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Electricity is dangerous-plain and simple. The world has become electrified and electricity has almost universally improved the standard of living around the world. However, when we put electricity into our homes, work places, and more, we are taking a risk that the protection system won't fail and that we will remain safe. As your everyday experience should tell you, the safeguards put in place in the United States have massively mitigated the risk of electrical shock. Things like grounding, high-grade insulation, and an ever-improving knowledge of electrical design all make a huge difference ensuring our electrical safety. Even in homes with wiring much older than the design life of 25-30 years, it's not uncommon to see the electrical system still working robustly. Still, there's always the potential that things go wrong. A few missteps and you could be looking at a painful shock when you touch something like a receptacle or a light switch in your home. But what decides whether that shock is life-threatening or just a simple inconvenience? Dalziel's equation, as described in IEEE 80, applies to this situation: Where: I is the current that can safely pass through the body in milliamps (mA) 116 is a conservatively low constant determined by Dalziel in their research t is the time in seconds that the electrical shock is endured The amount of current that can safely pass through the body is nonlinearly related to how long the shock occurs. The form of this equation could have been derived from Ohm's Law. The power lost in a resistor is proportional to the square of the current. If we think of the human body as a big resistance, then this all makes sense. Dalziel's formula says that for a 1 second shock duration, the maximum current that can pass through a person safely is 116 mA. That's only .116 A, a really small current flow. Load calculations assume that a typical household 120V receptacle has about 1.5A flowing through it. Yikes! So how can anything like this be considered remotely safe? Well there are two key pieces of information I have not included in the above assessment: The resistance of the human body is usually modeled as 2000 Ohms. In reality, the human body could have a much higher resistance when skin is dry. 120V across a 2000 Ohm resistance would only produce about 60 mA of current, around half of what is described above. 1 second is an extremely long time for a fault to clear. In areas where a shock is most likely to occur, ground fault circuit interruptors (GFCI) are commonly used to mitigate the risk of a shock. These devices will trip in MUCH less than 1 second at 116 mA. Put those together and we realize that the threat of dying from a shock in your home, with a properly designed electrical system, is not that high. The situation would require numerous failures of design against the code and often some particularly bad luck by the person being shocked. What about at a higher voltage, like the medium voltage distribution lines that bring power to your step-down transformer? Even for a lower MV system, like 7.2kV, the current that could pass through the body touching line-to-line would be 3.6A. Using Dalziel's equation, the fault would need to be cleared in .001 seconds to ensure the person's safety. This level of speed is impractical. Generally, it's not possible to protect somebody from direct contact with an energized medium voltage conductor. But, we can put in safeguards to prevent this contact from taking place and ensure that line-to-ground faults, where current flows through the earth and not directly through a person, remain safe. This is the standard of safety that has been adopted across the world for electrical systems.

The Problem - Consider this hypothetical example: an XHHW-2 circuit is designed for operation at 90°C. The engineer or designer believes they have all the information they need to maximize the usage of this conductor, loading it at that maximum operating temperature. Unfortunately, they've made a mistake and neglected some additional temperature derating that lowers the conductor's ampacity. Now, the installed conductor operates at a steady-state temperature of 95°C, 5°C more than its operating temperature limit. What happens now? Does the cable melt? No. Although this situation is far from ideal, it's not uncommon. Conductors are typically designed for annual peak conditions, not all-time worst-case conditions. If an intense, historically-high heat wave passes through an area, it's sure to wreak some havoc on the electrical system but the result won't be every insulated conductor melting, even if they were previously operating at or near their maximum operating temperature. In reality, the melting temperature of conductor insulation is much higher than the insulation's steady-state temperature limit. The Arrhenius Equation - Nevertheless, the lifespan of cables subjected to these enhanced ambient conditions will be shortened. The reason why comes from chemistry, The Arrhenius Equation: Where: k is the rate constant, a value that describes the rate of change of concentration of a chemical reactant as part of any reaction. The rate constant is inversely proportional to the half-life of a chemical reaction. A is a constant value that must be determined for any reaction E is the activation energy of the reaction in J R is the ideal gas constant in J/K T is the absolute temperature in K Applying this equation in detail requires a lot of knowledge about the cable itself and could only reasonably be obtained from the manufacturer. Fortunately, actual application of this equation is seldom required. It's more important to understand it at a conceptual level. In the Arrhenius Equation, A, E, and R are all constants. The only thing that impacts the rate of the equation is the temperature T. As the temperature increases, the rate constant will also increase. The effect is nonlinear since the rate constant is proportional to e^-T. In other words, a small increase in the operating temperature can lead to a substantial change in the rate constant. Application - How does all of this apply to conductor lifespans? If we neglect damage from mechanical stresses, then conductor insulation will only fail after some period of time due to chemical reactions. The insulation will react with the air, soil, or water around it. This reaction will be driven by the rate constants k for each reaction. Conductor insulation is generally designed to last 20-30 years. This means that a conductor loaded to its operating temperature will last this long in the absence of physical damage. Of course, all kinds of projects have wiring much older than this installed with no problems. The reason conductors can last so long is twofold: Conductors are typically loaded well below their operating temperature. It is common for conductors that are loaded continuously to be operated at no more than 80% of their ampacity. This significant reduction in temperature can drastically improve lifespans because of the nonlinearity in the Arrhenius equation. Effects are cumulative. Even if a conductor operates near or slightly over its operating temperature for a few hours each year, there are likely many more times where the conductors will be operated significantly below its operating temperature. The chemical equations governing decomposition of the insulation are always ongoing, so negative effects from slight overtemperature can theoretically be overcome with colder periods. Conclusion - A bit of chemistry knowledge can go a long way in electrical engineering. Although the Arrhenius equation will rarely be applied in practice, we need to understand it to truly get what "ampacity" means. Conductors don't immediately melt when they exceed their operating temperature, which is why designers don't rely on all-time worst-case temperatures for design. However, predicting the impacts of overtemperature on lifespans can be very challenging and should never be utilized to justify a design.

What are Transients? - Transients describe the behavior of a circuit before it reaches a steady-state condition. This means that some new event takes place like a voltage source being turned on or a breaker being closed in, and, before the currents and voltages in the circuit can stabilize, there will be some short-lived (transient) timeframe where the old circuit parameters are transitioning to the new ones. Transient behavior is caused by inductance and capacitance in circuits. Inductors do not permit the current flowing through them to change instantaneously. An instantaneous change in current (say from 0A to 1A in 0 seconds) would require an infinite amount of power. For the same reason, capacitors do not permit an instantaneous change in the voltage across them. All real-world circuits have inductance and capacitance. Inductance always exists when current flows because of magnetic fields and capacitance always exists when voltages are present because of electric fields. Even for bare conductors, like on an overhead transmission line, there can be considerable amounts of inductance and/or capacitance present. First Order Transients - In many circuits, either capacitance or inductance is dominant and the effect of the other can be neglected. A good example is a resistive load like a heater, fed by a transformer, being switched into service. The transformer is inductive and the heater is resistive. These types of situation are considered first order transients. We can model the circuit's behavior under these conditions with a single resistance R and a single inductance L (or capacitance C, if applicable). The images below show the two different first order transient circuits. An RL Circuit with a DC Voltage Source An RC Circuit with a DC Voltage Source Let's assume both the circuits above are completely de-energized before we turn on the voltage V. For the RL circuit, initially no current will flow. Over time though, the current will build its way up to a steady-state value equal to V/R. For the RC circuit, a reversed situation occurs. Current will flow initially at a magnitude of V/R, but it will taper off over time until no current flows at all. Now, consider turning the same circuits' voltage sources off. For the RL circuit, current will continue to flow through the circuit because of the inductor. Eventually the resistor will burn off all of the stored energy in the inductor and the current will stop. For the RC circuit, the capacitor will act as the new voltage source using its stored energy and begin to discharge a current at a value of Vc/R. In other words, both circuits behave the same when discharging their stored energy. How long do Transients Last? - The time it takes for a circuit to charge or discharge in the circuits above is given by a value known as the time constant 𝜏. 𝜏 is a measure of time that applies to both RL and RC circuits and describes the decay of the transient effect. Within three time constants, the transient effect will be about 95% gone and within 5 time constants, the transient effect is all but absent from the circuit. Time constants can be computed as follows: RL Circuit: 𝜏 = L / R RC Circuit: 𝜏 = R C Where: 𝜏 is the time constant in seconds R is the resistance in Ohms L is the inductance in Henries C is the capacitance in Farads Time constants can be converted to power frequency cycles instead of seconds by multiplying the time constants by the frequency (60 Hertz in the United States). Higher Order Transients - Some circuits have capacitances and inductances that both contribute to the circuit's behavior significantly. This could be described by a situation where a capacitor bank is switched into service near a transformer. The transformer has a large inductance, the capacitor bank has a large capacitance, and both of them have some resistance. Neglecting either value could lead to incorrect results. Below is an image of an RLC circuit, a simplified model of the transformer & capacitor bank example discussed here. A Series RLC Circuit, One of the Simplest Higher-Order Systems Higher order transient behavior is different from first order systems. The characterization of these systems requires us to know how "damped" the system is. Systems that are highly damped will behave like first order systems. Systems that are undamped will have ringing in their transient response. Instead of transitioning from a starting value to an ending value in a steadily increasing or decreasing way, they will oscillate. The series RLC circuit above is a simple model, but is useful for approximating results in many instances. The damping coefficient of this circuit is given by: d = R / 2 √(C / L) Where d is the damping coefficient, a unitless measure of how damped the system is. When d > 1, the system is damped and will not exhibit any oscillations in its transient response. Notice that increasing the resistance and capacitance increases the damping coefficient, making the response more stable. For real systems with many elements, there is no simple formula that can be applied to determine how the system will be damped. We have to perform a detailed time-domain analysis using the full device equations (current-voltage relationships) for inductors, capacitors, and resistors to make a determination. This same analysis is also used to determine the duration of transient effects.

Designing and building a good electrical power system is about more than just making sure that all of the studies turn out okay. A common construction problem that is often overlooked by engineers is working space. Working space refers to the room a qualified person has to maintain and inspect electrical equipment. The required working space varies by voltage level. In the 2020 edition of the NEC, Table 110.26(A)(1) defines the requirements for low voltage equipment and Table 110.34(A) defines the requirements for medium voltage equipment. As voltages increase, additional working space is required. Likewise, if there are other obstacles or electrical equipment nearby, the working space needs to be increased. Between these tables, working space varies from a minimum of 3' to a maximum of 12'. Working space isn't required on side of the equipment that can't access the electrical systems inside. 3' isn't much space. Although it may be code-compliant and it should allow professionals to get into a space to do their work, you may need to increase working space beyond the minimum requirements of the NEC. Project-specific considerations and long-term maintenance needs should be evaluated prior to shrinking down projects for a minimum footprint. There are also requirements for the practicality of the working space. It's not just about the offset distance from the equipment, but also height and width. The NEC requires that the height of the working space be at least 6' or the height of the electrical equipment, whichever is greater. The Code also requires that the width of the working space be the greater of 30" or the electrical equipment width. These kinds of requirements may seem like common sense, but they can easily be overlooked when the person building the project isn't the person putting design plans together.

Introduction - If you take a college ethics class, chances are you'll be learning about philosophers and the abstract ideas. My purpose here is to discuss ethics in a much simpler, more pragmatic way. Many engineering societies, like the IEEE, have a "code of ethics", a set of high-level principles that engineers must follow. Generally, these principles are something like the following: Care for the welfare of society Communicate professional information honestly Only perform work you are knowledgeable enough to complete safely A number of different variations of these points could be included, but I generally view these as the guiding principles. Care for the Welfare of Stakeholders - Engineers need to care about those affected by their work. This first point covers the moral aspects of being an engineer and is easily the most ambiguous. What one person may consider beneficial for society may not at all be something others do. Suppose you are building a large industrial facility near a residential area. The residents are protesting its construction, but the company behind the plant produces a life-saving product in short supply. How do you weigh the interests of the people at large who want the facility against those in the vicinity of the project you are actually building? There's no easy answer, but an engineer that cares for the welfare of society will consider the issue seriously. A total disregard for parties and a focus purely on selfish reasons like monetary incentives does not meet the criterion above. Communicate Professional Information Honestly - Perhaps the most common issue engineers have to deal with is honesty. Engineers of all levels and disciplines possess unique knowledge that many others do not; this makes it easy to lie about design choices and not be called out for it. Non-engineers, and even other engineers of a different discipline, rely on engineers to be honest about their design choices, calculations, and communication with construction. Engineers are often urged to alter designs to reduce costs or improve schedules, but this can never come at the expense of technical compliance. Borrowing a line from my favorite superhero, "with great power comes great responsibility." Only Perform Work You Are Knowledgeable Enough to Complete - Competency is a difficult thing to define. It's easy to say that electrical engineers shouldn't be doing hydrology work since this is a civil engineering function. But what about this scenario?: An electrical engineer who has previously only worked on residential projects is asked to design a high voltage switchyard. The project is still electrical, but is the engineer competent to perform the task? Once again, there's not a clear answer to this question. You, as the engineer, have to know your limits and ensure that projects that push your skillset are only undertaken with appropriate support from other qualified engineers. An engineer should never sign and seal a drawing set if they do not understand the design shown. Conclusion - So how do you ensure that you're working ethically as an engineer? I think it's as simple as taking these criteria and reforming them as questions. Are you considering the welfare of all stakeholders? Who is impacted negatively by the project and who is impacted positively? Is the negative impact too great? Are you communicating honestly? Are you telling the truth? Have you intentionally omitted important information? Do you know how to design this project? Have you done enough research to compensate for any unfamiliar topics? Do you have people you can reach out to if you encounter a problem? If you're asking these question to yourself, you'll know the ethical implications of the choice you are making.

Basics - The danger most people associate with electrical systems is shock: You touch a wire and a metal frame and experience a jolt of electricity. There is another related safety issue that can be just as dangerous, an arc flash. Arc flashes are the light and heat produced by an arcing fault, a short circuit where ionization occurs. Personnel in the presence of an arc flash event can be killed without ever coming into contact with an electrical current due to the arc blast. These two terms are technically separate, but for the remainder of this article we will refer only to "arc flash". A Photograph of an Arc Flash Event (Source: Schneider Electric) NFPA 70E, the Standard for Electrical Safety in the Workplace lists extensive requirements for mitigating the risk of arc flash events. In particular, personnel working on energized electrical equipment must wear proper personal protective equipment (PPE). Working on energized equipment means performing electrical maintenance without disconnecting all possible sources, a dangerous practice that should only be done by highly qualified individuals when absolutely necessary. People working in the proximity of energized equipment may be exposed to arc flashes. Therefore, in addition to risks from dangerous voltages, PPE must be rated to withstand the incident energy, usually in units of cal/cm^2. A Worker in Arc Flash PPE (Source: Honeywell) Once the incident energy becomes large enough, the required PPE to wear may become impractical. In these cases, no energized work should be performed. If energized maintenance is necessary, additional mitigation techniques must be employed, such as arc-resistant equipment and advanced arc-flash detection schemes (more on this below). In addition to understanding the potential incident energy during an arc flash event, we also need to know the arc flash boundary. The arc flash boundary tells us the distance at which we are "safe" during an arc flash event. The incident energy at the arc flash boundary is low enough (1.2 cal/cm^2) that unprotected individuals would only receive second degree burns. Maybe "safe" isn't the right word, but chances of death at this distance are very low. Arc Flash Hazard Analysis - The simplest way to determine the level of PPE necessary is by taking information directly from tables provided in NFPA 70E. This method is referred to as the "PPE Category" method. Using the category method, the PPE required is based on expected fault clearing time, available fault current, and the working distance. The PPE Category method covers a wide range of conditions up to 40 cal/cm^2 incident energy. The more sophisticated approach calculates the incident energy directly. Instead of offering discrete options for PPE, incident energy calculations allow us to determine exactly what level of protection we require. There are a variety of calculation methods to use, the most important of which can be identified in Annex D of NFPA 70E. Three common methods are referenced here: DC Maximum Power Method: Applies only to direct current (DC) circuits 1000V and below Ralph Lee Method: Applies to alternating current (AC) systems across all voltages, Results become especially conservative over 600V IEEE 1584 Method: Applies to 3-Phase AC systems rated 208V to 15kV, Additional requirements on the conductor gap distance and the available fault current are also included IEEE 1584 is often incorporated into software packages that can complete arc flash hazard studies, but we will focus on the Ralph Lee and DC Maximum Power Methods here. The underlying principle of both calculations is an assumption that the available incident energy is equivalent to the maximum transferred electrical energy during a fault. Ralph Lee applies to AC systems while DC Maximum Power applies to DC systems. For the Ralph Lee Method, the relevant equations are as follows: E = 793 F V t / (D^2) B = √( 2.65 Sf t ) Where: E is the incident energy in cal/cm^2 F is the fault current in kA V is the line-to-line system voltage in kV t is the arc duration in seconds D is the distance from the arc source in inches (also known as the working distance) Sf is the bolted fault apparent power rating in MVA B is the arc flash boundary in feet The equations above are simple to apply, but first we need to determine the bolted fault current F and the clearing time t. The bolted fault current is the results of a short circuit study. The fault clearing time is determined by comparing the bolted fault current with the trip curves of the upstream overcurrent protection devices. NFPA 70E provides some recommendations on clearing times, but a detailed analysis in accordance with manufacturer data and actual system settings is necessary to get an accurate assessment. The Key Components in an AC Arc Flash Event The equations for the DC Maximum Power Method are similar to the Ralph Lee Method: E = .000775 F V t / (D^2) B = .00212 √( F V t ) Where variables have the same definitions and units as described for the Ralph Lee Method. Determining the fault current F in a DC system requires a detailed understanding of the source and its limitations (whether the source is a batter bank, solar modules, or something else). Arc Flash Mitigation Techniques - The incident energy from an arc flash is directly proportional to the time it takes to clear the arcing fault. Overcurrent protective devices operating in their instantaneous region may still operate too slowly (especially if there is a time delay for coordination) to clear the arcing fault quickly. The result can be extremely high incident energy levels, perhaps with PPE requirements beyond any reasonable limit. There are several ways that this problem can be mitigated: Utilize a dedicated arc flash detection relay: These devices have sensors for light, temperature, or pressure in addition to typical overcurrent protection. Trip curves can be set based on these inputs, allowing for minimum opening times during an arcing fault. Alter system impedances: Either a reduction or increase in upstream transformer impedance may help. When the upstream impedance is increased, there will be a reduced fault current that flows. Conversely, a decrease in upstream impedance may allow the fault to clear more quickly. Determining if a change in impedance will help requires coordination between trip curves and short circuit currents. Switch to Arc-Resistant Equipment: Equipment like switchgear is sometimes offered in an "arc-resistant" variety. This means that the gear has been tested to a particular ANSI standard that minimizes the risk of arc faults. The specifics of how "arc-resistant" the equipment is should be discussed with the manufacturer.

General - Transformers are one of the most common components of any electrical power system. People see them all the time but don't know what they're looking at. The image below is of larger padmount (mounted on a concrete pad) transformers. These are usually placed outside of larger commercial buildings, industrial areas, and more. Smaller versions of padmount transformers are also common outside of homes in neighborhoods. Padmount Transformers Installed at a Construction Site Another common type of transformer is the pole-mount variety. Pole-mount transformers are commonly seen on wooden poles for distributing electricity in residential areas. Three Single-Phase Polemount Transformers Ratings - Transformers are often represented on electrical one-line diagrams as shown below. The most important ratings and configuration details are provided to show the system architecture: Apparent Power Rating: Typically in kVA or MVA, the amount of apparent power that can be provided at the secondary of the transformer. Since transformers lose apparent power through their impedance and efficiency, the input limits to the transformer are actually higher than the output rating. Together with the input voltage, we can use the apparent power rating of the transformer to determine the nameplate current. Impedance: Transformer are magnetic devices and, as such, are dominated by inductance. This inductive reactance can be modeled as a single impedance for calculation purposes. The impedance of a transformer is typically written as a percentage, referencing the per unit system. Voltage: The voltage ratings describe what voltage goes into the primary and what comes out of the secondary. Winding configuration: Three-phase transformers can be wired in a number of configurations, with the most common types being Wye, Delta, Wye Grounded, and Wye Impedance Grounded. The primary and secondary each have a different winding configuration and the type of winding impacts the design of the system, including fault currents, grounding, and more. The concept of winding configuration doesn't apply to single-phase transformers. Example Transformer with Ratings The Code - Transformers are covered in general by Article 450 of the 2020 National Electrical Code, but you'll find ampacity requirements under Article 215: Feeders. Feeders supplying transformers must be able to carry 100% of the nameplate rating of the transformer. You might be thinking "Why not 125% of the nameplate like with most loads?". That's because a transformer is always upstream of loads and should be sized to already account for continuous loading of downstream devices. If we were to size to 125% of the nameplate of the transformer we would actually be sizing to 156% of the downstream load current (or more, depending on how the load currents were calculated). The requirements for overcurrent protection of transformers are provided in Table 450.3(A) and Table 450.3(B). Transformers may be required to have protection on their primary (where power comes in) and secondary (where power goes out). The voltage level, type of installation, and the transformer's impedance rating all impact how overcurrent protection must be applied. Example: A 480V primary, 208V secondary three-phase transformer with Z=4% impedance and an apparent power rating of 100 kVA is installed in a public location. What size should the feeder conductors be to supply this transformer and what overcurrent protective device trip ratings are required on the primary and secondary if breakers are used? Assume there are no applicable derating factors for ambient temperature or burial depth and the conductors are fed into the transformer through a conduit. Solution: The transformer described in this problem is the same as the one shown in the Ratings section above. Let's start by finding the transformer nameplate current. Since the transformer is three-phase, the equation for the apparent power is: S = √(3) V I Where: S is the apparent power of the transformer V is the line-line voltage rating of the transformer I is the current passing through the transformer This equation can be rearranged to get the current that can safely flow through this transformer: I = S / ( √(3) V) = 100kVA / ( √(3) * 480V ) = 120.3A Transformer feeder conductors are sized to 100% of the nameplate current. Since the conductors are fed via conduit with no other derating factors to the transformer, the applicable ampacity table for consideration is 310.16 of the 2020 National Electrical Code. Since the current is greater than 100A, 75°C terminals are applicable. Per 310.16, a 1 AWG Copper conductor can carry 130A at 75°C, so this is the minimum feeder conductor size. Next, we have to determine the overcurrent protective device trip ratings based on the installation conditions. NEC Table 450.3(B) states that transformers may employ various protective schemes. We will use primary-only protection, and thus require a trip rating of 125% of the nameplate current: 1.25 * 120.3A =150.375A 150.375A isn't a standard size of overcurrent protection, so we can use the next standard size up per NEC 450. This would be a 175A breaker for the primary, with no secondary protection required. This result might seem strange, but keep in mind that the overcurrent device specified above is to protect the transformer, not the feeder circuit. Because our feeder circuit was only sized to have an ampacity of 130A, the feeder circuit will not be adequately protected by the transformer primary protection device. An additional upstream overcurrent protection device at a lower rating would be required to ensure protection on a low voltage system like this.

Ohm's Law is the most important equation in all of electrical engineering. It is simple, used all the time, and underpins the physics of circuits to ensure we are sizing our conductors and equipment correctly. Ohm's Law can be stated as follows: V = I Z Where: V is the voltage across an impedance in Volts I is the current flowing through an impedance in Amperes Z is the value of the complex impedance in Ohms Simple Circuit Showing Ohm's Law Let's break down each of the variables in Ohm's Law with some more detail. Voltage - Voltage describes the electrical potential of a source and is only well-defined between two points. In Ohm's Law, the voltage V is applied across the load impedance Z. Here are some common misconceptions we need to eliminate right now about voltage: Voltage is not defined for a point by itself. It's common in power systems that we say "the voltage of the line" or the "system voltage", but that is always with an understanding that we are measuring between a certain point (say an energized line) and the neutral/ground point referenced to zero Volts. So remember, voltage is always across something. The voltage in Ohm's Law refers to the root-mean-square (rms) voltage of an AC waveform. In other words, think nominal system voltage levels like the 120VAC in your house. In reality, the AC voltage waveform is varying all the time and the peak value will actually exceed the nominal number at times. Current - Current describes the movement of electrons through some point in space. In Ohm's law, the current I flows because a voltage V is present across the impedance. Just like AC voltages, AC currents are varying all the time and will actually have peak values that exceed nominal rms values. Current determines the heat produced in a circuit, and is the basis for ampacity limitations described in many of the other articles on Breaker & Fuse. Impedance - Impedance is just what its name says: it is an impediment to the flow of current when a voltage is applied. As you can see from Ohm's Law, when the voltage goes up the current flowing through an impedance will also go up. Impedance is a complex number consisting of a real part, resistance, and an imaginary part, reactance. Z = R + j X Where: Z is the complex impedance in Ohms R is the resistance in Ohms X is the reactance in Ohms j is the imaginary number √(-1) Resistance is due to the fact that materials aren't perfect conductors or insulators. If a voltage, AC or DC, is applied across a material, that material's chemical properties and temperature will lead to a resistance that limits the flow of current. In an ideal conductor, electrons would all move nicely, but in a real conductor there are obstacles in the path that prevent flow. Unfortunately, due to a phenomenon known as the skin effect, the AC resistance of a conductor is higher than the DC resistance. Higher frequencies make the skin effect worse. Reactance is only defined for AC systems. Reactance is an effect created by time-varying fields. Magnetic fields (from electric currents) create inductances, and electric fields (from electric charge) create capacitances. Reactances are dependent upon the configuration of the system. If conductors are spaced differently, systems will have different reactances. Moreover, the materials in the vicinity of a system impact the reactance. You can see this by looking at the reactances for common cable configurations in NEC Chapter 9 Table 9 as an example. Often, electrical engineers are only concerned with magnitudes in a power system and not the particular phase. Under these conditions, we can convert the impedance to its magnitude: | Z | = √( R^2 + X^2 ) Computing resistances and reactances from scratch is difficult to do. For equipment like transformers, this information should be taken from the manufacturer based on their final testing. There are often significant tolerances in values that can lead to deviations from specified numbers. Motors have time-varying impedance, and their behavior is usually identified at certain load conditions such as starting (also known as locked-rotor) and full-load. For conductors, values are easier to compute, but it is still a best practice to take information from the supplier/manufacturer. If this information is not available, then using NEC Chapter 9 Table 9 as a starting point can be very helpful. Actual determination of resistances and reactances requires careful application of Maxwell's equations and simplifications can often lead to considerable error. Analogy - Ohm's Law is often analogized to a hose. You can think of the pressure in the hose as the voltage in the electrical circuit, current as the flow of water, and impedance as the nozzle. There can be pressure in the hose with no flow, and altering the opening of the nozzle will change how much water flows out. An electrical circuit is no different: you can have voltage with no current (an open circuit), and altering the impedance of the load will alter how much current flows to it. Example: What is the magnitude of the current that will flow through a load with a resistance of 1 Ohm and a reactance of 2 Ohms when the applied voltage is 120V? Solution: Start by drawing a picture. The same image from above is copied below with values provided. In order to determine the current flowing through the load, we need to rewrite Ohm's Law into a more useful form: V= I Z becomes I = V / Z Next, since we're only worried about magnitudes, we can neglect the phases of the complex impedance, voltage, and current: | I | = | V | / √( R^2 + X^2 ) Lastly, we just need to plug in our values to get an answer: 120 / √( 1^2 + 2^2 ) = 120 / √( 5 ) = 53.7 A So, for our load of 1+2j Ohms, we can expect a magnitude of 53.7A of current to flow.

Scattered throughout standards like the National Electrical Code, you'll find reference to an entity known as "The Authority Having Jurisdiction". In fact, this same language is common beyond the codes; you'll see references to The Authority Having Jurisdiction (often shortened to AHJ) in project contracts, electrical textbooks and more. The term is ubiquitous and sounds like a comic book villain, but what does it really mean? The Authority Having Jurisdiction is a placeholder term for the person with ultimate authority on the installation. The reason why the Code began to use references to the AHJ is because of the Code's scope. In different cities, counties, and states across the United States of America, electrical installations are subject to different kinds of permitting and approval requirements. The AHJ is simply the person or entity responsible for enforcing the Code and certifying plans for construction and/or installation. This could be an inspector, a qualified government official, or even an engineer of record who stamps the design. Requirements vary, often from city to city. Wherever you are planning on working, it's always important to reach out to the local government at the onset of the project and determine who will be the AHJ. Understanding the expectations of the AHJ is exceptionally important. The AHJ should always be included on design set review, both preliminary and final. It can be easy to get ahead of yourself as the Engineer of Record on a design; However, getting to the Issued for Construction stage and realizing that your project won't be signed off by the governing authority is bad news for everyone involved. You may be tempted to avoid working with the AHJ, especially if you feel confident in your abilities as a designer. Unfortunately, the NEC is subject to interpretation. The Code is notoriously complex and filled with cross-references between sections. No matter how smart you may be, there are bound to be disagreements around both the intent and the language of the NEC.

At its most basic, power is the product of a current and a voltage at any point in time. In other words: Pn = Vn In Where: Pn is the instantaneous real power delivered to a load in Watts In is the instantaneous current flowing through the load in Amperes Vn is the instantaneous voltage across the load in Volts This definition of power is universally true, but it's not that useful for the modern world's power systems. AC power in the United States alternates its voltage and current 60 times per second, so the particular power at any point in time isn't valuable. Instead, we like to know what happens over one cycle of the AC waveform, the average power flow: P = V I cos(θ) Where: P is the average real power delivered to the load V is the magnitude of the root-mean-square (rms) voltage across the load I is the magnitude of the rms current through the load cos(θ) is the power factor, where θ is the phase angle difference between the voltage and the current and cos() is the cosine function The current, voltage, and power in the above equation are all straightforward to apply. When we're talking about the US power system, everything is reported in rms values (e.g. 120V, 208V, and 480V services are all rms values). But what about power factor? Power factor relates back to impedance. Recall that a complex impedance Z can be broken down into its resistance R and reactance X as: Z = R + j X The impedance, just like any other complex number can also be written in terms of a magnitude and a phase using trigonometry. The polar form of Z is: Z = √( R^2 + X^2 ) ∠ atan( X / R) Where ∠ is the angle operator for a complex number and atan() is the inverse tangent function from trigonometry. The angle of the complex number in terms of X/R is actually equivalent to the phase angle difference between the current and the voltage because of Ohm's Law. Thus: Z = √( R^2 + X^2 ) ∠ θ In short, the angle of the impedance is the same as the phase difference between the voltage and the current. The cosine of this angle is known as the power factor. The triangle below summarizes the relationships we've discussed. Only resistive loads can absorb real power. Reactive loads cannot. This is why the power factor is essential for determining how much real power is actually absorbed by a load. Currents and voltages could be huge, but if there's no resistance in the load to absorb the power, then no real work can be done by the load. The Impedance Triangle and Power Factor Angle What you likely realize by now is that real power doesn't tell the full story. If we know the real power a load is absorbing, that just tells us about the resistive component of that load. If we want to understand the reactive component of the load, as well as the total current flowing through the lines to feed that load, we need to define a new quantity. This is the reactive power: Q = V I sin(θ) Where: Q is the reactive power, measured in Volts-Amperes-Reactive (the same units as Watts, but with a distinct name to make sure we understand the difference from real power) sin() is the sine operator from trigonometry V, I, and θ are the same variables from the real power equation above Although reactive loads are not capable of absorbing real power like a resistive load, the idea of reactive power is very helpful for electrical designers. Understanding the reactive power allows us to speak about loads in terms of their power and mechanical work while still realizing that there's more to the story than just resistance. We can combine the real and reactive power, just like resistance and reactance, to define a composite power, the apparent power: S = P + j Q Apparent power is measured in Volt-Amperes. Once again, the unit is technically the same as the Watt or the Volt-Ampere-Reactive, but a different name is given to help distinguish between the related quantities. The apparent power has the same phase relationships as the impedance triangle above. This means that the following relationship hold true: P = S cos(θ) Q = S sin(θ) In words, the power factor can be defined as the ratio of the real power to the apparent power. The definition of power factor makes more sense this way. Apparent power is the product of the current and voltage, a statement on what the power flow in the system looks like. The real power is the actual real power that is being absorbed by the load. The power factor is just the ratio of the real to the apparent. Typical Power Factors - Loads can be categorized into general power factor ranges based on the type of equipment: Heaters will generally have a power factor near 1. Heating is done with resistive elements and therefore has little reactance required. Induction motors running at their full load generally have a power factor of around .8. At no load, induction motors will have a much lower power factor, as magnetic effects dominate and no real work is done. Synchronous motors can adjust their power factor to be unity, leading, or lagging. Devices like reactors and capacitors are purely reactive. They have a power factor of near 0. Transformers generally also have a power factor near 0, but this factor only matters during short circuit conditions, as transformers by themselves are not considered to be loads. The power factor of lights can be all over the place based on the technology used. Example: Consider a voltage of 277V is applied to a single-phase load with an impedance of 1+2j Ohms. What is the reactive power drawn by this load? Solution: Start by drawing a picture: The first thing that we need to determine is the current flowing into the load. We can do this using Ohm's Law: | I |= |V | / | Z | = 277 / √( 1^2 + 2^2) = 123.9A Next, we can compute the reactive power using: Q = V I sin(θ) = V I sin( atan(X / R) ) = 277 * 123.9 * sin( atan(2/1) ) = 30.7 kVAR The total reactive power consumed by the load is 30.7 kiloVAR (kVAR for short).

I once had a professor tell me that grounding was the "black magic" of the electrical world. I thought it was funny until I started hearing similar things over and over again. Grounding is a special subfield, and it is absolutely critical to do it right to ensure that a design will be safe. Grounding is underappreciated. Much of the time, a system doesn't need proper grounding to function under typical operating conditions. This can lead to pressure from non-electrical folks to minimize grounding designs and lower construction costs. It's usually only when something goes wrong that we realize how important a good grounding design is. I think the confusion around grounding comes from the fact that the term itself, "grounding", can refer to a couple of different objectives. NEC Article 250 covers grounding and bonding, in all of their applications. What I believe is the best way to understand grounding is by separating it into 2 key categories: Equipment and System. Equipment Grounding - Equipment grounding is the method by which an electrically continuous path is provided for circuits between their overcurrent protection device and their downstream point of termination. Equipment grounding is largely unrelated to making a physical connection to the earth (soil). Equipment grounding is all about making sure that an overcurrent protection device operates and de-energizes a circuit during a fault from a live, current-carrying conductor to a metallic case, metallic raceway, or piece of equipment. NEC Table 250.122 is used to determine the size of an equipment grounding conductor based on the upstream overcurrent device trip rating. You might be thinking, "Why size off of the overcurrent trip rating and not something else, like the load current?". The reason is that the equipment grounding conductor is used to clear short circuits. When a fault occurs between a live wire and the equipment ground conductor (either directly or through a metallic pathway), the impedance of the circuit is drastically reduced and short circuit current will flow. In most cases, this current will be substantially higher than the operating current and will flow only for a short period of time limited by the overcurrent protection device. The upstream overcurrent protective device determines the withstand requirements of the equipment grounding conductor. Table 250.122 isn't the end of the equipment grounding conductor sizing problem, though. For circuits with conductor sizes that have to be increased due to voltage drop or short circuit withstand requirements, the equipment grounding conductor is required to be upsized as well. The NEC is somewhat vague about these requirements. Moreover, the NEC actually allows metallic raceways to be used as equipment grounding conductors if properly bonded. This approach is generally not advisable since conduit and tray raceways can easily become separated and make the system ungrounded. In any case, the equipment grounding conductor never needs to be larger than the circuit's current-carrying conductors conductors. The bottom prong in an electrical outlet is used for connection to the equipment grounding conductor. Some devices don't make use of this connection and have alternative ground protection means. System Grounding - System grounding is the connection of an electrical system to the actual earth (soil). System grounding is achieved by connecting a neutral point of a single-phase, three-phase, or DC system to a grounding electrode through a grounding electrode conductor. The grounding electrode is a metal system, typically ground rods, ground rings, and structural metals, which comes into direct contact with the soil. The grounding electrode conductors is the electrical pathway from the neutral point to the grounding electrode. The grounding electrode conductor is typically installed at the point of supply. Many times, projects will require grounding electrodes to be designed to meet safe voltages under the event of an electrical fault with a current path through the earth per IEEE 80 and 81. Grounding Electrode Conductors (GEC), the wiring connecting the neutral point to the ground electrode, are sized per NEC 250.66. The largest ungrounded conductor is the determinant of the GEC size, not the overcurrent protective device rating. The method here differs from the requirements of equipment grounding and NEC 250.122. This makes sense; An equipment grounding conductor is designed to ensure circuits are de-energized at the right time, but a GEC is only designed to ensure that there is a sufficiently low impedance connection to the soil. Understand the Difference - System grounding and equipment grounding are separate design activities that go hand-in-hand. Equipment grounding ensures that a circuit is de-energized whenever a dangerous condition is present. Without an equipment grounding conductor, a live conductor, when damaged or loose from its termination, could energize its metal casing and leave an unsafe voltage waiting to harm somebody. System grounding serves different purposes: stabilizing voltages relative to the earth and providing a path for lightning strikes to dissipate. The diagram below is a single-phase circuit with grounding. The green equipment grounding conductor is bonded at the neutral point from the source (secondary of the transformer) and bonded on the other end to the metal case around the load. Only the positive and negative conductors will carry current on a regular basis and are connected internally to the load. The equipment grounding conductor is only used to support the clearing of electrical faults. The brown grounding electrode conductor bonds to neutral point as well, but on the other end it bonds to the grounding electrode (a rod, pipe, or similar). The grounding electrode conductor does not follow the same route as the circuit and does not assist with clearing a fault. Grounding is complicated. However, if you can remember the difference between system grounding and equipment grounding you're a long way on the right path. A Single Phase Load with System and Equipment Grounding

General - The 2020 edition of the National Electrical Code outlines the requirements for raceways, channels for routing conductors and cables, in Chapter 3. General requirements are provided in Article 300 and more specific requirements are provided throughout the remainder of Chapter 3 for various raceways, including conduits, cable trays, messenger wire systems, and more. Raceways get wiring from point A to point B while ensuring safety and functionality in the design. Metal Conduit Routing Conductors Between Pull Locations Conduit is the most common form of raceway. If you go look around your house, outside at power poles, or in many public spaces, you will find some form of conduit being used to route electrical power safely. Some of the most common types of conduit used for construction are Electrical Metallic Tubing (EMT) and Polyvinyl Chloride (PVC). Both conduits can be used in similar applications, which is why you'll see them all over the place. Other conduit types, like Rigid Metal Conduit (RMC), High-Density Polyethylene (HDPE), and several others, are also used but generally in specialty applications where the conduits' particular properties are relevant. Conduit is provided in standard trade sizes generally varying from 1/2" to 6". These trade sizes are just the inside diameter of the conduit being used. Outer Diameters of conduit will vary based on the type used. Thicker conduits are used when additional physical protection is required, as outlined in NEC Article 300. Conduit is usually sold in 10' sticks. There's a good chance your local home repair store will have 10' sticks of more basic conduit types available. Diagram of Conduit Diameter as the Trade Size Cable trays (covered in Article 392) and messenger wire systems (covered in Article 396) are two other commonly used types of raceways, although generally for commercial and industrial applications, not residential. Cable tray has special fill requirements that may lead to ampacity modifications depending on the amount of conductors, the spacing between them, and so on. This means that conductors installed in cable tray, even when installed close to one another, may not be subject to the same derating factors of NEC Article 310. Messenger wire systems have a much more limited section than cable tray, but they also see an ampacity shift. Conductors routed in a messenger wire system have a unique ampacity table for low voltage applications, NEC Table 310.20. In either case, when a conduit isn't totally enclosing conductors, an improved ampacity may be available. This is why systems like cable tray and messenger wires are often used in large, engineered facilities. Conduit Fill - The number of conductors that are installed inside of a conduit is limited by more than the bundling derating factors for ampacity. Additionally, designers need to consider the size of the conductors relative to the size of the conduit. Placing too many conductors inside of a conduit can lead to challenging installation conditions, and, consequently, an increased chance of damaging the conductors. Conduit fill limitations are prescribed by the NEC to prevent these situations from happening. NEC Chapter 9 Table 1 provides the basis for these conduit fill requirements: For 1 conductor/cable, the conduit can be filled to no more than 53% of its cross-sectional area For 2 conductors/cables, the conduit can be filled to no more than 31% of its cross-sectional area For 3 or more conductors/cables, the conduit can be filled to no more than 40% of its cross-sectional area The vast majority of applications utilize either a single cable (think 2 or 3 conductors with a ground in a single assembly) or multiple conductors. For this reason, most people just remember conduit fill as "the 40% rule". Note that when two cables are pulled the allowable conduit fill is actually lower than 40%. NEC Chapter 9 has a lot of additional information regarding conduit fill, including how many low voltage conductors of standard types can be pulled through conduits of standard sizes. Calculations are required for medium voltage installations, as conductor sizes can vary considerably. Conduit Bending - Fill isn't the only problem that we have to consider when designing conduit. Conductors are also limited to safe bending radii. If a cable is bent at a radius which is too tight, the cable itself can be damaged. This could be the insulation, the shield (for medium voltage), the jacket, or all of it. Bending radius requirements are provided in NEC Article 300. The minimum bending radius for shielded cable is 12 times the conductor diameter. Unshielded cable can be installed with a radius of no more than 8 times the conductor diameter. Conduits can usually be purchased with prefabricated elbow connectors that are already bent to a radius suitable for conductors. Between any two pull points, conduit is not permitted to bend more than 360 degrees. This rule is found under each of the various conduit Articles throughout Chapter 3. There is no limit on the number of turns required, so (4) 90 degree turns could be used, (8) 45 degree turns could be used, or any other combination. Jamming - The last recommendation for proper conduit sizing is to minimize the possibility of jamming. Jamming is only a significant concern when pulling exactly three conductors through a conduit, provided the conduit fill requirements above have been met. Jamming is caused by the tendency of three conductors to level out as they're pulled around bends. The jamming ratio, J, is defined as: J = d / D Where: J is the jamming ratio, a unitless metric used to determine when jamming is probable d is the inside diameter of the raceway (the trade size) in inches D is the diameter of a single conductor pulled through the raceway in inches If the jamming ratio, J, is between 2.8 and 3.2, and three conductors are being pulled simultaneously, jamming is more likely to occur. Conduits should be changed in size, where possible, to mitigate the potential for jamming. Example: Determine the appropriate conduit size and bending radius for (3) XHHW-2 500 KCMIL Copper conductors. Solution: Begin by determining the acceptable conduit fill. The area and diameter of XHHW-2 500KCMIL conductors can be found in NEC Chapter 9 Table 5. The area of each conductors is .6894 in^2 and the diameter is .943 in. Next, determine the required conduit area. For 3 or more conductors, the conductors can fill no more than 40% of the conduit's interior cross-sectional area. This means that the conduit must have sufficient area, a, as follows: a = (.6894 in^2 * 3) / .4 = 5.1705 in^2 This area can be converted into an equivalent conduit interior diameter (trade size), d, using circular geometry: d = 2 √( a / π ) = 2 √( 5.1705 / π ) = 2.566 in This means that a conduit with a minimum diameter of 2.566 in is required. The next standard trade size can be found from NEC Table 300.1. 3 in conduit is the next size up and should be used. Depending on the exact dimensions of the conduit, a 2.5 in conduit may be suitable. Where bends occur, conduit must have sufficient radius to protect the conductors from damage during pulling. XHHW-2 conductors are unshielded, so they require a minimum bending radius of at least 8 times the conductor diameter. This equates to 7.544 in for the conduit bending radius. Since three conductors will be pulled through simultaneously, jamming must be verified. The jam ratio, J, can be computed: J = 3 / .943 = 3.181 Since the jamming ratio is less than 3.2 and greater than 2.8, jamming may occur. Upsizing the conduit to 3.5 in, the new jamming ratio is: J = 3.5 / .943 = 3.71 With a 3.5 in conduit, jamming should not occur. For this reason, a 3.5 in conduit is recommended for installation of (3) XHHW-2 500 KCMIL conductors installed at the same time.