Average Energy of modified QAM Constellation
The procedure is always the same. You need to compute the expectation $E\{|A_k|^2\}$, where $A_k$ are the complex symbols of the constellation:

$$E\{|A_k|^2\}=\sum_kP_k|A_k|^2\tag{1}$$

$P_k$ is the probability that the $k^{th}$ symbol is chosen. Usually you can assume that all symbols are equally likely, i.e., $P_k=1/M$, where $M$ is the number of symbols.