Some 500 families in the area say they are being "forced" to apply for electricity connections by power distributor BSES Rajdhani.
The families claim that they were promised free power by then Prime Minister Rajiv Gandhi as part of rehabilitation of victims of November 84 carnage. However, they have nothing to show on record.
BSES on its part says that they did not make any promise and people must get new connections for uninterrupted supply.
The residents of this area are now enduring long power cuts of at least 16 hours a day.
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According to sources in BSES, the distribution company suffers an annual loss of Rs five crore because of non-payment by consumers in this area.
"Life has become hell. My children's studies are getting affected during exam times. What do we do?. We get power only for storing water in the morning and evening. We can't sleep properly. We don't get power during nights. These last 30 days have been terrible," said Rupinder Kaur.
A BSES official said all their efforts to convince residents to get the meters installed have failed.
"It's not that we want to harass people. The annual loss that we incur is more than five crore. We keep talking to them, ...But there is no positive response," the official, who is involved in the talks with residents, told PTI.
"Earlier, there were only bulbs or fans in their rooms but now they have air conditioners too. People use heaters. Due to overload, the transformer gets burst early...We surely don't want to harass them," he said.
"After my father's death, I lost my mother in 1986. I could not study properly and don't earn much. You know how costly power is. Unless we are given in written assurance that we will not have to pay bills of previous years I am not going to get a meter installed in my house," he said.