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# Energy Systems II Spring Two Wattmeter Method The TwoWattmeter Method In a three phase wye or delta three wire system under balanced or unbalanced conditions with any power factor the tw owattmeter

A simplified circuit diagram of the twowattm eter connections is shown in Fig1 Figure1 is simplified in the sense that the ammeters current transformers selection switch and polarity switch have been omitted The polari ties of the voltage and curre

## Energy Systems II Spring Two Wattmeter Method The TwoWattmeter Method In a three phase wye or delta three wire system under balanced or unbalanced conditions with any power factor the tw owattmeter

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## Presentation on theme: "Energy Systems II Spring Two Wattmeter Method The TwoWattmeter Method In a three phase wye or delta three wire system under balanced or unbalanced conditions with any power factor the tw owattmeter"â€” Presentation transcript:

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Energy Systems II Spring 2014 Two Wattmeter Method 1/5 The Two-Wattmeter Method In a three phase, wye or delta three wire system, under balanced or unbalanced conditions, with any power factor, the tw o-wattmeter method is a practical and commonly used method of measur ing total three phase power. A simplified circuit diagram of the two-wattm eter connections is shown in Fig.1. Figure1 is simplified in the sense that the ammeters , current transformers, selection switch, and polarity switch have been omitted. The polari ties of the voltage and current connections to the

wattmeters are significant. Note that the line in which the current is not measured, line “c”, is connected to the negative voltage terminal on both wattmeters. Figure 1: Connections for the two-wattmeter method. Notice that this is a three-wire system. The total power delivered to the load is given by Eq.1. total = P + P 2 (1)
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Energy Systems II Spring 2014 Two Wattmeter Method 2/5 As indicated in Fig.1, each wattmeter measures a line current and a li ne to line voltage. The wattmeter reading indicates the product of line current, the line to line voltage, and the cosine of

the angle between them. At unity power factor ( = 0, cos = 1), the angle between phase current and line to line voltage is 30 . Referring to Fig.1 and with the aid of a phasor diagram, Fig. 2, it can be shown that the wattmeter readings at any power factor are: = V ac I cos( - 30 ) (2) = V bc I cos( + 30 ) (3) Figure 2: Phasor diagram for a lagging power factor. Note that depending on the phase angle, , the signs on P and P can be positive or negative. Table 1 shows the sign of P and P 2 for values of ranging from –90 to 90 . At | | = 60 , one of the wattmeters will read zero. If | | > 60 ,

one of the readings will be negative and the othe r will be positive.
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Energy Systems II Spring 2014 Two Wattmeter Method 3/5 Sign of P Sign of P (Degrees) = V ac I cos( -30 ) P = V ac I cos( +30 ) -90 - + -80 - + -60 0 + -30 + + 0 + + 30 + + 60 + 0 80 + - 90 + - Table 1: Polarities of wattmeter readings at different phase angles. This table assumes that the wattmeters are connected as shown in Fig.1. This partic ular data is for a balanced load. Otherwise would not necessarily be the same in each phase. Procedure In the lab, only one wattmeter will be used per test table. The

ammeter patch plug, voltage selection switch, and the polarity switch are used to select the desired voltages and currents that are connected to the wattm eter. An ammeter is always and a current transformer is normally used with the wattmeter in this laboratory. The use of the ammeter and the current transf ormer along with the wattmeter makes it impractical and very inconvenient to actually use two wattmeters. Figure 3 shows the wattmeter connected in both positions at once to the three lines runni ng through the test table. Polarities are important in th e two-wattmeter method. The volta ge

is measured from line “a” to line “c” (V ac ) with the wattmeter in position 1 as shown in Fig. 3.The voltage is measured from line “b” to line “c” (V bc ) with the wattmeter in position 2 as shown in Fig.3. When switching from one position to the ot her, the voltage sel ection switch must be changed to insure that measurements ar e made between the correct two lines and the polarity switch must be set such that wattmeter reads upscale.
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Energy Systems II Spring 2014 Two Wattmeter Method 4/5 Ammeter Plug and CT Selector Switch Polarity Switch Selector Switch Polarity Switch

Ammeter Plug and CT ac or ca ac or ca Three - Phase Wye or Delta Three wire Load Figure 3: A laboratory test table set up for the two-wattmeter method. Notice that only one wattmeter, ammeter, and CT are used. They are shown in two different positions as facilitated by the combination of switches on the table. A few examples might help explain the situation. 1. If the voltage line selection and polarity switch positions are as shown in Fig. 3 and both readings are positive, simply add th e two readings dire ctly to obtain P total . 2. If voltage line selection and polarity switc h positions

are as s hown in Fig. 3 and one reading is positive and the other negativ e, the magnitude of the phase angle, , is greater than 60 (assuming a balanced load, for this case). Positive meter deflection can be obtained for the negative reading by re versing the polarity sw itch. Record this reading as negative. It is important that the original polarity switch positions be tried when making any additional measurements. In this case, the opposite polarity switch position is only being used as a convenience while obtaining positive meter deflection for recording negative values. 3. If voltage line

selection and polarity switc h positions are as shown in Fig. 3, but both readings turn out to be negative, a positive meter deflection can be obtained by exchanging the two current lead s or by reversing the polarity switch. In this case, both readings are negative. The total power can be negative if the load is replaced by an AC generator. Again, it is wise to trace through the lines on the test table to be sure that you understand what you are doing.
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Energy Systems II Spring 2014 Two Wattmeter Method 5/5 In the lab, it is always a good idea to set up a pu rely resistive

load to start with. With resistive loads, the wattmeter should read upscale in both positions. This quick test provides an easy check on your polarities. Reactive Power and Power Factor The magnitude of the reactive power can be obtained using Eq. 4. Q total = 3 ( P - P 2 ) (4) The phase angle, , and the power factor, cos and be determined from the wattmeter readings alone, if the system is balanced. | | = tan –1 Ptotal Qtotal (5) For example: 1. P = -80 Watts P = 127 Watts | P total | = 47.0 Watts | Q total | = 358.5 VARS | | = tan –1 47 358 = 82.53 2. P = 127 Watts P = -80 Watts | P total |

= 47.0 Watts | Q total | = 207.0 VARS | | = tan –1 47 207 = 77.21