Power analysis for logistic regression [duplicate]

I have to deliver a statistical analysis plan that will have to be approved by an ethic commettee before I could start a clinical trial.

I usually deal with different kinds of tests, whose power analysis is straightforward and, given the expected effect size, a given statistical significance (Type I error), and a desired power (1 - Type II error), I can easily obtain the needed sample size.

However, this time I am planning to use logistic and ordinal regressions. How can I determine the sample size needed to perform an analysis with a given power, a given statistical significance, and an expected effect size (in terms of odds ratio, I guess)?

Before asking such a question I googled, but I found only some tables related to "standard" cases with one or two regressors, wheras in my case I have several predictors: discrete variables, dummy variables, ordinal variables, and continuous variables.