 # Basic three-phase power measurements explained in detail

Basics of three-phase systems

Although single-phase electricity is used to power common household and office electrical appliances, three-phase AC systems are almost universally used to distribute electrical power and to directly supply electricity to higher wattage equipment.

Three-phase power measurements explained in detail (photo credit: d.mike36 via Flickr)

This technical article describes the basic principles of three-phase systems and the difference between the different measurement connections it is possible.

• Three-phase systems
• Star or star connection
• Delta Connection
• Wye and Delta comparison
• Power measurements
• Three-phase single-phase connection
• Three-phase three-wire connection (two-wattmeter method)
• Three-phase three-wire connection (three-wattmeter method)
• Blondel’s theorem: Number of wattmeters required
• Three-phase four-wire connection
• Configuration of measuring equipment

Three phase systems

Three-phase electricity consists of three alternating voltages of identical frequency and similar amplitude .

Why use three-phase systems? For two reasons:

1. All three vector voltages can be used to create a rotating field in a motor. Motors can thus be started without the need for additional windings.
2. A three-phase system can be connected to a load so that the number of copper connections needed (and therefore the transmission losses) are half of what they would otherwise be .

Consider three single-phase systems each providing 100W at a load (Figure 3). The total load is 3 × 100W = 300W . To supply, 1 ampere crosses 6 wires and there are therefore 6 units of loss.

Alternatively, all three supplies can be connected to a common return, as shown in Figure 4. When the load current in each phase is the same, the load is said to be balanced. With the load balanced and the three currents phase shifted 120 ° from each other, the sum of the current at all times is zero and there is no current in the return line.

In a three-phase 120 ° system, 3 wires are enough to transmit the current, otherwise 6 wires would be required. Half the copper is needed and the wire transmission losses will be halved.

Star or star connection

A three phase system with a common connection is normally drawn and is known as a “star” or “star” connection .

The common point is called the neutral point. This point is often grounded at the source for safety reasons. In practice, the loads are not perfectly balanced and a fourth “neutral” wire is used to carry the resulting current.

The neutral conductor can be considerably smaller than the three main conductors , if permitted by local codes and standards.

Delta Connection

The three single phase power supplies discussed previously could also be connected in series. The sum of the three voltages out of phase by 120 ° at any time is equal to zero. If the sum is zero, then both ends are at the same potential and can be joined .

The connection is generally drawn and is known as a delta connection after the shape of the Greek letter delta , Δ .

Wye and Delta comparison

The Wye configuration is used to distribute electricity to everyday single phase appliances found in the home and office. Single-phase loads are connected to a branch of the triangle between the line and the neutral. The total load of each phase is distributed as much as possible to present a balanced load to the primary three-phase supply.

The star configuration can also provide one or more three-phase current for higher loads at higher voltage. Single phase voltages are phase to neutral voltages. A higher phase-to-phase voltage is also available, as indicated by the black vector in Figure 8.

The delta configuration is most often used to supply higher power three phase industrial loads . However, different voltage combinations can be obtained from a three-phase delta power supply, by making connections or “taps” along the windings of the power transformers.

In the United States, for example, a 240V delta system may have a split-phase or center tap winding to provide two 120V supplies (Figure 9).

The center plug may be earthed to the transformer for safety reasons. 208V is also available between the center plug and the third “high leg” of the delta connection.

Power measurements

Power is measured in AC systems using power meters. A modern digital sampling power meter, such as one of the Tektronix power analyzers, multiplies the instantaneous voltage and current samples to calculate the instantaneous watts, then takes an average of the instantaneous watts over a cycle to display the actual power.

A power meter will provide accurate measurements of actual power, apparent power, reactive voltages-amps, power factor, harmonics and many more over a wide range of waveforms, frequencies and power factors .

For the power analyzer to perform well, you must be able to correctly identify the wiring configuration and correctly connect the power meters to the analyzer.

Single-phase power meter connection

Only one power meter is required, as shown in Figure 10. Connecting the system to the voltage and current terminals of the power meter is simple. The voltage terminals of the power meter are connected in parallel across the load and current flows through the current terminals which are in series with the load.

Three-phase single-phase connection

In this system, shown in Figure 11, voltages are produced from a center tap transformer winding and all voltages are in phase . This is common in North American residential applications, where one 240V power supply and two 120V power supplies are available and may have different loads on each leg.

To measure total power and other quantities, connect two power meters as shown in Figure 11 below .

Three-phase three-wire connection (two-wattmeter method)

Where three wires are present, two wattmeters are needed to measure the total power. Connect the power meters as shown in Figure 12. The voltage terminals of the power meters are connected phase by phase.

Three-phase three-wire connection (three-wattmeter method)

Although only two wattmeters are needed to measure total wattage in a three-wire system, as discussed earlier, sometimes it is convenient to use three wattmeters . In the connection shown in Figure 13, a false neutral was created by connecting the low voltage terminals of the three power meters together.

The three-wire, three-wattmeter connection has the advantage of indicating the power in each individual phase (not possible in the two-wattmeter connection) and phase-to-neutral voltages.

Blondel’s theorem: Number of wattmeters required

In a single phase system, there are only two wires. Power is measured using a single wattmeter. In a three-wire system, two power meters are required, as shown in Figure 14.

In general, the number of wattmeters required = the number of wires – 1

Proof of a wire sorting system

Instantaneous power measured by a power meter is the product of instantaneous voltage and current samples.

• Wattmeter 1 reading = i 1 (v 1 – v 3 )
• Wattmeter 2 reading = i 2 (v 2 – v 3 )

Sum of readings W1 + W2 = i 1 v 1 – i 1 v 3 + i 2 v 2 – i 2 v 3 = i 1 v 1 + i 2 v 2 – (i 1 + i 2 ) v 3

From Kirchoff’s law: i 1 + i 2 + i 3 = 0, therefore i 1 + i 2 = -i 3 )

2 readings W1 + W2 = i 1 v 1 + i 2 v 2 + i 3 v 3 = instantaneous total of watts .

Three-phase four-wire connection

Three power meters are required to measure total watts in a four-wire system . The voltages measured are the true phase at neutral voltages. Phase-to-phase voltages can be accurately calculated from the magnitude and phase of the phase-to-neutral voltages using vector mathematics.

A modern power analyzer will also use Kirchoff’s law to calculate the current flowing in the neutral line .

Configuration of measuring equipment

For a given number of wires, N, N-1 wattmeters are needed to measure total quantities such as power. You must make sure that you have a sufficient number of channels (3 wattmeter method) and connect them correctly.

Modern multi-channel power analyzers will calculate total or total quantities such as watts, volts, amps, volt-amps and power factor directly using appropriate built-in formulas

Formulas are selected based on the wiring configuration, so wiring tuning is critical to getting good total power measurements. A power analyzer that supports vector math will also convert phase-to-neutral (or star) quantities to phase-to-phase (or delta) quantities.

The √3 factor can only be used to convert from one system to another or to scale the measurements of a single wattmeter on balanced linear systems.

Understanding the wiring configurations and making the correct connections is essential for performing power measurements. Knowing well about common wiring systems and remembering Blondel’s theorem will help you make connections and results you can rely on.

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