The torques of the synchronous tie

Abstract

T HE PERFORMANCE of a synchronous tie-that is, of a synchronized drive consisting of two induction ma chines with interconnected rotors-has been analyzed 1 in terms of the loci of the stator currents. The torques im pressed upon the rotors of these machines by their revolving fields can be expressed in the form τι««ΐΘΓ = το + (τ π -r 0 ) sin 2 -+T* sin δ = r m +r s τlagger = το+ (τ* -r 0 ) sin 2 -rk sin δ = r m -TSwhere the subscript "leader" applies to the machine whose induced rotor voltages lead in time the corresponding rotor voltages of the other machine (called "lagger") by the angle δ in electrical degrees.The quantities ro,r x , and r k are functions of s which de pend upon the constants of the general equivalent circuit of the tie. The quantity r m is the motor torque; 2r m repre^ sents the over-all power transmitted through both air gaps into the rotors; if friction and windage are considered part of the loads, the sum of the mechanical powers delivered by both shafts is represented by 2r OT (l -s), while the losses in the resistances of the rotor windings and additional rotor networks are given by 2r m s.The quantity r s is the syn chronizing torque. It is this term of the expressions for torque which, acting in opposite directions on the two ro tors, acts to keep them in step. For s>0, r m and ricader are positive, while TiaggCr can be negative.The two remote stations to be kept in synchronous opera tion consist in general each of a driver (prime mover or mo tor of any kind) and of a mechanical load with given torque-<M*O«}0(V| ^ Λθοοοο J · -Figure 1. Chart for the determination of s and 6.and TS constant Data were obtained for rm speed characteristics. For each station the algebraic sum of the prime mover and load torques and of the torque de veloped by the corresponding induction machine of the tie is zero; thus two equations are provided from which the unknown s and δ can be obtained. Such equilibrium equa tions can be written in various forms but are difficult or im possible to solve by algebraic means. A convenient pro cedure is suggested by the chart in Figure 1 in which r m = constant and r, = constant are drawn in terms of the two independent variables s and δ. The motoring and syn chronizing torque requirements T m and T t of the mechani cal loads are known functions of s. Then -T m and -T t are plotted on the chart, and the values of s and δ are obtained from the intersection of these two plots.In some instances the synchronous tie is required to act as a load divider to reapportion the burdens of the two drivers by means of adequate synchronizing torques, but not to contribute much net mechanical power. In such cases external rotor networks are not used. Approximate solutions for s and δ are found immediately if r m is neglected. The rotation of the air gap fields may be chosen to make either 0Ό< 1 or s>\, and the latter kind of operation often is preferred as it generally gives larger values of τ Α , thus making it possible to reapportion larger load differences.Sometimes only one station ...