The District of Columbia Public Service Commission yesterday granted Potomac Electric Power Co. a $34 million rate increase--only about one-third of the record $97 million rate hike the company sought.

The commission exempted small electric customers from any rate increase and accepted a Pepco plan to cut rates for low-income customers by 6 percent.

In trimming Pepco's proposed price hike by $63 million, the PSC rejected the company's claim that customers should pay $19 million for work done on a cancelled power plant at Dickerson, Md. The commission also rejected a request to add about $9 million to rates in case the D.C. city council adopts a gross receipts tax on Pepco's revenue.

The rate increase granted yesterday will cover only about half of the utility company's customers, because the commission ruled that there should be no increase in the cost of the first 400 kilowatt hours of electricity a month.

"Basically about half of the customers will get no rate increase because they use 400 kilowatt hours or less, another 20,000 to 25,000 will get the 6 percent rate reduction, and a typical customer who uses 475 kilowatt hours will get a rate increase of about $1 a month," said Pepco spokesman William H. Jones.

The 6 percent rate reduction will go to 20,000 to 25,000 low-income families who qualify for assistance under the federal Low-Income Home Energy Assistance Program. Jones said he believes that Pepco was the first utility in the country to ask for and receive such a reduction for low-income customers.

Utilities increasingly have supported special assistance for the poor, but contend those who can should pay market rates.

The commission's decision is designed to result in an increase in revenues to Pepco of 7.5 percent, less than half of the increase in revenues it had asked for. Under the new rates, Pepco's rate of return on its investment in facilities to serve D.C. customers will rise from 10.09 percent to 10.71 percent, short of the 11.9 percent return the company sought. Return on equity will rise to 14.9 percent from 14.2 percent, short of the 17.75 percent Pepco sought.

"The company is financially healthy and doesn't need the money," said D.C. People's counsel Brian Lederer. Lederer had also argued against making customers pay for the cancelled Dickerson plant, maintaining that they shouldn't be forced to pay for bad management.

Lederer said that documents filed in the rate proceeding indicated that Pepco assumes the price of electricity will increase by 30 percent between now and the end of 1986. He said that bond rating filings by Pepco indicated that bills may increase by $800 million in that period.