HD 170582 is an interacting binary of the double periodic variable (DPV) type, showing ellipsoidal variability with a period of 16.87 d along with a long photometric cycle of 587 d. It was recently studied by Mennickent et al., who found a slightly evolved B-type star surrounded by a luminous accretion disc fed by a Roche lobe overflowing A-type giant. Here we extend their analysis presenting new spectroscopic data and studying the Balmer emission lines. We find orbitally modulated double-peak H alpha and H beta emissions whose strength also vary in the long term. In addition, Doppler maps of the emission lines reveal sites of enhanced line emission in the first and fourth velocity quadrants, the first one consistent with the position of one of the bright zones detected by the light-curve analysis. We find a difference between Doppler maps at high and low stage of the long cycle; evidence that the emission is optically thicker at high state in the stream-disc impact region, possibly reflecting a larger mass transfer rate. We compare the system parameters with a grid of synthetic binary evolutionary tracks and find the best-fitting model. The system is found to be semi-detached, in a conservative Case-B mass transfer stage, with age 7.68 x 10(7) yr and mass transfer rate 1.6 x 10(-6) M-circle dot yr(-1). For five well-studied DPVs, the disc luminosity scales with the primary mass and is much larger than the theoretical accretion luminosity.