How to determine sample size in stratified random sampling? I would like to make a discriminant analysis with 2715 data points ;
each representing either Wind, Wood (Bio), or Landfill (Bio) Energy.
However, the number of data points for each type of energy plant differs :
Wind : 865 data points, 
Landfill : 347 data points,
and Wood : 195 datapoints.
Therefore, I am unsure of how many data points should I include for the model.
ie ) 
If I include the same proportion of data points (ex 70% for model & 30% for test set),
I am afraid the model will become biased, since there are too many wind energy in the data set.
I wonder if including the same number of data points for each energy type is reasonable.
Forexample : 140 Wind Energy data points, 140 Wood Energy data points, and 140 Landfill Energy Datapoints. 
 A: Your sampling scheme should depend on what you would like to get from your inferential methods and how your sample data were collected or are intended to be collected.
I immediately see two types of inference you might want to make: (a) inference across plants regardless of type, and (b) inference for each type of plant.
For (a), if you have a target population to which you would like to make inference and know or have estimates for the distribution of plant type in your population, you can construct sampling weights for your data and weight a ccordingly (this might be your 2,714 data points, I'm not sure I understand whether these describe your population or your sample that you have already collected). In this way, the weighted inferences would reflect the makeup of the population and you wouldn't need to worry too much about the makeup of your sample. 
If you wanted to make inferences conditioned on plant type as in (b), you would want to pay more attention to the representation of the plant type in your sample because you would want enough data to perform estimaton with standard errors of reasonable size.  
Note that both of these can be accomplished if you use sampling weights. If you want to include the same number of plants of each type, this can produce valid estimates conditioned on plant type, but estimates made across plant type will likely be biased unless you weight.
See Sarndaal (https://www.amazon.com/Assisted-Survey-Sampling-Springer-Statistics/dp/0387406204)  or this link looked appropriate (https://www.nlsinfo.org/content/cohorts/nlsy97/using-and-understanding-the-data/sample-weights-design-effects).
A: @bobavenger1 has written about the importance of understanding your intentions and to have this reflected in your sampling procedures. I will address your question about the stratum-specific sample sizes.
First, some notation.


*

*$N$ and $n$ are the total population and sample sizes, respectively.

*$K$ is the number of strata.

*$N_k$ is the the number of units in stratum $k$ and $\sum N_k=N$.

*$n_k$ is the number of sampled units in stratum $k$ and $\sum n_k=n$.


In general, you can calculate stratum-specific sample sizes naively by retaining a constant sampling fraction across all the strata:
$$n_k = \dfrac{n}{N} \cdot N_k$$
This is sampling option is called the proportional option. As you point out, one drawback is that it does not take the variability of each stratum into account. However, it is intuitively understood and perfectly valid in specific situations.
Another method, called the optimal method, we introduce two issues. First, we recognise that each stratum has its own variability $\sigma_k$ and we wish to develop a strategy that samples more from strata that have high $\sigma_k$. Second, we recognise that the costs of sampling $C$ may not be trivial and some strata may be more costly to sample than others. In your case, perhaps the "wind" and "landfill" data are taken from sites that are easily accessible by pulic transportation, but the "wood" data are located in sites on the side of a steep hill and accessing them will involve the hiring of helicopters. We wish to develop a strategy that samples less from the more costly strata. You can see that we may need to balance these two competing interests.
We can disaggregate costs into 'overhead' costs $c_0$ that are constant across all strata and the cost of selecting a sampling in a particular stratum $c_k$. So, $C = c_0 + \sum c_kn_k$.
Let's assume that the costs aren't a factor. Then, we wish to select samples on the basis of minimising the variability. If so, then 
$$ n_k = \dfrac{nN_k\sigma_k}{\sum N_k\sigma_k} $$
Now, let's assume that costs are a factor. Then, the stratum-specific sample size is
$$ n_k = (C-c_0) \cdot \dfrac{N_k\sigma_k/\sqrt{c_k}}{\sum N_k\sigma_k\sqrt{c_k}} $$
Good luck!
PS. I can recommend two books on basic sampling methodology: 


*

*Elementary Survey Sampling by Scheaffer,  Mendenhall, Ott and Gerow 

*Sampling of Populations: Methods and Applications by Levy and Lemeshow 
