Hi Alex,
Thanks for the interesting question.
I think the question about the type of neural network is not the main question here. The more important question is how to train a neural network to accomplish what you want. This is not a supervised learning problem because there is no available dataset that shows what the output (power used) should be for different values of inputs (available power, cost of electricity, etc).
Instead this seems more like a reinforcement learning problem. With reinforcement learning you can train a policy represented by a neural network (a simple fully-connected network would be a good way to start) by repeated interactions with a simulation environment to maximize a reward. Please take a look at the tech talks on reinforcement learning to get started and see the documentation on how to do this in MATLAB. A relevant example that could be useful is here, in this case the RL policy was defined using LSTM network.
I’d like to mention that you could also solve this problem using receding horizon optimization approach, using Model Predictive Control Toolbox. Here is a link to a very similar problem.
This approach solves an optimization problem at each time step to determine optimal amount of available power to use. Once you solve the problem a number of times for different scenarios, you can then train a neural network to provide the same results as the optimization algorithm, but with faster computations. This is an approach called imitation learning, please see an example here.
Once you have the trained network you can add it to your Simulink model to implement the overall control system, and can do simulations and implement the controller using code generation. Please see this video.
HTH
