The Three Wattmeter Method

Electrical Circuit Analysis > Polyphase Systems

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The power delivered to a balanced or an unbalanced four-wire, Y-connected load can be found by the three-wattmeter method, that is, by using three watt-meters in the manner shown in Fig. 1.

Fig. 1: Three-wattmeter method for a Y-connected load.

Each wattmeter measures the power delivered to each phase. The potential coil of each wattmeter is connected parallel with the load, while the current coil is in series with the load. The total average power of the system can be found by summing the three wattmeter readings; that is,

$$\bbox[10px,border:1px solid grey]{P_{T_{Y}} = P_1 + P_2 + P_3}$$

Fig. 2: Three-wattmeter method for a $\Delta$-connected load.

For the load (balanced or unbalanced), the watt-meters are connected as shown in Fig. 2. The total power is again the sum of the three wattmeter readings:

$$\bbox[10px,border:1px solid grey]{P_{T_{\Delta}} = P_1 + P_2 + P_3}$$

If in either of the cases just described the load is balanced, the power delivered to each phase will be the same. The total power is then just three times any one wattmeter reading.

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