The Two-Wattmeter Method

Transcription

1 The Two-Wattmeter Method In a three phase, wye or delta three wire system, under balanced or unbalanced conditions, with any power factor, the two-wattmeter method is a practical and commonly used method of measuring total three phase power. A simplified circuit diagram of the two-wattmeter 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 polarities 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. Ptotal = P1 P2 (1) 1/5

2 As indicated in Fig.1, each wattmeter measures a line current and a line 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 o. 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: P1 = Vac Ia cos( - 30 o ) (2) P2 = Vbc Ib cos( 30 o ) (3) Figure 2: Phasor diagram for a lagging power factor. Note that depending on the phase angle,, the signs on P1 and P2 can be positive or negative. Table 1 shows the sign of P1 and P2 for values of ranging from 90 o to 90 o. At = 60 o, one of the wattmeters will read zero. If > 60 o, one of the readings will be negative and the other will be positive. 2/5

3 Sign of P1 Sign of P2 (Degrees) P1 = Vac Ia cos( -30 o ) P2 = Vac Ia cos( 30 o ) Table 1: Polarities of wattmeter readings at different phase angles. This table assumes that the wattmeters are connected as shown in Fig.1. This particular 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 wattmeter. 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 transformer 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 running through the test table. Polarities are important in the two-wattmeter method. The voltage is measured from line a to line c (Vac) with the wattmeter in position 1 as shown in Fig. 3.The voltage is measured from line b to line c (Vbc) with the wattmeter in position 2 as shown in Fig.3. When switching from one position to the other, the voltage selection switch must be changed to insure that measurements are made between the correct two lines and the polarity switch must be set such that wattmeter reads upscale. 3/5

4 a Ammeter Plug and CT A M Selector Switch Polarity Switch I a V ac or V ca P 1 b Ammeter Plug and CT A M Three - Phase Wye or Delta Three wire Load Selector Switch Polarity Switch I b V ac or V ca P 2 c 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 the two readings directly to obtain Ptotal. 2. If voltage line selection and polarity switch positions are as shown in Fig. 3 and one reading is positive and the other negative, the magnitude of the phase angle,, is greater than 60 o (assuming a balanced load, for this case). Positive meter deflection can be obtained for the negative reading by reversing the polarity switch. 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 switch 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 leads 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. 4/5

5 In the lab, it is always a good idea to set up a purely 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. Qtotal = 3 ( P1 - P2 ) (4) The phase angle,, and the power factor, cos, and be determined from the wattmeter readings alone, if the system is balanced. = tan 1 Qtotal Ptotal (5) For example: 1. P1 = -80 Watts P2 = 127 Watts Ptotal = 47.0 Watts Qtotal = VARS = tan = o 2. P1 = 127 Watts P2 = -80 Watts Ptotal = 47.0 Watts Qtotal = VARS = tan = o 47 5/5