EXHIBIT 23.1 INDEPENDENT AUDITORS' CONSENT We consent to the incorporation by reference in registration statement on Form S-3 (333-107296) of Reliant Resources, Inc. of our Report dated March 5, 2004 (which report expresses an unqualified opinion and includes explanatory paragraphs relating to the change in method of accounting for asset retirement obligations and the change in presentation of revenues and costs of sales associated with non-trading commodity derivative activities in 2003, goodwill and other intangibles in 2002, and the application of procedures relating to certain disclosures and reclassifications related to the 2001 financial statements that were audited by other auditors who have ceased operations and for which Deloitte & Touche LLP has expressed no opinion or other form of assurance other than with respect to such disclosures and reclassifications) on the consolidated financial statements of Orion Power Holdings, Inc. as of December 31, 2002 and 2003 and for the periods from January 1, 2002 to February 19, 2002 and February 20, 2002 to December 31, 2002 and for the year ended December 31, 2003, appearing in this Annual Report on Form 10-K of Orion Power Holdings, Inc. for the year ended December 31, 2003. Deloitte & Touche LLP Houston, Texas March 11, 2004