Current Transformer in power meter
Calculating the power (assuming a balanced load), using voltage and current readings alone, would be a problem in a single phase AC system itself, since the power factor would not be known.
AC Power = V * I * Cos φ
Hence an AC Wattmeter is a must.
With a star-connected load, the power in one phase could be measured with line current being fed to the current coil of the wattmeter and the phase voltage (line-to-neutral voltage) to the potential coil. The total power would be 3 * wattmeter reading.

In the case of a delta-connected load, the measurement would require the phase current to be fed to the current coil of the wattmeter and the line voltage to the potential coil. However, access to measure the phase current would be the main problem. The solution would be to use two wattmeters, with line currents and line voltages being fed to the current and potential coils. The total power would be the sum of the wattmeter readings.

This method would be applicable to a star-connected load also.