As FERC’s enforcement director, Norman Bay worked with former Federal Energy Regulatory Commission Chairman Jon Wellinghoff to put more muscle in the commission’s enforcement program, seeking substantial fines from financial firms such as J.P. Morgan Chase and Barclays BARC.LN +0.90% PLC.Now Mr. Bay, nominated by President Barack Obama to head FERC earlier this year, is in the cross hairs of some of FERC’s targets, prompting questions from senators about his record at the commission.

Twin brothers Kevin and Richard Gates, who manage the investment partnership Powhatan Energy Fund LLC, have pushed a lobbying and public-relations campaign against Mr. Bay. The brothers, in public statements and in a website called “,” challenge FERC’s preliminary finding that their partnership contracted with a trader who manipulated the energy market.

Mr. Bay, speaking at his confirmation hearing at the Senate Energy and Natural Resources Committee, didn’t specifically address claims by the Gates brothers, who attended Tuesday’s hearing. But he did defend his record as FERC enforcement director as being impartial and fair.

“Fairness has to be a cornerstone of your office,” Mr. Bay said Tuesday in response to a question by Senate Energy and Natural Resources Chairman Mary Landrieu (D., La.). “It goes to the very legitimacy of the work that you do. So [to] examine cases, you have to be fair, have to be thoughtful, you have to be impartial.”

Mr. Bay testified before the panel two days after William Scherman, a lawyer and former general counsel for FERC, alleged in a Wall Street Journal opinion piece that the Gates brothers’ concerns are just the “tip of the iceberg” and that the agency’s enforcement office violates due process to extract large settlements.

“It’s one thing to be the tough cop on the beat,” said Sen. Lisa Murkowski (R., Alaska), the top Republican on the Senate Energy and Natural Resources Committee. “It is quite another to make the rules up as one goes and deny those under investigation basic due process rights.”

Mr. Bay refuted the allegations. “Honestly, FERC provides a tremendous amount of due process to the subjects of investigations,” Mr. Bay said in response to questioning by Sen. Mike Lee (R., Utah). “And in my view there is a lot of transparency into the work of the office of enforcement.”

As director of FERC’s enforcement office, Mr. Bay’s job is to ensure companies in the electricity market comply with FERC’s regulations, investigate possible rules violations and impose penalties when the agency concludes companies are violating its rules.

Last year, during Mr. Bay’s tenure, FERC issued one of its largest fines ever at $435 million against Barclays for allegedly manipulating electricity markets in California and other Western states. Barclays has refused to pay the fine and denies the allegations and the dispute is facing legal review in a California federal court.

Sen. Maria Cantwell (D., Wash.), defended Mr. Bay, saying he has been doing the job that Congress asked when it created market-manipulation rules in the Energy Policy Act of 2005, a law that followed the Western energy crisis and the collapse of Enron in 2001.

FERC has been “the shining light” when it comes to enforcing rules of honest conduct in the nation’s deregulated energy markets, Ms. Cantwell said.

Ms. Landrieu said she shared Ms. Murkowski’s concerns about FERC’s enforcement activities but sought to separate that from Mr. Bay.

“The question is the FERC process. Is it as transparent, as fair or impartial as it should be? That’s a question we need to continue to pursue.” Ms. Landrieu said after the hearing.

Within the next few weeks the committee is expected to vote on confirming Mr. Bay as chairman and acting FERC Chairman Cheryl LaFleur as a commissioner, who also testified at Tuesday’s hearing. The nominations would then go to a final vote in front of the full Senate.