Growing demand for satellite systems services gave Communications Satellite Corp. 76 percent higher profits for the second quarter of 1982, officials of the D.C.-based firm said yesterday.

Profits soared from last year's second-quarter level of $6.1 million (77 cents a share) to $10.8 million ($1.35).

Comsat officials attributed the sharp rise in profits to smaller increases in costs and to increased revenues by three subsidiaries, one of which, Amplica, was purchased by Comsat this year.

Operating revenues for 1982's second quarter totaled $99.9 million--up $18.3 million from last year's level of $81.6 million. Operating expenses, meanwhile, climbed by only $13.7 million, from $71.3 million to $84.9 million.

Virginia Electric and Power Co. yesterday reported a 9 percent increase in earnings for the 12 months ended June 30, primarily because of increased dependence on energy generated from coal and nuclear plants rather than oil-fired generators.

Net income for the 12-month period was $267.4 million ($1.97 a share) compared with $236.8 million ($1.81). Operating income was $2.3 billion compared with $2.1 billion. June earnings were $21.3 million (14.8 cents) compared with $16.2 million (11.3 cents). Operating revenue was $193.9 million compared with $185.7 million.

United Virginia Bankshares, the holding company of Virginia's largest bank, yesterday reported increased earnings for the second quarter and first half. Income before securities transactions for the second quarter was $10.3 million ($1.82 a share) compared with $8.8 million ($1.62).

Securities losses reduced earnings to $8.2 million ($1.45) compared with $8.1 million ($1.50).

For the half, United Virginia had earnings of $21.4 million ($3.76) compared with $19.2 million ($3.55) before securities losses.

After losses, the Richmond-based bank holding company had earnings of $18.3 million ($3.22) compared with $18.5 million ($3.42). There were more average shares outstanding in both the quarter and half.

Assets after the six months were $4.3 billion compared with $3.7 billion. Loans were $3 billion compared with $2.5 billion.

"Given the depressed economic climate, we are generally pleased with the second quarter's earnings results, especially commercial," said Chairman Joseph A. Jennings.