Added GMM to Project

[PhilippSchmelter]

Closes #12

This pull request introduces a major enhancement to the simulation pipeline by integrating Gaussian Mixture Models (GMMs) for more accurate load value generation. It adds functionality to fit GMMs to historical load data, simulate synthetic time series using Markov chains and GMMs, and visualize both original and simulated data distributions. The changes primarily focus on expanding the project's capabilities and improving simulation accuracy.

New Features and Enhancements:

• Integration of GMMs for Load Simulation:

  • Added the fit_gmms function in src/markov/gmm.py to fit GMMs to load data for each bucket and state, enabling probabilistic modeling of load values.
  • Implemented the sample_value function in src/markov/gmm.py to sample load values from fitted GMMs during simulation.

• Synthetic Time Series Generation:

  • Added _simulate_series function in src/main.py to generate synthetic load time series using transition probabilities and GMMs.
  • Introduced a constant SIM_DAYS in src/main.py to define the number of days for simulation.

Visualization Improvements:

• Diagnostic Plots for Simulation:
  • Added _plot_simulation_diagnostics function in src/main.py to compare original and simulated load distributions and visualize simulated load patterns by hour of day.
  • Added _plot_first_25_buckets function in src/main.py to generate heatmap grids for transition probabilities across buckets.

Updates to Documentation:

• Changelog Update:
  • Updated CHANGELOG.md to document the addition of the GMM feature to the project.