Exhibit 23(b) INDEPENDENT AUDITORS' CONSENT We consent to the incorporation by reference in Post-Effective Amendment No. 1 to Registration Statement No. 33-55732 of Tucson Electric Power Company (TEP) on Form S-3, Registration Statement No. 333-31043 of UniSource Energy Corporation (the Company) on Form S-3, Registration Statement No. 333-60809 of the Company on Form S-4, Amendment No. 2 to Registration Statement No. 333-65143 of TEP on Form S-4, and Registration Statement No. 333-43765, No. 333-43767, No. 333-43769, No. 333-53309, No. 333-53333 and No. 333-53337 of the Company on Form S-8 of our report dated February 23, 1998 (March 11, 1999 as to information with respect to 1997 and 1996 periods in Note 4 and in Note 12), appearing in this Annual Report on Form 10-K of the Company and TEP for the year ended December 31, 1998. DELOITTE & TOUCHE Tucson, Arizona March 30, 1999