A woven structure includes thermoelectric ribbons interwoven with thread. Each thermoelectric ribbon includes a folded matrix of thermoelectric elements, the matrix having an insulating substrate that supports plural rows of thermoelectric elements, a plurality of conductive elements, and two terminals. The conductive elements form a series connection of the thermoelectric elements between the two terminals. A set of first conductive elements have a first temperature and a set of second conductive contacts have a second temperature lower than the first temperature when a first current flows in a first direction between the first matrix terminal and the second matrix terminal. The folded matrix is configured to form spaced-apart alternating stacks of the first conductive contacts and second conductive contacts. Each length of the yard or thread is interwoven such that it passes alternately under stacks of first conductive contacts and over stacks of second conductive contacts.