Potomac Electric Power Co. yesterday experienced the highest demand for electricity in its 82-year history.

At the same time, pepco reported a slight decline in profits for the second quarter of 1977 - a decrease likely to be followed before long by requests to area public utility commissions for higher electricity rates.

Earnings totaled $14.173 million in the three months ended June 30, essentially unchanged from $14,175 million in the same period of 1976. On a per-share basis, however, earnings declined to 26 cents from 29, reflecting an increase in the number of common shares outstanding over the past year.

The decrease in profits at Pepco came despite a sharp increase in overall revenue to $142.9 million from $122.9 million in the 1976 period.

For the first six months of 1977, Pepco profits were $30.7 million compared with $29.7 million in the same period last year, with per-share earnings unchanged at 61 cents. Revenues rose to $289 million from $246 million.

The record for power consumption by Pepco's customers was set at 4 p.m. yesterday, as sweltering users turned on air conditioners and puhed the utility's putput to 3,853,000 kilowatts - surpassing two records set earlier in this hot summer.

Before this year, Pepco's highest output was 3,680,000 kilowatts on Aug. 30, 1973. After energy conservation measures were adopted in the wake of the oil embargo, power consumption here dipped sharply. The peak for 1976, for example, was 3,500,000 kilowatts on July 29.

Nationwide growth in electricity use this year has returned to pre-Arab oil embargo days of the early 1973s and some industry officials believe parts of the U.S., soon will be without adequate reserves of power.

The Edison Electric Institute, in a report to be made public today, says output has growth 6.7 per cent so far in 1977 - about the same rate of gain as before the embargo. According to the Associated Press, officials of the industry group will say there is no immediate problem in meeting power needs but that by 1986, reserve capacities will be too low in the Northeast, Great Lakes, southeast, north central and south central sections of the nation.

As of yesterday, Pepco had no requests pending before regulatory agencies in the District, Maryland or Virginia for higher rates. But company spokesman John Grasser said that, in the wake of a decline in earnings, "gears are probably rolling" within the firm on applications for higher consumer charges.

For the most recent 12-month period - ended June 30 - Pepco's profits totaled $78 million, up slightly from a record $77 million earned for calendar 1976.

Pepco's directors yesterday approved regular quarterly dividends of 32 cents a share on common stock, payable Sept. 30 to owners of record Aug. 30. Pepco raised its payout rate from 29 cents a share quarterly, earlier this year.