Suppose there are 2 sinusoidal signals $\cos(\omega t)$ and $\cos(\omega t)$, which implies that their individual power is $1/2$ unit and total power is $1$ unit. When added, the signal $2\cos(\omega t)$, however, has power $2$ unit.
Obviously,
$$\rm Energy_{signal} = Power_{signal}\times Time_{period}$$
So, how does the principle of energy conservation hold in this case?