone.

Incandescent lamps provide pleasant color tones, bringing out the warm red flesh tones similar to those of natural light. This is particularly true for the “soft” and “natural” white lamps.

Tungsten filament halogen lamps have a gas filling and an inner coating that reflects heat. This keeps the filament hot with less electricity. Their light output is “whiter.” They are more expensive than the standard incandescent lamp.

Fluorescent lamps are available in a wide range of “coolness” to “warmth.” Warm fluorescent lamps bring out the red tones. Cool fluorescent lamps tend to give a person’s skin a pale appearance.

Fluorescent lamps might be marked daylight D (very cool), cool white CW (cool), white W (moderate), warm white WW (warm). These categories break down further into a deluxe X series (i.e., deluxe warm white—deluxe cool white), specification SP series, and specification deluxe SPX series.

Typical color temperature ratings for lamps are 2800K (incandescent), 3000K (halogen), 4100K (cool white fluorescent), and 5000K (fluorescent that simulates daylight). Note that a halogen lamp
is “whiter” than a typical incandescent lamp.Catalogs from lamp manufacturers provide detailed information about lamp characteristics.

Fluorescent lamps and ballasts are a moving target. In recent years, there have been dramatic improvements in both lamps and electronic ballast efficiency.

First, the now-antiquated T12 fluorescent lamps (40 watts) were replaced by energy-saving T8 fluorescent lamps. These original T8 lamps are becoming a thing of the past. The latest T8 high efficiency, energy saving (25 watts vs. 32 watts) lamps have an expected 50% longer life than the original T8 lamps.

The newer T8 lamps use approximately 40% less energy than the older T12 lamps. At $0.06 per kWh, one manufacturer claims a savings of $27.00 per lamp over the life (30,000 hours) of the lamp. At $0.10 cents per kWh, the savings is said to be $45.00 per lamp over the life of the lamp. Using the newer T8 lamps on new installations and as replacements for existing installations makes the payback time pretty attractive.

One electronic ballast can operate up to four lamps, whereas the older style magnetic ballast could operate only two lamps. For a three- or four-lamp luminaire, one ballast instead of two results in quite a saving. Some electronic ballasts can operate six lamps.

Hard to believe! You now can have reduced power consumption and increased light output using electronic ballasts. Today’s high-efficiency ballasts are available with efficiencies of from 98% to 99%.

The only way you can stay on top of these rapid improvements is to check out the Web sites of the various lamp and ballast manufacturers. Today’s magnetic and electronic ballasts handle most of the fluorescent lamp types sold, including standard and energy-saving preheat, rapid start, slimline, high output, and very high output. Again, check the label on the ballast.


The market for magnetic (core and coil) ballasts is shrinking! The National Appliance Energy Conservation Amendment of 1988, Public Law 100-357 prohibited manufacturers from producing ballasts having a power factor of less than 90%.

Ballasts that meet or exceed the federal standards for energy savings are marked with a letter “E” in a circle. Dimming ballasts and ballasts designed specifically for residential use were exempted.

Today’s electronic ballasts are much lighter in weight and considerably more energy efficient than older style magnetic ballasts (core and coil). Energy saving ballasts might cost more initially, but the payback is in the energy consumption saving over time.

Old-style fluorescent ballasts get very warm and might consume 14 to 16 watts, whereas an electronic ballast might consume 8 to 10 watts. Combined with energy-saving fluorescent lamps that use 32 or 34 watts instead of 40 watts, energy savings are considerable. You are buying light, not heat.

When installing fluorescent luminaires, check the label on the ballast that shows the actual volt amperes that the ballast and lamp will draw in combination. Do not attempt to use lamp wattage only when making load calculations because this could lead to an overloaded branch circuit.

For example, a high-efficiency ballast might draw a total of 42 volt-amperes, whereas an old-style magnetic ballast might draw 102 voltamperes.

The higher the power factor rating of a ballast, the more energy efficient. Look for a power factor rating in the mid to high 90s.

Various line currents, volt-amperes, wattages, and overall power factor for various single-lamp
fluorescent ballasts.

Ballast Line Current Line Voltage Line Volt-Amperes Lamp Wattage Line Power Factor
No. 1   0.35                120                              42                    40                    0.95(95%)
No. 2   0.45                120                              54                    40                    0.74(74%)
No. 3   0.55                120                              66                    40                    0.61(61%)
No. 4   0.85                120                              102                  40                    0.39(39%)
No. 5   0.22                120/277                       26                    30                    0.99(99%)


Be sure to use the proper lamp for a given ballast. Mismatching a lamp and ballast may result in poor starting and poor performance, as well as shortened lamp and/or ballast life.

The manufacturer’s ballast and/or lamp warranty may be null and void. T8 lamps are designed to be used interchangeably on magnetic or electronic rapid-start ballasts or electronic instant-start ballasts. Lamp life is reduced slightly when used with an instant-start ballast.

Operating a ballast at an over-voltage condition will cause the it to run hot and shorten its life. Operating a ballast at an under-voltage situation can result in premature lamp failure and unreliable

Most ballasts today will operate satisfactorily within a range of 15% to 27% of their rated voltage. The higher quality CBM certified ballasts will operate satisfactorily within a range of 610%.

Ballast Sound Rating
Most ballasts will hum, some more than others. Ballasts are sound rated and are marked with letters “A” through “F.” “A” is the quietest, and “F” is the noisiest. Look for an “A” or “B” sound rating for residential applications.

Magnetic ballasts (core and coil) hum when the metal laminations vibrate because of the alternating current reversals. This hum can be magnified by the luminaire itself, and/or the surface the luminaire is mounted on. Electronic ballasts have little, if any, hum.

CAUTION: Do not insert spacers, washers, or shims between a ballast and the luminaire to make the ballast more quiet. This will cause the ballast to run much hotter and could result in shortened ballast life and possible fire hazard.

Instead, replace the noisy ballast with a quiet, sound-rated one. Sometimes checking and tightening the many nuts, bolts, and screws of the luminaire will solve the problem.


Preheat ballasts are connected in a simple series circuit. They are easily identified because they have a “starter.” One type of starter is automatic and looks like a small roll of Lifesavers with two “buttons” on one end.

Another type of starter is a manual “ON–OFF” switch that has a momentary “make” position just beyond the “ON” position. When you push the switch on and hold it there for a few seconds, the lamp filaments glow. When the switch is released, the start contacts open, an arc is initiated within the lamp, and the lamp lights up.

Preheat lamps have two pins on each end. Preheat lamps and ballasts are not used for dimming applications.

Rapid Start.
Probably the most common type used today. Rapid start ballasts/lamps do not require a starter. The lamps start in less than 1 second. For reliable starting, ballast manufacturers recommend that there be a grounded metal surface within ½ in. (12.7 mm) of the lamp and running the full length of the lamp, that the ballast be grounded, and that the supply circuit originates from a grounded system.

T5 rapid start lamps do not require a grounded surface for reliable starting. Rapid start lamps have two pins on each end. Rapid start lamps can be dimmed using a special dimming ballast.

Instant Start.
Instant start lamps do not require a starter. These ballasts provide a high-voltage “kick” to start the lamp instantly. They require special fluorescent lamps that do not require preheating of the lamp filaments.

Because instant start fluorescent lamps are started by brute force, they have a shorter life (as much as 40% less) than rapid start lamps when older style magnetic ballasts are used. With electronic ballasts, satisfactory lamp life can be expected.

Instant start lamps have one pin on each end. Instant start ballasts/lamps cannot be used for dimming applications.

Dimming Ballasts.
Special dimming ballasts and dimmers are needed for controlling the light output of fluorescent lamps. Rapid start lamps are used. Incandescent lamp dimmers cannot be used to control fluorescent lamps. An exception to this is that dimmers marked “Incandescent Only” can be used to dim compact fluorescent lamps.


NEC defines a luminaire as a complete lighting unit consisting of a light source such as lamp or lamps, together with the parts designed to position the light source and connect it to the power supply.*
Luminaire is the international term for “lighting fixture” and is used throughout the NEC.

There are literally thousands of different types of luminaries from which to choose to satisfy certain needs, wants, desires, space requirements, and, last but not least, price considerations. Whether the luminaire is incandescent or fluorescent, the basic categories are surface mounted, recessed mounted, and suspended ceiling mounted.

The Code Requirements
Article 410 sets forth the requirements for installing luminaires. The electrician must “meet Code” with regard to mounting, supporting, grounding, live-parts exposure, insulation clearances, supply
conductor types, maximum lamp wattages, and so forth.

Probably the two biggest contributing factors to fires caused by luminaries are installing lamp wattages that exceed that for which the luminaire has been designed, and burying recessed luminaries under thermal insulation when the luminaire has not been designed for such an installation.

Mountings for basic categories of luminaires.

Fluorescent                Incandescent
• Surface                     • Surface
• Recessed                   • Recessed
• Suspended Ceiling   • Suspended Ceiling

Nationally Recognized Testing Laboratories (NRTL) tests, lists, and labels luminaires that are in conformance with the applicable UL safety standards. Always install luminaires that bear the label from a qualified NRTL.

In addition to the NEC, the UL Electrical Construction Materials Directory (Green Book) and the UL Guide Information for Electrical Equipment (White Book), and manufacturers’ catalogs and literature
are excellent sources of information about luminaires.

NEC 110.3(B) states that Listed or labeled equipment shall be installed and used in accordance with any instructions included in the listing or labeling.* It is important to carefully read the label and any instructions furnished with a luminaire.  Most Code requirements can be met by simply following this information. Here are a few examples of label and instruction information:

• Maximum lamp wattage
• Type of lamp
• For supply connections, use wire rated for at
least 8C
• Type-IC
• Type Non-IC
• Suitable for wet locations
• Thermally protected


No single cable characteristic should be emphasized to the serious detriment of others. A balance of cable characteristics, as well as good installation, design, and construction practices, is necessary to provide a reliable cable system.

Service conditions
a) Cables should be suitable for all environmental conditions that occur in the areas where they are installed.

b) Cable operating temperatures in substations are normally based on 40 °C ambient air or 20 °C ambient earth.

Special considerations should be given to cable installed in areas where ambient temperatures differ from these values.

c) Cables may be direct buried, installed in duct banks, conduits, and trenches below grade, or in cable trays, conduits, and wireways above ground. Cable should be suitable for operation in wet and dry locations.

High-voltage power cables are designed to supply power to substation utilization devices, other substations, or customer systems rated higher than 1000 V.

NOTE — Oil-filled and gas-insulated cables are excluded from this definition.

Low-voltage power cables are designed to supply power to utilization devices of the substation auxiliary systems rated 1000 V or less.

Control cables are applied at relatively low current levels or used for intermittent operation to change the operating status of a utilization device of the substation auxiliary system.

NOTE — leads from current and voltage transformers are considered control cables since in most cases they are used in relay protection circuits. However, when current transformer leads are in a primary voltage area exceeding 600 volts they should be protected as required by the NESC, Rule 150.

As used in this document, instrumentation cables consist of cables for Supervisory Controls and Data Acquisition (SCADA) systems or event recorders, and thermocouple and resistance temperature detector cables.

Instrumentation cables are used for transmitting variable current or voltage signals (analog) or transmitting coded information (digital).


The selection of the cable voltage rating is based on the service conditions of 2.1, the electrical circuit frequency, phasing, and grounding configuration, and the steady-state and transient conductor voltages with respect to ground and other energized conductors.

A voltage rating has been assigned to each standard configuration of shield and insulation material and thickness in NEMA WC 3-1980, NEMA WC 5-1973, NEMA WC 7-1988, NEMA WC 8-1988, and in AEIC CS5-1987, AEIC CS6-1987, and AEIC CS7-1987.

The selected voltage rating must result in a cable insulation system that maintains the energized conductor voltage, without installation breakdown under normal operating conditions.

For high-voltage cables, it is usual practice to select an insulation system that has a voltage rating equal to or greater than the expected continuous phase-to-phase conductor voltage. The NEMA standards provide for a cable voltage rating that is only 95% of the actual continuous voltage.

For solidity grounded systems, it is usual to select the 100 Percent Insulation Level, but the 133 Percent Insulation Level is often selected where additional insulation thickness is desired. The 133 Percent Insulation Level is also applied on systems without automatic ground fault protection.

Distribution substations often utilize cable for the distribution circuits from the substation secondary switch-yard (substation getaways). The insulation system selected for this distribution cable may have a voltage rating that is a class above the minimum NEMA rating for the actual circuit voltage and ground fault protection, because it is believed that the additional insulation will result in a lower probability of insulation failure.

Research conducted by the Electric Power Research Institute has led to cable construction recommendations published in EPRI EL-6271 [B10].11 The EPRI recommendations for cable insulation systems have insulation thickness that are the same as those of the NEMA and AEIC standards.

For power and control cables applied at 600 V and below, some engineers use 1000 V-rated insulation because of past insulation failures caused by inductive voltage spikes from de-energizing electromechanical devices, e.g., relays, spring winding motors.

The improved dielectric strength of today's insulation materials prompted some utilities to return to using 600 V rated insulation for this application. Low voltage power and control cable rated 600 V and 1000 V is currently in use.

The selection of the power cable insulation system also includes consideration of cost and performance under normal and abnormal conditions. Dielectric losses, resistance to flame propagation, and gas generation when burned are the most common performance considerations.


The following site-dependent parameters have been found to have substantial impact on the grid design: maximum grid current IG, fault duration tf, shock duration ts, soil resistivity ρ, surface material resistivity (ρs), and grid geometry.

Several parameters define the geometry of the grid, but the area of the grounding system, the conductor spacing, and the depth of the ground grid have the most impact on the mesh voltage, while parameters such as the conductor diameter and the thickness of the surfacing material have less impact.

Fault duration (tf) and shock duration (ts)
The fault duration and shock duration are normally assumed equal, unless the fault duration is the sum of successive shocks, such as from reclosures. The selection of tf should reflect fast clearing time for transmission substations and slow clearing times for distribution and industrial substations.

The choices tf and ts should result in the most pessimistic combination of fault current decrement factor and allowable body current. Typical values for tf and ts range from 0.25 s to 1.0 s.

Soil resistivity (ρ)
The grid resistance and the voltage gradients within a substation are directly dependent on the soil resistivity. Because in reality soil resistivity will vary horizontally as well as vertically, sufficient data must be gathered for a substation yard.

Because the equations for Em and Es given assume uniform soil resistivity, the equations can employ only a single value for the resistivity.

Resistivity of surface layer (ρs)
A layer of surface material helps in limiting the body current by adding resistance to the equivalent body resistance.

Grid geometry
In general, the limitation on the physical parameters of a ground grid are based on economics and the physical limitations of the installation of the grid. The economic limitation is obvious. It is impractical to install a copper plate grounding system.

Clause 18 describes some of the limitations encountered in the installation of a grid. For example, the digging of the trenches into which the conductor material is laid limits the conductor spacing to approximately 2 m or more.

Typical conductor spacings range from 3 m to 15 m, while typical grid depths range from 0.5 m to 1.5 m. For the typical conductors ranging from 2/0 AWG (67 mm2) to 500 kcmil (253 mm2), the conductor diameter has negligible effect on the mesh voltage.

The area of the grounding system is the single most important geometrical factor in determining the resistance of the grid. The larger the area grounded, the lower the grid resistance and, thus, the lower the GPR.


What Are The Benefits Of Installing Capacitors?

Power capacitors provide several benefits to power systems. Among these include power factor correction, system voltage support, increased system capacity, reduction of power system losses, reactive power support, and power oscillation damping.

Power Factor Correction.
In general, the efficiency of power generation, transmission, and distribution equipment is improved when it is operated near unity power factor. The least expensive way to achieve near unity power factor is with the application of capacitors.

Capacitors provide a static source of leading reactive current and can be installed close to the load. Thus, the maximum efficiency may be realized by reducing the magnetizing (lagging) current requirements throughout the system.

System Voltage Support.
Power systems are predominately inductive in nature and during peak load conditions or during system contingencies there can be a significant voltage drop between the voltage source and the load. Application of capacitors to a power system results in a voltage increase back to the voltage source, and also past the application point of the capacitors in a radial system.

The actual percentage increase of the system voltage is dependent upon the inductive reactance of the system at the point of application of the capacitors. The short-circuit impedance at that point is approximately the same as the inductive reactance; therefore, the 3-phase short-circuit current at that location can be used to determine the approximate voltage rise.

Increased System Capacity.
The application of shunt or series capacitors can affect the power system capacity. Application of shunt capacitors reduces the inductive reactive current on the power system, and thus reduces the system kVA loading. This can have the effect of increasing system to serve additional load.

Series capacitors are typically used to increase the power carrying capability of transmission lines. Series capacitors insert a voltage in series with the transmission line that is opposite in polarity to the voltage drop across the line, which decreases the apparent reactance and increases the power transfer capability of the line.

Power System Loss Reduction.
The installation of capacitors can reduce the current flow in a power system. Since losses are proportional to the square of the current, a reduction in current will lead to reduced system losses.

Reactive Power Support.
Capacitors can help support steady-state stability limits and reactive power requirements at generators.

Power Oscillation Damping.
Controlled series capacitors can provide an active damping for power oscillations that many large power systems experience. They can also provide support after significant disturbances to the power system and allow the system to remain in synchronous operation.


NEC rules for the ends of a wire differ from those for the middle. (Adapted from Practical Electrical Wiring, 20th edition, © Park Publishing, 2008, all rights reserved).

The key to applying these rules, and the new NEC Example D3(a) in Annex D on this topic is to remember that the end of a wire is different from its middle. Special rules apply to calculating wire sizes based on how the terminations are expected to function.

Entirely different rules aim at assuring that wires, over their length, don’t overheat under prevailing loading and conditions of use. These two sets of rules have nothing to do with each other—they are based on entirely different thermodynamic considerations.

Some of the calculations use, purely by coincidence, identical multiplying factors. Sometimes it is the termination requirements that produce the largest wire, and sometimes it is the requirements to prevent conductor overheating.

You can’t tell until you complete all the calculations and then make a comparison. Until you are accustomed to doing these calculations, do them on separate pieces of paper.

Current is always related to heat.
Every conductor has some resistance and as you increase the current, you increase the amount of heat, all other things being equal. In fact, as is covered in Sec. 110 of Div. 1 and elsewhere, you increase the heat by the square of the current.

The ampacity tables in the NEC reflect heating in another way. As the reproduction of NEC Table 310.16 (see Table 18 in Div. 12) shows, the tables tell you how much current you can safely (meaning without overheating the insulation) and continuously draw through a conductor under the prevailing conditions—which is essentially the definition of ampacity in NEC Article 100: The current in amperes that a conductor can carry continuously under the conditions of use without exceeding its temperature rating.

Ampacity tables show how conductors respond to heat.
The ampacity tables (such as Table 18 in Div. 1) do much more than what is described in the previous paragraph. They show, by implication, a current value below which a wire will run at or below a certain temperature limit.

Remember, conductor heating comes from current flowing through metal arranged in a specified geometry (generally, a long flexible cylinder of specified diameter and metallic content). In other words, for the purposes of thinking about how hot a wire is going to be running, you can ignore the different insulation styles.

As a learning tool, let’s make this into a “rule” and then see how the NEC makes use of it: A conductor, regardless of its insulation type, runs at or below the temperature limit indicated in an ampacity column when, after adjustment for the conditions of use, it is carrying equal or less current than the ampacity limit in that column.

For example, a 90 C THHN 10 AWG conductor has an ampacity of 40 amps. Our “rule” tells us that when 10 AWG copper conductors carry 40 amps under normal-use conditions, they will reach a worst-case, steady-state temperature of 90 C just below the insulation.

Meanwhile, the ampacity definition tells us that no matter how long this temperature continues, it won’t damage the wire. That’s not true of the device, however. If a wire on a wiring device gets too hot for too long, it could lead to loss of temper of the metal parts inside, cause instability of nonmetallic parts, and result in unreliable performance of overcurrent devices due to calibration shift.

Termination rules protect devices.
Because of the risk to devices from overheating, manufacturers set temperature limits for the conductors you put on their terminals. Consider that a metal-to-metal connection that is sound in the electrical sense probably conducts heat as efficiently as it conducts current. If you terminate a 90 C conductor on a circuit breaker, and the conductor reaches 90 C (almost the boiling point of water), the inside of the breaker won’t be much below that temperature.

Expecting that breaker to perform reliably with even a 75 C heat source bolted to it is expecting a lot. Testing laboratories take into account the vulnerability of devices to overheating, and there have been listing restrictions for many, many years to prevent use of wires that would cause device overheating. These restrictions now appear in the NEC.

Smaller devices (generally 100 amp and lower, or with termination provisions for 1 AWG or smaller wire) historically weren’t assumed to operate with wires rated over 60 C such as TW. Higherrated equipment assumed 75 C conductors but generally no higher for 600-volt equipment and below. This is still true today for the larger equipment. (Note that medium-voltage equipment, over 600 volts, has larger internal spacings and the usual allowance is for 90 C, but that equipment will not be further considered at this point.)

Today, smaller equipment increasingly has a “60/75 C” rating, which means it will function properly even where the conductors are sized based on the 75 C column of Table 18, Div. 1.


There can be completely different definitions for power quality, depending on one’s frame of reference. For example, a utility may define power quality as reliability and show statistics demonstrating that its system is 99.98 percent reliable.

Criteria established by regulatory agencies are usually in this vein. A manufacturer of load equipment may define power quality as those characteristics of the power supply that enable the equipment to work properly. These characteristics can be very different for different criteria.

Power quality is ultimately a consumer-driven issue, and the end user’s point of reference takes precedence Therefore, the following definition of a power quality problem is used:

"Any power problem manifested in voltage, current, or frequency deviations that results in failure or misoperation of customer equipment."

There are many misunderstandings regarding the causes of power quality problems. The utility’s and
customer’s perspectives are often much different. While both tend to blame about two-thirds of the events on natural phenomena (e.g., lightning), customers, much more frequently than utility personnel, think that the utility is at fault.

When there is a power problem with a piece of equipment, end users may be quick to complain to the utility of an “outage” or “glitch” that has caused the problem. However, the utility records may indicate no abnormal events on the feed to the customer.

We recently investigated a case where the end-use equipment was knocked off line 30 times in 9 months, but there were only five operations on the utility substation breaker. It must be realized that there are many events resulting in end-user problems that never show up in the utility statistics.

One example is capacitor switching, which is quite common and normal on the utility system, but can cause transient overvoltages that disrupt manufacturing machinery.

Another example is a momentary fault elsewhere in the system that causes the voltage to sag briefly at the location of the customer in question. This might cause an adjustable-speed drive or a distributed
generator to trip off, but the utility will have no indication that anything was amiss on the feeder unless it has a power quality monitor installed.

In addition to real power quality problems, there are also perceived power quality problems that may actually be related to hardware, software, or control system malfunctions. Electronic components can degrade over time due to repeated transient voltages and eventually fail due to a relatively low magnitude event.

Thus, it is sometimes difficult to associate a failure with a specific cause. It is becoming more common that designers of control software for microprocessor-based equipment have an incomplete knowledge of how power systems operate and do not anticipate all types of malfunction events.

Thus, a device can misbehave because of a deficiency in the embedded software. This is particularly common with early versions of new computer-controlled load equipment.

One of the main objectives of this site is to educate utilities, end users, and equipment suppliers alike to reduce the frequency of malfunctions caused by software deficiencies.

In response to this growing concern for power quality, electric utilities have programs that help them respond to customer concerns. The philosophy of these programs ranges from reactive, where the utility responds to customer complaints, to proactive, where the utility is involved in educating the customer and promoting services that can help develop solutions to power quality problems.

The regulatory issues facing utilities may play an important role in how their programs are structured. Since power quality problems often involve interactions between the supply system and the customer facility and equipment, regulators should make sure that distribution companies have incentives to work with customers and help customers solve these problems.

The economics involved in solving a power quality problem must also be included in the analysis. It is not always economical to eliminate power quality variations on the supply side.

In many cases, the optimal solution to a problem may involve making a particular piece of sensitive equipment less sensitive to power quality variations. The level of power quality required is that level which will result in proper operation of the equipment at a particular facility.

Power quality, like quality in other goods and services, is difficult to quantify. There is no single accepted definition of quality power. There are standards for voltage and other technical criteria that may be measured, but the ultimate measure of power quality is determined by the performance and productivity of end-user equipment.

If the electric power is inadequate for those needs, then the “quality” is lacking. Perhaps nothing has been more symbolic of a mismatch in the power delivery system and consumer technology than the “blinking clock” phenomenon.

Clock designers created the blinking display of a digital clock to warn of possible incorrect time after loss of power and inadvertently created one of the first power quality monitors. It has made the homeowner aware that there are numerous minor disturbances occurring throughout the power delivery system that may have no ill effects other than to be detected by a clock.

Many appliances now have a built-in clock, so the average household may have about a dozen clocks that must be reset when there is a brief interruption. Older-technology motor-driven clocks would simply lose a few seconds during minor disturbances and then promptly come back into synchronism.


Electric power quality has emerged as a major area of electric power engineering. The predominant reason for this emergence is the increase in sensitivity of end-use equipment. The various aspects of power quality as it impacts utility companies and their customers and includes material on (1) grounding, (2) voltage sags, (3) harmonics, (4) voltage flicker, and (5) long-term monitoring.

While these five topics do not cover all aspects of power quality, they provide the reader with a broad based overview that should serve to increase overall understanding of problems related to power quality.

Proper grounding of equipment is essential for safe and proper operation of sensitive electronic equipment. In times past, it was thought by some that equipment grounding as specified in the U.S. By the National Electric Code was in contrast with methods needed to insure power quality.

Since those early times, significant evidence has emerged to support the position that, in the vast majority of instances, grounding according to the National Electric Code is essential to insure proper and trouble free equipment operation, and also to insure the safety of associated personnel.

Other than poor grounding practices, voltage sags due primarily to system faults are probably the most significant of all power quality problems. Voltage sags due to short circuits are often seen at distances very remote from the fault point, thereby affecting a potentially large number of utility customers.

Coupled with the wide-area impact of a fault event is the fact that there is no effective preventive for all power system faults. End-use equipment will, therefore, be exposed to short periods of reduced voltage which may or may not lead to malfunctions.

Like voltage sags, the concerns associated with flicker are also related to voltage variations. Voltage flicker, however, is tied to the likelihood of a human observer to become annoyed by the variations in the output of a lamp when the supply voltage amplitude is varying.

In most cases, voltage flicker considers (at least approximately) periodic voltage fluctuations with frequencies less than about 30–35 Hz that are small in size. Human perception, rather than equipment malfunction, is the relevant factor when considering voltage flicker.

For many periodic waveform (either voltage or current) variations, the power of classical Fourier series theory can be applied. The terms in the Fourier series are called harmonics; relevant harmonic terms may have frequencies above or below the fundamental power system frequency.

In most cases, non fundamental frequency equipment currents produce voltages in the power delivery system at those same frequencies. This voltage distortion is present in the supply to other end-use equipment and can lead to improper operation of the equipment.

Harmonics, like most other power quality problems, require significant amounts of measured data in order for the problem to be diagnosed accurately. Monitoring may be short- or long-term and may be relatively cheap or very costly and often represents the majority of the work required to develop power
quality solutions.

In summary, the power quality problems associated with grounding, voltage sags, harmonics, and voltage flicker are those most often encountered in practice. It should be recognized that the voltage and current transients associated with common events like lightning strokes and capacitor switching can also negatively impact end-use equipment.


Impedances in parallel with the arc may be either capacitors or resistors, or both, in various combinations. Although such impedances modify the shape of the specified inherent transient recovery voltage, the type and degree of modification in the synthetic test should be the same as in the direct test.

For example, the insertion of a resistor equal to the surge impedance of the line will reduce the line side rate-of-rise to half value. The effect is not as pronounced for a bus fault where a large number of lines are in parallel because their combined surge impedance is much lower than the resistance in parallel with the arc.

Where the shunt impedance is a resistor, particularly if the ohmic value of the resistor is low, the actual peak transient recovery voltage (TRV) in a synthetic test may not attain the value it would in a direct test because of the limited energy available from the voltage source.

Furthermore, the shunt resistor may cause a too rapid decay of the dc voltage following the TRV crest.

In some cases, to meet the TRV requirements of ANSI/IEEE C37.09-1979 [3], it may be possible

1) To adjust the parameters of the voltage circuit to provide the necessary additional energy absorbed by the shunt resistor

2) To switch over to an additional ac voltage source capable of maintaining voltage across the resistor.

An equivalent transient recovery voltage waveform across the terminals of the test circuit breaker can be produced by replacement of resistance at other appropriate places in test circuits.


How power circuit breaker works?

Circuit Breaker Performance During Interruption; Basic Intervals
The Circuit breaker has two basic positions: closed and opened. In the closed position the circuit breaker conducts full current with negligible voltage drop across its contacts. In the open position it conducts negligible current but with full voltage across the contacts.

This defines two main stresses, the current stress and the voltage stress, that are separated in time. However, the main function of the circuit breaker is neither to conduct nor to isolate. It performs its main function in changing from one condition to the other, that is, the switching operation.

If closer attention is paid to the voltage and current stresses during the interrupting test (figure below), three main intervals can be recognized.

1. High-Current Interval
The high-current interval is the time from contact separation to the significant change in arc voltage preceding the interaction and high-voltage intervals.

2. Interaction Interval
The interaction interval is the time from the significant change in arc voltage prior to current zero to the time when the current including the post arc current, if any, ceases to flow through the test breaker.

3. High-Voltage Interval
The high-voltage interval is the time from the moment when the current including the post arc current, if any, ceases to flow through the test breaker to the end of the test.

State of Interrupting Process
The three intervals described in 1 to 3 follow each other immediately, that is, they cover the whole interrupting process without any discontinuities, even though it might be difficult to establish precisely the moment when one interval ends and the other begins. However, this accuracy may not be required.

State of Interrupting Process During Three Basic Intervals
The quantities determining the physics of the interrupting process change considerably during the circuit breaking operation. In fact, the prevailing physical conditions have different importance during the three time intervals.

High-Current Interval
During the high-current interval, short-circuit current is flowing through the circuit breaker with a relatively small voltage drop across the contacts. A large amount of energy is supplied to the arc establishing the state of ionization, temperature, dynamic pressure, etc, important for the switching function.

Interaction Interval
During the interaction interval, the short-circuit current stress changes into high-voltage stress and the breaker performance can significantly influence the currents and voltages in the circuit. As the current decreases to zero, the arc voltage may rise to charge parallel capacitance and distort current passing through the arc.

After the current zero the post arc conductivity may result in additional damping of the transient recovery voltage and thus influence the voltage across the breaker and the energy supplied to the ionized contact gap.

The mutual interaction between the circuit and the circuit breaker immediately before and after current zero (that is, during the interaction interval) is of extreme importance to the switching process.

High-Voltage Interval
During the high-voltage interval, the gap of the breaker is stressed by recovery voltage. The circuit breaker is now a passive element in the circuit.


Theoretically, LV faults can be handled in precisely the same manner as the HV faults. All differences between HV and LV side construction (transformer connections, line conductors, length, pole footing impedance, etc.) will reflect in the calculation of zero- and positive-sequence LV L-G and balanced fault currents.

As opposed to HV systems, which usually carry overhead ground wires, some LV lines, delta or wyeconnected, carry no neutrals. When neutrals are present on LV systems, LV bus fault calculations follow the same method, and LV line faults will be the same as HV line fault calculations.

When neutrals are not present on LV system, both LV bus and line-fault GPR can be calculated using the simplified method. For a LV bus fault, ZL will consist of the parallel combination of impedances-to-remote earth of all HV overhead ground wire-tower ladder networks only.

The rest of the method still applies.

For LV line faults, assuming a radial LV line, a single fault infeed can be assumed if no generation exists on the load side of the line. This assumption is correct for most cases, but it should be pointed out that, for instance, a large induction motor can become a zero-sequence current generator at the instant of the fault, due to the inertia of the rotor and the mechanical load.

If this can be neglected, the worst fault then occurs outside and near the station. The HV bus fault is modified by inserting, in series with Zs, the self-impedance of the faulted phase conductor, and inserting, in series with Za, a faulted pole footing impedance.

The methods described in this subclause should be used for hand calculation and estimation purposes only. For a more complicated network, that is, the network with a high number of ROWs, circuits, transformers, ground sources, and short lines such as could be found between generating and switching stations, hand calculations cannot be used for either exact or approximate solutions; a computer program shall be used.

In such a program, the theoretical approach should include the effect of other forms of grounding, such as rails, pipes, etc.; the effect of the length of lines; the effect of positive-sequence current phase shift in certain transformer windings; etc.


A complex power station may have a large number of rights-of-way (ROW) with multi circuit power lines on each ROW. These circuits may be operated at different voltage levels. A fault current study for an L-G fault at each transformer voltage level should be produced. Each fault current study should be examined as follows:

a) If the vectorial sum of all zero-sequence fault current contributions to the transformer bus fault from all transmission and distribution lines entering the station under study is greater than the sum of all current contributions from all grounded sources at that station (including generators, grounded transformers, shunt capacitors, etc.), then at the voltage level for which the fault current study is presently being examined, the bus fault will usually produce a worse GPR than the line fault.

b) If the reverse is true, that is, the vectorial sum of the line contributions is smaller than the local ground source current sum, the line fault will produce a greater GPR.

This is because the local ground current will return partially, in the case of the line fault, through the station ground impedance, adding to the GPR caused previously by the line current contribution.

In the bus fault case, the current merely circulates through the faulted transformer winding, the station ground bus, and the fault impedance.

Having determined the worst-fault location (bus versus out on the-line), to select that fault current study with the highest fault current is not appropriate.

Variances between grounding networks of lines with the various voltage levels may, for instance, cause the study showing lower zero-sequence fault currents to result in a GPR greater than that caused by the higher currents. Instead, all faults should be investigated for fault locations as determined above.


Basically, three types of faults should be investigated:

a) Line-to-ground faults (L-G). These are predominant in terms of frequency of occurrence.  Zero sequence and positive-sequence currents will be required.

In practice, GPR is a function of zero sequence currents only, but positive-sequence currents are required to determine magnitudes of the individual zero-sequence currents ßowing in each phase of the faulted circuit.

b) Double line-to-ground faults (2L-G). These are statistically less frequent than L-G faults but could produce zero-sequence currents far exceeding those caused by L-G faults.

Theoretically, this is because of different connections of sequence networks during these faults. For an L-G fault, the positive-sequence, negative-sequence, and zero-sequence networks are connected in series and driven by the prefault voltage source; whereas, for a 2L-G fault, positive-sequence impedance is connected in series with the parallel combination of zero-sequence and negative-sequence impedances, with less overall impedance in the path of the fault current.

[For instance, many high MVA autotransformers may be added to power stations. These could have their primary-to-secondary, or primary-to-tertiary, zero-sequence reactance ratios so high that their primary current is small compared with the tertiary (ground) current.

In addition to this, if more such transformers are added to the station, the resulting tertiary currents will be very large due to further paralleling of reactances.]

c) Three-phase faults. These are statistically less frequent than L-G and 2L-G faults. Three-phase faults produce positive sequence currents, and detailed calculations are required to determine magnitudes of the individual zero-sequence currents ßowing in each phase of the faulted circuit.

If X1 and X0 are positive-sequence and zero-sequence reactances, respectively, of the system impedance at the point of fault and X1 is less than X0, the 2L-G fault will result in higher zero sequence fault currents, often twice as high as the L-G fault currents calculated at the same fault location.

The GPR produced by 2LG faults is not normally considered, due to its low probability. For an overview of the frequency of occurrence of different types of faults as a function of voltage levels on which they occur and other parameters.


Exciter power circuit
The exciter power circuit includes all components not electrically isolated from the exciter output. For static exciters, this includes the rectifier and thyristor circuits, transformer windings, line filters, shaft current suppressors, and any auxiliary components connected to either the input or output of the rectifier/thyristor bridge.

For rotating exciters, it includes armature windings, commutators, and brushes. For rotating exciter rated outputs 350 V dc or less, the ac rms test voltage shall be 10 times the rated output voltage of the exciter, but with a minimum of 1500 V.

For static exciter rated outputs 350 V dc or less, the ac rms test voltage shall be the greater of 10 times the rated output voltage of the exciter, but with a minimum of 1500 V, or twice the rated ac rms input voltage of the exciter plus 1000 V.

For rotating exciter rated outputs greater than 350 V dc, the ac rms test voltage shall be 2800 V plus twice the rated output voltage of the exciter. For static exciter rated outputs greater than 350 V dc, the ac rms test voltage shall be the greater of 2800 V plus twice the rated output voltage of the exciter, or twice the rated ac rms input voltage of the exciter plus 1000 V.

The synchronous-machine field winding is not included as it is covered by ANSI C50.10-1990. The exciter rated output voltage (for determination of the test voltage) shall not be less than the voltage
required at the associated generator field terminals when the generator is operated at rated kilovolt amperes, rated power factor, and rated voltage with the generator field winding at

- 75°C for field windings designed to operate at rating with a temperature rise of 60°C or less, or

- 100°C for field windings designed to operate at rating with a temperature rise greater than 60° C.

The exciter rated input voltage shall not be less than the voltage at the exciter input terminals when the generator is operated at rated kilovolt-amperes, rated power factor, and rated voltage with the generator field winding at

- 75°C for field windings designed to operate at rating with a temperature rise of 60°C or less, or

- 100° C for field windings designed to operate at rating with a temperature rise greater than 60° C.

All other circuits (electrically isolated from the exciter power circuit)
For circuits rated above 60 V or above 60 VA and not greater than 600 V, the ac rms test voltage shall be 1000 V plus twice the rated voltage. For circuits rated above 600 V, the ac rms test voltage shall be 2000 V plus 2.25 times the rated voltage.

Circuits rated at 60 V or less and 60 VA or less need not be given a high-potential test.


In areas where the soil resistivity is rather high or the substation space is at a premium, it may not be possible to obtain a low impedance grounding system by spreading the grid electrodes over a large area, as is done in more favorable conditions.

Such a situation is typical of many GIS installations and industrial substations, occupying only a fraction of the land area normally used for conventional equipment. This often makes the control of surface gradients difficult.

Some of the solutions include

a) Connection(s) of remote ground grid(s) and adjacent grounding facilities, a combined system utilizing separate installations in buildings, underground vaults, etc. A predominant use of remote ground electrodes requires careful consideration of transferred potentials, surge arrester locations, and other critical points.

A significant voltage drop may develop between the local and remote grounding facilities, especially for high-frequency surges (lightning).

b) Use of deep-driven ground rods and drilled ground wells.

c) Various additives and soil treatments used in conjunction with ground rods and interconnecting conductors.

d) Use of wire mats. It is feasible to combine both a surface material and fabricated mats made of wire mesh to equalize the gradient field near the surface.

A typical wire mat might consist of copper-clad steel wires of No. 6 AWG, arranged in a 0.6 m × 0.6 m (24 in × 24 in) grid pattern, installed on the earth’s surface and below the surface material, and bonded to the main grounding grid at multiple locations.

e) Where feasible, controlled use of other available means to lower the overall resistance of a ground system, such as connecting static wires and neutrals to the ground. Typical is the use of metallic objects on the site that qualify for and can serve as auxiliary ground electrodes, or as ground ties to other systems. Consequences of such applications, of course, have to be carefully evaluated.

f) Wherever practical, a nearby deposit of low resistivity material of sufficient volume can be used to install an extra (satellite) grid. This satellite grid, when sufficiently connected to the main grid, will lower the overall resistance and, thus, the ground potential rise of the grounding grid.

The nearby low resistivity material may be a clay deposit or it may be a part of some large structure, such as the concrete mass of a hydroelectric dam.


Conceptual analysis of a grid system usually starts with inspection of the substation layout plan, showing all major equipment and structures. To establish the basic ideas and concepts, the following points may serve as guidelines for starting a typical grounding grid design:

a) A continuous conductor loop should surround the perimeter to enclose as much area as practical. This measure helps to avoid high current concentration and, hence, high gradients both in the grid area and near the projecting cable ends. Enclosing more area also reduces the resistance of the grounding grid.

b) Within the loop, conductors are typically laid in parallel lines and, where practical, along the structures or rows of equipment to provide for short ground connections.

c) A typical grid system for a substation may include 4/0 bare copper conductors buried 0.3–0.5 m (12–18 in) below grade, spaced 3–7 m (10–20 ft) apart, in a grid pattern. At cross-connections, the conductors would be securely bonded together.

Ground rods may be at the grid corners and at junction points along the perimeter. Ground rods may also be installed at major equipment, especially near surge arresters. In multilayer or high resistivity soils, it might be useful to use longer rods or rods installed at additional junction points.

d) This grid system would be extended over the entire substation switchyard and often beyond the fence line. Multiple ground leads or larger sized conductors would be used where high concentrations of current may occur, such as at a neutral-to-ground connection of generators, capacitor banks, or transformers.

e) The ratio of the sides of the grid meshes usually is from 1:1 to 1:3, unless a precise (computer-aided) analysis warrants more extreme values. Frequent cross-connections have a relatively small effect on lowering the resistance of a grid.

Their primary role is to assure adequate control of the surface potentials. The cross-connections are also useful in securing multiple paths for the fault current, minimizing the voltage drop in the grid itself, and providing a certain measure of redundancy in the case of a conductor failure.


For dc and 50 Hz or 60 Hz ac currents, the human body can be approximated by a resistance. The current path typically considered is from one hand to both feet, or from one foot to the other one.

The internal resistance of the body is approximately 300 Ω, whereas values of body resistance including skin range from 500 Ω to 3000 Ω, as suggested in Daziel, Geddes and Baker , Gieiges, Kiselev [B94], and Osypka [B118].

The human body resistance is decreased by damage or puncture of the skin at the point of contact. Conducted extensive tests using saltwater to wet hands and feet to determine safe let-go currents, with hands and feet wet.

Values obtained using 60 Hz for men were as follows: the current was 9.0 mA; corresponding voltages were 21.0 V for hand-to-hand and 10.2 V for hand-to-feet.

Hence, the ac resistance for a hand-to-hand contact is equal to 21.0/0.009 or 2330 Ω, and the hand-to feet resistance equals 10.2/0.009 or 1130 Ω, based on this experiment.

Thus, for the purposes of this guide, the following resistances, in series with the body resistance, are assumed as follows:

a) Hand and foot contact resistances are equal to zero.
b) Glove and shoe resistances are equal to zero.

A value of 1000 Ω in Equation (10), which represents the resistance of a human body from hand-to-feet and also from hand-to-hand, or from one foot to the other foot, will be used throughout this guide. RB = 1000 Ω


a. The simple grounding of elements of a communications facility is only one of several measures necessary to achieve a desired level of protection and electrical noise suppression. To provide a low impedance path for

(1) the flow of ac electrical current to/from the equipment and
(2) the achievement of an effective grounding system, various conductors, electrodes, equipment, and other metallic objects must be joined or bonded together.

Each of these bonds should be made so that the mechanical and electrical properties of the path are determined by the connected members and not by the interconnection junction. Further, the joint must maintain its properties over an extended period of time, to prevent progressive degradation of the degree of performance initially established by the interconnection.

Bonding is concerned with those techniques and procedures necessary to achieve a mechanically strong, low-impedance interconnection between metal objects and to prevent the path thus established from subsequent deterioration through corrosion or mechanical looseness.

b. The ability of an electrical shield to drain off induced electrical charges and to carry sufficient out of-phase current to cancel the effects of an interfering field is dependent upon the shielding material and the manner in which it is installed.

Shielding of sensitive electrical circuits is an essential protective measure to obtain reliable operation in a cluttered electromagnetic environment. Solid, mesh, foil, or stranded coverings of lead, aluminum, copper, iron, and other metals are used in communications facilities, equipment, and conductors to obtain shielding.

These shields are not fully effective unless proper bonding and grounding techniques are employed during installation. Shielding effectiveness of an equipment or subassembly enclosure depends upon such considerations as the frequency of the interfering signal, the characteristics of the shielding material, and the number and shapes of irregularities (openings) in the shield.

Interference-causing signals are associated with time-varying, repetitive electromagnetic fields and are directly related to rates of change of currents with time. A current-changing source generates either periodic signals, impulse signals, or a signal that varies randomly with time.

To cause interference, a potentially interfering signal must be transferred from the point of generation to the location of the susceptible device. The transfer of noise may occur over one or several paths. There are several modes of signal transfer (i.e., radiation, conduction, and inductive and capacitive.


What Is Keraunic Level?

Keraunic level is defined as the average annual number of thunderstorm days or hours for a given locality. A daily keraunic level is called a thunderstorm-day and is the average number of days per year on which thunder will be heard during a 24-h period.

By this definition, it makes no difference how many times thunder is heard during a 24-h period. In other words, if thunder is heard on any one day more than one time, the day is still classified as one thunder-day (or thunderstorm day).

The average annual keraunic level for locations in the U.S. can be determined by referring to isokeraunic maps on which lines of equal keraunic level are plotted on a map of the country.

What Is Ground Flash Density?

Ground flash density (GFD) is defined as the average number of strokes per unit area per unit time at a particular location. It is usually assumed that the GFD to earth, a substation, or a transmission or distribution line is roughly proportional to the keraunic level at the locality. If thunderstorm days are to be used as a basis, it is suggested that the following equation be used (Anderson, 1987):

Nk = 0.12Td


Nm = 0.31Td

Nk is the number of flashes to earth per square kilometer per year

Nm is the number of flashes to earth per square mile per year

Td is the average annual keraunic level, thunderstorm days

Lightning Detection Networks
A new technology is now being deployed in Canada and the U.S. that promises to provide more accurate information about ground flash density and lightning stroke characteristics. Mapping of lightning flashes to the earth has been in progress for over a decade in Europe, Africa, Australia, and Asia.

Now a network of direction-finding receiving stations has been installed across Canada and the U.S. By means of triangulation among the stations, and with computer processing of signals, it is possible to pinpoint the location of each lightning discharge.

Hundreds of millions of strokes have been detected and plotted to date. Ground flash density maps have already been prepared from this data, but with the variability in frequency and paths taken by thunderstorms from year to year, it will take a number of years to develop data that is statistically significant. Some electric utilities are, however, taking advantage of this technology to detect the approach of thunderstorms and to plot the location of strikes on their system. This information is very useful for dispatching crews to trouble spots and can result in shorter outages that result from lightning strikes.


Substation design involves more than installing apparatus, protective devices, and equipment. The significant monetary investment and required reliable continuous operation of the facility requires detailed attention to preventing surges (transients) from entering the substation facility.

These surges can be switching surges, lightning surges on connected transmission lines, or direct strokes to the substation facility. The origin and mechanics of these surges, including lightning, are discussed in detail in Chapter 10 of The Electric Power Engineering Handbook (CRC Press, 2001).

This article focuses on the design process for providing effective shielding (that which permits lightning strokes no greater than those of critical amplitude [less design margin] to reach phase conductors [IEEE Std. 998-1996]) against direct lightning stroke in substations.

The Design Problem
The engineer who seeks to design a direct stroke shielding system for a substation or facility must contend with several elusive factors inherent in lightning phenomena, namely:

• The unpredictable, probabilistic nature of lightning
• The lack of data due to the infrequency of lightning strokes in substations
• The complexity and economics involved in analyzing a system in detail

There is no known method of providing 100% shielding short of enclosing the equipment in a solid metallic enclosure. The uncertainty, complexity, and cost of performing a detailed analysis of a shielding system has historically resulted in simple rules of thumb being utilized in the design of lower voltage facilities. Extra high voltage (EHV) facilities, with their critical and more costly equipment components, usually justify a more sophisticated study to establish the risk vs. cost benefit.

Because of the above factors, it is suggested that a four-step approach be utilized in the design of a protection system:

1. Evaluate the importance and value of the facility being protected.

2. Investigate the severity and frequency of thunderstorms in the area of the substation facility and the exposure of the substation.

3. Select an appropriate design method consistent with the above evaluation and then lay out an appropriate system of protection.

4. Evaluate the effectiveness and cost of the resulting design.


Surge arresters may be of the valve or expulsion type. They are rated not only on their normal voltage classification in kV, but also on their crest voltage capability in kV at a standard 1.5 × 40-μs wave (or other specified wave), and their discharge-current capability in amperes or thousands of amperes (kA).

For high-voltage application, surge arresters may consist of a number of unit-value valve arresters connected in series in one overall unit, as shown in below for a 69-kV arrester.

Cross section of a 69-kV Thyrite (valve) surge arrester.

Lightning or surge arrester elements are enclosed in an insulated casing. Under severe operating conditions, or as a result of multiple operations, the pressure generated within the casing may rise to the point where pressure relief ratings are exceeded.

The arrester then may fail, with or without external flashover, exploding and violently expelling fragments of the casing as well as the internal components, causing possible injury to personnel and damage to surrounding structures. The action represents a race between pressures building up within the casing and an arcing or flashover outside the casing.

The ‘length’ of the casing of the arrester limits its ability to vent safely. The use of polymer insulation for the casing permits puncturing to occur, without the fragmentation that may accompany breakdown and failure of porcelain.


What Is A Helmholtz Coil?

A Helmholtz coil, in its usual, basic configuration, consists of two similar concentrated coils of small winding cross section compared to coil radius, arranged on a single axis, at a spacing of one coil radius along their common centerline.

If electric current is passed through the coils, a very uniform magnetic field is produced in the space between them.

If a Helmholtz coil is connected as a sensor to a fluxmeter, then if a bar, plate, or arc magnet is placed in the center with the magnetic axis parallel to the coil axis, and the magnet is then removed (or rotated 180°), the resultant output of the fluxmeter can be shown to be proportional to the magnetic moment of the magnet.

The magnetic moment may be defined either as the product of the magnetic flux through the magnet\ times the pole spacing of the magnet, or as the average axial flux density of the magnet times the magnet volume:

M = φ I2 = Bav Vm (2.62)

where M = magnetic moment
φ = flux through the magnet
Iρ = pole spacing within the magnet
Bav = average flux density in the axial direction, in the magnet
Vm = magnet geometric volume

The combination of a fluxmeter and a Helmholtz coil becomes an accurate, fast, and easy way to determine the strength of a magnet with one measurement.

Although originally intended for use with bar or plate magnets, the method can also be used with arc segments (which are used in some permanent-magnet motor rotors).