Question regarding AC power of ergodic process
Considering real valued WSS processes whose auto-correlation and auto-covariance functions are defined as
$$ r_x(\tau) = E[ x(t)x(t+\tau) ] $$

$$ c_x(\tau) = E[ (x(t)-\mu_x)(x(t+\tau)-\mu_x) ] = r_x(\tau) - \mu_x^2 $$

Then the following are just basic observations.


The total power of a WSS random process is given by
$$ P_x = E[ x^2(t) ] = E[ x(t)x(t) ] = r_x(0) $$ 
For a nonperiodic, WSS, RP to be ergodic in the mean, a necessary and sufficient condition is such that the auto covariance function $c_x(\tau)$ goes to zero as $\tau$ goes to $\infty$ : 
$$ \lim_{\tau \to \infty}  c_x(\tau) = 0$$
Since auto correlation sequence and autocovariance sequences are related by 
$$ r_x(\tau) = c_x(\tau) + \mu_x^2 $$


then the value of ACF as $\tau$ goes infinity yields the DC power as 
$$ \lim_{\tau \to \infty} r_x(\tau) =\lim_{\tau \to \infty} c_x(\tau) + \mu_x^2 = 0 + \mu_x^2 $$

hence $r_x(\infty)$ is the DC power for an ergodic process.


The difference between the total power and the DC power is the AC power. 


For a zero-mean RP, the total power and the AC power are the same.