# Power

Power is the rate of work (work over time) or the rate of energy transfer and common units include watt, one joule per second, (and multiples, such as kilowatts, kW, and megawatts, MW) and horsepower (hp).

## Electric motor power measurement and analysis

### Understand the basics to drive greater efficiency.

Energy is one of the highest cost items in a plant or facility, and motors often consume the lion’s share of plant power, so making sure motors are operating optimally is vital. Accurate power measurements can help to reduce energy consumption, as measurement is always the first step toward better performance and can also help extend the life of a motor. Small misalignment or other issues are often invisible to the naked eye, and the slightest wobble in a shaft can negatively affect productivity and quality, and even shorten the life of the motor.

Over the next three issues of Applied Automation, we will discuss a three-step process for making precision electrical and mechanical power measurements on a variety of motors and variable speed drive (VFD) systems. We will also show how these measurements are used to calculate the energy efficiency for motor and drive systems.

In addition, we will provide an understanding of how to make precision power measurements on complex distorted waveforms, as well as what instruments to use for different applications.

## Basic electrical power measurements

Electric motors are electromechanical machines that convert electric energy into mechanical energy. Despite differences in size and type, all electric motors work in much the same way: an electric current flowing through a wire coil in a magnetic field creates a force that rotates the coil, thus creating torque.

Understanding power generation, power loss, and the different types of power measured can be intimidating, so let’s start with an overview of basic electric and mechanical power measurements.

What is power? In the most basic form, power is work performed over a specific amount of time. In a motor, power is delivered to the load by converting electrical energy per the following laws of science.

In electrical systems, voltage is the force required to move electrons. Current is the rate of the flow of charge per second through a material to which a specific voltage is applied. By taking the voltage and multiplying it by the associated current, the power can be determined.

P = V * I where power (P) is in watts, voltage (V) is in volts, and current (I) is in amperes

A watt (W) is a unit of power defined as one Joule per second. For a dc source the calculation is simply the voltage times the current: W = V x A. However, determining the power in watts for an ac source must include the power factor (PF), so:
W = V x A x PF for ac systems.

The power factor is a unitless ratio ranging from -1 to 1, and represents the amount of real power performing work at a load. For power factors less than unity, which is almost always the case, there will be losses in real power. This is because the voltage and current of an ac circuit are sinusoidal in nature, with the amplitude of the current and voltage of an ac circuit constantly shifting and not typically in perfect alignment.

Since power is voltage times current (P = V*I), power is highest when the voltage and current are lined up together so that the peaks and zero points on the voltage and current waveforms occur at the same time. This would be typical of a simple resistive load. In this situation, the two waveforms are “in phase” with one another and the power factor would be 1. This is a rare case, as almost all loads aren’t simply and perfectly resistive.

Two waveforms are said to be “out of phase” or “phase shifted” when the two signals do not correlate from point to point. This can be caused by inductive or nonlinear loads. In this situation, the power factor would be less than 1, and less real power would be realized.

Due to the possible fluctuations in the current and the voltage in ac circuits, power is measured is a few different ways.

Real or true power is the actual amount of power being used in a circuit, and it’s measured in watts. Digital power analyzers use techniques to digitize the incoming voltage and current waveforms to calculate true power, following the method in Figure 2:

### Figure 2: True power calculation

In this example the instantaneous voltage is multiplied by the instantaneous current (I) and then integrated over a specific time period (t). A true power calculation will work on any type of waveform regardless of the power factor (Figure 3).

### Figure 3: These equations are used to calculate a true power measurement and true RMS measurements.

Harmonics create an additional complication. Even though the power grid nominally operates at a frequency of 60Hz, there are many other frequencies or harmonics that potentially exist in a circuit, and there can also be a dc or direct current component. Total power is calculated by considering and summing all content, including harmonics.

The calculation methods in Figure 3 are used to provide a true power measurement and true RMS measurements on any type of waveform, including all harmonic content, up to the bandwidth of the instrument.

## Power measurement

We’ll next look at how to actually measure watts in a given circuit. A wattmeter is an instrument that uses voltage and current to determine power in watts. The Blondel Theory states that total power is measured with a minimum of one fewer wattmeter than the number of wires. For example, a single-phase two-wire circuit will use one wattmeter with one voltage and one current measurement.

A single-phase three-wire split-phase system is often found in common housing wiring. These systems require two wattmeters for power measurement.

Most industrial motors use three-phase three-wire circuits that are measured using two wattmeters. In the same fashion, three wattmeters would be necessary for a three-phase four-wire circuit, with the fourth wire being the neutral.

Figure 4 shows a three-phase three-wire system with load attached using the two-wattmeter method for measurement. Two line-to-line voltages and two associated phase currents are measured (using wattmeters Wa and Wc). The four measurements (line-to-line and phase current and voltage) are utilized to achieve the total measurement.

### Figure 4: Measuring power in a three-phase three-wire system with two wattmeters.

Since this method requires monitoring only two current and two potential transformers instead of three, installation and wiring configuration are simplified. It can also measure power accurately on a balanced or an unbalanced system. Its flexibility and low-cost installation make it a good fit for production testing in which only the power or a few other parameters need measurement. For engineering and research and development work, the three-phase three-wire with three-wattmeter method is best as it provides additional information that can be used to balance loading and determine true power factor. This method uses all three voltages and all three-currents. All three voltages are measured (a to b, b to c, c to a), and all three-currents are monitored.

## Power factor measurement

In determining the power factor for sine waves, the power factor is equal to the cosine of the angle between the voltage and current (Cos Ø). This is defined as the “displacement” power factor, and is correct for sine waves only. For all other waveforms (non-sine waves), the power factor is defined as real power in watts divided by apparent power in voltage-amperes. This is called the “true” power factor and can be used for all waveforms, both sinusoidal and non-sinusoidal.

### Figure 7: Using the two-wattmeter method, the sum of the total watts (W1 + W2) is divided by the VA measurements.

However, if the load is unbalanced (the phase currents are different), this could introduce an error in calculating the power factor because only two VA measurements are used in the calculation. The two VAs are averaged because it’s assumed they’re equal; however, if they’re not, a faulty result is obtained.

Therefore, it’s best to use the three-wattmeter method for unbalanced loads because it will provide a correct power factor calculation for either balanced or unbalanced loads.

### Figure 8: With the three-wattmeter method, all three VA measurements are used in the above power factor calculation.

Power analyzers use the method above, which is called the 3V-3A (three-voltage three-current) wiring method. This is the best method for engineering and design work because it will provide a correct total power factor and VA measurements for a balanced or unbalanced three-wire system.

## Basic mechanical power measurements

In an electric motor, the mechanical power is defined as the speed times the torque. Mechanical power is typically defined as kilowatts or horsepower, with one W equaling 1 Joule/sec or 1 Nm/sec.

### Figure 9: Mechanical power measurements in watts are defined as two times Pi times the rotating speed (rpm) divided by 60 times the torque (Newton-Meter).

Horsepower is the work done per unit of time. One hp equals 33,000 pound feet per minute. Converting hp to watts is achieved using this relationship: 1 hp = 745.69987 W. However, the conversion is often simplified by using 746W per hp (Figure 10).

### Figure 10: Mechanical power measurement equations for horsepower often use a rounded figure of 1 hp = 746W.

For ac induction motors, the actual or rotor speed is the speed at which the shaft (rotor) rotates, typically measured using a tachometer. The synchronous speed is the speed of the stator’s magnetic field rotation, calculated as 120 times the line frequency divided by the number of poles in the motor. Synchronous speed is the motor’s theoretical maximum speed, but the rotor will always turn at a slightly slower rate than the synchronous speed due to losses, and this speed difference is defined as slip.

Slip is the difference in the speed of the rotor and the synchronous speed. To determine the percentage of slip, a simple percentage calculation of the synchronous speed minus the rotor speed divided by the synchronous speed is used.

Efficiency can be expressed in simplest form as the ratio of the output power to the total input power or efficiency = output power/input power. For an electrically driven motor, the output power is mechanical while the input power is electrical, so the efficiency equation becomes efficiency = mechanical power/electrical input power.

Bill Gatheridge is the product manager for power measuring instruments at Yokogawa Test & Measurement, and has more than 20 years of experience with the company in the area of precision electrical power measurements. He is a member and vice chairman of the ASME PTC19.6 committee on electrical power measurements for utility power plant performance testing.

This article appears in the Applied Automation supplement for Control Engineering and Plant Engineering

## Power FAQ

• ### Why is power important in manufacturing?

Power is important in manufacturing because it:

• Provides energy to operate machines and equipment.
• Helps to control and regulate the speed and operation of machines.
• Ensures consistent and reliable operation, reducing downtime and maintenance costs.
• Provides energy for lighting and heating, maintaining a safe and comfortable working environment.
• Supports the use of automation, control and communication systems, improving production processes and efficiency.
• Enables use of advanced technologies, such as robotics, artificial intelligence and the internet of things.
• Enables the production of high-quality products with consistent performance and specifications.

Effective management of power is essential for maintaining a productive and efficient manufacturing operation.Power is important in manufacturing because it:

• Provides energy to operate machines and equipment.
• Helps to control and regulate the speed and operation of machines.
• Ensures consistent and reliable operation, reducing downtime and maintenance costs.
• Provides energy for lighting and heating, maintaining a safe and comfortable working environment.
• Supports the use of automation, control and communication systems, improving production processes and efficiency.
• Enables use of advanced technologies, such as robotics, artificial intelligence and the internet of things.
• Enables the production of high-quality products with consistent performance and specifications.
• ### How is power different than energy?

Power and energy are two related, but distinct concepts in physics and engineering.

Energy refers to the ability to do work and is typically measured in units of joules (J) or kilowatt-hours (kWh). Energy is a scalar quantity that measures the amount of work that can be performed.

Power, on the other hand, refers to the rate at which work is done and is typically measured in watts (W) or kilowatts (kW). Power is a vector quantity that measures the rate of energy transfer or conversion.

In simple terms, energy is the amount of work that can be done, and power is the rate at which work is done. For example, a light bulb has energy because it can produce light, but it also has power because it produces light at a specific rate, measured in watts.

In electrical systems, power is often expressed as the product of voltage (V) and current (I), and is described by the equation: P = VI. This equation highlights the relationship between power and energy, as energy can be calculated by multiplying power by time (E = PT).

• ### How can power quality be achieved?

Power quality can be achieved through a combination of technical measures, system design and management practices. Some key steps to achieving power quality include:

• Load management: Proper load management, including the reduction of harmonic distortions and the elimination of unbalanced loads, can help improve power quality.
• Power factor correction: Power factor correction can help improve power quality by reducing the reactive power in a system and increasing the efficiency of energy usage.
• Harmonic filters: Harmonic filters can be used to reduce harmonic distortions in electrical systems and improve power quality.
• Surge protection: Surge protection devices, such as transient voltage suppressors, can be used to protect electrical systems from power disturbances and improve power quality.
• Grounding and bonding: Proper grounding and bonding practices, including the use of low impedance grounding systems, can help improve power quality and reduce the risk of electrical interference.
• Power conditioning: Power conditioning devices, such as uninterruptible power supplies (UPS), voltage regulators and power line filters, can be used to condition the electrical supply and improve power quality.
• Monitoring and diagnostics: Regular monitoring and diagnostics of electrical systems can help identify power quality problems and provide early warning of potential issues.
• Education and training: Proper education and training for personnel on power quality issues and best practices can help ensure that power quality is maintained and improved over time.
• ### What challenges prevent power quality from being achieved?

Achieving power quality can be challenging due to several factors, including:

• Complex electrical systems: Complex electrical systems, such as those used in large industrial facilities or data centers, can be difficult to manage and maintain, making it challenging to achieve desired levels of power quality.
• Aging infrastructure: Aging electrical infrastructure, such as power distribution systems and transformers, can contribute to power quality problems and make it difficult to achieve desired levels of performance and reliability.
• Increasing power demand: The increasing demand for power, especially from energy-intensive industries, can put stress on the electrical grid and make it difficult to maintain desired levels of power quality.
• System interactions: Complex interactions between various electrical systems, such as those that use AC and DC power, can contribute to power quality problems and make it difficult to achieve desired levels of performance and reliability.
• Harmonic distortions: Harmonic distortions, caused by non-linear loads, can negatively impact power quality and make it difficult to achieve desired levels of performance and reliability.
• Power electrification: The trend toward power electrification, especially in the transportation and industrial sectors, is increasing the demand for power and putting stress on the electrical grid, making it difficult to achieve desired levels of power quality.
• Lack of awareness: A lack of awareness or understanding of power quality issues among personnel responsible for maintaining electrical systems can make it difficult to identify and address power quality problems.
• Budgetary constraints: Implementing solutions to improve power quality can be costly, and limited budgets can prevent organizations from making necessary investments to achieve desired levels of power quality.

Some FAQ content was compiled with the assistance of ChatGPT. Due to the limitations of AI tools, all content was edited and reviewed by our content team.