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When we quote average power, we do so because often on a mains feeder the power to various loads fluctuates a bit, so we work out the real power Vrms x Irms for a resistive load (more complex for non linear and L or C loads) and average this every second or so, in the digital realm you might compute the real power every 20mS (16.666mS in the US) and keep a running average of this on a per second basis.

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