Which is the best Machine learning technique for this Load forecasting problem?
I think this is one of the time series forecasting because you want to predict the future load of residence with the past dataset of residence's load by time. By my experience I recommend using LSTM RNN for the solution. An LSTM is well-suited to classify, process and predict time series given time lags of unknown size and duration between important events. Of course, this is supervised learning.

As for difference between supervised learning and unsupervised learning on your case, you don't need to use unsupervised learning for this solution because you have already dataset with input/correct output. if you are training your machine learning task for every input with corresponding target, it is called supervised learning, which will be able to provide target for any new input after sufficient training. Contrary, if you are training your machine learning task only with a set of inputs, it is called unsupervised learning, which will be able to find the structure or relationships between different inputs. It says you should use supervised learning - RNN or CNN.

PS: as for framework, I recommend using Tensorflow or Keras.