Three-Phase Systems<\/h2>\n
Three-phase electricity consists of three AC voltages of identical frequency and similar amplitude. Each AC voltage phase is separated by 120\u00b0 from the other (Figure 1).<\/p>\n This system can be represented diagrammatically by both waveforms and a vector diagram (Figure 2).<\/p>\n Why use three-phase systems? For two reasons:<\/p>\n Consider three single-phase systems each supplying 100 W to a load (Figure 3). The total load is 3 \u00d7 100 W = 300 W.\u00a0 To supply the power, 1 amp flows through 6 wires, and there are thus 6 units of loss.<\/p>\n Alternatively, the 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 by 120\u00b0 from each other, the sum of the current at any instant is zero, and there is no current in the return line.<\/p>\n In a three-phase 120\u00b0 system, only 3 wires are required to transmit the power that would otherwise require 6 wires. One-half of the copper is required, and the wire transmission losses will be halved.<\/p>\n A three-phase system with a common connection is normally drawn as shown in Figure 5 and is known as a \u201cwye\u201d or \u201cstar\u201d connection.<\/p>\n The common point is called the neutral point. This point is often grounded at the supply for safety reasons. In practice, loads are not perfectly balanced, and a fourth neutral wire is used to carry the resultant current.<\/p>\n The neutral conductor may be considerably smaller than the three main conductors if allowed by local codes and standards.<\/p>\n The three single-phase supplies discussed earlier could also be connected in series. The sum of the three 120\u00b0 phase shifted voltages at any instant is zero. If the sum is zero, then both end points are at the same potential and may be joined together.<\/p>\n The connection is usually drawn as shown in Figure 7 and is known a delta connection after the shape of the Greek letter delta, \u0394.<\/p>\n The Wye configuration is used to distribute power to everyday single-phase appliances found in the home and office. Single-phase loads are connected to one leg of the wye between line and neutral. The total load on each phase is shared out as much as possible to present a balanced load to the primary three-phase supply.<\/p>\n The wye configuration can also supply single- or three-phase power to higher power loads at a higher voltage. The single-phase voltages are phase-to-neutral voltages. A higher phase-to-phase voltage is also available as shown by the black vector in Figure 8.<\/p>\n The delta configuration is most often used to supply higher power three-phase industrial loads. Different voltage combinations can be obtained from one three-phase delta supply, however, by making connections or \u201ctaps\u201d along the windings of the supply transformers.<\/p>\n In the US, for example, a 240-V delta system may have a split-phase or center-tapped winding to provide two 120 V supplies (Figure 9).<\/p>\n The center-tap may be grounded at the transformer for safety reasons. 208 V is also available between the center tap and the third \u201chigh leg\u201d of the delta connection.<\/p>\n Power is measured in ac systems using wattmeters.\u00a0 A modern digital sampling wattmeter, such as any of the Tektronix power analyzers, multiplies instantaneous samples of voltage and current together to calculate instantaneous watts and then takes an average of the instantaneous watts over one cycle to display the true power.<\/p>\n A wattmeter will provide accurate measurements of true power, apparent power, volt-amperes reactive, power factor, harmonics and many others over a broad range of wave shapes, frequencies, and power factor.<\/p>\n For the power analyzer to give good results, you must be able to correctly identify the wiring configuration and connect the analyzer\u2019s wattmeters correctly.<\/p>\n Only one wattmeter is required, as shown in Figure 10. The system connection to the voltage and current terminals of the wattmeter is straightforward. The voltage terminals of the wattmeter are connected in parallel across the load, and the current is passed through the current terminals which are in series with the load.<\/p>\n In this system, shown in Figure 11, the voltages are produced from one center-tapped transformer winding, and all voltages are in phase. This system is common in North American residential applications, where one 240 V and two 120 V supplies are available and may have different loads on each leg.<\/p>\n To measure the total power and other quantities, connect two wattmeters as shown in Figure 11 below.<\/p>\n Where three wires are present, two wattmeters are required to measure total power. Connect the wattmeters as shown in Figure 12. The voltage terminals of the wattmeters are connected phase to phase.<\/p>\n Although only two wattmeters are required to measure total power in a three-wire system as shown earlier, it is sometimes convenient to use three wattmeters. In the connection shown in Figure 13, a false neutral has been created by connecting the voltage low terminals of all three wattmeters together.<\/p>\n The three-wire, three-wattmeter connection has the advantages of indicating the power in each phase (not possible in the two-wattmeter connection) and phase to neutral voltages.<\/p>\n In a single-phase system, there are just two wires. Power is measured using a single wattmeter. In a three-wire system, two wattmeters are required as shown in Figure 14.<\/p>\n In general, the number of wattmeters required equals the number of wires minus one.<\/p>\n The instantaneous power measured by a wattmeter is the product of the instantaneous voltage and current samples.<\/p>\n Three wattmeters are required to measure total watts in a four-wire system. The voltages measured are the true phase-to-neutral voltages. The phase-to-phase voltages can be accurately calculated from the phase-to-neutral voltages\u2019 amplitude and phase using vector mathematics.<\/p>\n A modern power analyzer will also use Kirchoff\u2019s law to calculate the current flowing in the neutral line.<\/p>\n For a given number of wires, N, N-1 wattmeters are required to measure total quantities such as power. You must make sure you have a sufficient number of (3 wattmeter method) channels, and connect them properly.<\/p>\n Modern multi-channel power analyzers will calculate total or sum quantities such as watts, volts, amps, volt-amperes and power factor directly using appropriate built-in formulas. The formulas are selected based on the wiring configuration, so setting the wiring is critical to get good total power measurements. A power analyzer with vector mathematics capability will also convert phase-to-neutral (or wye) quantities to phase-to-phase (or delta) quantities.<\/p>\n The factor \u221a3 can only be used to convert between systems or scale the measurements of only one wattmeter on balanced, linear systems.<\/p>\n Understanding wiring configurations and making proper connections is critical to performing power measurements. Being familiar with common wiring systems, and remembering Blondel\u2019s Theorem will help you get the connections right and results you can rely upon.<\/p>\n The Fundamentals of Three-phase Power Measurements \u2013 Application Note<\/em> by Tektronix<\/p>\n The wattmeter is an instrument for measuring the electric power (or the supply rate of electrical energy) in watts of any given circuit. Electromagnetic wattmeters are used for measurement of utility frequency and audio frequency power; other types are required for radio frequency measurements.\u00a0 Source:\u00a0 Wikipedia<\/p>\n![\"Figure](\"https:\/\/iaeimagazine.org\/images\/2017_02\/17b_EdFIg1.jpg\")
![\"Figure](\"https:\/\/iaeimagazine.org\/images\/2017_02\/17b_EdFIg2.jpg\")
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![\"Figure](\"https:\/\/iaeimagazine.org\/images\/2017_02\/17b_EdFIg3.jpg\")
![\"Figure](\"https:\/\/iaeimagazine.org\/images\/2017_02\/17b_EdFIg4.jpg\")
Wye or Star Connection<\/h2>\n
![\"Figure](\"https:\/\/iaeimagazine.org\/images\/2017_02\/17b_EdFIg5.jpg\")
![\"Figure](\"https:\/\/iaeimagazine.org\/images\/2017_02\/17b_EdFIg6.jpg\")
Delta Connection<\/h2>\n
![\"Figure](\"https:\/\/iaeimagazine.org\/images\/2017_02\/17b_EdFIg7.jpg\")
Wye and Delta Comparison<\/h2>\n
![\"Figure](\"https:\/\/iaeimagazine.org\/images\/2017_02\/17b_EdFIg8.jpg\")
![\"Figure](\"https:\/\/iaeimagazine.org\/images\/2017_02\/17b_EdFIg9.jpg\")
Power Measurements<\/h3>\n
Single-Phase Wattmeter Connection<\/h3>\n
![\"Figure](\"https:\/\/iaeimagazine.org\/images\/2017_02\/17b_EdFIg10.jpg\")
Single-Phase Three-Wire Connection<\/h3>\n
![\"Figure](\"https:\/\/iaeimagazine.org\/images\/2017_02\/17b_EdFIg11.jpg\")
Three-phase Three-Wire Connection (Two Wattmeter Method)<\/h3>\n
![\"Figure](\"https:\/\/iaeimagazine.org\/images\/2017_02\/17b_EdFIg12.jpg\")
Three-phase Three-Wire Connection\u00a0(Three Wattmeter Method)<\/h3>\n
![\"Figure](\"https:\/\/iaeimagazine.org\/images\/2017_02\/17b_EdFIg13.jpg\")
Blondel\u2019s Theorem: Number of\u00a0 Wattmeters Required<\/h3>\n
![\"Figure](\"https:\/\/iaeimagazine.org\/images\/2017_02\/17b_EdFIg14.jpg\")
Proof for a three-wire wye system<\/h3>\n
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Three-Phase, Four-Wire Connection<\/h2>\n
Configuring Measurement Equipment<\/h2>\n
References<\/h2>\n