Is it possible to calculate effective value of a signal from its average value?
This is the average value of the current flowing on the power line,
  isn't it so? However, I need the effective value of the current in
  order to calculate the power.


Be careful. If the shapes of the currents or voltages are not sinusoidal, knowing the RMS values for them, and the phase difference between them, is not enough. For arbitrary waveforms (as in your figure) for either one of the two (voltage or current), the only way to have an accurate calculation of the power is by integrating the product of the instantaneous voltage and the instantaneous current.

\$P=\dfrac{1}{T}\int v(t)i(t)dt \$

Nowadays, that is usually done in the digital domain. You have two ADCs (or a single ADC with two S/H front-ends). One converts v(t) and the other one converts i(t). In the digital domain, you multiply those two signals, and do the integral.

You can also do it in an analog way, using an analog multiplier and a low pass filter, but analog multipliers are tricky to use.

In summary: the circuit that you posted, that filters the shape of the current, is not valid for computing power, if the current may have the shape that you show in the figure.