EXHIBIT 23.1

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We hereby consent to the incorporation by reference in the Registration Statements on Form S-8 (File Nos. 33-44962, 33-44963, 33-64832, 33-74418, 33-86106, 33-86108, 333-39653, 333-37163, 333-71539, 333-58016 and 333-111477) and Form S-3 (File Nos. 333-108347 and 333-109429) of American Superconductor Corporation of our reports dated May 5, 2004 relating to the financial statements and financial statement schedule, which appear in this Form 10-K.

/s/    PricewaterhouseCoopers LLP

Boston, Massachusetts

June 14, 2004