## What are the basics of power measurement?

Direct current or DC power measurement is very easy and simple. It is measured in watts. Watts = Volts x Amperes. For the measurement of the alternate current or AC power, the complexity is introduced by the power factor (PF). Here, watts= volts x amperes x PF. The measurement of the power of AC is known as active power, true power, or real power.

In AC systems, we find apparent power by multiplying volts and amperes (volts x amperes= volt-amps). Using at least one complete cycle, the power consumption is measured by calculating it over real-time. The instantaneous voltage is multiplied with the instantaneous current to get instantaneous power by the use of digital techniques which are then accumulated and integrated to provide a measurement over a specific time. This method for any waveform gives us the true average power measurement or true root mean square or RMS measurement like sine or distorted, which consists of harmonic content up to the bandwidth of the measurement.

The total power is a mixture of real power and reactive power.

## Single-phase and Three-phase power measurement

According to Blondel's theorem, the total power is measured with one less number of wattmeters than the number of wires present in the system. So, a single-phase and two-wire system will require one wattmeter and a single-phase and the three-wire system will require two wattmeters, and a three-phase and the three-wire system will also require two wattmeters and a three-phase and the four-wire system will require three wattmeter devices. The wattmeter is a device that measures power using one voltage and one current input as shown in the above figure. Multiple current or voltage input pair cables are used by many power analyzers and digital storage oscilloscopes (DSOs) for measuring watts, in effect within a single instrument acting as multiple wattmeters. It is possible to measure three-phase and four-wire power with one correctly specified power analyzer.

The total power dissipated by the load is equal to the voltage and current detected by the wattmeter device in a single-phase and two-wire system. The voltage is measured between the two wires and the wire that supplies power to the load measures the current is the hot wire. A power analyzer measures the voltage signal up to 1000 V RMS. In the case of higher voltages, the voltage transformer (VT) is required for an AC system. It helps lower the voltage to a measurable level. Up to 50 A, the currents can be typically measured using a power analyzer depending on the instrument. The current transformer (CT) is required for high current measurement. There are many different kinds of CTs and some are placed directly in-line and others have a window through which the cable carrying current passes. The clamp-on type is the third type and a shunt is typically used for DC currents. The shunt is placed inline and a low-level signal (millivolt) is measured by the instrument.

In a single-phase and three-wire type system, the total power measured is the algebraic sum of the powers of the two wattmeters. The wattmeter is connected from any of the hot wires to the neutral, and in each hot wire, the current is measured. The total power output calculated is given by $P$ = ${P}_{1}+{P}_{2}$.

In a three-phase and four-phase wire system, from a hot wire to a neutral, there are three wattmeters. Each measure the voltage, and in one of the three hot wires, each wattmeter measures the current. The total power is now shown by the algebraic sum of all the readings of the three wattmeters. Total power output is given by : $P={P}_{1}+{P}_{2}+{P}_{3}$.

In a three-phase and three-wire system, in any of the two of three wires, the two wattmeters measure phase current. Between two of the three power supply lines, each wattmeter measures a line-to-line voltage. By the algebraic sum of two wattmeter values, the total power of the power supply in watts is accurately measured in this configuration. The total power output is given by $P={P}_{1}+{P}_{2}$. Even if the system is balanced or unbalanced, this holds.

If there is an unbalanced load, the phase currents are different, and the total electrical power analysis is correct but there could be an error in the total VA and PF. To ensure accurate measurements on three-phase and three-wire systems with balanced or unbalanced load, the power analyzers may have a special configuration of 3V3A wiring configuration. To monitor all three phases, this method uses three wattmeters. In power system we know there are three phases that is R for red, Y for yellow and B for blue phase. Between R and Y phases, one wattmeter measures voltage, whereas the second wattmeter measures voltage between the B and Y phases, and between R and B phases, the third wattmeter measures voltage. Each wattmeter measures the phase current also. To calculate the total electrical power, the two-wattmeter method is still used.

## Power factor measurement

The value of the power factor should always be kept near unity and it must be often measured. For the same amount of useful power transferred a low power factor load draws more current than a high power factor load in an electrical power system. The energy lost in the distribution system is increased by the higher currents hence the system requires large wires and other equipment. Because of the wasted energy and the cost of the larger equipment, the electrical utilities will charge usually a higher cost to commercial or industrial customers exhibiting a low power factor.

Whenever the power factor drops in a system, the power factor correction devices are used often. Because the bulk of most power consumption loads is inductive, these devices are typically capacitors. To find out the power factor in a 3 phase and 4 wires system the three wattmeters are needed where each meter measures watts. By dividing the total watts from each meter by total volt-amps, the power factor is calculated.

Power factor should be measured in a 3 phase and 3 wires system by using three wattmeter methods instead of two wattmeters if the load is unbalanced. The frequency measurement is also one of the important factors other than power measurement in a power system. The main causes of frequency variations are distributed generation, faults, system non-linear loads, and so on.

## Tools for power measurement

With the help of a digital power analyzer or DSO which includes a power analysis, firmware the power is typically measured. The modern power analyzers are entirely electronic and to convert analog signal to digital signal, it uses digitizers. To make true power measurements, the power analysis DSO uses special firmware.

For board and component level work, their current probe and voltage probe makes them well suited where power frequency is relatively high and absolute accuracy is not a must. To make power measurements, the DSO requires a current probe and voltage probe. Around one of the main wires carrying current, the current probe is connected. The voltages often are not referred to a ground level.

To isolate the DSO ground from a component ground, a differential voltage probe is required. In addition to DSO, power analyzers, CTs and PTs, other components such as probes, clamps, and wires are used for power measurement.

## Context and Applications

This topic is significant in the professional exam for undergraduate, graduate, and postgraduate courses.

- Bachelors of Technology in Electrical Engineering
- Masters of Technology in Electrical Engineering

## Practice Problems

**Q1.** How many wattmeters are required for a single-phase and two-wire system?

- One wattmeter
- Two wattmeter
- Three wattmeter
- Four wattmeter

**Answer**: Option a

**Explanation**: According to Blondel's theorem, the total power is measured with one less number of wattmeters than the number of wires present in the system. Therefore a single-phase and two-wire system will require one wattmeter only.

**Q2. **Which of the following is responsible for the complexity in measureing power in an AC system?

- Voltage
- Current
- Power factor
- None

**Answer**: Option c

**Explanation**: For AC power measurement the complexity is introduced by the power factor (PF) as watts = volts x amperes x PF.

**Q3.** How much current does a load with a low power factor draw?

- Low current
- High current
- Does not draw any current
- None

**Answer**: Option b

**Explanation**: In an electrical power system, for the same amount of useful power transferred a load with a low power factor draws more current than a load with a high power factor.

**Q4.** Which of the following devices help to measure the power?

- Wattmeter
- CT and PT
- DSO
- All of the above.

**Answer**: Option d

**Explanation**: Power is measured using wattmeters, DSOs, CTs and PTs, and so on.

**Q5.** What is the range of measuring power using a power analyzer?

- Up to 500 V RMS
- Up to 1000 V RMS
- Up to 2000 V RMS
- Up to 5000 V RMS

**Answer**: Option b

**Explanation**: The range of a power analyzer is up to 1000 V RMS.

## Related concept

- Electricity meters
- Oscilloscope
- CT and PT

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