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, 333-111477, 333-119125 and 333-119126) and Form S-3 (File Nos. 333-108347, 333-109429, 333-121946 and 333-124235) of American Superconductor Corporation of our report dated June 14, 2005 relating to the financial statements, financial statement schedules, management’s assessment of the effectiveness of internal control over financial reporting and the effectiveness of internal control over financial reporting, which appears in this Form 10-K.

/s/    PricewaterhouseCoopers LLP

Boston, Massachusetts

June 14, 2005