The power cuts, that lasted for up to six hours, occurred multiple times in areas such as CR Park, Okhla, Lodhi Colony, Jangpura Extension, Malviya Nagar, parts of Lajpat Nagar and South Extension and Dwarka.
The outages happened despite relatively less power demand as compared to weekdays when it had breached the 6,000 MW.
The State Load Despatch Centre recorded peak power load of 5,583 MW at 12 AM, indicating that power demand did not cross that figure through the day.
"We have directed the DERC that if any area has unscheduled power cuts and it is not rectified in two hours then people of that area has to be compensated.
This policy will be implemented soon so that their (discoms) accountability is fixed," Chief Minister Arvind Kejriwal told reporters.
The discoms have been called fora meeting with the Chief Minister on Tuesday.