Voltage Drop Formula


Voltage Drop Formula

The voltage drop formula is V = I × R, where V represents the voltage drop, I represents the current in amperes, and R represents the resistance in ohms. It calculates the amount of voltage lost through a conductor and is essential for designing safe and efficient electrical systems.

 

What is Voltage Drop Formula?

A voltage drop formula can help you manually calculate the voltage drop in cables under full load in branch circuits. It does not matter if you are working with copper or aluminum conductors. To accurately calculate the voltage drop for a given cable size, length, and current, you need to know the resistance of the type of cable you’re using. 

✅ V = I × R for DC circuits

✅ Accounts for impedance in AC circuits

✅ Helps ensure safe, efficient electrical design

Use our voltage drop calculator to quickly determine wire size, conductor efficiency, and line loss for safer, more reliable electrical installations.

 

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To determine voltage drop in an electrical system, engineers and electricians use a standard formula that accounts for conductor resistance, current, and circuit length. The National Electrical Code (NEC) provides guidelines for the maximum voltage drop allowed in various installations to ensure efficiency and safety. For both single-phase and three-phase circuits, excessive voltage drop can lead to poor equipment performance and energy loss. To simplify calculations, a voltage drop calculator can quickly assess whether a circuit meets NEC recommendations and optimize conductor sizing accordingly. You can learn more about how electrical resistance affects circuits in our detailed voltage drop guide, which explains causes, calculations, and solutions for safe, efficient power distribution.

 

DC / single phase calculation

The voltage drop V in volts (V) is equal to the wire current I in amps (A) times 2 times one way wire size length L in feet (ft) times the wire resistance per 1000 feet R in ohms (Ω/kft) divided by 1000:

 

Vdrop (V) = Iwire (A) × Rwire(Ω)

Iwire (A) × (2 × L(ft) × Rwire(Ω/kft) / 1000(ft/kft))

 

The voltage drop V in volts (V) is equal to the wire current I in amps (A) times 2 times one way wire length L in meters (m) times the wire resistance per 1000 meters R in ohms (Ω/km) divided by 1000:

 

Vdrop (V) = Iwire (A) × Rwire(Ω)

Iwire (A) × (2 × L(m) × Rwire (Ω/km) / 1000(m/km))

 

3 phase calculation

The line-to-line voltage drop V in volts (V) is equal to the square root of 3 times the wire current I in amps (A) times one-way wire length L in feet (ft) times the wire resistance per 1000 feet R in ohms (Ω/kft) divided by 1000:

 

Vdrop (V) = √3 × Iwire (A) × Rwire (Ω)

= 1.732 × Iwire (A) × (L(ft) × Rwire (Ω/kft) / 1000(ft/kft))

 

The line-to-line voltage drop V in volts (V) is equal to the square root of 3 times the wire current I in amps (A) times one-way wire length L in meters (m) times the wire resistance per 1000 meters R in ohms (Ω/km) divided by 1000:

 

Vdrop (V) = √3 × Iwire (A) × Rwire (Ω)

= 1.732 × Iwire (A) × (L(m) × Rwire (Ω/km) / 1000(m/km))

 

Wire diameter calculations

The n gauge wire diameter, dn in inches (in), is equal to 0.005in times 92 raised to the power of 36 minus gauge number n, divided by 39:

 

dn (in) = 0.005 in × 92(36-n)/39

 

The n gauge wire diameter dn in millimetres (mm) is equal to 0.127mm times 92 raised to the power of 36 minus gauge number n, divided by 39:

 

dn (mm) = 0.127 mm × 92(36-n)/39

 

Wire cross-sectional area calculations

The n gauge wire's cross-sectional area An in kilo-circular mils (kcmil) is equal to 1000 times the square wire diameter d in inches (in):

 

An (kcmil) = 1000×dn2 = 0.025 in2 × 92(36-n)/19.5

 

The n gauge wire's cross-sectional area An in square inches (in2), is equal to pi divided by 4 times the square wire diameter d in inches (in):

 

An (in2) = (π/4)×dn2 = 0.000019635 in2 × 92(36-n)/19.5

 

The n gauge wire's cross-sectional area, An, in square millimetres (mm2), is equal to pi divided by 4 times the square wire diameter d in millimetres (mm):

 

An (mm2) = (π/4)×dn2 = 0.012668 mm2 × 92(36-n)/19.5

 

Wire resistance calculations

The n gauge wire resistance R in ohms per kilofeet (Ω/kft) is equal to 0.3048×1000000000 times the wire's resistivity ρ in ohm-meters (Ω·m) divided by 25.42 times the cross-sectional area An in square inches (in2):

 

R(Ω/kft) = 0.3048 × 109 × ρ(Ω·m) / (25.42 × An (in2))

 

The n gauge wire resistance R in ohms per kilometre (Ω/km) is equal to 1000000000 times the wire's resistivity ρ in ohm-meters (Ω·m) divided by the cross-sectional area An in square millimetres (mm2):

 

R(Ω/km) = 109 × ρ(Ω·m) / An (mm2)

 

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Voltage Drop Calculator

A voltage drop calculator helps electricians and engineers estimate line loss, wire size, and circuit efficiency. By inputting conductor length, current, and material, it ensures proper electrical design, safe voltage regulation, and compliance with power distribution standards.

 

What is a Voltage Drop Calculator?

A voltage drop calculator (VDC) is crucial for any electrical engineer or designer. It enables them to calculate VD accurately, which is essential for maintaining an efficient and safe electrical system.

✅ Quickly estimates voltage loss in electrical circuits

✅ Helps select the correct wire size for load and distance

✅ Supports NEC code compliance and system efficiency

 

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Voltage drop calculators are used in various applications, including residential, commercial, and industrial settings, and offer several benefits, such as accurate calculations, time savings, cost reduction, and hazard prevention. Additionally, engineers can ensure the electrical system operates efficiently and safely by considering factors such as cable sizing, wire gauge, and the type of conductor used. Want the full math? Visit our voltage drop formula guide for detailed equations and examples.

There are numerous VDCs available on the internet, and one of the best places to find them is on Google Play.


Applications of Voltage Drop Calculators

VDCs are used in various residential, commercial, and industrial applications. For instance, in residential applications, VDCs help determine the appropriate wire size for the electrical service panel, the length of wires, and the type of installation, ensuring that the electrical system operates correctly and safely. Additionally, VD formulas can be used to calculate resistance and reactance in both single-phase and three-phase electrical systems. It is measured in feet over a specified length.

In commercial applications, voltage drop calculators are used to design and maintain electrical systems in buildings such as hospitals, schools, and offices. These buildings require careful design to ensure that they meet the power requirements of the building and are safe for occupants. VDCs play a crucial role in this process by calculating the VD in the circuit and determining the appropriate wire size and other specifications.

In industrial applications, VDCs are used to design and maintain electrical systems in factories and other industrial settings. These systems require careful design to ensure they meet the equipment's power requirements and are safe for workers. VDCs determine the circuit's VD, the appropriate wire size, and other specifications to ensure that the electrical system operates efficiently and safely. For an overview of the general principles of voltage drop across AC and DC systems, read our article.

 

Benefits of Using a VDC

Using a VDC offers several benefits, including:

Accurate Calculations: VDCs use complex algorithms to calculate VD accurately. This ensures that the electrical system operates efficiently and safely.

Saves Time: VDCs save time by automating the process of calculating VD. This allows engineers to focus on other aspects of the design process, such as equipment selection and installation.

Reduces Costs: By accurately calculating VD, engineers can select the appropriate wire size and other specifications, thereby reducing the cost of the electrical system.

Prevents Hazards: Accurate calculation of VD prevents electrical hazards, including fires and shocks. 

 

FREE Voltage Drop Calculator 

 

Cable Sizing and Wire Gauge

One of the most critical factors to consider when designing an electrical system is cable sizing and wire gauge. The conductor's or wire gauge's size is critical in determining the amount of current that can flow through the conductor without causing excessive VD or overheating. American Wire Gauge (AWG) is the standard system used to specify wire sizes, providing a range of conductor sizes based on the wire's cross-sectional area. Additionally, the National Electrical Code (NEC) provides guidelines for ampacity and voltage drop (VD) for various conductor sizes and types of installations.

 

Copper or Aluminum Conductors

The type of conductor used in an electrical system also affects the voltage drop (VD). Copper and aluminum conductors are the most commonly used materials, with copper being preferred due to its lower resistance and higher conductivity. However, aluminum conductors are less expensive and commonly used in larger conductors and power transmission lines.

 

Frequently Asked Questions


How do I calculate voltage drop?

To calculate VD, you can use the VD formula, which is V = IR, where V is the voltage drop, I is the current flowing through the conductor, and R is the resistance of the conductor. By knowing the current, resistance, and length of the conductor, you can calculate the VD and determine whether it falls within acceptable limits.


How do I use it?

To use a VDC, you need to input the current flowing through the conductor, the length of the conductor, and the wire gauge or cable size. The tool then uses complex algorithms to calculate the VD in the circuit accurately. Based on the results, you can determine the appropriate wire size, cable length, and other specifications necessary to maintain an efficient and safe electrical system.


How is voltage drop calculated in a circuit?

VD is calculated in a circuit using Ohm's Law, which states that the VD across a conductor is equal to the product of the current and resistance. By knowing the current, resistance, and length of the conductor, you can calculate the VD and determine whether it falls within acceptable limits.


What factors affect voltage drop in a circuit?

The factors that affect VD in a circuit include the current flowing through the conductor, the length of the conductor, the resistance of the conductor, and the wire gauge or cable size. Other factors, such as the type of conductor and installation, can also affect VD.


Why is it important to calculate voltage drop?

Calculating VD is essential in maintaining an efficient and safe electrical system. VD can impact the performance of electrical equipment and devices, leading to hazards such as fires and electrical shock. By accurately calculating VD, engineers can select the appropriate wire size, cable length, and other necessary specifications to maintain an efficient and safe electrical system.


What are the benefits of using a VDC?

Using a VDC offers several benefits, including accurate calculations, time savings, cost reduction, and hazard prevention. By accurately calculating VD, engineers can select the appropriate wire size and other specifications, thereby reducing the cost of the electrical system. In addition, calculating VD accurately can prevent electrical hazards such as fires and shocks.


Are there any limitations to using a VDC?

While VDCs offer numerous benefits, they also have some limitations. For example, they rely on the accuracy of the input parameters, but may overlook other factors that can affect voltage drop, such as temperature and ambient conditions. Additionally, they may not be suitable for complex electrical systems.


What is the voltage drop per 100 ft?

The VD per 100 ft depends on various factors, including the current flowing through the conductor, the conductor's length, its resistance, and the wire gauge or cable size. Therefore, it is essential to calculate the VD accurately to determine the appropriate wire size and cable length necessary to maintain an efficient and safe electrical system.


What is a rule of thumb for voltage drop?

The rule of thumb for VD is that the VD in a circuit should not exceed 3% for power circuits and 5% for lighting circuits. These values are based on the National Electrical Code (NEC) guidelines, ensuring the electrical system operates efficiently and safely.

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Biot Savart Law Explained

The Biot Savart Law describes how electric current generates magnetic fields, showing the relationship between current, distance, and field intensity. It is a key principle in physics, electromagnetism, and electrical engineering used to calculate magnetic effects in circuits.

 

What is Biot Savart Law?

The Biot Savart Law is a fundamental principle in electromagnetism that quantifies the magnetic field generated by an electric current.

✅ Relates magnetic field strength to current magnitude and distance.

✅ Provides a mathematical basis for calculating magnetic fields in circuits.

✅ Essential for understanding electromagnetism, physics, and engineering design.

 

Biot Savart Law and the study of electromagnetism have always been a fascinating field of science that deals with the interaction between electric and magnetic fields. One of the cornerstones in this domain is this law, named after the French scientists Jean-Baptiste Biot and Félix Savart. This law plays a vital role in understanding the behaviour of magnetic fields produced by electrical currents. The relationship between electricity and magnetism is at the heart of the Biot Savart Law, showing how moving charges generate magnetic effects.

Delving deeper into this fascinating concept, Biot Savart Law describes the magnetic field generated by a tiny current flowing through a conductor. The law states that the magnetic field at a point is directly proportional to the current and inversely proportional to the square of the distance between the point and the current-carrying conductor. Furthermore, the magnetic field's direction is perpendicular to the plane formed by the unit vector and the straight wire carrying the current. When studying current flow, it helps to compare this law with Ampere’s Law, which is often applied to symmetrical conductors and steady-state conditions.


Biot Savart Law Explained

It is a fundamental principle in electromagnetism that describes the magnetic field produced by a steady electric current. It is named after French physicists Jean-Baptiste Biot and Félix Savart, who formulated the law in 1820. It provides a means to calculate the magnetic field at any point in space due to a specific current distribution.

In mathematical terms, the Biot Savart Law can be expressed as:

dB = (μ₀ / 4π) * (Idl × r̂) / r²

Here,

  • dB represents the tiny magnetic field vector produced by an infinitesimal current element (Idl),

  • μ₀ is the permeability of free space (a constant with a value of 4π × 10^(-7) Tm/A),

  • I is the current flowing through the current element,

  • dl is the infinitesimal length vector of the current element,

  • r is the distance between the current element and the point in space where the magnetic field is being calculated,

  • r̂ is the unit vector pointing from the current element to the point of interest.

The Biot Savart Law states that the magnetic field produced by a small segment of a current-carrying conductor is proportional to the current, inversely proportional to the square of the distance from the point of interest, and depends on the angle between the current segment and the line connecting the segment to the point of interest.

To find the total magnetic field at a point in space due to an entire current distribution, you need to integrate the magnetic field contributions from each infinitesimal current element over the entire current-carrying conductor:

B = ∫dB

The Biot Savart Law is particularly useful for calculating the magnetic field in cases with complex current configurations or where symmetry is not apparent. In addition, it is often applied in situations where Ampere's Law would be difficult or impossible to use. Common applications include calculating magnetic fields due to straight wires, loops, and solenoids. A foundation in basic electricity concepts makes it easier to understand how current elements combine to produce magnetic fields.


Maxwell's Equations

One might wonder about the relationship between the Biot Savart Law and Maxwell's Equations, a set of fundamental equations that govern the behaviour of electric and magnetic fields. It can be derived from Maxwell's Equations, specifically Ampere's Law, which establishes a connection between an electric current and the magnetic field it generates.

While the Biot Savart Law and Ampere's Law address magnetic fields, their focus and applicability differ. For example, the Biot Savart Law is more useful for calculating magnetic fields due to current loops or irregular current-carrying conductors. In contrast, Ampere's Law best suits symmetrical geometries and steady-state currents.

The practical applications of the Biot Savart Law are abundant, ranging from designing and analyzing electromagnets and generators to determining the magnetic moment of a current loop, an essential parameter in magnetostatics. The law has also significantly advanced technologies such as magnetic resonance imaging (MRI), particle accelerators, and magnetic storage devices.

The versatility of the Biot Savart Law is exemplified by its ability to calculate magnetic fields of various geometries. From a straight wire or a solenoid to more complex configurations, such as toroidal or saddle-shaped coils, this law is a reliable tool for understanding the behaviour of magnetic fields in various scenarios.

Delving into the connections between different laws, the relationship between the Biot Savart Law and Faraday's Law is quite intriguing. While the Biot Savart Law is concerned with the magnetic field generated by a current, Faraday's Law deals with the electromotive force (EMF) induced in a conductor due to a changing magnetic field. Together, these laws form the basis of electromagnetic induction, which underpins the functioning of electric generators, transformers, and inductors.

The study of electromagnetism would only be complete by touching upon the concept of electric fields. Like magnetic fields, electric fields are fundamental aspects of electromagnetism, originating from electric charges. Coulomb's Law governs the interaction between electric charges, drawing parallels with the Biot Savart Law, which deals with magnetic fields generated by electric currents.

In the realm of vector calculus, the Biot Savart Law uses the cross product and the dot product to define the magnitude and direction of the magnetic field. These mathematical tools enable scientists and engineers to model and analyze the behaviour of magnetic fields in various applications.

One of the key parameters in the Biot Savart Law is the permeability of free space, denoted by the symbol μ₀. This constant defines the ease with which a magnetic field can permeate a vacuum and is crucial in determining the strength and range of the magnetic field generated by a current.

It is an essential concept in the study of electromagnetism. It provides a foundation for understanding magnetic fields generated by electric currents and connects with other fundamental laws, such as Ampere's Law, Faraday's Law, and Coulomb's Law. Moreover, the diverse applications of the Biot Savart Law, ranging from designing electromagnets to analyzing complex magnetic field geometries, showcase its versatility and importance.

As we continue to explore the world of electromagnetism, the Biot Savart Law will remain a crucial tool in our arsenal. Through rigorous research and innovative technologies, scientists and engineers will continue to unlock the mysteries of electric and magnetic fields, ultimately leading to groundbreaking discoveries and advancements that have the potential to transform our world.

From powering our homes with electricity to enabling cutting-edge technologies like MRI machines and particle accelerators, it plays a central role in shaping the science and engineering landscape. As we progress into the future, the Biot Savart law will undoubtedly continue to serve as a beacon of knowledge and understanding in the ever-evolving realm of electromagnetism. For a broader perspective on how energy sources shape our electrical systems, exploring alternative electricity provides useful context.

 

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Types of Electricity - Static and Current

Types of electricity include static electricity and current electricity, which flows as direct current (DC) or alternating current (AC). Electricity can be generated from various sources, including solar, wind, and hydro, but all supply either static or current electricity.

 

What are the Types of Electricity?

There are two types of electricity: Static Electricity and Current Electricity.

Static electricity results from the buildup of electric charges.

✅ Current electricity includes alternating (AC) and direct (DC) flow.

Static Electricity is made by rubbing together two or more objects, creating friction, while Current electricity is the flow of electric charge across an electrical field.

 

Static Electricity

Static electricity is when electrical charges build up on the surface of a material. It is usually caused by rubbing materials together. The result of a build-up of static electricity is that objects may be attracted to each other or may even cause a spark to jump from one to the other. For Example, rub a balloon on a wool and hold it up to the wall.

Before rubbing, like all materials, the balloons and the wool sweater have a neutral charge. This is because they each have an equal number of positively charged subatomic particles (protons) and negatively charged subatomic particles (electrons). When you rub the balloon with the wool sweater, electrons are transferred from the wool to the rubber because of differences in the attraction of the two materials for electrons. The balloon becomes negatively charged because it gains electrons from the wool, and the wool becomes positively charged because it loses electrons.

 

Current Electricity

Current is the rate of flow of electrons. The movement of electrons produces it, and it is measured in amperes. Unlike static electricity, current electricity must flow through a conductor, usually copper wire. Electricity is similar to the flow of water in a river. The river flows from one spot to another, and the speed of the current determines the speed at which it moves. With electricity, current is a measure of the amount of energy transferred over a period of time. That energy is referred to as an electron flow. One of the results of the current is the heating of the conductor. When an electric stove heats up, it's because of the flow of current.

There are various sources of current electricity, including the chemical reactions that occur in a battery. The most common source is the generator. A simple generator produces electricity when a coil of copper turns inside a magnetic field. In a power plant, electromagnets spinning inside many coils of copper wire generate vast quantities of electricity.

There are two main kinds of electric current. Direct (DC) and Alternating (AC). It's easy to remember. Direct current is similar to the energy you obtain from a battery. Alternating current is like the plugs in the wall. The big difference between the two is that DC is a flow of energy, while AC can turn on and off. AC reverses the direction of the electrons.

 

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Electricity Cost Principles Explained

Electricity cost reflects kWh rates, tariffs, demand charges, power factor penalties, and TOU peak/off-peak pricing, driven by load profiles, utility billing, transmission and distribution fees, and efficiency measures in industrial, commercial, and residential systems.

 

What Is Electricity Cost?

Electricity cost is the total price per kWh including energy, demand, and network charges under applicable tariffs.

✅ Includes energy (kWh), demand (kW), and fixed charges

✅ Varies by TOU tariffs, peak/off-peak, and seasons

✅ Affected by power factor, load profile, and efficiency

 

Electricity Cost principles involve looking at how much electricity consumption and we have to understand how it's measured.

At its core, understanding power use starts with grasping what electricity is and how it behaves in circuits.

It is determined at any moment and is measured in watts consumed. For example: if you want to determine the bill energy or bill electricity rate: For a refresher, see what a watt represents to relate device ratings to instantaneous power.

  • A 100-watt light bulb uses 100 watts.
  • A typical desktop computer uses 65 watts.
  • A central air conditioner uses about 3500 watts.

These device ratings illustrate electric load in practical terms as each appliance contributes to total demand.

If you want to know how to rate electricity pricing, you want to know how much energy you're using. When you use 1000 watts for an hour, that's a kilowatt-hour. For example:

  • Ten 100-watt light bulbs on for an hour, is 1 kWh
  • Ten 100-watt light bulbs on for 1/2 an hour, is 0.5 kWh
  • Ten 50-watt light bulbs on for an hour, is 0.5 kWh
  • One 60-watt light bulb on for an hour, is 0.06 kWh (60/1000)
  • Running a 3500-watt air conditioner for an hour is 3.5 kWh.

The average U.S. household used 10,654 kWh a year in 2001, or 888 kWh/mo. (Dept. of Energy) The U.S. as a whole used 3,883 billion kWh in 2003, or 13,868 kwH per person based on a population of 300 million. (Dept. of Energy)

 

Watt-hours

For smaller items we use the term watt-hours instead of kilowatt-hours. For example, we say a 60-watt light bulb uses 60 watt-hours of electricity billed, not 0.060 kWh. If you're unsure, this overview of what a watt-hour means clarifies the relationship between power and time.

Note that the "-hours" part is important. Without it we'd have no idea what period of time we were talking about.

If you ever see a reference without the amount of time specified, it's almost certainly per hour.

If your device lists amps instead of watts, then just multiply the amps times the voltage to get the watts. For example:

2.5 amps x 120 volts = 300 watts

Trivia: On a peak day in 2009, California used 50,743 megawatt-hours of electricity, or 50,743,000,000 watt-hours.

How much does electricity cost?

 

Electricity Cost

It depends on where you live (like Ontario), how much you use, and possibly when you use it. There are also fixed charges that you pay every month no matter how much electricity you use. For example, I pay $6/mo. for the privilege of being a customer of the electric company, no matter how much energy I use. Local infrastructure and electricity supply conditions can also influence pricing tiers.

Check your utility bill for the rates in your area. If it's not on your bill then look it up on the utility's website. National summaries of electricity prices help you compare trends across regions.

The electric company measures how much electricity you use in kilowatt-hours. The abbreviation for killowatt-hour is kWh. Note that on your bill there can be multiple charges per kWh (e.g., one for the "base rate", another for "fuel") and you have to add them all up to get the total cost per kWh. This measurement is recorded by a watt-hour meter that cumulatively tracks energy over time.

Most utility companies charge a higher rate when you use more than a certain amount of energy, and they also charge more during summer months when electric use is higher. As an example, here are the residential rates prices electricity for Austin, Texas (as of 11-03):

First 500 kilowatts5.8¢ per kilowatt hour (kWh)

Additional kilowatts (May-Oct.)10¢ per kilowatt hour

Additonal kilowatts (Nov.-Apr.)8.3¢ per kilowatt hour

These figures include a fuel charge of 2.265¢ per kWh.

The average cost of residential electricity was 9.86¢/kWh in the U.S. in March 2006. The average household used 888 kWh/mo. in 2001 and would pay $87.56 for it based on the March 2006 average rate. (Dept. of Energy)

The cost of electricity varies by region. In 2003 the price ranged from 5.81¢ in Tennessee to 12¢ in California, 14.314¢ in New York, and 16.734¢ in Hawaii. In Summer 2001, electricity was a whopping 20¢/kWh in parts of California.

 

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Harmonic Distortion

Harmonic distortion is the deviation from the ideal electrical waveform caused by nonlinear loads. It impacts power quality, increases heat in equipment, and can lead to system inefficiencies. Monitoring and mitigation are essential in industrial electrical systems.

 

What is Harmonic Distortion?

Harmonic distortion is not a new phenomenon in power systems. Concern over distortion has fluctuated several times throughout the history of AC electric power systems.

✅ Reduces overall power quality and system reliability

✅ Can damage equipment and increase heat generation

✅ Requires monitoring to ensure system efficiency and safety

In the 1930s and 1940s, the primary sources were transformers, with the primary problem being inductive interference with open-wire telephone systems. Early arc lighting caused similar concern due to its harmonic content, just as today’s electronic power converters do.

Today, nonlinear devices like variable frequency drives (VFDs), arc furnaces, computer power supplies, and LED lighting introduce significant harmonic distortion into electrical systems. Nonlinear devices do not draw current in a linear relationship to voltage, which distorts the sinusoidal waveform and introduces harmonic currents. Harmonic distortion is one of the many issues covered in our comprehensive Power Quality resource channel, which explores causes, effects, and solutions.

 

Why It Matters

  • Harmonics degrade power quality

  • Increase energy losses and heat in conductors and transformers

  • Lead to premature failure of motors and sensitive electronics

  • Interfere with communication lines

In contrast, voltage sags and interruptions are nearly universal to every feeder and represent the most numerous and significant power quality deviations. The end-user sector suffers more from harmonic problems than the utility sector. Industrial users with adjustable speed drives, arc furnaces, induction furnaces, and similar equipment are significantly more susceptible to problems caused by harmonic distortion. To understand the relationship between harmonics and apparent energy flow, see our explanation of Apparent Power vs Real Power.

A good assumption for most utilities in the United States is that the sine wave voltage generated in central power stations is very good. In most areas, the voltage found on transmission systems typically has much less than 1% distortion. However, the distortion increases as the load approaches. At some loads, the current waveforms barely resemble a sine wave. Electronic power converters can chop the current into seemingly arbitrary waveforms. Managing nonlinear loads often requires Power Factor Correction to reduce harmonic effects and improve efficiency.

 

Industry Standards

  • IEEE 519: Sets recommended harmonic limits for both voltage and current.

  • IEC 61000-4-7: Defines methods of measuring harmonics and interharmonics.

 

Harmonic Distortion and Nonlinear Devices

Harmonic distortion is caused by nonlinear devices in the power system. A nonlinear device is one in which the current is not proportional to the applied voltage. Figure 1 illustrates this concept using the case of a sinusoidal voltage applied to a simple nonlinear resistor, where the voltage and current vary according to the curve shown. While the applied voltage is perfectly sinusoidal, the resulting current is distorted. Increasing the voltage by a few percent may cause the current to double and exhibit a different waveform. You can calculate your system’s power quality impact using our Apparent Power Calculator for precise performance metrics.

This is the source of most harmonic distortion in a power system. Figure 1 illustrates that any periodic, distorted waveform can be expressed as a sum of sinusoids. When a waveform is ideal from one cycle to the next, it can be represented as a sum of pure sine waves in which the frequency of each sinusoid is an integer multiple of the fundamental frequency of the distorted wave. This multiple is called a harmonic of the fundamental, hence the name of this subject matter. The sum of sinusoids is referred to as a Fourier series, named after the great mathematician who discovered the concept. Nonlinear loads like VFDs and arc furnaces can affect grounding; learn more in our guide to Electrical Grounding.

 


 

Fig. 1. Current distortion caused by nonlinear resistance

 

Voltage and Current Distortion

The term "harmonics" is often used by itself without further qualification. Generally, it could mean one of the following three:

  1. The harmonic voltages are too great (the voltage is too distorted) for the control to properly determine firing angles.

  2. The harmonic currents are too great for the capacity of some devices in the power supply system, such as transformers, and the machine must be operated at a lower than rated power.

  3. The harmonic voltages are too great because the harmonic currents produced by the device are too great for the given system condition.

Clearly, there are separate causes and effects for voltages and currents, as well as some relationship between them. Thus, the term harmonics by itself is inadequate to describe a problem definitively. Nonlinear loads appear to be sources of harmonic current, injecting harmonic currents into the power system. For nearly all analyses, it is sufficient to treat these harmonic-producing loads simply as current sources. There are exceptions to this as described later.

 


 

Fig 2. Harmonic currents flowing through the system impedance result in harmonic voltages at the load.

Voltage distortion is the result of distorted currents passing through the linear, series impedance of the power delivery system, as illustrated in Fig. 2. Although assuming that the source bus is ultimately a pure sinusoid, there is a nonlinear load that draws a distorted current. The harmonic currents passing through the system's impedance cause a voltage drop for each harmonic. This results in voltage harmonics appearing at the load bus. The amount of voltage distortion depends on the impedance and the current. Assuming the load bus distortion stays within reasonable limits (e.g., less than 5%), the amount of harmonic current produced by the load is generally constant.

While the load current harmonics ultimately cause voltage distortion, it is worth noting that the load has no control over the voltage distortion. The same load put in two different locations on the power system will result in two different voltage distortion values. Recognition of this fact is the basis for the division of responsibilities for harmonic control that is found in standards such as IEEE Std 519-1992.

  • Control over the amount of harmonic current injected into the system occurs at the end-use application.

  • Assuming the harmonic current injection is within reasonable limits, the control over voltage distortion is exercised by the entity that controls the system impedance, typically the utility.

One must be careful when describing harmonic distortion phenomena, as there are distinct differences between the causes and effects of harmonic voltages and currents. The use of the term harmonics should be qualified accordingly. By popular convention in the power industry, the term is used by itself most of the time when referring to load apparatus, indicating that the speaker is referring to the harmonic currents. When referring to the utility system, the voltages are generally the subject. For systems affected by harmonic-induced overheating, understanding Capacitor Bank applications is essential for voltage support and harmonic filtering. For in-depth harmonic analysis, explore our guide to using a Power Quality Analyzer to identify waveform distortion and power anomalies.

 

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Electricity Production

Electricity production converts primary energy into power via thermal, hydro, wind, and solar systems, optimizing efficiency, capacity factor, grid stability, transmission reliability, and emissions through turbines, generators, inverters, and advanced SCADA control.

 

What Is Electricity Production?

Electricity production converts energy to electric power, prioritizing efficiency, safety, and grid reliability.

✅ Conversion via turbines, generators, inverters, and transformers

✅ Control with SCADA, protective relays, and load-frequency regulation

✅ Optimization of efficiency, capacity factor, and emissions

 

Electricity Production continues to grow around the world, from a variety of energy power sources. In terms of world electricity generation, the US Department of Energy predicts advances strongly from 2004 to 2030. Global production increases by 2.4 percent per year over the projection period, from 16,424 billion kilowatthours in 2004 to 30,364 billion kilowatthours in 2030. Much of the growth in electric power demand is projected for nations outside the OECD. Although the non-OECD nations consumed 26 percent less electricity than the OECD nations in 2004, total generation in the non-OECD region in 2030 is projected to exceed generation in the OECD by 30 per cent. For context, the International Energy Outlook provides a concise overview of electricity generation trends worldwide today.

Total electricity demand in the non-OECD nations is expected to grow from 2004 to 2030 at an annual rate that is nearly triple the rate of growth for electricity demand in the OECD. The difference reflects the relative maturity of electricity infrastructure in the more developed OECD region, as well as the expectation that populations in the OECD countries generally will grow slowly or decline over the next 25 years. In addition, fast-paced growth in the developing non-OECD economies translates to rising standards of living and robust growth in consumer demand for lighting and appliances. Total electricity generation in the non-OECD region increases by an average of 3.5 percent per year in the IEO2007 reference case, as compared with a projected annual growth rate for OECD electricity generation that averages 1.3 per cent per year from 2004 to 2030. Among the energy end-use sectors, the most rapid growth in total world demand for electricity is projected for the buildings (residential and commercial) sectors.

Understanding the diversity of sources of electricity helps explain regional growth patterns in demand.

In Power plants, electricity Production involves the generation or creation of electric power, using rotating turbines attached to an energy generator. This mechanical manufacturing of electricity produces most commercially available electricity. Turbines are driven by a fluid which acts as an intermediate energy carrier. The fluids typically used are:

For readers new to plant design, this primer on how electricity is generated clarifies the roles of turbines, generators, and working fluids.

  • steam - Water is boiled by nuclear fission or the burning of fossil fuels (coal, natural gas, or petroleum). Some newer plants use the sun as the heat source: solar parabolic troughs and solar power towers concentrate sunlight to heat a heat transfer fluid, which is then used to produce steam. Another renewable source of heat used to drive a turbine is Geothermal power. Either steam under pressure emerges from the ground and drives a turbine or hot water evaporates a low boiling liquid to create vapour to drive a turbine.
  • water - Turbine blades are acted upon by flowing water, produced by hydroelectric dams or tidal forces,
  • wind - Most wind turbines generate electricity from naturally occurring wind. Solar updraft towers use wind that is artificially produced inside the chimney by heating it with sunlight.
  • hot gases - Turbines are driven directly by gases produced by the combustion of natural gas or oil. Combined cycle gas turbine plants are driven by both steam and gas. They generate power by burning natural gas in a gas turbine and use residual heat to generate additional electricity generation from steam. These plants offer efficiencies of up to 60%.

Hydropower and tidal technologies illustrate how water-based electricity remains a cornerstone in many regions.

Various other technologies have been studied and developed for power generation. Solid-state generation (without moving parts) is of particular interest in portable applications. This area is largely dominated by thermoelectric (TE) devices, though thermionic (TI) and thermophotovoltaic (TPV) systems have been developed as well. Typically, TE devices are used at lower temperatures than TI and TPV systems. Piezoelectric devices are used for power generation from mechanical strain, particularly in power harvesting. Betavoltaics are another type of solid-state power generator which produces electricity from radioactive decay. Beyond conventional turbines, a range of alternative electricity options are being explored for niche and distributed applications.

Fluid-based magnetohydrodynamic (MHD) electricity generation has been studied as a method for extracting electrical power from nuclear reactors and also from more conventional fuel combustion systems. These advanced concepts broaden our understanding of how we generate electricity under extreme conditions.

Electrochemical is also important in portable and mobile applications. Currently, most electrochemical power comes from closed electrochemical cells ("batteries"), which are arguably utilized more as storage systems than generation systems, but open electrochemical systems, known as fuel cells, have been undergoing a great deal of research and development in the last few years. Fuel cells can be used to extract power either from natural fuels or from synthesized fuels (mainly electrolytic hydrogen) and so can be viewed as either generation systems or storage systems depending on their use. In many systems the electricity generator ultimately interfaces with inverters and controls for grid integration.

 

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